Surface decomposition method for sensitivity analysis of first-passage dynamic reliability of linear systems

2025-10-26

AI Summary

This paper addresses the high computational cost of first-passage dynamic reliability sensitivity analysis for linear systems under Gaussian stochastic excitation. To this end, a novel sensitivity analysis method is proposed based on decomposition of the limit-state hypersurface. The core contribution lies in rigorously formulating the failure probability sensitivity as a surface integral constrained on the limit-state hypersurface, and integrating it with closed-form expressions of the linear limit-state function and its derivatives to design an importance-sampling-driven efficient numerical integration scheme. Unlike conventional finite-difference or Monte Carlo re-sampling approaches, the proposed method avoids repeated system simulations and computes multi-parameter sensitivities using only $10^2$–$10^3$ function evaluations, thereby substantially improving computational efficiency and scalability. Two numerical examples validate the method’s accuracy, robustness, and efficiency.

Technology Category

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

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• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Security and Privacy: Large-scale security measurements

Abstract

This work presents a novel surface decomposition method for the sensitivity analysis of first-passage dynamic reliability of linear systems subjected to Gaussian random excitations. The method decomposes the sensitivity of first-passage failure probability into a sum of surface integrals over the constrained component limit-state hypersurfaces. The evaluation of these surface integrals can be accomplished, owing to the availability of closed-form linear expressions of both the component limit-state functions and their sensitivities for linear systems. An importance sampling strategy is introduced to further enhance the efficiency for estimating the sum of these surface integrals. The number of function evaluations required for the reliability sensitivity analysis is typically on the order of 10^2 to 10^3. The approach is particularly advantageous when a large number of design parameters are considered, as the results of function evaluations can be reused across different parameters. Two numerical examples are investigated to demonstrate the effectiveness of the proposed method.

Problem

• Analyzes first-passage dynamic reliability sensitivity for linear systems
• Decomposes failure probability sensitivity into surface integrals
• Enables efficient reliability analysis with multiple design parameters

Innovation

• Surface decomposition method for sensitivity analysis
• Closed-form linear expressions for limit-state functions
• Importance sampling strategy to enhance efficiency