Modeling and Control of Nonlinear Processes Using Sparse Identification: Using Dropout to Handle Noisy Data

Sparse identification of nonlinear dynamics (SINDy) is a recent nonlinear modeling technique that has demonstrated superior performance in modeling complex time-series data in the form of first-order ordinary differential equations (ODEs), which are explicit and continuous in time. However, a crucial step in the SINDy algorithm involves estimating the time derivative of the states from the discrete, measured data. Therefore, the presence of noise can greatly deteriorate the performance if it is not carefully considered and accounted for. In this work, SINDy is used with ensemble learning, where multiple models are identified to improve the overall/final nonlinear model's performance. Specifically, in the SINDy algorithm, a fraction of the library functions considered for the ODE model representation are randomly dropped out in each submodel to favor model sparsity and stability at the possible risk of lowering the model accuracy. This trade-off is controlled by manipulating the fraction of the library functions dropped out and the total number of models generated, both of which are considered as hyperparameters to be tuned in the proposed algorithm. Data from open-loop simulations of a large-scale chemical plant are generated using the well-known high-fidelity process simulator, Aspen Plus Dynamics, and corrupted with substantial sensor noise to be implemented in the newly proposed algorithm, dropout-SINDy. The dropout-SINDy models obtained from training with the noisy data are then tested in open-loop simulations to demonstrate accurate identification of the steady-state and reasonably close transient behavior under a variety of initial conditions and manipulated input values. Finally, the constructed models are used in a Lyapunov-based model predictive controller to control the large-scale Aspen process, meeting desired closed-loop stability and performance specifications.