论文标题
部分可观测时空混沌系统的无模型预测
Exploiting sparseness in damage characterization: A close look at the regularization techniques
论文作者
论文摘要
储层计算是预测湍流的有力工具，其简单的架构具有处理大型系统的计算效率。然而，其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间，然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用，该系统模拟了湍流的若干特征。我们表明，使用径向基函数作为非线性投影器，即使只有部分观测并且不知道控制方程，也能稳健地捕捉复杂的系统非线性。最后，我们表明，当测量稀疏、不完整且带有噪声，甚至控制方程变得不准确时，我们的网络仍然可以产生相当准确的预测，从而为实际湍流系统的无模型预测铺平了道路。
The idea of exploiting sparseness in under-determined damage characterization problems is not new, and regularizations techniques that tend to promote sparseness, such as L1-norm minimization, have been investigated in the last ten years or so. Although various claims of merit have been made, two interconnected issues put these claims into question, and this paper brings some attention to the matter. The first is that the relationship between the structural parameters and the modal features previously considered has been linear and to ensure that the premise was closely realized, only very small damage severities have been considered. The second issue, intimately related to the first, is the fact that the noise, which has been typically taken as small relative to the "change in the features", is then unrealistically small. In problems where the damage is sufficiently large, the nonlinear dependence of the features on the parameters cannot be generally discarded. It is found that the attainable performance is much less "impressive" that what has been often claimed. The paper also examines the potential merit of using Lp-norm (0<p<1) minimization, instead of L1-norm minimization which, to the knowledge of the writers, has not been previously examined in damage characterization research. In this case we also find that, contrary to claims made in other areas, this norm does not lead to any general improvement over the performance attained by minimizing the L1-norm.
