Optimized Relative Transformation Matrix Using Bacterial Foraging Algorithm for Process Fault Detection

Fault diagnosis of an aluminum electrolysis cell has long been a challenging industrial issue due to its inherent difficulty in extracting meaningful features from numerous nonlinear and highly coupled parameters. To solve this problem, this paper presents optimized relative transformation matrix (RTM) using bacterial foraging algorithm (BFA-ORTM). In particular, the operator of relative transformation is introduced to change the original variables in the spatial distribution and eigenvalues of the covariance matrix in the feature space. Then, optimization objective function on the comprehensive index φ, the squared prediction error (SPE), and Hotelling's T-squared (T 2 ) statistics are established. Furthermore, bacterial foraging algorithm is applied to obtain the optimized operator to facilitate extracting the representative principal components. Compared with traditional approaches, BFA-ORTM not only overcomes the drawback of losing feature after the normalization of nonlinear variables, but also improves the accuracy of fault diagnosis. Extensive experimental results on real-world aluminum electrolytic production process validated our proposed method's effectiveness.