Berru-Cms Predictive Modeling Of Coupled Multiphysics Systems

Abstract

This Chapter presents the “BERRU-CMS” methodology, which extends the BERRU-SMS predictive modeling methodology presented in Chapter 1 to predictive modeling of coupled (as opposed to “single”) multi-physics systems. The BERRU-CMS methodology is build on the same principles as the BERRU-SMS predictive modeling methodology that was presented in Chapter 1. Thus, the maximum entropy principle is used to construct an optimal approximation of the unknown a priori distribution based on a priori known mean values and uncertainties characterizing the parameters and responses for both multi-physics models. This “maximum entropy”-approximate a priori distribution is combined, using Bayes’ theorem, with the “likelihood” provided by the multi-physics simulation models. Subsequently, the posterior distribution thus obtained is evaluated using the saddle-point method to obtain analytical expressions for the optimally predicted values for the multi-physics models parameters and responses along with corresponding reduced uncertainties. Noteworthy, the predictive modeling methodology for the coupled systems is constructed such that the systems can be considered sequentially rather than simultaneously, while preserving exactly the same results as if the systems were treated simultaneously. Consequently, very large coupled systems, which could perhaps exceed available computational resources if treated simultaneously, can be treated with the BERRU-CMS methodology presented in this work sequentially, without any loss of generality or information while requiring just the resources that would be needed if the systems were treated separately.