# Application of Artificial Neural Networks to Predict Insulation Properties of Lightweight Concrete
## 2 Materials and Methods
### Applications of ANN  
Based on literature analysis and research results [3; 18; 19; 20; 23; 30; 31; 32], it is known ANNs in case of issue analysis, often give better results than analytical methods in which there are problems with prediction, classification of results or monitoring. The advantage of ANNs is their unique feature, which is the ability to learn and possibility generalize the acquired knowledge on the basis of even relatively small datasets. Compared to software that performs algorithmic data processing, for example, polynomial approximation, ANNs can reasonably generalize knowledge based on new input data, that were not known before, during the network training process. This property of ANNs results from their ability to approximate a sufficiently wide class of functions of several variables (e.g., continuous functions) [33; 34; 35]. An example of the use of ANN is the analysis of concrete properties. This method is especially useful for cases where the analytical description is difficult or impossible due to the large number of variables and the difficulty of their precise determination or measurement. In the present study, ANN was used to predict the properties of the LWC. LWC features such as density, porosity and compressive strength as well as thermal conductivity were analyzed for each mixture of three types of lightweight aggregates from 0% to 100% (with a 25% change): GEGA 2 mm, GEGA 4 mm, and GAA 8 mm using the authors' previous tests results [36]. In order to perform the ANN's learning process, the laboratory test data was divided into three separate datasets in which the training dataset it was 70% of the total number of cases, whereas the test dataset was 15% of the number of cases. The validation dataset it was 15% of the number of cases. As a result of such data division, by the learning process, through the appropriate adjustment of ANN weights, took place on a set of 85% of randomly selected experimental input data. The test dataset allowed to compare properties of LWC as compressive strength and thermal conductivity vs. porosity and density. A comparison was also possible properties obtained through research with the values predicted by the network, also when on which the ANN was not trained and validated. In ANN analysis, individual LWC 1-15 samples differed in the percentages of the individual LWAs. The shares of three different aggregates, i.e., GEGA 2 mm, GEGA 4 mm, and GAA 8 mm were a sum 100%. The main assumption was, that there were two independent variables in the calculated examples, incl. the contents of GEGA 2 mm and GEGA 4 mm. The GAA content is the remainder so that the sum of the percentages of all LWAs is 100%. For the purpose of a given task, we used the feedforward ANN with two hidden layers, two input neurons corresponding to the share of GEGA 2 mm and GEGA 4 mm and one output neuron corresponding to the predicted value e.g., density, porosity, compressive strength, or thermal conductivity. The connections between neurons were of \"each other\" type (full connection) and it were applied according to backward error propagation algorithm. The number of neurons in the first hidden layer varied from 2 to 12 and in the second hidden layer from 2 to 17, depending on the forecasted variable. Error function was a mean square error of ANN, and a sigmoid function was applied as function of neuron activation. The three-input dataset consisted of 15 measurement values as properties of LWC and was used to study the quality of prediction of LWC these features using ANN. The training data set for each predicted properties LWC, consisted of 13 randomly selected measurement values from among 15 values from the input dataset involving various content of GEGA 2 mm and GEGA 4 mm. The other two values formed a testing data set. This procedure was repeated 10 times to obtain 10 different testing data sets using cross-validation.