2.4.1 Wavelets

Bakshi [28, 29] has proposed the use of a nonlinear multiscale principal component analysis methodology for process monitoring and fault detection based on multilevel wavelet decomposition and nonlinear component extraction by the use of input-training neural networks. In this case, wavelets are first used to decompose the data into different scales, after which PCA was applied to the reconstituted time series data. Choi et al. [30] have proposed nonlinear multiscale multivariate monitoring of dynamic processes based on kernel PCA, while Xuemin and Xiaogang [31] have proposed an integrated multiscale approach where kernel PCA is used on measured process signals decomposed with wavelets and have also proposed a similarity factor to identify fault patterns.
