关键词: Gappy 本征正交分解, 相关系数过滤法, 有限传感器布局优化, 流场重构

Abstract:

To address the low efficiency of point selection based on the condition number criterion in optimizing limited sensor layout for the Gappy proper orthogonal decomposition （POD） method, a correlation coefficient filtering method is proposed to enhance both selection efficiency and reconstruction accuracy. The proposed method is grounded on the global correlation maximization hypothesis, utilizing a correlation coefficient matrix to select optimal measurement point location and introducing the expected coefficient of correlation degree and remaining points as key parameters. Simulation experiments are performed on the one-dimensional Burgers’ equation and two-dimensional lid-driven cavity flow numerical example, comparing the influence of different expectation of relevance level and remaining points on the reconstruction accuracy of Gappy POD. The results indicate that the proposed method reduces the number of sensors while ensuring reconstruction accuracy, and outperforms traditional methods such as the condition number criterion and genetic algorithm in both efficiency and precision. The proposed method has high application value in sparse sensor layout optimization and can provide an efficient strategy for flow field reconstruction in complex systems.

Key words: Gappy proper orthogonal decomposition （POD）, correlation coefficient filtering method, finite sensor layout optimisation, flow field reconstruction