A novel method for non-parametric identification of nonlinear restoring forces in nonlinear vibrations from noisy response data: A conservative system

Abstract

A novel procedure is proposed to identify the functional form of nonlinear restoring forces in the nonlinear oscillatory motion of a conservative system. Although the problem of identification has a unique solution, formulation results in a Volterra-type of integral equation of the "first" kind: the solution lacks stability because the integral equation is the "first" kind. Thus, the new problem at hand is ill-posed. Inevitable small errors during the identification procedure can make the prediction of nonlinear restoring forces useless. We overcome the difficulty by using a stabilization technique of Landweber's regularization in this study. The capability of the proposed procedure is investigated through numerical examples.

A Numerical Investigation on Nonparametric Identification of Nonlinear Roll Damping Moment of a Ship from Transient Response~!2009-08-29~!2009-09-05~!2010-02-08~!

“…In fact, a direct discretization of the right hand side of Eq. 8results in a matrix in which the condition number is extremely large so that the numerical inverse of the matrix does not work because the determinant of the matrix is nearly zero [10,18,[20][21][22][23][24][25][26]. In order to overcome the difficulty of the numerical instability, a regularization method (i.e., stabilization technique) is introduced.…”

“…The solution ( ) x t to the integral equation (8) can be obtained by the following iteration, known as Landweber's regularization [10,11,18,[20][21][22][23]27]…”

Simultaneous detection of the nonlinear restoring and excitation of a forced nonlinear oscillation: an integral approach

“…The nonlinear oscillators are well studied by many researchers for instant see [8][9][10][11][12][13][14][15][16] and references therein. A valuable investigation has been conducted to detect the parameters from noisy data for forced nonlinear oscillators [17][18][19][20][21][22][23][24] and provides base for the new exploration in area of inverse problems.…”

A numerical scheme for recovering the nonlinear characteristics of a single degree of freedom structure: non-parametric system identification

“…In the last two decades, there has been a lot of research work on the subject of dynamic system identification conducted by Masri et al [1], Chassiakos and Masri [2], Liang et al [3,4], Spina et al [5], Iourtchenko and Dimentberg [6], and others [7][8][9][10][11][12][13][14][15][16][17]. However, most of this research has identified the nonlinear characteristics of either damping or the restoring force.…”