Efficient Estimation of A-basis and B-Basis Value under Epistemic Uncertainty using Importance Sampling and Control Variates

2026-06-11

AI Summary

This work addresses the challenge of estimating conservative design quantiles—specifically A- and B-basis values—in safety-critical domains such as aerospace, where material data are scarce and uncertainties are mixed (both aleatory and epistemic). The authors propose an efficient, unbiased computational framework with rigorous statistical guarantees. Built upon a verified deterministic numerical model, the approach employs a surrogate model solely as a variance-reduction tool, integrating importance sampling and control variates to achieve consistent quantile estimates under a fixed computational budget while seamlessly incorporating all sources of uncertainty. Notably, Sobol’ global sensitivity indices are obtained at no additional computational cost. Numerical experiments on structural models and large-scale industrial simulations demonstrate that the method delivers high reliability and computational efficiency, making it directly applicable to real-world certification processes.

Abstract

In aerospace certification and other safety-critical domains, conservative quantile estimation such as A- and B-basis values is essential to guarantee reliability. While these metrics are traditionally derived from experimental campaigns, this work focuses on their estimation using a validated deterministic numerical model. The problem is formulated under mixed aleatory-epistemic uncertainty, accounting for limited material data, finite sampling effects, and surrogate modeling errors. We propose a methodology for estimating conservative design quantiles with statistical guarantees under mixed uncertainties. The proposed method leverages importance sampling and control variates to achieve accurate and efficient estimates within a fixed computational budget. One key point is the surrogate model's role solely as a variance reduction device, which guarantees unbiased and consistent quantile estimation. By explicitly integrating all sources of uncertainty, the proposed framework provides a numerical alternative to estimate A-basis and B-Basis. Furthermore, Sobol-based sensitivity indices are obtained at no additional cost, offering insight into the dominant epistemic sources. Numerical experiments on structural models demonstrate the method's reliability and computational efficiency. In particular, the application to large-scale industrial simulations confirms its suitability for aerospace certification workflows and highlights its relevance for real world engineering environments.

Problem

• A-basis
• B-basis
• epistemic uncertainty
• quantile estimation
• mixed uncertainty

Innovation

• importance sampling
• control variates
• A-basis and B-basis
• epistemic uncertainty
• surrogate model