Sparse identification of nonlinear dynamics with high accuracy and reliability under noisy conditions for applications to industrial systems

This paper proposes a sparse identification of nonlinear dynamics (SINDy) with control and exogenous inputs for highly accurate and reliable prediction. The method is applied to the diesel engine airpath systems, which are known as a nonlinear complicated industrial system. 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, we propose an emphasized SINDy by incorporating ensemble learning, elite gathering, and classification techniques while keeping convex calculation. 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 show the same trends. After the classification, discrete model candidates are obtained by taking the mean of each classified elite. Finally, the best model is selected. The simulation results show that the proposed method realizes multi-step prediction for the airpath system, which is known to be a complicated industrial system under noisy conditions.