Likelihood-Based Approach for Uncertainty Quantification in Multi-Physics Systems

This chapter presents a computational methodology for uncertainty quantification in multi-physics systems that require iterative analysis between models corresponding to each discipline of physics. This methodology is based on computing the probability of satisfying the inter-disciplinary compatibility equations, conditioned on specific values of the coupling (or feedback) variables, and this information is used to estimate the probability distributions of the coupling variables. The estimation of the coupling variables is analogous to likelihood-based parameter estimation in statistics and thus leads to the likelihood approach for multi-disciplinary analysis (LAMDA). Using the distributions of the feedback variables, the coupling can be removed in any one direction without loss of generality, while still preserving the mathematical relationship between the coupling variables. The calculation of the probability distributions of the coupling variables is theoretically exact and does not require a fully coupled system analysis. The LAMDA methodology is first illustrated using a mathematical example and then applied to the analysis of a fire detection satellite.