The Levenberg-Marquardt method to fit parameters in the Monod kinetic model

Abstract

Mathematical models can describe biochemical processes. Accurately measured data are fundamental for the estimation of the model parameters. This research uses the Monod model describing the bacterial kinetic degradation. The Levenberg-Marquardt method was applied successfully in order to fit the parameters of the model expressing the substrate concentration as a function of time. Hereby the method of steepest ascent and the iterative Gauss-Newton method with its quadratic convergence rate were used to find optimized parameter values of the Monod kinetic model. These results are compared with the results of other minimization methods. Orthogonal error measurement is introduced as uncertainty is present for all variables. This corrected type of error measurement is used to validate the parameter estimations.

Subject Classification:

• 80A30
• 92C45
• 93E24

Keywords:

• Kinetic
• Biodegradation
• Optimization
• Mathematical modeling
• Bioprocess engineering
• Numerical simulation