Data-driven modeling and optimization of semibatch reactors using artificial neural networks

Abstract

In this study, a new data-driven approach has been proposed for modeling and trajectory optimization of a batch or a semibatch process. The approach is based on parametrization of input and output trajectories as finite-dimensional vectors using orthonormal polynomials (i.e., Fourier coefficients). Using input/output trajectory information available in historical databases, an artificial neural network (ANN) based model has been developed for capturing the dynamics of semibatch processes operated over a fixed interval of time. The parametrized input trajectories, initial states, and process parameters are considered as inputs to the ANN-based model, which predicts output trajectories in terms of Fourier coefficients. Single-rate as well as multirate systems can be modeled by this approach with equal ease. The resulting algebraic model is further used to formulate an optimal control problem, which can be solved using conventional nonlinear programming techniques to generate open-loop optimal input policies or optimal set-point trajectories. The effectiveness of the proposed ANN-based modeling and trajectory optimization scheme is demonstrated using simulation studies on a benchmark multiple-input multiple-output semibatch process reported in the literature. Analysis of the simulation results reveals that the proposed ANN-based modeling approach is capable of capturing the nonlinear as well as the time-varying behavior inherent in the semibatch system fairly accurately. In addition, it also captures batch-to-batch variations in initial conditions and other process parameters. The results of operating trajectory optimization based on the proposed single-rate as well as the multirate ANN model are comparable to the results of trajectory optimization obtained using the exact first principles model.