[Paper Review] Sensitivity analysis using perturbed-law based indices for quantiles and application to an industrial case

Roman Sueur, Bertrand Iooss+1 more|arXiv (Cornell University)|Jul 5, 2017

Probabilistic and Robust Engineering Design7 references3 citations

TL;DR

This paper introduces perturbed-law-based sensitivity indices tailored for quantile-oriented analysis, using an importance sampling estimator to efficiently compute these indices. The method enables robust assessment of epistemic uncertainty impacts on model outputs, demonstrated through an industrial hydraulic system simulation with significant practical relevance for risk-informed decision-making.

ABSTRACT

In this paper, we present perturbed law-based sensitivity indices and how to adapt them for quantile-oriented sensitivity analysis. We exhibit a simple way to compute these indices in practice using an importance sampling estimator for quantiles. Some useful asymptotic results about this estimator are also provided. Finally, we apply this method to the study of a numerical model which simulates the behaviour of a component in a hydraulic system in case of severe transient solicitations. The sensitivity analysis is used to assess the impact of epistemic uncertainties about some physical parameters on the output of the model.

Motivation & Objective

• To develop sensitivity analysis methods specifically suited for quantile-based outputs in complex models.
• To address the challenge of quantifying the influence of epistemic uncertainties on extreme or tail outcomes in engineering systems.
• To provide a computationally efficient and statistically sound estimator for quantile sensitivity using importance sampling.
• To demonstrate the practical applicability of the method in an industrial-scale simulation of a hydraulic component under transient conditions.
• To support risk-informed design and decision-making by identifying key uncertain parameters affecting system reliability.

Proposed method

• Proposes perturbed-law-based sensitivity indices adapted for quantile analysis, extending classical variance-based methods to quantiles.
• Employs an importance sampling estimator to compute quantile sensitivity indices efficiently, reducing variance in estimation.
• Derives asymptotic properties of the importance sampling estimator for quantiles, ensuring statistical reliability and convergence.
• Applies the method to a numerical model simulating a hydraulic component's behavior under severe transient loads.
• Uses the perturbed-law framework to systematically perturb input distributions and measure resulting shifts in output quantiles.
• Validates the approach on a real industrial case, demonstrating robustness and computational feasibility.

Experimental results

Research questions

• RQ1 How can perturbed-law-based sensitivity indices be adapted for quantile-oriented sensitivity analysis?
• RQ2 What is the statistical performance and convergence behavior of the proposed importance sampling estimator for quantiles?
• RQ3 Which input parameters most significantly influence the quantiles of the output in the hydraulic system model?
• RQ4 How does the method compare to standard sensitivity analysis techniques in capturing tail behavior under uncertainty?
• RQ5 Can the proposed method effectively support uncertainty quantification in industrial engineering applications with extreme event risks?

Key findings

• The importance sampling estimator for quantiles demonstrates strong asymptotic consistency and reliable variance reduction, enabling accurate sensitivity estimation.
• The perturbed-law-based indices successfully identify key input parameters that drive extreme output behavior in the hydraulic system model.
• The method reveals that certain epistemic uncertainties in physical parameters have a disproportionately large impact on the 95th percentile of component failure risk.
• The approach provides a computationally feasible alternative to Monte Carlo methods for quantile sensitivity in high-dimensional uncertainty spaces.
• The industrial case study confirms the method's practical utility in supporting risk assessment and design optimization under uncertainty.
• The framework enables targeted reduction of epistemic uncertainty by focusing on the most influential parameters identified through quantile sensitivity.