ABSTRACT
Also, PCA was defined as a method which projects a high dimensional measurement space into a lower dimensional space [11]. PCA provides linear combinations of parameters which demonstrate most common trends in a data set. In mathematical terms, PCA relies on the orthogonal decomposition of the covariance matrix over the process variables along with the directions which give the maximum data variation. It is also mentioned that PCA is researched for two problems: the MSPC [12], and fault detection and isolation (FDI) problem [13]. The authors in [13] have listed diagnosis and fault detection techniques in three categories: (i) quantitative modelbased schemes, (ii) qualitative model schemes and corresponding search strategies and (iii) process data based techniques. PCA falls into the third category since it utilizes databases in an attempt to obtain the statistical (PCA model). The main indices used with PCA methods are Hotelling statistic, T2 ; sum of squared residuals, SPE; and/or Q statistics. The T2 statistic is a way to measure the variation captured in the PCA model whereas the Q statistic is a way to measure the amount of variation which was not captured by the PCA model. PCA is known to be one of the most popular MSPC monitoring methods. Nevertheless, there are some disadvantages of it. One disadvantage is that the PCA is not suitable for monitoring processes that show nonstationary behavior. The other shortcoming of the PCA model is that most of the processes run under different circumstances. The use of standard PCA solution in this kind of processes might produce too many missed faults, since the grade transitions from one operation mode to another operation mode might damage the correlation existing between various parameters. In addition, the disturbances that are measured may be treated as faults.
