Non-intrusive imprecise stochastic simulation by line sampling

The non-intrusive imprecise stochastic simulation (NISS) is a general framework for the propagation of imprecise probability models and analysis of reliability. The most appealing character of this methodology framework is that, being a pure simulation method, only one precise stochastic simulation is needed for implementing the method, and the requirement of performing optimization analysis on the response functions can be elegantly avoided. However, for rare failure events, the current NISS methods are still computationally expensive. In this paper, the classical line sampling developed for precise stochastic simulation is injected into the NISS framework, and two different imprecise line sampling (ILS) methods are developed based on two different interpretations of the classical line sampling procedure. The first strategy is devised based on the set of hyperplanes introduced by the line sampling analysis, while the second strategy is developed based on an integral along each individual line. The truncation errors of both methods are measured by sensitivity indices, and the variances of all estimators are derived for indicating the statistical errors. A test example and three engineering problems of different types are introduced for comparing and demonstrating the effectiveness of the two ILS methods.