Figure 1 outlines the steps and methodology adopted for the development of this work.

The raw materials selected for this work were based in previous research works developed by the authors regarding to the mortars formulation, physical, mechanical and severe temperature exposure behavior (32-33, 51-52).

The selected materials were Portland cement (CEM), aerial lime (AL), natural hydraulic lime (HL), gypsum (G), superplasticizer (SP), fibers, sand and phase change material (PCM). The materials densities are presented in Table 1.

The used aerial lime had a purity of 90%. The gypsum corresponds to a traditional one, with high fineness. The hydraulic lime was a natural one (NHL5) and the cement is a CEM II B-L 32.5N. The used sand has an average particle size of 439. 9 μm. The fibers used are synthetic polyamide fibers, with a length of 6 mm and 22.3 μm of thickness.

The PCM selected for this work is a microencapsulated solution commercialized by the Devan Chemicals (Mikathermic D24). The PCM microcapsules consist of a melamine-formaldehyde capsule and a core in paraffin, with the characteristics present in Table 2. The selection of this PCM was based on its transition temperature, so that it was ideal to operate in the range of comfort temperatures inside buildings (53-55).

In this work, twelve different compositions were studied and simulated (Table 3 and Figure 2). The mortars formulation was based on the flow table method, according to the European standard EN 1015-3 (56). The resulting value from the test was only considered when between 200-220 mm.

The selected compositions possess different PCM contents (0% and 40% of aggregate mass) and different type of binders (AL, HL, G and CEM). The use of different PCM contents and different binder types allow to obtain a broader study of the PCM influence in mortars for interior coating with capacity for application in different buildings, since mortars can be obtained with greater propensity for application in new buildings or in rehabilitation operations.

The obtainment of experimental data for this study was based on the performance in flexural and compression of mortars with PCM, when submitted to different temperatures (20ºC, 200ºC and 600ºC).

The mechanical performance of the mortars was based in the European standard EN 1015-11 (57). The flexural and compression tests were performed with load control at a speed of 50 N/s and 150 N/s, respectively. Three specimens with dimensions of 40×40×160 mm³ were used for the flexural tests. Regarding the compression tests the 6 half parts resulting from the flexural test were used with approximate dimensions of 40×40×80 mm³. However, the load was applied uniformly distributed over a section of 40×40 mm².

The mortars submission to different temperatures was performed using an oven, after 28 days of curing.

Table 4 shows the compositions, the temperature exposure and experimental results of tests for obtaining the flexural and compressive strengths. Table 5 shows the statistical assessments of the parameters of Table 3 and Table 4.

Table 4 constitutes the database for the DM analyses and the type of binders were labelled as categorical variable: AL, HL, CEM and G.

The compressive strength and flexural strength of mortars incorporating phase change materials are modeled through three data mining techniques namely multiple linear regression (MLR), artificial neural networks and support vector machines. The overall process was carried out in the R software using the RMiner library (58) which allows the easier use of DM algorithms.

MLR is an expansion of the simple regression that allows the use of more than one independent variable.

Neural networks try to mimic the functioning of the human brain. To do so, they consist of artificial neuron that are interconnected and send signals among them, each one having an associated weight, w_i,j, where i and j represent neurons. Each neuron has an activation function that allows introducing a non-linear component. This study used the logistic function defined by the expression 1/ (1 + e-x) and the following general Equation [1]:

In this study, a widely used architecture called multilayer perceptron was adopted with one intermediate layer called hidden layer. Therefore, there is one input layer, one hidden layer that has a number of nodes equal to HN (Hidden Nodes) and one output layer. In this study, the search space for HN assumed the values {0, 2, 4, 6, 8, 10} (59).

Support vector machines were initially designed for classification tasks and later adapted to regression tasks with the introduction of the ε-insensitive loss function (60-61). The main idea of SVM is to transform the input data into a multidimensional feature space using a nonlinear mapping and find the best hyperplane of linear separation within the characteristic space. The nonlinear mapping requires a kernel function k(x,x’) that in this study was adopted the Equation [2]:

In addition to the kernel parameter, γ, and ε-insensitive zone width, the regression performance is also affected by a penalty parameter, C. The high number of possible combinations of ε and C would require a huge computational cost. To avoid this, the heuristics developed by Cherkasy and Ma (62) was used to evaluate these parameters. Therefore, the search space was limited to γ by using the following values: {2-15, 2-13, 2-11, 2-9, 2-7, 2-6, 2-5, 2-4, 2-3, 2-2, 2-1, 20, 21, 22, 23}.

To evaluate the performance of the models, mean absolute deviation (MAD), root mean squared error (RMSE) and coefficient of determination (R²) given by Equations [3], [4] and [5] were used:

The higher the MAD and RMSE are, the better the performance of the models. The opposite is valid for R.

In the data mining learning process, an algorithm is applied to the database to develop a model applicable to new cases. The performance of data mining algorithms can be evaluated using several methods. In this study, the cross-validation method was used, which allows using all available data (63). The database was divided into five parts each containing roughly the same number of data. Ten runs were performed using four parts of the data for training and one part for testing. This allowed obtaining ten validation metrics whose average allowed establishing the final validation metrics.

To assess the importance of each of the input parameters in the models, a sensitivity analysis was performed. In this context, the average values of all input parameters were maintained except the parameter whose sensitivity was being analyzed. Then, the value of that parameter was varied from its minimum value to its maximum value. In the end, the most important parameter in the model is the one that causes the greatest variance in the model output.

To carry out the DM process, firstly all the input parameters (binder, fibers, PCM, binder type, Temperature, Sand, Superplasticizer and water) (Tables 3 and 4) were used and based on the sensitivity analysis, the number of input parameters was reduced bearing in mind their importance. This approach was applied to develop models to predict the output parameter: compressive strength in chapter 3.1 and flexural strength in chapter 3.2.

As it was mentioned before, the data mining process was started using all input parameters given in Tables 3 and 4. Through a cross-validation scheme using the eight parameters, the metrics shown in Table 6 were obtained. Table 6 allows to conclude that all the determination coefficients are above 0.64, that, according Johnson (64) may be an indication of a good forecasting capacity of these models. Table 6 also shows that the ANN model has the best predictive capacity, given that this model has the highest R² and the lowest errors.

Figures 3 to 5 show the performances of the three DM models for compressive strength. Analyzing these figures, it is possible to confirm that artificial neural networks have the best predictive capacity. Furthermore, Figure 3 shows that up about 10 MPa the SVM model has a good forecasting capacity.

To assess the relative importance of each one of the input parameters a sensitivity analysis was performed. Results for all used techniques are presented in Table 7 and shown graphically in Figure 6. It should be underlined the strong importance of the binder type in all the models. It should be noted that the sum of the three most important parameters (binder type, temperature and sand) is around 72% in the ANN model and 76% in the SVM model. The importance of binder type and temperature in compressive strength translates the experimental results. However, an experimental study carried out by Pilehvar et al. (65) showed that the compressive strength is only slightly affected by temperature of the specimen at the testing time and models developed by Marani and Nehdi (49) yielded low importance values for this temperature. Maybe the high temperatures applied in this study can justify this difference of importances. As for the importance of sand, once its packing is altered by its replacement by softer PCM, the porosity and microstructure of the mortar are also altered and, consequently, its compressive strength. This importance was demonstrated by experimental studies (65-66), and confirmed by the developed models of Marani and Nehdi (49). The superplasticizer dosage is of residual importance in the MLR and SVM models which is in accordance with the models prediction of Marani and Nehdi (49). Conversely, superplasticizer content is the fourth most important feature in the ANN model. The models developed by Marani and Nehdi (49) attribute a great importance to PCM dosage and it was demonstrated in previous studies that (66-68) the strength of the paste mixtures reduce with the increase of PCM percentage. In this study PCM is the most important feature proposed by the MLR model, the seventh in the ANN model and the fifth in the SVM model.

To reduce the number of input parameters, binder, fibers and SP were extracted from the database. This is because they present the worst averages of the amounts obtained in all models. In this way, another analysis was done using only five input parameters (PCM, binder type, Temperature, sand, superplasticizer and water).

Table 8 shows the performance of the different models through the mean values of the three used metrics obtained using the cross-validation scheme. Once again it is verified that a correlation coefficient greater than 0.64 is obtained for all models. This result is indicative of the good predictive capacity of all models. It should be stressed the great improvement of the ANN and SVM models in relation to the models based on eight input parameters. Figure 7 to 9 show the comparison between the measured and estimated compressive strength using only five input parameters (PCM, binder type, Temperature, sand and water). Looking at these figures, it is possible to confirm the better predictive capacity of the ANN model. Regarding the SVM model, it is found a good predictive capacity up to about 15 MPa (Figure 9).

In this analysis, steps similar to those carried out in the analysis of compressive strength were followed. Therefore, initially all parameters were used for data mining analysis. Table 9 presents the results obtained in the cross-validation scheme.

It is possible to see in Table 9 that both MLR and SVM models have R² lower than 0.64. Furthermore, the ANN model has higher R² and lower RMSE but SVM has the lower MAD. Therefore, ANN model has the best performance. Figure 10 to 12 allow to see the performance of the three models. Both ANN and SVM models have a very good forecasting capacity whereas MLR has a poor forecasting capacity.

Table 10 and Figure 13 present the importance of each input parameter obtained through a sensitive analysis. It should be stressed the great importance of temperature and binder type both for ANN and SVM models. The sum of the importances of these two input parameters is about 68% for ANN model and 75% for SVM model. The third most important feature is the water for ANN model and sand for SVM model. It should be stressed that three of the four models developed by Marani and Nedhi (49) to predict compressive strength, not flexural strength, considered the water-to-cement ratio as the fourth most important feature. PCM dosage has the fourth position of importance given by ANN and SVM models. In fact, experimental studies showed that flexural strength of a cement mortar incorporating phase change material decreases with increasing amount of PCM (69-70). In relation to compressive strength for ANN model only one feature of the three most important was changed: sand was replaced by water. SVM model maintained the same top three important features.

To reduce the number of input parameters, binder content, fibers and superplasticizer content were extracted from the database. This is because they present the worst importance obtained in ANN and SVM models. Therefore, taking this into account, the analyses with only five parameters include the same input parameters as those used in the analysis performed with the compressive strength (PCM, binder type, temperature, sand, superplasticizer and water).

Table 11 shows the performance of the different models though the mean values of the three used metrics obtained using the cross-validation scheme. In this study the coefficient of determination of MLR is lower than 0.64 and this model has the highest errors. Comparing the ANN and SVM models it can be seen that ANN have higher R² and lower RMSE but higher MAD. Figure 14 to 16 show the comparison between the measured and estimated compressive strength using only five input parameters (PCM, binder type, temperature, Sand and water). Looking at these figures, it is possible to confirm that both ANN and SVM models have very good performances.