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Project
Advanced numerical techniques for optimal experimental design: from theory to practice in the (bio)chemical industry.
This thesis investigates optimal experiment design for parameter estimation of nonlinear dynamic systems in the (bio)chemical industry. A globalized market situation and sustainability aspects are a driver to improve the (bio)chemical industry's performance. A useful tool for this goal is the use of model based optimization techniques. However, before a model can be used in daily practice, the process has to be modeled accurately. This involves the selection of an appropriate model structure and the determination of accurate model parameter values.
In this thesis, it is assumed that a correct model structure has already been determined. So, the focus of the dissertation is in the optimal design of experiments for obtaining accurate parameter estimates. As optimal experiment design is an optimization problem, a first challenge relates to the fast and efficient computation of an approximation of the parameter variance-covariance matrix which is needed in the objective function. A second challenge results from the fact that the optimized design typicallydepends on the current estimate of the parameters which are not exactlyknown. Consequently, a design has to be robust both with respect to theinformation content and with respect to constraint satisfaction. The information content in optimal experiment design is expressed in matrix form. However, in the optimization formulation a scalar function of the variance-covariance matrix is required. Hence, a third challenge concerns the question of how to select the most appropriate optimal experiment design criterion. Moreover, some design criteria pose computational challenges (e.g., with respect to differentiability). As a result, a fourth challenge involves the search for proper reformulations.
In thefirst part of the thesis, the mathematical formulation of optimal experiment design for parameter estimation is presented. Several parameter variance-covariance matrix approximation techniques are discussed and formulated in an optimal control setting. In the second part of the thesis the propagation of uncertainty is tackled. A first contribution is a computational method for the approximation of the parameter variance-covariance matrix using Riccati equations. It is shown that the resulting approach is more efficient than the corresponding Fisher information matrix approach. A second contribution is an efficient expected value formulation related to the information content in an experiment. The proposed formulation can also be extended to be robust with respect to constraint satisfaction. The third part discusses how to select an appropriate criterion for optimal experiment design. A third contribution is the investigation of different possible choices as objective function in a multi-objective optimization framework such that the experimenter can make a well-informed choice. The fourth contribution is the formulation of optimal experiment design such that an improvement on a matrix inequality level isensured. This approach also allows to avoid problems with respect to, e.g., differentiability of the minimum eigenvalue function.
Several case studies from different fields have been used throughout the dissertation. The case study of a fed-batch bioreactor using Monod kinetics has been investigated in every contribution of the presented dissertation. Besides this model, a kinetic growth model in function of temperature from the field of predictive microbiology has been studied. Also, a Lotka Volterra model has been examined. A slightly larger chemical case study has been the Williams-Otto reactor.
In this thesis, it is assumed that a correct model structure has already been determined. So, the focus of the dissertation is in the optimal design of experiments for obtaining accurate parameter estimates. As optimal experiment design is an optimization problem, a first challenge relates to the fast and efficient computation of an approximation of the parameter variance-covariance matrix which is needed in the objective function. A second challenge results from the fact that the optimized design typicallydepends on the current estimate of the parameters which are not exactlyknown. Consequently, a design has to be robust both with respect to theinformation content and with respect to constraint satisfaction. The information content in optimal experiment design is expressed in matrix form. However, in the optimization formulation a scalar function of the variance-covariance matrix is required. Hence, a third challenge concerns the question of how to select the most appropriate optimal experiment design criterion. Moreover, some design criteria pose computational challenges (e.g., with respect to differentiability). As a result, a fourth challenge involves the search for proper reformulations.
In thefirst part of the thesis, the mathematical formulation of optimal experiment design for parameter estimation is presented. Several parameter variance-covariance matrix approximation techniques are discussed and formulated in an optimal control setting. In the second part of the thesis the propagation of uncertainty is tackled. A first contribution is a computational method for the approximation of the parameter variance-covariance matrix using Riccati equations. It is shown that the resulting approach is more efficient than the corresponding Fisher information matrix approach. A second contribution is an efficient expected value formulation related to the information content in an experiment. The proposed formulation can also be extended to be robust with respect to constraint satisfaction. The third part discusses how to select an appropriate criterion for optimal experiment design. A third contribution is the investigation of different possible choices as objective function in a multi-objective optimization framework such that the experimenter can make a well-informed choice. The fourth contribution is the formulation of optimal experiment design such that an improvement on a matrix inequality level isensured. This approach also allows to avoid problems with respect to, e.g., differentiability of the minimum eigenvalue function.
Several case studies from different fields have been used throughout the dissertation. The case study of a fed-batch bioreactor using Monod kinetics has been investigated in every contribution of the presented dissertation. Besides this model, a kinetic growth model in function of temperature from the field of predictive microbiology has been studied. Also, a Lotka Volterra model has been examined. A slightly larger chemical case study has been the Williams-Otto reactor.
Date:7 Sep 2010 → 31 Dec 2014
Keywords:Chemical industry, Numerical techniques
Disciplines:Applied mathematics in specific fields, Computer architecture and networks, Distributed computing, Information sciences, Information systems, Programming languages, Scientific computing, Theoretical computer science, Visual computing, Other information and computing sciences, Catalysis and reacting systems engineering, Chemical product design and formulation, General chemical and biochemical engineering, Process engineering, Separation and membrane technologies, Transport phenomena, Other (bio)chemical engineering
Project type:PhD project