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.

中文翻译：

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基于动力辨识的正则化参数选取准则比较研究

对逆问题的研究广泛存在于航空航天、机械、识别、检测、扫描成像等领域。它的不适定特性往往会导致逆问题的求解出现较大的振荡。在这项研究中，截断广义奇异值分解（TGSVD）方法被引入识别两种移动力，单轴力和多轴力。截断点是TGSVD影响最大的正则化参数，它最初由两个经典的正则化参数选择标准选择，即L曲线标准和广义交叉验证（GCV）标准。由于移动力识别 (MFI) 中的数值非唯一性和噪声干扰，数值模拟结果表明，这两种标准都不能有效地帮助选择TGSVD的最佳截断点。因此，提出了一个相对百分比误差（RPE）标准来选择TGSVD的截断点。对比研究表明，相对于GCV准则和L曲线准则，RPE准则可以更准确地选择TGSVD的最佳截断点。此外，RPE 准则可用于反映某些性质与 MFI 中存在的不适定问题之间的联系，在 TGSVD 的最佳截断点选择中应优先采用。对比研究表明，相对于GCV准则和L曲线准则，RPE准则可以更准确地选择TGSVD的最佳截断点。此外，RPE 准则可用于反映某些属性与 MFI 中存在的不适定问题之间的联系，在 TGSVD 的最佳截断点选择中应优先采用。对比研究表明，相对于GCV准则和L曲线准则，RPE准则可以更准确地选择TGSVD的最佳截断点。此外，RPE 准则可用于反映某些性质与 MFI 中存在的不适定问题之间的联系，在 TGSVD 的最佳截断点选择中应优先采用。