**4. Discussion**

In the past, the authors found that permeable covering tended to control indoor partial vapour pressure during the unoccupied period as a consequence of low air changes [6–10]. In this regard, permeable covering materials such as paper and wood reach a lower maximum humidity in the summer and a higher minimum humidity in the winter than impermeable ones [6]. As a consequence, permeable coverings are considered as very resourceful internal covering material for seeking thermal comfort and, at the same time, for improving the energy saving [8,9].

From these works it was concluded that, as a consequence of long periods of inoccupation—which can be considered to be longer than 4 h, permeable internal coverings can serve to control indoor ambiences to comfortable levels, thereby resulting in lower energy consumption for air conditioning the indoor ambiences during the first hour of occupation.

As explained earlier (Figures 3–6), NNT can be trained to predict indoor partial vapour pressure as a function of outdoor weather conditions. From these trained networks, the effect of permeable internal coverings can be analysed during the winter season for different experimental values of the outdoor weather conditions.

Furthermore, as the networks were trained for unoccupied and occupied periods, the respective effects could be analysed separately (Figures 7 and 8, respectively). Figure 7 depicts examples of outdoor winter weather conditions for this region (Galicia, a humid region of the Northwest Spain), which presents lower partial vapour pressure than that in summers. In this figure, the red line indicates a partial pressure evolution from 1200 to 1400 Pa and from 1200 to 1000 Pa. As a consequence of this

evolution, during the unoccupied period, permeable materials like paper (represented by a yellow line) allow indoor partial vapour pressure to reach the higher value of nearly 1300 Pa and, when this outdoor value is reduced to 1000 Pa, the permeable coverings tended to release the cumulated moisture to indoor ambience and increase the partial vapour pressure till 1225 Pa, which is in clear agreemen<sup>t</sup> with the main results obtained in previous research works [6–10].

At the same time, in accordance with its permeability level, the remaining internal coverings act in a similar or less intense manner. For wooden materials (represented in green line), a similar behaviour as of paper was seen, albeit with a lower peak of indoor partial vapour values.

On the other hand, more impermeable materials such as paint demonstrated no sensitivity to the outdoor weather conditions and maintained its initial value during all experiments. An example of the behaviour of relay impermeable materials by impermeable materials like plastic is represented by a black dashed line (see Figure 7). As can be seen, when the outdoor weather condition changes, these materials exert lower partial vapour pressure on the indoor ambiences. This e ffect is in contraposition with the comfort conditions and the related energy consumption to condition this ambience; which is in in clear agreemen<sup>t</sup> with previous papers [6–10].

If the e ffect of these same outdoor weather conditions is analysed during the occupation period when the air changes are much higher, the e ffect of internal covering cannot be clearly detected and may be neglected (see Figure 8). From this figure, it can be can conclude that most of the o ffices tended to maintain their partial vapour pressure to an average value of 1100 Pa, and, only permeable materials showed an average value during this occupation period. In particular, indoor ambiences of o ffices with paper (yellow) or wooden (green) internal coverings showed an evolution influenced by outdoor weather conditions. This result is in agreemen<sup>t</sup> with previous research works [6–10].

According to the need of the technicians to understand the proposed procedure to relate indoor and outdoor conditions and internal coverings properties and, in particular, with the aim to define an adequate mathematical model that could be employed for engineers and architects, di fferent simulations were needed to obtain this relation to our particular buildings, like in previous studies [30,31]. In this sense, NNT results revealed that it was possible to define an adequate three-dimensional model obtained, like in previous research works [31], by curve fitting of data previously obtained from software resources like Energy Plus or by neuronal networks for di fferent internal covering materials (see Figures 9 and 10). This behaviour was simulated under an outdoor partial vapor pressure of 800–1200 Pa to show the expected indoor partial vapor pressure.

**Figure 9.** Indoor vapour pressure as a function of outdoor conditions and permeability during the unoccupied period.

**Figure 10.** Indoor vapour pressure as a function of outdoor conditions and permeability during the occupied period.

Owing to both the need for an initial permeability value for each internal covering material to develop a final model that considers this variable and the values reflected in previous research works from test laboratories about the permeability level of the same materials [6–10], previously defined values were employed as the second input variable for the curve-fitting process. In this case, the determination factor was *r*2 = 0.806 and the model obtained was reflected in Equation (2).

$$P\_{\rm v\\_indoor} = 1072.1 - \frac{5494.6}{P\_{\rm v\\_outdoor}} + 5460.7 \times k\_{\rm d} \tag{2}$$

where *P*v\_indoor is the indoor water vapor pressure (Pa), *P*v\_outdoor is the outdoor water vapor pressure (Pa) and *k*d is the internal coverings water vapor permeability (g·<sup>m</sup>/MN·s).

It is interesting to highlight that, if the obtained Equation (2) is employed in an inverse way, it is possible to define the real permeability value in these real buildings through the sampled indoor and outdoor partial vapor pressure. Therefore, it could be a new and original methodology to determine the real effect of internal coverings and to determine how it was changing through the time due to materials' waste and damage.

Considering that this process occurs during long periods of time and in accordance with the moisture transfer equation (Equation (2)), only the first term must be modelled in this process as a consequence of the study period is concluded. In this sense, the second term of Equation (2) shows the effect of cumulated moisture in internal coverings. This effect will control indoor ambiences during a maximum of 4 h, after which its control capability remains only a function of the water vapour permeability, the first term of Equation (2).

On the other hand, the three-dimensional model of the occupied period revealed a horizontal plane that shows an indoor ambience experimenting a nearly null influence of the permeability level of internal coverings as a consequence of a grea<sup>t</sup> number of air changes during the working hours. This result is in clear agreemen<sup>t</sup> with that in previous works [6–10], and, as a result, it cannot be defined a clear difference between material behaviours when the number of air changes in an indoor ambience is high. In conclusion, indoor ambience is a function of outdoor weather conditions.

Our results sugges<sup>t</sup> that neuronal networks allow the definition of an accurate model that can be employed in prediction studies unlike traditional statistical studies. In this sense, a map of the relationship between indoor and outdoor partial vapor pressure was obtained. Furthermore, this chart depicts an example of a new methodology to define hygroscopic material properties after they are placed in their final construction position, which can be considered as the first step toward future indoor ambience simulation and optimization.

Finally, this method, based on sampled data and a new generation of data mining techniques is just an example of application to improve indoor ambiences towards thermal comfort improvement and energy saving optimization. Furthermore, future applications of this procedure will help to improve indoor ambiances based on the amount and type of internal covering employed in an indoor ambience towards a natural control system of indoor ambience based on this building constants and passive methods.

Future works of this e ffect during the summer must be done to validate the e ffect of internal coverings materials, as it was concluded by previous researchers [32,33], and try to model this. Furthermore, final works about the e ffect of local thermal comfort and the energy peak during the first hours of occupation must be done and, furthermore, about the optimization of passive and active strategies in the early phase of a building's life cycle [30].

More other points of view can be considered at the time of selecting internal coverings, e.g., the prevention of fire expansion in o ffice buildings. Anyway, based on the obtained experience, impermeable coverings are usually employed because plastic and glass are easier to be cleaned than paper and wood, which turns out to be a decisive aspect in the selection of coatings for public buildings.
