Directional PCA for Fast Detection and Accurate Diagnosis: A Unified Framework
提出定向主成分分析方法，通过将故障限定在指定方向或正交方向，加快检测速度并提高诊断准确性，统一了现有监控指标如Hotelling T²和SPE，并给出最优组合统计量。
Many methods for monitoring multivariate processes are built on principal component analysis (PCA), which, however, simply tells whether the process is faulty or not. In fact, there is still room for the improvement of the early detection performance by exploiting fully the information given by fault directions. To this end, this article proposes a novel directional PCA (diPCA) approach. First, by narrowing down faults to a specified direction or composite mutually orthogonal directions, diPCA can speed fault detection and facilitate accurate fault diagnosis. It also has good theoretical properties that guarantee concise control limits. Second, with appropriate fault directions, diPCA provides a unified framework for process monitoring and includes existing monitoring indices, such as Hotelling’s <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$T^{2}$ </tex-math></inline-formula> and the squared prediction error (SPE), as special cases. Third, diPCA also naturally results in a new combined monitoring statistic, which is composed of both <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$T^{2}$ </tex-math></inline-formula> and SPE, and provides an optimal ratio of their combination. The Monte Carlo simulation results have demonstrated the power of the proposed monitoring and diagnostic methods stemming from diPCA. The proposed methods have also been implemented into the Tennessee Eastman process.