Generalized Gaussian Distribution-Based Interval Principal Component Analysis (GGD-IPCA) for Anomaly Detection of Processes With Uncertainty
Shumei Zhang, Sijia Wang, Feng Dong
Abstract
The performance of traditional multivariate statistical process monitoring approaches highly depends on data quality. Due to noise disturbance, sensor drift, and some circumstance factors, process data are inevitably contaminated with uncertainty, which may destroy the correlation structure of original process data, resulting in an increase in false alarms and missed detections of traditional methods. In such cases, it is urgent to explore a new form to scientifically describe uncertainty and establish a reliable fault detection model. Inspire by the demands, a generalized Gaussian distribution-based interval principal component analysis (GGD-IPCA) method is proposed for industrial processes with uncertainty. First, a GGD-based interval estimation method is developed to transform uncertainty-contaminated data into interval-valued data, and represent process uncertainty in a generalized distribution form. Then, a new interval feature extraction algorithm called GGD-IPCA is proposed by redefining mean, inner product, and square norm operators under an adjustable interval distribution form of process uncertainty with different shape parameters. Two monitoring statistics applicable to interval data are defined to monitor the operating conditions. The key to discriminate GGD-IPCA from many well-established IPCA methods including centers PCA and complete-information PCA is its ability to flexibly reduce the dimension of interval data with full consideration of various interval distribution. Experiments show that compared with the other eight algorithms, GGD-IPCA averagely reduces MDR by 4.35% with FAR no more than 2.00% in a numerical example, and reduces FAR by 15.60% with average MDR as low as 2.94% in Tennessee-Eastman process.