Berru Predictive Modeling For Single Multiphysics Systems (Berru-Sms)
This Chapter presents the predictive modeling methodology developed by Cacuci and Ionescu-Bujor (2010a), which will be called the “BERRU-SMS Predictive Modeling” methodology, since it is conceived for a single, albeit large-scale, nonlinear multi-physics system, for which it combines uncertain computational and experimental data in order to predict best-estimate values for model responses and parameters, along with reduced predicted uncertainties for these best-estimate values. In contradistinction to the customary methods used currently for data assimilation, the BERRU-SMS predictive modeling methodology developed by Cacuci and Ionescu-Bujor (2010a) uses the maximum entropy principle to avoid the need for minimizing an arbitrarily user-chosen “cost functional” (usually a quadratic functional that represents the weighted errors between measured and computed responses), thus generalizing and significantly extending the customary “data adjustment” and/or 4D-VAR data assimilation procedures. The BERRU-SMS predictive modeling methodology also provides a quantitative indicator, constructed from sensitivity and covariance matrices, for determining the consistency (agreement or disagreement) among the a priori computational and experimental information available for parameters and responses. This consistency indicator measures, in the corresponding metric, the deviations between the experimental and nominally computed responses. This consistency indicator can be evaluated directly from the originally given data (i.e., given parameters and responses, together with their original uncertainties), once the response sensitivities have become available. Section 1.2 presents the mathematical framework underlying the BERRU-SMS methodology of Cacuci and Ionescu-Bujor (2010a) for both time-independent and time-dependent physical systems. Sections 1.3 and 1.4 present the application of this methodology to perform predictive modeling of two-phase water-flow and, respectively, liquid sodium flow, illustrating the reduction of predicted uncertainties for both the optimally-predicted model responses and calibrated model parameters. Section 1.5 presents the application of the BERRU-SMS predictive modeling methodology to a multi-physics benchmark (BWR-TT2) which involves coupled neutron kinetics/thermal-hydraulics numerical simulations characterized by 6 660 imprecisely known model parameters (6090 macroscopic neutron cross sections, and 570 thermal-hydraulics parameters involved in modeling the phase-slip correlation, transient outlet pressure, and total mass flow), showing reductions of up to 50% in the predicted standard deviation of the optimally predicted benchmark’s power response.
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