1 Mathematical Statistics, Department of Informatics and Mathematical Modeling, Technical University of Denmark2 Department of Informatics and Mathematical Modeling, Technical University of Denmark3 Department of Applied Mathematics and Computer Science, Technical University of Denmark
In this thesis dynamic models of typical components in Danish heating systems are considered. Emphasis is made on describing and evaluating mathematical methods for identification of such models, and on presentation of component models for practical applications. The thesis consists of seven research papers (case studies) together with a summary report. Each case study takes it's starting point in typical heating system components and both, the applied mathematical modelling methods and the application aspects, are considered. The summary report gives an introduction to the scope of application and the applied modelling method and summarizes the research papers. The foundation of the identification process is the grey box modelling method. The grey box modelling method is characterized by using information from measurements in conjunction with physical knowledge. The combination of statistical methods and physical interpretation is exploited in the modelling procedure, from the design of experiments to parameter estimation and model validation. The presented models are mainly formulated as state space models in continuous time with discrete time observation equations. The state equations are expressed in terms of stochastic differential equations. From a theoretical viewpoint the techniques for experimental design, parameter estimation and model validation are considered. From the practical viewpoint emphasis is put on how this methods can be used to construct models adequate for heating system simulations. Significant parts of the research work have been done in cooperation with leading companies from the Danish heating industry. The presented models have been developed for the purpose of analyzing typical heating system installations. The focal point of the developed models is that the model structure has to be adequate for practical applications, such as system simulation, fault detection and diagnosis, and design of control strategies. This also reflects on the methods used for identification of the component models. The main result from this research is the identification of component models, such as e.g. heat exchanger and valve models, adequate for system simulations. Furthermore, the thesis demonstrates and discusses the advantages and disadvantages of using statistical methods in conjunction with physical knowledge in establishing adequate component models of heating systems.