A Systematic Online Update Method for Reduced-Order-Model-Based Digital Twin

Abstract A digital twin (DT) is a model that mirrors a physical system and is continuously updated with real-time data from the physical system. Recent implementations of reduced-order-model-based DT (DT-ROM) have been applied in aerodynamics and structural health monitoring, where partial differential equations (PDEs) are utilized to update reduced bases and coefficients. However, these methods are not directly applicable when the PDEs of the system are unknown. This paper addresses the online update challenge for DT-ROM in scenarios lacking known PDEs of the system. To tackle the challenge, a systematic online update and application method is proposed. During the online update, the projection residual of online data on the reduced bases determines the necessity of updating reduced bases, while the prediction residual of online data obtained by the current DT-ROM is used to decide whether to update the coefficient model. By sequentially evaluating both criteria, the method selectively incorporates essential online data for the online DT model update. During the online application, a criterion defined based on online data is adopted to determine whether the offline DT-ROM or the online one is applied to output final predictions. The capability of the proposed method is tested through three numerical and three engineering problems. Results indicate that the proposed online update method consistently reduces both projection and prediction residuals, thereby progressively enhancing the performance of the online DT-ROM on test data. Meanwhile, the online application method provides a prediction performance better than using offline DT-ROM only. Both demonstrate that the proposed work could be applied to online DT update where the PDEs of the system are unknown.