Sequential Ensemble Monte Carlo Sampler for On-Line Bayesian Inference of Time-Varying Parameter In Engineering Applications

Abstract

Several online identification approaches have been proposed to identify parameters and evolution models of engineering systems and structures when sequential datasets are available via Bayesian inference. In this work, a robust and “tune-free” sampler is proposed to extend one of the Sequential Monte Carlo implementations for the identification of time-varying parameters which can be assumed constant within each set of data collected, but might vary across different sequences of data sets. The proposed approach involves the implementation of the Affine-invariant Ensemble sampler in place of the Metropolis-Hastings sampler to update the samples. An adaptive-tuning algorithm is also proposed to automatically tune the step size of the Affine-invariant ensemble sampler which, in turn, controls the acceptance rate of the samples across iterations. Furthermore, a numerical investigation behind the existence of inherent lower and upper bounds on the acceptance rate, making the algorithm robust by design, is also conducted. The proposed method allows for the offline and online identification of the most probable models under uncertainty. It works independently of the underlying (often unknown) error model. The proposed sampling strategy is first verified against the existing sequential Monte Carlo sampler in a numerical example. Then, it is validated by identifying the time-varying parameters and the most probable model of a non-linear dynamical system using experimental data.