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Evaluation of generalized polynomial function specification methods

机译：广义多项式函数指定方法的评估

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摘要

The sequential function specification method (SFSM) for solution of the inverse heat conduction problem was introduced by Beck (1968) , and described in more detail [2] in 1985. This method assumes a functional form for the unknown heat flux in order to add more (future) data to regularize the problem and facilitate estimation of the next heat flux component. Two basic forms for the unknown heat flux have been well-explored: a constant function (zeroth order polynomial), and a linear function of time (a first order polynomial). Until now, only these two “traditional” forms have been used and higher order polynomial function approximations have not been considered.A generalized polynomial sequential function specification method (SFSM) is developed and evaluated in this paper. For higher order polynomials, the proper balance of past and future time step information is not obvious; the optimal balance is investigated herein. A generalized algorithm is used to define polynomials of any degree and estimate heat fluxes using SFSM with any number of past and future data. Seven heat flux test cases, including three non-polynomial heat flux variations, are used to evaluate the traditional and new methods, and the “optimal” number of future time steps is chosen for each case. The filter coefficient concept [3] provides additional insights into the new SFSM approaches. Filter coefficients are calculated with the optimal number of future time steps and the results are discussed.
机译：Beck（1968）引入了求解逆热传导问题的序贯函数规范方法（SFSM），并在1985年进行了更详细的描述[2]。该方法假定未知热通量为函数形式，以便增加更多（未来）数据来解决问题并简化下一热通量的估算。未知热通量的两种基本形式已经得到了很好的探索：一个常数函数（零阶多项式）和一个时间线性函数（一阶多项式）。到目前为止，仅使用了这两种“传统”形式，而未考虑高阶多项式函数逼近。本文开发并评估了广义多项式顺序函数指定方法（SFSM）。对于高阶多项式，过去和将来的时间步长信息之间的适当平衡并不明显。在此研究最佳平衡。通用算法用于定义任意次数的多项式，并使用SFSM和任意数量的过去和将来的数据来估计热通量。七个热通量测试用例（包括三个非多项式热通量变化）用于评估传统方法和新方法，并为每种情况选择“最佳”数量的未来时间步长。滤波器系数概念[3]提供了对新SFSM方法的更多见解。使用未来时间步长的最佳数量来计算滤波器系数，并讨论结果。

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  • 来源
    《International Journal of Heat and Mass Transfer》 |2018年第7期|1116-1127|共12页
  • 作者

    F. Samadi; K.A. Woodbury; J.V. Beck;

  • 作者单位

    Mechanical Engineering Department, The University of Alabama;

    Mechanical Engineering Department, The University of Alabama;

    Michigan State University;

  • 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
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