Time-Variant Digital Twin Modeling through the Kalman-Generalized Sparse Identification of Nonlinear Dynamics

A digital twin is a computer-based digital representation that simulates the behavior of a physical system. Digital twins help users to interact with real-world processes digitally. Time-variant modeling is critical to preserving the accuracy of digital twin models as the process dynamics change with time. Kalman filter is a well-known recursive algorithm that adjusts the process state estimates using real-time measurements. Sparse identification of nonlinear dynamics (SINDy) is an algorithm that automatically identifies system models from large data sets using sparse regression so as to prevent overfitting and find an ideal trade-off between model complexity and accuracy. In this paper, the SINDy approach is first extended to the generalized SINDy (GSINDy). Then, the GSINDy is integrated with Kalman filter to automatically identify time-variant digital twin models for online applications. The effectiveness of the algorithm is revealed through a simulation example based on Lorenz system and an industrial diesel hydrotreating unit example.