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Inverse ARX (IARX) method for boundary specification in heat conduction problems

机译：导热问题中边界规范的逆ARX（IARX）方法

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摘要

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.
机译：导热问题通常用分析或数值模拟来解决，或者使用系统识别使用减少的模型。使用多项式模型，通常用于自动化理论，在过去的几十年中获得了热量社区的注意，以便在简单和性能表征不变系统的简单性和性能方面来精致这些型号。它们允许例如用已知的输入热源估计局部温度。然而，在逆导通问题中使用多项式模型（或识别的系统）并不简单，通常需要第二反转步骤。在本文中，我们介绍了一种基于多项式模型ARX（自回归与外源输入）的逆技术，其允许使用已知输出（温度测量）估计未知的输入（如边界上的施加热通量）。这种命名为逆ARX或IARX的新方法只需要校准步骤作为常规多项式模型，然后，它可以通过通过识别的参数直接计算来估计输入。 IARX和ARX之间的差异是使用ARX模型的初始离散形式推断出未来外源参数的存在。我们在本文中存在使用1D热传导仿真的IARX的数值示例以及IARX成功地估计了输入热量通量，即使具有高不连续性和高测量噪声。最后，我们将提出的方法与经典Beck的功能规范方法进行比较。 IARX提出了没有限制模型中使用的未来术语的数量，并更快地执行45％，并且存储器空间消耗远低于Beck的方法。

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  • 来源
    《International Journal of Heat and Mass Transfer》 |2021年第12期|121783.1-121783.12|共12页
  • 作者

    A.V.S. Oliveira; C. Zacharie; B. Remy; V. Schick; D. Marechal; J. Teixeira; S. Denis; M. Gradeck;

  • 作者单位

    IRT M2P 4 rue Augustin Fresnel 57070 Metz France Universite de Lorraine CNRS LEMTA F-54000 Nancy France Institut Jean Latnour UMR 7198 CNRS Universit de Lorraine Nancy France;

    Universite de Lorraine CNRS LEMTA F-54000 Nancy France;

    Institut Jean Latnour UMR 7198 CNRS Universit de Lorraine Nancy France;

    Universite de Lorraine CNRS LEMTA F-54000 Nancy France;

    IRT M2P 4 rue Augustin Fresnel 57070 Metz France;

    Institut Jean Latnour UMR 7198 CNRS Universit de Lorraine Nancy France Laboratory of Excellence Design of Alloy Metals for Low-mass Structures (DAMAS) Univ. Lorraine Nancy France;

    Institut Jean Latnour UMR 7198 CNRS Universit de Lorraine Nancy France Laboratory of Excellence Design of Alloy Metals for Low-mass Structures (DAMAS) Univ. Lorraine Nancy France;

    Universite de Lorraine CNRS LEMTA F-54000 Nancy France;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    Inverse method; Parametric models; Polynomial models; System identification; Exogenous; Autoregressive; Future time steps;

    机译：逆方法;参数模型;多项式模型;系统识别;外源;自回归;未来的时间步骤;

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