Ensemble of radial basis neural networks with k-means clustering for heating energy consumption prediction

The study of the building energy demand has become a topic of great importance, because of the significant increase of interest in energy sustainability, especially after the emanation of the EPB European Directive. In Europe, buildings account for 40% of total energy use and 36% of total CO2 emission [1]. According to [2] 66% of the total energy consumption of residential buildings in Norway occurs in the space heating sector. Therefore, the estimation or prediction of building energy consumption has played a very important role in building energy management, since it can help to indicate above-normal energy use and/or diagnose the possible causes, if there has been enough historical data gathered. Scientists and engineers are lately moving from calculating energy consumption toward analyzing the real energy use of buildings. One of the reasons is that, due to the complexity of the building energy systems, non-calibrated models cannot predict well building energy consumption, so there is a need for real time image of energy use (using measured and analyzed data). The classic approach to estimate the building energy use is based on the application of a model with known system structure and properties as well as forcing variables (forward approach). Using different software tools, such as EnergyPlus, TRNSYS, BLAST, ESP-r, HAP, APACHE requires detailed knowledge of the numerous building parameters (constructions, systems) and behavior, which are usually not available. In recent years, considerable attention has been given to a different approach for building energy analysis, which is based on the so called "inverse" or data-driven models [3]. In a data-driven approach, it is required that the input and output variables are known and measured, and the development of the "inverse" model consists in determination of a mathematical description of the relationship between the independent variables and the dependent one. The data-driven approach is useful when the building (or a system) is already built, and actual consumption (or performance) data are measured and available. For this approach, different statistical methods can be used. Artificial neural networks (ANN) are the most used artificial intelligence models for different types of prediction. The main advantages of an ANN model are its self-learning capability and the fact that it can approximate a nonlinear relationship between the input variables and the output of a complicated system. Feedforward neural networks are most widely used in energy consumption prediction. Ekici et al. in [4] proposed a backpropagation three-layered ANN for the prediction of the heating energy requirements of different building samples. Dombayci [5] used hourly heating energy consumption for a model house calculated by degree-hour method for training and testing the ANN model. In [6] actual recorded input and output data that influence Greek long-term energy consumption were used in the training, validation and testing process. In [7] Li et al. proposed the hybrid genetic algorithm-adaptive network-based fuzzy inference system (ANFIS) which combined the fuzzy if-then rules into the neural networklike structure for the prediction of energy consumption in the library building. An excellent review of the different neural network models used for building energy use prediction was done by Kumar [8]. The ensemble of neural networks is a very successful technique where the outputs of a set of separately trained neural networks are combined to form one unified prediction [9]. Since an ensemble is often more accurate than its members, such a paradigm has become a hot topic in recent years and has already been successfully applied to time series prediction [10], weather forecasting [11], load prediction in a power system [12]. The main idea of this paper is to propose ensemble of radial basis neural networks for prediction of heating energy use.