An analysis of stochastic properties of room air temperature and heating load - influences of randomness parameters

This paper discusses the use of a building thermal analysis methodology in which the stochastic nature of the external climates and randomness of physical parameters are considered. Methods of thermal calculation which give the density function of the room air temperature and heating and/or cooling loads are proposed. Weather data is modeled by linear time series models with white noises as inputs, which take into account the auto-correlations and cross-correlations of the raw climatic data. The basic equations are the simultaneous ordinary difference (or differential) equations, that is, the state space equations. A set of moment equations are derived from these state space equations and solved to provide with the mean and standard deviation in room air temperature and heating load. Particularly, the impact of random infiltration rate and thermophysical properties (here, thermal conductivity of the wall and heat capacity of the room) on room temperature and heating load are emphasized in this paper. Furthermore, methods of analysis that give the influence of the random variation in internal heat generation and the optimal starting time of an HVAC system in intermittent heating, are outlined. Simple example calculations are shown for illustrations. For the analysis and design of a thermal system, this method provides a rational and convenient way of handling uncertainties caused by the degree of imprecision of construction works (workmanship) and the variation of the way in which the room is used.