## 2 Materials and Methods
### Data Collection and Selection  
An initial dynamic building simulation model was developed and built with IDA-ICE 4.7.1 by EQUA Simulation [9], starting from the available information concerning the building. IDA ICE is a simulation application for the multi-zonal and dynamic study of indoor climate and energy use. IDAICE can be used for complete energy and design studies, involving the envelope, systems, the plant and control strategies. The flexible architecture of the software allows to develop and to expand it with new capabilities. Additional features, like parametric simulation runs and visual scripting, support the user in a parametric design process. The coupling with optimization engines like GenOpt is available directly in the program.  
From the original drawings, it had been possible to define the context, the geometry and the thermal zones of the building. According to the material properties, walls and roofs layers but also openings were specified.  
Finally, plants, equipment and users-related data allowed the setting of the plant system (in terms of set points but also time schedules) and thermal gains.  
Apart from the physical data related to the initial building model, other information were specifically required for the calibration procedure. To define the climate file involved in the simulation process for the calibration but also to obtain data to be compared with the simulation outputs, a measurement campaign had been settled. As multi-stage calibration was applied, a multi-phase campaign had been carried out.  
Since the number of possible parameters influencing calibration was relatively high, a sensitive analysis using the Elementary Effect (EE) method, based on the Morris random sampling method [40], had been performed before the automatic calibration process identifying the most relevant ones.  
Coupling MatLab with IDA-ICE, the EE method had been applied considering the hourly-simulated indoor temperature (T) for the period of each single stage of the whole calibration. According to the method, the number of EEs of each parameter (\(r\)), the number of parameters (\(k\)) _and_ the number of levels (L) in which parameters range, were considered. A MatLab script was built that could open the IDA ICE environment iteratively, varying only one of the candidate inputs at each step while all the others were fixed to the previous value. \(N=r\) (\(k+1\)) simulations had then been performed and the difference between simulated T and T from the initial guess model was expressed in terms of Mean Absolute Error (MAE). A single EE was defined as follows:  
\[EE(x)=\frac{MAE(f(x_{1},x_{2},\ldots,x_{i}+\Delta x,\ldots,+x_{k}),\ f(x))}{ \Delta x} \tag{5}\]  
where \(f(x_{1},x_{2},\ldots,x_{i}+\Delta x,\ldots,+x_{k})\) and \(f(x)\) are T trends for current and first guess model respectively.  
Absolute value of the mean (\(\mu\)*), standard deviation (\(\sigma\)) of the distribution of the EEs and the ratio \(\frac{\sigma}{\mu*}\) were finally evaluated. The relevance of the parameter was related to \(\mu\)*, the larger \(\mu\)* was, the more the corresponding input contributed to the dispersion of the output. \(\sigma\) was a measure of non-linear and/or interaction effects of the corresponding input. So, the ratio \(\frac{\sigma}{\mu*}\) expressed the nature of the dependence of each parameter effect (\(\frac{\sigma}{\mu*}<0.1\) linear, \(0.1\leq\frac{\sigma}{\mu*}<0.5\) monotonic, \(0.5\leq\frac{\sigma}{\mu*}<1\) almost monotonic, \(\frac{\sigma}{\mu*}\geq 1\) not-linear and/or not-monotonic) [41].  
Figure 1: Methodology scheme.