Comparative studies on the criteria for regularization parameter selection based on moving force identification

Abstract

The studies on inverse problems exist extensively in aerospace, mechanical, identification, detection, scanning imaging and other fields. Its ill-posed characteristics often lead to large oscillations in the solution of the inverse problem. In this study, the truncated generalized singular value decomposition (TGSVD) method is introduced to identify two kinds of moving forces, single and multi-axial forces. The truncating point is the most influential regularization parameter of TGSVD, which is initially selected by two classic regularization parameter selection criteria, namely, the L-curve criterion and the generalized cross-validation (GCV) criterion. Due to numerical non-uniqueness and noise disturbance in moving force identification (MFI), numerical simulation results show that neither of the two criteria can effectively help select the optimal truncating point of TGSVD. Hence, a relative percentage error (RPE) criterion is proposed for selecting the truncating point of TGSVD. Comparative studies show that the RPE criterion can be used to select the optimal truncating point of TGSVD more accurately against the GCV criterion and L-curve criterion. Moreover, the RPE criterion can be used to reflect the connections between certain properties and the ill-posedness problem existing in MFI, which should be adopted priority for the optimal truncating point selection of TGSVD.