Building and Environment, Vol. 28, No. 4, pp. 509518, 1993. 0360-1323/93 $6.00+0.00 Printed in Great Britain. C 1993 Pergamon Press Ltd. Stochastic Analysis of Building Thermal Processes YI JIANG* TIANZHEN HONG* A methodology is presented for investigating the uncertainty properties of the building thermal processes caused by the random behaviour of the meteorological processes and the casual gains. A detailed building thermal model is used with a stochastic weather model and a random casual gain model. The probability distribution of the zone temperature of the building is calculated directly from these models. The overheating risk has been analysed as an example. The probability distribution of the periods when the zone temperature is higher than the demand temperature is calculated. The result shows all the possible situations rather than only a sample as would be obtained by running a normal simulation using given weather data. The influence of different building components on the overheating risk has been studied. The result shows that the most likely component for overheating risk in a residential building in Beijing is the window size. The thermal mass of the internal walls and the placing of windows have little effect on overheating risk. NOMENCLATURE A vector, each element is united independent normal distribution C the overheating ratio D matrix, to transfer the random part of the weather process into unit random process K matrix, defined by the building structure and its thermal properties P matrix, defined by the building structure and its thermal properties S matrix, transfer the daily data into hourly data U vector, external or internal disturbance on the building T vector, temperature. It consists of temperatures at all the nodes in the building if there is not a subscript. It is the zone temperature if there is a subscript X vector, the random part of the daily weather data W vector, the daily weather data M vector, the deterministic part of the daily weather data H, Z, ~, ~, ®, ~F matrices depend upon the building structure, thermal properties and behaviour of the climate R matrix, the correlation between the hourly zone tem- peratures at different times E expectation operator D deviation operator r time Subscripts and superscripts z for the zone temperature d for the deterministic part r for the random part for time T transpose INTRODUCTION ALTHOUGH research in the field of building thermal modelling has been undertaken for more than 20 years, there are still some major problems waiting to be solved. *Department of Thermal Energy, Tsinghua University, Beijing 100084, P.R. China. 509 One of the major problems is the uncertainty associated with the building and its external environment. Generally speaking, the influences on thermal processes within a building can be categorized into three parts : --The thermal properties of the building, such as the building structure and material. --The external and internal environment of the building, such as the solar radiation and the outdoor air tem- perature; the casual gain from occupants and other internal heat source. --The activities of t~i~ occupants in the building such as opening windows or turning a TV set on or off. For the first part, the building and materials properties' data may be determined within a relatively small range. The other two parts have quite a high degree of uncer- tainty. This means that the building thermal processes become random in nature. However, most of the building thermal analysis programs apply a deterministic analysis, predicting what will happen when given the weather and casual gain data. After this simulation, some data, e.g. hourly zone temperatures, are produced. What do these data mean? Only that if the weather was the same as the weather data used in the simulation, and if the casual gains were the same as in the simulation, the building thermal behaviour would be as predicted. However, the weather will never be the same, and it is difficult to predict when occupants will open or close windows. What will the real building thermal behaviour be? If the weather data are uncertain, what uncertainty range will there be in the building thermal behaviour? The simulated hourly data can hardly give a clear answer to these questions. As the weather is a stochastic process and the internal casual gain is also a random variable, the building ther- mal behaviour such as the zone temperature, energy con-