Fault detection method based on a copula probability model built from historical normal and failure samples

As modern information technology continues to advance, industrial processes are increasingly defined by their digital, informational, and intelligent characteristics. Control systems not only store a wealth of operational data reflecting normal system functioning but also retain data related to malfunctions. Unfortunately, due to the constraints of the computational framework, this fault-related information is often overlooked during the conventional fault detection process. As a result, the fault detection model may become overly sensitive to minor variations in normal operating conditions while lacking the necessary sensitivity to detect genuine fault signals. To address this issue, this paper improves the parameter estimation process of the fault detection method based on vine copula dependency description (VCDD). Traditionally, VCDD estimates parameters for individual bivariate copula functions sequentially. In contrast, this paper introduces a novel vine copula-based fault detection method (VCDD-PCFD), which utilizes a global parameter estimation approach. This approach employs an intelligent search algorithm that calculates penalties based on fault data. A training dataset is constructed from a historical database, comprising both normal operational data and fault operational data. The model structure is determined through a stepwise VCDD solution process, utilizing only the normal data from the training set. Subsequently, the Particle Swarm Optimization (PSO) algorithm is applied to identify the optimal parameters for all bivariate copulas, using the complete training set with normal data to assess the first part of fitness, while fault data is used to compute penalties. The integration of the VCDD model with the VCDD-PCFD model has strengthened the model's stability and improved the detection rate of unknown faults. The application of this dual-model detection method to a numerical example and the Tennessee Eastman benchmark process (TE process) has demonstrated its effectiveness when compared to other fault detection methods, including the VCDD method. The results show that the proposed method achieves significantly better detection performance.