Effective anomaly detection of sensing data is essential for identifying potential system failures. Because they require no prior knowledge or accumulated labels, and provide uncertainty presentation, the probability prediction methods (e.g., Gaussian process regression (GPR) and relevance vector machine (RVM)) are especially adaptable to perform anomaly detection for sensing series. Generally, one key parameter of prediction models is coverage probability (CP), which controls the judging threshold of the testing sample and is generally set to a default value (e.g., 90% or 95%). There are few criteria to determine the optimal CP for anomaly detection. Therefore, this paper designs a graphic indicator of the receiver operating characteristic curve of prediction interval (ROC-PI) based on the definition of the ROC curve which can depict the trade-off between the PI width and PI coverage probability across a series of cut-off points. Furthermore, the Youden index is modified to assess the performance of different CPs, by the minimization of which the optimal CP is derived by the simulated annealing (SA) algorithm. Experiments conducted on two simulation datasets demonstrate the validity of the proposed method. Especially, an actual case study on sensing series from an on-orbit satellite illustrates its significant performance in practical application.
Keywords: Gaussian process regression; anomaly detection; coverage probability; prediction interval; relevance vector machine; satellite.