MODIFIED GENETIC ALGORITHM APPROACH TO SYSTEM IDENTIFICATION WITH STRUCTURAL AND OFFSHORE APPLICATION MICHAEL JOHN PERRY NATIONAL UNIVERSITY OF SINGAPORE 2006 MODIFIED GENETIC ALGORITHM APPROACH TO SYSTEM IDENTIFICATION WITH STRUCTURAL AND OFFSHORE APPLICATION MICHAEL JOHN PERRY B.Eng (NUS) A THESIS SUMBITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF CIVIL ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2006 Acknowledgements Acknowledgements I would like to first thank my PhD advisors, Professor Koh Chan Ghee and Associate Professor Choo Yoo Sang, for their guidance throughout this study. Their advice and support is most appreciated, and our discussions have led to many useful breakthroughs throughout the duration of this work. I would also like to acknowledge the contribution of Mr Peter C. Sandvik and the team at MARINTEK who guided me for the work on hydrodynamics completed while I was in Norway. Many thanks also to all the staff in the Structures Laboratory for their assistance with the experimental work. Their experience and efforts helped make the experimental phase a success. This study has been completed under a research scholarship from the National University of Singapore. In addition, I received funding from the President’s Graduate Fellowship in 2004 and 2006. This financial support is much appreciated. Thanks to my good friends and fellow students for the many necessary coffee breaks, good laughs and fun times we had along the way. Finally, I thank my family for their encouragement and support. i Table of Contents Table of Contents Acknowledgement i Table of Contents ii Summary vi List of Figures viii List of Tables xi Chapter 1. Introduction 1.1 Overview of Identification Techniques 1.1.1 Frequency Domain Methods 1.1.2 Time Domain Methods 1.1.3 Non-Classical Methods 16 1.2 Objectives 18 1.3 Organisation of Thesis 19 Chapter 2. Genetic Algorithms 23 2.1 Introduction to GA 23 2.2 A Simple GA 27 2.3 Classical GA Theory 31 2.4 Advances in GA 35 2.5 Chapter Summary 38 Chapter 3. Identification Strategy 39 3.1 SSRM 3.1.1 Runs for Evaluation of Limits and Total Runs 40 41 ii Table of Contents 3.1.2 Reducing the Search Space 42 3.1.3 Example 44 3.2 MGAMAS 46 3.2.1 Solution Representation 48 3.2.2 Multiple Species and Focus on Mutation 49 3.2.3 Regeneration, Reintroduction and Migration 49 3.2.4 Mutation Operators 50 3.2.5 Crossover Operators 53 3.2.6 Fitness Evaluation and Selection 56 3.2.7 Reduced Data Length Procedure 59 3.3 Chapter Summary Chapter 4. Structural Identification 4.1 Structural Systems, Modelling and Test Procedure 4.1.1 Numerical Integration Scheme 4.2 Known Mass Systems 4.2.1 Known Mass Systems - Results 4.3 Unknown Mass Systems 4.3.1 Unknown Mass Systems - Results 4.4 Effect of Noise and Data Length 60 62 63 67 73 76 81 82 86 4.4.1 Reduced Data Length Procedure 90 4.4.2 Effect of Noise and Data Length - Summary 94 4.5 Chapter Summary 94 Chapter 5. Structural Damage Detection 96 5.1 Damage Detection Strategy 96 5.1.1 Verification of Strategy – Simulated Data 99 iii Table of Contents 5.2 Experimental Study 107 5.2.1 Preliminary Calculations and Testing 109 5.2.2 Main Dynamic Tests 114 5.2.3 Analysis of Experimental Data 126 5.3 Chapter Summary Chapter 6. Structural Identification without Input Force Measurement 141 143 6.1 Modification of the Identification Strategy 144 6.2 Numerical Study 147 6.3 Experimental Study 153 6.3.1 Using Multiple Test Data 6.4 Chapter Summary Chapter 7. Application to Non-linear Identification in Hydrodynamics 155 161 163 7.1 Traditional Modelling and Identification of Heave Response 164 7.2 Application of the SSRM 166 7.2.1 Modified Euler Method 7.3 Experimental Study – Perforated Foundation Pile 7.3.1 Results 7.4 Chapter Summary Chapter 8. Conclusions and Future Work 168 170 175 185 186 8.1 Conclusions 186 8.2 Recommendations for Future Work 190 References 192 iv Table of Contents Appendix A. Structural Identification Results 197 A.1 Known Mass Systems 197 A.1.1 Primary Tests 197 A.1.2 Additional Tests 217 A.2 Unknown Mass Systems 220 A.3 Effect of Noise and Data Length 224 A.4 Reduced Data Length Procedure 227 Appendix B. Structural Damage Detection Results 239 B.1 Verification of Strategy 239 B.2 Model Tests 249 B.2.1 Static Test – Undamaged Structure 249 B.2.2 Dynamic Tests – Identification of Undamaged Structure 251 B.2.3 Dynamic Tests – Structural Damage Detection 253 Appendix C. Identification without Measured Force 271 C.1 Identification Using One Test 271 C.2 Identification Using Two Tests 275 Publications Resulting from this Research 285 v Summary Summary This study aims to develop a robust and efficient strategy for identifying parameters of dynamic systems. The strategy is developed using genetic algorithms (GA), a heuristic optimisation technique based on Darwin’s theory of natural selection and survival of the fittest. Darwin observed that individuals with characteristics better suited for survival in their given environment would be more likely to survive to reproduce and have their genes passed on to the next generations. Through mutations, natural selection and reproduction, species could evolve and adapt to changes in the environment. The identification strategy proposed in this thesis works on two levels. At the first level a modified GA based on migration and artificial selection (MGAMAS) uses multiple species and operators to search the current search space for suitable parameter values. At the second level a search space reduction method (SSRM) uses the results of several runs of the MGAMAS in order to reduce the search space for those parameters that converge quickly. The search space reduction allows further identification of the parameters to be conducted with greater accuracy and improves convergence of the less sensitive system parameters. The MGAMAS is the heart of the strategy. The population is split into several species significantly reducing the trade off between exploration and exploitation that exists within many search algorithms. Several mutation operators are used to direct the search and other novel ideas such as tagging and a reduced data length procedure help the strategy to remain robust and efficient. The application of the strategy focuses on structural identification problems considering shearbuilding systems. Identification of systems with known mass are first considered in order to gain understanding into the effect that various GA parameters have on the accuracy of identification. Extension is then made to systems with unknown mass, stiffness and damping properties. Identification of such systems is rarely considered due to the difficulty associated vi Summary with separating mass and stiffness properties. The proposed SSRM strategy is used within a damage detection strategy whereby the undamaged state of the structure is first identified and used to direct the search for parameters of the damaged structure. An important extension is also made to output-only identification problems where the input excitation cannot be measured. The effectiveness of the proposed strategy is illustrated on numerically simulated data as well as using model tests of a 7-story steel structure. Results are generally excellent. Numerical simulations on 5, 10 and 20-DOF systems show that, even when no force measurement is available and limited accelerations are contaminated with 10% noise, the stiffness parameters are identified with mean error of less than 1%. Damage to the 7-story steel frame, representing a change in story stiffness of only 4%, is identified using as few as acceleration measurements. Finally, in order to illustrate the versatility of the proposed strategy, identification of the heave motion of submerged bodies is studied. A case study of a perforated foundation pile is used to demonstrate how the SSRM is easily adapted to identify highly non-linear hydrodynamic models with an amplitude dependant added mass term and a combination of damping terms. While a solid pile can be modelled using constant added mass, the perforated pile has added mass that varies significantly with the amplitude of motion. vii List of Figures List of Figures Chapter 1. Introduction Fig. 1.1 (a) Direct analysis (simulation); (b) inverse analysis (identification) Fig. 1.2 Kalman filter Fig. 1.3 Layout of a simple neural network Chapter 2. Genetic Algorithms Fig. 2.1 Function f(x) to be maximised Fig. 2.2 Layout of a simple GA Fig. 2.3 Function maximisation – GA solution Chapter 3. Identification Strategy Fig. 3.1 Search Space Reduction Method Fig. 3.2 Example of weights used Fig. 3.3 Variation of function due to x1 and x2 Fig. 3.4 Modified Genetic Algorithm based on Migration and Artificial Selection Fig. 3.5 Representation and storage of solutions Fig. 3.6 Average magnitude of mutations for species and Fig. 3.7 Survival probabilities for a population of 50 individuals Chapter 4. Structural Identification Fig. 4.1 n-DOF Structure Fig. 4.2 Automated testing procedure Fig. 4.3 Variation of parameters about best results Fig. 4.4 Effect of noise on identification Fig. 4.5 Effect of noise and data length viii Appendix B. Structural Damage Detection Results Table B.45 D9 – 4% damage at level and Incomplete measurement (2 and 6) Input force U D Same Force for U and D A A B B C C D D E E Average Damage Success floor floor Max false damage 3.591 2.064 2.955 3.529 2.561 2.940 (0.648) 4.221 4.967 4.585 4.443 4.703 4.584 (0.280) 1.063 1.289 1.858 1.007 2.142 1.472 (0.504) rd th 1X 2X 4X 9/9 6/9 7/9 9/9 5/9 36/45 80% 7/9 4/9 2/9 7/9 4/9 24/45 53% 3/9 0/9 0/9 3/9 1/9 7/45 16% 270 Appendix C. Identification without Measured Force Appendix C. Identification without Measured Force This appendix contains a summary of results of the tests carried out for chapter 6. In each of the tables the damage identified at the damaged level is reported as well as the maximum damage falsely identified at one of the other levels. The difference between these values is essential in achieving a useful identification result. For all of the results presented in this appendix, the same force is used for the identification of the damaged and undamaged structures. This follows from the results presented in chapter 5. C.1 Identification Using One Test The results here are for the damage detection using only a single test to identify the parameters of the structure. In the following section (C.2) tests are combined in order to improve the identification accuracy. Table C.1 D0 – Undamaged Single test, Full measurement Maximum False Damage Input force A B C D E Mean % > 2% > 4% 8.924 3.522 6.758 6.435 4.748 6.077 6/6 5/6 6/6 6/6 5/6 28/30 93% 5/6 2/6 6/6 5/6 4/6 22/30 73% Table C.2 D1 – 4% damage at level Single test, Full measurement Input force A B C D E Average Damage % th Sucess floor Max false damage 1X 2X 4X 4.597 4.644 2.608 4.752 3.567 4.034 8.779 2.120 3.791 3.480 3.921 4.418 0/9 8/9 4/9 6/9 5/9 23/45 51% 0/9 6/9 3/9 3/9 3/9 15/45 33% 0/9 1/9 0/9 0/9 0/9 1/45 2% 271 Appendix C. Identification without Measured Force Table C.3 D2 – 17% damage at level Single test, Full measurement Average Damage % Input force th Sucess floor Max false damage 1X 2X 4X 21.107 19.700 13.828 18.053 12.949 17.127 10.666 5.473 6.653 4.735 7.981 7.102 9/9 9/9 7/9 9/9 7/9 41/45 91% 6/9 9/9 6/9 8/9 2/9 31/45 69% 2/9 8/9 3/9 6/9 1/9 20/45 44% A B C D E Table C.4 D3 – 17% damage at level and 4% at level Single test, Full measurement Average Damage % Input force th A B C D E floor floor 18.788 19.307 15.779 19.104 17.744 18.144 3.761 3.271 2.718 2.524 4.980 3.451 Sucess Max false damage 7.429 3.035 6.143 4.350 5.294 5.250 th 1X 2X 4X 2/9 4/9 2/9 5/9 3/9 16/45 36% 0/9 1/9 1/9 0/9 3/9 5/45 11% 0/9 0/9 0/9 0/9 0/9 0/45 0% Table C.5 D4 – 17% damage at level and 4% at level and Single test, Full measurement Input force A B C D E Average Damage % rd th th floor floor floor 12.230 7.508 2.303 3.055 6.296 6.278 18.871 17.961 16.483 18.362 16.609 17.657 5.633 5.494 5.020 4.263 3.135 4.709 Sucess Max false damage 8.037 2.141 5.130 4.570 9.648 5.905 1X 2X 4X 4/9 8/9 1/9 3/9 1/9 17/45 38% 0/9 6/9 0/9 0/9 0/9 6/45 13% 0/9 4/9 0/9 0/9 0/9 4/45 9% Table C.6 D5 – 17% damage at level and and 4% at level Single test, Full measurement Input force A B C D E Average Damage % rd th th floor floor floor 7.600 8.166 3.871 4.513 11.677 7.165 18.552 18.695 16.078 19.066 17.006 17.879 19.692 20.689 18.088 17.864 19.240 19.115 Sucess Max false damage 6.386 3.418 4.180 4.085 2.720 4.158 1X 2X 4X 7/9 9/9 3/9 5/9 9/9 33/45 73% 4/9 6/9 1/9 2/9 8/9 21/45 47% 3/9 1/9 0/9 1/9 4/9 9/45 20% 272 Appendix C. Identification without Measured Force Table C.7 D6 – 17% damage at level 3, and Single test, Full measurement Input force A B C D E Average Damage % rd th Sucess Max false damage 5.857 2.269 4.135 6.502 4.284 4.609 th floor floor floor 23.854 22.394 15.694 16.366 26.237 20.909 18.957 17.122 16.827 17.523 16.447 17.375 19.102 21.004 19.260 18.600 19.927 19.578 1X 2X 4X 8/9 9/9 9/9 9/9 9/9 44/45 98% 7/9 9/9 8/9 6/9 9/9 39/45 87% 6/9 9/9 4/9 1/9 4/9 24/45 53% Table C.8 D7 – 4% damage at level Single test, Full measurement Input force Average Damage % th Sucess floor Max false damage 1X 2X 4X 8.372 0.824 4.624 3.385 7.544 4.950 7.040 3.431 5.191 3.420 6.883 5.193 7/9 0/9 5/9 7/9 7/9 26/45 58% 1/9 0/9 1/9 4/9 3/9 9/45 20% 0/9 0/9 0/9 0/9 0/9 0/45 0% A B C D E Table C.9 D8 – 4% damage at level Single test, Full measurement Input force Average Damage % rd Sucess floor Max false damage 1X 2X 4X 7.472 5.657 4.318 2.882 3.442 4.754 7.801 2.983 6.714 3.112 12.143 6.551 6/9 8/9 2/9 4/9 3/9 23/45 51% 4/9 3/9 0/9 2/9 1/9 10/45 22% 0/9 2/9 0/9 1/9 1/9 4/45 9% A B C D E Table C.10 D9 – 4% damage at level and Single test, Full measurement Input force A B C D E Average Damage % rd th floor floor 12.091 4.603 3.852 3.603 0.331 4.896 10.155 3.103 6.880 5.109 5.749 6.199 Sucess Max false damage 7.121 3.618 5.545 2.836 10.756 5.975 1X 2X 4X 8/9 4/9 1/9 7/9 3/9 23/45 51% 4/9 0/9 1/9 4/9 0/9 9/45 20% 0/9 0/9 0/9 2/9 0/9 2/45 4% 273 Appendix C. Identification without Measured Force Table C.11 D10 – 13% damage at level Single test, Full measurement Input force A B C D E Average Damage % th Sucess floor Max false damage 1X 2X 4X 17.368 15.777 11.436 13.948 9.713 13.648 6.479 3.622 7.022 4.787 11.677 6.718 9/9 9/9 7/9 9/9 3/9 37/45 82% 7/9 9/9 2/9 7/9 1/9 26/45 58% 4/9 6/9 2/9 4/9 0/9 16/45 36% Table C.12 D11 – 13% damage at level Single test, Full measurement Input force A B C D E Average Damage % th Sucess floor Max false damage 1X 2X 4X 14.787 16.037 13.699 14.204 16.612 15.068 10.600 2.897 4.360 2.821 5.738 5.283 5/9 9/9 9/9 9/9 9/9 41/45 91% 3/9 9/9 6/9 9/9 9/9 36/45 80% 1/9 8/9 4/9 8/9 2/9 23/45 51% Table C.13 D12 – 13% damage at level Single test, Full measurement Input force A B C D E Average Damage % rd Sucess floor Max false damage 1X 2X 4X 17.487 15.488 12.284 12.411 16.472 14.828 3.105 1.053 3.621 3.940 3.849 3.113 9/9 9/9 9/9 9/9 9/9 45/45 100% 8/9 9/9 7/9 7/9 8/9 39/45 87% 8/9 9/9 4/9 4/9 6/9 31/45 69% Table C.14 D13 – 13% damage at level and Single test, Full measurement Input force A B C D E Average Damage % rd th floor floor 13.143 16.071 13.697 13.720 21.277 15.582 14.160 16.370 14.933 14.972 17.321 15.551 Sucess Max false damage 9.740 0.695 4.161 3.715 5.547 4.772 1X 2X 4X 5/9 6/9 9/9 9/9 9/9 38/45 84% 3/9 6/9 7/9 7/9 9/9 32/45 71% 2/9 6/9 3/9 5/9 2/9 18/45 40% 274 Appendix C. Identification without Measured Force C.2 Identification Using Two Tests The results presented in this section are achieved using the modified strategy, whereby data from tests using different input forces are combined in order to more reliably identify the structural parameters. For each case there are trials carried out. For example the results for input forces A and B contain results using force A1 and B1, A2 and B2, and A3 and B3 to identify both the undamaged and damaged structures. Thus there are identification results for the undamaged structure and for the damaged structure. Comparing these to detect damage results in the combinations. Table C.15 D0 – Undamaged Two tests, Full measurement Maximum False Damage Input forces A and B A and C A and D A and E B and C B and D B and E C and D C and E D and E Mean % > 2% > 4% 4.325 3.620 5.753 3.936 4.094 4.437 3.128 2.736 5.562 4.079 4.167 5/6 5/6 6/6 5/6 6/6 6/6 5/6 5/6 5/6 6/6 54/60 90% 3/6 4/6 4/6 4/6 2/6 5/6 1/6 0/6 4/6 1/6 28/60 47% Table C.16 D1 – 4% damage at level Two tests, Full measurement Input force A and B A and C A and D A and E B and C B and D B and E C and D C and E D and E Average Damage % th Sucess floor Max false damage 1X 2X 4X 3.802 2.607 3.948 3.636 3.394 4.912 4.435 3.802 3.738 4.865 3.914 4.383 3.052 4.603 3.032 2.240 2.264 2.020 2.076 1.817 2.380 2.787 4/9 5/9 4/9 7/9 6/9 8/9 8/9 9/9 7/9 9/9 67/90 74% 0/9 3/9 1/9 2/9 4/9 6/9 6/9 3/9 7/9 4/9 36/90 40% 0/9 0/9 0/9 0/9 0/9 1/9 3/9 0/9 2/9 0/9 6/90 7% 275 Appendix C. Identification without Measured Force Table C.17 D2 – 17% damage at level Two tests, Full measurement Average Damage % Input force th A and B A and C A and D A and E B and C B and D B and E C and D C and E D and E Sucess floor Max false damage 1X 2X 4X 19.086 15.652 17.849 18.487 16.869 19.154 18.442 15.981 14.340 17.411 17.327 5.975 5.267 6.454 6.475 4.175 3.459 4.275 3.461 6.411 3.662 4.961 9/9 9/9 9/9 9/9 9/9 9/9 9/9 9/9 8/9 9/9 89/90 99% 7/9 7/9 6/9 8/9 8/9 9/9 9/9 9/9 6/9 9/9 78/90 87% 2/9 2/9 5/9 4/9 6/9 7/9 4/9 6/9 2/9 7/9 45/90 50% Table C.18 D3 – 17% damage at level and 4% at level Two tests, Full measurement Average Damage % Input force th A and B A and C A and D A and E B and C B and D B and E C and D C and E D and E floor floor 19.517 17.254 19.473 19.119 17.340 19.350 19.273 17.257 17.106 19.056 18.475 3.371 3.190 2.708 4.667 3.752 2.728 4.405 3.612 3.792 3.709 3.593 Sucess Max false damage 4.195 3.653 4.219 3.016 4.237 3.683 2.961 4.524 3.798 3.224 3.751 th 1X 2X 4X 4/9 3/9 4/9 7/9 4/9 4/9 7/9 4/9 5/9 5/9 47/90 52% 0/9 2/9 2/9 3/9 0/9 0/9 3/9 0/9 2/9 1/9 13/90 14% 0/9 0/9 0/9 0/9 0/9 0/9 0/9 0/9 0/9 0/9 0/90 0% Table C.19 D4 – 17% damage at level and 4% at level and Two tests, Full measurement Input force A and B A and C A and D A and E B and C B and D B and E C and D C and E D and E Average Damage % rd th th floor floor floor 8.266 3.698 5.655 7.921 3.587 4.438 6.896 2.134 3.633 4.203 5.043 18.680 17.458 18.758 19.907 16.752 18.432 18.251 17.053 16.543 18.139 17.997 5.091 4.192 4.261 3.384 4.922 4.354 4.123 4.677 4.150 3.033 4.219 Sucess Max false damage 3.479 3.312 3.827 4.447 4.126 3.478 3.433 4.132 6.594 4.584 4.141 1X 2X 4X 7/9 5/9 6/9 6/9 3/9 4/9 5/9 2/9 2/9 2/9 42/90 47% 4/9 1/9 2/9 2/9 0/9 1/9 2/9 0/9 0/9 1/9 13/90 14% 0/9 0/9 0/9 0/9 0/9 0/9 2/9 0/9 0/9 1/9 3/90 3% 276 Appendix C. Identification without Measured Force Table C.20 D5 – 17% damage at level and and 4% at level Two tests, Full measurement Input force A and B A and C A and D A and E B and C B and D B and E C and D C and E D and E Average Damage % rd th th floor floor floor 7.511 5.234 5.590 10.156 4.722 5.146 10.793 3.935 6.170 7.956 6.721 19.083 17.812 18.960 19.212 18.070 19.584 19.225 17.389 16.444 18.760 18.454 19.823 18.558 18.058 19.885 19.958 18.601 21.436 18.948 17.832 18.820 19.192 Sucess Max false damage 3.303 2.651 4.126 2.213 3.697 3.606 1.142 2.638 3.943 1.656 2.898 1X 2X 4X 7/9 7/9 6/9 9/9 6/9 7/9 9/9 6/9 8/9 9/9 74/90 82% 6/9 5/9 5/9 7/9 3/9 2/9 9/9 3/9 3/9 9/9 52/90 58% 4/9 2/9 1/9 6/9 0/9 1/9 7/9 0/9 0/9 4/9 25/90 28% Table C.21 D6 – 17% damage at level 3, and Two tests, Full measurement Input force A and B A and C A and D A and E B and C B and D B and E C and D C and E D and E Average Damage % rd th th floor floor floor 21.944 18.359 18.842 24.239 17.401 17.950 25.066 16.194 19.015 20.582 19.959 18.163 17.523 18.009 18.511 17.537 18.041 17.608 16.833 16.247 17.283 17.575 19.984 19.282 18.650 20.121 20.330 19.027 21.971 20.001 17.860 19.027 19.625 Sucess Max false damage 3.471 3.168 5.092 3.068 3.851 4.921 0.426 3.981 4.557 3.062 3.560 1X 2X 4X 9/9 9/9 9/9 9/9 9/9 9/9 9/9 9/9 9/9 9/9 90/90 100% 9/9 9/9 7/9 9/9 9/9 9/9 9/9 9/9 9/9 9/9 88/90 98% 7/9 6/9 5/9 7/9 6/9 2/9 9/9 5/9 3/9 8/9 58/90 64% Table C.22 D7 – 4% damage at level Two tests, Full measurement Input force A and B A and C A and D A and E B and C B and D B and E C and D C and E D and E Average Damage % th Sucess floor Max false damage 1X 2X 4X 3.773 4.128 4.563 6.680 3.126 2.511 4.741 4.388 5.818 5.881 4.561 2.796 2.471 2.805 2.814 3.126 2.805 2.907 3.223 4.859 2.103 2.991 9/9 8/9 9/9 9/9 6/9 7/9 7/9 7/9 6/9 9/9 77/90 86% 1/9 2/9 3/9 5/9 2/9 1/9 4/9 2/9 2/9 7/9 29/90 32% 1/9 2/9 0/9 3/9 0/9 0/9 1/9 0/9 1/9 2/9 10/90 11% 277 Appendix C. Identification without Measured Force Table C.23 D8 – 4% damage at level Two tests, Full measurement Input force Average Damage % rd Sucess floor Max false damage 1X 2X 4X 5.133 4.608 4.278 5.069 4.829 3.703 5.074 2.793 4.362 2.592 4.244 3.405 3.269 2.747 4.963 3.358 2.338 4.073 3.894 7.095 4.315 3.946 7/9 7/9 7/9 6/9 8/9 7/9 6/9 3/9 3/9 2/9 56/90 62% 3/9 6/9 5/9 6/9 4/9 3/9 3/9 0/9 0/9 1/9 31/90 34% 2/9 0/9 1/9 1/9 0/9 0/9 1/9 0/9 0/9 0/9 5/90 6% A and B A and C A and D A and E B and C B and D B and E C and D C and E D and E Table C.24 D9 – 4% damage at level and Two tests, Full measurement Input force A and B A and C A and D A and E B and C B and D B and E C and D C and E D and E Average Damage % rd floor floor 7.354 4.654 6.809 5.662 4.429 3.921 3.651 3.527 3.569 2.898 4.647 5.486 5.120 6.086 5.424 4.303 4.141 4.460 5.445 6.168 5.219 5.185 Sucess Max false damage 2.337 2.387 1.792 3.211 2.643 2.222 2.756 2.232 6.301 3.243 2.912 th 1X 2X 4X 9/9 8/9 9/9 7/9 7/9 7/9 5/9 9/9 4/9 5/9 70/90 78% 6/9 5/9 9/9 3/9 2/9 2/9 4/9 3/9 2/9 2/9 38/90 42% 3/9 0/9 3/9 1/9 1/9 0/9 1/9 1/9 1/9 0/9 11/90 12% Table C.25 D10 – 13% damage at level Two tests, Full measurement Input force A and B A and C A and D A and E B and C B and D B and E C and D C and E D and E Average Damage % th Sucess floor Max false damage 1X 2X 4X 15.884 13.362 14.468 15.412 13.918 14.958 14.657 12.656 10.980 13.180 13.948 4.018 4.121 4.623 6.052 3.869 3.252 5.221 4.264 7.865 5.184 4.847 9/9 9/9 9/9 9/9 9/9 9/9 9/9 9/9 7/9 9/9 88/90 98% 9/9 8/9 7/9 7/9 9/9 9/9 7/9 8/9 3/9 8/9 75/90 83% 5/9 5/9 5/9 4/9 4/9 6/9 2/9 2/9 0/9 0/9 33/90 37% 278 Appendix C. Identification without Measured Force Table C.26 D11 – 13% damage at level Two tests, Full measurement Input force A and B A and C A and D A and E B and C B and D B and E C and D C and E D and E Average Damage % th Sucess floor Max false damage 1X 2X 4X 15.508 14.981 14.409 17.077 15.807 14.894 18.052 14.961 14.267 16.275 15.623 4.931 2.843 3.574 3.513 2.305 2.430 4.282 2.172 3.387 3.915 3.335 9/9 9/9 9/9 9/9 9/9 9/9 9/9 9/9 9/9 9/9 90/90 100% 7/9 9/9 9/9 9/9 9/9 9/9 9/9 9/9 9/9 9/9 88/90 98% 4/9 7/9 4/9 7/9 8/9 8/9 4/9 9/9 5/9 5/9 61/90 68% Table C.27 D12 – 13% damage at level Two tests, Full measurement Input force A and B A and C A and D A and E B and C B and D B and E C and D C and E D and E Average Damage % rd Sucess floor Max false damage 1X 2X 4X 15.591 13.849 14.032 15.674 13.305 13.497 15.996 12.761 13.685 13.714 14.210 1.936 1.838 2.305 2.632 1.644 2.332 1.601 2.387 2.755 2.869 2.230 9/9 9/9 9/9 9/9 9/9 9/9 9/9 9/9 9/9 9/9 90/90 100% 9/9 9/9 9/9 8/9 9/9 9/9 9/9 9/9 9/9 9/9 89/90 99% 8/9 9/9 7/9 8/9 9/9 8/9 9/9 9/9 8/9 6/9 81/90 90% Table C.28 D13 – 13% damage at level and Two tests, Full measurement Input force A and B A and C A and D A and E B and C B and D B and E C and D C and E D and E Average Damage % rd th floor floor 14.903 15.224 13.967 17.714 14.325 14.131 19.504 14.365 15.958 17.096 15.719 15.678 15.737 15.027 17.320 16.198 15.338 18.610 16.065 14.296 16.489 16.076 Sucess Max false damage 4.195 2.881 3.820 2.534 1.655 2.762 0.727 2.093 4.333 1.486 2.649 1X 2X 4X 9/9 9/9 9/9 9/9 9/9 9/9 9/9 9/9 9/9 9/9 90/90 100% 7/9 9/9 7/9 9/9 9/9 9/9 9/9 9/9 9/9 9/9 86/90 96% 5/9 7/9 5/9 7/9 9/9 7/9 9/9 7/9 3/9 9/9 68/90 76% 279 Appendix C. Identification without Measured Force Table C.29 D0 – Undamaged Two tests, Incomplete measurement (2, 6, 7) Maximum False Damage Input forces A and B A and C A and D A and E B and C B and D B and E C and D C and E D and E Mean % > 2% > 4% 5.996 4.268 6.015 2.475 6.038 5.852 5.090 2.735 7.128 3.828 4.942 6/6 5/6 6/6 5/6 6/6 6/6 6/6 6/6 6/6 6/6 58/60 97% 5/6 5/6 4/6 0/6 4/6 5/6 5/6 0/6 5/6 3/6 36/60 60% Table C.30 D1 – 4% damage at level Two tests, Incomplete measurement (2, 6, 7) Input force A and B A and C A and D A and E B and C B and D B and E C and D C and E D and E Average Damage % th Sucess floor Max false damage 1X 2X 4X 4.352 2.382 4.060 2.525 3.351 5.480 3.286 3.622 2.902 4.303 3.626 4.938 3.918 4.726 3.613 3.288 3.251 3.812 2.462 3.388 3.346 3.674 4/9 5/9 4/9 1/9 5/9 7/9 4/9 7/9 5/9 6/9 48/90 53% 1/9 3/9 1/9 0/9 4/9 4/9 0/9 2/9 3/9 1/9 19/90 21% 0/9 0/9 0/9 0/9 1/9 2/9 0/9 0/9 1/9 0/9 4/90 4% Table C.31 D2 – 17% damage at level Two tests, Incomplete measurement (2, 6, 7) Input force A and B A and C A and D A and E B and C B and D B and E C and D C and E D and E Average Damage % th Sucess floor Max false damage 1X 2X 4X 20.861 15.754 18.988 18.693 16.654 20.746 17.284 15.924 13.467 16.771 17.514 7.503 6.570 6.409 9.267 5.113 4.162 9.114 4.087 9.035 5.040 6.630 9/9 9/9 9/9 9/9 9/9 9/9 9/9 9/9 7/9 9/9 88/90 98% 7/9 6/9 7/9 6/9 7/9 9/9 3/9 9/9 4/9 9/9 67/90 74% 2/9 2/9 3/9 0/9 6/9 7/9 1/9 4/9 0/9 3/9 28/90 31% 280 Appendix C. Identification without Measured Force Table C.32 D3 – 17% damage at level and 4% at level Two tests, Incomplete measurement (2, 6, 7) Average Damage % Input force th A and B A and C A and D A and E B and C B and D B and E C and D C and E D and E floor floor 20.550 17.083 20.049 18.402 18.030 20.662 19.564 17.477 16.512 18.274 18.660 1.935 2.792 0.446 3.135 3.682 1.430 4.765 3.040 3.355 2.457 2.704 Sucess Max false damage 5.901 4.827 5.432 4.528 5.001 4.480 5.800 5.051 6.303 3.796 5.112 th 1X 2X 4X 0/9 2/9 0/9 3/9 3/9 2/9 3/9 0/9 2/9 2/9 17/90 19% 0/9 0/9 0/9 0/9 0/9 0/9 0/9 0/9 0/9 0/9 0/90 0% 0/9 0/9 0/9 0/9 0/9 0/9 0/9 0/9 0/9 0/9 0/90 0% Table C.33 D4 – 17% damage at level and 4% at level and Two tests, Incomplete measurement (2, 6, 7) Input force A and B A and C A and D A and E B and C B and D B and E C and D C and E D and E Average Damage % rd th th floor floor floor 8.987 3.722 6.135 8.599 5.212 5.613 9.224 1.737 3.246 4.553 5.703 19.353 17.387 19.090 19.525 17.287 19.662 17.941 17.741 16.233 17.678 18.190 4.130 4.166 2.556 3.681 4.841 2.711 5.130 4.378 4.375 2.781 3.875 Sucess Max false damage 3.455 4.139 4.490 5.709 4.502 3.729 5.530 4.757 7.931 4.300 4.854 1X 2X 4X 6/9 3/9 3/9 6/9 5/9 3/9 3/9 1/9 1/9 1/9 32/90 36% 3/9 1/9 0/9 4/9 2/9 0/9 2/9 0/9 0/9 0/9 12/90 13% 1/9 0/9 0/9 1/9 1/9 0/9 0/9 0/9 0/9 0/9 3/90 3% Table C.34 D5 – 17% damage at level and and 4% at level Two tests, Incomplete measurement (2, 6, 7) Input force A and B A and C A and D A and E B and C B and D B and E C and D C and E D and E Average Damage % rd th th floor floor floor 8.045 5.263 6.580 10.450 7.263 6.940 12.917 4.133 7.418 9.150 7.816 19.678 17.700 18.531 19.042 18.574 20.309 19.515 17.755 15.835 17.465 18.441 19.425 18.256 17.585 18.736 19.752 18.052 21.379 18.771 18.234 18.436 18.863 Sucess Max false damage 4.114 4.431 4.522 3.970 3.349 3.510 2.376 3.763 6.206 2.739 3.898 1X 2X 4X 8/9 5/9 6/9 9/9 6/9 8/9 9/9 6/9 6/9 9/9 72/90 80% 5/9 4/9 2/9 6/9 6/9 5/9 9/9 1/9 3/9 8/9 49/90 54% 2/9 1/9 1/9 3/9 4/9 3/9 6/9 0/9 0/9 3/9 23/90 26% 281 Appendix C. Identification without Measured Force Table C.35 D6 – 17% damage at level 3, and Two tests, Incomplete measurement (2, 6, 7) Input force A and B A and C A and D A and E B and C B and D B and E C and D C and E D and E Average Damage % rd th th floor floor floor 21.547 18.293 19.461 23.776 18.819 19.372 25.763 16.478 19.938 22.005 20.545 18.003 16.992 17.585 17.690 18.374 18.862 17.637 17.343 15.418 15.976 17.388 20.560 19.211 18.866 19.444 20.600 19.403 22.200 20.215 18.541 19.273 19.831 Sucess Max false damage 3.419 5.662 4.348 5.205 3.882 3.583 0.497 4.161 6.673 3.644 4.107 1X 2X 4X 9/9 9/9 9/9 9/9 9/9 9/9 9/9 9/9 8/9 9/9 89/90 99% 9/9 7/9 8/9 9/9 9/9 9/9 9/9 9/9 7/9 9/9 85/90 94% 8/9 4/9 6/9 4/9 5/9 6/9 9/9 5/9 0/9 4/9 51/90 57% Table C.36 D7 – 4% damage at level Two tests, Incomplete measurement (2, 6, 7) Input force A and B A and C A and D A and E B and C B and D B and E C and D C and E D and E Average Damage % th Sucess floor Max false damage 1X 2X 4X 3.816 3.717 3.879 5.144 3.520 3.343 4.082 4.086 4.733 5.152 4.147 3.256 2.886 3.230 5.803 3.656 3.893 5.491 3.623 4.510 2.901 3.925 7/9 7/9 6/9 4/9 5/9 5/9 1/9 7/9 4/9 7/9 53/90 59% 1/9 3/9 2/9 0/9 2/9 2/9 1/9 0/9 2/9 5/9 18/90 20% 0/9 0/9 0/9 0/9 0/9 0/9 0/9 0/9 0/9 1/9 1/90 1% Table C.37 D8 – 4% damage at level Two tests, Incomplete measurement (2, 6, 7) Input force A and B A and C A and D A and E B and C B and D B and E C and D C and E D and E Average Damage % rd Sucess floor Max false damage 1X 2X 4X 4.356 3.585 3.950 4.292 3.824 3.282 4.917 1.727 3.437 2.171 3.554 3.467 3.269 3.440 5.936 3.834 3.500 3.563 4.327 5.918 3.194 4.045 7/9 5/9 6/9 6/9 5/9 5/9 7/9 1/9 2/9 4/9 48/90 53% 0/9 1/9 2/9 2/9 2/9 2/9 0/9 0/9 0/9 11/90 12% 0/9 0/9 1/9 0/9 1/9 1/9 0/9 0/9 0/9 3/90 3% 282 Appendix C. Identification without Measured Force Table C.38 D9 – 4% damage at level and Two tests, Incomplete measurement (2, 6, 7) Input force A and B A and C A and D A and E B and C B and D B and E C and D C and E D and E Average Damage % rd floor floor 6.484 3.764 5.850 4.046 3.687 3.098 0.832 2.470 2.286 1.114 3.363 5.970 5.078 5.917 5.679 4.681 4.600 4.450 5.410 5.739 5.466 5.299 Sucess Max false damage 3.699 2.788 2.569 4.080 2.935 3.579 3.925 3.281 5.054 3.386 3.530 th 1X 2X 4X 8/9 5/9 7/9 5/9 6/9 6/9 2/9 4/9 3/9 3/9 49/90 54% 1/9 3/9 5/9 2/9 3/9 2/9 0/9 3/9 1/9 2/9 22/90 24% 1/9 0/9 4/9 1/9 1/9 0/9 0/9 1/9 0/9 1/9 9/90 10% Table C.39 D10 – 13% damage at level Two tests, Incomplete measurement (2, 6, 7) Input force A and B A and C A and D A and E B and C B and D B and E C and D C and E D and E Average Damage % th Sucess floor Max false damage 1X 2X 4X 17.236 13.656 15.548 16.586 13.710 16.089 14.468 12.755 10.813 13.020 14.388 5.000 4.783 4.729 8.587 5.150 3.585 8.218 4.852 9.703 4.621 5.923 9/9 9/9 9/9 8/9 9/9 9/9 9/9 9/9 6/9 9/9 86/90 96% 9/9 6/9 7/9 4/9 7/9 9/9 3/9 8/9 2/9 8/9 63/90 70% 5/9 4/9 3/9 2/9 3/9 5/9 0/9 1/9 0/9 1/9 24/90 27% Table C.40 D11 – 13% damage at level Two tests, Incomplete measurement (2, 6, 7) Input force A and B A and C A and D A and E B and C B and D B and E C and D C and E D and E Average Damage % th Sucess floor Max false damage 1X 2X 4X 15.946 14.695 15.416 15.629 15.668 15.767 17.124 15.043 14.490 16.101 15.588 4.470 2.870 3.170 3.769 3.298 2.109 4.925 2.773 4.995 4.802 3.718 9/9 9/9 9/9 9/9 9/9 9/9 9/9 9/9 9/9 9/9 90/90 100% 8/9 9/9 9/9 9/9 9/9 9/9 9/9 9/9 8/9 9/9 88/90 98% 5/9 7/9 6/9 6/9 5/9 9/9 3/9 8/9 2/9 3/9 54/90 60% 283 Appendix C. Identification without Measured Force Table C.41 D12 – 13% damage at level Two tests, Incomplete measurement (2, 6, 7) Input force A and B A and C A and D A and E B and C B and D B and E C and D C and E D and E Average Damage % rd Sucess floor Max false damage 1X 2X 4X 14.663 13.752 13.767 14.878 12.450 13.352 14.748 12.878 13.489 14.145 13.812 2.162 2.279 2.541 3.915 2.334 2.096 2.815 2.301 3.105 1.939 2.549 9/9 9/9 9/9 9/9 9/9 9/9 9/9 9/9 9/9 9/9 90/90 100% 9/9 9/9 9/9 8/9 9/9 9/9 9/9 9/9 9/9 9/9 89/90 99% 9/9 9/9 7/9 6/9 7/9 9/9 8/9 8/9 5/9 9/9 77/90 86% Table C.42 D13 – 13% damage at level and Two tests, Incomplete measurement (2, 6, 7) Input force A and B A and C A and D A and E B and C B and D B and E C and D C and E D and E Average Damage % rd th floor floor 13.798 15.132 14.184 16.586 14.348 14.569 18.199 14.999 17.243 18.273 15.733 17.130 15.691 16.732 16.363 16.558 17.156 17.989 16.553 14.811 16.962 16.594 Sucess Max false damage 3.014 3.441 3.102 4.312 2.351 1.439 2.486 2.346 4.628 2.030 2.915 1X 2X 4X 9/9 9/9 9/9 9/9 9/9 9/9 9/9 9/9 9/9 9/9 90/90 100% 8/9 9/9 7/9 9/9 9/9 9/9 9/9 9/9 9/9 9/9 87/90 97% 6/9 4/9 6/9 5/9 8/9 9/9 8/9 8/9 3/9 9/9 66/90 73% 284 Publications Resulting from this Research Publications Resulting from this Research: Koh, C.G. and Perry, M.J. (2006), Genetic Algorithms in Structural Identification and Damage Detection, in Lagaros, N.D. and Yiannis Tsompanakis, Y., Intelligent Computational Paradigms in Earthquake Engineering, Idea Group Publishing, (Book due to be released in January 2007) Koh C.G. and Perry, M.J. (2005), Damage Detection of Structures Using a Modified Genetic Algorithm, Keynote paper for 9th International Conference on Inspection, Appraisal, Repairs and Maintenance of Structures, 19-21 October, Fuzhou, China, 57-67 Perry, M.J., Koh, C.G. and Choo, Y.S. (2006a), Modified Genetic Algorithm Strategy for Structural Identification, Computers and Structures 84, 529-540 Perry, M.J., Koh, C.G. and Choo (2006b), Y.S., Identification of Damage in a Steel Frame using a Modified Genetic Algorithm, Fourth World Conference on Structural Control and Monitoring, San Diego, 11-13 July Perry, M.J., Koh, C.G. and Choo, Y.S. (2005), Modified Genetic Algorithm Approach to Structural Identification, ICSSD 05 International Conference on Structural Stability and Dynamics, 19-22 June, Florida, USA Perry, M.J. and Sandvik, P.C. (2005), Identification of Hydrodynamic Coefficients for Foundation Piles, ISOPE 05, 19-24 June, Seoul, Korea, 328-333 285 [...]... excitation and initial conditions Known (assumed) system Simulated response Applied excitation and initial conditions (may be unknown) Unknown system (to be identified) Measured response Fig 1.1 (a) Direct analysis (simulation); (b) inverse analysis (identification) The identification of mass, stiffness and damping of a structural system is commonly referred to as structural identification Structural identification. .. understand some of strengths and weaknesses of other identification methods Modelling and simulation of dynamic systems is generally concerned with determining the response of the system to some given initial conditions and external excitation For inverse analysis or identification problems however, the response of the system is measured and it is our aim to determine the unknown system properties, and. .. linear stochastic difference equation (1.13) with input u, and measurement z, which is related to the state by equation 1.14 The system matrices A and B relates the current state to the previous stat end the system inputs while the matrix H relates the measurement to the state of the system The process and measurement noise (w and v respectively) are assumed to be zero mean Gaussian noise with covariances... dynamic systems can be broadly categorized as direct analysis and inverse analysis Direct analysis (simulation) for dynamic systems aims to predict the response (output) for given excitation (input) and known system parameters Inverse analysis (identification) on the other hand, deals with identification of system parameters based on given input and output (I/O) information (fig 1.1) The usefulness of system. .. not need to be specifically known In fact, input characteristics may also be identified along with the system parameters Shi et al (2000) applied an extended Kalman filter method to the frequency domain to identify system and input parameters for both simulated and experimental examples Spanos and Lu (1995) introduced a decoupling method in frequency domain to identify the structural properties and force... is able to search a given solution space using ideas borrowed from nature and Darwin’s theory of natural selection and survival of the fittest The strategy is applied to problems in structural and offshore engineering, but the ideas are general enough that the strategy could easily be adapted to deal with other dynamic systems such as those in finance, electronics, transportation, biology and so on... level 4 and 6 and 4% damage at level 3 Incomplete measurement (2 and 6) Table B.42 D6 – 17% damage at level 3, 4 and 6, Incomplete measurement (2 and 6) Table B.43 D7 – 4% damage at level 6, Incomplete measurement (2 and 6) Table B.44 D8 – 4% damage at level 3, Incomplete measurement (2 and 6) Table B.45 D9 – 4% damage at level 3 and 6, Incomplete measurement (2 and 6) Appendix C Identification without... identification can be applied to update or calibrate 1 Chapter 1 Introduction structural models so as to better predict response and achieve more cost-effective designs By recording and comparing identified parameters over a period of time, system identification can also be used for structural health monitoring (SHM) and damage assessment in a nondestructive way by tracking changes in pertinent structural parameters... of the system is available and a model to simulate time-histories is to be obtained, time domain methods should be adopted A good review and comparison of time domain techniques is given in Ghanem and Shinozuka (1995) and Shinozuka and Ghanem (1995) Using measurements of steel model structures, they compared the performance of extended Kalman filter, maximum likelihood, recursive least squares and recursive... Caravani et al (1977) developed a recursive algorithm for computing the least squares estimate without matrix inversion and applied it to the identification of a 2-DOF shear building An interesting iterative method was proposed by 12 Chapter 1 Introduction Ling and Haldar (2004) They used a least squares method with iteration to identify structural properties without using any input force information . MODIFIED GENETIC ALGORITHM APPROACH TO SYSTEM IDENTIFICATION WITH STRUCTURAL AND OFFSHORE APPLICATION MICHAEL JOHN PERRY . NATIONAL UNIVERSITY OF SINGAPORE 2006 MODIFIED GENETIC ALGORITHM APPROACH TO SYSTEM IDENTIFICATION WITH STRUCTURAL AND OFFSHORE APPLICATION MICHAEL JOHN PERRY B.Eng. to remain robust and efficient. The application of the strategy focuses on structural identification problems considering shear- building systems. Identification of systems with known mass