5. Nonlinear Process Monitoring: Part 1

Conventional kernel principal component analysis (KPCA) may not function well for nonlinear process monitoring, 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 has been incorporated into KPCA. Through this method, a new score variable which was called improved residual in the statistical local approach is constructed. This new variable approximately follows Gaussian distribution, in spite of which distribution the original data follow. Like the traditional method, two statistics can be constructed for process monitoring, with their corresponding confidence limits determined by a $${{\chi }^{2}}$$ distribution. Besides of the improvement made on KPCA, the joint local approach-KPCA method also shows superiority on detection sensitivity, especially for small faults slow changes of the process.