Nonlinear dynamical system identification using the sparse regression and separable least squares methods. (4th August 2021)

• Record Type: Journal Article
• Authors: Lin, Miaomiao; Cheng, Changming; Peng, Zhike; Dong, Xingjian; Qu, Yegao; Meng, Guang
• Is Part Of: Journal of sound and vibration. Volume 505(2021)
• Publication Date: 2021-08-04
• Subjects: Nonlinear dynamical system identification -- Sparse regression -- Separable least squares method -- Reproducing Kernel Hilbert Space; Sound -- Periodicals; Vibration -- Periodicals; Son -- Périodiques; Vibration -- Périodiques; Sound; Vibration; Periodicals; Electronic journals; 620.205
• DOI: 10.1016/j.jsv.2021.116141
• Languages: English
• ISSNs: 0022-460X

Abstract

Abstract: This paper proposes a novel nonlinear dynamical system identification method based on the sparse regression algorithm and the separable least squares method. To effectively avoid solving the second derivative of the displacement signal and reduce the effect of noise, the Duhamel's integral is adopted to represent the dynamic relationship between the system input and output. In the expression form of Duhamel's integral, nonlinear dynamical system identification can be cast as a separable least squares problem. Thus, the separable least squares method is leveraged to separately identify the parameters of the linear subsystem and the coefficients corresponding to nonlinearities among the nonlinear dynamical system. During the identification process of nonlinear restoring forces, one complete set of nonlinear basis functions are used to represent the nonlinear restoring forces. Not all the candidate nonlinear terms are contributing, however, thus the sparse regression algorithm is adopted to select the actual contributing nonlinear components in the candidate nonlinear terms and eliminate the non-contributing nonlinear components, and then the corresponding parameters of contributing nonlinear components are estimated by the unbiased least squares method. Finally, one RKHS (Reproducing Kernel Hilbert Space)-based non-parametric de-noise method is further proposed to reduce the noise in the vibration displacement and obtain the noise-reduced velocity from the displacement signal. The numerical simulation about the identification of the rotating blade-casing system and the dynamic experiment of the HSLDS (high-static-low-dynamic stiffness) isolator system verify the effectiveness of the new identification method for nonlinear dynamical systems proposed in this paper.