Importance Sampling for Time-Variant Reliability Analysis

Jian Wang,Zhili Sun,Runan Cao

doi:10.1109/access.2021.3054470

Abstract

Importance sampling methods are extensively used in time-independent reliability analysis. However, the kind of methods is barely studied in the field of time-variant reliability analysis. This article presents an importance sampling method for time-variant reliability analysis. It increases the probability of sampling failure trajectories of a time-variant performance function. To develop the method, the instantaneous performance function at a predefined time instant is regarded as a time-independent one. A time-independent importance sampling is first implemented on the instantaneous performance function in order to obtain instantaneous samples of stochastic processes and random variables. Then, conditional trajectories of stochastic processes are generated on the condition of instantaneous samples achieved above, which utilizes the correlationship among instantaneous uncertainties at different time instants associated with stochastic processes. Subsequently, trajectories of the time-variant performance function are obtained. Validation results show that comparing with crude Monte Carlo simulation, the proposed method remarkably increases the probability of sampling failure trajectories. The efficiency and accuracy of the proposed method are demonstrated.

Highlights

Uncertainties in geometric dimensioning, material properties and loads have drawn significant attention in the design of mechanical structures or systems
Time-independent importance sampling (IS) method is implemented on the instantaneous limit state surface at a predefined time instant in order to obtain instantaneous samples of stochastic processes and random variables
The number of failure trajectories of the time-variant performance remarkably increases comparing to crude Monte Carlo simulation (MCS) with the same size of random population

Summary

INTRODUCTION

Uncertainties in geometric dimensioning, material properties and loads have drawn significant attention in the design of mechanical structures or systems. To handle problems involving time-consuming codes, the idea of surrogate model-based methods for time-independent reliability analysis is usually adopted. Hu and Mahadevan [39] modified the learning function U which was initially proposed for timeindependent reliability analysis to adapt time-variant reliability analysis [40] and developed a single-loop Kriging surrogate modeling method. Time-independent IS method is implemented on the instantaneous limit state surface at a predefined time instant in order to obtain instantaneous samples of stochastic processes and random variables. The instantaneous samples of stochastic processes at the time instant are used to generate conditional trajectories of the stochastic processes at the rest of instants By this way, the number of failure trajectories of the time-variant performance remarkably increases comparing to crude MCS with the same size of random population. This article uses a set of correlated random variables to model {Z (m)(t)}

DISCRETIZATION OF STOCHASTIC PROCESSES

MCS FOR TIME-VARIANT RELIABILITY ANALYSIS

VALIDATION OF THE PROPOSED METHOD

CONCLUSION