Implementation of supervised principal component analysis for global sensitivity analysis of models with correlated...

Area of Science:

• Environmental modeling
• Computational statistics
• Data science

Background:

• Global Sensitivity Analysis (GSA) quantifies input impact on model uncertainty.
• Correlated inputs pose challenges for traditional GSA methods, often requiring computationally expensive solutions.
• Existing GSA techniques struggle with computational cost and implementation complexity for correlated inputs.

Purpose of the Study:

• To develop a novel, computationally efficient, and easy-to-implement regression-based strategy for GSA with correlated inputs.
• To address the limitations of existing GSA methods that are computationally expensive and difficult to implement.
• To evaluate the proposed method's effectiveness in identifying input variable importance in complex models.

Main Methods:

• A novel regression-based strategy utilizing Supervised Principal Component Analysis (SPCA) and Reproducing Kernel Hilbert Space.
• Applying variance-based sensitivity analysis to SPCA regression to account for input correlation.
• Evaluating the method using five test cases and three hydrologic/hydraulic models, comparing results with the correlation ratio method.

Main Results:

• The proposed SPCA-based method satisfactorily identifies the sensitivity ordering of model inputs.
• The method's performance is supported by the total contribution index in covariance decomposition.
• Compared to the correlation ratio method, the proposed approach is computationally efficient and simpler to implement.

Conclusions:

• The developed SPCA-based GSA strategy is suitable for high-dimensional, nonlinear, or expensive models with correlated inputs.
• The method offers a practical and efficient alternative for sensitivity analysis in complex systems.
• The proposed scheme demonstrates robust performance and ease of implementation for GSA with correlated variables.