Global Sensitivity Analysis of Discontinuous Responses Using Domain Decomposition

In this paper, the problem of identifying the influence of random parameters, also known as global sensitivity analysis (GSA), of stochastic responses exhibiting discontinuity is tackled. Although there are many studies related to GSA of continuous responses, GSA for discontinuous responses has not been studied previously. To this end, an adaptive approach is presented that involves decomposing the parameter space into disjoint subdomains in which the response is locally continuous. It involves spectral clustering to label the data in the first step, followed by constructing the support vector machines (SVM) for classification and domain decomposition. Gaussian Process models are then utilized for function approximation in local subdomains so that the GSA can be performed efficiently. The GSA has been performed with both variance-based and moment-independent methods. Furthermore, a new weighted measure for GSA is presented to account for the overall variation of the response and discontinuities appropriately. The proposed approach was applied to analytical problems and an engineering non-linear sink problem exhibiting discontinuity of varying nature. The new weighted measure was found to be consistent in identifying the influential random parameter. Furthermore, the estimation of weighted global sensitivity with the adaptive approach is computationally efficient and yielded similar results as that of a large number of Monte Carlo simulations.