System characterisation and identification of non-linear systems (with particular reference to hysteretic systems)

Abstract

System identification is the process of building mathematical models of dynamical systems based on observed data. Many effective techniques have been developed for linear systems. For non-linear systems, some progress has been achieved, but techniques for practical use and which can deal with a large class of systems are limited. In particular few identification techniques have been found in the literature which can be applied to hysteretic systems. This thesis is devoted to the development of a system identification technique which can be applied to a relatively large class of non-linear systems, including hysteretic systems. The key to this technique is to select an appropriate subset of the state vector describing the system and generate a non-linear surface in this subspace which characterises the non-linearity. For non-hysteretic systems, this space is the normal state space. For hysteretic systems, the selection of the appropriate space usually needs some prior knowledge about the system. The procedure involves estimating the non-linear component as a function of time. This is approached via a deconvolution method, and a section of this thesis shows how an optimal deconvolution method may be used. The method of creating the surface is described, and identification is then conducted by analysing and fitting the surface. The success of identification is obviously affected by the quality of the surface, which is, in turn, affected by factors such as the type and the level of the excitation, the frequency range and the magnitude of the spectrum of the process, and errors in the signal processing. These problems are discussed in the application of this technique to several simulated non-linear systems (including both non-hysteretic and hysteretic types) and also to the practical case of a cable type vibration isolator.

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