ABSTRACT 
 
 
 
 
Title of Document: EXPERIMENTAL DETECTION AND 
QUANTITATIVE INTERROGATION OF 
DAMAGE IN A JOINTED COMPOSITE 
STRUCTURE 
 
 Vanessa J. Gentzen, Master of Science, 2008 
Directed By: Professor Norman Wereley, Department of 
Aerospace Engineering 
 
 
The aerospace field has concentrated substantial attention toward the development of 
structural health monitoring (SHM) systems for multidisciplinary applications.  Research 
is motivated by catastrophic failures of operational systems which may have been 
avoided with the prior implementation of a successful damage prediction method. This 
research utilizes a smart sensor array to collect sensing information over a variety of 
damaged scenarios on a composite lap-joint assembly.  Damage was implemented as bolt 
torque loss within the joint.  A damage index was used as the key diagnostic feature to 
interrogate damage within the structure.  Pattern recognition of the damage index, in 
addition to a rule-based, statistical discrimination method was employed to detect, 
localize and quantify damage due to bolt torque loss in the structure.  The methodology 
accurately detected the presence of damage within the joint, localized the damage within 
the structures four quadrants, and assessed the level of torque loss.   
 
 
 
 
 
 
EXPERIMENTAL DETECTION AND QUANTITATIVE INTERROGATION OF 
DAMAGE IN A JOINTED COMPOSITE STRUCTURE 
 
 
 
By 
 
 
Vanessa J. Gentzen 
 
 
 
 
 
Thesis submitted to the Faculty of the Graduate School of the  
University of Maryland, College Park, in partial fulfillment 
of the requirements for the degree of 
Master of Science 
2008 
 
 
 
 
 
 
 
 
 
 
Advisory Committee: 
Professor Norman Wereley, Chair/Advisor 
Professor Darryll Pines 
Professor Sung Lee 
 
 
Acknowledgements 
 
 I would like to sincerely thank my advisor, Professor Norman Wereley for not 
only providing me the opportunity to explore an exciting and challenging area of 
research, but for consistently believing in my abilities even when I found myself in doubt.  
Also, thanks to Dr. Young-Tai Choi for his continual guidance and enthusiasm in the 
research lab.  In particular, I must thank Dr. Mary Bowden and Dr. James Hubbard for 
providing me the first sparks of inspiration upon entering College Park.  I am 
monumentally grateful to my advisory committee and to the entire faculty of the 
University of Maryland?s Department of Aerospace Engineering; my brief time in the 
department has been more rewarding than I could have anticipated.     
 To my fellow graduate students, you provided a sense of community to a new 
face on campus and for that, I am deeply grateful.  I have learned a great deal from you as 
colleagues and friends.   
 I would be remiss not to extend my deep appreciation to my family and friends 
for their abiding patience, love and support.  In particular, I?d like to thank my dear friend 
Gregory Miller for keeping me positive throughout my graduate experience. 
 Most importantly, I acknowledge the strength and support that is continually 
provided to me by God.  For that, I am the most thankful and forever will be. 
 ii  
Table of Contents 
 
Acknowledgements............................................................................................................ ii 
Table of Contents..............................................................................................................iii 
List of Tables ..................................................................................................................... v 
List of Figures................................................................................................................... vi 
Chapter 1: Introduction................................................................................................. 1 
1.1 Motivation........................................................................................................... 1 
1.2 Overview of the Structural Health Monitoring Process...................................... 4 
1.3 Previous Work and Fundamental Theory ........................................................... 7 
1.3.1 Modal parameter analysis ........................................................................... 8 
1.3.2 Acousto-Ultrasonics.................................................................................... 9 
1.3.3 Lamb wave method................................................................................... 11 
1.3.4 Signal processing using wavelet transformation....................................... 12 
1.3.5 Interrogation of bolted composite structures ............................................ 13 
1.4 Discrimination Techniques ............................................................................... 14 
1.5 Research Aim.................................................................................................... 15 
Chapter 2: Experimental Procedure............................................................................ 17 
2.1 Jointed Composite Panel................................................................................... 17 
2.2 Wireless Smart Sensor System ......................................................................... 19 
2.3 Signal Noise Filtration and Running Average Method..................................... 22 
2.4 Damage Due to Bolt Torque Loss .................................................................... 23 
2.5 Data Compression: Damage Index ................................................................... 24 
2.6 Baseline Sensing Variation Over Time............................................................. 27 
2.7 Baseline Sensing Variation due to Temperature Increase ................................ 28 
Chapter 3: Damage Due to Bolt Torque Loss ............................................................ 30 
3.1 Bolt 0 damage due to torque loss...................................................................... 30 
3.1.1 Bolt 0, Excitation Case I ........................................................................... 30 
3.1.2 Bolt 0, Excitation Case II.......................................................................... 39 
3.1.3 Bolt 0, Excitation Case III ........................................................................ 48 
3.1.4 Bolt 0, Excitation Case IV ........................................................................ 57 
3.1.5 Comparison of Bolt 0 excitation configurations....................................... 66 
3.1.6 Detection of smaller torque loss percentages............................................ 70 
3.2 Bolt 1 damage due to torque loss...................................................................... 72 
3.2.1 Bolt 1, Excitation Case I ........................................................................... 72 
3.2.2 Bolt 1, Excitation Case II.......................................................................... 77 
3.2.3 Bolt 1, Excitation Case III ........................................................................ 81 
3.2.4 Bolt 1, Excitation Case IV ........................................................................ 85 
3.2.5 Comparison of Bolt 1 excitation configurations....................................... 89 
3.3 Bolt 2 damage due to torque loss...................................................................... 92 
3.3.1 Bolt 2, Excitation Case I ........................................................................... 93 
3.3.2 Bolt 2, Excitation Case II.......................................................................... 97 
3.3.3 Bolt 2, Excitation Case III ...................................................................... 101 
3.3.4 Bolt 2, Excitation Case IV ...................................................................... 105 
3.3.5 Comparison of Bolt 2 excitation configurations..................................... 109 
 iii  
 iv  
3.4 Bolt 6 damage due to torque loss.................................................................... 112 
3.4.1 Bolt 6, Excitation Case I ......................................................................... 113 
3.4.2 Bolt 6, Excitation Case II........................................................................ 116 
3.4.3 Bolt 6, Excitation Case III ...................................................................... 119 
3.4.4 Bolt 6, Excitation Case IV ...................................................................... 122 
3.4.5 Comparison of Bolt 6 excitation configurations..................................... 125 
3.5 Dual-bolt damage due to torque loss .............................................................. 129 
3.5.1 Bolt 0 and Bolt 1, Excitation Case I ....................................................... 130 
3.5.2 Bolt 0 and Bolt 1, Excitation Case II ...................................................... 133 
3.5.3 Bolt 0 and Bolt 1, Excitation Case III..................................................... 136 
3.5.4 Bolt 0 and Bolt 1, Excitation Case IV..................................................... 139 
3.5.5 Comparison of dual Bolt 0 and Bolt 1 excitation configurations ........... 142 
3.5.6 Bolt 0 and Bolt 6, Excitation Case I ....................................................... 145 
3.5.7 Bolt 0 and Bolt 6, Excitation Case II ...................................................... 149 
3.5.8 Bolt 0 and Bolt 6, Excitation Case III..................................................... 152 
3.5.9 Bolt 0 and Bolt 6, Excitation Case IV..................................................... 155 
3.5.10 Comparison of dual Bolt 0 and Bolt 6 excitation configurations ........... 158 
3.6 Sensing Variation of Undamaged Composite Jointed Panel over Time......... 162 
3.7 Sensing Variation due to Temperature Increase of an Active Sensor ............ 168 
Chapter 4: Damage Discrimination .......................................................................... 171 
4.1 Damage index pattern recognition.................................................................. 171 
4.2 Level 2: Damage localization algorithm......................................................... 174 
4.3 Level 3: Damage quantification algorithm ..................................................... 180 
Chapter 5: Concluding Remarks............................................................................... 184 
Appendix........................................................................................................................ 187 
Bibliography .................................................................................................................. 197 
 
 
 
 
 
 
 
 
 
 
List of Tables 
 
Table 4-1-1: DI grid, 100% B0 torque loss ?????????????????.170 
Table 4-1-2: DI grid, 75% B1 torque loss ?????????????????...172 
Table 4-1-3: DI grid, 25% B2 torque loss ?????????????????...172 
Table 4-1-4: DI
mag
;B0 100% torque loss, B1 75% torque loss, B2 25% torque loss ?..173 
Table 4-1-5: Validation experimental run matrix ...??????????????181 
 v 
List of Figures 
 
Figure 1-1-1: Fuselage damage to Aloha Airlines Flight 243, April 1988......................... 2 
Figure 1-1-2: Military aircraft graveyard............................................................................ 3 
Figure 1-2-1. Flowchart, implementation of a structural health monitoring program [8] .. 5 
Figure 1-3-1. Acousto-Ultrasonic schematic within a structure. ...................................... 10 
Figure 2-1-1: The jointed composite panel....................................................................... 18 
Figure 2-2-1: The jointed composite panel with piezoelectric patch assembly................ 19 
Figure 2-2-2: Formula excitation output signal with 20 kHz excitation frequency.......... 20 
Figure 2-2-3: Wireless data acquisition system................................................................ 21 
Figure 2-2-4: Specimen quadrants and configuration Cases I, II, III, IV. ........................ 22 
Figure 2-7-1: Baseline temperature variation of S1, E2 excitation. ................................. 29 
Figure 3-1-1. Excitation Case I, Bolt 0 torque loss........................................................... 30 
Figure 3-1-2. Sensing time response, B0 torque loss, E1 40 kHz excitation.................... 31 
Figure 3-1-3. Scattering signals, B0 torque loss, E1 40 kHz excitation. .......................... 33 
Figure 3-1-4. Normalized scattering signals, B0 torque loss, E1 40 kHz excitation........ 34 
Figure 3-1-5.  Damage index using the energy magnitudes in frequency vs. B0 torque loss 
and excitation frequency, E1 excitation............................................................................ 35 
Figure 3-1-6. Damage index using the signals in time vs. B0 torque loss and excitation 
frequency, E1 excitation. .................................................................................................. 36 
Figure 3-1-7. Average damage index, B0 torque loss, E1 excitation. .............................. 38 
Figure 3-1-8. Total damage index, B0 torque loss, E1 excitation. ................................... 39 
Figure 3-1-9. Excitation Case II, variable Bolt 0 torque loss. .......................................... 40 
Figure 3-1-10. Sensing time response, B0 torque loss, E2 40 kHz excitation.................. 41 
Figure 3-1-11. Scattering signals, B0 torque loss, E2 40 kHz excitation. ........................ 42 
Figure 3-1-12. Normalized Scattering signals, B0 torque loss, E2 40 kHz excitation. .... 43 
Figure 3-1-13. Damage index using the energy magnitudes in frequency vs. B0 torque 
loss and excitation frequency, E2 excitation..................................................................... 44 
Figure 3-1-14. Damage index using signals in time in vs. B0 torque loss and excitation 
frequency, E2 excitation. .................................................................................................. 45 
Figure 3-1-15. Average damage index, B0 torque loss, E2 excitation. ............................ 47 
Figure 3-1-16. Total damage index, B0 torque loss, E2 excitation. ................................. 48 
Figure 3-1-17. Excitation Case III, variable Bolt 0 torque loss........................................ 49 
Figure 3-1-18. Sensing time response, B0 torque loss, E3 40 kHz excitation.................. 50 
Figure 3-1-19. Scattering signals, B0 torque loss, E3 40 kHz excitation. ........................ 51 
Figure 3-1-20. Normalized scattering signals, B0 torque loss, E3 40 kHz excitation...... 52 
Figure 3-1-21.  Damage index using the energy magnitudes in frequency vs. B0 torque 
loss and excitation frequency, E3 excitation..................................................................... 53 
Figure 3-1-22. Damage index using the signals in time vs. B0 torque loss and excitation 
frequency, E3 excitation. .................................................................................................. 54 
Figure 3-1-23. Average damage index, B0 torque loss, E3 excitation. ............................ 56 
Figure 3-1-24. Total damage index, B0 torque loss, E3 excitation. ................................. 57 
Figure 3-1-25. Excitation Case IV, variable Bolt 0 torque loss........................................ 58 
Figure 3-1-26. Sensing time response, B0 torque loss, E4 40 kHz excitation.................. 59 
Figure 3-1-27. Scattering signals, B0 torque loss, E4 40 kHz excitation. ........................ 60 
 vi  
Figure 3-1-28. Normalized scattering signals, B0 torque loss, E4 40 kHz excitation...... 61 
Figure 3-1-29. Damage index using the energy magnitudes in frequency vs. B0 torque 
loss and excitation frequency, E4 excitation..................................................................... 62 
Figure 3-1-30. Damage index using the signals in time vs. B0 torque loss and excitation 
frequency, E4 excitation. .................................................................................................. 63 
Figure 3-1-31. Average damage index, B0 torque loss, E4 excitation. ............................ 65 
Figure 3-1-32. Total damage index, B0 torque loss, E4 excitation. ................................. 66 
Figure 3-1-33. Comparison of normalized average damage index, B0 torque loss.......... 68 
Figure 3-1-34. Comparison of normalized average damage indices, B0 torque loss; DI
E2,S3 
and
 
 DI
E4,S1
......................................................................................................................... 69 
Figure 3-1-35. Estimated damage area due to B0 torque loss. ......................................... 70 
Figure 3-1-36. Normalized average damage index due to smaller B0 torque loss........... 71 
Figure 3-1-37. Total damage index due to smaller B0 torque loss................................... 72 
Figure 3-2-1. Excitation Case I, variable Bolt 1 torque loss............................................. 73 
Figure 3-2-2. Scattering signals, B1 torque loss, E1 40 kHz excitation. .......................... 74 
Figure 3-2-3.  Damage index using the energy magnitudes in frequency vs. B1 torque loss 
and excitation frequency, E1 excitation............................................................................ 75 
Figure 3-2-4. Damage index using the signals in time vs. B1 torque loss and excitation 
frequency, E1 excitation. .................................................................................................. 76 
Figure 3-2-5. Excitation Case II, variable Bolt 1 torque loss. .......................................... 77 
Figure 3-2-6. Scattering signals, B1 torque loss, E2 40 kHz excitation. .......................... 78 
Figure 3-2-7.  Damage index using the energy magnitudes in frequency vs. B1 torque loss 
and excitation frequency, E2 excitation............................................................................ 79 
Figure 3-2-8. Damage index using the signals in time vs. B1 torque loss and excitation 
frequency, E2 excitation. .................................................................................................. 80 
Figure 3-2-9. Excitation Case III, variable Bolt 1 torque loss.......................................... 81 
Figure 3-2-10. Scattering signals, B1 torque loss, E3 40 kHz excitation. ........................ 82 
Figure 3-2-11.  Damage index using the energy magnitudes in frequency vs. B1 torque 
loss and excitation frequency, E3 excitation..................................................................... 83 
Figure 3-2-12. Damage index using the energy magnitudes in frequency vs. B1 torque 
loss and excitation frequency, E3 excitation..................................................................... 84 
Figure 3-2-13. Excitation Case IV, variable Bolt 1 torque loss........................................ 85 
Figure 3-2-14. Scattering signals, B1 torque loss, E4 40 kHz excitation. ........................ 86 
Figure 3-2-15.  Damage index using the energy magnitudes in frequency vs. B1 torque 
loss and excitation frequency, E4 excitation..................................................................... 87 
Figure 3-2-16. Damage index using the energy magnitudes in frequency vs. B1 torque 
loss and excitation frequency, E4 excitation..................................................................... 88 
Figure 3-2-17. Comparison of normalized average damage index, B1 torque loss.......... 90 
Figure 3-2-18. Comparison of normalized average damage indices, B1 torque loss; DI
E4,S1
 
and DI
E2,S3.
......................................................................................................................... 91 
Figure 3-2-19. Estimated damage area due to B1 torque loss. ......................................... 92 
Figure 3-3-1. Excitation Case I, variable Bolt 2 torque loss............................................. 93 
Figure 3-3-2. Scattering signals, B2 torque loss, E1 40 kHz excitation. .......................... 94 
Figure 3-3-3.  Damage index using the energy magnitudes in frequency vs. B2 torque loss 
and excitation frequency, E1 excitation............................................................................ 95 
 vii  
Figure 3-3-4. Damage index using the energy magnitudes in frequency vs. B2 torque loss 
and excitation frequency, E1 excitation............................................................................ 96 
Figure 3-3-5. Excitation Case II, variable Bolt 2 torque loss. .......................................... 97 
Figure 3-3-6. Scattering signals, B2 torque loss, E2 40 kHz excitation frequency. ......... 98 
Figure 3-3-7.  Damage index using the energy magnitudes in frequency vs. B2 torque loss 
and excitation frequency, E2 excitation............................................................................ 99 
Figure 3-3-8. Damage index using the signals in time vs. B2 torque loss and excitation 
frequency, E2 excitation. ................................................................................................ 100 
Figure 3-3-9. Excitation Case III, variable Bolt 2 torque loss........................................ 101 
Figure 3-3-10. Scattering signals, B2 torque loss, E3 40 kHz excitation. ...................... 102 
Figure 3-3-11.  Damage index using the energy magnitudes in frequency vs. B2 torque 
loss and excitation frequency, E3 excitation................................................................... 103 
Figure 3-3-12. Damage index using the energy signals in time vs. B2 torque loss and 
excitation frequency, E2 excitation................................................................................. 104 
Figure 3-3-13. Excitation Case IV, variable Bolt 2 torque loss...................................... 105 
Figure 3-3-14. Scattering signals, B2 torque loss, E4 40 kHz excitation frequency. ..... 106 
Figure 3-3-15. Damage index using the energy magnitudes in frequency vs. B2 torque 
loss and excitation frequency, E4 excitation................................................................... 107 
Figure 3-3-16. Damage index using the signals in time vs. B2 torque loss and excitation 
frequency, E4 excitation. ................................................................................................ 108 
Figure 3-3-17. Comparison of normalized average damage index, B2 torque loss........ 110 
Figure 3-3-18. Comparison of normalized average damage indices, B2 torque loss; DI
E2,S3
 
and DI
E4,S1
. ...................................................................................................................... 111 
Figure 3-3-19. Estimated damage area due to B2 torque loss. ....................................... 112 
Figure 3-4-1. Excitation Case I, variable Bolt 6 torque loss........................................... 113 
Figure 3-4-2.  Damage index using the energy magnitudes in frequency vs. B6 torque loss 
and excitation frequency, E1 excitation.......................................................................... 114 
Figure 3-4-3. Damage index using the signals in time vs. B6 torque loss and excitation 
frequency, E1 excitation. ................................................................................................ 115 
Figure 3-4-4. Excitation Case II, variable Bolt 6 torque loss. ........................................ 116 
Figure 3-4-5.  Damage index using the energy magnitudes in frequency vs. B6 torque loss 
and excitation frequency, E2 excitation.......................................................................... 117 
Figure 3-4-6. Damage index using the signals in time vs. B6 torque loss and excitation 
frequency, E2 excitation. ................................................................................................ 118 
Figure 3-4-7. Excitation Case III, variable Bolt 6 torque loss........................................ 119 
Figure 3-4-8.  Damage index using the energy magnitudes in frequency vs. B6 torque loss 
and excitation frequency, E3 excitation.......................................................................... 120 
Figure 3-4-9. Damage index using the signals in time vs. B6 torque loss and excitation 
frequency, E3 excitation. ................................................................................................ 121 
Figure 3-4-10. Excitation Case IV, variable Bolt 6 torque loss...................................... 122 
Figure 3-4-11.  Damage index using the energy magnitudes in frequency vs. B6 torque 
loss and excitation frequency, E4 excitation................................................................... 123 
Figure 3-4-12. Damage index using the signals in time vs. B6 torque loss and excitation 
frequency, E4 excitation. ................................................................................................ 124 
Figure 3-4-13. Comparison of normalized average damage index, B6 torque loss........ 126 
 viii  
Figure 3-4-14. Comparison of normalized average damage indices, B6 torque loss; DI
E3,S2
 
and DI
E1,S4
. ...................................................................................................................... 127 
Figure 3-4-15. Comparison of normalized average damage indices, B6 torque loss; DI
E1,S2
 
and DI
E3,S4
. ...................................................................................................................... 128 
Figure 3-4-16. Estimated damage area due to B6 torque loss. ....................................... 129 
Figure 3-5-1. Excitation Case I, dual Bolt 0 and Bolt 1 variable torque loss. ................ 130 
Figure 3-5-2.  Damage index using the energy magnitudes in frequency vs. B0 and B1 
torque loss and excitation frequency, E1 excitation. ...................................................... 131 
Figure 3-5-3. Damage index using the signals in time vs. B0 and B1 torque loss and 
excitation frequency, E1 excitation................................................................................. 132 
Figure 3-5-4. Excitation Case II, dual Bolt 0 and Bolt 1 variable torque loss................ 133 
Figure 3-5-5.  Damage index using the energy magnitudes in frequency vs. B0 and B1 
torque loss and excitation frequency, E2 excitation. ...................................................... 134 
Figure 3-5-6. Damage index using the signals in time vs. B0 and B1 torque loss and 
excitation frequency, E2 excitation................................................................................. 135 
Figure 3-5-7. Excitation Case III, dual Bolt 0 and Bolt 1 variable torque loss. ............. 136 
Figure 3-5-8.  Damage index using the energy magnitudes in frequency vs. B0 and B1 
torque loss and excitation frequency, E3 excitation. ...................................................... 137 
Figure 3-5-9. Damage index using the signals in time vs. B0 and B1 torque loss and 
excitation frequency, E3 excitation................................................................................. 138 
Figure 3-5-10. Excitation Case IV, dual Bolt 0 and Bolt 1 variable torque loss. ........... 139 
Figure 3-5-11. Damage index using the energy magnitudes in frequency vs. B0 and B1 
torque loss and excitation frequency, E4 excitation. ...................................................... 140 
Figure 3-5-12. Damage index using the signals in time vs. B0 and B1 torque loss and 
excitation frequency, E4 excitation................................................................................. 141 
Figure 3-5-13. Comparison of normalized average damage index, Bolt 0 and Bolt 1 dual-
bolt torque loss................................................................................................................ 143 
Figure 3-5-14. Comparison of normalized average damage indices, Bolt 0 and Bolt 1 
torque loss; DI
E4,S1
 and DI
E2,S3
. ....................................................................................... 144 
Figure 3-5-15. Estimated damage area due to Bolt 0 and Bolt 1 torque loss. ................ 145 
Figure 3-5-16. Excitation Case I, dual Bolt 0 and Bolt 6 variable torque loss. .............. 146 
Figure 3-5-17.  Damage index using the energy magnitudes in frequency vs. B0 and B6 
torque loss and excitation frequency, E1 excitation. ...................................................... 147 
Figure 3-5-18. Damage index using the signals in time vs. B0 and B6 torque loss and 
excitation frequency, E1 excitation................................................................................. 148 
Figure 3-5-19. Excitation Case II, dual Bolt 0 and Bolt 6 variable torque loss.............. 149 
Figure 3-5-20.  Damage index using the energy magnitudes in frequency vs. B0 and B6 
torque loss and excitation frequency, E2 excitation. ...................................................... 150 
Figure 3-5-21. Damage index using the signals in time vs. B0 and B6 torque loss and 
excitation frequency, E2 excitation................................................................................. 151 
Figure 3-5-22. Excitation Case III, dual Bolt 0 and Bolt 6 variable torque loss. ........... 152 
Figure 3-5-23.  Damage index using the energy magnitudes in frequency vs. B0 and B6 
torque loss and excitation frequency, E3 excitation. ...................................................... 153 
Figure 3-5-24. Damage index using the signals in time vs. B0 and B6 torque loss and 
excitation frequency, E3 excitation................................................................................. 154 
Figure 3-5-25. Excitation Case IV, dual Bolt 0 and Bolt 6 variable torque loss. ........... 155 
 ix  
 x 
Figure 3-5-26.  Damage index using the energy magnitudes in frequency vs. B0 and B6 
torque loss and excitation frequency, E4 excitation. ...................................................... 156 
Figure 3-5-27. Damage index using the signals in time vs. B0 and B6 torque loss and 
excitation frequency, E4 excitation................................................................................. 157 
Figure 3-5-29. Comparison of normalized average damage indices, Bolt 0 and Bolt 6 
torque loss; DI
E4,S1
 and DI
E2,S3
. ....................................................................................... 160 
Figure 3-5-30. Comparison of normalized average damage indices, Bolt 0 and Bolt 6 
torque loss; DI
E3,S2
 and DI
E1,S4
. ....................................................................................... 161 
Figure 3-5-31. Estimated damage area due to Bolt 0 and Bolt 1 torque loss. ................ 162 
Figure 3-6-1. Normalized baseline time response over five months, E2 40 kHz excitation.
......................................................................................................................................... 164 
Figure 3-6-2. Normalized baseline voltage response vs. E2 excitation frequency over five 
months............................................................................................................................. 166 
Figure 3-6-3.  Average baseline time response, E2 40 kHz excitation........................... 168 
Figure 3-7-1. S1 maximum time response vs. temperature, E2 excitation..................... 169 
Figure 3-7-2. S1 normalized time response vs. temperature, E2 excitation. .................. 170 
Figure 4-1-1. Path of straight-across excitation.............................................................. 175 
Figure 4-1-2. Path of diagonally-across excitation on the composite jointed panel....... 177 
Figure 4-1-3. Quadrant 1 vs. Quadrant 3 damage index sensing information................ 180 
Figure 4-1-4. Quadrant 1 vs. Quadrant 3 damage with damage threshold bands........... 181 
Figure 4-1-5. Quadrant 1 vs. Quadrant 3 discriminator validation run results............... 183 
  
Chapter 1: Introduction 
1.1 Motivation 
The ability to continually monitor an engineering structure has been the motivated 
a great deal of research in the structural health monitoring (SHM) arena.  Research 
contributions across multi-disciplinary engineering fields have proven functional in 
various experimental and operational applications.  In particular, the aerospace field has 
concentrated substantial attention toward the development of SHM systems for 
applications in space, rotorcraft, commercial and military aerospace structures.   
Precipitous advances in engineering and technology demand that SHM methods 
increase their adaptability to include more complex structural applications.  Massive, 
multifaceted structures have prompted the need for global damage detection methods.  
However, technological advances are not the sole motivation behind the demand for more 
concentrated SHM efforts.  Federal funding of large-scale defense and civilian contracted 
engineering programs have gained the attention of tax-paying citizens and prompted 
ample media coverage.  Spectacular failures can involve a colossal monetary loss, and 
more significantly, the loss of human life in the most tragic instances.  Malfunction in the 
public eye results in exceeding concern and a new outcry for additional preventative 
research and maintenance advances.  The public voice prompts political interest which 
provokes industry and regulatory agencies to re-direct spending toward the advancement 
of structural safety programs.   
One incident in particular, the April 1988 in-flight fuselage detachment of Aloha 
Airlines Flight 243 resulted in the death of one flight attendant.  Figure 1-1-1 shows the 
 1 
 
result of this structural failure.  A pre-flight visual inspection according to Federal 
Aviation Administration (FAA) standards concluded operable flight conditions prior to 
take-off.  Considerable media coverage of this incident triggered the prioritization of 
SHM development among the civilian aircraft community. 
 
 
Figure 1-1-1: Fuselage damage to Aloha Airlines Flight 243, April 1988. 
 
The spacecraft industry is another which has experienced heavy public scrutiny.  
Due to a thermal protection system failure on the leading edge of the ill-fated Space 
Shuttle Columbia, the vehicle suffered a catastrophic failure upon re-entry, resulting in 
the death of seven National Aeronautics and Space Administration (NASA) astronauts.  
This tragedy prompted a painstakingly detailed investigation of the structural basis for 
failure and brought light to a critical need for NASA?s implementation of a reliable health 
monitoring system [1].  The development of a Shuttle Modal Inspection System (SMIS) 
addresses the difficulties of accessing and identifying structural damage underneath the 
shuttle?s thermal protection system [2]. 
 2 
 
As the aerospace field continues to make advancements in aircraft and structural 
designs, the aging systems of the past are approaching the end of their predicted lifetimes.  
System maintenance becomes a prominent and costly topic for concern.  Figure 1-1-2 
shows the popular airplane graveyard at Davis-Monthan Air Force Base in Tucson, 
Arizona.  The picture shows a fraction of the large number of military aircraft that are 
decommissioned due to exceeded lifetime, irreparable damage, or out-dated technology.  
While it is not always possible to prolong the lifetime of an aging aerospace structure, 
advancements in SHM and a similar program for Condition Based Maintenance (CBM) 
may extend the serviceability of these vehicles which are not easily or inexpensively 
replaced.  A successful CBM system will assess a system?s current structural health and 
provide a quantitative approach to establishing a vehicle?s serviceable lifetime.  This 
eliminates the unnecessary decommissioning of a structurally healthy aircraft based on a 
prior ?safe-life? approach toward aircraft maintenance schedules [3].  Aerospace system 
retirement is not something that can be entirely avoided.  However, engineers are capable 
of optimizing the use of costly existing systems and components, thus extending the 
aircraft?s lifetime beyond the original design prediction. 
 
 
Figure 1-1-2: Military aircraft graveyard 
 3 
 
 Supplemental benefits of a SHM system include the cost savings due to 
maintenance which becomes significant over the serviceable lifetime of an aerospace 
structure.  In a study conducted by the U.S. Air Force, an average of $1.4 million is spent 
on a single comprehensive F-15E maintenance event [4].  The FAA enforces four specific 
inspection checks on commercial transport aircraft before the aircraft is considered flight-
worthy [5].  The cost for these maintenance practices totals up to 11% of the total life 
cycle cost of the aircraft [6].  For a fleet of 108 Boeing 737 airplanes, this amount 
exceeds $4 billion over a 25 year life cycle [7]. 
 Several motivational factors have contributed to the recent spotlight and funding 
for SHM and CBM systems.  The principal aim of developmental research and 
operational success continues to point toward safer and more reliable aircraft, rotorcraft 
and space vehicles to better ensure the safety of the crew.  Prolonging structural 
serviceability and improving cost effectiveness in terms of routine maintenance, repair 
and system reusability adds to the overall benefit of implementing more efficient and 
comprehensive structural health monitoring systems. 
1.2 Overview of the Structural Health Monitoring Process 
A complete chart of the structural health monitoring process is summarized in 
Figure 1-2-1 [8].  This chart details a comprehensive approach toward the development 
and implementation of a structural health monitoring system for a specific application.  
The process begins with an operational evaluation, during which an experimental 
investigation and its corresponding limitations are defined.  This research focuses on the 
application of this health monitoring process as it pertains to vibration-based, non-
destructive techniques for damage detection in a multi-part, composite structure. 
 4 
 
 
Figure 1-2-1. Flowchart, implementation of a structural health monitoring program [8] 
 5 
 
In a structural health monitoring application, data acquisition often ranges over a variety 
of damage scenarios, levels, types and quantities.  Data compression is a necessity as the 
quantity of experimental data becomes large; a robust data compression technique can 
provide the ability to label key features which will give insight into damage 
discrimination from experimental data.  Figure 1-2-1 emphasizes the importance of key 
features which afford insight to the identification between an undamaged and damaged 
system.  This suggests the health monitoring system is a successful method for damage 
identification within the specific application. 
It is often not enough to simply detect the presence of damage within a system; in 
multi-part systems, damage location may vary widely.  Damage intensity may also vary 
within a system from negligible to potentially catastrophic.  In addition to detection, 
damage localization and quantification can be achieved through the exploitation of key 
features to develop a comprehensive, statistical model.  Statistical models provide the 
ability for quantitative damage interrogation within a specific structural system.  An 
additional classification system for SHM methods is outlined by Rytter [9], which divides 
damage identification into four levels: 
Level 1: Determination that damage is present in the structure 
 Level 2: Level 1 plus geometric localization of the damage 
 Level 3: Level 2 plus quantification of the damage severity 
 Level 4: Level 3 plus prediction of the remaining structure service life 
The procedure outlined in Figure 1-2-1 encompasses all four levels of damage 
identification. 
 
 6 
 
1.3 Previous Work and Fundamental Theory 
The earliest form of structural damage detection includes a global and/or locally- 
conducted visual inspection.  Enhanced methods include localized experimental 
techniques which employ acoustic, ultrasonic, magnetic field, eddy-current, thermal field 
or radiography methods [10].   These methods have proven effective in experimental and 
operational applications, but are specifically localized to a single component or segment 
of a much larger structure.  Further, these techniques require that the damaged component 
or the close proximity to damage be known for the localized experiment to be conducted 
successfully.  This also implies that the damaged component or area must be readily 
accessible in order to apply the method. 
Experimental and finite element efforts in the area of vibration-based damage 
diagnostic techniques have afforded the opportunity for quantitative damage assessments.  
Appropriately, the SHM community is directing new attention toward the development of 
comprehensive damage detection techniques which serve multiple purposes.  Discerning 
the incidence of damage, localizing the damaged component or vicinity, distinguishing 
and quantifying the type of damage present are key elements to a cohesive diagnostic 
process.   
Technological advancements in piezoelectric sensing agents have greatly 
contributed to the recent strides in vibration-based damage detection.  Over years of 
structural health monitoring research and development, many vibration-based methods 
have been developed and employed which utilize sensing improvements [10].  Levels of 
success range widely and are typically application-specific.  An investigation of the 
 7 
 
benefits and downfalls of widely-used modal parameter analysis and acousto-ultrasonic 
(AU) methods for damage diagnostics is included within this section. 
1.3.1 Modal parameter analysis  
 The key idea behind a modal analysis approach as a damage detection method is 
the comparison between the structure?s modal characteristics in a baseline (undamaged) 
condition and a secondary condition under which damage has been implemented.  The 
structure?s baseline information can be gathered experimentally or constructed 
analytically from identified modal parameters of the actual system.  The structure will 
experience a shift in natural frequencies and mode shapes as damage progresses within 
the structure.  A prominent example of a damage detection system which implements 
modal dynamic data analysis is NASA?s space shuttle modal inspection system [2] which 
was developed to interrogate damage within the exterior surface under the protection of a 
thermal protection system.  A review of damage detection methods based on modal 
dynamics has been compiled by Doebling, et. al [10] and Sohn, et. al [11].  Farrar, et. al 
[12] and Doebling, et. al [13] have shown that a structure?s resonant frequencies are 
statistically resistant to random error sources as compared to other modal parameters.  
Modal analysis techniques have proven effective for a wide variety of civil, mechanical 
and architectural engineering applications [14] [15] [16].  The aerospace engineering 
community has utilized the method as well, specifically in the arena of composite 
materials research [17] [18].   
 Limitations of this method should be considered on an application-specific basis.  
Low sensitivity of frequency shifts due to progressive structural damage necessitates 
either very precise frequency measurements or limits experimentation to large levels of 
 8 
 
damage [13].  Further, frequency shift methods for damage diagnostics must be 
conducted on specimens with highly accurate, predetermined types and quantities of 
damage.  Standard modal properties are experimentally approximated from sensor time-
history measurements; these approximations represent a form of data compression as the 
measurements are averaged.  While data compression makes the modal properties easier 
to visualize, information about the current state of the experimental specimen is lost 
during the data reduction process.  Experimentally measured modal parameters are also 
susceptible to changes due to fluctuating environmental conditions during a test. 
 For the purposes of this research, excitation frequency ranges outside the 
limitations of current modal parameter analysis methods.  These methods utilize 
frequency information in the Hertz (Hz) range; this research study intends to examine the 
jointed composite structure using frequencies in the kHz range.  Since modal parameter 
methods do not provide high sensitivity from high frequency ranges, it is necessary to 
explore other means for damage detection. 
1.3.2 Acousto-Ultrasonics 
 In particular, the implementation of the AU method has been popular in the 
structural health monitoring field primarily due to the method?s non-destructive scheme 
for gathering acoustic wave information. Fundamentally, the AU approach attempts to 
detect small incidences of damage over a wide area using transducers attached to the 
structure.  Figure 1-3-1 shows a simple AU schematic within an arbitrary structure.  
Sanders, et. al [19] investigated a similar experimental setup using a laminated composite 
beam and discovered good agreement between the experimental results and predictions.  
Purekar [20] and Mahapatra, et. al [21] have proven experimentally and through finite 
 9 
 
element means that the AU method can successfully capture the dynamics of a 
delaminated composite structure in structural health monitoring applications. 
 
 
Figure 1-3-1. Acousto-Ultrasonic schematic within a structure. 
 
 
Interrogation waves originate upon excitation at a singular point on the system.  
These waves propagate through the system and pass through any defects, whether due to 
structural cracks, composite delamination or thickness changes.  In a bolted joint 
specimen, a possible damage scenario could be inherent to the joint, potentially as 
damage due to torque loss within one or more of the bolts; this research study suggests 
damage due to bolt torque loss within the composite lap joint.  Active sensors located on 
the structure continually monitor the excitation waves during propagation and reflection 
about the structure.   
 Limitations of AU arise from the method?s inherent goal of detecting small 
damages over large areas.  There is a sensitivity exchange between detection of small 
damages and the ability to globally interrogate a structure.  The understanding of wave 
propagation in a structure is paramount in the implementation of AU methods.  Lamb 
wave propagation is typically examined for aerospace applications dealing with thin 
plates and is examined further in a subsequent section. 
 
 10 
 
1.3.3 Lamb wave method  
Lamb waves classify the dispersive wave within a plate which propagates over the 
plate thickness and the plate width and length.  Lamb wave propagation and speed are 
influenced by plate thickness, and thus are easily changed due to alterations in the 
thickness due to damage.  This feature proves useful in the employment of Lamb wave 
analysis in a damage detection methodology. Lamb wave analysis can be used along with 
an active smart sensing system on a variety of experimental specimens to assess its 
success as a damage detection method [20].  As part of an ongoing research project at the 
University of Maryland, Lamb wave analysis techniques have been employed on thin 
plates and shells made from aluminum and carbon-fiber composite materials [22].  A 
variety of damage types have been instigated in each specimen: machined cracks, damage 
due to bolt torque loss and added mass.  To date, each specimen has been a single-piece 
structure.   
 In particular, the aerospace community has devoted extensive research and 
monetary efforts toward the development and operation of composite materials.  
Considering the area of structural health monitoring using AU and Lamb wave analysis 
techniques, it becomes necessary to build a thorough understanding of the wave 
propagation properties in composite materials if a successful, vibration-based damage 
diagnostic method is to be implemented in composite structures.  While classical 
laminated plate theory provides insight into wave propagation within composite 
materials, a popular route for accurately assessing the wave characteristics in specific 
composite materials moves toward a finite element modeling approach.  Extensive finite 
element research has provided insight into the wave proliferation of undamaged 
 11 
 
composites.  Galan and Abascal [23] developed a very useful wave dispersion prediction 
for an arbitrary composite laminate.  Unlike isotropic materials, the orthogonality of 
composite plates plays an important role in the direction of wave dispersion and will vary 
depending on the specific composite lay-up scheme.  Clark and Thwaites [24] showed 
through experimentation the importance of fiber orientation with wave propagation and 
wave speed in a composite material. 
 Another important phenomenon to be investigated is the wave propagation in a 
damaged composite, and how the damaged area influences the wave dispersion 
characteristics.  Typical defects in a composite material can include cracks, thickness 
inconsistencies, and delamination sites.  In addition to changes in normal wave 
propagation, modal parameters of the damaged composite are usually examined to detect 
the presence of a defect, assuming the baseline modal parameters are previously known.  
Tan, et. al [25] experimentally observed a decrease in amplitude as wave modes traveled 
through a composite delamination site.  This observation indicated a detectable energy 
loss in the wave mode as a result of the composite damage. 
1.3.4 Signal processing using wavelet transformation 
 In a wide variety of studies and applications, focus has been placed on the 
utilization of wavelet transformation and analysis in the field of damage diagnostics as a 
detection device.  Yen and Lin [26] introduced wavelet packet transforms as an 
alternative method for extracting time-frequency information from vibration signatures 
recorded from the aft main power transmission of a U.S. Navy CH-46R helicopter.  The 
wavelet packets are formed by taking linear combinations of typical wavelet functions, 
and proved to be more successful as compared to Fourier based feature results with the 
 12 
 
same application.  Ma and Fu [27] used the wavelet analysis method applied to Lamb 
wave signals in conjunction with a smart active sensing technique on a composite plate.  
Their experimental method showed successful crack detection of a damaged composite 
plate.  A similar experiment was conducted by Guo and Cawley [28] which investigated 
the interaction of Lamb waves with delamination sites in orthogonal laminates.  Their 
study proved the Lamb wave analysis as a successful detection means for damage due to 
composite delamination.  Wilcox, Lowe and Cawley [29] have published an extensive 
review on the transducer selection process for use in Lamb wave experimental and 
analysis methods; the selection is heavily reliant upon the required resolution, the 
particular defect and the available transduction options. 
1.3.5 Interrogation of bolted composite structures 
Adaptive materials have been employed to interrogate damage within a bolted 
joint as damage due to bolt torque loss.  Yang and Chang [30] developed a non-
destructive interrogation technique which used PZT (lead zirconate titanate) embedded 
sensor washers to constitute a sensor network on a carbon-carbon composite thermal 
protection system.  The smart sensor system successfully identified loosened bolts after a 
series of shaker verification tests which simulated a re-entry process.  Another 
investigation by Chang, Hung and Wang [31] examined the bearing failure of laminated 
composite double-lap metal/composite/metal bolted joints.  This particular experiment 
investigated pure and bolt bearing damage.  The experiment concluded that shear cracks 
formed due to compression failure, which could be suppressed with lateral supports and 
clamping pressure to increase bearing strength. 
 13 
 
1.4 Discrimination Techniques 
To successfully achieve a Level 2 damage prediction within a structure, there 
becomes a need for a damage discrimination method.  Not all research studies go beyond 
simple detection of damage, a Level 1 prediction.  Arguably, the graduation past Level 1 
prediction is paramount and provides the most useful contributions to the structural health 
monitoring field of study. Operational practices will benefit greatly from a geometric 
localization discriminator associated with a specific damage diagnostic method.  Further, 
the quantification of damage can prove to be useful when determining the need for 
damage repair and assessing the operational lifetime of a structural system.  Many 
discrimination techniques are developed to be application-specific.  This is due to the 
importance of key features which are specific to an application and are vital to the 
discriminator development process.  Discrimination methods are also heavily based on 
the goals of the technique: is the aim to distinguish a damaged scenario from an 
undamaged scenario, to distinguish the type of damage (crack, delamination, torque loss), 
or is the aim to quantify of damage level?  The overall discriminatory goal could also be 
a combination of many singular damage detection aims.  Expert discrimination systems 
are largely application-specific and rule-based, depending on feature selection.  The 
trends and ideas behind an expert system can make it useful to other applications that are 
similar in experimental set-up or damage classification.  The development of damage 
indices has been performed by Stubbs, et. al [32] [33] and applied to aerospace 
engineering structures.  A number of statistical methods provide a means to validate a 
specific expert system.  Fisher discrimination techniques [34] [35] can be used to 
statistically validate an expert-based system. Simpler methods such as the Euclidean 
 14 
 
distance classifier [36] can provide one-or-the-other discrimination capabilities, most 
useful in the distinction between damaged and undamaged scenarios.  In this research 
study, a damage index is adopted and used as the key feature in damage detection and 
localization for a jointed composite specimen; this damage index is clearly defined in a 
subsequent chapter.  Simple statistical means provide a method to reach Level 3 damage 
prediction due to bolt torque loss. 
1.5 Research Aim 
This research study utilizes the Lamb wave and smart active sensing method on a 
multi-part structure, consisting of composite plates and a bolted composite joint.  It is the 
aim of this research study to utilize these techniques to develop a comprehensive damage 
diagnostic on the jointed composite structure which will undergo damage due to bolt 
torque loss.  The goal is specific to the experimental specimen and damage type.  The 
ideas and results are presented with five main intentions: 
1) Apply a smart sensor array and utilize Lamb wave analysis techniques on 
the composite jointed specimen as a means for structural health 
monitoring.   
2) Compress experimentally obtained signal information into a singular 
damage index for a variety of damage scenarios due to bolt torque loss in 
the composite jointed specimen. 
3) Attain Level 1 prediction: utilize smart sensor signal response and damage 
index to determine the presence of damage due to bolt torque loss. 
4) Attain Level 2 prediction: exploit pattern recognition of the damage index 
to develop a qualitative damage localization method. 
 15 
 
5) Attain Level 3 prediction: quantify damage due to bolt torque loss through 
rule-based and statistical discrimination methodology. 
In combination, fulfilling these aims will successfully develop a comprehensive 
health monitoring system for the jointed composite structure up to a Level 3 prediction.  
Level 4 damage identification is typically associated with fracture mechanics, fatigue-life 
analysis or structural design assessment [9].  It is not the goal of this research study to 
achieve Level 4 damage prediction capability for the jointed composite structure.  
 
 
 
 16 
 
Chapter 2: Experimental Procedure 
2.1 Jointed Composite Panel 
The experimental specimen used in this research was prepared in the Composites 
Research (CORE) Laboratory of the University of Maryland at College Park.  The 
specimen was composed of four flat Hexcel IM7/8552 carbon/epoxy composite pieces in 
an 8-layer [90/0/0/90]s lay-up.  The experimental configuration of the jointed composite 
panel is shown in Figure 2-1-1.  The joint was composed of 12 bolts and nuts.  The 
distance between each bolt was 2? and each bolt was tightened using a hand-torque 
wrench to a value of 5 N-m.  A bolt numbering scheme starting with Bolt 0 at the upper, 
right corner and progressed down the right side of the joint.  Upon completed assembly, 
the jointed panel was 36? long and 12? wide.  The panel was mounted on the left and 
right side to simulate a clamped-free-clamped-free boundary condition.  The bottom side 
of the panel (unseen in Figure 2-1-1a) sat three inches from the laboratory table without 
obstruction.  The assembly was allowed to rest unmoved in a temperature controlled 
laboratory at the University of Maryland.   
 
 17 
 
 
 
(a) Photograph of top view. 
 
 
 
 
(b) side view 
 
Figure 2-1-1: The jointed composite panel. 
 
 
 
 18 
 
2.2 Wireless Smart Sensor System 
 A square type of PZT-4 piezoelectric patch was bonded to composite panels 1 and 
2; these piezo-patches are shown bonded to the jointed specimen in Figure 2-1-1 and 
below in Figure 2-2-1.  The piezoelectric transducers were 0.25? x 0.25?.  On composite 
1, the center of piezo-patches 1 and 2 were placed 6? from the bolts on the left-hand side 
of the joint and 3? from the top and bottom edges of the experimental assembly.  The 
patches were oriented 6? from one another.  Patches 3 and 4 were situated on composite 2 
in a mirrored configuration.   
 
 
 
Figure 2-2-1: The jointed composite panel with piezoelectric patch assembly. 
 
For excitation of the jointed panel, a windowed five-cycle tone burst was used at six 
interrogation frequencies: 20 kHz, 40 kHz, 60 kHz, 80 kHz, 100 kHz and 120 kHz.  An 
A/D and D/A data acquisition board (National Instruments: USB-6259) was used with a 
set sampling frequency of 1500 kHz.  LabVIEW SignalExpress? software created a 
formula excitation signal in the form of a Gaussian cosine burst signal according to the 
smart active sensing technique using a wavelet analysis method [30].  An example of this 
signal at an excitation frequency of 20 kHz is shown in Figure 2-2-2. 
 19 
 
 
 
Figure 2-2-2: Formula excitation output signal with 20 kHz excitation frequency. 
 
A block size of 3000 samples was recorded at a sample rate of 1.500 kHz.  In conjunction 
with the National Instruments data acquisition board, a Belkin
?
 Bluetooth
? 
Technology 
USB adapter was used to transmit signal information wirelessly.  Both of these devices 
are shown in Figure 2-2-3.  
 
 
(a) National Instruments data acquisition board and Bluetooth
?
 USB Adapter. 
 20 
 
 
(b) National Instruments? USB-6259. 
Figure 2-2-3: Wireless data acquisition system. 
 
For the purposes of experimentation, four excitation configuration cases were 
used corresponding to the numbered piezoelectric exciters (E1, E2, E3 and E4).  The 
sensor array permitted active sensing capabilities at multiple points along the jointed 
composite specimen.  Using one piezo-patch to excite the composite panel, time- and 
frequency-response information was gathered by the remaining three piezos and actively 
transmitted to the LabVIEW SignalExpress? software.  The jointed composite panel was 
separated into four quadrants, corresponding to the four piezo locations and numbers; 
these quadrants and the four excitation/active-sensing configuration cases are shown in 
Figure 2-2-4.  Under this condition, the bolt-to-sensor ratio was 3:1; within each 
quadrant, a single piezo-patch is responsible for gathering information that would help to 
indicate damage within one or more of the quadrant?s three bolts.   
 
 21 
 
 
Figure 2-2-4: Specimen quadrants and configuration Cases I, II, III, IV. 
2.3 Signal Noise Filtration and Running Average Method 
 To evaluate the obstructive effects of noise on experimental method performance, 
100mVrms and 200mVrms white Gaussian noise was added to the excitation tone burst 
input applied to the actuator piezo-patch.  To smooth out the corrupted time response 
signal, a running-average method was imposed during collection of time-response data by 
the active sensors.  The average number was 100 with an elapsed time of approximately 
two seconds.  The resulting time response signal using the running average method had 
the effects of noise filtered out; thus, the resulting signal could give better insight into the 
damage severity present in the jointed composite specimen. 
 
 22 
 
2.4 Damage Due to Bolt Torque Loss 
  This research investigates the capability of the smart sensor system to detect 
damage due to bolt torque loss in the jointed composite panel.  This represents a linear 
damage situation within the joint, since a loosened bolt does not change the linear-elastic 
properties of the composite structure.  Initially, each of the 12 bolts was set to a torque 
value of 5 N-m using a hand torque wrench; this initial condition represented an 
?undamaged? scenario within the composite specimen.  To simulate a damage situation, a 
single bolt was intentionally loosened to percentage values of the undamaged torque: 
25% torque loss (3.75 N-m), 50% torque loss (2.5 N-m), 75% torque loss (1.25 N-m) and 
100% torque loss (0 N-m).  The undamaged case and four damaged cases are 
implemented individually on Bolt 0, Bolt 1, Bolt 2 and Bolt 6 in the initial phase of 
experimentation.  Smaller torque values were examined for Bolt 0 to test the sensitivity 
capabilities of the Lamb wave method: 5% torque loss (4.75 N-m), 10% torque loss (4.5 
N-m), 15% torque loss (4.25 N-m) and 20% torque loss (4 N-m) were examined and 
included in the Bolt 0 results.   
A secondary experimentation phase investigated the effects of a dual-bolt torque 
loss configuration.  Bolt pairs would undergo identical torque loss scenarios.  The first 
bolt pair consisted of Bolt 0 and Bolt 1, each located within Quadrant 3.  A second bolt 
pair consisted of Bolts 0 and 6, located on opposite sides of the composite joint and in 
diagonally oriented quadrants (Quadrant 3 and Quadrant 2).  The bolt pairs were 
intentionally loosened to percentage values of the undamaged torque: 25% torque loss 
(3.75 N-m), 50% torque loss (2.5 N-m), 75% torque loss (1.25 N-m) and 100% torque 
loss (0 N-m), similar to the single-bolt experimentation.  Collecting a variety of torque 
 23 
 
loss information using four excitation/sensing configurations provided a database of 
information specific to the jointed composite panel that was used to gain insight into the 
smart sensor array system?s capability as an insightful damage detection and damage 
localization method. 
2.5 Data Compression: Damage Index 
For each undamaged and damaged scenario, excitation and active sensing 
information was gathered for Cases I, II, III and IV (excitation at E1, E2, E3 and E4) at 
the six aforementioned interrogation frequencies (20 kHz, 40 kHz, 60 kHz, 80 kHz, 100 
kHz, 120 kHz).  Six sets of three time- and frequency magnitude responses from the 
active sensing piezo-patches for a single configuration case yielded a total of 18 time and 
frequency-response data sets.  Four configuration cases would bring the total number of 
time- and frequency magnitude response data sets to 72.  The variation of five bolt torque 
values at each of the four configuration cases yielded 360 time and frequency-response 
data sets for a single bolt consideration.  The initial phase of experimentation focuses on 
four individual bolts (B0, B1, B2 and B6) which were each varied at 0, 25%, 50%, 75% 
and 100% torque losses, totaling 2880 sets of time and frequency magnitude response 
data.  A secondary experimentation phase examined smaller torque loss values in Bolt 0 
(5%, 10%, 15% and 20% torque loss) for the Case II configuration.  This increased the 
total to 3072 pairs of time and frequency magnitude response data sets.  Additionally, the 
consideration of two bolt pairs brought the total number of sensing information data sets 
to 4512.  The large amount of data necessitated a data compression method of the time- 
and frequency magnitude response information gathered at each of the active sensing 
piezo-patches during each experimental scenario.   
 24 
 
According to the Lamb wave method, a total damage index (DI) was adopted [33] 
and used to identify, localize and quantify the damage present in the jointed composite 
system due to bolt torque loss.  Initially, the active sensing data using the signals in time 
were separated into undamaged and damaged cases.  At each excitation frequency, ?
e
, 
the time signal of the undamaged system, x
u
(t,?
e
), and the time signal of the damaged 
system, x
d
(t,?
e
) was used to calculate a damage index using the signals in time, DI
t
.  This 
damage index is defined by [22] 
                                              (2-5-1) 
Further, the frequency magnitude of the spectrogram of undamaged systems, ?
u
(t,?
e
), 
and the frequency magnitude of the spectrogram of damaged systems, ?
d
(t,?
e
) was used 
to calculate a damage index using the frequency amplitude extracted from the 
spectrogram, DI
f
.  This damage index is defined by [22] 
                                          (2-5-2) 
For improvement of the damage index sensitivity, the time and frequency magnitude 
response indices are combined and normalized according to [22] 
                                            (2-5-3) 
where, 
max(DI
f
) = max{max[DI
f,20kHz
, DI
f,40kHz
, DI
f,60kHz
, DI
f,80kHz
, DI
f,100kHz
, DI
f,120kHz
]}
S1,S2,S3,S4    
 (2-5-4) 
max(DI
t
) = max{max[DI
t,20kHz
, DI
t,40kHz
, DI
t,60kHz
, DI
t,80kHz
, DI
t,100kHz
, DI
t,120kHz
]}
S1,S2,S3,S4    
 (2-5-5) 
 25 
 
 
As a note, for the E1 excitation case (E1, S2, S3, S4) the time- and frequency magnitude 
response at S1 does not exist since the piezo was acting as an actuator at the Quadrant 1 
location.  Thus, the S1 responses did not factor into (2-5-4) and (2-5-5) calculations.  An 
average damage index at sensor i location is given by [22] 
 
DI
average, i
 = average [DI
20kHz
, DI
40kHz
, DI
60kHz
, DI
80kHz
, DI
100kHz
, DI1
20kHz
]         (2-5-6) 
 
where, 
Case I:     i = 2, 3, 4 
Case II:     i = 1, 3, 4 
Case III:     i = 1, 2, 4 
Case IV:     i = 1, 2, 3 
 
The total damage index, DI
total
, proposed in this study was separated into two categories 
that focus on the individual sensor location.  For the sensor pair located across the joint 
from the exciter, DI
total, across joint
, is defined as [22] 
 
DI
total, across joint
 = average [DI
a,n
, DI
a,m
]                                     (2-5-7) 
 
where,  
Case I and II:     m = 3, n = 4 
Case III and IV:     m = 1, n = 2 
 26 
 
 
In each configuration case, combining all sensor data into a single total damage index,          
DI
total, all sensors
, is defined as [22] 
 
DI
total, all sensors
 = average [DI
a,n
, DI
a,m
, DI
a,j
]                                 (2-5-8) 
 
where, 
Case I:     j = 2, m = 3, n = 4 
Case II:     j = 1, m = 3, n = 4 
Case III:     j = 4, m = 1, n = 2 
Case IV:     j = 3, m = 1, n = 2 
 
This process is automated using a MATLAB code which is included in the 
Appendix.  Utilizing the Lamb wave method and experimental damage index for the 
jointed composite system, this research study aims to fulfill three chief goals: damage 
indication, damage localization within the specimen?s quadrants, and damage 
quantification within the identified quadrant. 
2.6 Baseline Sensing Variation Over Time 
 A supplemental investigation took advantage of the large quantities of undamaged 
?baseline? time response data taken over the course of the research study.  Over five 
months (October 2007 to February 2008) the undamaged data sets were compiled and 
compared against one another to examine the effects of time on the piezo-actuating and 
sensing capabilities and the overall experimental method.  For experimental repeatability, 
 27 
 
it would be undesirable to notice that an aging piezo-patch yields significantly altered 
results over time when used on a specific composite specimen.  If a noticeable change 
does occur, it is wise to predict the shift in data response and account for such a change 
over time in order to more accurately examine experimental results.  To note any 
significant changes, the difference in baseline time response data was quantified and 
examined over the five months of experimentation. 
2.7 Baseline Sensing Variation due to Temperature Increase 
 Another supplemental investigation was carried out to investigate the baseline 
variation and sensing capabilities of the piezo-patches due to temperature effects in the 
research lab.  This issue has the potential to become more impacting in an operational 
environment that is subject to large temperature variation; the jointed composite 
specimen in this research study would only experience a variation of 10?F throughout the 
months of experimentation.  To impose more elevated temperatures on the active sensor, 
a heat gun was used to elevate the temperature of the piezo-patch in Quadrant 1 from 
22?C (room temperature) to 30?C, 40?C, 50?C, 60?C, 70?C, and 80 ?C.  The panel was 
excited using the same aforementioned formula signal with excitation frequencies of 20 
kHz, 40 kHz, 60 kHz, 80 kHz, 100 kHz, and 120 kHz at the piezo-actuator in Quadrant 2.  
All 12 bolts remained at their full undamaged torque value of 5 N-m for the entire 
investigation.  Active sensing information in the form of time- and frequency magnitude 
response was gathered from Quadrant 1; the path of excitation and the sensing location is 
shown in Figure 2-7-1.   
 28 
 
 
Figure 2-7-1: Baseline temperature variation of S1, E2 excitation. 
 29 
 
Chapter 3: Damage Due to Bolt Torque Loss  
 
3.1 Bolt 0 damage due to torque loss 
In this section, the torque of Bolt 0 was manipulated to evaluate the damage 
detection capabilities of the smart sensor array system on the jointed composite panel.  
Five torque values were tested at each of the four excitation configuration cases.   
3.1.1 Bolt 0, Excitation Case I  
 
Using the piezo-patch in Quadrant 1 (E1) for excitation of the jointed composite 
panel, sensing information is compiled at the three remaining sensors (S2, S3, S4) located 
within the remaining three quadrants.  Figure 3-1-1 displays the excitation and sensing 
configuration and indicates the Bolt 0 location of simulated damage.  Figure 3-1-2 
represents the time response signals at S2, S3 and S4 sensors with respect to Bolt 0 
torque loss at a 40 kHz excitation frequency.  Each figure displays the damaged scenario 
time response as compared to the undamaged (all bolts at 5 N-m) time response, for the 
purposes of overlap comparison over the signal duration. 
 
 
Figure 3-1-1. Excitation Case I, Bolt 0 torque loss. 
 30 
 
 
Figure 3-1-2. Sensing time response, B0 torque loss, E1 40 kHz excitation. 
 
The magnitude of the time response signal from the S2 sensor location is 
noticeably greater than the sensor time response signal at locations S3 and S4.  This 
higher magnitude occurs due to the sensor's shared panel location as the actuator.  Since 
E1 and S2 are both located on composite 1, the majority of incident and reflected signals 
are measured without a great signal loss.  The comparably smaller S3 and S4 time 
response signals are located on composite 2, across the bolted joint.  Since the actuation 
signal must pass through the composite joint area consisting of two flat panels (composite 
 31 
 
3 and composite 4) and a series of tightened bolts, the incident signal magnitudes suffer a 
loss resulting in the smaller signal magnitude as compared to the S2 signal magnitude.  
While smaller in magnitude, the signals at S3 and S4 still provide insight toward the 
identification of damage within the jointed composite panel, as shown by their difference 
between undamaged and damaged time response signals. 
The difference between the undamaged and damaged time response signals, 
shown in Figure 3-1-2 as the black and red lines, respectively, represents the scattering 
signal for a 40 kHz excitation frequency under E1 actuation.  This scattering signal is 
plotted separately and shown in Figure 3-1-3.  The same scattering signal is normalized 
and shown in Figure 3-1-4.  The signal scattering at S3 and S4 sensors increase in 
magnitude as torque loss increases. 
 32 
 
 
Figure 3-1-3. Scattering signals, B0 torque loss, E1 40 kHz excitation. 
 
 
 
 
 
 
 33 
 
 
Figure 3-1-4. Normalized scattering signals, B0 torque loss, E1 40 kHz excitation. 
 
Figure 3-1-5 presents the damage index using the energy magnitudes due to 
frequency response (DI
f
) at S2, S3 and S4 under E1 excitation.  Figure 3-1-6 presents the 
damage index using the signals in time (DI
t
) at S2, S3 and S4 sensing locations.  For 
each, the damage index variation increased with bolt torque loss.  There was less 
variation in damage index over the range of excitation frequencies.  The damage index is 
more sensitive to changes in damage level as compared to changes in excitation 
frequency.   
 34 
 
 
Figure 3-1-5.  Damage index using the energy magnitudes in frequency vs. B0 torque loss 
and excitation frequency, E1 excitation. 
 35 
 
 
 
Figure 3-1-6. Damage index using the signals in time vs. B0 torque loss and excitation 
frequency, E1 excitation. 
 36 
 
 
Figure 3-1-6 displays smaller damage sensitivity in S2 as compared to the damage 
sensitivity in S3 and S4 sensors.  This trend presents the idea that sensors located on the 
same panel as signal actuation will have a decreased ability to detect damage present 
within the bolted composite joint. 
Figure 3-1-7 presents the normalized average damage index (DI
average
) of the 
jointed composite panel due to torque loss in Bolt 0 for E1 excitation.  The details of this 
calculation are outlined in the previous chapter.  The trend indicates an immediate 
increase in damage index from the undamaged scenario to the scenario of smallest 
damage, a torque loss of 25% (3.75 N-m).  The damage index as a damage detection 
method is capable of indicating such small levels of torque loss within the composite 
joint specimen.  The trend line due to S2 sensor is lower than the trend lines due to the S3 
and S4 sensors.  This presents a second indication of the S2 sensor location?s decreased 
ability to perceive damage within the composite joint.  The magnitude of average damage 
indices from sensors S3 and S4 are similar for each torque loss value; the S3 damage 
index is slightly larger in magnitude as compared to the S4 sensor index.   
 37 
 
 
Figure 3-1-7. Average damage index, B0 torque loss, E1 excitation. 
 
Figure 3-1-8 presents the total damage index as outlined in Equations 2-5-7 and  
2-5-8.  The total damage index contribution from the S3 and S4 sensors across the joint 
makes up nearly the entire damage index contribution from all three sensors, S2, S3 and 
S4.  This further indicates the importance of sensing capability on panels across the 
composite joint when damage is due to bolt torque loss within the joint. 
 
 38 
 
 
Figure 3-1-8. Total damage index, B0 torque loss, E1 excitation. 
 
3.1.2 Bolt 0, Excitation Case II  
 
Using the piezo-patch in Quadrant 2 (E2) for excitation of the jointed composite 
panel, sensing information is compiled at the three remaining sensors (S1, S3, S4) located 
within the remaining three quadrants.  Figure 3-1-9 displays the excitation and sensing 
configuration and indicates the Bolt 0 location of simulated damage.  Figure 3-1-10 
represents the time response signals at S1, S3 and S4 sensors with respect to Bolt 0 
torque loss at a 40 kHz excitation frequency.   
 
 39 
 
 
Figure 3-1-9. Excitation Case II, variable Bolt 0 torque loss. 
 
As shown in Figure 3-1-10, the magnitude of the time response signal from the S1 
sensor location is noticeably greater than the sensor time response signal at locations S3 
and S4.  This higher magnitude occurs due to the sensor's shared panel location as the 
actuator, as noted similarly in the Case I configuration with S2.  The comparably smaller 
S3 and S4 time response signals are located on composite 2, across the bolted joint.  
Again, this emphasizes the incident signal magnitudes loss as a result of the signal?s 
journey through the composite joint area consisting of two flat panels (composite 3 and 
composite 4) and a series of tightened bolts. 
Figure 3-1-11 shows the scattering signal for a 40 kHz excitation frequency under 
E2 actuation.  The same scattering signal is normalized and shown in Figure 3-1-12.  The 
signal scattering at S3 and S4 sensors increase in magnitude as torque loss increases. 
 
 40 
 
 
Figure 3-1-10. Sensing time response, B0 torque loss, E2 40 kHz excitation. 
 
 
 
 
 
 
 
 41 
 
 
Figure 3-1-11. Scattering signals, B0 torque loss, E2 40 kHz excitation. 
 
 
 
 
 
 42 
 
 
Figure 3-1-12. Normalized Scattering signals, B0 torque loss, E2 40 kHz excitation. 
 
Figure 3-1-13 and Figure 3-1-14 present the damage index using the energy 
magnitudes due to frequency response (DI
f
) and using the signals in time (DI
t
) at S1, S3 
and S4 under E2 excitation.  For each, the damage index is more sensitive to changes in 
damage level as compared to changes in excitation frequency.  The damage detection 
capabilities of each sensor using time and frequency response magnitudes are favorable 
within the jointed composite panel due to Bolt 0 torque loss under the E2 excitation 
configuration. 
 43 
 
 
Figure 3-1-13. Damage index using the energy magnitudes in frequency vs. B0 torque 
loss and excitation frequency, E2 excitation. 
 44 
 
 
 
Figure 3-1-14. Damage index using signals in time in vs. B0 torque loss and excitation 
frequency, E2 excitation. 
 45 
 
Figure 3-1-14 displays smaller damage sensitivity in S1 as compared to the 
damage sensitivity in S3 and S4 sensors.  Such a trend was displayed in the S2 sensor 
under E1 excitation, as noted in the previous section. 
Figure 3-1-15 presents the normalized average damage index (DI
average
) of the 
jointed composite panel due to torque loss in Bolt 0 for E2 excitation.  The trend 
indicates an immediate increase in damage index from the undamaged scenario to the 
scenario of smallest damage, a torque loss of 25% (3.75 N-m).  The damage index as a 
damage detection method is capable of indicating such small levels of torque loss within 
the composite joint specimen.  The trend line due to S1 sensor is lower than the trend 
lines due to the S3 and S4 sensors.  Similar to the S2 trend line in Figure 3-1-7, this 
indicates S1 sensor?s decreased ability to perceive damage within the composite joint as 
compared to the S3 and S4 sensors.  The magnitude of average damage index from the S3 
sensor is higher than the damage index from S4 at each torque loss value.  This presents 
the idea that, under E2 excitation, the sensor in Quadrant 3 indicates a higher incidence of 
damage than the sensor in Quadrant 4.     
 46 
 
 
Figure 3-1-15. Average damage index, B0 torque loss, E2 excitation. 
 
Figure 3-1-16 presents the total damage index under E2 excitation with respect to 
Bolt 0 torque loss.  The total damage index contribution from the S3 and S4 sensors 
across the joint makes up nearly the entire damage index contribution from all three 
sensors, S1, S3 and S4.  As noted in Figure 3-1-8, this further indicates the importance of 
sensing capability of sensors across the composite joint when damage is due to bolt 
torque loss within the joint. 
 
 47 
 
 
Figure 3-1-16. Total damage index, B0 torque loss, E2 excitation. 
 
3.1.3 Bolt 0, Excitation Case III  
 
Using the piezo-patch in Quadrant 3 (E3) for excitation of the jointed composite 
panel, sensing information is compiled at the three remaining sensors (S1, S2, S4) located 
within the remaining three quadrants.  In this excitation case, the actuation occurs in the 
same quadrant as the present damage due to torque loss.  Figure 3-1-17 displays the 
excitation and sensing configuration and indicates the Bolt 0 location of simulated 
damage.  Figure 3-1-18 represents the time response signals at S1, S2 and S4 sensors 
with respect to Bolt 0 torque loss at a 40 kHz excitation frequency. 
 
 48 
 
 
Figure 3-1-17. Excitation Case III, variable Bolt 0 torque loss. 
 
As shown in Figure 3-1-18, the magnitude of the time response signal from the S4 
sensor location is noticeably greater than the sensor time response signal at locations S1 
and S2.  This higher magnitude occurs due to the sensor's shared panel location as the 
actuator, as noted similarly in the Case I configuration with S2 and in the Case II 
configuration with S1.  The comparably smaller S1 and S2 time response signals are 
located across the joint on composite 1, further emphasizing the incident signal loss after 
passing through the composite joint. 
Figure 3-1-19 shows the scattering signal for a 40 kHz excitation frequency under 
E3 actuation.  The same scattering signal is normalized and shown in Figure 3-1-20.  The 
signal scattering at S1 and S2 sensors increase in magnitude as torque loss increases. 
 
 
 
 49 
 
 
Figure 3-1-18. Sensing time response, B0 torque loss, E3 40 kHz excitation. 
 
 
 
 
 
 
 
 50 
 
 
Figure 3-1-19. Scattering signals, B0 torque loss, E3 40 kHz excitation. 
 
 
 
 
 51 
 
 
Figure 3-1-20. Normalized scattering signals, B0 torque loss, E3 40 kHz excitation. 
 
Figure 3-1-21 and Figure 3-1-22 present the damage index using the energy 
magnitudes due to frequency response (DI
f
) and using the signals in time (DI
t
) at S1, S2 
and S4 under E3 excitation.  Even when actuation is performed in the same quadrant 
where damage is present due to torque loss, the damage detection capabilities of each 
sensor using time and frequency response magnitudes are favorable under the E3 
excitation configuration with respect to Bolt 0 torque loss.   
 52 
 
 
Figure 3-1-21.  Damage index using the energy magnitudes in frequency vs. B0 torque 
loss and excitation frequency, E3 excitation. 
 53 
 
 
 
Figure 3-1-22. Damage index using the signals in time vs. B0 torque loss and excitation 
frequency, E3 excitation. 
 54 
 
Figure 3-1-22 displays smaller damage sensitivity in S4 as compared to the 
damage sensitivity in S1 and S2 sensors.  Such a trend was displayed in the S2 sensor 
under E1 excitation, and in the S1 sensor under E2 excitation, as noted in the previous 
sections.  This reiterates the smaller capacity for damage detection within sensors that are 
located on the same composite panel as frequency actuation. 
Figure 3-1-23 presents the normalized average damage index (DI
average
) of the 
jointed composite panel due to torque loss in Bolt 0 for E3 excitation.  As in E1 and E2 
excitation cases, the damage index trend-lines of all three sensors indicates an immediate 
increase in damage index from the undamaged scenario to the scenario of 25% torque 
loss.  The damage index as a method for damage detection is capable of indicating such 
small levels of torque loss within the composite jointed panel.  The trend line due to S4 
sensor is lower than the trend lines due to the S1 and S2 sensors.  Similar to the S2 trend 
line in Figure 3-1-7 and the S1 trend in Figure 3-1-15, this indicates the S4 sensor?s 
decreased ability to perceive damage within the composite joint as compared to the S1 
and S2 sensors.   
 
 55 
 
 
Figure 3-1-23. Average damage index, B0 torque loss, E3 excitation. 
 
In Figure 3-1-23, the magnitude of average damage index from the S1 sensor is 
nearly indistinguishable from the values associated with S1 at torque loss values below 
75%.  This presents the idea that, under E3 excitation, it is difficult to distinguish whether 
the sensing capability at S1 or S2 provides more insight into damage detection in the 
composite jointed specimen. 
Figure 3-1-24 presents the total damage index under E3 excitation with respect to 
Bolt 0 torque loss.  The total damage index contribution from the S1 and S2 sensors 
across the joint makes up nearly the entire damage index contribution from all three 
sensors, S1, S2 and S4.  As noted in Figure 3-1-8 and Figure 3-1-16, this further indicates 
the importance of sensing capability of sensors across the composite joint when damage 
is located within the joint. 
 56 
 
 
Figure 3-1-24. Total damage index, B0 torque loss, E3 excitation. 
 
3.1.4 Bolt 0, Excitation Case IV  
 
Using the piezo-patch in Quadrant 4 (E4) for excitation of the jointed composite 
panel, sensing information is compiled at the three remaining sensors (S1, S2, S3) located 
within the remaining three quadrants.  In this excitation case, the actuation occurs on the 
same composite panel (composite 2) as the present damage due to torque loss, but in a 
different quadrant.  Figure 3-1-25 displays the excitation and sensing configuration and 
indicates the Bolt 0 location of damage due to torque loss.  Figure 3-1-26 shows the time 
response signals at S1, S2 and S3 sensors with respect to Bolt 0 torque loss at a 40 kHz 
excitation frequency. 
 
 57 
 
 
Figure 3-1-25. Excitation Case IV, variable Bolt 0 torque loss. 
 
As shown in Figure 3-1-26, the magnitude of the time response signal from the S3 
sensor location is noticeably greater than the sensor time response signal at locations S1 
and S2.  This higher magnitude occurs due to the sensor's shared panel location as the 
actuator, as noted similarly in the Case III configuration with S4.  The signal loss from 
E4 over the joint to S1 and S2 is evident in the comparably smaller S1 and S2 time 
response signals  
Figure 3-1-27 shows the scattering signal for a 40 kHz excitation frequency under 
E4 actuation.  The same scattering signal is normalized and shown in Figure 3-1-28.  The 
signal scattering at S1 and S2 sensors increase in magnitude as torque loss increases. 
 
 58 
 
 
Figure 3-1-26. Sensing time response, B0 torque loss, E4 40 kHz excitation. 
 
 
 
 
 
 59 
 
 
Figure 3-1-27. Scattering signals, B0 torque loss, E4 40 kHz excitation. 
 
 
 
 
 
 
 60 
 
 
Figure 3-1-28. Normalized scattering signals, B0 torque loss, E4 40 kHz excitation. 
 
Figure 3-1-29 and Figure 3-1-30 present the damage index using the energy 
magnitudes due to frequency response (DI
f
) and using the signals in time (DI
t
) at S1, S2 
and S3 under an E4 excitation case.  Even when actuation is performed on the same 
composite panel (composite 2) where damage is present, the damage detection 
capabilities of each sensor using time and frequency response magnitudes are favorable 
under the E4 excitation configuration with respect to Bolt 0 torque loss.   
 61 
 
 
Figure 3-1-29. Damage index using the energy magnitudes in frequency vs. B0 torque 
loss and excitation frequency, E4 excitation. 
 62 
 
 
 
Figure 3-1-30. Damage index using the signals in time vs. B0 torque loss and excitation 
frequency, E4 excitation. 
 63 
 
Figure 3-1-30 displays smaller damage sensitivity in S3 as compared to the 
damage sensitivity in S1 and S2 sensors.  This same trend was displayed in the S4 sensor 
under E3 excitation, once again reiterating the smaller capacity for damage detection 
within sensors that are located on the same composite panel as frequency actuation. 
Figure 3-1-31 presents the normalized average damage index (DI
average
) of the 
jointed composite panel due to torque loss in Bolt 0 for E4 excitation.  As in the three 
previous excitation cases, the damage index trend-lines of all three sensors indicates an 
immediate increase in damage index from the undamaged scenario to the scenario of 25% 
torque loss, indicating the damage detection method?s ability to detect small quantities of 
damage due to torque loss in the jointed composite specimen.  The trend line due to S3 
sensor is lower than the trend lines due to the S1 and S2 sensors.  Similar to the S4 trend 
line in Figure 3-1-23, this indicates the S3 sensor?s decreased ability to perceive damage 
within the composite joint as compared to the S1 and S2 sensors.   
 
 64 
 
 
Figure 3-1-31. Average damage index, B0 torque loss, E4 excitation. 
 
In Figure 3-1-31, the magnitude of average damage index from the S1 sensor is 
higher than the average damage index values associated with S2 at torque loss values 
above 25%.  This is similar to the trend in Figure 3-1-15, where the magnitude of average 
damage index from the S3 sensor was higher than the damage index from S4.  
Correspondingly, the trend presents the notion that under E4 excitation, the sensor in 
Quadrant 1 indicates a higher incidence of damage than the sensor in Quadrant 2 for 
torque loss values greater than 25%.   
Figure3-1-32 presents the total damage index under E4 excitation with respect to 
Bolt 0 torque loss.  The total damage index contribution from the S1 and S2 sensors 
across the joint makes up nearly the entire damage index contribution from all three 
sensors, S1, S2 and S3.  As noted in previous total damage index figures, this again 
 65 
 
displays the importance that when damage is present within the joint, sensing ability at 
locations across the joint contributes greatly toward damage detection capability. 
 
 
Figure 3-1-32. Total damage index, B0 torque loss, E4 excitation. 
3.1.5 Comparison of Bolt 0 excitation configurations 
 Figure 3-1-33 shows the side-by-side comparison of the normalized average 
damage index of the composite jointed panel due to Bolt 0 torque loss for each excitation 
configuration case (E1, E2, E3 and E4).  For each excitation configuration, the damage 
detection capability was favorable and provided insight into the presence and location of 
damage due to bolt torque loss.  It is possible to use the average damage index for each 
excitation case to provide a rough estimate of the location of damage due to torque loss 
within the jointed composite panel by analyzing and comparing the overall trend-line 
 66 
 
from each sensor on each of the plots.  As seen from Figure 3-1-33, the average damage 
index is as follows: 
 
DI
E1,S3
 ? DI
E1,S4
 >> DI
E1,S2
  Figure 3-1-33 (a) 
DI
E2,S3
 > DI
E2,S4
 >> DI
E2,S1
  Figure 3-1-33 (b) 
DI
E3,S1
 ? DI
E3,S2
 >> DI
E3,S4
  Figure 3-1-33 (c) 
DI
E4,S1
 > DI
E4,S2 
>> DI
E4,S3
  Figure 3-1-33 (d) 
 
The analysis and comparison of damage index trends under each excitation case implies 
that the damage due to torque loss is in the common area in-between sensors S1 and S3, 
within Quadrant 1 or Quadrant 3.  The average damage index values from S3 and S4 
under E1 excitation are nearly indistinguishable.  Similarly, the average damage index 
values from S1 and S2 under E3 excitation are nearly indistinguishable among the 
percentage torque loss values.  It can be determined that, when actuation exists within the 
quadrants of possible damage, the average damage index trends can not provide great 
insight toward precise damage localization.   
 
 67 
 
 
Figure 3-1-33. Comparison of normalized average damage index, B0 torque loss. 
 
Focusing on only excitation cases under E2 and E4, there is a clear distinction 
between the average damage index trends; DI
E2,S3
 is distinguishably larger than DI
E2,S4
 
and DI
E4,S1
 is distinguishably larger than DI
E4,S2
 over the torque loss values.  When 
actuation is present in quadrants furthest from the predicted damage areas, the sensing 
information provides great insight toward the localization of damage within the 
composite jointed panel.  Comparing the average damage index from Figure 3-1-33 (b) 
and Figure 3-1-33 (d) clearly shows: 
 
DI
E2,S3
  >  DI
E4,S1
 
 68 
 
The information is isolated to show this comparison graphically in Figure 3-1-34. 
 
 
Figure 3-1-34. Comparison of normalized average damage indices, B0 torque loss; DI
E2,S3 
and
 
 DI
E4,S1
. 
 
This trend indicates a higher damage index within proximity to S3, thus the greater 
likelihood of damage due to bolt torque loss in Quadrant 3 as compared to Quadrant 1.  
Figure 3-1-35 shows the shaded area of the highest likelihood of damage. 
 
 69 
 
 
Figure 3-1-35. Estimated damage area due to B0 torque loss. 
 
3.1.6 Detection of smaller torque loss percentages 
 
 In the previous sections, it was shown that the wireless smart sensor array system 
and the utilization of average damage index values as a method for data compression 
could accurately predict the incidence of bolt torque loss values as low as 25% (100% 
torque: 5 N-m).  The examination of damage due to torque loss in Bolt 0 at smaller 
percentage values provided insight into the damage detection method?s ability to sense 
smaller levels of damage.  Under an E2 excitation configuration, Bolt 0 torque loss was 
varied by 5%, 10%, 15% and 20%.  These results were added to the previous E2 
excitation information shown in section 3.1.2.  Figure 3-1-36 shows the normalized 
average damage index of the composite jointed panel due to Bolt 0 torque loss.  As 
shown, the damage detection method is capable of detecting the incidence of damage due 
to bolt torque loss for values as low as 5%.  Figure 3-1-37 shows the total damage index 
under E2 excitation with respect to the smaller Bolt 0 torque loss values. 
 70 
 
The bolt torque loss is adjusted using a hand torque wrench; using this method, there was 
difficulty adjusting the torque loss lower than 5%.  This value was used as the lowest 
threshold for damage detection using this method. 
 
 
Figure 3-1-36. Normalized average damage index due to smaller B0 torque loss. 
 
 71 
 
 
Figure 3-1-37. Total damage index due to smaller B0 torque loss. 
 
3.2 Bolt 1 damage due to torque loss 
In this section, the torque of Bolt 1 is manipulated in the same manner as Bolt 0 to 
evaluate the damage detection capabilities of the smart sensor array system on the jointed 
composite panel.  Five torque values were tested at each of the four excitation 
configuration cases.  Experimental results were compiled exactly as the Bolt 0 phase of 
experimentation.  In this section, the results are presented in a condensed version to 
highlight the most important discoveries.   
3.2.1 Bolt 1, Excitation Case I  
 
Using the piezo-patch in Quadrant 1 (E1) for excitation of the jointed composite 
panel, sensing information is compiled at the three remaining sensors (S2, S3, S4) located 
within the remaining three quadrants.  Figure 3-2-1 displays the excitation and sensing 
 72 
 
configuration and indicates the Bolt 1 location of simulated damage.  Figure 3-2-2 
represents the scattering signal for a 40 kHz excitation frequency under E1 actuation.  
The signal scattering at S3 and S4 sensors increase in magnitude as torque loss increases.  
The scattering signals at sensors across the joint from the source of actuation (S3, S4) are 
smaller in magnitude than the signal from the sensor that shares a composite panel with 
the source of actuation (S2).  This phenomenon is due to the incident signal loss as it 
passes through the composite joint. 
 
 
Figure 3-2-1. Excitation Case I, variable Bolt 1 torque loss. 
 
 
 73 
 
 
Figure 3-2-2. Scattering signals, B1 torque loss, E1 40 kHz excitation. 
 
Figure 3-2-3 presents the damage index using the energy magnitudes due to 
frequency response (DI
f
) at S2, S3 and S4 under E1 excitation.  Figure 3-2-4 presents the 
damage index using the signals in time (DI
t
) at S2, S3 and S4 sensing locations.  For 
each, the damage index variation increased with bolt torque loss.  There was less 
variation in damage index over the range of excitation frequencies.  The damage index is 
more sensitive to changes in damage level as compared to changes in excitation 
frequency.   
 74 
 
 
Figure 3-2-3.  Damage index using the energy magnitudes in frequency vs. B1 torque loss 
and excitation frequency, E1 excitation. 
 75 
 
 
 
Figure 3-2-4. Damage index using the signals in time vs. B1 torque loss and excitation 
frequency, E1 excitation. 
 76 
 
3.2.2 Bolt 1, Excitation Case II  
 
Using the piezo-patch in Quadrant 2 (E2) for excitation of the jointed composite 
panel, sensing information is compiled at the three remaining sensors (S1, S3, S4) located 
within the remaining three quadrants.  Figure 3-2-5 displays the excitation and sensing 
configuration and indicates the Bolt 1 location of simulated damage.  Figure 3-2-6 
represents the scattering signal for a 40 kHz excitation frequency under E2 actuation.  
The signal scattering at S3 and S4 sensors increase in magnitude as torque loss increases.  
The scattering signals at sensors across the joint from the source of actuation (S3, S4) are 
smaller in magnitude than the signal from the sensor that shares a composite panel with 
the source of actuation (S1).  This phenomenon is due to the incident signal loss as it 
passes through the composite joint and is noted in previous chapter sections. 
 
 
Figure 3-2-5. Excitation Case II, variable Bolt 1 torque loss. 
 
 
 
 
 77 
 
 
Figure 3-2-6. Scattering signals, B1 torque loss, E2 40 kHz excitation. 
 
Figure 3-2-7 and Figure 3-2-8 present the damage index using the energy 
magnitudes due to frequency response (DI
f
) and using the signals in time (DI
t
) at S1, S3 
and S4 under E2 excitation.  In each plot, the damage index is more sensitive to changes 
in damage level as compared to changes in excitation frequency.  The damage detection 
capabilities of each sensor using time and frequency response magnitudes are favorable 
within the jointed composite panel due to Bolt 1 torque loss under the E2 excitation 
configuration. 
 78 
 
 
Figure 3-2-7.  Damage index using the energy magnitudes in frequency vs. B1 torque loss 
and excitation frequency, E2 excitation. 
 79 
 
 
 
Figure 3-2-8. Damage index using the signals in time vs. B1 torque loss and excitation 
frequency, E2 excitation. 
 80 
 
3.2.3 Bolt 1, Excitation Case III  
 
Using the piezo-patch in Quadrant 3 (E3) for excitation of the jointed composite 
panel, sensing information is compiled at the three remaining sensors (S1, S2, S4) located 
within the remaining three quadrants.  In this excitation case, the actuation occurs in the 
same quadrant as the present damage due to torque loss.  Figure 3-2-9 displays the 
excitation and sensing configuration and indicates the Bolt 1 location of simulated 
damage.  Figure 3-2-10 represents the scattering signal for a 40 kHz excitation frequency 
under E3 actuation.  The signal scattering at S1 and S2 sensors increase in magnitude as 
torque loss increases.  The scattering signals at sensors across the joint from the source of 
actuation (S1, S2) are smaller in magnitude than the signal from the sensor that shares a 
composite panel with the source of actuation (S4).   
 
 
Figure 3-2-9. Excitation Case III, variable Bolt 1 torque loss. 
 
 
 
 
 81 
 
 
Figure 3-2-10. Scattering signals, B1 torque loss, E3 40 kHz excitation. 
 
Figure 3-2-11 and Figure 3-2-12 present the damage index using the energy 
magnitudes due to frequency response (DI
f
) and using the signals in time (DI
t
) at S1, S2 
and S4 under E3 excitation.  In each plot, the damage index is more sensitive to changes 
in damage level as compared to changes in excitation frequency.  Despite the excitation 
source?s close proximity to the actual damage location, the damage detection capabilities 
of each sensor using time and frequency response magnitudes are favorable within the 
jointed composite panel due to Bolt 1 torque loss under the E3 excitation configuration. 
 82 
 
 
Figure 3-2-11.  Damage index using the energy magnitudes in frequency vs. B1 torque 
loss and excitation frequency, E3 excitation. 
 83 
 
 
Figure 3-2-12. Damage index using the energy magnitudes in frequency vs. B1 torque 
loss and excitation frequency, E3 excitation. 
 84 
 
3.2.4 Bolt 1, Excitation Case IV  
 
Using the piezo-patch in Quadrant 4 (E4) for excitation of the jointed composite 
panel, sensing information is compiled at the three remaining sensors (S1, S2, S3) located 
within the remaining three quadrants.  In this excitation case, the actuation occurs on the 
same composite panel (composite 2) as the present damage due to torque loss, but in a 
different quadrant.  Figure 3-2-13 displays the excitation and sensing configuration and 
indicates the Bolt 1 location of damage due to torque loss.  Figure 3-2-14 represents the 
scattering signal for a 40 kHz excitation frequency under E4 actuation.  The signal 
scattering at S1 and S2 sensors increase in magnitude as torque loss increases.  The 
scattering signals at sensors across the joint from the source of actuation (S1, S2) are 
smaller in magnitude than the signal from the sensor that shares a composite panel with 
the source of actuation (S3).   
 
 
Figure 3-2-13. Excitation Case IV, variable Bolt 1 torque loss. 
 
 
 
 85 
 
 
Figure 3-2-14. Scattering signals, B1 torque loss, E4 40 kHz excitation. 
 
Figure 3-2-15 and Figure 3-2-16 present the damage index using the energy 
magnitudes due to frequency response (DI
f
) and using the signals in time (DI
t
) at S1, S2 
and S3 under an E4 excitation case.  Even when actuation is performed on the same 
composite panel (composite 2) where damage is present, the damage detection 
capabilities of each sensor using time and frequency response magnitudes are favorable 
under the E4 excitation configuration with respect to Bolt 1 torque loss.   
 
 86 
 
 
Figure 3-2-15.  Damage index using the energy magnitudes in frequency vs. B1 torque 
loss and excitation frequency, E4 excitation. 
 87 
 
 
Figure 3-2-16. Damage index using the energy magnitudes in frequency vs. B1 torque 
loss and excitation frequency, E4 excitation. 
 88 
 
3.2.5 Comparison of Bolt 1 excitation configurations 
 
 Figure 3-2-17 shows the side-by-side comparison of the normalized average 
damage index of the composite jointed panel due to Bolt 1 torque loss for each excitation 
configuration case (E1, E2, E3 and E4).  Similar to the results of Bolt 0 torque loss 
(Figure 3-1-33), the damage detection capability provided insight into the presence and 
location of damage due to bolt torque loss.  To provide a rough estimate of the location of 
damage due to torque loss within the jointed composite panel, the following analysis is 
made: 
DI
E1,S3
 ? DI
E1,S4
 >> DI
E1,S2
  Figure 3-2-17 (a) 
DI
E2,S3
 > DI
E2,S4
 >> DI
E2,S1
  Figure 3-2-17 (b) 
DI
E3,S1
 ? DI
E3,S2
 >> DI
E3,S4
  Figure 3-2-17 (c) 
DI
E4,S1
 > DI
E4,S2
 >> DI
E4,S3 
 Figure 3-2-17 (d) 
 
The comparison of average damage index trends over each excitation case indicates that 
the damage due to torque loss is somewhere within the area between sensors S1 and S3, 
thus within Quadrant 1 or Quadrant 3.  The average damage index DI
E3,S1
 and DI
E3,S2
 are 
nearly indistinguishable among the percentage torque loss values.   
 
 89 
 
 
Figure 3-2-17. Comparison of normalized average damage index, B1 torque loss. 
 
Similar to the analysis of Bolt 0 average damage index in section 3.1.5, the 
clearest distinction of data for a possible damage location in-between sensors S1 and S3 
comes from the E2 and E4 excitation cases.  When actuation is present in quadrants 
furthest from the predicted damage areas, the sensing information provides great insight 
toward the localization of damage within the composite jointed panel.  Figure 3-2-18 
shows the graphical comparison of the DI
E4,S1
 and DI
E2,S3
 taken from Figure 3-2-17 (b) 
and Figure 3-2-17 (d). 
 
 90 
 
 
Figure 3-2-18. Comparison of normalized average damage indices, B1 torque loss; DI
E4,S1
 
and DI
E2,S3.
 
 
As compared to the Bolt 0 average damage index values for S3 and S1 
information in Figure 3-2-18, the information present for damage due to torque loss in 
Bolt 1 is not as clear.  However, a trend still remains.  There is a clear difference between 
DI at 75% torque loss which does not correlate with resulted expected from a similar 
analysis performed on Bolt 0 information.  At 25% and 50% torque loss, DI
E2,S3
 was only 
slightly higher than DI
E4,S1
.  At 100% torque loss, DI
E2,S3 
was clearly higher than DI
E4,S1
.  
This demonstration raises the question as to whether damage quantification does affect 
the level of confidence behind damage localization using this method.  Given that three 
of the four inflicted damage levels indicate a damage position closest to S3,             
 91 
 
Figure 3-2-19 shows the shaded area of the highest likelihood of damage to be within the 
joint area located in Quadrant 3. 
 
 
Figure 3-2-19. Estimated damage area due to B1 torque loss. 
 
3.3 Bolt 2 damage due to torque loss 
In this section, the torque of Bolt 2 is manipulated in the same manner as Bolt 0 
and Bolt 1 to evaluate the damage detection capabilities of the smart sensor array system 
on the jointed composite panel.  In this case, the damaged bolt was further toward the 
center of the composite panel, and borders Quadrant 2.  Five torque values were tested at 
each of the four excitation configuration cases.  Experimental results were compiled 
exactly as the Bolt 0 and Bolt 1 phases of experimentation, and monitored closely to 
determine if the bolt?s proximity to Quadrant 2 would affect the trends noticed from Bolts 
0 and 1.   
 
 92 
 
3.3.1 Bolt 2, Excitation Case I  
 
Using the piezo-patch in Quadrant 1 (E1) for excitation of the jointed composite 
panel, sensing information is compiled at the three remaining sensors (S2, S3, and S4).  
Figure 3-3-1 shows the excitation and sensing configuration and indicates the Bolt 2 
location of simulated damage.  Figure 3-3-2 represents the scattering signal for a 40 kHz 
excitation frequency under E1 actuation.  The signal scattering at S3 and S4 sensors 
increase in magnitude as torque loss increases.  Due to the incident signals loss as it 
passes through the composite joint, the scattering signals at sensors S3 and S4 are smaller 
in magnitude than the signal from sensor S2. 
 
 
Figure 3-3-1. Excitation Case I, variable Bolt 2 torque loss. 
 
Figure 3-3-3 presents the damage index using the energy magnitudes due to 
frequency response (DI
f
) at S2, S3 and S4 under E1 excitation.  Figure 3-3-4 presents the 
damage index using the signals in time (DI
t
) at S2, S3 and S4 sensing locations.  In each 
plot, the damage index is more sensitive to changes in damage level as compared to 
changes in excitation frequency.   
 93 
 
 
Figure 3-3-2. Scattering signals, B2 torque loss, E1 40 kHz excitation. 
 
 
 
 
 
 94 
 
 
Figure 3-3-3.  Damage index using the energy magnitudes in frequency vs. B2 torque loss 
and excitation frequency, E1 excitation. 
 95 
 
 
Figure 3-3-4. Damage index using the energy magnitudes in frequency vs. B2 torque loss 
and excitation frequency, E1 excitation. 
 96 
 
3.3.2 Bolt 2, Excitation Case II  
 
Using the piezo-patch in Quadrant 2 (E2) for excitation of the jointed composite 
panel, sensing information is compiled at the three remaining sensors (S1, S3, S4) located 
within the remaining three quadrants.  Figure 3-3-5 displays the excitation and sensing 
configuration and indicates the Bolt 2 location of simulated damage.  Figure 3-3-6 
represents the scattering signal for a 40 kHz excitation frequency under E2 actuation.  
The signal scattering at S3 and S4 sensors increase in magnitude as torque loss increases.  
The scattering signals at sensors across the joint from the source of actuation (S3, S4) are 
smaller in magnitude than the signal from the sensor that shares a composite panel with 
the source of actuation (S1).   
 
 
Figure 3-3-5. Excitation Case II, variable Bolt 2 torque loss. 
 
 
 97 
 
 
Figure 3-3-6. Scattering signals, B2 torque loss, E2 40 kHz excitation frequency. 
 
 
 
 98 
 
 
Figure 3-3-7.  Damage index using the energy magnitudes in frequency vs. B2 torque loss 
and excitation frequency, E2 excitation. 
 99 
 
 
Figure 3-3-8. Damage index using the signals in time vs. B2 torque loss and excitation 
frequency, E2 excitation. 
 100 
 
3.3.3 Bolt 2, Excitation Case III  
 
Using the piezo-patch in Quadrant 3 (E3) for excitation of the jointed composite 
panel, sensing information is compiled at the three remaining sensors (S1, S3, S4) located 
within the remaining three quadrants.  In this scenario, the actuation occurred in the same 
quadrant where damage was present due to torque loss.  Figure 3-3-9 displays the 
excitation and sensing configuration and indicates the Bolt 2 location of simulated 
damage.  Figure 3-3-10 represents the scattering signal for a 40 kHz excitation frequency 
under E3 actuation.  The signal scattering at S1 and S2 sensors increase in magnitude as 
torque loss increases.  The scattering signals at sensors across the joint from the source of 
actuation (S1, S2) are smaller in magnitude than the signal from the sensor that shares a 
composite panel with the source of actuation (S4).   
 
 
Figure 3-3-9. Excitation Case III, variable Bolt 2 torque loss. 
 
Figure 3-3-11 presents the damage index using the energy magnitudes due to 
frequency response (DI
f
) at S1, S2 and S4 under E3 excitation.  Figure 3-3-12 presents 
the damage index using the signals in time (DI
t
) at S1, S2 and S4 sensing locations.  In 
 101 
 
each plot, the damage index displays a higher sensitivity to increased bolt torque loss and 
a lesser sensitivity over the range of excitation frequencies.   
 
 
Figure 3-3-10. Scattering signals, B2 torque loss, E3 40 kHz excitation. 
 
 102 
 
 
Figure 3-3-11.  Damage index using the energy magnitudes in frequency vs. B2 torque 
loss and excitation frequency, E3 excitation. 
 103 
 
 
 
Figure 3-3-12. Damage index using the energy signals in time vs. B2 torque loss and 
excitation frequency, E2 excitation. 
 104 
 
3.3.4 Bolt 2, Excitation Case IV 
 
In the final excitation configuration case (E4), sensing information is compiled at 
the three remaining sensors (S1, S2, S3) located within the remaining three quadrants.  In 
this scenario, the actuation occurred in the same composite panel (composite 2) where 
damage was present due to torque loss.  Figure 3-3-13 displays the excitation and sensing 
configuration and indicates the Bolt 2 location of simulated damage.  Figure 3-3-14 
represents the scattering signal for a 40 kHz excitation frequency under E4 actuation.  
The signal scattering at S1 and S2 sensors increase in magnitude as torque loss increases.  
The scattering signals at sensors across the joint from the source of actuation (S1, S2) are 
smaller in magnitude than the signal from the sensor that shares a composite panel with 
the source of actuation (S3).   
 
 
Figure 3-3-13. Excitation Case IV, variable Bolt 2 torque loss. 
 
Figure 3-3-15 presents the damage index using the energy magnitudes due to 
frequency response (DI
f
) at S1, S2 and S3 under E4 excitation.  Figure 3-3-16 presents 
the damage index using the signals in time (DI
t
) at S1, S2 and S3 sensing locations.  
 105 
 
Damage index due to time signal and due to frequency magnitude both exhibit a higher 
sensitivity to damage due to torque loss as compared to excitation frequency.  Similar to 
Bolt 0 and Bolt 1, the damage detection capabilities using time and frequency response 
magnitudes are favorable within the jointed composite panel due to Bolt 2 torque loss 
even when actuation occurred in the same composite panel (composite 2) as damage due 
to torque loss. 
 
Figure 3-3-14. Scattering signals, B2 torque loss, E4 40 kHz excitation frequency. 
 
 106 
 
 
Figure 3-3-15. Damage index using the energy magnitudes in frequency vs. B2 torque 
loss and excitation frequency, E4 excitation. 
 107 
 
 
Figure 3-3-16. Damage index using the signals in time vs. B2 torque loss and excitation 
frequency, E4 excitation. 
 108 
 
3.3.5 Comparison of Bolt 2 excitation configurations 
 
 Figure 3-3-17 shows the side-by-side comparison of the normalized average 
damage index of the composite jointed panel due to Bolt 2 torque loss for each excitation 
configuration case (E1, E2, E3 and E4).  Due to the proximity of Bolt 2 to Quadrant 4, 
the trends become less clear as compared to the trends from Bolt 0 and Bolt 1.  To 
provide a rough estimate of the location of damage due to torque loss within the jointed 
composite panel, the following analysis is made: 
 
DI
E1,S3
 ? DI
E1,S4
 >> DI
E1,S2
  Figure 3-3-17 (a) 
DI
E2,S3
 > DI
E2,S4
 >> DI
E2,S1
  Figure 3-3-17 (b) 
DI
E3,S1
 ? DI
E3,S2
 >> DI
E3,S4
  Figure 3-3-17 (c) 
DI
E4,S1
 ? DI
E4,S2
 >> DI
E4,S3
  Figure 3-3-17 (d) 
 
While the difference between trends is less clear, the estimation still indicates damage 
present in-between sensors S1 and S3, thus within Quadrant 1 or Quadrant 3.  The 
damage index quantities from S2 and S4 sensors have increased as compared to the 
information obtained from Bolt 0 and Bolt 1 torque loss (Figures 3-1-33 and 3-2-17).  
Therefore, the damage location can be identified toward the bottom of the area in-
between the S1 and S3 sensors. 
 
 
 
 
 109 
 
 
Figure 3-3-17. Comparison of normalized average damage index, B2 torque loss. 
 
Similar to the analysis of Bolt 0 and Bolt 1 average damage index in sections 
3.1.5 and 3.2.5, the clearest distinction of data for a possible damage location in-between 
sensors S1 and S3 comes from the E2 and E4 excitation cases.  Due to Bolt 2 close 
proximity to Quadrant 4, the information obtained under excitation configuration E4 is 
not as clear when compared to information obtained under excitation configuration E3.  
However, at 100% torque loss, the distinction between S1 and S2 trends in Figure          
3-3-17 (d) becomes clear.  Again, this contributes to the idea that damage quantification 
plays a role in the discrimination between quadrants with possible damage.              
 110 
 
Figure 3-3-18 shows the graphical comparison of the average damage index values from 
DI
E4,S1
 and DI
E2,S3
 taken from Figure 3-3-17 (b) and Figure 3-3-17 (d). 
 
Figure 3-3-18. Comparison of normalized average damage indices, B2 torque loss; DI
E2,S3
 
and DI
E4,S1
. 
 
Comparing DI
E4,S1
 and DI
E2,S3
, Figure 3-3-18 clearly shows that for all torque loss values: 
 
DI
E2,S3
  >  DI
E4,S1
 
 
This trend indicates a higher damage index within proximity to S3, thus the greater 
likelihood of damage due to bolt torque loss in Quadrant 3 as compared to Quadrant 1, 
shown in Figure 3-3-19. 
 
 111 
 
 
 
Figure 3-3-19. Estimated damage area due to B2 torque loss. 
 
3.4 Bolt 6 damage due to torque loss 
Similar to previous sections, the torque of Bolt 6 is varied to evaluate the damage 
detection capabilities of the Lamb wave method under a different damage scenario.  In 
this case, the damaged bolt lies within Quadrant 2 and on composite 1; this is directly 
diagonal of the previous cases which were present within composite 2 in Quadrant 3.  
Five torque values were tested at each of the four excitation configuration cases.  
Experimental results were compiled exactly as the previous sections.  Analysis of results 
due to torque loss within Quadrant 2 provided insight into the symmetry properties of the 
Lamb wave method as a damage detection device. 
 
 
 112 
 
3.4.1 Bolt 6, Excitation Case I  
 
Figure 3-4-1 shows the excitation and sensing configuration and indicates the Bolt 6 
location of damage due to torque loss.  Figure 3-4-2 presents the damage index using the 
energy magnitudes due to frequency response (DI
f
) at S2, S3 and S4 under E1 excitation.  
Figure 3-4-3 presents the damage index using the signals in time (DI
t
) at S2, S3 and S4 
sensing locations.  Similarly to bolts in Quadrant 3, the damage index displays a higher 
sensitivity due to damage level as compared to the sensitivity due to excitation frequency.  
Similar to bolts in Quadrant 3, the damage detection capabilities using time and 
frequency response magnitudes are favorable within the jointed composite panel due to 
Bolt 6 torque loss even when actuation occurred in the same composite panel (composite 
1) as damage due to torque loss. 
 
 
Figure 3-4-1. Excitation Case I, variable Bolt 6 torque loss. 
 
 
 113 
 
 
Figure 3-4-2.  Damage index using the energy magnitudes in frequency vs. B6 torque loss 
and excitation frequency, E1 excitation. 
 114 
 
 
Figure 3-4-3. Damage index using the signals in time vs. B6 torque loss and excitation 
frequency, E1 excitation. 
 115 
 
3.4.2 Bolt 6, Excitation Case II  
 
Using the piezo-patch in Quadrant 2 (E2) for excitation of the jointed composite 
panel, sensing information is compiled at the three remaining sensors (S1, S3, S4) located 
within the remaining three quadrants.  In this excitation configuration, the actuation 
source was in the same quadrant as the damaged bolt.  Figure 3-4-4 displays the 
excitation and sensing configuration and indicates the Bolt 6 location of simulated 
damage.   
 
 
Figure 3-4-4. Excitation Case II, variable Bolt 6 torque loss. 
 
Figure 3-4-5 presents the damage index using the energy magnitudes due to 
frequency response (DI
f
) at S1, S3 and S4 under E2 excitation.  Figure 3-4-6 presents the 
damage index using the signals in time (DI
t
) at S1, S3 and S4 sensing locations.  Similar 
to bolts in Quadrant 3 under excitation configuration E3, the damage index displays the 
same sensitivity to bolt torque loss. 
 
 116 
 
 
Figure 3-4-5.  Damage index using the energy magnitudes in frequency vs. B6 torque loss 
and excitation frequency, E2 excitation. 
 117 
 
 
Figure 3-4-6. Damage index using the signals in time vs. B6 torque loss and excitation 
frequency, E2 excitation. 
 118 
 
3.4.3 Bolt 6, Excitation Case III  
 
Figure 3-4-7 displays the excitation and sensing configuration and indicates the 
Bolt 6 location of simulated damage for the E3 excitation configuration case. 
 
 
Figure 3-4-7. Excitation Case III, variable Bolt 6 torque loss. 
 
Figure 3-4-8 presents the damage index using the energy magnitudes due to 
frequency response (DI
f
) at S1, S2 and S4 under E3 excitation.  Figure 3-4-9 presents the 
damage index using the signals in time (DI
t
) at S1, S2 and S4 sensing locations.  The 
damage detection capabilities using time and frequency response magnitudes were 
favorable within the jointed composite panel due to Bolt 6 torque loss under the E3 
excitation configuration. 
 
 
 
 
 
 119 
 
 
Figure 3-4-8.  Damage index using the energy magnitudes in frequency vs. B6 torque loss 
and excitation frequency, E3 excitation. 
 120 
 
 
 
Figure 3-4-9. Damage index using the signals in time vs. B6 torque loss and excitation 
frequency, E3 excitation. 
 121 
 
3.4.4 Bolt 6, Excitation Case IV  
 
Figure 3-4-10 displays the excitation and sensing configuration and indicates the 
Bolt 6 location of simulated damage for the E4 excitation configuration case. 
 
 
Figure 3-4-10. Excitation Case IV, variable Bolt 6 torque loss. 
 
Figure 3-4-11 presents the damage index using the energy magnitudes due to 
frequency response (DI
f
) at S1, S2 and S3 under E4 excitation.  Figure 3-4-12 presents 
the damage index using the signals in time (DI
t
) at S1, S2 and S3 sensing locations.  The 
damage detection capabilities using time and frequency response magnitudes were 
favorable within the jointed composite panel due to Bolt 6 torque loss under the E4 
excitation configuration. 
 
 
 
 122 
 
 
Figure 3-4-11.  Damage index using the energy magnitudes in frequency vs. B6 torque 
loss and excitation frequency, E4 excitation. 
 123 
 
 
Figure 3-4-12. Damage index using the signals in time vs. B6 torque loss and excitation 
frequency, E4 excitation. 
 124 
 
3.4.5 Comparison of Bolt 6 excitation configurations 
 
 Figure 3-4-13 shows the comparison of the normalized average damage index of 
the composite jointed panel due to Bolt 6 torque loss for each excitation configuration 
case (E1, E2, E3 and E4).  The sensitivity to damage was favorable in all excitation cases, 
as indicated by the average damage index quantities at all values of torque loss.  While 
Bolt 6 is located in a different quadrant from Bolts 0, 1 and 2, the average damage index 
trends remain the same, although in a symmetrically opposite manner.  The following 
analysis was made to provide a rough estimate of the location of damage due to torque 
loss using the Lamb wave method: 
 
DI
E1,S4
 > DI
E1,S3
 >> DI
E1,S2
  Figure 3-4-13 (a) 
DI
E2,S4
 ? DI
E2,S3
 >> DI
E2,S1
  Figure 3-4-13 (b) 
DI
E3,S2
 > DI
E3,S1
 >> DI
E3,S4 
 Figure 3-4-13 (c) 
DI
E4,S2
 ? DI
E4,S1
 >> DI
E4,S3
  Figure 3-4-13 (d) 
 
Using these relationships, the estimation damage location lies in-between sensors S2 and 
S4, thus within Quadrant 2 or Quadrant 4.  There was a clearer distinction between 
average DI trends in Figure 3-4-13 (a) and Figure 3-4-13 (c); the information under E1 
and E3 excitation configurations yielded more distinguishable results.  This confirms the 
symmetry properties of the Lamb wave method under the experimental damage scenario, 
as the trends between Quadrant 2 and Quadrant 3 are directly opposite.  This provides 
insight into the prediction of other bolt torque loss scenarios within Quadrant 2, namely 
Bolt 7 and Bolt 8.  The average DI values in Figure 3-4-13 (b) and Figure 3-4-13 (d) are 
 125 
 
less clear at torque loss values less than 75%.  It was determined that, similar to the 
results from Bolts 0, 1, and 2, when actuation exists within the quadrants of possible 
damage, the average damage index trends can not provide great insight toward precise 
damage localization.   
 
 
Figure 3-4-13. Comparison of normalized average damage index, B6 torque loss. 
 
A clear distinction of data for possible damage location in-between sensors S2 
and S4 comes from the E1 and E3 excitation cases.  Figure 3-4-14 shows the comparison 
of DI
E3,S2
 and DI
E1,S4
 from Figure 3-4-13 (a) and Figure 3-4-13 (c). 
 126 
 
 
Figure 3-4-14. Comparison of normalized average damage indices, B6 torque loss; DI
E3,S2
 
and DI
E1,S4
. 
 
Figure 3-4-14 clearly shows that for all torque loss values of 25% and 100%: 
 
DI
E3,S2
  >  DI
E1,S4
 
 
This trend indicates a higher damage index within proximity to S2, thus the greater 
likelihood of damage due to bolt torque loss in Quadrant 2 as compared to Quadrant 4.  
However, at Bolt 6 torque loss values of 50% and 75%: 
 
DI
E3,S2
  <  DI
E1,S4
 
 127 
 
This would indicate the opposite to be true, that Quadrant 4 hosts a greater likelihood of 
damage due to torque loss.  To determine which of these statements provides the accurate 
insight, another damage index trend comparison was made, this time utilizing the same-
composite actuation-sensing information.  Figure 3-4-15 shows the comparison of DI
E1,S2
 
and DI
E3,S4
 from Figure 3-4-13 (a) and Figure 3-4-13 (c). 
 
 
Figure 3-4-15. Comparison of normalized average damage indices, B6 torque loss; DI
E1,S2
 
and DI
E3,S4
. 
 
Comparing damage index information using the excitation configurations on the 
same composites as the sensors, a difference in trends was clearer.  Figure 3-4-15 shows 
a higher average DI at S3 compared to S4 at all values of Bolt 6 torque loss.  Through 
this relationship, the ambiguity from Figure 3-4-14 was diminished and the estimated 
 128 
 
damage area was shown to be closer to S2, thus in Quadrant 2.  Figure 3-4-16 shows the 
shaded area of the highest likelihood of damage. 
 
 
Figure 3-4-16. Estimated damage area due to B6 torque loss. 
 
3.5 Dual-bolt damage due to torque loss 
Previously, all experimentation has been performed with the isolation of a single 
bolt for damage due to torque loss.  In this section, a multiple bolt damage scenario was 
examined to test the Lamb wave method sensitivity and performance. Two different bolt 
pairs were examined.  The first pair consisted of two bolts within the same quadrant, Bolt 
0 and Bolt 1, which are located in Quadrant 3.  A second pair consisted of Bolt 0 and Bolt 
6, which are located in different quadrants (Quadrant 3 and Quadrant 2) and are oriented 
on opposite sides of the composite joint.  Bolt pairs underwent identical torque loss 
manipulation and were tested under each of the four excitation configuration cases.  
Results were compiled in the same manner as the single bolt experimentation and 
 129 
 
analysis, and the Lamb wave method was scrutinized as a damage detection and 
localization method for a multiple bolt damage scenario. 
3.5.1 Bolt 0 and Bolt 1, Excitation Case I  
 
Figure 3-5-1 shows the excitation and sensing configuration and indicates the Bolt 0 
and Bolt 1 locations of damage due to torque loss.  Figure 3-5-2 presents the damage 
index using the energy magnitudes due to frequency response (DI
f
) at S2, S3 and S4 
under E1 excitation.  Figure 3-5-3 presents the damage index using the signals in time 
(DI
t
) at S2, S3 and S4 sensing locations.  Similar to the single bolt scenarios, the damage 
detection capabilities using time and frequency response magnitudes are favorable under 
a dual-bolt damage scenario.  Damage index is shown to be more sensitive to bolt torque 
variation, while its sensitivity to excitation frequency is less clear. 
 
 
Figure 3-5-1. Excitation Case I, dual Bolt 0 and Bolt 1 variable torque loss. 
 
 
 
 130 
 
 
Figure 3-5-2.  Damage index using the energy magnitudes in frequency vs. B0 and B1 
torque loss and excitation frequency, E1 excitation. 
 131 
 
 
Figure 3-5-3. Damage index using the signals in time vs. B0 and B1 torque loss and 
excitation frequency, E1 excitation 
 132 
 
3.5.2 Bolt 0 and Bolt 1, Excitation Case II  
 
Figure 3-5-4 shows the excitation and sensing configuration and indicates the Bolt 0 
and Bolt 1 locations of damage due to torque loss.  Figure 3-5-5 presents the damage 
index using the energy magnitudes due to frequency response (DI
f
) at S1, S3 and S4 
under E2 excitation.  Figure 3-5-6 presents the damage index using the signals in time 
(DI
t
) at S1, S3 and S4 sensing locations.  The damage index under E2 excitation displays 
a similar sensitivity to bolt torque loss and excitation frequency as compared to the E1 
excitation configuration in the previous sub-section. 
 
 
Figure 3-5-4. Excitation Case II, dual Bolt 0 and Bolt 1 variable torque loss. 
 
 
 
 
 
 
 133 
 
 
Figure 3-5-5.  Damage index using the energy magnitudes in frequency vs. B0 and B1 
torque loss and excitation frequency, E2 excitation. 
 134 
 
 
Figure 3-5-6. Damage index using the signals in time vs. B0 and B1 torque loss and 
excitation frequency, E2 excitation. 
 135 
 
3.5.3 Bolt 0 and Bolt 1, Excitation Case III 
 
Figure 3-5-7 shows the excitation and sensing configuration and indicates the Bolt 0 
and Bolt 1 locations of damage due to torque loss.  In this excitation case, the origin of 
actuation was located within the same quadrant as the implemented damage.  Figure      
3-5-8 presents the damage index using the energy magnitudes due to frequency response 
(DI
f
) at S1, S2 and S4 under E3 excitation.  Figure 3-5-9 presents the damage index using 
the signals in time (DI
t
) at S1, S2 and S4 sensing locations.  There was a quantifiable 
damage index for each sensor over the range of excitation frequencies, which indicates 
favorable damage detection capability using time and frequency response magnitudes 
under a dual-bolt damage scenario.  The damage index under E3 excitation displays a 
similar sensitivity to bolt torque loss and excitation frequency as compared to the E1 and 
E2 excitation configurations, previously shown. 
 
 
Figure 3-5-7. Excitation Case III, dual Bolt 0 and Bolt 1 variable torque loss. 
 
 
 
 136 
 
 
Figure 3-5-8.  Damage index using the energy magnitudes in frequency vs. B0 and B1 
torque loss and excitation frequency, E3 excitation. 
 137 
 
 
Figure 3-5-9. Damage index using the signals in time vs. B0 and B1 torque loss and 
excitation frequency, E3 excitation. 
 138 
 
3.5.4 Bolt 0 and Bolt 1, Excitation Case IV 
 
Figure 3-5-10 shows the fourth excitation and sensing configuration and indicates the 
Bolt 0 and Bolt 1 locations of damage due to torque loss.  Figure 3-5-11 presents the 
damage index using the energy magnitudes due to frequency response (DI
f
) at S1, S2 and 
S3 under E4 excitation.  Figure 3-5-12 presents the damage index using the signals in 
time (DI
t
) at S1, S2 and S3 sensing locations.  The damage indices sensitivity to 
increasing torque loss remains clearer as compared to the sensitivity due to excitation 
frequency. 
 
 
Figure 3-5-10. Excitation Case IV, dual Bolt 0 and Bolt 1 variable torque loss. 
 
 
 
 
 
 
 139 
 
 
Figure 3-5-11. Damage index using the energy magnitudes in frequency vs. B0 and B1 
torque loss and excitation frequency, E4 excitation. 
 140 
 
 
 
Figure 3-5-12. Damage index using the signals in time vs. B0 and B1 torque loss and 
excitation frequency, E4 excitation. 
 141 
 
3.5.5 Comparison of dual Bolt 0 and Bolt 1 excitation configurations 
 
 Figure 3-5-13 shows the comparison of the normalized average damage index of 
the composite jointed panel due to dual-bolt torque loss within Bolt 0 and Bolt 1 for each 
excitation configuration.  The Lamb wave method exhibited favorable sensitivity to 
damage in all excitation cases, as indicated by the average damage index quantities at all 
values of torque loss.  Additionally, the damage indices sensitivity to increasing bolt 
torque loss was higher than the sensitivity due to increasing excitation frequency; this 
was the case for all excitation configurations.  The ability of the Lamb wave method to 
localize damage under a dual-bolt damage scenario was examined in the same manner as 
the single-bolt damage cases.  The following analysis was made to provide a rough 
estimate of the location of damage due to torque loss: 
 
DI
E1,S3
 > DI
E1,S4
 >> DI
E1,S2
  Figure 3-5-13 (a) 
DI
E2,S3
 > DI
E2,S4
 >> DI
E2,S1
  Figure 3-5-13 (b) 
DI
E3,S1
 ? DI
E3,S2
 >> DI
E3,S4
  Figure 3-5-13 (c) 
DI
E4,S1
 ? DI
E4,S2
 >> DI
E4,S3
  Figure 3-5-13 (d) 
 
These relationships provided an estimation of damage within the area between sensors S1 
and S1, thus within Quadrant 1 or Quadrant 3.  The average damage index values under 
this dual-bolt damage scenario are capable of providing insight into the detection and 
localization of damage due to bolt torque loss within the composite joint. 
 142 
 
 
Figure 3-5-13. Comparison of normalized average damage index, Bolt 0 and Bolt 1 dual-
bolt torque loss. 
 
To examine these trends in a similar manner to single-bolt damage scenarios in 
Quadrant 3, a comparison between the information in Figure 3-5-13 (b) and (d) was 
performed using the sensing information at S3 and S1, respectively.  Comparing the 
DI
E4,S1
 and DI
E2,S3
 from Figure 3-5-13 (b) and Figure 3-5-13 (d) clearly shows: 
 
DI
E2,S3
  >  DI
E4,S1
 
 
The information is isolated to show this comparison graphically in Figure 3-5-14. 
 143 
 
 
Figure 3-5-14. Comparison of normalized average damage indices, Bolt 0 and Bolt 1 
torque loss; DI
E4,S1
 and DI
E2,S3
. 
 
A similar result to the single-bolt damage scenarios, this dual-bolt damage trend 
indicates a higher damage index within proximity to S3, thus the greater likelihood of 
damage due to bolt torque loss in Quadrant 3 as compared to Quadrant 1.  Figure 3-5-15 
shows the shaded area of the highest likelihood of damage. 
 
 144 
 
 
Figure 3-5-15. Estimated damage area due to Bolt 0 and Bolt 1 torque loss. 
 
3.5.6 Bolt 0 and Bolt 6, Excitation Case I  
 
Figure 3-5-16 shows the excitation and sensing configuration and indicates the Bolt 
0 and Bolt 6 locations of damage due to torque loss.  In this scenario, damage was 
implemented in two different quadrants, Quadrants 2 and 3 on opposite sides of the 
bolted composite joint.  Previously, damage had always been in-between a single bolt 
sensing pair; in this case, damage was located in-between sensor pair S1 and S3 as well 
as in-between sensor pair S2 and S4. Figure 3-5-17 presents the damage index using the 
energy magnitudes due to frequency response (DI
f
) at S2, S3 and S4 under E1 excitation.  
Figure 3-5-18 presents the damage index using the signals in time (DI
t
) at S2, S3 and S4 
sensing locations.  For each sensor and over the complete range of excitation frequencies, 
a quantifiable damage index due to time and frequency responses is shown, indicating 
favorable damage detection capabilities under this new dual-bolt damage scenario.   
 145 
 
 
Figure 3-5-16. Excitation Case I, dual Bolt 0 and Bolt 6 variable torque loss. 
 
 
 
 
 
 
 
 
 
 
 
 
 146 
 
 
Figure 3-5-17.  Damage index using the energy magnitudes in frequency vs. B0 and B6 
torque loss and excitation frequency, E1 excitation. 
 147 
 
 
Figure 3-5-18. Damage index using the signals in time vs. B0 and B6 torque loss and 
excitation frequency, E1 excitation. 
 148 
 
3.5.7 Bolt 0 and Bolt 6, Excitation Case II  
 
Figure 3-5-19 shows the excitation and sensing configuration and indicates the Bolt 
0 and Bolt 6 locations of damage due to torque loss.  In this scenario, excitation occurred 
in one of the quadrants of damage, Quadrant 2, close to Bolt 6. Figure 3-5-20 presents the 
damage index using the energy magnitudes due to frequency response (DI
f
) at S1, S3 and 
S4 under E2 excitation.  Figure 3-5-21 presents the damage index using the signals in 
time (DI
t
) at S1, S3 and S4 sensing locations.  Quantifiable damage index due to time and 
frequency responses is shown, indicating favorable damage detection capabilities under a 
scenario where excitation was present in the same quadrant as damage due to torque loss 
of Bolt 6.  In both plots the damage index trends display a higher sensitivity due to 
increasing bolt torque loss and a lower sensitivity across the range of excitation 
frequencies. 
 
 
Figure 3-5-19. Excitation Case II, dual Bolt 0 and Bolt 6 variable torque loss. 
 
 
 
 149 
 
 
Figure 3-5-20.  Damage index using the energy magnitudes in frequency vs. B0 and B6 
torque loss and excitation frequency, E2 excitation. 
 150 
 
 
Figure 3-5-21. Damage index using the signals in time vs. B0 and B6 torque loss and 
excitation frequency, E2 excitation. 
 151 
 
3.5.8 Bolt 0 and Bolt 6, Excitation Case III  
 
Figure 3-5-22 shows the excitation and sensing configuration and indicates the Bolt 
0 and Bolt 6 locations of damage due to torque loss.  In this scenario, excitation occurred 
in another of the quadrants of damage, Quadrant 3, close to Bolt 0. Figure 3-5-23 presents 
the damage index using the energy magnitudes due to frequency response (DI
f
) at S1, S2 
and S4 under E3 excitation.  Figure 3-5-24 presents the damage index using the signals in 
time (DI
t
) at S1, S2 and S4 sensing locations.  As shown previously under the E2 
excitation case, quantifiable damage index due to time and frequency responses is shown, 
indicating favorable damage detection capabilities under a scenario where excitation was 
present in the same quadrant as damage due to torque loss. 
 
 
Figure 3-5-22. Excitation Case III, dual Bolt 0 and Bolt 6 variable torque loss. 
 
 
 
 
 
 152 
 
 
Figure 3-5-23.  Damage index using the energy magnitudes in frequency vs. B0 and B6 
torque loss and excitation frequency, E3 excitation. 
 153 
 
 
 
Figure 3-5-24. Damage index using the signals in time vs. B0 and B6 torque loss and 
excitation frequency, E3 excitation. 
 154 
 
3.5.9 Bolt 0 and Bolt 6, Excitation Case IV  
 
Figure 3-5-25 shows the excitation and sensing configuration and indicates the Bolt 
0 and Bolt 6 locations of damage due to torque loss.  Figure 3-5-26 presents the damage 
index using the energy magnitudes due to frequency response (DI
f
) at S1, S2 and S3 
under E4 excitation.  Figure 43-5-27 presents the damage index using the signals in time 
(DI
t
) at S1, S2 and S3 sensing locations.  As shown in the three previous excitation cases, 
there was quantifiable damage index due to time and frequency responses, indicating 
favorable damage detection capabilities under the fourth excitation configuration case. 
 
 
Figure 3-5-25. Excitation Case IV, dual Bolt 0 and Bolt 6 variable torque loss. 
 
 
 
 
 
 155 
 
 
Figure 3-5-26.  Damage index using the energy magnitudes in frequency vs. B0 and B6 
torque loss and excitation frequency, E4 excitation. 
 156 
 
 
 
Figure 3-5-27. Damage index using the signals in time vs. B0 and B6 torque loss and 
excitation frequency, E4 excitation. 
 157 
 
3.5.10 Comparison of dual Bolt 0 and Bolt 6 excitation configurations 
 
 The investigate the effects of two damaged bolts within two different quadrants, 
Figure 3-5-28 shows the comparison of the normalized average damage index of the 
composite jointed panel due to dual-bolt torque loss within Bolt 0 and Bolt 6 for each 
excitation configuration.  The Lamb wave method exhibited favorable sensitivity to 
damage in all excitation cases, as indicated by the average damage index quantities at all 
values of torque loss.  In each configuration scenario, the damage indices show a higher 
sensitivity to changes in bolt torque loss and a lower sensitivity to changes in excitation 
frequency.  The ability of the Lamb wave method to localize damage under a dual-bolt 
damage scenario was examined in the same manner as the single-bolt damage cases.  The 
following analysis was made to provide a rough estimate of the location of damage due to 
torque loss: 
 
DI
E1,S4
 ? DI
E1,S3
 >> DI
E1,S2
  Figure 3-5-28 (a) 
DI
E2,S4
 ? DI
E2,S3
 >> DI
E2,S1
  Figure 3-5-28 (b) 
DI
E3,S2
 ? DI
E3,S1
 >> DI
E3,S4
  Figure 3-5-28 (c) 
DI
E4,S2
 ? DI
E4,S1
 >> DI
E4,S3
  Figure 3-5-28 (d) 
 
These relationships imply that the damage was located in the common area between 
sensing locations S2 and S4 and also within the area between sensing locations S1 and 
S3.  From this information alone, all quadrants were likely candidates for damage due to 
bolt torque loss. 
 
 158 
 
 
Figure 3-5-28. Comparison of normalized average damage index, Bolt 0 and Bolt 6 dual-
bolt torque loss. 
 
To discriminate between Quadrants 1 and 3, these trends were compared in a 
similar manner to single-bolt damage scenarios in Quadrant 3.  The isolation and 
comparison between the information in Figure 3-5-28 (b) and (d) was performed using 
the sensing information at S3 and S1, respectively.  Comparing DI
E4,S1
 and DI
E2,S3
 from 
Figure 3-5-28 (b) and Figure 3-5-28 (d) clearly shows: 
 
DI
E2,S3 
 >  DI
E4,S1
 
 
The information is isolated to show this comparison graphically in Figure 3-5-29. 
 159 
 
 
Figure 3-5-29. Comparison of normalized average damage indices, Bolt 0 and Bolt 6 
torque loss; DI
E4,S1
 and DI
E2,S3
. 
 
It is necessary to perform a second comparison in an effort to distinguish between 
damage within Quadrant 2 and Quadrant 4.  This analysis is performed in a similar 
manner to Bolt 6 information in section 3.4.5.  A method for distinction between data for 
possible damage located in-between sensors S2 and S4 comes from the E1 and E3 
excitation cases.  Figure 3-5-30 shows the comparison of DI
E3,S2
 and DI
E1,S4
 from Figure 
3-5-28 (a) and Figure 3-5-28 (c).  The information is isolated in Figure 3-5-30 and clearly 
shows: 
DI
E3,S2 
 >  DI
E1,S4
 
 
 160 
 
This indicates damage was likely within Quadrant 2 as compared to Quadrant 4 for the 
second damaged bolt due to torque loss.   
 
 
 
Figure 3-5-30. Comparison of normalized average damage indices, Bolt 0 and Bolt 6 
torque loss; DI
E3,S2
 and DI
E1,S4
. 
 
The average damage index values under this dual-bolt damage scenario are 
capable of providing insight into the detection and localization of damage due to bolt 
torque loss within the composite joint.  Combining the two relationships indicates a dual-
damage scenario present in Quadrant 3 and Quadrant 2.  Figure 3-5-31 shows the two 
shaded areas of the highest likelihood of damage. 
 
 161 
 
 
Figure 3-5-31. Estimated damage area due to Bolt 0 and Bolt 1 torque loss. 
 
3.6 Sensing Variation of Undamaged Composite Jointed Panel over Time 
 The normalized voltage response of sensors S1, S3 and S4 at 40 kHz under E2 
excitation was compiled during the period of experimentation spanning from October 
2007 to February 2008.  Figure 3-6-1 shows the normalized time response of each sensor 
over the time-span of experimentation. 
 162 
 
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0 0.0002 0.0004 0.0006 0.0008 0.001 0.0012 0.0014 0.0016
Time (s)
N
o
rmalized
 Vo
lt
a
g
e
 Re
sp
on
se
 (
V
)
Oct-07
Nov-07
Dec-07
Jan-08
Feb-08
 
(a) S1 signal 
 
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0 0.0002 0.0004 0.0006 0.0008 0.001 0.0012 0.0014 0.0016
Time (s)
N
o
rmalized
 Vo
lt
ag
e R
es
p
o
n
se (V)
Oct-07
Nov-07
Dec-07
Jan-08
Feb-08
 
(b) S3 signal 
 163 
 
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0 0.0002 0.0004 0.0006 0.0008 0.001 0.0012 0.0014 0.0016
Time (s)
No
rmalized
 Voltag
e R
esp
o
n
s
e (
V
)
Oct-07
Nov-07
Dec-07
Jan-08
Feb-08
 
(c) S4 signal 
Figure 3-6-1. Normalized baseline time response over five months, E2 40 kHz excitation. 
 
The voltage response plots nearly coincide for each month of experimentation, 
demonstrating a slight but noticeable change in undamaged (baseline) time-response 
information over the duration of experimentation on the composite jointed panel.  At each 
sensor, the plots deviate from one another within 3%.  To further investigate the time-
response signal deviation over the five month period of experimentation, the maximum 
time-response from the non-normalized sensing information was compared over all 
excitation frequencies (20 kHz, 40 kHz, 60 kHz, 80 kHz, 100 kHz, and 120 kHz).  Figure 
3-6-2 shows the maximum time response values for each of the sensors under the E2 
excitation configuration and over a range of excitation frequencies. 
 164 
 
 
(a) S1 signal 
 
 
(b) S3 signal 
 165 
 
 
(c) S4 signal 
Figure 3-6-2. Normalized baseline voltage response vs. E2 excitation frequency over five 
months. 
 
The average difference between time-response signals over a range of excitation 
frequencies and at three sensing locations under an E2 excitation configuration is 4%.  
Since the damage index relies on an undamaged (baseline) set of time-response 
information to assess the damage level in the composite jointed panel, it was determined 
that while the change in sensing response over five months was slight, the fluctuations 
may have an impact on overall damage index.  Using the information from Figure 3-6-1, 
an average normalized time response for each sensor location was calculated to form an 
average baseline time-response data set at 40 kHz excitation frequency under E2 
excitation configuration.  Figure 3-6-3 displays the average normalized baseline plots at 
each of the three sensing locations. 
 166 
 
 
(a) S1 signal 
 
 
(b) S3 signal 
 167 
 
 
(c) S4 signal 
Figure 3-6-3.  Average baseline time response, E2 40 kHz excitation. 
 
 
3.7 Sensing Variation due to Temperature Increase of an Active Sensor 
In this chapter, the sensitivity of a piezo-patch to temperature was evaluated to 
determine the effects on sensing capability.  This experimentation was conducted by 
changing the temperature of the S1 sensor under the E2 excitation case, as explained in 
Figure 2-7-1.  The temperature of S1 was increased beyond ambient temperature (21.7?C) 
to 30, 40, 50, 60, 70, 80?C.  Figure 3-7-1 presents the temperature sensitivity of the piezo-
patch sensor by analyzing the maximum time-response.  As seen in this figure, at 
relatively lower excitation frequencies such as 20 kHz and 40 kHz, the sensing signal 
increases with temperature.  After 60?C, the sensing signal decreases as the temperature 
increases above ambient.  For higher excitation frequencies, the sensing voltage 
 168 
 
monotonically decreases as the temperature increases. This phenomenon is more clearly 
observed in the normalized voltage response, shown in Figure 3-7-2. As the excitation 
frequency increases, the sensing voltage becomes more strongly dependent on the piezo-
patch sensor temperature. Under operations which experience a large temperature 
variance at sensing locations, it would be necessary to compensate for this demonstrated 
temperature sensitivity of sensors.  For the purposes of this research, the temperature 
conditions under which the composite jointed panel was tested did not experience a shift 
of more than positive or negative 5?C.  It was deemed unnecessary to compensate the 
sensor signal response in the damage index calculations under such a slight change in 
laboratory temperature over the months of experimentation. 
 
0
1
2
3
4
5
6
7
8
9
20 30 40 50 60 70 80 90 100
Sensor Temperature (deg C)
M
axi
m
u
m
 V
o
l
t
ag
e Res
p
o
n
se (
V
)
20 kHz
40 kHz
60 kHz
80 kHz
100 kHz
120 kHz
 
Figure 3-7-1. S1 maximum time response vs. temperature, E2 excitation. 
 
 169 
 
0.5
0.6
0.7
0.8
0.9
1
20 30 40 50 60 70 80 90 100
Sensor Temperature (deg C)
M
axi
m
u
m
 V
o
l
t
ag
e
 R
esp
o
n
se (
V
)
20 kHz
40 kHz
60 kHz
80 kHz
100 kHz
120 kHz
 
Figure 3-7-2. S1 normalized time response vs. temperature, E2 excitation. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 170 
 
Chapter 4: Damage Discrimination 
An expert, rule-based discriminator was built in an attempt to exploit pattern 
recognition of the experimental results to fulfill two main goals in a simple manner:  
1) Localize damage in the composite structure?s four quadrants. 
2) Quantify the damage due to bolt torque loss in a single bolt. 
As outlined in the previous chapter, pattern recognition of DI trends provided insight to 
the localization of damage within a quadrant.  In particular, patterns shown in the side-
by-side comparison of average normalized damage index over four excitation 
configurations were the most useful in localizing a single damaged bolt.  These plots 
were previously shown for Bolts 0, 1 and 2 in Figure 3-1-33, Figure 3-2-17 and Figure 3-
3-17, respectively. 
4.1 Damage index pattern recognition 
Upon the completion of all four excitation cases (E1, E2, E3, E4) of a single 
damaged bolt, the DI was organized into a grid; the DI grid for Bolt 0, 100% torque loss 
is shown in Table 4-1-1.   
 
Table 4-1-1. DI grid, 100% B0 torque loss. 
 
S1 S2 S3 S4
E1 excitation -- 0.04 0.53 0.41
E2 excitation 0.09 -- 0.68 0.40
E3 excitation 0.59 0.45 -- 0.06
E4 excitation 0.55 0.25 0.09 --
SUM 1.14 0.70 1.21 0.81
 
 
 
 171 
 
 The shaded cells in Table 4-1-1 indicate DI values from situations where the 
sensor shares the same composite panel as the origin of excitation signal.  For example, 
excitation at E1 was sensed by S2; this excitation wave does not cross the bolted joint 
before being sensed at S2.  In the previous chapter, it was determined that same-panel 
excitation/sensing response does not provide insight into the damage level within the 
joint.  It was only in situations where the excitation wave traveled through the joint that a 
sensing response would provide details into the bolt damage levels.  The MATLAB 
discriminator does not consider these DI values in subsequent calculations and reasoning. 
 The summation of non-shaded columns in Table 4-1-1 provided insight into the 
likely damaged area.  Comparing the DI sums at each sensor: 
 
DI
S3
  >  DI
S1
  >  DI
S4
  >  DI
S2
 
 
As previously stated, a rule of thumb indicates higher likelihood of damage in the vicinity 
of the sensor with highest DI.  From the summations in Table 4-1-1, it was determined 
that the highest likelihood of damage was geometrically closest to S3, in Quadrant 3.  
This confirmed the actual location of damage.  Damage index grids were compiled for 
Bolt 0, Bolt 1, Bolt 2 over all torque loss values (100%, 75%, 50%, and 25%) to 
determine whether Quadrant 3 had the highest likelihood of damage.  The DI summations 
were ranked for each grid; nearly all grids confirmed the correct damage quadrant.  A 
single inaccurate ranking occurred for Bolt 1, 75% torque loss; the grid is shown in Table 
4-1-2. 
 
 172 
 
Table 4-1-2. DI grid, 75% B1 torque loss. 
S1 S2 S3 S4
E1 excitation -- 0.05 0.18 0.18
E2 excitation 0.05 -- 0.20 0.11
E3 excitation 0.18 0.19 -- 0.09
E4 excitation 0.30 0.20 0.08 --
SUM 0.48 0.39 0.38 0.29
 
 
Comparing the DI sums at each sensor: 
 
DI
S1
  >  DI
S2
  >  DI
S3
  >  DI
S4
 
 
From the summations in Table 4-1-2, it was determined that the highest likelihood of 
damage was geometrically closest to S1, in Quadrant 1.  This did not correlate with the 
actual location of damage in Quadrant 3. 
 Comparing the DI values in Table 4-1-1 and 4-1-2, there was a noticeable 
difference in DI magnitude.  Table 4-1-2 shows the DI for a 75% torque loss case, while 
Table 4-1-1 shows the DI for a total loss in bolt torque.  Table 4-1-3 shows the DI grid 
for Bolt 2, 25% torque loss. 
 
Table 4-1-3. DI grid, 25% B2 torque loss. 
S1 S2 S3 S4
E1 excitation -- 0.05 0.11 0.12
E2 excitation 0.01 -- 0.12 0.08
E3 excitation 0.11 0.14 -- 0.07
E4 excitation 0.06 0.08 0.02 --
SUM 0.17 0.22 0.23 0.20
 
 173 
 
The magnitude of the four DI summations, DI
mag
 were calculated according to: 
 
(DI
mag
)
2
 = (DI
SUM,S1
)
2 
+ (DI
SUM,S2
)
2
 + (DI
SUM,S3
)
2
 + (DI
SUM,S4
)
2     
         (4-1-1) 
 
Table 4-1-4 shows the magnitude calculations for the DI grids in Tables 4-1-1, 4-1-2, and 
4-1-3.  It was determined that the magnitude of DI is directly proportional to damage 
severity due to bolt torque loss. 
 
Table 4-1-4. DI
mag
; B0 100% torque loss, B1 75% torque loss, B2 25% torque loss. 
B0, 100% B1, 75% B2, 25%
DI magnitude 1.98 0.61 0.17
 
 
4.2 Level 2: Damage localization algorithm 
The MATLAB discriminator code is an expert-guided, rule-based series of if-
statements that examine the damage index values and rank a specified set of values.  The 
main goal was to localize a damage site according to recognized DI trends.  To 
distinguish between Quadrants 1/3 (top half of the composite panel, in-between sensors 
S1 and S3) and Quadrants 2/4 (bottom half of the composite panel, in-between sensors S2 
and S4) the discriminator focuses on straight-across signals, as illustrated in Figure 4-1-1.  
This technique was based on the recognized patterns and trends collected during analysis 
of a single bolt torque loss scenario.  This process, as well as the DI grid for a single 
damage scenario is outlined in section 4.1.  This grid was input into the MATLAB 
discrimination code to exploit the DI trends; a sample input is shown in the Appendix. 
 174 
 
 
Figure 4-1-1. Path of straight-across excitation. 
 
Figures 4-1-1(a) and 4-1-1(b) show the excitation/sensing path used to calculate 
DI
E1,S3
 and DI
E3,S1
.  Table 4-1-1 is shown again with highlighted DI information from the 
excitation/sensing scenarios in Figure 4-1-1(a) and Figure 4-1-1(b).  The MATLAB 
discriminator used these values to localize damage within Quadrants 1 or 3.   
 
Table 4-1-1. DI grid, 100% B0 torque loss. 
 
 
 175 
 
Similarly, sensing information and damage index values obtained from the experimental 
configurations in Figures 4-1-1(c) and 4-1-1(d) were used by the discriminator to localize 
damage within Quadrants 2 and 4.  Table 4-1-1 is shown again with highlighted DI 
information from the excitation/sensing scenarios in Figure 4-1-1(c) and Figure 4-1-1(d). 
 
Table 4-1-1. DI grid, 100% B0 torque loss. 
 
 
As a simple rule, a higher damage index represents a higher likelihood of damage present 
within the vicinity of active sensing.  If the damage indices obtained from active sensing 
agents in Quadrants 1/3 are higher than those obtained from the signals in Quadrants 2/4, 
the damage is more likely to be present in Quadrants 1 or 3.  Using Table 4-1-1 as an 
example, the DI values highlighted in red indicated a higher likelihood of damage in 
Quadrants 1 and 3.  The MATLAB program examines DI and outputs a simple statement 
indicating which of the quadrant pairs is most likely to contain the damaged bolt due to 
torque loss. 
Once the discriminator determines which sensor pair the damage lies between, the 
next goal was the discrimination between the left and right quadrant within the top or 
bottom half of the composite jointed panel.  To discriminate between the left and right 
 176 
 
quadrant, the diagonally-across signals provided insight.  Figure 4-1-2 shows the 
excitation/sensing path of the diagonal excitation. 
 
 
Figure 4-1-2. Path of diagonally-across excitation on the composite jointed panel. 
 
An actuator?s proximity to damage negates the insight provided from scenarios in 
Figures 4-1-2(c) and 4-1-2(d); it was shown in previous results that actuators with close 
proximity to damage yielded damage index trends that were less clear as compared to 
results from actuators that were further from a known area of damage.  For example, the 
information in Table 4-1-1 indicated damage in-between sensing agents S1 and S3; the 
most useful sensing information for this possible damage scenario comes from Figures         
4-1-2(a) and 4-1-2(b).  Figure 4-1-2(a) shows the wave path used to calculate DI
E2,S3
; 
Figure 4-1-2(b) shows the wave path for DI
E4,S1
.  Table 4-1-1 is shown again with these 
values highlighted.  The general rule still applies; a higher damage index implies a 
greater probability of damage within the sensing vicinity.   
 177 
 
Table 4-1-1. DI grid, 100% B0 torque loss. 
 
 
A higher damage index obtained from the scenario in Figure 4-1-2(a) as compared 
to the damage index from scenario in Figure 4-1-2(b) would imply the highest likelihood 
of damage in Quadrant 3.  Alternately, a higher damage index obtained from scenario in 
Figure 4-1-2(b) as compared to scenario in Figure 4-1-2(a) will predict with greater 
confidence that the damaged bolt lies in Quadrant 1.  For this example, DI
E2,S3 
was higher 
than DI
E4,S1
; thus, the greater likelihood of damage was in Quadrant 3.  This agreed with 
the actual damage location in Bolt 0 for 100% torque loss. 
A graphical method was used to more plainly display the results over all 
experimental damage scenarios.  The DI grids for bolts in Quadrant 3 (Bolts 0, 1 and 2) 
and Quadrant 1 (Bolt 9, 10, and 11) were used to compile a plot over all torque loss 
values.  As the experimentation and analysis of Bolt 6 indicated, the DI methodology 
produced symmetrical results; this reasoning allowed the approximation of DI for bolts in 
Quadrant 1 based on Quadrant 3 damage information, and thus no further time-
consuming experimentation was needed.  The results obtained from multiple damage 
scenarios in Bolt 0 (top bolt in Quadrant 3), Bolt 1 (middle bolt in Quadrant 3), Bolt 2 
(bottom bolt in Quadrant 3), Bolt 9 (bottom bolt in Quadrant 1), Bolt 10 (middle bolt in 
 178 
 
Quadrant 1), and Bolt 11 (top bolt in Quadrant 1) were plotted, using the DI from in 
DI
E2,S3 
on the x-axis and the DI
E4,S1 
on the y-axis.  Figure 4-1-3 shows DI
E2,S3
 vs. DI
E4,S1
 
for all six bolts within Quadrants 1 and 3 for all experimental damage scenarios: 100% 
torque loss (circle), 75% torque loss (square), 50% torque loss (triangle) and 25% torque 
loss (diamond).  The open markers represent damage indices from Bolts 9, 10, 11 
(Quadrant 1).  The closed markers represent damage indices taken from Bolts 0, 1 and 2 
(Quadrant 3).  The black 45-degree ray graphically represents the separation between 
areas where Quadrant 3 sensing information is smaller or greater than Quadrant 1 
information; a DI point below the threshold indicates a higher likelihood of damage in 
Quadrant 3, while a DI point above the threshold indicates a higher likelihood of damage 
in Quadrant 1.   
The groupings of DI markers representing 100% torque loss have a clear 
separation; the average coordinate location of the two separated groups is plotted as an 
?X? and ?+? and noted for each grouping.  As the torque loss values decrease, the 
separation between Quadrants 1 and 3 DI groupings is less clear.  Independent of torque 
loss, each group average lays on the side of the 45-degree ray which correctly 
corresponds to the damaged quadrant.  The successful geometric localization of damage 
within the composite assembly?s four quadrants fulfilled the requirements for a Level 2 
prediction method. 
 
 179 
 
 
Figure 4-1-3. Quadrant 1 vs. Quadrant 3 damage index sensing information. 
 
4.3 Level 3: Damage quantification algorithm 
To fulfill a Level 3 prediction method for structural health monitoring of the 
composite lap-joint assembly, a statistical threshold was implemented to discriminate 
between torque loss values.  Threshold bands were calculated using the groupings? 
average markers.  A Euclidean distance classifier [27] was employed to determine the 
central radius between the 100% torque loss and 75% torque loss average markers.  The 
general distance formula between two points follows: 
 
r
2,1
 = r
1
 + ? (r
2
 ? r
1
) 
 180 
 
This calculation was performed to find the center radius between 100% and 75% 
torque loss groupings, 75% and 50% torque loss groupings, and 50% and 25% torque loss 
groupings.  Figure 4-1-4 shows the same plot of DI in Figure 4-1-3 with the threshold 
bands that separate damage levels due to torque loss.  A fourth band, shown in grey, 
separates the graphical area of indistinguishable damage.  As outlined in Chapter 4, 
experimental results indicated quantifiable sensing capability above a DI
total
 value of 0.1.  
It was determined that damage index values below 0.1 would not give clear insight into 
the damage presence or location within the composite joint.   
 
 
Figure 4-1-4. Quadrant 1 vs. Quadrant 3 damage with damage threshold bands. 
 181 
 
To investigate the confidence of these threshold predictions, a series of validation 
experiments were performed.  This supplemental experimentation was conducted in the 
same manner as the experimentation described in Chapters 2 and 3.  Multiple levels of 
damage were implemented on all six bolts within Quadrants 1 and 3.  The validation run 
matrix is listed in Table 4-1-5.  
 
Table 4-1-5: Validation experimental run matrix. 
 
Run Damaged Bolt Damaged Quadrant Percent torque loss
19 1 10
210
311 1 10
40 3
51 10
62 3
710 1 75
82 3
99 1 50
10 0 3 50
11 11 1 25
12 1 3 25
 
 
For each validation run, DI
E2,S3
 and DI
E4,S2
 was plotted on Figure 4-1-4 to observe 
their location within the prediction bands.  The validation run results are shown in Figure 
4-1-5.  All result markers were located on the correct side of the 45-degree threshold line 
which verified the actual quadrant of damage.  Additionally, all but one of the validation 
run results was located in the shaded band which correctly corresponded to the torque 
loss level.  One outlier existed with Run 8 which was the result of 25% torque loss in 
Bolt 2; this result was found in the 25% - 50% torque loss prediction band.  It has been 
previously stated in Chapter 3 that Bolt 2 yielded results that were less clear relative to 
Bolts 0 and 1, which are also in Quadrant 3.  A potential reason for this was because of 
 182 
 
its proximity to Quadrant 4.  Also, since 25% torque loss is relatively low, it is reasonable 
to state that the discriminator can predict with higher confidence the location and 
quantification of damage due torque loss values above 50%.  The successful development 
of a comprehensive localization and damage quantification technique fulfilled the 
requirements for a Level 3 prediction methodology. 
 
 
Figure 4-1-5. Quadrant 1 vs. Quadrant 3 discriminator validation run results. 
 
 
 183 
 
Chapter 5: Concluding Remarks 
 
 The objective of this research was to utilize the Lamb wave method to formulate a 
cohesive structural health monitoring methodology for the composite lap-joint assembly.  
Sensing information was collected to construct a sizeable database of baseline and 
damage information with respect to single and dual-bolt torque loss over a range of 
damage levels and multiple locations within the composite joint.  Exploitation of this 
database information along with key features inherent to the structural system allowed for 
the development of a prediction Level 3 damage diagnostic.  To realize this aim, several 
experimental and analytical elements were employed: 
1) The damage index for an individual sensor (Figure 3-1-5 and Figure      
3-1-6) displayed a higher sensitivity to bolt torque loss as compared to 
the sensitivity due to excitation frequency.   
2) Damage index information from wave paths which crossed over the joint 
(Figure 4-1-1 and Figure 4-1-2) provided excellent insight into the 
damage levels within the joint.  Damage indices from waves that did not 
cross the joint (Figure 3-4-15) provided little insight into the damage 
present within the bolted joint.  This pattern recognition was exploited to 
attain damage prediction Level 1. 
3) The damage index taken from excitation piezos that were far from an 
implemented damage site provided useful insight toward the localization 
of damage.  Pattern recognition of the damage index as a key feature led 
to the successful localization of a damaged bolt within one of the 
 184 
 
composite structure?s four quadrants.  This methodology attained 
damage prediction Level 2 for the composite jointed system. 
4) Plotting total damage index (Figure 4-1-3) yielded a clear separation 
between results of higher damage levels.  As damage due to torque loss 
decreased (approximately 25% torque loss), damage index provided the 
location of damage with less clarity. 
5) Total damage index was used to build a rule-based discriminator which 
accurately predicted the damaged quadrant and quantity of damage due 
to bolt torque loss in 11 validation cases (Figure 4-1-5).  A 12
th
 
validation case resulted in an outlier.  This discrimination method 
provided a damage prediction Level 3 for the composite jointed system. 
The results of this research indicate a strong potential for using the Lamb wave 
method along with simple discrimination techniques for damage due to torque loss in the 
composite lap-joint assembly.  Further, the DI proved to be a robust feature for the 
development of a damage diagnostic up to a Level 3 prediction. This research did not 
examine types of damage beyond single and dual-bolt torque loss.  Extending the Lamb 
wave method to applications where the composite jointed panel undergoes other damaged 
scenarios, such as damage due to machined cracks, composite delamination or added 
mass is suggested as a topic for future investigation.  Further, it is suggested that this 
diagnostic methodology be applied to structures composed of other materials, both 
composite and isotropic. 
 Supplemental experimentation was performed to examine the smart sensor array?s 
sensing capability over time.  Over the five month duration of this research, the baseline 
 185 
 
sensing information showed a slight variation.  The damage index relies entirely the 
difference between damaged and undamaged sensing information.  The idea that even a 
slight variance in baseline information would affect the overall damage index should not 
be overlooked.  The results in section 3.6 give rise to the opinion that additional 
investigation should be devoted to understanding this phenomenon and its impact into the 
use of damage index as a key discrimination feature.  The capabilities of the 
discriminator would be compromised if the damage index were to experience an 
unpredictable shift due to smart sensor aging.  To determine the sensor array?s 
operational capability, a life-span of acceptable use should be quantified. 
 Additional experimentation examined the sensing capability of the piezo-actuators 
at elevated temperatures.  The results in section 3.7 indicate a shift in time signal 
response as the sensor temperature was increased.  A decrease in voltage response was 
potentially due to decreased strain as the piezo became malleable at higher temperatures.  
In this research study, the smart sensor array and composite jointed system did not 
experience a large temperature variation within the laboratory environment.  However, if 
a similar experimental set-up were used in a laboratory or operational environment which 
did experience a large temperature variation, the effects of temperature should be 
investigated further.  Since the damage index as a key feature relies entirely on the 
sensing response, any change may affect the overall damage index, and thus the 
discrimination capabilities of the diagnostic system. 
 
 186 
 
Appendix 
 
%DI.m 
  
%calculate the damage index from sensing information over range 
%of excitation frequencies 
  
clc 
close all 
clear all 
  
%%% 20kHz %%%%% 
% Sensor 2 
num=xlsread('C1B020kHzS2_torque0p'); 
nx=length(num); 
ns=88;     aa1=num(ns:nx,:); 
num=xlsread('C1B020kHzS2_torque25p');    aal1_1=num(ns:nx,:); 
num=xlsread('C1B020kHzS2_torque50p');    aal1_2=num(ns:nx,:); 
num=xlsread('C1B020kHzS2_torque75p');    aal1_3=num(ns:nx,:); 
num=xlsread('C1B020kHzS2_torque100p');     aal1_4=num(ns:nx,:);   
  
% Sensor 3 
num=xlsread('C1B020kHzS3_torque0p');   aa2=num(ns:nx,:); 
num=xlsread('C1B020kHzS3_torque25p');    aal2_1=num(ns:nx,:); 
num=xlsread('C1B020kHzS3_torque50p');    aal2_2=num(ns:nx,:); 
num=xlsread('C1B020kHzS3_torque75p');    aal2_3=num(ns:nx,:); 
num=xlsread('C1B020kHzS3_torque100p');     aal2_4=num(ns:nx,:); 
  
% Sensor 4 
num=xlsread('C1B020kHzS4_torque0p');   aa1h=num(ns:nx,:); 
num=xlsread('C1B020kHzS4_torque25p');    aal1h_1=num(ns:nx,:); 
num=xlsread('C1B020kHzS4_torque50p');    aal1h_2=num(ns:nx,:); 
num=xlsread('C1B020kHzS4_torque75p');    aal1h_3=num(ns:nx,:); 
num=xlsread('C1B020kHzS4_torque100p');     aal1h_4=num(ns:nx,:);   
  
fsp=0; 
fpp=80; 
spt=.1;  %frequency increment in kHz 
ik=(40-fsp)/spt+1; 
  
%%%%% 40kHz %%%%% 
% % % Sensor 2 
num=xlsread('C1B040kHzS2_torque0p'); 
nx=length(num); 
ns=88;     aa1=num(ns:nx,:); 
num=xlsread('C1B040kHzS2_torque25p');    aal1_1=num(ns:nx,:); 
num=xlsread('C1B040kHzS2_torque50p');    aal1_2=num(ns:nx,:); 
num=xlsread('C1B040kHzS2_torque75p');    aal1_3=num(ns:nx,:); 
num=xlsread('C1B040kHzS2_torque100p');     aal1_4=num(ns:nx,:); 
%  
% % Sensor 3 
num=xlsread('C1B040kHzS3_torque0p');   aa2=num(ns:nx,:); 
 187 
 
num=xlsread('C1B040kHzS3_torque25p');    aal2_1=num(ns:nx,:); 
num=xlsread('C1B040kHzS3_torque50p');    aal2_2=num(ns:nx,:); 
num=xlsread('C1B040kHzS3_torque75p');    aal2_3=num(ns:nx,:); 
num=xlsread('C1B040kHzS3_torque100p');     aal2_4=num(ns:nx,:); 
%  
% % Sensor 4 
num=xlsread('C1B040kHzS4_torque0p');   aa1h=num(ns:nx,:); 
num=xlsread('C1B040kHzS4_torque25p');    aal1h_1=num(ns:nx,:); 
num=xlsread('C1B040kHzS4_torque50p');    aal1h_2=num(ns:nx,:); 
num=xlsread('C1B040kHzS4_torque75p');    aal1h_3=num(ns:nx,:); 
num=xlsread('C1B040kHzS4_torque100p');     aal1h_4=num(ns:nx,:); 
%  
fsp=0; 
fpp=80; 
spt=.1;  %frequency increment in kHz 
ik=(40-fsp)/spt+1; 
  
% %%%%% 60kHz %%%%% 
% Sensor 2 
num=xlsread('C1B060kHzS2_torque0p'); 
nx=length(num); 
ns=88;     aa1=num(ns:nx,:); 
num=xlsread('C1B060kHzS2_torque25p');    aal1_1=num(ns:nx,:); 
num=xlsread('C1B060kHzS2_torque50p');    aal1_2=num(ns:nx,:); 
num=xlsread('C1B060kHzS2_torque75p');    aal1_3=num(ns:nx,:); 
num=xlsread('C1B060kHzS2_torque100p');     aal1_4=num(ns:nx,:); 
  
% Sensor 3 
num=xlsread('C1B060kHzS3_torque0p');   aa2=num(ns:nx,:); 
num=xlsread('C1B060kHzS3_torque25p');    aal2_1=num(ns:nx,:); 
num=xlsread('C1B060kHzS3_torque50p');    aal2_2=num(ns:nx,:); 
num=xlsread('C1B060kHzS3_torque75p');    aal2_3=num(ns:nx,:); 
num=xlsread('C1B060kHzS3_torque100p');     aal2_4=num(ns:nx,:); 
  
% Sensor 4 
num=xlsread('C1B060kHzS4_torque0p');   aa1h=num(ns:nx,:); 
num=xlsread('C1B060kHzS4_torque25p');    aal1h_1=num(ns:nx,:); 
num=xlsread('C1B060kHzS4_torque50p');    aal1h_2=num(ns:nx,:); 
num=xlsread('C1B060kHzS4_torque75p');    aal1h_3=num(ns:nx,:); 
num=xlsread('C1B060kHzS4_torque100p');     aal1h_4=num(ns:nx,:); 
  
fsp=20; 
fpp=100; 
spt=.1;  %frequency increment in kHz 
ik=(60-fsp)/spt+1; 
  
%%%%%% 80kHz %%%%% 
% % Sensor 2 
num=xlsread('C1B080kHzS2_torque0p'); 
nx=length(num); 
ns=88;     aa1=num(ns:nx,:); 
num=xlsread('C1B080kHzS2_torque25p');    aal1_1=num(ns:nx,:); 
num=xlsread('C1B080kHzS2_torque50p');    aal1_2=num(ns:nx,:); 
num=xlsread('C1B080kHzS2_torque75p');    aal1_3=num(ns:nx,:); 
num=xlsread('C1B080kHzS2_torque100p');     aal1_4=num(ns:nx,:); 
  
 188 
 
% Sensor 3 
num=xlsread('C1B080kHzS3_torque0p');   aa2=num(ns:nx,:); 
num=xlsread('C1B080kHzS3_torque25p');    aal2_1=num(ns:nx,:); 
num=xlsread('C1B080kHzS3_torque50p');    aal2_2=num(ns:nx,:); 
num=xlsread('C1B080kHzS3_torque75p');    aal2_3=num(ns:nx,:); 
num=xlsread('C1B080kHzS3_torque100p');     aal2_4=num(ns:nx,:); 
  
% Sensor 4 
num=xlsread('C1B080kHzS4_torque0p');   aa1h=num(ns:nx,:); 
num=xlsread('C1B080kHzS4_torque25p');    aal1h_1=num(ns:nx,:); 
num=xlsread('C1B080kHzS4_torque50p');    aal1h_2=num(ns:nx,:); 
num=xlsread('C1B080kHzS4_torque75p');    aal1h_3=num(ns:nx,:); 
num=xlsread('C1B080kHzS4_torque100p');     aal1h_4=num(ns:nx,:); 
  
fsp=40; 
fpp=120; 
spt=.1;  %frequency increment in kHz 
ik=(80-fsp)/spt+1; 
  
%%%%% 100kHz %%%%% 
% % Sensor 2 
num=xlsread('C1B0100kHzS2_torque0p'); 
nx=length(num); 
ns=88;     aa1=num(ns:nx,:); 
num=xlsread('C1B0100kHzS2_torque25p');    aal1_1=num(ns:nx,:); 
num=xlsread('C1B0100kHzS2_torque50p');    aal1_2=num(ns:nx,:); 
num=xlsread('C1B0100kHzS2_torque75p');    aal1_3=num(ns:nx,:); 
num=xlsread('C1B0100kHzS2_torque100p');     aal1_4=num(ns:nx,:); 
  
% Sensor 3 
num=xlsread('C1B0100kHzS3_torque0p');   aa2=num(ns:nx,:); 
num=xlsread('C1B0100kHzS3_torque25p');    aal2_1=num(ns:nx,:); 
num=xlsread('C1B0100kHzS3_torque50p');    aal2_2=num(ns:nx,:); 
num=xlsread('C1B0100kHzS3_torque75p');    aal2_3=num(ns:nx,:); 
num=xlsread('C1B0100kHzS3_torque100p');     aal2_4=num(ns:nx,:); 
  
% Sensor 4 
num=xlsread('C1B0100kHzS4_torque0p');   aa1h=num(ns:nx,:); 
num=xlsread('C1B0100kHzS4_torque25p');    aal1h_1=num(ns:nx,:); 
num=xlsread('C1B0100kHzS4_torque50p');    aal1h_2=num(ns:nx,:); 
num=xlsread('C1B0100kHzS4_torque75p');    aal1h_3=num(ns:nx,:); 
num=xlsread('C1B0100kHzS4_torque100p');     aal1h_4=num(ns:nx,:); 
  
fsp=60; 
fpp=140; 
spt=.1;  %frequency increment in kHz 
ik=(100-fsp)/spt+1; 
  
%%%% 120kHz %%%%% 
% % Sensor 2 
num=xlsread('C1B0120kHzS2_torque0p'); 
nx=length(num); 
ns=88;     aa1=num(ns:nx,:); 
num=xlsread('C1B0120kHzS2_torque25p');    aal1_1=num(ns:nx,:); 
num=xlsread('C1B0120kHzS2_torque50p');    aal1_2=num(ns:nx,:); 
 189 
 
num=xlsread('C1B0120kHzS2_torque75p');    aal1_3=num(ns:nx,:); 
num=xlsread('C1B0120kHzS2_torque100p');     aal1_4=num(ns:nx,:); 
  
% Sensor 3 
num=xlsread('C1B0120kHzS3_torque0p');   aa2=num(ns:nx,:); 
num=xlsread('C1B0120kHzS3_torque25p');    aal2_1=num(ns:nx,:); 
num=xlsread('C1B0120kHzS3_torque50p');    aal2_2=num(ns:nx,:); 
num=xlsread('C1B0120kHzS3_torque75p');    aal2_3=num(ns:nx,:); 
num=xlsread('C1B0120kHzS3_torque100p');     aal2_4=num(ns:nx,:); 
  
% Sensor 4 
num=xlsread('C1B0120kHzS4_torque0p');   aa1h=num(ns:nx,:); 
num=xlsread('C1B0120kHzS4_torque25p');    aal1h_1=num(ns:nx,:); 
num=xlsread('C1B0120kHzS4_torque50p');    aal1h_2=num(ns:nx,:); 
num=xlsread('C1B0120kHzS4_torque75p');    aal1h_3=num(ns:nx,:); 
num=xlsread('C1B0120kHzS4_torque100p');     aal1h_4=num(ns:nx,:); 
  
fsp=80; 
fpp=160; 
spt=.1;  %frequency increment in kHz 
ik=(120-fsp)/spt+1; 
  
%%%%%%%%%%%%%%%%% 
n_aal=length(aal2_2); 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%% 
kp=2384;  %5.14e-5s to 0.0016s 
tal=aal2_2(1:kp,1); 
  
n_aa=length(aa2); 
ta=aa2(1:kp,1); 
  
nfft=128*.5; 
ovp=60; 
Fs=1/(ta(3)-ta(2)); 
  
[ssl,ffl,ttl,pp1]=spectrogram(aa1(1:kp,2),nfft,ovp,[fsp:spt:fpp]*1e3,Fs
); 
[ssl,ffl,ttl,ppl1_1]=spectrogram(aal1_1(1:kp,2),nfft,ovp,[fsp:spt:fpp]*
1e3,Fs); 
[ssl,ffl,ttl,ppl1_2]=spectrogram(aal1_2(1:kp,2),nfft,ovp,[fsp:spt:fpp]*
1e3,Fs); 
[ssl,ffl,ttl,ppl1_3]=spectrogram(aal1_3(1:kp,2),nfft,ovp,[fsp:spt:fpp]*
1e3,Fs); 
[ssl,ffl,ttl,ppl1_4]=spectrogram(aal1_4(1:kp,2),nfft,ovp,[fsp:spt:fpp]*
1e3,Fs); 
  
[ss,ff,tt,pp2]=spectrogram(aa2(1:kp,2),nfft,ovp,[fsp:spt:fpp]*1e3,Fs); 
[ssl,ffl,ttl,ppl2_1]=spectrogram(aal2_1(1:kp,2),nfft,ovp,[fsp:spt:fpp]*
1e3,Fs); 
[ssl,ffl,ttl,ppl2_2]=spectrogram(aal2_2(1:kp,2),nfft,ovp,[fsp:spt:fpp]*
1e3,Fs); 
[ssl,ffl,ttl,ppl2_3]=spectrogram(aal2_3(1:kp,2),nfft,ovp,[fsp:spt:fpp]*
1e3,Fs); 
 190 
 
[ssl,ffl,ttl,ppl2_4]=spectrogram(aal2_4(1:kp,2),nfft,ovp,[fsp:spt:fpp]*
1e3,Fs); 
  
[ssl,ffl,ttl,pp1h]=spectrogram(aa1h(1:kp,2),nfft,ovp,[fsp:spt:fpp]*1e3,
Fs); 
[ssl,ffl,ttl,ppl1h_1]=spectrogram(aal1h_1(1:kp,2),nfft,ovp,[fsp:spt:fpp
]*1e3,Fs); 
[ssl,ffl,ttl,ppl1h_2]=spectrogram(aal1h_2(1:kp,2),nfft,ovp,[fsp:spt:fpp
]*1e3,Fs); 
[ssl,ffl,ttl,ppl1h_3]=spectrogram(aal1h_3(1:kp,2),nfft,ovp,[fsp:spt:fpp
]*1e3,Fs); 
[ssl,ffl,ttl,ppl1h_4]=spectrogram(aal1h_4(1:kp,2),nfft,ovp,[fsp:spt:fpp
]*1e3,Fs); 
  
  
ns=length(aa1(1:kp,2));      % 100kHz--> ss1=33,sf1=106,ss2=69,sf2=141 
ss1=1;             % 100kHz--> ss1=36,sf1=108,ss2=77,sf2=180 
sf1=ns;            % 120kHz--> ss1=33,sf1=108,ss2=69,sf2=180 
ts1=ta(ss1:sf1); 
  
ss2=1;  
sf2=ns; 
ts2=ta(ss2:sf2); 
  
disp('S2 using time') 
trapz(ts1,abs(aal1_1(ss1:sf1,2)-
aa1(ss1:sf1,2)))/trapz(ts1,abs(aa1(ss1:sf1,2))) 
trapz(ts1,abs(aal1_2(ss1:sf1,2)-
aa1(ss1:sf1,2)))/trapz(ts1,abs(aa1(ss1:sf1,2))) 
trapz(ts1,abs(aal1_3(ss1:sf1,2)-
aa1(ss1:sf1,2)))/trapz(ts1,abs(aa1(ss1:sf1,2))) 
trapz(ts1,abs(aal1_4(ss1:sf1,2)-
aa1(ss1:sf1,2)))/trapz(ts1,abs(aa1(ss1:sf1,2))) 
  
disp('S3 using time') 
trapz(ts2,abs(aal2_1(ss2:sf2,2)-
aa2(ss2:sf2,2)))/trapz(ts2,abs(aa2(ss2:sf2,2))) 
trapz(ts2,abs(aal2_2(ss2:sf2,2)-
aa2(ss2:sf2,2)))/trapz(ts2,abs(aa2(ss2:sf2,2))) 
trapz(ts2,abs(aal2_3(ss2:sf2,2)-
aa2(ss2:sf2,2)))/trapz(ts2,abs(aa2(ss2:sf2,2))) 
trapz(ts2,abs(aal2_4(ss2:sf2,2)-
aa2(ss2:sf2,2)))/trapz(ts2,abs(aa2(ss2:sf2,2))) 
  
disp('S4 using time') 
trapz(ts1,abs(aal1h_1(ss1:sf1,2)-
aa1h(ss1:sf1,2)))/trapz(ts1,abs(aa1h(ss1:sf1,2))) 
trapz(ts1,abs(aal1h_2(ss1:sf1,2)-
aa1h(ss1:sf1,2)))/trapz(ts1,abs(aa1h(ss1:sf1,2))) 
trapz(ts1,abs(aal1h_3(ss1:sf1,2)-
aa1h(ss1:sf1,2)))/trapz(ts1,abs(aa1h(ss1:sf1,2))) 
trapz(ts1,abs(aal1h_4(ss1:sf1,2)-
aa1h(ss1:sf1,2)))/trapz(ts1,abs(aa1h(ss1:sf1,2))) 
  
value1=(10*log10(abs(ppl2_1(ik,:)))-10*log10(abs(pp2(ik,:)))); 
 191 
 
value2=(10*log10(abs(ppl2_2(ik,:)))-10*log10(abs(pp2(ik,:)))); 
value3=(10*log10(abs(ppl2_3(ik,:)))-10*log10(abs(pp2(ik,:)))); 
value4=(10*log10(abs(ppl2_4(ik,:)))-10*log10(abs(pp2(ik,:)))); 
  
value1L1=(10*log10(abs(ppl1_1(ik,:)))-10*log10(abs(pp1(ik,:)))); 
value2L1=(10*log10(abs(ppl1_2(ik,:)))-10*log10(abs(pp1(ik,:)))); 
value3L1=(10*log10(abs(ppl1_3(ik,:)))-10*log10(abs(pp1(ik,:)))); 
value4L1=(10*log10(abs(ppl1_4(ik,:)))-10*log10(abs(pp1(ik,:)))); 
  
value1L1h=(10*log10(abs(ppl1h_1(ik,:)))-10*log10(abs(pp1h(ik,:)))); 
value2L1h=(10*log10(abs(ppl1h_2(ik,:)))-10*log10(abs(pp1h(ik,:)))); 
value3L1h=(10*log10(abs(ppl1h_3(ik,:)))-10*log10(abs(pp1h(ik,:)))); 
value4L1h=(10*log10(abs(ppl1h_4(ik,:)))-10*log10(abs(pp1h(ik,:)))); 
  
  
  
disp('S2 using frequency') 
trapz(tt,abs(value1L1))/trapz(tt,abs(10*log10(abs(pp1(ik,:))))) 
trapz(tt,abs(value2L1))/trapz(tt,abs(10*log10(abs(pp1(ik,:))))) 
trapz(tt,abs(value3L1))/trapz(tt,abs(10*log10(abs(pp1(ik,:))))) 
trapz(tt,abs(value4L1))/trapz(tt,abs(10*log10(abs(pp1(ik,:))))) 
  
disp('S3 using frequency') 
trapz(tt,abs(value1))/trapz(tt,abs(10*log10(abs(pp2(ik,:))))) 
trapz(tt,abs(value2))/trapz(tt,abs(10*log10(abs(pp2(ik,:))))) 
trapz(tt,abs(value3))/trapz(tt,abs(10*log10(abs(pp2(ik,:))))) 
trapz(tt,abs(value4))/trapz(tt,abs(10*log10(abs(pp2(ik,:))))) 
  
disp('S4 using frequency') 
trapz(tt,abs(value1L1h))/trapz(tt,abs(10*log10(abs(pp1h(ik,:))))) 
trapz(tt,abs(value2L1h))/trapz(tt,abs(10*log10(abs(pp1h(ik,:))))) 
trapz(tt,abs(value3L1h))/trapz(tt,abs(10*log10(abs(pp1h(ik,:))))) 
trapz(tt,abs(value4L1h))/trapz(tt,abs(10*log10(abs(pp1h(ik,:))))) 
  
%enter in damage indices to form 3-D plots 
  
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
% Total time: 1.6sec 
% Using time 
%          20kHz    40kHz    60kHz   80kHz  100kHz  120kHz   
S2aaaB0B1t=[     0       0       0       0      0        0;  
            0.0837  0.0935  0.0469  0.044   0.0559  0.0737; 
            0.1054  0.01316 0.0886  0.0587  0.0606  0.0779; 
            0.0929  0.1159  0.1072  0.0797  0.0818  0.0734; 
            0.106   0.1503  0.1141  0.0908  0.0852  0.0745]; 
      
S3aaaB0B1t=[     0       0       0       0      0        0;  
            0.3246  0.2546  0.1435  0.2154  0.3282  0.1956; 
            0.4889  0.3488  0.1926  0.2307  0.2634  0.2640; 
            0.589   0.4025  0.2678  0.319   0.4009  0.3594; 
            0.894   0.677   0.4738  0.4545  0.4552  0.5434]; 
         
S4aaaB0B1t=[     0       0       0       0      0        0;  
            0.1936  0.346   0.1923  0.1536  0.2312  0.1878; 
            0.3926  0.4635  0.276   0.2066  0.2265  0.2403; 
 192 
 
            0.4526  0.507   0.3236  0.2801  0.3152  0.3565; 
            0.7272  0.7191  0.4819  0.4401  0.4241  0.4858]; 
         
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
% Using frequency 
%          20kHz    40kHz    60kHz   80kHz  100kHz  120kHz  
S2aaaB0B1f=[     0       0       0       0      0        0;   
            0.0159  0.0221  0.0121  0.0186  0.0202  0.0097; 
            0.0183  0.0367  0.0255  0.0262  0.0225  0.0090; 
            0.0134  0.0322  0.0284  0.0259  0.0245  0.0109; 
            0.0199  0.0414  0.0355  0.0286  0.0235  0.0110]; 
      
S3aaaB0B1f=[     0       0       0       0      0        0;  
            0.0272  0.0394  0.0321  0.0388  0.0326  0.0250; 
            0.0546  0.056   0.0394  0.0303  0.0424  0.0288; 
            0.0523  0.0562  0.0433  0.0404  0.047   0.0338; 
            0.0688  0.0811  0.0716  0.0568  0.0528  0.0541];         
  
S4aaaB0B1f=[     0       0       0       0      0        0;  
            0.0242  0.0393  0.0278  0.028   0.0309  0.0212; 
            0.0415  0.0528  0.041   0.0364  0.0346  0.0247; 
            0.0535  0.0481  0.0443  0.0413  0.0383  0.0265; 
            0.062   0.0744  0.0496  0.0502  0.0451  0.0402]; 
              
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
        
a_x=[0 25 50 75 100]; 
a_y=[20 40 60 80 100 120]; 
a_z1t=[S2aaaB0B1t(:,1)';S2aaaB0B1t(:,2)';S2aaaB0B1t(:,3)';S2aaaB0B1t(:,
4)';S2aaaB0B1t(:,5)';S2aaaB0B1t(:,6)']; 
a_z2t=[S3aaaB0B1t(:,1)';S3aaaB0B1t(:,2)';S3aaaB0B1t(:,3)';S3aaaB0B1t(:,
4)';S3aaaB0B1t(:,5)';S3aaaB0B1t(:,6)']; 
a_z1f=[S2aaaB0B1f(:,1)';S2aaaB0B1f(:,2)';S2aaaB0B1f(:,3)';S2aaaB0B1f(:,
4)';S2aaaB0B1f(:,5)';S2aaaB0B1f(:,6)']; 
a_z2f=[S3aaaB0B1f(:,1)';S3aaaB0B1f(:,2)';S3aaaB0B1f(:,3)';S3aaaB0B1f(:,
4)';S3aaaB0B1f(:,5)';S3aaaB0B1f(:,6)'];  
  
a_z1th=[S4aaaB0B1t(:,1)';S4aaaB0B1t(:,2)';S4aaaB0B1t(:,3)';S4aaaB0B1t(:
,4)';S4aaaB0B1t(:,5)';S4aaaB0B1t(:,6)']; 
a_z1fh=[S4aaaB0B1f(:,1)';S4aaaB0B1f(:,2)';S4aaaB0B1f(:,3)';S4aaaB0B1f(:
,4)';S4aaaB0B1f(:,5)';S4aaaB0B1f(:,6)']; 
  
figure(31) %DI_t at S2 
set(gca,'FontSize',22,'linewidth',3,'fontweight','demi') 
h=surf(a_x,a_y,a_z1t); 
set(h,'Marker','o','MarkerSize',15,'LineWidth',1,'MarkerFaceColor','aut
o') 
axis([0 100 20 120 0 1]) 
set(h,'MarkerSize',15,'LineWidth',4) 
xlabel('Torque loss (%)') 
ylabel('Frequency (kHz)') 
zlabel('Damage Index') 
  
figure(32) %DI_t at S3 
set(gca,'FontSize',22,'linewidth',3,'fontweight','demi') 
 193 
 
h=surf(a_x,a_y,a_z2t); 
set(h,'Marker','o','MarkerSize',15,'LineWidth',1,'MarkerFaceColor','aut
o') 
axis([0 100 20 120 0 1]) 
set(h,'MarkerSize',15,'LineWidth',4) 
xlabel('Torque loss (%)') 
ylabel('Frequency (kHz)') 
zlabel('Damage Index') 
  
figure(33) %DI_t at S4 
set(gca,'FontSize',22,'linewidth',3,'fontweight','demi') 
h=surf(a_x,a_y,a_z1th); 
set(h,'Marker','o','MarkerSize',15,'LineWidth',1,'MarkerFaceColor','aut
o') 
axis([0 100 20 120 0 1]) 
set(h,'MarkerSize',15,'LineWidth',4) 
xlabel('Torque loss (%)') 
ylabel('Frequency (kHz)') 
zlabel('Damage Index') 
  
figure(34) %DI_f at S2 
set(gca,'FontSize',22,'linewidth',3,'fontweight','demi') 
h=surf(a_x,a_y,a_z1f); 
set(h,'Marker','o','MarkerSize',15,'LineWidth',1,'MarkerFaceColor','aut
o') 
axis([0 100 20 120 0 0.08]) 
set(h,'MarkerSize',15,'LineWidth',4) 
xlabel('Torque loss (%)') 
ylabel('Frequency (kHz)') 
zlabel('Damage Index') 
  
figure(35) %DI_f at S3 
set(gca,'FontSize',22, inewidth',3,'fontweight','demi') 'l
h=surf(a_x,a_y,a_z2f); 
set(h,'Marker','o','MarkerSize',15,'LineWidth',1,'MarkerFaceColor','aut
o') 
axis([0 100 20 120 0 0.08]) 
set(h,'MarkerSize',15,'LineWidth',4) 
xlabel('Torque loss (%)') 
ylabel('Frequency (kHz)') 
zlabel('Damage Index') 
  
figure(36) %DI_f at S4 
set(gca,'FontSize',22,'linewidth',3,'fontweight','demi') 
h=surf(a_x,a_y,a_z1fh); 
set(h,'Marker','o','MarkerSize',15,'LineWidth',1,'MarkerFaceColor','aut
o') 
axis([0 100 20 120 0 0.08]) 
set(h,'MarkerSize',15,'LineWidth',4) 
xlabel('Torque loss (%)') 
ylabel('Frequency (kHz)') 
zlabel('Damage Index') 
 
 
 194 
 
% discriminator.m 
  
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
%%RULE-BASED DISCRIMINATOR  
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
%% Will determine Quadrant of single damaged bolt using DI as 
%% key discriminatory feature 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
clear;clc;clear all; 
% % input Case 1-4 damage index into 4x4 array, DI_array 
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
% %             S1       S2       S3       S4 
% %         %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
% % CASE 1  %        %        %        %        % 
% %         %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
% % CASE 2  %        %        %        %        % 
% %         %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
% % CASE 3  %        %        %        %        % 
% %         %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
% % CASE 4  %        %        %        %        % 
% %         %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
% % 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
  
DI_array = [0.00, 0.09, 0.48, 0.49; 
            0.13, 0.00, 0.85, 0.50; 
            0.64, 0.75, 0.00, 0.26; 
            0.47, 0.40, 0.12, 0.00]  ;
% % create column array for DI sums 
sum = zeros(4,1); 
sum(1,1) = DI_array(3,1) + DI_array(4,1); 
sum(2,1) = DI_array(3,2) + DI_array(4,2); 
sum(3,1) = DI_array(1,3) + DI_array(2,3); 
sum(4,1) = DI_array(1,4) + DI_array(2,4); 
  
% % sort sensor sums in ascending order, in separate column vector 
asc_sum = zeros(4,2); 
asc_sum(:,2) = sort(sum); 
  
% % display sensor sums in ascending order 
if sum(1,1) == asc_sum(1,2) 
     asc_sum(1,1) = 1; 
elseif sum(1,1) == asc_sum(2,2) 
     asc_sum(2,1) = 1; 
elseif sum(1,1) == asc_sum(3,2) 
     asc_sum(3,1) = 1; 
elseif sum(1,1) == asc_sum(4,2) 
     asc_sum(4,1) = 1; 
end 
  
if sum(2,1) == asc_sum(1,2) 
     asc_sum(1,1) = 2; 
elseif sum(2,1) == asc_sum(2,2) 
     asc_sum(2,1) = 2; 
elseif sum(2,1) == asc_sum(3,2) 
     asc_sum(3,1) = 2; 
 195 
 
elseif sum(2,1) == asc_sum(4,2) 
     asc_sum(4,1) = 2; 
end 
  
if sum(3,1) == asc_sum(1,2) 
     asc_sum(1,1) = 3; 
elseif sum(3,1) == asc_sum(2,2) 
     asc_sum(2,1) = 3; 
elseif sum(3,1) == asc_sum(3,2) 
     asc_sum(3,1) = 3; 
elseif sum(3,1) == asc_sum(4,2) 
     asc_sum(4,1) = 3; 
end 
  
if sum(4,1) == asc_sum(1,2) 
     asc_sum(1,1) = 4; 
elseif sum(4,1) == asc_sum(2,2) 
     asc_sum(2,1) = 4; 
elseif sum(4,1) == asc_sum(3,2) 
     asc_sum(3,1) = 4; 
elseif sum(4,1) == asc_sum(4,2) 
     asc_sum(4,1) = 4; 
end 
  
% % display which half (top or bottom) where the damaged area is 
located 
if asc_sum(4,1) == 3 
    disp('Damage located on top half on plate, Quadrants 1 or 3') 
    t = 1; 
elseif asc_sum(4,1) == 1 
    disp('Damage located on top half on plate, Quadrants 1 or 3') 
    t = 1; 
else 
    disp('Damage located on bottom half of plate, Quadrants 2 or 4') 
    t = 2; 
end 
  
 
 
 
 196 
 
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