Method for Determining the Model Order for Model Order Reduction of the Linear Parameter Varying Heat Conduction Model using the Monte Carlo Method

Digital twins are considered to be one of the most promising technologies for both green transformation and digital transformation. To facilitate the early adoption of digital twin technology, it is crucial to reduce the development time of models that can simulate with low computational cost and high accuracy. However, verifying the accuracy of these models can be time-consuming due to the significant variations in boundary conditions caused by changes in environmental conditions, design requirements, and specifications of products. In this study, we proposed an evaluation method for evaluating the accuracy of reduced order models built through parametric model order reduction. We utilized the conceptual idea of the Monte Carlo method with Latin Hypercube Sampling to randomly and comprehensively generate boundary conditions. Based on these evaluation methods, we have developed an algorithm to determine the order of the projection matrix, which is obtained through singular value decomposition of the original projection matrix generated by parametric model order reduction techniques. We applied this algorithm to a 3D FEM model with linear parameter varying convective heat transfer. The results show that the simulation time of the reduced order model, with an accuracy of 0.1 ℃ or less, can be reduced to 1/200 compared to the original FEM model (full order model), and to 1/12 compared to the original reduced order model generated by conventional parametric model order reduction techniques. This significant reduction in simulation time would enable real-time simulations in the digital twins environment.