Genetic Algorithm Based Tikhonov Regularization Method for Displacement Reconstruction
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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.
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.
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.
引文
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[8]OH S Y,KWON S J. Preconditioned GL-CGLS method using regularization parameters chosen from the global generalized cross validation[J].Journal of the Chungcheong Mathematical Society, 2014,27(4):675-688.
[9]TURCO E.A strategy to identify exciting forces acting on structures[J].International Journal for Numerical Methods i-n Engineering,2005,64(11):1483-1508.
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[11]ENGL H W.Discrepancy principles for Tikhonov regularization of ill-posed problems leading to optimal convergence rates[J].Journal of Optimization Theory and Applications,1987,52(2):209-215.
[12]LUO Y,LIU T L,TAO D C.Decomposition-based transfer distance metric learning for Image classification[J].IEEE Transactions on Image Processing,2014,23(9):3789-801.
[2]TURCO E.A strategy to identify exciting forces acting on structures[J].International Journal for Numerical Methods in Engineering,2005,64(11):1483-1508.
[3]TURCO E.Load distribution modelling for pin-jointed trusses by an inverse approach[J].Computer Methods in Applied Mechanics and Engineering, 1998,165(1):291-306.
[4]WEBER B,PAULTRE P,PROULX J.Structural damage detection using nonlinear parameter identification with Tikhonov regularization[J].Structural Control and Health Monitoring,2007,14(3):406-427.
[5]ROWLEY C,GONZALEZ A,OBRIEN E,et al.Comparison of conventional and regularized bridge weigh-in-motion algorithms[C]//Proceedings of International Conference on Heavy Vehicles.Paris,France:John Wiley,2008:271-282.
[6]GE X F.Research on displacement response reconstruction and machinery error processing[D].Hefei,China:School of Engineering and Science,University of Science and Technology of China,2014(in Chinese).
[7]PANDA S S,JENA G,SAHU S K.Image super resolution reconstruction using iterative adaptive regularization method and genetic algorithm[J].Computational Intelligence in Data Mining,2015,2:675-681.
[8]OH S Y,KWON S J. Preconditioned GL-CGLS method using regularization parameters chosen from the global generalized cross validation[J].Journal of the Chungcheong Mathematical Society, 2014,27(4):675-688.
[9]TURCO E.A strategy to identify exciting forces acting on structures[J].International Journal for Numerical Methods i-n Engineering,2005,64(11):1483-1508.
[10]WU I M,BIAN S F,XIANG C B,et al.A new method for TSVD regularization truncated parameter selection[J].Mathematical Problems in Engineering,2013,2013:161834.
[11]ENGL H W.Discrepancy principles for Tikhonov regularization of ill-posed problems leading to optimal convergence rates[J].Journal of Optimization Theory and Applications,1987,52(2):209-215.
[12]LUO Y,LIU T L,TAO D C.Decomposition-based transfer distance metric learning for Image classification[J].IEEE Transactions on Image Processing,2014,23(9):3789-801.