Model Calibration vs. Physics-guided Coverage Mapping: Case Study - Pressure Drop Calculations
This work deals with a fundamental question in model validation: given a body of available experiments and an envisaged domain of nuclear reactor operating conditions (referred to as the reactor application), how can one develop a quantitative approach that measures the portion of the prior uncertainties of the reactor application that is covered by the available experiments? Coverage here means that the uncertainties of the reactor application are originating from and behaving in exactly the same way as those observed at the experimental conditions. This approach is valuable as it provides a scientifically defendable criterion by which experimentally measured biases can be credibly extrapolated (i.e., mapped) to biases for the reactor applications. This work focuses on the application of a new methodology, referred to as physics-guided coverage mapping (PCM), to the estimation of hydraulic pressure losses in reactor pipes. PCM provides a generic, calibration-free approach to the mapping of experimental biases by relying on high fidelity physics simulation and information theoretic measure how much of the application domain is covered by the experiments. The idea is to employ the physics models to establish a joint probability distribution that relates the application and the available body of experiments. An information-theoretic measure, referred to as the mutual information, is used to calculate a quantitative metric that measures the inter-dependence between the application and the experiment. A virtual experiment is employed to demonstrate the application of PCM, wherein the pressure drop is calculated for both the experiment and the application using two different flow conditions, i.e., laminar and turbulent, and the experimental values are simulated. All parameters introducing uncertainties, such as geometry, friction factor formulas and their associated parameters are also incorporated. The results obtained with PCM are compared to a conventional calibration-based approach. This work show that the proposed approach can circumvent a number of challenges that face calibration-based methods, such as nonlinearity, ill-posedness and error compensation in high dimensional models with many parameters. This work focus primarily in this summary on parameter uncertainties and how they can be treated using PCM. In a separate summary, discuss performance of PCM under the presence of modeling uncertainties. This simple study has shown that calibration techniques for very simple situations cannot correctly scale the measurements from the experimental to the application domain. It is our view that is occurs primarily due the phenomenon of error compensation where on artificially changes the value of selected parameters to account for all sources of uncertainties. The situation gets more complicated when one calibrates multiple parameters where now the problem could potentially have an infinite number of ways by which the errors can be compensated. (authors)