Genetic Algorithm Based Tikhonov Regularization Method for Displacement Reconstruction

doi:10.1007/s12204-019-2060-z

Abstract

Abstract: In this paper, a genetic algorithm based Tikhonov regularization method is proposed for determination of globally optimal regularization factor in displacement reconstruction. Optimization mathematic models are built by using the generalized cross-validation (GCV) criterion, L-curve criterion and Engl’s error minimization (EEM) criterion as the objective functions to prevent the regularization factor sinking into the locally optimal solution. The validity of the proposed algorithm is demonstrated through a numerical study of the frame structure model. Additionally, the influence of the noise level and the number of sampling points on the optimal regularization factor is analyzed. The results show that the proposed algorithm improves the robustness of the algorithm effectively, and reconstructs the displacement accurately.

Key words: genetic algorithm| Tikhonov regularization| displacement reconstruction| inverse problem| parameter optimization

摘要： In this paper, a genetic algorithm based Tikhonov regularization method is proposed for determination of globally optimal regularization factor in displacement reconstruction. Optimization mathematic models are built by using the generalized cross-validation (GCV) criterion, L-curve criterion and Engl’s error minimization (EEM) criterion as the objective functions to prevent the regularization factor sinking into the locally optimal solution. The validity of the proposed algorithm is demonstrated through a numerical study of the frame structure model. Additionally, the influence of the noise level and the number of sampling points on the optimal regularization factor is analyzed. The results show that the proposed algorithm improves the robustness of the algorithm effectively, and reconstructs the displacement accurately.

关键词: genetic algorithm| Tikhonov regularization| displacement reconstruction| inverse problem| parameter optimization

CLC Number:

TN 911.7

PENG Zhen (彭真), YANG Zhilong (杨枝龙), TU Jiahuang* (涂佳黄). Genetic Algorithm Based Tikhonov Regularization Method for Displacement Reconstruction[J]. Journal of Shanghai Jiao Tong University (Science), 2019, 24(3): 294-298.

References 12

[1]	LEE H S, HONG Y H, PARK HW. Design of an FIRfilter for the displacement reconstruction using measuredacceleration in low-frequency dominant structures[J]. International Journal for Numerical Methodsin Engineering, 2010, 82(4): 403-434.
[2]	TURCO E. A strategy to identify exciting forces actingon structures [J]. International Journal for NumericalMethods in Engineering, 2005, 64(11): 1483-1508.
[3]	TURCO E. Load distribution modelling for pin-jointedtrusses by an inverse approach [J]. Computer Methodsin Applied Mechanics and Engineering, 1998, 165(1):291-306.
[4]	WEBER B, PAULTRE P, PROULX J. Structuraldamage detection using nonlinear parameter identificationwith Tikhonov regularization [J]. Structural Controland Health Monitoring, 2007, 14(3): 406-427.
[5]	ROWLEY C, GONZALEZ A, OBRIEN E, et al.Comparison of conventional and regularized bridgeweigh-in-motion algorithms [C]//Proceedings of InternationalConference on Heavy Vehicles. Paris, France:John Wiley, 2008: 271-282.
[6]	GE X F. Research on displacement response reconstructionand machinery error processing [D]. Hefei,China: School of Engineering and Science, Universityof Science and Technology of China, 2014 (in Chinese).
[7]	PANDA S S, JENA G, SAHU S K. Image super resolutionreconstruction using iterative adaptive regularizationmethod and genetic algorithm [J]. ComputationalIntelligence in Data Mining, 2015, 2: 675-681.
[8]	OH S Y, KWON S J. Preconditioned GL-CGLSmethod using regularization parameters chosen fromthe global generalized cross validation [J]. Journal ofthe Chungcheong Mathematical Society, 2014, 27(4):675-688.
[9]	TURCO E. A strategy to identify exciting forces actingon structures [J]. International Journal for NumericalMethods in Engineering, 2005, 64(11): 1483-1508.
[10]	WU I M, BIAN S F, XIANG C B, et al. A new methodfor TSVD regularization truncated parameter selection[J]. Mathematical Problems in Engineering, 2013,2013: 161834.
[11]	ENGL HW. Discrepancy principles for Tikhonov regularizationof ill-posed problems leading to optimal convergencerates [J]. Journal of Optimization Theory andApplications, 1987, 52(2): 209-215.
[12]	LUO Y, LIU T L, TAO D C. Decomposition-basedtransfer distance metric learning for Image classification[J]. IEEE Transactions on Image Processing, 2014,23(9): 3789-801.

[1]	ZHANG Cong, SHU Bingnan, ZHANG Jiangtao, JIN Yong. Multi-Objective Optimization Design of Ship Propulsion Shafting Based on Response Surface Methodology and Genetic Algorithm [J]. Journal of Shanghai Jiao Tong University, 2025, 59(4): 466-475.
[2]	SUN Dongyi, PU Yuting, ZHANG Jianbang. Target Assignment Method of Air Defense Missile Based on GA-BP Neural Network [J]. Air & Space Defense, 2025, 8(1): 62-70.
[3]	LU Qingchang, LIU Peng, QIN Han, XU Pengcheng. Optimization of Road Network Recovery Decisions Considering Road Section Recovery Differences [J]. Journal of Shanghai Jiao Tong University, 2024, 58(7): 1118-1129.
[4]	XIONG Jingyi, HU Weijun, YIN Wei, ZHANG Weijie, YANTao. Research on Collaborative Optimization Decision Algorithm for Multi-Missile Clusters [J]. Air & Space Defense, 2024, 7(3): 86-93.
[5]	SUN Qianyang, ZHOU Li, DING Shifeng, LIU Renwei, DING Yi. An Artificial Neural Network-Based Method for Prediction of Ice Resistance of Polar Ships [J]. Journal of Shanghai Jiao Tong University, 2024, 58(2): 156-165.
[6]	ZHONG Kexing, DING Lesheng, ZHANG Cong, MAO Yandong, CHEN Jinlong. Optimization Design of Marine cable of Wind Farm Bend Restrictor Based on Neural Network [J]. Ocean Engineering Equipment and Technology, 2024, 11(1): 70-76.
[7]	ZHAO Zhibin, LUO Bin, TANG Ting, WANG Chunfang, SUN Zhonghua. Improved Self-Excited Resonant Wireless Power Transmission System [J]. Journal of Shanghai Jiao Tong University, 2023, 57(7): 859-867.
[8]	JIANG Ruimin, WANG Xuanling, ZHANG Mingen, ZHAO Bin. An Anti-ship Missile Route Planning Method Based on Quantum Genetic Algorithm [J]. Air & Space Defense, 2023, 6(4): 31-34.
[9]	XIA Yunsong, TAN Jianfeng, HAN Shui, GAO Jin’e. Optimization of Wind Turbine Vortex Generator Based on Back Propagation Neural Network [J]. Journal of Shanghai Jiao Tong University, 2023, 57(11): 1492-1500.
[10]	YAN Qing, LU Jiansha, JIANG Weiguang, SHAO Yiping, TANG Hongtao, LI Yingde. Path Optimization of Stacker in Compact Storage System with Dual-Port Layout [J]. Journal of Shanghai Jiao Tong University, 2022, 56(7): 858-867.
[11]	WANG Xiaojian, HONG Jun, CHEN Jinghua, LI Hongguang. Weight Reduction Study of Box Structure Based on Parametric Modeling and Response Surface Optimization [J]. Air & Space Defense, 2022, 5(4): 60-66.
[12]	ZHOU Tianyan, FENG Xiaoen, FAN Yunfeng, DONG Shiyin, LI Yuqing, JIN Huizhong. Optimization Model of Ground Air Defense Force Deployment to Avoid Excessive Air Defense Firepower [J]. Air & Space Defense, 2022, 5(4): 19-23.
[13]	LIU Jiea (刘洁), ZHANG Baojib∗ (张宝吉). Multiobjective Optimization of Hull Form Based on Global Optimization Algorithm [J]. J Shanghai Jiaotong Univ Sci, 2022, 27(3): 346-355.
[14]	ZHANG Mingzhu(张明珠), MA Yixin* (马艺馨), HUANG Ningning (黄宁宁), GE Hao (葛浩). Survey of EIT Image Reconstruction Algorithms [J]. J Shanghai Jiaotong Univ Sci, 2022, 27(2): 211-218.
[15]	WANG Zhuoxin, ZHAO Haitao, XIE Yuehan, REN Hantao, YUAN Mingqing, ZHANG Boming, CHEN Ji’an. Prediction of Modulus of Composite Materials by BP Neural Network Optimized by Genetic Algorithm [J]. Journal of Shanghai Jiao Tong University, 2022, 56(10): 1341-1348.