A reduced order model based on adaptive proper orthogonal decomposition incorporated with modal coefficient learning for digital twin in process industry

The digital twin (DT) technology provides a viable and promising direction for improving the level of the production status monitoring and the overall product quality in various fields. However, the accuracy of working condition identification, the timeliness of process adjustment, and the stability of product quality are put forward higher requirements in the process industry, which is characterized by nonlinear, large-scale, and dynamic complex systems. Therefore, it still remains a tricky challenge to construct and maintain an effective and accurate DT model in the process industry. A reduced order model (ROM) with the adaptive updating ability is proposed. The adaptive proper orthogonal decomposition (APOD) is adopted to achieve the continuous iteration and the adaptive optimization of the reduced basis set. Correspondingly, an adaptive learning algorithm based on the least squares support vector regression (LS-SVR) is developed to quickly obtain the modal coefficients and effectively circumvent the prohibitively high computational cost. In this way, the physical field of interest is expressed in a low-dimensional approximation with a high accuracy. The effectiveness of the method is verified by a case study in the process industry. Results show that the proposed model displays a high-precision fitting and a significant time saving for the full order model (FOM).