Incipient fault detection of nonlinear chemical processes based on probability-related randomized slow feature analysis

Slow feature analysis (SFA) has achieved the successful applications in the chemical process fault detection field. However, the basic SFA omits the process nonlinearity and lacks the sufficient mining of the features' probability information so that the incipient fault monitoring performance is unsatisfactory. To alleviate this problem, this paper proposes an improved SFA method, referred to as probability-related randomized SFA (PRSFA), to enhance the detection of incipient faults. Different from the current nonlinear SFA version based on the kernel function, which results in the huge computation complexity, the proposed method uses random Fourier mapping to deal with the data nonlinear transformation more efficiently. By combining the random Fourier mapping and SFA, a randomized SFA model is developed to capture the nonlinear slow features. Furthermore, in order to mine the probability distribution information hidden in these slow features, the Kullback Leibler divergence (KLD) is introduced to measure the changing of the slow features' probability distributions. The original nonlinear slow features are converted into the corresponding KLD features, which are more sensitive to the incipient faults. Considering the random property of KLD features resulted from the random Fourier mapping, multiple randomized SFA sub-models are developed and all the sub-models are integrated through Bayesian inference mechanism to construct the global statistics for the whole system monitoring. The simulation results on a continuous stirred tank reactor (CSTR) system show that the proposed method has better incipient fault detection performance than the traditional SFA and kernel SFA methods.

Automated summary

This paper proposes an improved SFA method, called probability-related randomized SFA (PRSFA), to enhance the detection of incipient faults. The proposed method combines random Fourier mapping and SFA to capture the nonlinear slow features, and introduces Kullback Leibler divergence (KLD) to measure the changing of the slow features' probability distributions. Multiple randomized SFA sub-models are developed and integrated through Bayesian inference mechanism to construct the global statistics for the whole system monitoring. Simulation results demonstrate that the proposed method outperforms traditional SFA and kernel SFA methods in incipient fault detection performance.