Geometry of the failure set (system events) : impact on the efficiency of simulation methods, adaptations of some standard methods

Abstract

System events (intersection or union of events - failure or safety domains) are of frequent interest in Structural Reliability, even for simple structures that are not mechanical systems. Intersections can be found when taking into account information about the structural state (conditional probability of failure). These events may result in irregular shapes of the failure set, and this may impact seriously the efficiency of the standard versions of the sampling methods used for reliability assessment.

Such a situation appeared in the penstock reliability assessments recently performed at EDF, where annual, potentially conditional, failure probabilities are calculated. Simple or double intersection events had to be considered for this, resulting in two kinds of failure set geometries : narrow strips and high curvature limit state surfaces (LSS). To handle these cases, a specific method was developed : the FISTARR method based on FORM-IS (importance sampling around a relevant U* point). As a complement, line sampling was also investigated and proved to be successful on this use case, provided an appropriate multiple root search algorithm was used. These methods are shortly presented in this paper.

However, for some penstock configurations these methods may converge slowly or not, and possible improvements were investigated. For doing this, idealized cases were considered, corresponding to the afore mentioned geometries : narrow strip and high curvature LSS. The last one was represented by two intersecting lines.

This article presents the investigations performed on these two toy cases.

For the two intersecting lines, the effect of the curvature (due to the angle between the two lines) on the efficiency of the sampling methods considered (FORM-IS and Line Sampling among others) is presented. As these methods can be seen as corrections of the FORM approximation, the effect of curvature (through an acute angle) is high, especially for line sampling which is particularly performant for linear LSS, and comes from the curvature itself, not from the probability reduction. For FORM-IS, an efficient improvement is to reduce the standard deviation of the multinormal density in relevant way depending on the curvature. Moreover, a combination of line sampling with importance sampling with an optimized density (LS-IS) proved to be very efficient.

For the narrow strip, the standard multinormal importance density was replaced by a density centered on the medium line between the two strip boudaries, leading to considerable computational time reduction. This improvement is being integrated into the EDF internal software for penstock reliability assessments, Persalys-Penstock.