Selection of Representative Buildings through Preliminary Cluster Analysis

The present work refers to a group of 59 schools located in the North Italian province of Treviso, for which metered energy consumption and seasonal degree days were available for the last five year period. Geometrical features of each school, such as the gross and net heated volume, the floor area, the window area, and the dispersing envelope surface were also known. Moreover, data about the thermal resistance of the building envelope components and the type of heating system were available. For each school, energy and geometric indicators have been calculated: the ratio between dispersing area and gross heated volume, the window to wall ratio, the energy consumption per volume unit and the energy per volume unit and Heating Degree Hours (HDH). To characterize the features and performance of the buildings, and to assess the possibility to select a sample of representative schools to be further monitored, a cluster analysis has been conducted. The main issues to be solved in order to develop this analysis are the definition of the type and the most suitable number of parameters to be correlated to energy consumption, and the determination of the adequate number of clusters. At first, the available parameters have been grouped in all possible combination sets from 2 to 8 elements and a multiple linear regression was calculated for each single configuration, in order to express the level of dependence of the school total energy consumption on a specific set of parameters. Since the coefficients of determination changes are negligible for more than 6 parameters, this seemed to be an acceptable compromise between representativeness and complexity. The sets of parameters, which better explain the energy performance, have been determined by considering the best results from the regressions. K-means cluster analysis was then performed on the school sample, considering the parameters in those sets, in order to find 3 clusters according to each parameters’ set. Regression analysis has been repeated for every group, to check if the correlation between parameters and energy consumption improves inside each cluster with respect to the whole sample. The same method was then repeated to find sub-clusters in those groups of buildings with the lowest correlation coefficients in order to divide them into more homogeneous groups, with a higher correlation between the buildings characteristics and their final energy consumption.