Exploiting convexification for Bayesian optimal sensor placement by maximization of mutual information
Exploiting convexification for Bayesian optimal sensor placement by maximization of mutual information
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DOI：
10.1002/stc.2605
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发表时间：
2020-08-03
影响因子：
5.4
通讯作者：
Beck, James
中科院分区：
文献类型：
--
作者：
Bhattacharyya, Pinaky;Beck, James
贝叶斯最优传感器布局，在其充分的一般性，旨在最大限度地提高不确定的模型参数和预测的数据之间的相互信息要收集的传感器进行贝叶斯推理的目的。等价地，对于给定的传感器预算，在所有可能的传感器配置上，模型参数的后验的期望信息熵被最小化。在结构动力系统的背景下，这种最小化是计算昂贵的，因为大量的可能的传感器配置。在这里，一个非常有效的凸松弛计划，以确定信息和可能的最佳解决方案的问题，从而绕过了一个详尽的，往往是不可行的，组合搜索的必要性。其关键思想是放松的二进制传感器位置向量，使其对应于所有可能的传感器位置的组件位于单位间隔。然后，在这个向量上的优化是一个凸问题，可以有效地解决。这种方法总是为松弛问题产生一个唯一的解，该解通常是二元的，因此是原始问题的最优解。当不是二元的时候，放松的解决方案通常暗示原始问题的最优解决方案是什么。一个说明性的例子，使用一个50层的剪切建筑模型受到正弦地面运动，包括一个情况下，有超过47万亿可能的传感器配置。将解和计算量与贪婪方法和启发式方法进行了比较。
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.