Sparse Mass-Constrained Nonlinear Dynamic Model Building from Noisy Data Using a Bayesian Approach

This work proposes two algorithms to guarantee the exact satisfaction of mass conservation laws by sparse data driven models. The initial model building is undertaken by employing the Bayesian Identification of Dynamic Sparse Algebraic Model (BIDSAM) algorithm. <i>Algorithm I</i> proposed in this work updates the model parameters through an optimization process that augments the original model with a data reconciliation step. <i>Algorithm II</i> derives a set of equality constraints for the original model parameters that ensure the exact satisfaction of the resulting closed form model. The proposed algorithms are tested on two case studies for which steady state and dynamic model building are undertaken, and the results show that both algorithms guarantee exact satisfaction of mass balance constraints while at the same time minimizing the deviations of model predictions from their <i>true</i> values even when model training is done with noisy data with bias. While <i>Algorithm II</i> generally resulted in relatively larger model size due to the basic model structure requirements, both algorithms preserve the sparsity and interpretability characteristics of the original BIDSAM model while achieving satisfaction of mass conservation laws.