Evolutionary divide and conquer strategy for identification of structural systems and moving forces

EVOLUTIONARY DIVIDE-AND-CONQUER STRATEGY FOR IDENTIFICATION OF STRUCTURAL SYSTEMS AND MOVING FORCES TRINH NGOC THANH NATIONAL UNIVERSITY OF SINGAPORE 2010 EVOLUTIONARY DIVIDE-AND-CONQUER STRATEGY FOR IDENTIFICATION OF STRUCTURAL SYSTEMS AND MOVING FORCES TRINH NGOC THANH B.Eng. (HCMUT) A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF CIVIL ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2010 Acknowledgement Acknowledgements First, I would like to thank my advisors Professor Koh Chan Ghee and Professor Choo Yoo Sang, for their invaluable guidance and support throughout as well as their dedication to the success of the thesis. Our discussions have led to many useful breakthroughs throughout the duration of this work. I would also like to acknowledge Dr Michael John Perry, a research engineer at Keppel Offshore & Marine, Singapore, for his helpful suggestion at the early stage of this research when he was a research fellow at NUS. Many thanks also go to Mr Lim Huay Bak, Ms Annie Tan, Mr Kamsan Bin Rasman, Mr Ang Beng Oon, Mr Koh Yian Kheng, Mr Choo Peng Kin, Mr Yong Tat Fah, Mr Yip Kwok Keong, Mr Wong Kah Wai Stanley and other staff members in the Structural Laboratory for their generous assistance with experimental work. Their experience and effort helped make the experimental phase a success. I gratefully acknowledge the financial support I have received as a research scholarship from National University of Singapore, and research grants by A*STAR and MPA of Singapore. In particular, I would like to express my gratitude to Dr John Halkyard (visiting Professor at NUS) for his recommendation for an outreach scholarship awarded by the Ocean, Offshore, and Arctic Engineering Division of the International Petroleum Technology Institute, American Society of Mechanical Engineers (ASME). I would like to thank my good friends and fellow students in Singapore and Vietnam for the many necessary coffee breaks, enjoyable times and exciting sport games we had along the way while at NUS. This thesis would not have been possible without the support of my family. I thank my mother, Dong Thi Khai, for devoting her lifetime to the luxury of my education. My gratitude is also to my three brothers, Trinh Ngoc Vu, Trinh Ngoc Tuan Anh and Trinh Ngoc Hiep for their great encouragement and support when I am away from home. I can never thank enough my wife, Ngo Thi Mai Khanh, for her unconditional support and listening. Finally, this work is dedicated to the memory of my father, Trinh Giai Thanh, who passed away when I was five years old. i Contents Table of Contents Acknowledgements i Table of Contents ii Summary v List of Tables List of Figures List of Symbols Chapter 1  Introduction viii x xiii 1  1.1  Background 1  1.2  Literature Review 5  1.2.1  Classical Methods 6  1.2.2  Non-classical Methods 11  1.2.3  Substructural Identification Methods 25  1.2.4  Moving Force Identification Methods 30  1.3  Objectives and Scope 32  1.4  Thesis Outline 35  Chapter 2  Evolutionary Divide-and-Conquer Strategy for Structural System Identification 37  2.1  Substructural Identification Strategy 38  2.2  Numerical Studies 44  2.2.1  Identification of 20-DOF Known-Mass System 45  2.2.2  Identification of 100-DOF Unknown-Mass System 48  2.3  Experimental Studies 52  2.3.1  Static Test 53  2.3.2  Impact Test 56  2.3.3  Dynamic Test 58  ii Contents 2.3.4  Identification with Complete Measurement 64  2.3.5  Identification with Incomplete Measurement 68  2.4  Chapter Summary Chapter 3  Output-only Substructural Identification 70  72  3.1  Output-only Substructural Identification Strategy 73  3.2  Numerical Studies 76  3.2.1  Identification of 20-DOF System without Input Forces 77  3.2.2  Identification of 100-DOF System without Input Forces 79  3.3  Experimental Studies 82  3.3.1  Identification with Complete Measurement 83  3.3.2  Identification with Incomplete Measurement 85  3.4  Chapter Summary Chapter 4  Local Structural Damage Quantification 85  87  4.1  Local Damage Quantification 88  4.2  Numerical Studies 89  4.2.1  Local Damage Quantification with Known Input Force 91  4.2.2  Local Damage Quantification with Unknown Input Force 93  4.3  Experimental Studies 4.3.1  Local Damage Quantification with Known Input Force 4.3.2  Local Damage Quantification with Unknown Input Force 4.4  Chapter Summary Chapter 5  Evolutionary Divide-and-Conquer Strategy for Moving Force Identification in Time Domain 97  99  109  113  115  5.1  Moving Force Formulation 116  5.2  Moving Force Identification 118  5.3  Numerical Studies 124  iii Contents 5.3.1  Comparison of Identified Results between Different Methods 126  5.3.2  Effects of Axle Spacing 129  5.3.3  Effects of Number of Measurement Points 130  5.4  Chapter Summary Chapter 6  Conclusions and Future Work 132  134  6.1  Conclusions 134  6.2  Recommendations for Future Work 138  References 140  Publications Resulting from this Research 148  iv Summary Summary Large structural systems such as high-rise buildings, long-span bridges and offshore platforms often require inspection and maintenance for purpose of sustainable and safe usage. The state of these large structures can be assessed by means of structural identification to determine their key parameters based on numerical analysis of measurement. Its feasibility for practical implementation has been enhanced greatly due to recently rapid advances in sensor technology, wireless communication and computational power. To make this work, however, it is essential to have a good numerical strategy to accurately and efficiently quantify system characteristics even with limited and noisy measurements. Although considerable progress has been made in this subject area, there remain many challenges in achieving robust convergence of identification for large systems. This study aims to develop a robust numerical strategy for identifying unknown parameters of large systems. The strategy is developed based on the combination of two complementary methods, working on different principles, i.e. a divide-andconquer approach and an evolutionary algorithm, to significantly enhance the accuracy of identification results. While the former reduces the identification problem size, the latter focuses on the improvement of the search effectiveness. Therefore, this strategy is named evolutionary divide-and-conquer strategy. It works by dividing a large system with many unknowns into many smaller systems each with manageable number of unknowns that are more accurately and efficiently identified by an improved genetic algorithm (GA). The GA search capability is significantly improved through adopting multiple populations with various roles, allowing both global and local searches to be conducted simultaneously. v Summary The first application of the proposed strategy focuses on identification for large structural systems. The large structures are sequentially decomposed into many smaller parts, called substructures, to be identified independently. One of the key issues to be resolved in the identification of a substructure is to appropriately account for interaction effects at the interface degrees of freedom of that substructure. This strategy does by directly using acceleration measurements and without employing velocity and displacement measurements. The effectiveness of the proposed strategy is illustrated on numerical simulation as well as experimental model tests of a 10storey steel structure. Numerical simulation study is carried out first for a seismically excited 20-storey shear building that is coupled to two adjacent buildings by two link bridges, and then for a larger structure of 100 degrees of freedom (DOFs). Results show that even with limited measurement data under 10% noise, the identified stiffness and mass parameters are relatively accurate with mean error of less than 3%. Results in the experimental study are also achieved with mean error of less than 4% and maximum error of less than 8% for the identification of a 7-storey substructure using only acceleration measurements. The proposed strategy is further developed for ‘output-only’ identification problems where the excitation forces within the substructures of interest are immeasurable. The same structural systems as above are examined. Although the input force data are not available and output acceleration responses are contaminated by 10% noise, the proposed strategy still achieves results with mean error of less than 3% for identified stiffness parameters. The viability of the proposed output-only strategy is also experimentally substantiated by identifying a 5-storey substructure of the steel frame. Besides achieving mean error of less than 6% and maximum error of less than 10% in vi Summary the identified stiffness of this substructure, the identified force agrees very well with the excitation force measured. In the context of structural health monitoring, the proposed strategy is applied for identifying damages in critical parts of large structures, commonly known as local damage quantification. Numerical studies are presented for the aforementioned 100DOF system and a long-span continuous truss. In addition, damages to the steel frame in the experimental study are accurately identified for various substructures. In order to illustrate the versatility of the proposed strategy, moving force identification in time domain is studied. The proposed strategy identifies forces moving across a road bridge by recursively decomposing the force time histories in a series of time subdomains in which the initial displacement of a bridge and force values are identified simultaneously. The accuracy of the proposed method is shown to be very good even when all response measurements are contaminated with 10% noise. The effects of axle spacing of vehicles and number of measurement points on the accuracy of identified results are also investigated. In conclusion, this study has developed an evolutionary divide-and-conquer strategy that is able to accurately and effectively identify physical parameters for large structural systems, even for the more challenging cases where the excitation forces on the structures are immeasurable. By means of substructural identification, damages at critical parts of these large structures are detected and quantified by comparing changes in key stiffness parameters. Finally, this strategy is successfully modified and applied for identification of moving forces in time domain. vii Tables List of Tables Table 2.1. GA parameters used for the known-mass and unknown-mass systems in the numerical simulation.  Table 2.2. Absolute error in identified stiffness of 20-DOF known-mass system.  Table 2.3. Absolute error in identified stiffness of 100-DOF unknown-mass system.  Table 2.4. Absolute error in identified mass of 100-DOF unknown-mass system.  Table 2.5. Measured storey stiffness values from static test in the experimental study.  Table 2.6. Accelerometer specification.  Table 2.7. GA parameters used for identification in the experiment.  Table 2.8. Identified storey stiffness values and corresponding errors of substructures to with complete measurements in the experimental study.  Table 2.9. Calculated and identified lumped mass results (kg) of the 10-storey steel frame with complete measurements in the experimental study.  Table 2.10. Absolute identification error (%) of stiffness values of substructure with incomplete measurements in the experimental study.  Table 3.1. Absolute error in identified stiffness of 20-DOF system using only output acceleration responses.  Table 3.2. Absolute error in identified stiffness of 100-DOF system using only output acceleration responses.  Table 3.3. Absolute error in identified stiffness of 10-storey frame model using only output acceleration responses in the experiment.  Table 4.1. Local damage quantification results in a substructure (storeys 60 to 67) of a 100-storey shear building with known input forces (damage 10% at storeys 62, 63 and 20% at storey 66).  Table 4.2. Local damage quantification results in a substructure (storeys 60 to 68) of a 100-storey shear building with unknown input forces (damage 10% at storey 63 and 20% at storey 66).  Table 4.3. Local damage quantification results in a mid-span substructure of a longspan continuous truss with unknown input forces (damage 10% and 20% at member 11).  Table 4.4. Damage scenarios considered in the experimental study.  viii Chapter 7. Conclusions and Future Work Chapter Conclusions and Future Work 6.1 Conclusions The primary objective of this study is to develop a robust and efficient identification strategy for large systems, based on a divide-and-conquer approach and an improved genetic algorithm. The strategy is named evolutionary divide-and-conquer strategy. It works by dividing a large system with many unknowns into many smaller systems with manageable number of unknowns that are identified by an improved genetic algorithm. First, the strategy has been applied for identifying the structural parameters of large structural systems. The large structures are decomposed into many smaller parts, called substructures. Hence, the proposed strategy can be referred to as substructural identification (SSI). The interaction effect at the interface DOFs of a substructure is ingeniously accounted for by directly using only measured accelerations and without resorting measured velocities and displacements. Its performance is illustrated on a seismically excited 20-storey shear building that is coupled to two adjacent buildings by link bridges. Its robustness and effectiveness is further assessed on a larger system of 100-storey shear buildings with unknown mass information (involving 202 unknowns). The results for the large structure are quite accurate. Based on incomplete acceleration measurements contaminated by 10% noise, both mass and stiffness parameters are accurately identified with mean error of less than 3%. The results also show that substructural identification directly using acceleration responses to account for the interaction effect at the interface DOFs yield more accurate identification 134 Chapter 7. Conclusions and Future Work results than those using relative acceleration responses. It is also found that for large and unknown mass structural systems, substructural identification gives much better results than complete structural identification. This finding is further confirmed in the experimental study. The good performance of SSI is again substantiated by achieving very good experimental results (mean error of less than 3%) for the identification of a 7-storey substructure using only sensors. The proposed strategy has successfully and effectively identified the physical parameters of large structural systems. Nevertheless, in reality there are situations where the measurement of input forces is difficult or even impossible for large structures. Thus, the SSI strategy is further developed to deal with this challenge. The SSI strategy is adapted to identify simultaneously stiffness and damping parameters as well as input forces. This is done ingeniously by adopting a predictor-corrector algorithm to correct the output response of internal (within substructure) accelerations, velocities, and displacements that are predicted using numerical integration. As the identification is carried out based on acceleration (output) responses only, this adapted SSI strategy can be called output-only substructural identification. Of course, a tradeoff of output-only SSI is that the mass values have to be determined or reasonably assumed. The results demonstrate that the output-only SSI strategy successfully identifies structural parameters not only in the numerical simulation but also in the experimental study. Using incomplete acceleration measurements with 10% noise in the numerical simulation, stiffness parameters of a 100-storey shear building are accurately achieved with mean absolute error of less than 2%. To attain the small error for this large structure just using acceleration responses is a remarkable feat thus far. Moreover, since the computation of input force is model based, and the structural model does not perfectly match the system, the experimental results are expectedly 135 Chapter 7. Conclusions and Future Work less accurate. Nevertheless, it is found that the output SSI strategy gives good result. Using only acceleration measurements, the identified stiffness value for a 5-storey substructure is very close to the measured stiffness with mean absolute error of less than 6%. The ability to identify a substructure, requiring no input measurement and thus eliminating the adverse effect of input measurement error, represents a significant step forward to local damage detection that is discussed in the next paragraph. In addition, the proposed strategy allows for appropriate force estimation that could be useful information for structural heath monitoring as well as help to verify the input parameters assumed in the design. The key advantage of substructural identification is capable of identifying each structural part independently. Therefore, it is particularly effective to apply SSI to quantify any damages at critical areas of large structures, so called local damage quantification. Damage that is manifested as a change in the stiffness of structural members, is localized and quantified by using acceleration responses and input excitation force within the considered substructure, or even more difficult by using only acceleration responses and without input force information. The local damage quantification strategy is numerically verified on a 100-storey shear building and a long-span continuous truss, and is further tested experimentally on a 10-storey steel frame model. Damage identification capability is indeed well demonstrated. Moreover, the experimental studies provide important insight of its performance as follows: - Not only a single damage but also multiple damages with some adjacent to one another are accurately detected and quantified at each specific area 136 Chapter 7. Conclusions and Future Work independently. The damage extent of a single damage is more accurately identified than that of multiple damages. - The accuracy of the identification results of many damages, taking place adjacent to one another with different magnitudes, can be improved by utilizing more acceleration measurements. - Damages taking place outside the substructure considered not significantly affect its damage identification result. - The accuracy of damage results is verified through identifying damages in various substructures. - The magnitude of true damage always exceeds that of maximum false damage by a reasonable margin (about twice). Finally, the versatility of the evolutionary divide-and-conquer strategy is demonstrated by applying it, in a different way, to identify interaction forces between a bridge and moving vehicles based on measured dynamic responses. Special attention is given to reducing the fluctuations at the start and end of force time histories where identification error tends to be high. To improve numerical efficiency, the strategy works by dividing the force time histories into a number of time sub-domains in which the initial displacement and force values are identified by means of a improved GA. It is found that the identified time histories closely match the exact time histories and the error of results are much smaller than that of published results. In particular, the problem of large fluctuations at both ends of the identified force time histories is significantly mitigated. 137 Chapter 7. Conclusions and Future Work In conclusion, a robust identification strategy based on a divide-and-conquer approach and an improved genetic algorithm has been developed in this thesis. This strategy is successfully applied for the identification of the structural parameters of large structures up to 202 unknowns, and for the quantification of local damages at critical areas in large structures, as well as for the identification of moving interaction forces between a bridge and moving vehicles, based on limited and noise contaminated acceleration measurements. 6.2 Recommendations for Future Work Based on the experimental and numerical simulation results obtained, some potential areas for further investigation and application of the evolutionary divide-and-conquer identification strategy are highlighted as below. - The proposed strategy generally succeeds in identifying the structural parameters for large structures by dividing it into many substructures. While large shear buildings and truss structures are studied in the content of this thesis, plate and shell structures have not been investigated. Therefore, it is highly recommended that future studies should apply this strategy to these specific structures. Moreover, an important consideration when applying SSI to identify these large structures is the selection of an appropriate substructure size. Based on this work, it is suggested that the number of unknowns for each substructure should not exceed 50. - It would be also interesting to apply output-only substructural identification to tackle current challenges in the identification of offshore structures such as jack-up platforms, where the measurement of wave forces acting on jack-up legs is very costly and even infeasible. The stiffness of each individual leg and 138 Chapter 7. Conclusions and Future Work the fixity between spud-can foundation and seabed would provide valuable information not only for designing a new jack-up but also for monitoring many existing ones around oceans. 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(2000), Substructural Identification Using Neural Networks. Computers and Structures 77(1): 41-52. Yun, C.-B. and Lee, H.-J. (1996), Damage Estimation Using Substructural Identification in Time Domain, Worcester, MA, USA, ASCE. Yun, C.-B., Yi, J.-H. and Bahng, E. Y. (2001), Joint Damage Assessment of Framed Structures Using a Neural Networks Technique. Engineering Structures 23(5): 425435. Zapico, J. L., Worden, K. and Molina, F. J. (2001), Vibration-Based Damage Assessment in Steel Frames Using Neural Networks. Smart Materials and Structures 10(3): 553-559. Zhang, S. and Zhang, F. (2005), Modified Genetic Algorithm and Its Application in the Structural Optimization Design. Journal of Mechanical Strength 27(6): 766-9. Zhang, Y., Liu, B., Zhu, C., Dong, J. and Li, Y. (2006), Improved Fibonacci Genetic Algorithm for Structural Optimization with Discrete Variables. Journal of Mechanical Strength 28(1): 55-60. Zhou, L., Wu, S. and Yang, J. N. (2008), Experimental Study of an Adaptive Extended Kalman Filter for Structural Damage Identification. Journal of Infrastructure Systems 14(1): 42-51. Zhu, X. Q. and Law, S. S. (2001), Orthogonal Function in Moving Loads Identification on a Multi-Span Bridge. Journal of Sound and Vibration 245(2): 329345. Zhu, X. Q. and Law, S. S. (2002), Moving Loads Identification through Regularization. Journal of Engineering Mechanics 128(9): 989-1000. 147 Publications Resulting from this Research Publications Resulting from this Research Koh, C. G. and Thanh, T. N. (2009). Challenges and Strategies in Using Genetic Algorithms for Structural Identification. Soft Computing in Civil and Structural Engineering. B. H. V. Topping and Y. Tsompanakis. Stirlingshire, UK, Saxe-Coburg Publications: 203-226. (Book chapter). Koh, C. G., Thanh, T. N. and Perry, M. J. (2009), Structural Damage Quantification for Disaster Management. International conference on Disaster Mitigation and Management, Dingdigul, India. (Keynote paper). Koh, C. G. and Thanh, T. N. (2010), Output-only Substructural Identification for Local Damage Detection. The Fifth International Conference on Bridge Maintenance, Safety and Management, Philadelphia, Pennsylvania, USA. Wang, X. M., Koh, C. G., Thanh, T. N. and Zhang, J. (2010), System Identification of Jack-up Platform by Spectral Analysis. Proceedings of the ASME 29th International Conference on Ocean, Offshore and Arctic Engineering, June 6-11, 2010, Shanghai, China, OMAE 2010-20627. Zhang, J., Koh, C. G., Wang X. M., Thanh T. N. and Zhang Z. (2010), Output-only Substructural Identification of Jack-up Spudcan Fixity. In proceedings of the IV European Conference on Computational Mechanics, Paris, France, 16-21. Thanh, T. N. and Koh, C. G. (2009), Substructural Identification for Health Monitoring of Large Structures. The 22th KKCNN Symposium on Civil Engineering, Chiangmai, Thailand, 19-24. Zhang, J., Thanh, T. N., Wang, X. M., Koh, C. G. and Zhang, Z. (2009), Substructural Identification of Jack-up Spudcan Fixity Using an Improved Genetic Algorithm. The 22th KKCNN Symposium on Civil Engineering, Chiangmai, Thailand, 25-28. Thanh, T. N., Koh, C. G. and Choo, Y. S. (2009), Identification of Spudcan Fixity for a Jack-Up Rig. The 28th International Conference on Ocean, Offshore, and Arctic Engineering, Honolulu, Hawaii, USA. Thanh, T. N., Koh, C. G. and Choo, Y. S. (2007), Multiple Moving Dynamic Force Identification using Time Sub-domain Genetic Algorithm Method. The 20th KKCNN Symposium on Civil Engineering, Jeju, Korea, 203-206. Thanh, T. N., Perry, M. J. and Koh, C. G. (2007), Moving Force Identification: A Time Sub-domain Genetic Algorithm Approach. The 6th International Workshop on Structural Health Monitoring, Stanford University, Stanford, CA, USA, 1399-1407. Koh, C. G. and Trinh, T. N. (2011), Structural Damage Detection by Substructure Identification: Experimental Verification. The Sixth International Structural Engineering and Construction Conference, Zürich, Switzerland. (accepted). 148 Publications Resulting from this Research Papers under review and in preparation to submit to journals Trinh, T. N. and Koh, C. G., Improved Substructural Identification Strategy for Large Structural Systems. Structural Control and Health Monitoring (under the second review). Trinh, T. N. and Koh, C. G., Output-only Substructural Identification Strategy: Numerical and Experimental Study. To submit to Computers & Structures in Dec. 2010. Trinh, T. N. and Koh, C. G., Local Damage Detection using Substructural Identification. To submit to Journal of Structural Engineering, ASCE in Jan 2011. Trinh, T. N., Koh, C. G. and Perry, M. J., Time Sub-domain for Moving Force Identification. To submit to Journal of Structural Health Monitoring in Mar. 2011. Zhang, J., Koh, C.G., Trinh, T.N., Wang, X.M., Zhang, Z., Time Domain Output-only Substructural Identification of Jackup Spudcan Fixity using an Enhanced Genetic Algorithm. To submit to Journal of Marine Structures in Feb. 2011. 149 [...]... able to track the variation of stiffness parameters, leading to the detection of structural damage For the identification of nonlinear structural systems, Meiliang and Smyth (2007) applied an unscented Kalman filter (UKF) (Julier et al 1995) to deal with the identification of highly nonlinear systems They compared the applicability of both EKF and UKF for nonlinear structural identification Simulation... procedure.  Figure 5.3 Identified moving forces for 5% noise: (a) force 1; (b) force 2; (c) total force; simulated force: continuous line; identified force: dash line  Figure 5.4 Identified moving force 1 for 10% noise: (a) 6 m axle spacing; (b) 10 m axle spacing; simulated force: continuous line; identified force: dash line.  Figure 5.5 Identified moving force 2 for 10% noise: (a) 3 measuring points;... and in the unfortunate events, result in structural failures From the viewpoint of functionality and safety, it is therefore essential to have means of detecting and quantifying structural damage In the past decade, some of the noteworthy efforts in SHM have been published in special issues of various journals such as Journal of Engineering Mechanics (Ghanem and Sture 2000; Bernal and Beck 2004), and. .. as substructural identification (SSI) While system identification is applied to determine structural properties, the input identification is employed to evaluate dynamic excitation forces on a structural system This identification also plays an important role to evaluate the performance of structural systems In this study, the input identification is applied to evaluate vehiclebridge interaction forces. .. Table 5.4 Relative errors (%) of identified moving forces for different axle spacings.  Table 5.5 Relative errors (%) of identified moving forces for different number of measurement points.  ix Figures List of Figures Figure 1.1 (a) Direct analysis; (b) system identification; (c) input identification.   Figure 1.2 A layout of backpropagation neural network.  Figure 1.3 A ‘standard’ genetic algorithm layout. ... advance of computer power in recent years, the non-classical methods, particularly genetic algorithms developed on Darwin’s theory for survival of the fittest, have received most attention The subsequent section provides the overview and discussion of identification methods that have been often used for identifying structural systems and moving forces 1.2 Literature Review It is important to understand... important to understand the strengths and weaknesses of many identification methods having been proposed prior to presenting a new identification strategy in this thesis In fact, there are so many methods developed for identification of structural systems and moving forces that it would be impossible to give a complete review 5 Chapter 1 Introduction However, identification methods can be generally... interaction forces based on known structural properties and measured output information of a bridge Thus, this identification is commonly termed as moving force 4 Chapter 1 Introduction identification Moving force identification is an important inverse problem in the civil and structural engineering field It is an effective way to better understand the interaction between the bridge and vehicles traversing it,... soft computing approach has been successfully used in civil engineering such as construction scheduling and structural optimization (Jiaping and Chee Kiong 1995; Yang and Soh 1997; Ye et al 2000; Zhang and Zhang 2005; Zhang et al 2006) Nevertheless, in the context of identification of structural system or moving forces with more challenging issues (such as multiple unknowns, presence of I/O noise and. .. identification of input information based on given output information and known system parameters (Figure 1.1c) While the former identification is commonly termed as system identification, the latter is sometimes known as input identification Both system and input identifications have been applied to electrical, mechanical and control engineering systems However, their application to structural engineering systems . EVOLUTIONARY DIVIDE- AND- CONQUER STRATEGY FOR IDENTIFICATION OF STRUCTURAL SYSTEMS AND MOVING FORCES TRINH NGOC THANH NATIONAL UNIVERSITY OF SINGAPORE. EVOLUTIONARY DIVIDE- AND- CONQUER STRATEGY FOR IDENTIFICATION OF STRUCTURAL SYSTEMS AND MOVING FORCES TRINH NGOC THANH B.Eng. (HCMUT) A THESIS SUBMITTED FOR. Input Force 109 4.4 Chapter Summary 113 Chapter 5 Evolutionary Divide- and- Conquer Strategy for Moving Force Identification in Time Domain 115 5.1 Moving Force Formulation 116 5.2 Moving Force