**1. Introduction**

In the last decade, several research papers have attempted to evaluate and model the e ffect of building materials overheat and mass transfer processes [1,2]. Taking into account that the construction of nearly zero energy buildings (nZEB) requires innovative design processes based on an integrated design approach facilitated by multidisciplinary work teams [3], di fferent research groups under the organisation of the International Energy Agency (IEA) shared real sampled laboratory data [4], new software resources like HAM tools [5] and real in-situ sampled data to validate the previous ones [6]. Thus, the aim of the present research was to validate software resources based on real sampled data to simulate and potentially predict and improve indoor conditions in buildings by using buildings construction materials as mechanical control systems in the future.

Accurate prediction of temperature and relative humidity in indoor ambiences is di fficult to obtain unless a realistic understanding of the existing buildings is available. In this sense, the real properties of building materials once placed in the structure and its e ffect on indoor conditions as a consequence of its real behaviour must be analysed in detail for future optimisation.

The e ffect of internal coverings on indoor ambiences was reflected by statistical analysis in previous research works [6–11]. Specifically, in previous studies carried out by the same research group of the present paper [6–10], authors sampled indoor conditions of 25 o ffice buildings in a year in a humid region of the Northwest Spain. The main results revealed how internal coverings exert a clear effect on indoor ambiences during non-occupancy period due to low air changes during the longer period at night. Furthermore, analysis of variance (ANOVA) revealed more interesting results that an average indoor relative humidity controlled by these passive methods reaches a more comfortable ambience with a lower need of energy for conditioning during the first hour of occupation [8,9].

As a consequence of these results, internal coverings were considered to be of special interest to act as permeable or impermeable barrier materials for use as building construction materials in order to control thermal comfort, energy saving and, in general, indoor conditions. The real sampled data demonstrated how this effect must be considered, although it was nearly depreciated during years in most of heat and mass transfer software resources—like, for instance, EnergyPlus—due to the difficulty understanding and define this process. Furthermore, the main results founded in previous papers of our research group [6–10] emphasize the importance of simulating and modelling real sampled data rather than just employing laboratory results as a consequence of the modifications that are experimented by these materials until its final placement.

On the other hand, artificial neuronal networks (ANNs) were described recently as the last step in data mining [12–16]. In particular, most times, statistical studies do not let us ge<sup>t</sup> a model of real processes despite the fact its main variables were previously statistically related. ANNs are the clearest solution to model and predict these non-linear processes with promising future applications.

In previous works [6–10], different indoor ambiences of 25 office buildings were classified based on both its internal coverings materials and the statistical studies of real sampled data of its indoor ambiences. In the present study, this hygroscopic behaviour of coverings materials will be modelled in a more exactly way by Multi-output Gaussian Process Regression Artificial Neural Networks (MGPR ANNs) once trained and tested with the aim to be employed in future indoor ambience predictions. Moreover, this more accurate model will help to improve office buildings envelope redesign [17] to control the heat and mass transfer process between indoor air and wall construction materials and, in consequence, it will serve as a guide to improve the existing indoor conditions [18–22].

## **2. Materials and Methods**

## *2.1. O*ffi*ce Buildings*

The present research is the second phase of a previous work in which solution to the prediction problem of indoors conditions based on real properties of building construction materials were discussed [6,7]. The office buildings used in this study were located in the city of A Coruña, which is identified as an extremely humid region in the Northwestern Spain. Their building construction characteristics, like in previous works, can be defined as identical as these buildings were constructed at the same time and with the same design criteria.

All these offices were destined to be bank offices placed in the ground floor of each respective building. In all these offices two main zones can be identified (Figure 1a): (i) clients' zone and (ii) employees' zone. In the employees' zone there are three employees during all the working period that goes from 8:00 till 14:00. Most of the day, the workers use to enter few minutes before to prepare for the morning's work, and from 16:00 till 19:00. Therefore, the unoccupied period was considered to be 19:00–09:00 h. On the other hand, an average value of three clients is estimated in the clients' zone during the working hours waiting to be attended. In this sense, this working period can be identified as a humidity generation period of time of 7 h.

It must be emphasised that these offices did not have any kind of air conditioning systems, except for mechanical ventilation which was rarely employed during the day under extreme occupation conditions and, more importantly, there were a high number of infiltrations due to the natural ventilation through the doors when they were open as a consequence of the transit of clients. In consequence, during this occupation period, the air changes in the office were high and humidity is released to outdoors. Once the office closes, the air changes are reduced, and the effect of wall constructions materials starts to work by controlling indoor ambience relative humidity based on the permeability level of the internal covering material employed in each office until the office will open again in the next morning.

**Figure 1.** Walls' distribution: (**a**) office buildings zones; (**b**) detail of layers' distribution in a standard wall and their thermal conductivities (*K*).

In particular, a typical wall structure can be defined as being composed of an external covering, concrete, brick, air barrier, polystyrene, brick, concrete, and internal covering, as it is shown in the walls' distribution in Figure 1. The only difference in the buildings was in the type of internal coverings used, as those ranged from paper, wood, paint and plastics, all of which differed in their water vapour permeability (*k*d) levels. In this sense, the levels of water vapour permeability in real buildings were not defined in that works in a quantitative way due to One Way ANOVA just let us define the similarity in indoor ambiences behaviours for a significance level of 0.05. As a consequence of this simple modification, different indoor temperature and relative humidity were identified with important effects on the thermal comfort and energy consumption. In particular, this effect was really intense during the first hours of occupation of the office buildings.

In previous studies [6–10], the external covering was of marble, while the internal coverings were of plastic, paint, wood, or paper, which were accordingly classified based on the real permeability levels (1/200, 1/100, 1/45, and 1/30 g·<sup>m</sup>/MN·s, respectively) obtained in laboratory test. In our case study, these same office buildings were employed with the same external covering of marble. This marble surface can be considered as do not act in moisture transfer through the wall due to its polished surface.

## *2.2. Sampled Variables and Mathematical Models*

In the present case study, based on previous research works on heat and mass transfer processes of wall construction materials [6–10], the evolution with time of the indoor and outdoor partial vapour pressure was selected as the study variable. As explained earlier, indoor conditions of temperature and relative humidity were sampled with Tinytag Plus 2 dual channel dataloggers with thermistor and capacitive sensors were also installed to record temperature and relative humidity values with accuracies +/−0.2 ◦C and +/−3% of relative humidity, respectively [23].

These data loggers were placed in both employees' zone and clients' zone section of the o ffice building with a sampling frequency of ten minutes for a period of one year. At the same time, based on weather information from nearer weather stations, it was possible to define the simultaneous indoor and outdoor conditions of temperature, relative humidity and pressure in each o ffice building. Based on these moist air variables, it was possible to determine the partial vapour pressure inside and outside the o ffice building.

Likewise, it must be remembered that moisture cumulated in building construction materials is released or adsorbed in only the first 4 h, as it was determined by Hameury and Lundstrom based on real sampled data of indoor ambiences [24]. Therefore, the unoccupied period can be considered a long period of time where, as revealed in previous research [6–9], the moisture transfer equation depended on the partial vapour pressure. Based on this, it was possible to define a clear relation between partial vapour pressure and moisture transfer equation during the night time, as detailed in Equation (1).

$$q\_{\rm M} = -k\_{\rm d}(\boldsymbol{u}, \boldsymbol{T})\nabla \boldsymbol{P}\_{\rm V} - \boldsymbol{\rho}\_{\rm o} \boldsymbol{D}\_{\rm W}(\boldsymbol{u}, \boldsymbol{T})\nabla \boldsymbol{u} + \boldsymbol{\upsilon}\_{\rm air} \boldsymbol{\rho}\_{\rm V} + \boldsymbol{K} \boldsymbol{\rho}\_{\rm W} \boldsymbol{g} \tag{1}$$

where *q*M is the mass flux (kg/(m<sup>2</sup>·s)), *k*d is the vapour permeability (kg/(s·m·Pa)), *u* is the moisture content (kgwater/kgDry air), *P*v is the partial pressure of water vapour (Pa), ρ0 is the dry density of porous material (kg/m3), and *D* w is the liquid moisture di ffusivity (m<sup>2</sup>/s).

Thus, it was possible to assume that, for long periods of time, despite the fact that during the first 4 h of the unoccupied period the air changes were reduced and materials actuated realising or adsorbing humidity, the partial vapour pressure depends on the first term of the Fick's law, as shown in Equation (1).

After the main data was obtained, it was possible to train an ANN with various input variables and only one output variable for future optimization. Thus, it was possible to train the network with the outdoor temperature and relative humidity as well as define indoor vapour pressure values.

## *2.3. Neural Nets Predictions and Software Resources*

An artificial neural network (ANN) or neural network toolbox (NNT) receives numeric inputs, performs di fferent computation processes with them and provides an output. To reach this objective, a neural network takes to connect units defined as nodes (neurons) arranged in layers. The first layer receives the input data and transmits this to the next hidden layers until reaching the final output value.

Based on these principles, an NNT is employed as an alternative to traditional statistical procedures and it is usually employed as a function of approximation to define complex relationships under grea<sup>t</sup> reliability when the output value is a single variable. Since in previous works [6–9] it was possible the aggrupation of 25 o ffice buildings based on a statistical similarity of its indoor moist air evolution as a function of weather conditions or, what is the same, 25 o ffice buildings with the same internal covering permeability level (permeable, semi-permeable and impermeable internal covering material), now it should be possible to find the same results by means NNT. What is more, if now we train some indoor ambiences of one representative o ffice building of each internal covering permeability level as a function of weather conditions by means of NNT, it would be a really interesting tool for redesign indoor ambiences in future o ffice buildings.

Di fferent considerations during the NNT configuration were done to reach this objective:

• Selection of NNT: There are di fferent types of nets such as Multi-Layer Feedforward Network (MLF), Generalized Regression Neural Nets (GRN) and Probabilistic Neural Nets (PN). In an MLF net, the user must define the topology (number of layers and nodes), while, in a GRN/PN net, there is no need to make topology decisions and two hidden layers are employed. It must be remembered that the net topology is the selection of the number of layers and the number of nodes in the layer that determines the network capacity to learn the relationship between independent and dependent variables. At the same time, the main literature conclusions [25–28] about network topology are that a single hidden layer with few nodes is su fficient for most cases. Considering that this was the first of its kind study, a probabilistic neural network (GRN/PN) was selected to reach a precision level during the training and testing processes, as shown in Figure 2.


**Figure 2.** Example of Generalized Regression Neural Nets (GRN) net.

Finally, once main considerations for our training procedure were done, Matlab Simulink Neural Network Toolbox (R2015b) [29] was selected as software resource to develop this task due to its so specific toolbox and configuration for this so simple initial case study.
