Improved Tikhonov regularization method for load identification and structural response reconstruction

To improve the accuracy and efficiency of load identification and structural response reconstruction, an improved Tikhonov regularization method that simultaneously considers transfer matrix error and measurement error was proposed. Firstly, the state space equation and transfer matrix were constructed through the structural dynamics model to obtain the reconstruction equation of the structural load and response. Secondly, the truncated randomized singular value decomposition method was used to calculate the approximate transfer matrix at the locations of the measurement points, while the total least squares method (TLSM) and the traditional Tikhonov regularization method were combined to identify the load, and then the unknown response was reconstructed by the transfer matrix at the locations. Finally, a numerical simulation and an experimental analysis were carried out for two-dimensional truss and simply supported beam to verify the proposed method. The results show that compared with the traditional Tikhonov regularization method, the proposed method can improve the reconstruction efficiency while guaranteeing the reconstruction accuracy.