Integration of local and global surrogates for failure probability estimation

2026-03-17

AI Summary

This work proposes a global–local hybrid surrogate (GLHS) model to address the high computational cost of estimating rare failure probabilities in high-dimensional complex systems. The approach integrates a global surrogate to capture the overall system response trend and a local surrogate to accurately resolve the critical region near the limit state surface. By employing a buffer zone mechanism combined with a Christoffel-based adaptive sampling strategy, the method iteratively refines the sample distribution to precisely approximate the failure domain. Leveraging generalized domain adaptation and hybrid modeling techniques, GLHS achieves high-accuracy failure probability estimates with substantially reduced computational expense, requiring far fewer model evaluations than conventional Monte Carlo simulation.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization
• Intelligent Robots: State Estimation

Application Category

• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

This paper presents the development of an algorithm, termed the Global-Local Hybrid Surrogate (GLHS), designed to efficiently compute the probability of rare failure events in complex systems. The primary goal is to enhance the accuracy of reliability analysis while minimizing computational cost, particularly for high-dimensional problems where traditional methods, such as Monte Carlo simulations, become prohibitively expensive. The proposed GLHS builds upon the foundational work of Li et al., by integrating an adaptive strategy based on the General Domain Adaptive Strategy (Adcock et al.). The algorithm aims to approximate the failure domain of a given system, defined as the region in the input domain where the system transitions from safe to failure modes, described by a limit state surface. This failure domain is not explicitly known and must be learned iteratively during the analysis. The method employs a buffer zone, defined as the region surrounding the limit state surface. Within this buffer zone, Christoffel Adaptive Sampling is utilized to select new samples for constructing localized surrogate models, which are designed to refine the approximation in regions critical to failure probability estimation. The iterative process proceeds until convergence is reached. This results in a hybrid methodology that integrates a global surrogate to capture the overall trend with local surrogates that concentrate on critical regions near the limit state function. By adopting this strategy, the GLHS method balances computational efficiency with accuracy in estimating the failure probability.

Problem

• failure probability estimation
• rare failure events
• high-dimensional problems
• limit state surface
• reliability analysis

Innovation

• Global-Local Hybrid Surrogate
• failure probability estimation
• adaptive sampling
• limit state surface
• reliability analysis