Structural source identification using a generalized Tikhonov regularization

Abstract

This paper addresses the problem of identifying mechanical exciting forces from vibration measurements. The proposed approach is based on a generalized Tikhonov regularization that allows taking into account prior information on the measurement noise as well as on the main characteristics of sources to identify like its sparsity or regularity. To solve such a regularization problem efficiently, a Generalized Iteratively Reweighted Least-Squares (GIRLS) algorithm is introduced. Proposed numerical and experimental validations reveal the crucial role of prior information in the quality of the source identification and the performance of the GIRLS algorithm.

Impact-force sparse reconstruction from highly incomplete and inaccurate measurements

“…As λ-0; f l2 converges to the least squares solution H þ y, where H þ ¼ ðH T HÞ À 1 H T is the Moore-Penrose pseudo-inverse of H. Hence, the most important issue in determining the l 2 -norm solution f l2 via Tikhonov regularization is to select an optimal regularization parameter. The L-curve criterion is a powerful method for determining a suitable regularization parameter in many inverse problems without the prior knowledge of noise [7,17,30,32,33]. The L-curve, when it is plotted in a log-log scale, clearly displays a compromise between minimizing the regularized solution norm and minimizing the corresponding residual norm.…”

“…Transfer functions can be determined analytically [5,9,11] numerically [16,18,29,30] or experimentally [10,[12][13][14]. An experiment method using impact testing of experimental modal analysis has the advantage of being applicable to various types of structures.…”

Bayesian source identification using local priors

“…Practically, this leads to impose a positivity constraint on the excitation field to identify, which implies the loss of the phase relationships between the identified sources. Another technique, based on the use of generalized Gaussian laws to reflect prior information on the noise and the sources to identify, has been proposed in [8]. This approach has the advantage to alleviate the positivity constraint and to be flexible enough to identify sources of various types.…”

“…From a mathematical point of view, the solution of the problem is defined as the maximum a posteriori estimate of the posterior distribution. Practically, one seeks the solution of the dual minimization problem, which is solved in an iterative manner using a Generalized Iteratively Reweighted Least-Squares (GIRLS) algorithm [8,10].…”

Sound source identification in a noisy environment based on inverse patch transfer functions with evanescent Green's functions

“…Williams [37] summarized several regularization methods for NAH and showed that the generalized cross-validation (GCV) did not require a knowledge of the noise variance. Aucejo [38] introduced a generalized iteratively reweighted least-squares (GIRLS) algorithm to identify mechanical exciting forces from vibration measurements. One main problem of regularization is the selection of breakpoints of the filter factors.…”