Uncertainty importance analysis using parametric moment ratio functions.

Area of Science:

• Engineering
• Computational Science
• Uncertainty Quantification

Background:

• Model output uncertainty is a critical concern in engineering and scientific applications.
• Existing importance analysis methods can be computationally intensive and dimensionality-dependent.
• Efficiently reducing model output uncertainty is crucial for reliable predictions.

Purpose of the Study:

• To introduce a novel importance analysis framework, the parametric moment ratio function (PMRF).
• To develop methods for measuring and targeting reductions in model output uncertainty by modifying input distribution parameters.
• To derive efficient Monte Carlo estimators for the PMRF.

Main Methods:

• Development of parametric mean and variance ratio functions to assess uncertainty reduction.
• Derivation of unbiased and progressive unbiased Monte Carlo estimators for PMRF.
• Application of the framework to a nonlinear analytical test case and a 10-bar planar structure.

Main Results:

• The PMRF framework effectively guides analysts in reducing model output mean and variance.
• Monte Carlo estimators are computationally efficient, independent of input dimensionality.
• Demonstrated successful application to a complex engineering problem, achieving a 50% variance reduction.

Conclusions:

• The parametric moment ratio function offers an efficient and dimensionality-independent approach to uncertainty reduction.
• The derived Monte Carlo estimators provide accurate and computationally feasible tools for importance analysis.
• This framework has significant engineering implications for optimizing models and managing uncertainty.