An experimental setup of a water based central heating system has been used to measure the thermo dynamical behavior of a thermostatic valve in order to identify an adequate mathematical model. The identification of the thermostatic valve is based on nonlinear Grey-Box modelling. Grey-Box modelling is characterized by the fact that, in the modelling procedure, partial known information from physics about a system is combined with information from data. The parameters of the model are estimated by a Maximum Likelihood Method. In the paper an overview of this modelling procedure is given.
In order to quantify uncertainty in thermal building simulation stochastic modelling is applied on a building model. An application of stochastic differential equations is presented in Part I comprising a general heat balance for an arbitrary number of loads and zones in a building to determine the thermal behaviour under random conditions. Randomness in the input as well as the model coefficients is considered. Two different approaches are presented namely equations for first and second order time varying statistical moments and Monte Carlo Simulation.
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