Multiresponse model building in systems described by ordinary differential equations with application to batch culture kinetics

In this thesis, multiresponse parameter estimation in systems described by ordinary differential equations was investigated. Contributions were made in three areas: development of optimization algorithms for the Box-Draper criterion, solution of first and second-order parametric sensitivity coefficients in ordinary differential equations and development of model building strategies.;The calculation of first-order sensitivity coefficients of the model responses with respect to the model parameters is essential to the evaluation of the gradient and approximate Hessian of the parameter estimation criterion with respect to the parameters. In this thesis, an efficient algorithm for the calculation of first-order sensitivity coefficients in ordinary differential equations, the decoupled direct method (DDM), was implemented in a multiresponse parameter estimation routine. The performance of the DDM was improved by using a pseudo error per unit step error control strategy. DDM was also extended to the simultaneous calculation of both first and second-order sensitivity coefficients. This extension of DDM was used in the development of a full Newton method for the optimization of the Box-Draper criterion. A new hybrid Gauss-Newton/Newton method was also developed. These two methods were shown to be very robust and performed better than multiresponse parameter estimation algorithms based on first-order approximations.;An effective model building strategy for batch culture kinetics was developed. The strategy combines rigorous multiresponse statistical techniques and process knowledge to build "pseudo-mechanistic" descriptions for batch culture kinetics. The strategy is based on an iterative approach which sequentially applies conjecture, design of experiments and analysis steps to enrich knowledge of the process. A simple model building exercise for the batch culture of E. coli was employed to demonstrate the strategy. This example also demonstrated a number of helpful techniques for using multiresponse parameter estimation procedures. The use of empirical parameter transformations was found to improve the convergence properties of multiresponse estimation procedures. A sequential approach to fitting complex multiresponse ODE models using a limited amount of data was also demonstrated. The approach consisted of fitting simple model forms initially and adding responses in a sequential manner in order to arrive at more complex model forms.;In this study, it was shown how optimization algorithms, developed for nonlinear least squares estimation, can be extended to the optimization of the Box-Draper multiresponse criterion. A hybrid general-purpose algorithm, based on the algorithm of Dennis, Gay and Welsch (DGW) for nonlinear least squares, was developed for the optimization of the Box-Draper criterion. The hybrid algorithm combines the Gauss-Newton method and the DGW update formula. A new switching procedure was developed to allow application of the hybrid algorithm with a line search algorithm. The general purpose hybrid algorithm was found to be more robust then the Gauss-Newton algorithm and was shown to perform as well as other published hybrid algorithms.