Bayesian Framework for Multidisciplinary Uncertainty Quantification and Optimization

This paper presents a comprehensive methodology that combines uncertainty quantification, propagation and robustness-based design optimization using a Bayesian framework. Two types of epistemic uncertainty regarding model inputs/parameters are emphasized: (1) uncertainty modeled as p-box, and (2) uncertainty modeled as interval data. A Bayesian approach is used to calibrate the uncertainty models, where the likelihood functions are constructed using limited experimental data. The calibrated (improved) models are validated by partially characterized data using an area metric. A global sensitivity analysis (GSA), which previously only considered aleatory uncertainty, is extended to identify the contribution of epistemic uncertainty using an auxiliary variable method. A decoupled robustness-based design optimization framework is developed for optimization under both aleatory and epistemic uncertainty. Gaussian Process (GP) surrogate modeling is employed to improve the computational efficiency. The proposed methodology is illustrated using the NASA Langley multidisciplinary uncertainty quantification challenge problem.