An Inverse Source Problem for a One-dimensional Wave Equation: An Observer-Based Approach
An Inverse Source Problem for a One-dimensional Wave Equation: An Observer-Based Approach
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DOI：
10.25781/kaust-5s244
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发表时间：
2013-05
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影响因子：
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通讯作者：
Sharefa Asiri
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作者：
Sharefa Asiri
一维波动方程的逆源问题：基于观测器的方法Sharefa Mohammad Asiri观测器在动力系统理论中是众所周知的。它们用于从一些测量中估计系统的状态。然而，最近观测器也被开发来估计由偏微分方程控制的系统的一些未知量。我们的目标是设计一个观测器来求解一维波动方程的源反问题。首先，问题在空间和时间上离散化，然后基于部分场测量（即测量采取的波动方程的解）的自适应观测器被应用于估计状态和源。我们看到了这种观察者在无噪声和有噪声情况下的有效性。在每种情况下，数值模拟，以说明这种方法的有效性。最后，我们比较了观测器方法与Tikhonov正则化方法的性能。
An Inverse Source Problem for a One-dimensional Wave Equation: An Observer-Based Approach Sharefa Mohammad Asiri Observers are well known in the theory of dynamical systems. They are used to estimate the states of a system from some measurements. However recently observers have also been developed to to estimate some unknowns for systems governed by partial differential equations. Our aim is to design an observer to solve inverse source problem for a onedimensional wave equation. Firstly, the problem is discretized in both space and time and then an adaptive observer based on partial field measurements (i.e measurements taken form the solution of the wave equation) is applied to estimate both the states and the source. We see the effectiveness of this observer in both noise-free and noisy cases. In each case, numerical simulations are provided to illustrate the effectiveness of this approach. Finally, we compare the performance of the observer approach with Tikhonov regularization approach.