Real–Virtual Sensor Parameterized-Background Data-Weak Method for Digital Twin State Estimation

The data assimilation and state estimation play an important role in the digital twin (DT) technology. The parameterized-background data-weak (PBDW) method is an emerging nonintrusive data assimilation algorithm that reconstructs the field distribution in the physical system by using the measured data combined with the best-knowledge model, and the reconstructed field can be further postprocessed to extract state parameters of interest for the state estimation of the physical system. However, the conventional PBDW method still faces great challenges for practical applications in electrical engineering. The main difficulties are the large number of required sensors to ensure the well-posedness of the PBDW system, the difficulty in accessing the optimal sensor locations, and the handling of the noisy measurement data. To address these problems, a real-virtual sensor PBDW (RV-PBDW) framework is proposed in this work. Virtual sensors with readings mapped from real sensors using a neural network (NN) are proposed to reach the optimal sensor locations and significantly reduce the number of required real sensors placed in the practical physical system. Furthermore, the data augmentation techniques are integrated with the NN to enhance the performance on handling noisy measurement data, and the regularization parameter, which is hard to decide in the conventional PBDW, is not needed. The performance of the proposed framework is verified and explored through an EI-core inductor and a rotating electrical machine case studies. The field distribution reconstructed by the RV-PBDW method can be further used in the postprocessing and facilitates various functions of DT system such as sensing, detection, and diagnosis, enabling more diverse, in-depth state estimation of the physical system. This work significantly extends the feasibility of the conventional PBDW method in the context of the DT technology for practical electrical engineering applications.