An Optimization-Based Framework for Nonlinear Model Selection and Identification

Abstract

This paper proposes an optimization-based framework to determine the type of nonlinear model present and identify its parameters. The objective in this optimization problem is to identify the parameters of a nonlinear model by minimizing the differences between the experimental and analytical responses at the measured coordinates of the nonlinear structure. The application of the method is demonstrated on a clamped beam subjected to a nonlinear electromagnetic force. In the proposed method, the assumption is that the form of nonlinear force is not known. For this reason, one may assume that any nonlinear force can be described using a Taylor series expansion. In this paper, four different possible nonlinear forms are assumed to model the electromagnetic force. The parameters of these four nonlinear models are identified from experimental data obtained from a series of stepped-sine vibration tests with constant acceleration base excitation. It is found that a nonlinear model consisting of linear damping and linear, quadratic, cubic, and fifth order stiffness provides excellent agreement between the predicted responses and the corresponding measured responses. It is also shown that adding a quadratic nonlinear damping does not lead to a significant improvement in the results.

Linear Control of a Nonlinear Equipment Mounting Link

“…To estimate and optimise the unknown parameters of the system, the optimisationbased framework is used by comparing the measured experimental data with the numerically simulated response of the system in the frequency domain. The objective function is defined to minimise the output error of the mathematical model of the system [23].…”

“…To acquire the dynamics of the nonlinear systems, the modified complex averaging technique (MCXA), finite element modelling (FEM), and arc-length continuation were utilised. A previously developed optimisation based framework (OBF) [23] was also employed on the cantilever beam, where the results were compared with those from the EDSM technique. It was found that the EDSM techniques were sensitive to any inaccuracies, but the resultant response may be employed as the initial parameter estimate for the OBF, lending to a more accurate representation of the response.…”

On the sensitivity of the equivalent dynamic stiffness mapping technique to measurement noise and modelling error

“…Besides, an additional section (Section 5 -Identification Using Optimization) has been added to the paper. In this section, an optimization-based framework proposed by Taghipour et al [22] is used to identify the nonlinear force of the cantilever beam studied in the paper. The main objective of using this method is to eliminate the necessity for the usage of expansion method to estimate the response at the unmeasured coordinates.…”

“…The literature has an extensive range of identification approaches such as the force-state mapping technique, the restoring force surface method, the Hilbert transform, Bayesian system identification, Volterra series approximation, optimization-based identification approach, and the Equivalent Dynamic Stiffness Mapping technique [10][11][12][13][14][15][16][17][18][19][20][21][22][23]. Some methods assume the type of the nonlinearity is pre-known, and others do not rely on this assumption.…”

“…Using a combination of time and frequency domain techniques, Haroon et al [21] presented a method to identify nonlinear systems in the absence of input measurements. Taghipour et al [22] proposed an optimizationbased identification approach in order to avoid different sources of error in the identification process. According to this framework, it is not necessary to have complete measurement of the response at all coordinates.…”