1 Department of Informatics and Mathematical Modeling, Technical University of Denmark
The problem of identification of physical models is considered within the frame of stochastic differential equations. Methods for estimation of parameters of these continuous time models based on descrete time measurements are discussed. The important algorithms of a computer program for ML or MAP estimation of the parameters of nonlinear stochastic differential equations are described and the implemented tool is validated with respect to bias and uncertainty of the estimated parameters. The different phases involved in identification of this type of models are considered in the thesis. This includes design of experiments, which is for instance the design of an input signal that are optimal according to a criterion based on the information provided by the experiment. Also model validation is discussed. An important verification of a physical model is to compare the physical characteristics of the model with the available prior knowledge. The methods for identification of physical models have been applied in two different case studies. One case is the identification of thermal dynamics of building components. The work is related to a CEC research project called PASSYS (Passive Solar Components and Systems Testing), on testing of building components related to passive solar energy conservation, tested under outdoor climate conditions. The second case study is related to the performance of a spark ignition car engine. A phenomenological model of the fuel flow is identified under various operating conditions of the engine. This engine submodel is important for controlling the air/fuel ratio, e.g. in a feed-forward controller.