TSVD Regularization-Parameter Selection Method Based on Wilson-θ and Its Application to Vertical Wheel-Rail Force Identification of Rail Vehicles

A parameter-selection method is proposed to improve the accuracy of the truncated singular value decomposition (TSVD) method, which is based on the Wilson-theta method and the principle of minimum response error, for dynamic load identification. First, using the Green kernel-function matrix, the dynamic load-identification model of the multi-degree-of-freedom system is established. Second, the response corresponding to the dynamic load is identified using the Wilson-theta method, and the minimum error between the response and the input response is obtained. Then, the best regularization parameters are obtained, and the dynamic load is identified using the TSVD regularization method. Finally, the SIMPACK dynamic model of a rail vehicle is established. Taking the German high-interference spectrum as the input, the axle-box displacement and the vertical wheel-rail force of each wheelset at speeds of 100, 160, and 200 km/h are simulated. Taking the simulated axle-box displacement response with 0%, 5%, and 10% noise as the input, the proposed load-identification model and regularization-parameter selection method are used to identify the vertical wheel-rail force of a rail vehicle. The effects of different track spectra on the identification results are considered. The results indicate that this method has a high identification accuracy for the wheel-rail vertical dynamic load. With an increase in the vehicle speed, the correlation coefficient for identifying the dynamic load decreases, but the correlation remains strong. At the speed of 200 km/h, when the input response noise level is 0%, the dynamic load identification correlation coefficient is 0.9556, which corresponds to extremely strong correlation. When the input response contains 5% noise, this method has stronger robustness than L-curve method, and the dynamic load identification correlation coefficient is 0.6354, which corresponds to strong correlation. The proposed load-identification model and regularization-parameter selection method have important theoretical and engineering application value for wheel-rail force monitoring and safety assessment of running trains.