An Inverse Gray-Box Model for Transient Building Load Prediction

Lower costs and improved performance of sensors, controllers, and networking is leading to the development of smart building features, such as continuous performance monitoring, automated diagnostics, and optimal supervisory control. For some of these applications, it is important to be able to predict transient cooling and heating requirements for the building using inverse models that are trained using on-site data. Existing inverse models for transient building loads range from purely empirical or “black-box” models to purely physical or “white-box” models. Generally, black-box (e.g., neural network) models require a significant amount of training data and may not always reflect the actual physical behavior, whereas white-box (e.g., finite difference) models require specification of many physical parameters. This paper presents a hybrid or “gray-box” modeling approach that uses a transfer function with parameters that are constrained to satisfy a simple physical representation for energy flows in the building structure. A robust method is also presented for training parameters of the constrained model, wherein initial values of and bounds on physical parameters are estimated from a rough building description, better estimates are obtained using a global direct search algorithm, and optimal parameters are identified using a nonlinear regression algorithm. The model and training method were extensively tested for different buildings and locations using data generated from a detailed simulation program. The approach was also tested using data from a field site located near Chicago, Illinois. It was found that one to two weeks of data are sufficient to train a model so that it can accurately predict transient cooling or heating requirements.