Using Neural Networks to Prediction of compressive strength of heavy concrete

. The article is devoted to the study of the process of predicting the compressive strength of concrete. Fully connected neural networks are used as a forecasting tool. The need for research is caused by the fact that concrete is one of the materials widely used in construction, and the existing automated tools have insufficient accuracy. The paper investigates the structure of a neural network: select of the number of layers, the number of neurons in layers, the activation function, the optimization method, the number of epochs, and the technique to prevent overfitting. Comparison of the obtained results with the results of laboratory tests showed that neural networks could achieve acceptable prediction accuracy. The coefficient of determination refers to the main indicators of the quality of forecasting. Now, the coefficient of determination is approximately equal to 0.889. In the future, the started research can be continued and the value of the coefficient of determination can be improved.


Introduction
Concrete is one of the most commonly used materials in construction.It owes this to its physical and mechanical characteristics, as well as durability.In addition, it can be obtained using local mineral materials.One of the main properties of concrete is compressive strength.In practice, the strength of concrete is usually determined based on the controlled hardening of concrete tested at the ages of 7, 14 and 28 days.In a real construction, concrete is subjected to multidirectional loads.However, in laboratory conditions, it is customary to conduct a uniaxial compression test [1].
To create an acceptable proportion of the concrete mixture, it is necessary to make several test mixtures and test them in the laboratory.Therefore, automated means of calculating the composition of the concrete mixture are used.One of these tools is an artificial neural network [2,3].A neural network can predict the proportions of a mixture based on statistical data from previously conducted experiments.
In [4], an analysis of works on predicting the properties of a concrete mixture, which use artificial intelligence methods to solve the problem, was carried out.In this paper, it is shown that the use of artificial intelligence methods gives better results compared to the results of mathematical modeling.And among the methods of artificial intelligence, neural networks show the highest accuracy.For example, in [5], on a training sample of 225 observations, a neural network with a direct connection and one hidden layer showed a determination coefficient R2 equal to 0.965.And in [6], a neural network trained on a data set of 168 observations showed R2 and RMSE values of 0.996 and 3.680 on the test set, respectively.

Materials and methods
The task of the study is to predict the compressive strength of a concrete mixture according to its specified ingredients.At the same time, a high accuracy of prediction should be achieved.
Neural networks are used in the work to solve the problem.Currently, there are various types of neural networks.Convolutional neural networks are mainly used for image processing, recurrent neural networks for natural language processing, and fully connected neural networks for data processing.Therefore, fully connected neural networks are used to solve the problem.Figure 1 shows the sequence of stages of the research process.At the first stage, data preparation is performed.
In addition to the listed ingredients, the predictors of the data set include the design capacity.The initial data set contained 13 observations (Table 1).The volume of statistical data provided is insufficient for the use of neural networks.Therefore, it is necessary to supplement the data set.For this purpose, additional data has been generated.

Data Synthesis
Theoretical calculations and tabular data were used to expand the data set.All calculations and tabular data corresponded to Russian interstate standards GOST 27006-2019 «Concrete.Squad Selection Rules» and GOST 24211 «Additives for concrete and mortar».The data set was expanded for each concrete class from B7.5 to B45 for concrete grade 40 (M40 grade concrete mix).The data set includes eight additional rows for each class.A fragment of the extended dataset is shown in Table 2.This approach allowed us to expand the data set to 495 rows.

Data normalization.
As can be seen from Table 2, there is an imbalance between the values of the features in the source data.Their measurement ranges differ by several orders of magnitude.This can cause instability of the model, worsen learning outcomes and slow it down.Therefore, data normalization was performed for each predictor, according to the formula (1): where   ,   -correspond to the boundaries of the measurement range of a particular predictor, х -is the current value of the predictor to be normalized,   -is the normalized value of the predictor.

Architecture Development of Fully connected Neural Network
Each output measurement depends on each input measurement.A fully connected layer is a function from R m in R n .Each output measurement depends on each input measurement.

Creating a model of Fully-connected Neural Network
The neural network consists of five layers.Its architecture is shown in Figure 2. The first hidden layer of Dense has 165 neurons, the next three hidden layers of Dense have 200 neurons each, and the last output layer of Dense has one neuron.The output signal Y is the predicted concrete density.All layers have a ReLU activation function.

Training the model
One of the common regularization methods is the Dropout method.This method allows you to deal with retraining.It is used when the curves of the loss function on the validation and

Selection of model parameters
In this paper, forecasting is solved as a regression problem.Therefore, the root-meansquare error and the mean absolute error are used as a loss function and metric, respectively.As an optimization method, the adamax optimizer is used, which is a variant of the Adam optimization algorithm with adaptive learning rates.

Result and Discussions
The main experiments carried out in the work included: the study of the network architecture (the number of neurons and layers) and the study of the parameters of the neural network.

Network architecture research
Four variants of the number of hidden layers were considered in the experiment: 2, 3, 4, 5 (Table 3).An increase in the number of hidden layers from 2 to 4 led to a decrease in the value of MAE.However, with a further increase in the number of hidden layers, the value of MAE increased.This indicates that adding additional hidden layers can improve the accuracy of the model and reduce the prediction error, however, too many layers can lead to a deterioration in the performance of the model and increase the error.For each layer, the number of neurons in the layer was determined in the range from 50 to 300 in increments of 50.Then the best interval was considered in increments of 10.Thus, it was found out that the optimal values for the hidden layers are as follows: the first one is 165, the rest are 200 neurons, the output layer is one neuron.Also, sigmoidal type activation functions and ReLU activation function were selected for each layer.As a result, the ReLU function is selected for all layers.
Experiments were also carried out to determine the optimal value of the butch (Table 4)).The analysis of the table shows that the optimal size of the batch is 256.
Next, a neural network with a given architecture was trained and tested.As a result, the values of the average absolute error (MAE) were obtained, which amounted to 0.543.The value is very high, therefore, it became necessary to investigate the external parameters of the neural network.

Investigation of neural network parameters
In this series of experiments, experiments with various optimizers were first carried out.The optimal optimizer turned out to be adamex.In addition, the number of epochs was determined (Table 5).Although an increase in the number of epochs generally leads to a decrease in parameter changes, there is some increase at the last stage of training (from 800 to 900 epochs).
In addition, experiments have been conducted with various optimizers.The optimal optimizer turned out to be adamex.

Final results of the conducted experiments:
 determination coefficient r2_score = 0.8893353477867147;  the root-mean-square error on the validation sample val_loss: 0.0056;  average absolute error val_mae: 0.0552.Dependency graphs are shown in Figure 3.

Comparison of results
Laboratory tests were carried out on concrete mixtures calculated theoretically and by a neural network.To do this, in the neural network architecture, three neurons corresponding to the main ingredients are specified in the output layer: sand, rubble and cement.The results are presented in tables 6 and 7.As a result, it can be noted that, in principle, the results obtained are not bad, but they can be improved by studying other external parameters of the neural network.

Conclusion
The prediction is based on a fully connected deep learning neural network.The study of the neural network structure and its external parameters is carried out.The results of the field experiment showed that the neural network calculates the predicted strength of concrete

E3SFig. 3 .
Fig. 3. Final results: a) dependences of accuracy on the number of epochs in the validation sample; b) curves of the loss function in the validation sample.

Table 1 .
The water demand of the concrete mixture depends on the fraction of crushed stone.

Table 2 .
A fragment of an extended dataset.

Table 3 .
Influence of the number of hidden layers purpose mae.

Table 4 .
The effect of the size of the butch on the value mae.

Table 5 .
Influence of the number of epochs assignment mae.

Table 6 .
Comparative table of neural network results and laboratory tests.

Table 7 .
Comparative table of the results of theoretical calculations and laboratory tests.