Development of Mass/Energy Constrained Sparse Bayesian Surrogate Models from Noisy Data

Abstract

This paper presents an algorithm for developing sparse surrogate models that satisfy mass/energy conservation even when the training data are noisy and violate the conservation laws. In the first step, we employ the Bayesian Identification of Dynamic Sparse Algebraic Model (BIDSAM) algorithm proposed in our previous work to obtain a set of hierarchically ranked sparse models which approximate system behaviors with linear combinations of a set of well-defined basis functions. Although the model building algorithm was shown to be robust to noisy data, conservation laws may not be satisfied by the surrogate models. In this work we propose an algorithm that augments a data reconciliation step with the BIDSAM model for satisfaction of conservation laws. This method relies only on known boundary conditions and hence is generic for any chemical system. Two case studies are considered-one focused on mass conservation and another on energy conservation. Results show that models with minimum bias are built by using the developed algorithm while exactly satisfying the conservation laws for all data.