Dynamic Mode Decomposition for Compressive System Identification
Dynamic Mode Decomposition for Compressive System Identification
复制标题
DOI：
10.2514/1.j057870
复制
发表时间：
2020-02-01
期刊：
影响因子：
2.5
通讯作者：
Brunton, Steven L.
中科院分区：
文献类型：
--
作者：
Bai, Zhe;Kaiser, Eurika;Brunton, Steven L.
动态模式分解已经成为一种领先的技术，以确定时空相干结构的高维数据，受益于强连接到非线性动力系统通过库普曼算子。在这项工作中，最近的两个创新，扩展动态模式分解系统的驱动和系统的大量子采样测量集成和统一。当结合起来，这些方法产生一个新的框架压缩系统识别。可以从有限的输入-输出数据中识别低阶模型，并利用压缩感知重建相关的全状态动态模式，从而为降阶模型的状态增加可解释性。此外，当完整状态数据可用时，可以通过首先压缩数据来显著加速下游计算。这个统一的框架在两个模型系统上进行了演示，研究了传感器噪声、不同类型的测量（例如，点传感器、高斯随机投影等），压缩比和不同的致动选择（例如，本地化、宽带等）。在第一个例子中，这种架构是探索一个测试系统与已知的低秩动态和人为膨胀的状态维度。第二个例子是一个实际的工程应用，给出了低雷诺数下流体流过俯仰翼型的情况。这个例子提供了一个具有挑战性的和现实的测试情况下，所提出的方法，结果表明，占主导地位的相干结构的特点，尽管驱动和大量的子采样数据。
Dynamic mode decomposition has emerged as a leading technique to identify spatiotemporal coherent structures from high-dimensional data, benefiting from a strong connection to nonlinear dynamical systems via the Koopman operator. In this work, two recent innovations that extend dynamic mode decomposition to systems with actuation and systems with heavily subsampled measurements are integrated and unified. When combined, these methods yield a novel framework for compressive system identification. It is possible to identify a low-order model from limited input-output data and reconstruct the associated full-state dynamic modes with compressed sensing, adding interpretability to the state of the reduced-order model. Moreover, when full-state data are available, it is possible to dramatically accelerate downstream computations by first compressing the data. This unified framework is demonstrated on two model systems, investigating the effects of sensor noise, different types of measurements (e.g., point sensors, Gaussian random projections, etc.), compression ratios, and different choices of actuation (e.g., localized, broadband, etc.). In the first example, this architecture is explored on a test system with known low-rank dynamics and an artificially inflated state dimension. The second example consists of a real-world engineering application given by the fluid flow past a pitching airfoil at low Reynolds number. This example provides a challenging and realistic test case for the proposed method, and results demonstrate that the dominant coherent structures are well characterized despite actuation and heavily subsampled data.