A metamodeling method to study the nonlinearity of building thermal behavior. (March 2020) - Jaffal, Issa; Inard, Christian
Abstract: Understanding the nonlinearity of the thermal behavior of buildings is important for their design and energy analysis. This paper presents a method for the study of the nonlinearity of building thermal behavior based on a metamodel for cooling energy needs. Four measures were introduced to assess nonlinearities using the metamodel coefficients. We studied the nonlinearity of the thermal behavior of an office. A higher metamodeling accuracy was generally obtained for hot climates, high internal heat gains and lightweight thermal mass. Conversely, the nonlinearity of thermal behavior was accentuated in cold climates and with low internal heat gains. The nonlinearity measures were strongly associated to the mean outdoor air temperature in fifteen typical European climates using power laws, with R 2 ranging from 0.75 to 0.96. They were also strongly associated to internal heat gains ( R 2  > 0.96) in the coldest climate, but low and almost stable in the hottest climate. Moreover, the interactions between the building components were more influential on cooling energy needs than quadratic behavior. A metamodel giving energy needs as a function of the physical and geometric parameters was derived. Its extrapolation with various window-wall ratios generally gave an acceptable accuracy, with quadratic variation of the errors. We propose a classification of building thermal behavior into three regimes: highly nonlinear when the energy needs are close to zero; intermediate with decreasing nonlinearities that can be expressed by power functions; and finally, a quasi-linear regime with almost-steady nonlinearities. Highlights: Four nonlinearity measures were introduced based on a metamodel. The nonlinearity was accentuated when the cooling energy needs were low. The interaction effects were higher than the quadratic effects. A classification of thermal behavior into three nonlinear regimes is proposed