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Resolution of two‐way data from spectroscopic monitoring of reaction or process systems by parallel vector analysis (PVA) and window factor analysis (WFA): inspection of the effect of mass balance, methods and simulations

The effect of mass balance on the analysis of two‐way data of reaction or process systems is investigated. It is shown that the rank‐deficient species‐related bilinear model can be converted to a full‐rank reaction‐related bilinear model, and in general situations the chemical rank for a system is the number of reactions plus one. Two slightly modified procedures are thus suggested to extract the spectral subspaces essential for resolution and to ascertain the number of reactions in different time domains. Based on the reaction‐related bilinear model, a procedure of window factor analysis (WFA) is implemented for resolving the extent curves of reactions. A new two‐way resolution approach, parallel vector analysis (PVA), is also developed. The idea of PVA is to construct a set of subspaces comprising only one common (spectral) component and then find a vector that is in parallel with a series of vectors coming from different subspaces. With suitably constructed subspaces the PVA procedure offers a versatile avenue to approach the unique resolution of spectral profiles. A four‐component system which comprises four different processes or reactions is simulated. Results obtained reveal that favorable resolution is achieved for the spectral and concentration profiles by the suggested procedures of WFA and PVA. Copyright © 2003 John Wiley & Sons, Ltd.