Academic Journal
Inverse ARX (IARX) method for boundary specification in heat conduction problems
| العنوان: | Inverse ARX (IARX) method for boundary specification in heat conduction problems |
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| المؤلفون: | Oliveira, A. v. s., Zacharie, C., Remy, Benjamin, Schick, Vincent, Maréchal, D., da Costa Teixeira, Julien, Denis, S., Gradeck, Michel |
| المساهمون: | Institut de recherche technologique Matériaux Métallurgie et Procédés (IRT M2P), Laboratoire d'Energétique et Mécanique Théorique et Appliquée (LEMTA ), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Institut Jean Lamour (IJL), Institut de Chimie - CNRS Chimie (INC-CNRS)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Labex DAMAS, Université de Lorraine (UL), French program Plan d’Investissement d’Avenir (PIA) |
| المصدر: | ISSN: 0017-9310 ; International Journal of Heat and Mass Transfer ; https://hal.univ-lorraine.fr/hal-03444243 ; International Journal of Heat and Mass Transfer, 2021, 180, pp.121783. ⟨10.1016/j.ijheatmasstransfer.2021.121783⟩. |
| بيانات النشر: | HAL CCSD Elsevier |
| سنة النشر: | 2021 |
| المجموعة: | Université de Lorraine: HAL |
| مصطلحات موضوعية: | Inverse method, Parametric models, Polynomial models, System identification, Exogenous, Autoregressive, Future time steps, [SPI.MAT]Engineering Sciences [physics]/Materials |
| الوصف: | International audience ; Heat conduction problems are usually solved either with analytical or numerical simulations, or with a reduced model using system identification. The use of polynomial models, often used in automation theory, gained the attention of the thermal community in the last decades to elaborate these reduced models because of their simplicity and performance to characterize an invariable system. They allow, for example, estimating a local temperature with a known input heat source. However, using polynomial models (or identified systems) in inverse conduction problems is not straightforward, usually requiring either a second inversion step. In this paper, we present a novel inverse technique based on the polynomial model ARX (autoregressive with exogenous input) that allows the estimation of an unknown input (like an imposed heat flux on a boundary) using a known output (temperature measurement). This new method, named inverse ARX or IARX, only requires a calibration step as a regular polynomial model and, then, it can estimate the input by a direct calculation with the identified parameters. The difference between IARX and ARX is the presence of future exogenous parameters, which were deduced using the initial discrete form of the ARX model. We present herein a numerical example using IARX of a 1D heat conduction simulation and IARX succeeded to estimate the input heat flux, even with high discontinuities and high measurement noises. Finally, we compare the proposed method with the classical Beck’s function specification method. IARX presented advantages like having no restriction for the number of future terms used in the model and performing the calculation 45% faster and with much less memory space consumption than with Beck’s method. |
| نوع الوثيقة: | article in journal/newspaper |
| اللغة: | English |
| Relation: | hal-03444243; https://hal.univ-lorraine.fr/hal-03444243; https://hal.univ-lorraine.fr/hal-03444243/document; https://hal.univ-lorraine.fr/hal-03444243/file/Article_ARXInverse_v4.pdf |
| DOI: | 10.1016/j.ijheatmasstransfer.2021.121783 |
| الاتاحة: | https://hal.univ-lorraine.fr/hal-03444243 https://hal.univ-lorraine.fr/hal-03444243/document https://hal.univ-lorraine.fr/hal-03444243/file/Article_ARXInverse_v4.pdf https://doi.org/10.1016/j.ijheatmasstransfer.2021.121783 |
| Rights: | http://creativecommons.org/licenses/by-nc-nd/ ; info:eu-repo/semantics/OpenAccess |
| رقم الانضمام: | edsbas.5662A393 |
| قاعدة البيانات: | BASE |
| DOI: | 10.1016/j.ijheatmasstransfer.2021.121783 |
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