Global sensitivity analysis for systems with independent and/or correlated inputs

Area of Science:

• Computational modeling
• Uncertainty quantification
• Systems analysis

Background:

• Global sensitivity analysis ranks input importance based on their uncertainty and influence on output uncertainty.
• Existing methods often struggle with correlated input probability distributions.
• A unified framework is needed for comprehensive sensitivity analysis across diverse systems.

Purpose of the Study:

• Introduce a novel, unified framework for global sensitivity analysis.
• Address systems with both independent and correlated input probability distributions.
• Provide a method applicable to mathematical models and empirical data.

Main Methods:

• Develop a new treatment based on covariance decomposition of unconditional output variance.
• Introduce three sensitivity indices for correlated inputs: total, structural, and correlative.
• Employ a meta-modeling approach, specifically random sampling-high dimensional model representation (RS-HDMR), for index estimation.

Main Results:

• The framework successfully handles independent and correlated input probability distributions.
• Three distinct indices quantify contributions from system structure and input correlations.
• For independent inputs, the indices align with established variance-based methods.
• RS-HDMR proves effective for estimating indices, particularly with uncontrolled input sampling in empirical data.

Conclusions:

• The proposed framework offers a comprehensive approach to global sensitivity analysis.
• Accurate input importance ranking requires considering structural and correlative contributions for correlated inputs.
• The method is versatile, applicable to both theoretical models and real-world data, enhancing uncertainty quantification.