Comparative Analysis of Sobol and Shapley Methods for Sensitivity Analysis in Civil Engineering: Case Studies on Fibre-Reinforced Concrete Performance

Abstract

Sensitivity analysis is a pivotal tool in civil engineering, facilitating the identification of influential parameters in complex systems and aiding in model optimization but also interpretability/explainability, especially in the fields of machine learning and nonlinear Finite Element modeling. This paper explores the comparative efficacy of Sobol and Shapley sensitivity analysis methods in addressing civil engineering challenges, with a focus on evaluating their applicability and reliability in real-world scenarios. Sobol's method, based on variance decomposition, provides a comprehensive measure of both individual and interaction effects of input variables. Meanwhile, the Shapley method, rooted in cooperative game theory, offers a fair allocation of variable contributions, particularly in nonlinear and interdependent systems. To demonstrate their effectiveness, this study proposes case studies involving the performance analysis of fiber-reinforced concrete (FRC). Using these case studies, the sensitivity results derived from Sobol and Shapley methods are compared in terms of computational efficiency, accuracy in capturing parameter interactions, and interpretation of results. This study underscores the strengths and limitations of these sensitivity analysis techniques and their potential to enhance the design and performance evaluation of civil engineering structures, particularly in realms of high-complexity, in terms of uncertainty and correlation. The proposed framework serves as a guide for selecting appropriate sensitivity methods based on problem-specific requirements, advancing robust and reliable uncertainty management.