Simultaneous digital twin identification and signal-noise decomposition through modified generalized sparse identification of nonlinear dynamics

A digital twin provides a digital replication of a physical system for remote monitoring, viewing, and control objectives. It has the potential to reshape the future of industrial processes, hence paving the way for smart manufacturing. Automatic system identification techniques that are robust to measurement noise are critical for the development of high-fidelity digital twins and their applications. By establishing a sparse regression framework, the sparse identification of nonlinear dynamics (SINDy) algorithm automatically determines the parsimonious governing equations for physical systems. However, there are some major challenges associated with using SINDy to identify digital twin models. First, the SINDy is restricted to solving the ordinary differential equation (ODE) and partial differential equation (PDE) problems. Second, measurement noise may significantly deteriorate the performance of SINDy. In this paper, the generalized SINDy (GSINDy) algorithm is first introduced to enlarge the SINDy's applicable range. Then, the modified GSINDy (MGSINDy) algorithm is proposed, in which an objective function is constructed to simultaneously identify the digital twin input time-series dynamics model and output model while separating noise from the noisy input. Two numerical examples and one industrial case study are analysed to demonstrate the advantages of applying the proposed MGSINDy to construct digital twin models. Furthermore, the proposed algorithm can be integrated with the existing SINDy-based online model-adjusting frameworks to become online-adjustable.