The Bhattacharyya distance: Enriching the P-box in stochastic sensitivity analysis

© 2019 Elsevier Ltd The tendency of uncertainty analysis has promoted the transformation of sensitivity analysis from the deterministic sense to the stochastic sense. This work proposes a stochastic sensitivity analysis framework using the Bhattacharyya distance as a novel uncertainty quantification metric. The Bhattacharyya distance is utilised to provide a quantitative description of the P-box in a two-level procedure for both aleatory and epistemic uncertainties. In the first level, the aleatory uncertainty is quantified by a Monte Carlo process within the probability space of the cumulative distribution function. For each sample of the Monte Carlo simulation, the second level is performed to propagate the epistemic uncertainty by solving an optimisation problem. Subsequently, three sensitivity indices are defined based on the Bhattacharyya distance, making it possible to rank the significance of the parameters according to the reduction and dispersion of the uncertainty space of the system outputs. A tutorial case study is provided in the first part of the example to give a clear understanding of the principle of the approach with reproducible results. The second case study is the NASA Langley challenge problem, which demonstrates the feasibility of the proposed approach, as well as the Bhattacharyya distance metric, in solving such a large-scale, strong-nonlinear, and complex problem