Integrating Data-Driven Modeling with First-Principles Knowledge

This Article addresses the problem of integrating subspace-based model identification with first-principles modeling for handling scenarios where the subspace model identifies spurious relationships between inputs and outputs. The key motivation is to suitably synergize the two approaches while retaining the simplicity of subspace-based model identification. In the proposed methodology, as is done with traditional subspace identification, state trajectories that best describe the input–output data are first computed (which implicitly correspond to an underlying linear time invariant model). In computing the system matrices using the state trajectories, constraints derived from first-principles understanding are incorporated into the optimization problem. To reconcile the resulting mismatch between the state trajectories and the system matrices, an iterative process is utilized. First, the system matrices computed from the optimization problem are utilized to re-estimate the state trajectories (this time utilizing a state estimator and the input and output trajectories). The state trajectories are, in turn, utilized to resolve the system matrices using the input–output data. The process is repeated until convergence occurs between successive state trajectories, thus yielding state trajectories and “consistent” system matrices. The efficacy of the proposed approach is shown via simulations using a nonlinear process example.