investigation of correlation between chemical model parameters in rank deficient data

Nonlinear fitting is a method for calculation of chemical model parameters. a problem that complicates some applications of nonlinear modeling is correlation between the parameters of the model. two interdependent parameters in a model fitting are said to be correlated, if the fitted value of each parameter depends on the fitted value of the other parameters. if correlation is very strong, convergence and /or unique estimates of each parameter may be difficult to achieve. in this condition often convergence cannot be obtained at all or requires a tedious search for a set of initial parameters from which convergence is attainable. models with partial correlations may often be used successfully but degraded precision in parameters compared to an uncorrelated model are the costs that may have to be paid. the chemical model fitting can be more complex when there are linear dependencies between concentration profiles. this situation is known as rank deficiency in measurement chemical data. in such cases, there are several different strategies, to treat rank deficiency problems in the concentration matrix and to allow the fitting of pure component spectra. the correlation between model parameters in rank deficient systems and also the effects of different rank deficiency breaking methods on these correlations have not been investigated systematically.in this research the relation between correlation of model parameters and rank deficiency in concentration profiles has been investigated. different kinetics and equilibria models with inherent linear dependency in their concentration profiles have been simulated and evaluated. the influence of some different experimental situation such as different initial concentrations, known spectra as initial information, extent of reaction progress and different values of model parameters on the correlation of them have been evaluated.