Identifying the stiffness and damping of a nonlinear system using its free response perturbed with Gaussian white noise

Abstract

Measurement uncertainty can affect the accuracy of estimating parameters of vibrating systems. This article is concerned with the development of a method for estimating parameters from the free vibration response of a nonlinear system in which the response signal is contaminated with Gaussian white noise. The backbone curve and envelope of the response are first estimated from the free vibration signal. An algorithm based on the Bayesian approach is then used to identify the stiffness and damping parameters of a nonlinear system excited at a single resonant frequency. A numerical example is provided to illustrate the proposed method, which is then applied to the experimental data from a nonlinear vibration absorber system that was excited at its first resonant frequency. The proposed approach provides the distribution and confidence intervals of the parameter estimates, which is an improvement on methods that provide a single number for each estimate. As the signal-to-noise ratio decreases, the variances of the posterior distributions increase as do the confidence intervals, reflecting greater uncertainty in the parameter estimates. The approach is effective provided that the signal-to-noise ratio is greater than about 10.

A Comparative Study of Parameter Identification Methods for Asymmetric Nonlinear Systems with Quadratic and Cubic Stiffness

“…The derivatives of the envelope, instantaneous frequency, and displacement should be obtained for the damping force curve method, so the result is disturbed by noise easily. A proper filter can be used to deal with the influence of the noise, and the Bayesian approach is a good way to measure the uncertainty of the identification results [ 29 ].…”

“…Cenedese and Haller [ 26 ] summarized approaches for constructing backbone curves of multi-degree-of-freedom systems. There are many applications to identify parameters using backbone curves, such as base-excited SDOF system [ 27 ], vibration absorber [ 28 , 29 ], beam-shaker system [ 30 ], aircraft wing structure [ 31 ], linear–arch composite beam piezoelectric energy harvester [ 32 ]. In addition to traditional contact measurement methods, non-contact measurement methods, such as video processing, can also be used to identify the backbone curves of an air wing prototype [ 33 ].…”

Dynamic Response of Asymmetric and Nonlinear Packaging System under Random Excitation

“…e piecewise programs are considering in Runge-Kutta calculation steps. irdly, the Monte Carlo approach, which was first proposed by Metropolis et al [29] and generalized by Hastings [30], is used to solve complex integrals [31]. e technology roadmap of numerical simulation process is shown in Figure 3, and afterwards the comparisons between the theoretical solution and numerical result can be given.…”

Characterizing the nonlinear behavior of viscoelastic materials: A Bayesian approach combining oberst beam experiments and digital-twin simulations

“…The key idea is to measure the backbone curves from free responses and thereafter relate these to a stochastic parametric model. Similar approaches to the one adopted are reported in experimental applications involving vibration absorbers [25,26], mechanical systems with geometric nonlinearities [27], and assembled structures [28,29,30]. When considering the Oberst beam, however, estimating backbone curves from resonance decay responses with nonlinear parametric approximations lack contributions.…”