This paper develops a robust dynamic mode decomposition (RDMD) method endowed with statistical and numerical robustness. Statistical robustness ensures estimation efficiency at the Gaussian and non-Gaussian probability distributions, including heavy-tailed distributions. The proposed RDMD is statistically robust because the outliers in the data set are flagged via projection statistics and suppressed using a Schweppe-type Huber generalized maximum-likelihood estimator that minimizes a convex Huber cost function. The latter is solved using the iteratively reweighted least-squares algorithm that is known to exhibit a better convergence property and numerical stability than the Newton algorithms. Several numerical simulations using canonical models of dynamical systems demonstrate the excellent performance of the proposed RDMD method. The results reveal that it outperforms several other methods proposed in the literature.
翻译:本文开发了具有统计和数字稳健度的强势动态模式分解(RDMD)方法。 统计稳健性确保了高山和非高山概率分布的估算效率, 包括重尾分布。 拟议的RDMD具有统计性强, 因为数据集的外部值通过投影统计来标注, 并使用Schweppe类的Huber通用最大相似度估计仪来抑制。 后者使用迭代再加权最小方程式算法来解决, 后者已知比牛顿算法具有更好的趋同属性和数字稳定性。 使用动态系统的卡通模型进行的若干数字模拟显示了拟议的RDMD方法的出色性能。 结果显示它比文献中提议的几种其他方法要好。