Linear and Nonlinear System Identification Using Evolutionary Optimisation

While system identification of linear systems is largely an established body of work encoded in a number of key references (including textbooks), nonlinear system identification remains a difficult problem and tends to rely on a "toolbox" of methods with no generally accepted canonical approach. Fairly recently, methods of parameter estimation using evolutionary optimisation have emerged as a powerful means of identifying whole classes of systems with nonlinearities which previously proved to be very difficult, e.g. systems with unmeasured states or with equations of motion nonlinear in the parameters. This paper describes and illustrates the use of evolutionary optimisation methods (specifically the self-adaptive differential evolution (SADE) algorithm) on a class of single degree-of-freedom (SDOF) dynamical systems with hysteretic nonlinearities. The paper shows that evolutionary identification also has some desirable properties for linear system identification and illustrates this using data from an experimental multi-degree-of-freedom (MDOF) system.