Effect of regression approach in the estimation of nonlinear model parameters on process design and simulation: applications to kinetic and thermodynamic models
An inside-variance estimation method (IVEM) for regression of the kinetic parameters in kinetic models and binary interaction parameters in thermodynamic models is proposed. This maximum likelihood method involves the re-computation of the variance for each iteration of the optimization procedure, automatically re-weighting the objective function. Once the objective function is selected, most regression strategies consist of weighting the objective function by pre-selected values, usually based on experimental error estimates (i.e. standard deviation), converting the problem into a traditional weighted least squares minimization. A problem with the traditional approach is that the experimental error estimation from the maximum-likelihood regression cannot be unbiased, without using replicates. Thus, the use of experimental variances to weight the objective function does not necessarily produce optimum parameters for prediction purposes, even if the values obtained represent the global minima of the objective function. The new method substantially improves the model predictions when compared with traditional least square regression methods. (C) 2000 Elsevier Science Ltd. All rights reserved.
thermodynamics kinetics parameters maximum likelihood objective functions nonlinear regression statistical methods liquid-liquid equilibria