Data-Driven Global Sensitivity Analysis for Engineering Design Based on Individual Conditional Expectations

2025-12-12

AI Summary

Traditional partial dependence plots (PDPs) yield distorted global sensitivity measures for engineering black-box models exhibiting strong input variable interactions. Method: This paper proposes a novel global sensitivity analysis framework based on individual conditional expectation (ICE) curves. It introduces a joint sensitivity metric combining ICE curve means and standard deviations—rigorously proven to lower-bound PDP-based sensitivity—and defines, for the first time, an ICE correlation metric quantifying the modulation strength of interaction effects on input–output relationships. The method integrates truncated orthogonal polynomial expansion with complementary interpretability tools (SHAP, Sobol’, PDP). Results: Evaluated on three canonical engineering benchmarks—a 5D analytical function, wind turbine fatigue modeling, and a 9D airfoil aerodynamic problem—the proposed approach consistently outperforms PDP, SHAP, and Sobol’ indices, delivering finer-grained insights into interaction effects and enhanced engineering interpretability via multi-perspective visualizations.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Graphical Models
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Security and Privacy: Large-scale security measurements

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.

Problem

• PDP-based global sensitivity metrics mislead with strong variable interactions
• Need better method to capture interaction effects in black-box models
• Require quantifiable measure of how interactions modify input-output relationships

Innovation

• Proposes ICE-based global sensitivity metric for engineering design
• Introduces ICE correlation to quantify input-output interaction effects
• Benchmarks ICE sensitivity against PDP, SHAP, and Sobol' indices