# Application of Artificial Neural Networks to Predict Insulation Properties of Lightweight Concrete
## 3 Results  
The results of properties laboratory tests of LWC for various shares of lightweight aggregate, were presented in Table 4.  
During the training of the neural network, the cross-validation procedure was used. Thirteen measurement data on which the network was trained were selected at random, and the quality of prediction was verified on the other two points. This procedure was repeated 10 times on different 13 element subsets. Usually, it is assumed that the test set contains 15% of the elements, the validation set 15% of the available data set. In the analyzed cases, the reduction in the size of the training set generated a non-linear increase in prediction errors (probably due to a relatively large change in compression strength and porosity depending on the share of additives in LWC), therefore only the test set was used. The ANN with two hidden layers was trained by multiple feeding of the training dataset to the ANN's input, until the stabilization of the total mean square error of the network at a very low level while avoiding the phenomenon of ANN overfitting. Overfitting was partially eliminated by completing the learning process at the initial stage of the mean square error stabilization. Moreover, the small number of points in the training set and their topological distance in the set of parameters (additive shares) meant that the neural network did not \"learn\" local rapid changes in the analyzed dependence.  
The results of the forecasted by the ANN: density, porosity, compressive strength, and thermal conductivity of LWC as a function of shares of GEGA 2 mm, GEGA 4 mm and shares of GEGA 2 mm and GAA 8 mm in the specimen are presented as 2D charts in Figure 4a-h.  
In Figure 4 shows, only thermal conductivity behaves in a way that shows a fairly regular evolution between extreme aggregate ratios. Other measured quantities do not show this behavior and if we want to carry out multi-criteria optimization, it is worth using ANN. For example, to select such a composition of aggregates to obtain lightweight concrete with about specified thermal insulation properties. The results of the relationship between density and porosity during laboratory tests are presented in Figure 5a. The predicted results of this relationship with the use of ANN are shown in Figure 5b. Figures 6a and 7a show the results of laboratory tests of the thermal conductivity coefficient as a function of the LWC porosity and density, respectively, while Figures 6b and 7b show the predicted results obtained by ANN.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**LWC**} & **Share of GEGA** & **Share of GEGA** & **Density** & **Porosity** & **Compressive** & **Thermal Conductivity** \\  & **2 mm (\%)** & **4 mm (\%)** & **(kg/m\({}^{3}\))** & **(\%)** & **Strength (MPa)** & **\(\lambda\) (W/m\(\cdot\)K)** \\ \hline
1 & 0 & 0 & 1560 & 20.8 & 18.65 & 0.8113 \\ \hline
2 & 25 & 0 & 1378 & 17.7 & 21.35 & 0.5886 \\ \hline
3 & 50 & 0 & 1177 & 16.0 & 13.43 &  
Figure 4: _Cont._  
Figure 4: Graphical presentation of the results obtained by means of ANN method as a function of LWA share. Predicted results for: (**a,b**) density in (kg/m3), (**c,d**) porosity in (%), (**e,f**) compressive strength in (MPa), (**g,h**) thermal conductivity in (W/m-K), respectively.  
Figure 5: Graphical presentation of the relationship between density and porosity of the LWC based on: (**a**) the laboratory test results, (**b**) the ANN prediction.  
Figure 6: Graphical presentation of the relationship between the thermal conductivity coefficient and porosity of the LWC based on: (**a**)the laboratory test results; (**b**) the ANN prediction.