To tackle this challenge, a large number of well-known techniques for selecting the number of PCs have been proposed. The choice of PCs is a crucial step for the interpretation of monitoring results or subsequent analysis because it could lead to the loss of important information or the inclusion of undesirable interference. However, the determination of the number of PCs is not unique, given that the sensor outputs are generally disturbed by noise ( Tamura and Tsujita, 2007). In this methodology, the dimension of the PCA model, which is the estimation of the optimal number of principal components (PCs) to retain, must be determined and has an important role on the process monitoring performance. PCA-based and related monitoring methods, which build statistical models from normal operation data and partition the measurements into a principal component subspace (PCS) and a residual subspace (RS), are among the most widely used multivariate statistical methods. Other complementary multivariate statistical process monitoring methods, including canonical variate analysis, kernel PCA, dynamic PCA, and independent component analysis, have been proposed to address the limitations of PCA- or PLS-based monitoring strategies ( Russell et al., 2000 Juricek et al., 2004 Lee et al., 2004a 2006). Multivariate statistical methods, such as principal component analysis (PCA) and partial least squares (PLS), are widely used in industry for process monitoring ( Nomikos and MacGregor, 1995 Qin, 2003 Ge and Song, 2008 Garcia-Alvarez et al., 2012).
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