Principal Component Analysis in Data Reconciliation

Correlation is inherent in chemical processes even if one could assume that there is no correlation among the data. PCA is an effective tool in multivariate data analysis. It transforms a set of correlated variables into a new set of uncorrelated ones, known as principal components. 

Principal components analysis (PCA) and project to latent structure (PLS) were suggested to absorb information from continued-process data (Kresta et ai, 1991 MacGregor and Kourti, 1995 Kourti and MacGregor, 1994). The key point of these approaches is to utilize PCA or PLS to compress the data and extract the information by projecting them into a low-dimension subspace that summarizes all the important information. Then, further monitoring work can be conducted in the reduced subspace. Two comprehensive reviews of these methods have been published by Kourti and Macgregor (1995) and Martin etal. (1996). 

The key idea of this section is to combine PCA and the steady-state data reconciliation model to provide sharper and less confounding statistical tests for gross errors, through exploiting the correlation. 

As shown in previous chapters, the residuals of the constraints for linear steady-state processes are defined as 

Note We have considered that all variables are measured. If this is not the case, the unmeasured variables can be removed using some of the techniques described in Chapters 3 and 4. 4 

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Principal Component Analysis in Data Reconciliation 219 11.5 Conclusions 223... 

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