Intelligent Detection for Key Performance Indicators in Industrial-Based Cyber-Physical Systems

Intelligent anomaly detection for key performance indicators (KPIs) is important for keeping services reliable in industrial-based cyber-physical systems (CPS). However, it is common in practice for various KPI sampling strategies to be utilized. We experimentally verify that anomaly detection is highly sensitive to irregular sampling, and accordingly go on to investigate low-cost anomaly detection for large-scale irregular KPIs. Irregular KPIs can be classified into four types: equal interval and unequal quantity (EIUQ) KPIs, unequal interval (UI) KPIs, unequal interval with equal duration (UIED) KPIs, and segmented irregular KPIs. In this article, we propose an anomaly detection framework based on these irregular types. Moreover, to handle the various lengths and phase shifts among EIUQ KPIs, we propose a normalized version of unequal cross-correlation, which slides the KPIs to enable finding the most similar position. To avoid high computational costs, we analyze the low-rank feature of KPIs data and propose a matrix factorization-based alignment algorithm for UIED KPIs; this algorithm treats UIED KPIs as an incomplete matrix and recovers the KPIs to align them before performing anomaly detection. Extensive simulations using three public datasets and two real-world datasets demonstrate that our algorithm can achieve a larger F1-score than Minkowski distance and less time than dynamic time warping distance.