Developing an Instantaneous Response Surface Method t-IRS for Time-Dependent Reliability Analysis

Abstract

In practical engineering, many uncertain factors in loading or degradation of material properties may vary with time. Stochastic process modeling constitutes a suitable approach for describing these time-dependent uncertainties. By adopting this approach, however, the time-dependent reliability calculation is a great challenge owing to the complexity and the huge computational burden. This paper presents a new instantaneous response surface method t-IRS for time-dependent reliability analysis. Different from the adaptive extreme response surface approach, the proposed method does not need to build and update surrogate models separately at each time node. It first uses the expansion optimal linear estimation method to discretize the stochastic processes into a set of independent standard normal variables together with some deterministic functions of time. Time is then treated as an independent one-dimensional variable. Next, initial samples are generated by Latin hypercube sampling, and the corresponding response values are calculated and utilized to construct an instantaneous response surrogate model of the Kriging type. The active learning method is applied to update the Kriging surrogate model until satisfactory accuracy is achieved. Finally, the instantaneous response surrogate model is used to compute the time-dependent reliability via Monte Carlo simulation. Four case studies are utilized to demonstrate the effectiveness of the t-IRS method for time-dependent reliability analysis.