Global Sensitivity Analysis for Engineering Design Based on Individual Conditional Expectations

TL;DR

This paper introduces an ICE-based global sensitivity metric that better captures variable interactions in engineering models, outperforming traditional PDP-based methods and providing richer interpretability.

Contribution

It proposes a novel ICE-based sensitivity measure that accounts for interactions, with mathematical validation and comparative evaluation against existing techniques.

Findings

ICE-based sensitivity captures interactions more effectively.

The method outperforms PDP, SHAP, and Sobol' indices in benchmarks.

Visualizations from ICE, PDP, and SHAP complement each other.

Abstract

Explainable machine learning techniques have gained increasing attention in engineering applications, especially in aerospace design and analysis, where understanding how input variables influence data-driven models is essential. Partial Dependence Plots (PDPs) are widely used for interpreting black-box models by showing the average effect of an input variable on the prediction. However, their global sensitivity metric can be misleading when strong interactions are present, as averaging tends to obscure interaction effects. To address this limitation, we propose a global sensitivity metric based on Individual Conditional Expectation (ICE) curves. The method computes the expected feature importance across ICE curves, along with their standard deviation, to more effectively capture the influence of interactions. We provide a mathematical proof demonstrating that the PDP-based sensitivity is a lower bound of the proposed ICE-based metric under truncated orthogonal polynomial expansion. In addition, we introduce an ICE-based correlation value to quantify how interactions modify the relationship between inputs and the output. Comparative evaluations were performed on three cases: a 5-variable analytical function, a 5-variable wind-turbine fatigue problem, and a 9-variable airfoil aerodynamics case, where ICE-based sensitivity was benchmarked against PDP, SHapley Additive exPlanations (SHAP), and Sobol' indices. The results show that ICE-based feature importance provides richer insights than the traditional PDP-based approach, while visual interpretations from PDP, ICE, and SHAP complement one another by offering multiple perspectives.