Correlation Coefficient Filtering Method for Optimal Sensor Layout Strategies in Inverse Problems - Qingyang Yuan; Xiangji Guo; Jiajie Han; Bingyue Han; Bo Zhang; Tian Lan (Journal of Engineering)
The gappy POD method is described as an inverse problem-solving technique based on proper orthogonal decomposition (POD). It is used to reconstruct global information with minimal measurement points and has applications in fields such as heat transfer and fluid dynamics. The accuracy and stability of the gappy POD method depend heavily on sensor number and placement. The paper proposes a correlation coefficient filtering method to optimize sensor layout, addressing the inefficiencies of traditional methods reliant on matrix condition numbers. The method’s effectiveness is tested using the one-dimensional Burgers’ equation and later the two-dimensional lid-driven cavity flow. The paper introduces two key indicators: expected coefficient of correlation (α) and remaining points (RPs). Finally, the study explores the impact of database sparsity and demonstrates the importance of this method in determining optimal sensor placement for future engineering applications. The study reflects the significant value of the correlation coefficient filtering method, based on the assumption of global correlation maximization, in evaluating optimal measurement points of the system, laying a foundation for the subsequent application of this algorithm in engineering.