论文标题
使用随机SVD实现特征系统实现的有效算法
Efficient Algorithms for Eigensystem Realization using Randomized SVD
论文作者
论文摘要
特征系统实现算法（ERA）是一种数据驱动的子空间系统识别方法，广泛用于工程领域。但是，该时代的计算成本由涉及具有块汉克尔结构的大型，密集的矩阵的奇异值分解（SVD）的步骤主导。本文通过使用随机的子空间迭代并利用矩阵的块汉克尔结构来开发用于降低SVD步骤的计算成本的计算有效算法。我们对已确定的系统矩阵中的误差和所提出算法的计算成本进行了详细的分析。我们证明了我们算法对两个测试问题的准确性和计算益处：第一个涉及一个部分微分方程，该方程对钢轨的冷却进行建模，第二个是来自Power Systems Angineering的应用。
Eigensystem Realization Algorithm (ERA) is a data-driven approach for subspace system identification and is widely used in many areas of engineering. However, the computational cost of the ERA is dominated by a step that involves the singular value decomposition (SVD) of a large, dense matrix with block Hankel structure. This paper develops computationally efficient algorithms for reducing the computational cost of the SVD step by using randomized subspace iteration and exploiting the block Hankel structure of the matrix. We provide a detailed analysis of the error in the identified system matrices and the computational cost of the proposed algorithms. We demonstrate the accuracy and computational benefits of our algorithms on two test problems: the first involves a partial differential equation that models the cooling of steel rails, and the second is an application from power systems engineering.
