Identification of nonlinear dynamical systems using approximate Bayesian computation based on a sequential Monte Carlo sampler

The Bayesian approach is well recognised in the structural dynamics community as an attractive approach to deal with parameter estimation and model selection in nonlinear dynamical systems. In the present paper, one investigates the potential of approximate Bayesian computation employing sequential Monte Carlo (ABC-SMC) sampling [1] to solve this challenging problem. In contrast to the classical Bayesian inference algorithms which are based essentially on the evaluation of a likelihood function, the ABC-SMC uses different metrics based mainly on the level of agreement between observed and simulated data. This alternative is very attractive especially when the likelihood function is complex and cannot be approximated in a closed form. Moreover, this flexibility allows one to use new features from either the temporal or the frequency domains for system identification. To demonstrate the practical applicability of the ABC-SMC algorithm, two illustrative examples are considered in this paper.