Data-driven optimal sensor placement for high-dimensional system using annealing machine

Abstract

We propose a novel method for solving optimal sensor placement problem for high-dimensional system using an annealing machine. The sensor points are calculated as a maximum clique problem of the graph, the edge weight of which is determined by the proper orthogonal decomposition mode obtained from data based on the fact that a high-dimensional system usually has a low-dimensional representation. Since the maximum clique problem is equivalent to the independent set problem of the complement graph, the independent set problem is solved using Fujitsu Digital Annealer. In contrast to existing greedy methods, which select the optimal point at each step and never reconsider the point selected previously, the proposed method is superior because it is able to find the optimal set of points. As a demonstration of high dimensional system, the pressure distribution measured by the pressure-sensitive paint method, which is an optical flow diagnose method, is reconstructed from the pressure data at the calculated sensor points. The root mean square errors (RMSEs) between the pressures measured by pressure transducers and the pressures reconstructed from the proposed method, an existing greedy method, and random selection method are compared. The similar RMSE is achieved by the proposed method using approximately 1/5 number of sensor points calculated by the existing method. This method is of great importance as a novel approach for optimal sensor placement problem and a new engineering application of an annealing machine.