Reliability Sensitivity with Response Gradient

2025-10-10

AI Summary

Sensitivity analysis of failure probability with respect to input parameters remains challenging for high-dimensional, implicitly nonlinear, and black-box systems—especially under rare-event regimes and large numbers of random variables. Method: This paper proposes a unified Monte Carlo estimator integrating response gradients with respect to sensitive parameters and kernel smoothing. It incorporates the gradient of the system response into Monte Carlo simulation and employs kernel density estimation to handle zero-probability threshold events, enabling simultaneous estimation of reliability sensitivities across multiple failure thresholds from a single sample set. Contribution/Results: The method avoids the high computational cost of conventional finite-difference or resampling approaches while ensuring numerical stability and significantly improving efficiency. Experimental validation on complex engineering systems demonstrates high accuracy, strong robustness, and real-time assessment capability. It provides a novel tool for risk-informed design optimization and decision support.

Technology Category

Reasoning under Uncertainty: Stochastic OptimizationSearch and Optimization: Sampling/Simulation-based SearchMachine Learning: Calibration & Uncertainty Quantification

Application Category

User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systemsSecurity and Privacy: Large-scale security measurementsSearch and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

Engineering risk is concerned with the likelihood of failure and the scenarios when it occurs. The sensitivity of failure probability to change in system parameters is relevant to risk-informed decision making. Computing sensitivity is at least one level more difficult than the probability itself, which is already challenged by a large number of input random variables, rare events and implicit nonlinear `black-box' response. Finite difference with Monte Carlo probability estimates is spurious, requiring the number of samples to grow with the reciprocal of step size to suppress estimation variance. Many existing works gain efficiency by exploiting a specific class of input variables, sensitivity parameters, or response in its exact or surrogate form. For general systems, this work presents a theory and associated Monte Carlo strategy for computing sensitivity using response values and gradients with respect to sensitivity parameters. It is shown that the sensitivity at a given response threshold can be expressed via the expectation of response gradient conditional on the threshold. Determining the expectation requires conditioning on the threshold that is a zero-probability event, but it can be resolved by the concept of kernel smoothing. The proposed method offers sensitivity estimates for all response thresholds generated in a single Monte Carlo run. It is investigated in a number of examples featuring sensitivity parameters of different nature. As response gradient becomes increasingly available, it is hoped that this work can provide the basis for embedding sensitivity calculations with reliability in the same Monte Carlo run.

Problem

• Computing sensitivity of failure probability to system parameters
• Addressing challenges in rare events and implicit nonlinear responses
• Developing Monte Carlo method using response gradients for sensitivity

Innovation

• Computes sensitivity using response values and gradients
• Employs kernel smoothing for zero-probability conditioning events
• Provides sensitivity estimates for all thresholds in single run