Efficient recursive kernel canonical variate analysis for monitoring nonlinear time-varying processes

Kernel canonical variate analysis (KCVA) cannot be adopted for monitoring nonlinear time-varying processes because of changes in variance, mean, and correlation between variables. Efficient recursive kernel canonical variate analysis (ERKCVA) is thus proposed to monitor the nonlinear time-varying processes. In a high-dimensional feature space, the covariance matrix can be updated recursively by the exponentially weighted moving average approach. The first-order perturbation theory is introduced to obtain the recursive singular value decomposition of the Hankel matrix, which can significantly reduce the computational cost of the proposed method. Prediction errors and state variables are non-Gaussian; thus, upper control limits can be derived from the estimated probability density function by kernel density estimation. The proposed method is demonstrated by simulating a continuous stirred tank reactor. Simulation results indicate that ERKCVA could efficiently capture the predefined normal and natural changes in nonlinear time-varying processes. In addition, ERKCVA can also identify 4 types of sensor faults.