Moving Force Identification Based On Truncated Singular Value Decomposition Regularization Improved Method

Moving force identification belongs to the inverse problem of structural dynamics,which can be used for monitoring of bridge structures and safety performance evaluation during operation period.Based on the theory of structural dynamics,the mapping relationship between the dynamic response of the bridge and the moving force on the bridge deck can be established.Then the moving force identification（MFI）can be transformed into the solution of linear equations by the time domain method with the response of the bridge.Due to the vehicle-bridge system matrix is usually super large sparse matrix and the typical ill-posed characteristics of existing is MFI,it is usually the difficulty to obtain accurate identification results by time domain method.Truncated singular value decomposition（TSVD）can improve the robustness and ill-posed problems of the identification method by truncating some small singular values,it is bound to the loss of some effective signals,resulting in the phenomenon of“over-fitting”.Therefore,this paper proposes a modified truncated singular value decomposition method（MTSVD）to identify moving force.By extracting effective signals from truncated signals and superimposing it into the original TSVD solution,the MTSVD method can effectively solve the“over-fitting”problem.In order to verify the theoretical correctness of the MTSVD algorithm,numerical simulations are carry out in this paper.The bending moment responses and acceleration responses at different positions of the bridge are measured and random noise is added into the response to simulate the interference of environmental noise.Simulation results show that MTSVD method is significantly improved in terms of robustness and discomfort resistance,which can maintain good identification effect even under the influence of high noise.Especially,the identification accuracy is the highest when the double diagonal matrix₂ is adopted.Truncating point6)is another important parameter of the MTSVD algorithm,which can be selected by the RPE criterion.Under the default condition of the optimal regularization matrix,the influence law of truncating point on the recognition results of TSVD and MTSVD is compared and analyzed from different perspectives.At the same time,the theoretical derivation of the piecewise polynomial truncated singular value decomposition（PP-TSVD）and MTSVD algorithm is compared in detail.Simulation results show that the MTSVD algorithm has higher identification accuracy than the PP-TSVD algorithm.When the noise level increases,the MTSVD algorithm can effectively reduce the increase of identification error,which indicates that the MTSVD algorithm is better than PP-TSVD algorithm in robustness.