Cutting-Edge Research Analysis
Data-Driven Global Sensitivity Analysis for Engineering Design Based on Individual Conditional Expectations
Pramudita Satria Palar et al. | December 16, 2025
Executive Impact
This paper introduces a novel global sensitivity analysis approach leveraging Individual Conditional Expectation (ICE) curves to provide richer insights into machine learning models for engineering design. Unlike traditional Partial Dependence Plots (PDPs), which can mask interaction effects through averaging, our ICE-based metric quantifies feature importance by considering the dispersion of ICE curves, thereby capturing the influence of variable interactions. We mathematically prove that PDP-based sensitivity is a lower bound of our proposed ICE-based metric under truncated orthogonal polynomial expansion. Additionally, we introduce an ICE-based correlation value to quantify how interactions modify input-output relationships. Validated across analytical, wind turbine fatigue, and airfoil aerodynamics cases, our method offers more comprehensive insights than PDP, SHAP, and Sobol' indices, enhancing explainability for critical engineering applications.
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Interaction Effects Captured
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Model Explainability Lift
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Prediction Accuracy Maintained
Deep Analysis & Enterprise Applications
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Explainable AI in Engineering
Explainable machine learning (XAI) is becoming crucial in engineering for understanding how models work, especially in aerospace design. This research focuses on enhancing XAI techniques to provide clearer insights into complex simulations, moving beyond simple predictions to knowledge discovery.
Global Sensitivity Analysis
Global Sensitivity Analysis (GSA) identifies the most influential input variables in complex systems. While variance-based methods like Sobol' indices are standard, they often provide only scalar measures. Our approach provides a more detailed, interaction-aware view, complementing traditional GSA by revealing functional forms and interaction structures.
Limitations of PDPs in Interaction Detection
Traditional Partial Dependence Plots (PDPs) can obscure significant interaction effects between variables by averaging their influence on the output. This can lead to misleading conclusions, particularly in systems with strong non-additive relationships.
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PDP Sensitivity for Interacting Variables (x2, x3)
Proposed ICE-based Sensitivity Framework
Our novel ICE-based sensitivity metric computes the expected feature importance across Individual Conditional Expectation (ICE) curves, along with their standard deviation. This method explicitly captures the influence of variable interactions that PDPs typically average out.
Enterprise Process Flow
Calculate ICE curves per instance
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Quantify variance of each ICE curve
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Aggregate mean & standard deviation of ICE variances
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Derive ICE-based Sensitivity Metrics
Comparative Analysis of Sensitivity Metrics
The ICE-based sensitivity provides richer insights than PDP and SHAP, especially in detecting variable interactions. While PDPs can be misleading and SHAP values can be hard to aggregate globally, ICE offers a more nuanced view of how individual instances behave.
| Metric | Interaction Awareness | Interpretability | Global Insight |
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| SHAP |
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| ICE-based (Proposed) |
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Case Study: Wind Turbine Fatigue Problem
Applying the ICE-based method to a 5-variable wind turbine fatigue problem revealed that Vhub, θw, and Hs were the most important variables. Crucially, interactions were strongest for θw and Hs, a detail often missed by traditional PDPs. The ICE-based correlation values further quantified how these interactions modify input-output relationships, guiding informed design decisions.
Wind Turbine Fatigue Problem Insights
Our analysis identified Vhub, θw, and Hs as critical variables. The ICE-based metrics highlighted strong interaction effects for θw and Hs, providing valuable insights for optimizing wind turbine design and performance under uncertainty.
- Vhub, θw, and Hs identified as most important.
- Strongest interactions observed for θw and Hs.
- ICE-based correlation values quantify interaction effects on trends.
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