Sparse Identification of Nonlinear Dynamics Enhanced by Ensemble Learning, Multi-Step Prediction Evaluation, Elite Strategy, and Classification Techniques for Applications to Industrial Systems

Abstract

This paper proposes a sparse identification of nonlinear dynamics (SINDy) with control and exogenous inputs for highly accurate and reliable prediction. Although SINDy is recognized as a remarkable approach for identifying nonlinear systems, several challenges remain. Its application to industrial systems remains limited, and multi-step predictions are not guaranteed due to overfitting and noisy data. This phenomenon is often caused by the increase in basis functions resulting from the extension of coordinates, such as time-delay embedding. To address these problems, this study proposes an emphasized SINDy framework by integrating ensemble-learning, multi-step prediction evaluations, elite strategy, and classification techniques (EMEC-SINDy), while preserving convex optimization. The proposed method employs library bagging and extracts elites with an R-squared greater than 90%. Then, clustering is performed on the surviving elites because physically motivated basis functions are not always available, and the elites obtained do not always have similar basis functions. After the classification, discrete model candidates are obtained by taking the mean of each classified elite. Finally, the best model is selected. Simulation results demonstrate that EMEC-SINDy significantly outperforms original SINDy approaches in multi-step prediction accuracy under noisy conditions, validating its applicability to the diesel engine airpath system, which is known as a complex and highly coupled nonlinear multi-input multi-output system.