Anomaly Detection of Nonstationary Long-Memory Processes Based on Fractional Cointegration Vector Autoregression

Aiming at the nonstationary characteristics of many practical industrial systems as well as the long memory and seasonality of some process data, this article proposes a novel nonstationary process anomaly detection method based on fractional cointegration vector autoregression (FCVAR). First, the augmented Dickey–Fuller (ADF) test is used to divide the variables into stationary and nonstationary categories. For the nonstationary variables, the trend extraction algorithm is used to extract the nonstationary trend of the variables to avoid the trend information from being overwhelmed due to the strong seasonality of the process data. Meanwhile, considering that the extracted trend time series have a long-memory characteristic and the fractional cointegration describes the intrinsic long-term equilibrium relationship of the trend series better than the integer cointegration, a novel anomaly detection algorithm based on the FCVAR model is proposed. For the stationary variables, including the original stationary variables and the detrended series of nonstationary variables after trend extraction, the proposed method merges the two components into a new matrix and establishes an anomaly detection model based on the kernel principal component analysis (kpca) algorithm. Finally, simulations using wastewater treatment process (WWTP) data have indicated that the proposed method achieves the desired results and exhibits high detection performance, particularly in the detection of tiny gradual-type anomalies.