应用Calerkin方法辨识一维抛物型偏微分方程及其边界条件中的参数
The Application of Galerkin's Method to Parame-ter Identification of One-Dimensional Parabolic Partial Differential Equation and its Boundary Conditions
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摘要: 本文提出了一种一维抛物型偏微分方程及其边界条件中定常参数的辨识方法.这一方法 将所研究的偏微分方程初-边值问题转化为具有已知初值的常微分方程组问题,然后再利用最 优化方法将参数估算出来.数值仿真与实验验证都表明这一辨识方法是可行的.
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关键词:
- 分布参数系统 /
- 系统辨识 /
- Ritz-Galerkin方法
Abstract: This paper presents a method which can simultaneously identify constant parameters in one-dimensional parabolic partial differential equation and its boundary conditions. Here the initial-boundary value problem of partial differential equation is reduced into a set of ordinary differential equations with known initial conditions. Then optimization approaches can be used to evaluate the parameters. Both the numerical example and the physical experiment show the applicability of this identification method.
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