Abstract
This work details the Bayesian identification of a nonlinear dynamical system using a novel MCMC algorithm: ‘Data Annealing’. Data Annealing is similar to Simulated Annealing in that it allows the Markov chain to easily clear ‘local traps’ in the target distribution. To achieve this, training data is fed into the likelihood such that its influence over the posterior is introduced gradually - this allows the annealing procedure to be conducted with reduced computational expense. Additionally, Data Annealing uses a proposal distribution which allows it to conduct a local search accompanied by occasional long jumps, reducing the chance that it will become stuck in local traps. Here it is used to identify an experimental nonlinear system. The resulting Markov chains are used to approximate the covariance matrices of the parameters in a set of competing models before the issue of model selection is tackled using the Deviance Information Criterion.
Highlights
This paper is concerned with the system identification of a nonlinear dynamical system using experimentally obtained training data
A probabilistic, Bayesian approach is utilised throughout. Such an approach is well established in the structural dynamics community – relatively recent advances include the use of Bayesian methods in structural health monitoring [1], modal identification [2], state-estimation [3], the sensitivity analysis of large bifurcating nonlinear models [4] as well as an interesting study investigating the relations between frequentist and Bayesian approaches to probabilistic parameter estimation [5]
One of the main aims of the current paper is to present a relatively cheap annealing algorithm which, within the context of Bayesian inference, can be applied to computationally demanding models
Summary
This paper is concerned with the system identification of a nonlinear dynamical system using experimentally obtained training data. A probabilistic, Bayesian approach is utilised throughout Such an approach is well established in the structural dynamics community – relatively recent advances include the use of Bayesian methods in structural health monitoring [1], modal identification [2], state-estimation [3] (through use of the particle filter), the sensitivity analysis of large bifurcating nonlinear models [4] as well as an interesting study investigating the relations between frequentist and Bayesian approaches to probabilistic parameter estimation [5]. Using Bayes' theorem a measure of the plausibility of a parameter vector θ, given experimental data D and assumed model structure M, is given by PðθjD; MÞ 1⁄4 PðDjθ; MÞPðθjMÞ. The likelihood represents the probability that the experimental training data D was witnessed according to the model M with parameters θ.
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