Rank Deficiency and Rank Augmentation

M. Amrhein, B. Srinivasan, N. Bhatt, S. Srinivasan, J. Billeter and D. Bonvin
Ongoing project (1994-1996, 2008, 2012)

This project was concerned with the development of solutions to the problem of rank deficiency in concentration data and spectroscopy. A first research campaign defined the concept of rank deficiency in spectroscopy and investigated rank augmentation solutions, such as the analysis of data from multiple batches or the addition of reactants/products during the reaction. In a second research campaign, the rank augmentation of Reaction-Variant (RV) and Reaction- and Mass-transfer-Variant (RMV) forms of spectroscopic data using calorimetric and gas consumption data was studied. Recently, rank augmentation of concentration data using calorimetry for the purpose of calculating extents of reaction and of mass transfer was investigated.

Rank Deficiency and Rank Augmentation

M. Amrhein, B. Srinivasan and D. Bonvin (1994-1996)

This work examined various cases where rank deficiency occurs. The most important case is when the number of independent reactions is less than the number of absorbing species. In such a case, rank analysis only reveals the number of independent reactions and standard Factor Analytical (FA) methods fail. A solution is to augment the rank of the data matrix to the number of absorbing species by (i) multiple process runs and/or (ii) addition of reactants/products during the reaction. The number of necessary runs/additions could be detected by determining the rank of both the original and column-mean-centered data matrices. The influence on the rank of data pretreatment such as mean centering, normalization, auto-scaling and differentiation were also examined.

Rank Augmentation of Spectroscopic Data

N. Bhatt, M. Amrhein and D. Bonvin (2008)

This work investigated an alternative solution to the problem of rank deficient spectroscopic data. For homogeneous reaction systems, calorimetric data were used for the rank augmentation of the Reaction-Variant (RV) form of rank deficient spectroscopic data, with the RV form containing only the contribution of the chemical reactions. Similarly, for gas-liquid reaction systems, gas consumption data were employed for the rank augmentation of the Reaction- and Mass-transfer-Variant (RMV) form of rank deficient spectroscopic data, with the RMV form containing only the contribution of the chemical reactions and of the mass transfers.

Rank Augmentation of Concentrations Data

S. Srinivasan, J. Billeter and D. Bonvin (2012)

This work incorporated calorimetric measurements into the extent-based incremental identification approach for two purposes: (i) to compute the extents in certain cases when only a subset of the concentrations is measured, and (ii) to estimate the enthalpies when all concentrations are measured.

Keywords

Rank analysis; Rank deficiency; Rank augmentation; Incremental identification; Concentrations; Spectroscopy; Calorimetry; Gas consumption

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