Treating Epistemic Uncertainty Using Bootstrapping Selection of Input Distribution Model for Confidence-Based Reliability Assessment

Abstract

To accurately predict the reliability of a physical system under aleatory (i.e., irreducible) uncertainty in system performance, a very large number of physical output test data is required. Alternatively, a simulation-based method can be used to assess reliability, but it remains a challenge as it involves epistemic (i.e., reducible) uncertainties due to imperfections in input distribution models, simulation models, and surrogate models. In practical engineering applications, only a limited number of tests are used to model input distribution. Thus, estimated input distribution models are uncertain. As a result, estimated output distributions, which are the outcomes of input distributions and biased simulation models, and the corresponding reliabilities also become uncertain. Furthermore, only a limited number of output testing is used due to its cost, which results in epistemic uncertainty. To deal with epistemic uncertainties in prediction of reliability, a confidence concept is introduced to properly assess conservative reliability by considering all epistemic uncertainties due to limited numbers of both input test data (i.e., input uncertainty) and output test data (i.e., output uncertainty), biased simulation models, and surrogate models. One way to treat epistemic uncertainties due to limited numbers of both input and output test data and biased models is to use a hierarchical Bayesian approach. However, the hierarchical Bayesian approach could result in an overly conservative reliability assessment by integrating possible candidates of input distribution using a Bayesian analysis. To tackle this issue, a new confidence-based reliability assessment method that reduces unnecessary conservativeness is developed in this paper. In the developed method, the epistemic uncertainty induced by a limited number of input data is treated by approximating an input distribution model using a bootstrap method. Two engineering examples are used to demonstrate that 1) the proposed method can predict the reliability of a physical system that satisfies the user-specified target confidence level and 2) the proposed confidence-based reliability is less conservative than the one that fully integrates possible candidates of input distribution models in the hierarchical Bayesian analysis.