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 hi...
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| Format: | Article |
| Language: | Japanese |
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The Japan Society of Mechanical Engineers
2024-12-01
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| Series: | Nihon Kikai Gakkai ronbunshu |
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| Online Access: | https://www.jstage.jst.go.jp/article/transjsme/91/941/91_24-00089/_pdf/-char/en |
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| _version_ | 1832584918814687232 |
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| author | Akiyasu MIYAMOTO |
| author_facet | Akiyasu MIYAMOTO |
| author_sort | Akiyasu MIYAMOTO |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-3066a16fd8ef4090902e6e0edd995733 |
| institution | Kabale University |
| issn | 2187-9761 |
| language | Japanese |
| publishDate | 2024-12-01 |
| publisher | The Japan Society of Mechanical Engineers |
| record_format | Article |
| series | Nihon Kikai Gakkai ronbunshu |
| spelling | doaj-art-3066a16fd8ef4090902e6e0edd9957332025-01-27T08:34:35ZjpnThe Japan Society of Mechanical EngineersNihon Kikai Gakkai ronbunshu2187-97612024-12-019194124-0008924-0008910.1299/transjsme.24-00089transjsmeMethod for Determining the Model Order for Model Order Reduction of the Linear Parameter Varying Heat Conduction Model using the Monte Carlo MethodAkiyasu MIYAMOTO0Research and Development Group, Hitachi, Ltd.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.https://www.jstage.jst.go.jp/article/transjsme/91/941/91_24-00089/_pdf/-char/endigital twinparametric model order reductiontemperature predictionfinite element methodsingular value decompositionmonte carlo method |
| spellingShingle | Akiyasu MIYAMOTO Method for Determining the Model Order for Model Order Reduction of the Linear Parameter Varying Heat Conduction Model using the Monte Carlo Method Nihon Kikai Gakkai ronbunshu digital twin parametric model order reduction temperature prediction finite element method singular value decomposition monte carlo method |
| title | Method for Determining the Model Order for Model Order Reduction of the Linear Parameter Varying Heat Conduction Model using the Monte Carlo Method |
| title_full | Method for Determining the Model Order for Model Order Reduction of the Linear Parameter Varying Heat Conduction Model using the Monte Carlo Method |
| title_fullStr | Method for Determining the Model Order for Model Order Reduction of the Linear Parameter Varying Heat Conduction Model using the Monte Carlo Method |
| title_full_unstemmed | Method for Determining the Model Order for Model Order Reduction of the Linear Parameter Varying Heat Conduction Model using the Monte Carlo Method |
| title_short | Method for Determining the Model Order for Model Order Reduction of the Linear Parameter Varying Heat Conduction Model using the Monte Carlo Method |
| title_sort | method for determining the model order for model order reduction of the linear parameter varying heat conduction model using the monte carlo method |
| topic | digital twin parametric model order reduction temperature prediction finite element method singular value decomposition monte carlo method |
| url | https://www.jstage.jst.go.jp/article/transjsme/91/941/91_24-00089/_pdf/-char/en |
| work_keys_str_mv | AT akiyasumiyamoto methodfordeterminingthemodelorderformodelorderreductionofthelinearparametervaryingheatconductionmodelusingthemontecarlomethod |