Bayesian inversion for imprecise probabilistic models using a novel entropy-based uncertainty quantification metric

Abstract

• Bayesian inversion techniques under mixed uncertainty are addressed. • A novel entropy-based uncertainty quantification metric is proposed. • An approximate Bayesian approach is developed for stochastic model updating. • A discretized binning algorithm is employed to reduce the computational cost. • Both static and dynamic case studies are demonstrated for validation. Uncertainty quantification metrics have a critical position in inverse problems for dynamic systems as they quantify the discrepancy between numerically predicted samples and collected observations. Such metric plays its role by rewarding the samples for which the norm of this discrepancy is small and penalizing the samples otherwise. In this paper, we propose a novel entropy-based metric by utilizing the Jensen–Shannon divergence. Compared with other existing distance-based metrics, some unique properties make this entropy-based metric an effective and efficient tool in solving inverse problems in presence of mixed uncertainty (i.e. combinations of aleatory and epistemic uncertainty) such as encountered in the context of imprecise probabilities. Implementation-wise, an approximate Bayesian computation method is developed where the proposed metric is fully embedded. To reduce the computation cost, a discretized binning algorithm is employed as a substitution of the conventional multivariate kernel density estimates. For validation purpose, a static case study is first demonstrated where comparisons towards three other well-established methods are made available. To highlight its potential in complex dynamic systems, we apply our approach to the NASA LaRC Uncertainty Quantification challenge 2014 problem and compare the obtained results with those from 6 other research groups as found in literature. These examples illustrate the effectiveness of our approach in both static and dynamic systems and show its promising perspective in real engineering cases such as structural health monitoring in conjunction with dynamic analysis.