Parameter Estimation Algorithms for Kinetic Modeling from Noisy Data

The aim of this work is to test the Levemberg Marquardt and BFGS (Broyden Fletcher Goldfarb Shanno) algorithms, implemented by the matlab functions lsqnonlin and fminunc of the Optimization Toolbox, for modeling the kinetic terms occurring in chemical processes of adsorption. We are interested in tests with noisy data that are obtained by adding Gaussian random noise to the solution of a model with known parameters. While both methods are very precise with noiseless data, by adding noise the quality of the results is greatly worsened. The semiconvergent behaviour of the relative error curves is observed for both methods. Therefore a stopping criterion, based on the Discrepancy Principle is proposed and tested. Great improvement is obtained for both methods, making it possible to compute stable solutions also for noisy data.