On evolutionary system identification with applications to nonlinear benchmarks

K. Worden,T.J. Rogers,G. Manson,R.J. Barthorpe,E.J. Cross,N. Dervilis,G.R. Holmes

doi:10.1016/j.ymssp.2018.04.001

K. Worden, T.J. Rogers + Show 5 more

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https://doi.org/10.1016/j.ymssp.2018.04.001

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Abstract

Abstract This paper presents a record of the participation of the authors in a workshop on nonlinear system identification held in 2016. It provides a summary of a keynote lecture by one of the authors and also gives an account of how the authors developed identification strategies and methods for a number of benchmark nonlinear systems presented as challenges, before and during the workshop. It is argued here that more general frameworks are now emerging for nonlinear system identification, which are capable of addressing substantial ranges of problems. One of these frameworks is based on evolutionary optimisation (EO); it is a framework developed by the authors in previous papers and extended here. As one might expect from the ‘no-free-lunch’ theorem for optimisation, the methodology is not particularly sensitive to the particular (EO) algorithm used, and a number of different variants are presented in this paper, some used for the first time in system identification problems, which show equal capability. In fact, the EO approach advocated in this paper succeeded in finding the best solutions to two of the three benchmark problems which motivated the workshop. The paper provides considerable discussion on the approaches used and makes a number of suggestions regarding best practice; one of the major new opportunities identified here concerns the application of grey-box models which combine the insight of any prior physical-law based models (white box) with the power of machine learners with universal approximation properties (black box).

Highlights

In March of 2016, an interesting meeting on the subject of nonlinear system identification (NLSI) took place at Vrije Universiteit Brussel (VUB) in the Belgian capital
Many of the insights here have come from machine learning work, along with very powerful parameter estimation and model structure detection techniques from the Mechanical and Electrical Engineering communities; this synergy is precisely what the VUB workshop was intended to expose
Apart from serving as a baseline and allowing the practitioner to decide if the extra complexity of a nonlinear ID is justified, the linear SI process is capable of highlighting the point at which a linear system approximation is no longer capable of reproducing the actual system behaviour to within some degree of error

Summary

Introduction

In March of 2016, an interesting meeting on the subject of nonlinear system identification (NLSI) took place at Vrije Universiteit Brussel (VUB) in the Belgian capital. As the current authors had already developed a successful evolutionary approach to BW system identification [15], the opportunity was taken to focus on two methodological issues: benchmarking the identification with a linear model, and choosing appropriate (if not optimal) excitation signals for the generation of training data. This benchmark presents a Wiener-Hammerstein (WH) electronic circuit where the main challenge results from high process noise, which is the dominant noise distortion [45]. It is comparable to the approach presented here, it requires more hyperparameters to be selected by the user

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Discussion

Conclusion