Abstract
This paper will introduce the use of the approximate Bayesian computation (ABC) algorithm for model selection and parameter estimation in structural dynamics. ABC is a likelihood-free method typically used when the likelihood function is either intractable or cannot be approached in a closed form. To circumvent the evaluation of the likelihood function, simulation from a forward model is at the core of the ABC algorithm. The algorithm offers the possibility to use different metrics and summary statistics representative of the data to carry out Bayesian inference. The efficacy of the algorithm in structural dynamics is demonstrated through three different illustrative examples of nonlinear system identification: cubic and cubic-quintic models, the Bouc-Wen model and the Duffing oscillator. The obtained results suggest that ABC is a promising alternative to deal with model selection and parameter estimation issues, specifically for systems with complex behaviours.
Highlights
In many areas of engineering and science, researchers or engineers are dealing with model selection and comparison issues, in particular when several competing models are consistent with the selection criteria and could potentially explain the data reasonably well
It has been demonstrated that the approximate Bayesian computation (ABC)-sequential Monte Carlo (SMC) algorithm is an excellent way to deal with model selection and parameter estimation issues with some advantages over traditional Bayesian methods in the specific circumstances described in this paper
The ABC-SMC algorithm has several very useful properties: (i) ease of implementation, (ii) generality of application and (iii) the ability to deal with model selection for larger numbers of models in a straightforward way
Summary
In many areas of engineering and science, researchers or engineers are dealing with model selection and comparison issues, in particular when several competing models are consistent with the selection criteria and could potentially explain the data reasonably well. The use of the approximate Bayesian computation (ABC) algorithm is introduced as a promising alternative to deal with model selection and parameter estimation. In structural dynamics with complex nonlinearity types, it is often the case that the hypothesis of Gaussianity is not guaranteed Another major advantage offered by the ABC algorithm is its independence of the dimensionality of the competing models; ABC jumps between the different model spaces without the need of any mapping function to be defined, which is a major benefit in dealing with larger numbers of models. The widespread use of ABC in several fields, and its efficiency to deal with model selection and parameter estimation, simultaneously motivated the current authors to investigate more the capability of the ABC to infer complex nonlinear systems in structural dynamics. The paper is closed with some conclusions about the strengths of the ABC method and future work
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