Efficient numerical simulation method for evaluations of global sensitivity analysis with parameter uncertainty

• Variance based sensitivity as integration problem for epistemic variable is derived.
• Direct sampling based procedure for the evaluation of sensitivity is given.
• A novel improved importance sampling (IS) method is proposed.
• An improved IS based procedure for efficient evaluation of sensitivity is proposed.

In this study, we propose an efficient numerical simulation method for structural systems with both epistemic and aleatory uncertainties to evaluate the effect of epistemic uncertainty on the failure probability measured by variance-based sensitivity analysis. The direct evaluation of this effect requires a “triple-loop” crude sampling procedure, which is time consuming. To circumvent the difficulty associated with the direct sampling-based procedure, we first construct an improved importance sampling (IS) method and an improved IS-based procedure is proposed for the efficient evaluation of the effect of epistemic uncertainty. The core of the proposed method is to construct the same IS probability density function for the failure probability corresponding to an individual realization of epistemic uncertainty. Using the proposed improved IS-based method, only one IS run with a set of input–output IS samples is needed to determine the estimated values of the effects for all epistemic uncertainties. Several examples are employed to demonstrate the feasibility of the proposed method for different situations. These examples demonstrate that the proposed method can obtain reasonably accurate results with fewer evaluations of the performance function compared with other existing methods.