Order selection of thermal models by frequency analysis of measurements for building energy efficiency estimation

Experimental identification of the dynamic models of heat transfer in walls is needed for optimal control and characterization of building energy performance. These models use the heat equation in time domain which can be put in matrix form and then, through state-space representation, transformed in a transfer function which is of infinite order. However, the model acts as a low-pass filter and needs to respond only to the frequency spectrum present in the measured inputs. Then, the order of the transfer function can be determined by using the frequency spectrum of the measured inputs and the accuracy of the sensors. The main idea is that from two models of different orders, the one with a lower order can be used in building parameter identification, when the difference between the outputs is negligible or lower than the output measurement error. A homogeneous light wall is used as an example for a detailed study and examples of homogeneous building elements with very high and very low time constants are given. The first order model is compared with a very high order model (hundreds of states) which can be considered almost continuous in space.