comparison of perturbation and augmentation to solve rank deficiency problem

Hard modeling (hm) and soft modeling (sm) approaches have been developed to resolve concentration profiles and pure absorption spectra from two-way kinetic-spectral data during a chemical reaction. hm techniques are based on fitting of experimental data to mathematical models.to estimate the reaction order and rate constants at the same time, different approaches are used (1).when the number of major contributions to data variance, as estimated by singular value decomposition or other related factor analysis approaches, is less than the real number of chemical components present in the system, the data matrix is rank-deficient. in the case of rank deficient system, analysis of single data matrix leads to correct estimation of rate constants and thus concentration profiles but the spectral profiles can not be estimated correctly. thus in presence of rank deficient system full resolving the system is impossible and it should be solved. the problem of rank deficiency can be solved by two strategies (i) matrix perturbation by adding a single component or combinations of components during the process; (ii) matrix augmentation by simultaneous analysis of two or more data matrices (2). in this study, both of these strategies was used for resolving two types of kinetic data. 1) a simple full rank first-order kinetic system which is not rank deficient and used totest the performance of perturbation and 2) a simulated rank deficient second order consecutive reaction in which the problem of rank deficiency is serious and should be solved for full resolving the kinetic data. then the method was applied for experimental data. in the experimental system, o-aba reacts with diazonium salt in a second order consecutive reaction.o-aba+diaz→i→pour results show that in the case of non bilinearity in data, augmentation leads to incorrect results and thus systematic errors whereas perturbation works properly ant its results are correct. in the next step the relation between the extent of reaction and perturbation was investigated. it was shown that the uncertainty of results in the case of perturbation strongly depends on the time of perturbation. it was shon that in the early stage of reaction the effect of perturbation is significant.