Improved kernel PCA-based monitoring approach for nonlinear processes

Conventional kernel principal component analysis (KPCA) may not function well for nonlinear processes, since the Gaussian assumption of the method may be violated through nonlinear and kernel transformation of the original process data. To overcome this deficiency, a statistical local approach is incorporated into KPCA. Through this method, a new score variable which was called improved residual in the statistical local approach is constructed. The new variable approximately follows Gaussian distribution, in spite of which distribution the original data follows. Two new statistics are constructed for process monitoring, with their corresponding confidence limits determined by a χ2χ2 distribution. Besides of the improvement made on KPCA, the new joint local approach-KPCA method also shows superiority on detection sensitivity, especially for small faults slow changes of the process. The new method is exemplified using a numerical study and also tested in the complicated Tennessee Eastman (TE) benchmark process.