Research on Dynamic Load Identification Based on Explicit Wilson-θ and Improved Regularization Algorithm

Shock and Vibration, Mar 2019

In the research of dynamic load identification, the method of obtaining kernel function matrix is usually rather cumbersome. To solve this problem, an explicit dynamic load identification algorithm based on the Wilson-θ (DLIAEW) method is proposed to easily obtain the kernel function matrix as long as the parameters of the system are known. To aim at the ill-posed problem in the inverse problem, this paper improves the Tikhonov regularization, proposes an improved regularization algorithm (IRA), and introduces the U-curve method to determine the regularization parameters. In the numeric simulation investigation of a four dofs vibrating system, effects of the sampling frequency and the noise level on the regularization parameters and the identification errors of impact and harmonic loads for the IRA are discussed in comparison with the Tikhonov regularization. Finally, the experiments of a cantilever beam excited by impact and harmonic loads are carried out to verify the advantages of the IRA.

A PDF file should load here. If you do not see its contents the file may be temporarily unavailable at the journal website or you do not have a PDF plug-in installed and enabled in your browser.

Alternatively, you can download the file locally and open with any standalone PDF reader:

http://downloads.hindawi.com/journals/sv/2019/8756546.pdf

Research on Dynamic Load Identification Based on Explicit Wilson-θ and Improved Regularization Algorithm

Research on Dynamic Load Identification Based on Explicit Wilson-θ and Improved Regularization Algorithm Yuchuan Fan, Chunyu Zhao, and Hongye Yu School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110819, China Correspondence should be addressed to Chunyu Zhao; nc.ude.uen.liam@oahzyhc Received 8 November 2018; Revised 23 January 2019; Accepted 28 January 2019; Published 25 March 2019 Academic Editor: Nerio Tullini Copyright © 2019 Yuchuan Fan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract In the research of dynamic load identification, the method of obtaining kernel function matrix is usually rather cumbersome. To solve this problem, an explicit dynamic load identification algorithm based on the Wilson-θ (DLIAEW) method is proposed to easily obtain the kernel function matrix as long as the parameters of the system are known. To aim at the ill-posed problem in the inverse problem, this paper improves the Tikhonov regularization, proposes an improved regularization algorithm (IRA), and introduces the U-curve method to determine the regularization parameters. In the numeric simulation investigation of a four dofs vibrating system, effects of the sampling frequency and the noise level on the regularization parameters and the identification errors of impact and harmonic loads for the IRA are discussed in comparison with the Tikhonov regularization. Finally, the experiments of a cantilever beam excited by impact and harmonic loads are carried out to verify the advantages of the IRA. 1. Introduction Load identification plays an important role in many engineering studies, such as reliability analysis, fault diagnosis, and health monitoring of mechanical power structures [1, 2]. Dynamic load identification methods include the frequency-domain method and the time-domain method [3]. Compared with the time-domain method, the study of dynamic load identification in the frequency domain starts earlier, and the theory is more mature. The frequency-domain method determines the dynamic force spectrum according to the relation between the transfer function matrix and the response spectrum of the system, or calculates the dynamic characteristics of the modal force in the frequency domain after the modal coordinate transformation [4]. The time-domain method is the inverse analysis based on the complex convolution relation between the load and the response, and the temporal history of dynamic loads is retrieved directly in the time domain. The time-domain method does not need Fourier transform, the result is intuitionistic, and the research of the time-domain method in recent years also has a great development. Dynamic load identification belongs to an ill-posedness of the inverse problem, which will lead to not useful solutions which cause large deviations from the exact solutions because of measured noise data and the randomness of structural parameters [5, 6]. In recent years, much effort on solving this ill-posed problem has been devoted to overcoming the effects of structural uncertainty and measurement noise and improving the accuracy of dynamic load identification. The effects of matrix ill-conditioning were overcome by using methods such as pseudoinversion of overdetermined matrixes, singular value rejection, singular value decomposition (SVD), and regularization techniques. Through both simulation and experiment on a flat rectangular plate, Thite and Thompson [7–9] proposed an assessment which was made of the success and failure of various strategies for dealing with the problems of ill-conditioning, in particular overdetermination and singular value rejection. Inoue et al. [10] utilized the SVD to locate the small singular values which were eliminated in computation of the frequency response function. Inoue et al. [11], Jacquelin et al. [12], and Adams and Doyle [13] described more systematic approaches of the SVD to solve the reconstruction problems of harmonic and nonharmonic forces. Using shape function to approximate dynamic load, kernel function response, and measured structure response, Liu et al. [14] established a time-domain dynamic Galerkin method (TDGM) to improve the accuracy of the identified dynamic load by taking shape function as the weighting function. Furthermore, they also proposed an efficient interpolation-based method to reduce ill-posedness by discretizing the load history into a series of time elements approximated through interpolation functions [15]. Qiao et al. [16–20] proposed the cubic B-spline collocation method and the sparse deconvolution method to identify impact loads. Through reconstructing the dynamic loads in the deterministic structure of the thin-walled cylindrical shell and airfoil structure, Wang et al. [21] developed a fast convergent iteration regularizat (...truncated)


This is a preview of a remote PDF: http://downloads.hindawi.com/journals/sv/2019/8756546.pdf

Yuchuan Fan, Chunyu Zhao, Hongye Yu. Research on Dynamic Load Identification Based on Explicit Wilson-θ and Improved Regularization Algorithm, Shock and Vibration, 2019, 2019, DOI: 10.1155/2019/8756546