This letter presents a closed-form solution to estimate space-dependent transport parameters of a linear one dimensional diffusion-transport-reaction equation. The infinite dimensional problem is approximated by a finite dimensional model by 1) taking a frequency domain approach, 2) linear parameterization of the unknown parameters, and 3) using a semi-discretization. Assuming full state knowledge, the commonly used output error criterion is rewritten as the equation error criterion such that the problem results in linear least squares. The optimum is then given by a closed-form solution, avoiding computational expensive optimization methods. Functioning of the proposed method is illustrated by means of simulation.

中文翻译：

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估计热量和质量传递中空间变化参数的封闭形式解决方案

这封信提出了一种封闭形式的解决方案，用于估计线性一维扩散-传输-反应方程的空间相关传输参数。无限维问题可以通过有限维模型来近似：1）采用频域方法； 2）未知参数的线性参数化； 3）使用半离散化。假设掌握全部状态，则将常用的输出误差准则重写为方程式误差准则，以使问题产生线性最小二乘法。然后，通过封闭形式的解决方案来提供最佳值，从而避免了计算量大的优化方法。通过仿真说明了所提出方法的功能。