Wang Tao, Guo Yunfei, Zhu Fubo, Li Zhonghua
School of Mathematics and Statistics, Huaiyin Normal University, Huai'an 223300, China.
Department of Mathematics, Yanbian University, Yanji 133002, China.
Entropy (Basel). 2025 Mar 13;27(3):297. doi: 10.3390/e27030297.
This study introduces an innovative two-stage framework for monitoring and diagnosing high-dimensional data streams with sparse changes. The first stage utilizes an exponentially weighted moving average (EWMA) statistic for online monitoring, identifying change points through extreme value theory and multiple hypothesis testing. The second stage involves a fault diagnosis mechanism that accurately pinpoints abnormal components upon detecting anomalies. Through extensive numerical simulations and electron probe X-ray microanalysis applications, the method demonstrates exceptional performance. It rapidly detects anomalies, often within one or two sampling intervals post-change, achieves near 100% detection power, and maintains type-I error rates around the nominal 5%. The fault diagnosis mechanism shows a 99.1% accuracy in identifying components in 200-dimensional anomaly streams, surpassing principal component analysis (PCA)-based methods by 28.0% in precision and controlling the false discovery rate within 3%. Case analyses confirm the method's effectiveness in monitoring and identifying abnormal data, aligning with previous studies. These findings represent significant progress in managing high-dimensional sparse-change data streams over existing methods.
本研究介绍了一种用于监测和诊断具有稀疏变化的高维数据流的创新型两阶段框架。第一阶段利用指数加权移动平均（EWMA）统计量进行在线监测，通过极值理论和多重假设检验识别变化点。第二阶段涉及一种故障诊断机制，该机制在检测到异常时能准确找出异常组件。通过广泛的数值模拟和电子探针X射线微分析应用，该方法展现出卓越的性能。它能快速检测到异常，通常在变化后的一两个采样间隔内即可检测到，实现近100%的检测功效，并将I类错误率维持在标称的5%左右。故障诊断机制在识别200维异常流中的组件时准确率达99.1%，在精度上比基于主成分分析（PCA）的方法高出28.0%，并将错误发现率控制在3%以内。案例分析证实了该方法在监测和识别异常数据方面的有效性，与先前的研究结果一致。这些发现表明，在管理高维稀疏变化数据流方面，该方法相对于现有方法取得了显著进展。
