多保真度传感器选择：在成本约束下放置廉价和昂贵传感器的贪婪算法
Multi-fidelity sensor selection: Greedy algorithms to place cheap and expensive sensors with cost constraints
摘要：
我们开发贪婪算法来近似多保真度传感器选择问题的最优解，这是一个成本约束优化问题，规定在环境或状态空间中的廉价（低信噪比）和昂贵（高信噪比）传感器的位置和数量。具体来说，我们评估廉价和昂贵的传感器的组成，以及它们的位置，需要实现准确的重建的高维状态。我们使用列枢轴QR分解，以获得初步的传感器位置。每种类型的传感器使用多少高度依赖于传感器噪声水平、传感器成本、总成本预算和测量数据的奇异值谱。这样的细微差别使我们能够提供传感器的选择建议的基础上计算结果的参数空间的渐近区域。我们还提出了一个系统的探索的模式和传感器的数量对重建误差的影响时，使用一种类型的传感器。我们广泛的探索多保真度传感器组成的数据特性的函数是第一次提供最佳的多保真度传感器选择的指导方针。
英文摘要：
We develop greedy algorithms to approximate the optimal solution to the multi-fidelity sensor selection problem, which is a cost constrained optimization problem prescribing the placement and number of cheap (low signal-to-noise) and expensive (high signal-to-noise) sensors in an environment or state space. Specifically, we evaluate the composition of cheap and expensive sensors, along with their placement, required to achieve accurate reconstruction of a high-dimensional state. We use the column-pivoted QR decomposition to obtain preliminary sensor positions. How many of each type of sensor to use is highly dependent upon the sensor noise levels, sensor costs, overall cost budget, and the singular value spectrum of the data measured. Such nuances allow us to provide sensor selection recommendations based on computational results for asymptotic regions of parameter space. We also present a systematic exploration of the effects of the number of modes and sensors on reconstruction error when using one type of sensor. Our extensive exploration of multi-fidelity sensor composition as a function of data characteristics is the first of its kind to provide guidelines towards optimal multi-fidelity sensor selection.
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