## 1 Introduction  
The construction sector has a primary role in CO\({}_{2}\) reduction in Europe since buildings use around 40% of total energy consumption and generate almost 36% of greenhouse gases [1]. Recent data on world energy consumption in both residential and commercial buildings are presented by [PERSON] et al., 2015 [2], together with an overview of measures and policies adopted by different countries for the reduction of energy consumption in buildings. They showed how in Asia, rapidly developing economies, essentially India and China, are looking to reduce the dramatic increase of energy consumption in buildings due to the fast urbanization rate [3]. Worldwide energy reduction will then benefit from the improvement of energy efficiency in buildings. This objective can be reached using two different and complementary approaches--measurements and simulations [4]. Simulation can be used to estimate the energy consumption of a building and consists of the construction of a virtual model of the building that has to reproduce the behaviour of the real building as accurately as possible. The reduction of the energy consumption can be pursued if the energy distribution throughout the building is known and understood. Building modelling can then be used both as a diagnostic tool, to better understand the physics laws of the building, and as a prognostic tool to predict the building's behaviour once the laws are known. Building energy performance simulation (BEPS) can be achieved using data driven (black box) or law driven (white box) models. Considering the white box approach, many BEPS tools are available for example, TRNSYS, Energy Plus, DOE-2, ESPr, IDA ICE [5; 6; 7; 8; 9] and for the most popular, accurate capabilities evaluations and comparisons have been made [10]. Retrofit projects and operations management for buildings require accurate modelling that can be achieved through calibration. Calibration consists of an iterative process where model input is changed to reconcile the model output with the measured data. Although this process can be considered essential for having reliable results, still few practitioners are capable to perform it. Typical variables that are involved in the calibration process are mainly energy consumption [11; 12; 13; 14] and indoor air temperature [11; 15; 16], for which simulated values are compared to measured ones on a specific time scale. Usually calibration at a small time scale (hourly of sub-hourly) results more difficult and time consuming than large scale such as annual and/or monthly rates. However, calibration with large time granularity (annual basis) can produce very good results while on a monthly basis can be affected by much larger errors. At present the most used statistical indices for the evaluation of the calibration accuracy are relative MBE (Mean Bias Error), RMSE (Root Mean Square Error), CVRMSE (Coefficient of Variation of RMSE) and NRMSE (Normalized RMSE), defined as follows [17; 18; 19]:  
\[MBE=\frac{\sum_{i=1}^{n}s_{i}-m_{i}}{\sum_{i=1}^{n}m_{i}}\cdot 100\% \tag{1}\]  
\[RMSE=\sqrt{\frac{\sum_{i=1}^{n}(s_{i}-m_{i})^{2}}{n}} \tag{2}\]  
\[CVRMSE=\frac{RMSE}{m_{mem}}\cdot 100\% \tag{3}\]  
\[NRMSE=\frac{RMSE}{m_{max}-m_{min}}\cdot 100\% \tag{4}\]  
where \(s\) and \(m\) refer to simulated and measured data respectively. They are mostly evaluated for energy consumption, for which acceptance criteria have been introduced by various organizations as showed in Table 1.  
For what concerns the calibration performed with environmental variables, such as indoor air temperature, usually the model is considered calibrated when the RMSE is within the uncertainty of the measurements however no reference values of performance indexes are commonly provided. A wide piece of literature deals with BEPS calibration and this is confirmed also by reviews on this topic [20; 21; 22]. Substantially two approaches can be adopted for model calibration--manual approach and automatic approach.