Efficient subset simulation for rare-event integrating point-evolution kernel density and adaptive polynomial chaos kriging

2022 ◽  
Vol 169 ◽  
pp. 108762
Author(s):  
Hongyuan Guo ◽  
You Dong ◽  
Paolo Gardoni
Keyword(s):  
Polynomial Chaos ◽  
Rare Event ◽  
Kernel Density ◽  
Subset Simulation ◽  
Evolution Kernel

scholarly journals Rare Event Chance-Constrained Optimal Control Using Polynomial Chaos and Subset Simulation

Processes ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 185 ◽  
Author(s):  
Patrick Piprek ◽  
Sébastien Gros ◽  
Florian Holzapfel
Keyword(s):  
Optimal Control ◽  
Failure Probability ◽  
Polynomial Chaos ◽  
Computational Cost ◽  
Rare Event ◽  
Subset Simulation ◽  
Battery Charging ◽  
Constrained Optimal Control ◽  
Efficient Sampling ◽  
Low Computational Cost

This study develops a ccoc framework capable of handling rare event probabilities. Therefore, the framework uses the gpc method to calculate the probability of fulfilling rare event constraints under uncertainties. Here, the resulting cc evaluation is based on the efficient sampling provided by the gpc expansion. The subsim method is used to estimate the actual probability of the rare event. Additionally, the discontinuous cc is approximated by a differentiable function that is iteratively sharpened using a homotopy strategy. Furthermore, the subsim problem is also iteratively adapted using another homotopy strategy to improve the convergence of the Newton-type optimization algorithm. The applicability of the framework is shown in case studies regarding battery charging and discharging. The results show that the proposed method is indeed capable of incorporating very general cc within an ocp at a low computational cost to calculate optimal results with rare failure probability cc.

Reliability Analysis in the Presence of Aleatory and Epistemic Uncertainties, Application to the Prediction of a Launch Vehicle Fallout Zone

2016 ◽  
Vol 138 (11) ◽  
Author(s):  
Loïc Brevault ◽  
Sylvain Lacaze ◽  
Mathieu Balesdent ◽  
Samy Missoum
Keyword(s):  
Computational Cost ◽  
Rare Event ◽  
Launch Vehicle ◽  
Probability Of Failure ◽  
Subset Simulation ◽  
Sequential Approach ◽  
Variance Estimate ◽  
Low Probability ◽  
Reliability Assessments ◽  
Refinement Strategy

The design of complex systems often requires reliability assessments involving a large number of uncertainties and low probability of failure estimations (in the order of 10−4). Estimating such rare event probabilities with crude Monte Carlo (CMC) is computationally intractable. Specific numerical methods to reduce the computational cost and the variance estimate have been developed such as importance sampling or subset simulation. However, these methods assume that the uncertainties are defined within the probability formalism. Regarding epistemic uncertainties, the interval formalism is particularly adapted when only their definition domain is known. In this paper, a method is derived to assess the reliability of a system with uncertainties described by both probability and interval frameworks. It allows one to determine the bounds of the failure probability and involves a sequential approach using subset simulation, kriging, and an optimization process. To reduce the simulation cost, a refinement strategy of the surrogate model is proposed taking into account the presence of both aleatory and epistemic uncertainties. The method is compared to existing approaches on an analytical example as well as on a launch vehicle fallout zone estimation problem.

Active Learning Kriging Model Combining With Kernel-Density-Estimation-Based Importance Sampling Method for the Estimation of Low Failure Probability

2018 ◽  
Vol 140 (5) ◽  
Author(s):  
Xufeng Yang ◽  
Yongshou Liu ◽  
Caiying Mi ◽  
Xiangjin Wang
Keyword(s):  
Active Learning ◽  
Density Estimation ◽  
Importance Sampling ◽  
Kernel Density Estimation ◽  
Failure Probability ◽  
Limit State ◽  
Rare Event ◽  
Kernel Density ◽  
Kriging Model ◽  
Performance Function

Strategies combining active learning Kriging (ALK) model and Monte Carlo simulation (MCS) method can accurately estimate the failure probability of a performance function with a minimal number of training points. That is because training points are close to the limit state surface and the size of approximation region can be minimized. However, the estimation of a rare event with very low failure probability remains an issue, because purely building the ALK model is time-demanding. This paper is intended to address this issue by researching the fusion of ALK model with kernel-density-estimation (KDE)-based importance sampling (IS) method. Two stages are involved in the proposed strategy. First, ALK model built in an approximation region as small as possible is utilized to recognize the most probable failure region(s) (MPFRs) of the performance function. Consequentially, the priori information for IS are obtained with as few training points as possible. In the second stage, the KDE method is utilized to build an instrumental density function for IS and the ALK model is continually updated by treating the important samples as candidate samples. The proposed method is termed as ALK-KDE-IS. The efficiency and accuracy of ALK-KDE-IS are compared with relevant methods by four complicated numerical examples.

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