Uncorrelated multi-sources load identification in frequency domain based on improved Tikhonov regularization method

Abstract

Due to ill-conditioned inverse characteristics of linear time invariant dynamic system uncorrelated multi-sources load identification in frequency domain, it have large condition number and errors for classic least-squares of generalization method. In order to overcome these shortcomings, an improved Tikhonov regularization method is put forward in this paper. This method uses minimization maximum relative error of identification multi-sources load as criterion to determine the optimal regularization parameter. At the same time, combination of improved Tikhonov regularization and least square of generalized matrix inverse method can reduce the time overhead of determining the best value of regularization parameter. Only when condition number in a frequency is larger than a threshold value, must the improved Tikhonov regularization is used. Uncorrelated multi-sources vibration load identification in frequency domain results on cylindrical shell simulation datasets shows that this new method works much better than classic least-squares of generalized matrix inverse when measurement noise exists and could basically meet the engineering precision requirement of ± 3 dB.