Bayesian Safety Validation for Failure Probability Estimation of Black-Box Systems

TL;DR

This paper presents a Bayesian optimization-based method for efficiently estimating failure probabilities in safety-critical black-box systems, reducing sample requirements and improving accuracy.

Contribution

It introduces a novel Bayesian safety validation framework with specialized acquisition functions for failure prediction and probability estimation in high-dimensional, expensive simulation scenarios.

Findings

Achieves more accurate failure probability estimates with fewer samples.

Performs well across multiple safety validation metrics.

Successfully applied to diverse test systems, including neural networks.

Abstract

Estimating the probability of failure is an important step in the certification of safety-critical systems. Efficient estimation methods are often needed due to the challenges posed by high-dimensional input spaces, risky test scenarios, and computationally expensive simulators. This work frames the problem of black-box safety validation as a Bayesian optimization problem and introduces a method that iteratively fits a probabilistic surrogate model to efficiently predict failures. The algorithm is designed to search for failures, compute the most-likely failure, and estimate the failure probability over an operating domain using importance sampling. We introduce three acquisition functions that aim to reduce uncertainty by covering the design space, optimize the analytically derived failure boundaries, and sample the predicted failure regions. Results show this Bayesian safety validation approach provides a more accurate estimate of failure probability with orders of magnitude fewer samples and performs well across various safety validation metrics. We demonstrate this approach on three test problems, a stochastic decision making system, and a neural network-based runway detection system. This work is open sourced (https://github.com/sisl/BayesianSafetyValidation.jl) and currently being used to supplement the FAA certification process of the machine learning components for an autonomous cargo aircraft.