Batch process fault detection and identification based on discriminant global preserving kernel slow feature analysis

As an attractive nonlinear dynamic data analysis tool, global preserving kernel slow feature analysis (GKSFA) has achieved great success in extracting the high nonlinearity and inherently time-varying dynamics of batch process. However, GKSFA is an unsupervised feature extraction method and lacks the ability to utilize batch process class label information, which may not offer the most effective means for dealing with batch process monitoring. To overcome this problem, we propose a novel batch process monitoring method based on the modified GKSFA, referred to as discriminant global preserving kernel slow feature analysis (DGKSFA), by closely integrating discriminant analysis and GKSFA. The proposed DGKSFA method can extract discriminant feature of batch process as well as preserve global and local geometrical structure information of observed data. For the purpose of fault detection, a monitoring statistic is constructed based on the distance between the optimal kernel feature vectors of test data and normal data. To tackle the challenging issue of nonlinear fault variable identification, a new nonlinear contribution plot method is also developed to help identifying the fault variable after a fault is detected, which is derived from the idea of variable pseudo-sample trajectory projection in DGKSFA nonlinear biplot. Simulation results conducted on a numerical nonlinear dynamic system and the benchmark fed-batch penicillin fermentation process demonstrate that the proposed process monitoring and fault diagnosis approach can effectively detect fault and distinguish fault variables from normal variables.