论文标题
传感器选择具有成本限制的动态相关基础
Sensor Selection With Cost Constraints for Dynamically Relevant Bases
论文作者
论文摘要
我们考虑用于全州重建的成本约束稀疏传感器选择，将众所周知的贪婪算法应用于动态系统，通常无法获得或优先使用通常的单数值分解（SVD）基础。我们将成本修改的，柱状QR的分解应用于物理相关的基础 - 枢轴对应于传感器位置，这些位置通过异质成本函数进行惩罚。在考虑不同的基础时，我们能够说明特定系统的动力学，从而产生几乎在所选的传感器成本和性能上几乎最佳的传感器阵列。这种灵活性将我们的框架扩展到包括驱动和动态估计，并在没有培训数据的情况下选择传感器。我们提供了来自物理和工程科学的三个示例，并在三个动态相关的基础上评估传感器选择：控制系统的截断平衡模式，动态模式分解（DMD）模式和分析模式的基础。我们发现这些基础都为其各自的系统产生有效的传感器阵列和重建。在可能的情况下，我们使用SVD基础进行比较，并评估方法之间的权衡。
We consider cost-constrained sparse sensor selection for full-state reconstruction, applying a well-known greedy algorithm to dynamical systems for which the usual singular value decomposition (SVD) basis may not be available or preferred. We apply the cost-modified, column-pivoted QR decomposition to a physically relevant basis -- the pivots correspond to sensor locations, and these locations are penalized with a heterogeneous cost function. In considering different bases, we are able to account for the dynamics of the particular system, yielding sensor arrays that are nearly Pareto optimal in sensor cost and performance in the chosen basis. This flexibility extends our framework to include actuation and dynamic estimation, and to select sensors without training data. We provide three examples from the physical and engineering sciences and evaluate sensor selection in three dynamically relevant bases: truncated balanced modes for control systems, dynamic mode decomposition (DMD) modes, and a basis of analytic modes. We find that these bases all yield effective sensor arrays and reconstructions for their respective systems. When possible, we compare to results using an SVD basis and evaluate tradeoffs between methods.
