Bayesian optimal sensor placement, in its full generality, seeks to maximize the mutual information between uncertain model parameters and the predicted data to be collected from the sensors for the purpose of performing Bayesian inference. Equivalently, the expected information entropy of the posterior of the model parameters is minimized over all possible sensor configurations for a given sensor budget. In the context of structural dynamical systems, this minimization is computationally expensive because of the large number of possible sensor configurations. Here, a very efficient convex relaxation scheme is presented to determine informative and possibly optimal solutions to the problem, thereby bypassing the necessity for an exhaustive, and often infeasible, combinatorial search. The key idea is to relax the binary sensor location vector so that its components corresponding to all possible sensor locations lie in the unit interval. Then, the optimization over this vector is a convex problem that can be efficiently solved. This method always yields a unique solution for the relaxed problem, which is often binary and therefore the optimal solution to the original problem. When not binary, the relaxed solution is often suggestive of what the optimal solution for the original problem is. An illustrative example using a 50‐story shear building model subject to sinusoidal ground motion is presented, including a case where there are over 47 trillion possible sensor configurations. The solutions and computational effort are compared with greedy and heuristic methods.

中文翻译：

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通过互信息最大化来利用贝叶斯最优传感器放置的凸化

就其全部通用性而言，贝叶斯最优传感器放置试图最大化不确定模型参数与要从传感器收集的预测数据之间的相互信息，以进行贝叶斯推理。等效地，对于给定的传感器预算，在所有可能的传感器配置上，模型参数后部的预期信息熵最小。在结构动力系统的情况下，由于可能的传感器配置数量众多，因此这种最小化在计算上是昂贵的。在这里，提出了一种非常有效的凸松弛方案来确定问题的信息性和可能的​​最佳解决方案，从而绕过了详尽且通常不可行的组合搜索的必要性。关键思想是放宽二进制传感器位置矢量，以使其对应于所有可能传感器位置的分量位于单位间隔内。那么，对该向量的优化是一个可以有效解决的凸问题。该方法始终为松弛问题提供唯一的解决方案，该问题通常是二进制的，因此是原始问题的最佳解决方案。如果不是二进制，则宽松的解决方案通常会暗示原始问题的最佳解决方案是什么。给出了一个使用50层剪力建筑模型进行正弦地面运动的示例，其中包括超过47万亿个可能的传感器配置的情况。将解决方案和计算量与贪婪和启发式方法进行比较。