Reliability analysis of discrete-state performance functions via adaptive sequential sampling with detection of failure surfaces

The paper presents a new efficient and robust method for rare event probability estimation for computational models of an engineering product or a process returning categorical information only, for example, either success or failure. For such models, most of the methods designed for the estimation of failure probability, which use the numerical value of the outcome to compute gradients or to estimate the proximity to the failure surface, cannot be applied. Even if the performance function provides more than just binary output, the state of the system may be a non-smooth or even a discontinuous function defined in the domain of continuous input variables. In these cases, the classical gradient-based methods usually fail. We propose a simple yet efficient algorithm, which performs a sequential adaptive selection of points from the input domain of random variables to extend and refine a simple distance-based surrogate model. Two different tasks can be accomplished at any stage of sequential sampling: (i) estimation of the failure probability, and (ii) selection of the best possible candidate for the subsequent model evaluation if further improvement is necessary. The proposed criterion for selecting the next point for model evaluation maximizes the expected probability classified by using the candidate. Therefore, the perfect balance between global exploration and local exploitation is maintained automatically. The method can estimate the probabilities of multiple failure types. Moreover, when the numerical value of model evaluation can be used to build a smooth surrogate, the algorithm can accommodate this information to increase the accuracy of the estimated probabilities. Lastly, we define a new simple yet general geometrical measure of the global sensitivity of the rare-event probability to individual variables, which is obtained as a by-product of the proposed algorithm.