Nonlinear identification in structural dynamics based on Wiener series and Kautz filters

Abstract

The present paper proposes a method to identify localized nonlinear parameters in structural dynamics using vibration data. The approach is based on the identification of the first and second-order Volterra kernels in an orthogonal basis, namely Wiener kernels, while taking the experimental data as exact values. The focus is to identify an already localized nonlinearity with known structure. An optimization procedure is implemented using a metric involving the difference between the experimental kernel and the simulated orthogonal kernel from model updating, which is function of the unknown nonlinear parameters. In order to reduce the problems of convergence, the Kautz filter is used to decrease the number of samples to estimate. The proposed methodology is illustrated on a numerical example using a cantilever beam and its advantages and drawbacks are discussed in detail.

Nonlinear features identified by Volterra series for damage detection in a buckled beam

“…Details about the Kautz functions and how to use it for nonlinear mechanical systems identification can be found in [7] and [5]. It is important to see that the order of projection B η i 1 , .…”

Identification of nonlinear mechanical systems: Comparison between Harmonic Probing and Volterra-Kautz methods

“…The first approach is a white box modeling and the solution is computed by the harmonic probing algorithm using the Fourier transform of the Votlerra kernels known as higher-order frequency response functions (HOFRFs) [1,3,9]. The second one uses the discrete-time Volterra series expanded onto orthonormal Kautz basis [4,7,8]. Thus, the goal of the present paper is to evaluate and to compare both methods seeking further applications of structural dynamics.…”

“…More information about Kautz filters structure and their applicability can be found in [4,7,8] . The Kautz filters parameters are obtained minimizing the normalized mean square error function (NMSE):…”

Identification of Hammerstein MIMO systems using the key-term separation principle

“…In general, various identification algorithms can be applied for various engineering applications [18], [19], [20], including chemical engineering [21], [22], biological engineering [23], [24], electrical engineering [25], [26], adaptive control [27], [28], [29] and so on [30], [31], [32]. For example, Lü and Ren proposed a non-iterative identification algorithm for Hammerstein systems in presence of asymmetric deadzone nonlinearities [33].…”