Chapter 11 - Parameter Estimation

Abstract

Parameter estimation is an important part of the development of a model. There are many ways to estimate the parameters for a model containing partial differential equations (PDEs), ordinary differential equations (ODEs), algebraic equations (Aes), or some combination of them. Since model parameter estimation is related to matching the model results with measured data, sensitivity of the model parameters, uncertainty of the measured data, and uncertainty of model-based predictions all have important roles. This chapter introduces the parameter estimation problem through examples taken from reaction kinetic modelling. The objective here is to create a model for use on a stand-alone basis as well as for use in different applications, such as part of other models and/or use of the models to generate chemical (reaction) system information. Various examples are provided, from simple steady-state least squares regression, to nonlinear least squares fitting, model selection, the use of maximum likelihood principle, and finally the use of orthogonal collocation for dynamic optimization. The maximum likelihood principle estimates are derived from the probability density function of the measurement errors.