Bayesian Uncertainty Modeling and Risk-Aware Optimization for Unknown Systems

This study explores uncertainty classification and modeling, differentiating between aleatory and epistemic uncertainties. Aleatory uncertainty arises from inherent randomness and is commonly represented using random variables, while epistemic uncertainty stems from a lack of precise knowledge about a parameter's true value. Addressing both types is crucial for constructing accurate uncertainty models, which must account for the physical nature of parameters and the available data. The research is motivated by the NASA and DNV 2025 challenge on optimization under uncertainty. To estimate probability densities for both uncertainty types, the study employs Bayesian Inference, which provides a structured approach to updating beliefs about uncertain parameters as new data becomes available. In the design optimization phase, the study utilizes the Shapley value concept to systematically address the subproblems. By fairly evaluating the contribution of each variable before the optimization process, this method enhances resource allocation and decision-making. The derived control inputs are optimized to meet various task-specific objectives, ensuring robust performance.

Keywords: Bayesian uncertainty modeling, Uncertainty quantification, Probability density estimation, Shapley value theorem, Performance and reliability-based design, Stochastic optimization.