发表机构
Georgia Institute of Technology（佐治亚理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对多元函数数据异常检测，提出ES-CP和FG-Lasso两种无监督稀疏张量分解方法，通过低秩CP分解和结构化稀疏惩罚，在模拟与锻造案例中显著提升检测与定位性能。
AI 中文摘要
多元函数数据出现在许多现代制造系统中，其中多个传感器记录密集采样的过程轨迹。监测此类数据具有挑战性，因为名义变异在样本、传感器和时间上强相关，而故障可能表现为孤立偏差或集中在有限数量的特定传感器时间轨迹中的结构化偏离。我们提出了两种保留这种多模态结构的无监督稀疏张量分解方法。逐项稀疏CP分解（ES-CP）使用逐项ℓ1惩罚来识别局部异常，而纤维稀疏组套索CP分解（FG-Lasso）结合逐项和纤维惩罚来检测局部偏差和集中在时间纤维内的异常。两种方法均通过低秩CP分解表示名义过程行为，并使用交替优化和闭式稀疏分量更新进行估计。两项模拟研究评估了不同故障结构、信号严重程度、噪声水平和缺失观测下的性能。在第一项研究中，FG-Lasso在几乎所有设置中达到或并列最高宏观F1分数，并取得最高宏观F1分数。在多通道锻造过程案例研究中，FG-Lasso和ES-CP分别获得0.85和0.82的宏观F1分数，而TRPCA和基于PCA的异常检测器为0.69或更低。结果表明，将稀疏惩罚与预期故障结构明确匹配可提高高维函数过程中的异常检测和故障定位性能。
英文摘要
Multivariate functional data arise in many modern manufacturing systems, where multiple sensors record densely sampled process trajectories. Monitoring such data is challenging because nominal variation is strongly correlated across samples, sensors, and time, while faults may appear either as isolated deviations or as structured departures concentrated within a limited number of sensor-specific temporal trajectories. We propose two unsupervised sparse tensor decomposition methods that preserve this multimode structure. Entrywise Sparse CP Decomposition (ES-CP) uses an entrywise \(\ell_1\) penalty to identify localized anomalies, whereas Fiberwise Sparse-Group Lasso CP Decomposition (FG-Lasso) combines entrywise and fiberwise penalties to detect both localized deviations and anomalies concentrated within temporal fibers. Both methods represent nominal process behavior through a low-rank CP decomposition and are estimated using alternating optimization with closed-form sparse-component updates. Two simulation studies evaluate performance under different fault structures, signal severities, noise levels, and missing observations. FG-Lasso attains or ties the highest macro F$_1$ score in almost all settings in the first study and achieves the highest macro F$_1$ score. In a multichannel forging-process case study, FG-Lasso and ES-CP obtain macro F$_1$ scores of 0.85 and 0.82, respectively, compared with 0.69 or lower for TRPCA and PCA-based anomaly detectors. The results demonstrate that explicitly matching the sparse penalty to the anticipated fault structure improves both anomaly detection and fault localization in high-dimensional functional processes.
