动态相关基下代价约束的传感器选择
Sensor Selection With Cost Constraints for Dynamically Relevant Bases
摘要：
我们考虑成本约束稀疏传感器选择全状态重建，应用一个众所周知的贪婪算法的动力系统，通常的奇异值分解（SVD）的基础可能无法使用或首选。我们应用成本修改，列枢轴QR分解的物理相关的基础-枢轴对应于传感器的位置，这些位置是惩罚与异构费用函数。在考虑不同的基地，我们能够考虑到特定系统的动态，产生传感器阵列，在所选择的基础上，传感器的成本和性能接近帕累托最优。这种灵活性扩展了我们的框架，包括驱动和动态估计，并选择传感器没有训练数据。我们提供了三个例子，从物理和工程科学和评估传感器的选择在三个动态相关的基础：截断平衡模式的控制系统，动态模式分解（DMD）模式，和分析模式的基础。我们发现，这些基地都产生有效的传感器阵列和重建各自的系统。在可能的情况下，我们比较结果使用SVD的基础和评估方法之间的权衡。
英文摘要：
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.
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