A method for non-parametric identification of non-linear vibration systems with asymmetric restoring forces from a resonant decay response

Abstract

A method for non-parametric identification of systems with asymmetric non-linear restoring forces is proposed in this paper. The method, named the zero-crossing method for systems with asymmetric restoring forces (ZCA), is an extension of zero-crossing methods and allows identification of backbones, damping curves and restoring elastic and dissipative forces from a resonant decay response. The validity of the proposed method is firstly demonstrated on three simulated resonant decay responses of the systems with off-centre clearance, bilinear and quadratic stiffness. Then, the method is applied to experimental data from a micro-electro-mechanical resonator in order to quantify its non-linear damping and stiffness effects. Throughout the paper the proposed method is also compared with the Hilbert vibration decomposition to demonstrate that the ZCA yields more accurate results with much less effort.

Reconstruction of Governing Equations from Vibration Measurements for Geometrically Nonlinear Systems

“…x(t) = f(x(t)) (1) where x(t) represents the state of the system at time t and the nonlinear function f(x(t)) represents the dynamic constraints that define the equation of motion of the system. The function f often consists only of a few terms, making it sparse in the space of possible functions.…”

“…, trigonometric functions, and other terms. Each column of Θ(X) represents a candidate function for the right-hand side of Equation (1). Only a few of these functions are active in each row of f, so a regression problem is set up to determine the vector of coefficients Ξ = [ξ 1 , ξ 2 , ξ 3 , .…”

“…x k = f k (x) in Equation (1). Once Ξ has been determined, the reconstructed set of each row of governing equations can be read directly from it .…”

“…In recent decades, the impelling need to monitor and supervise machine and structures operations has led to an increasing usage of sensors and measuring equipment. Time varying data are analyzed and processed to obtain high fidelity models able to describe and ideally predict the system behavior under varying excitations and boundary conditions [1][2][3][4][5]. To this end, many strategies have been developed for system identifications generally based on linear theory, such as modal analysis [6][7][8].…”

Recovery of Differential Equations from Impulse Response Time Series Data for Model Identification and Feature Extraction

“…1. Model identification, model validation and model updating for control and numerical simulation, mostly performed during the product development phase [1][2][3][4].…”