Design of machine learning model for precision manufacturing of waste granite powder modified green cementitious composites

Statistical analysis of the results obtained

In the experimental procedure, only three variables were changed: age (7, 28 and 90 days), curing conditions (air, moist air and water) and water-cement ratio (0.5, 0.56, 0.63 and 0.71) indicating that the cement The dosage is reduced and the amount of granite powder increased. Therefore, the total number of samples studied is 216 due to compression testing of the two halves after tensile strength testing. As shown in Figure 3, the compressive strength results are related to age, curing conditions and water-cement ratio.

image 3

Compressive strength and (One) age, (b) curing conditions and (C) amount of granite powder.

According to Fig. 3. There is only a correlation between age and compressive strength.This is supported by the coefficient of determination value, which is equal to R2= 0.807.For other variables and compressive strength, there is a lack of correlation, as evidenced by the very low values ​​of the coefficient of determination, less than R2= 0.4. As expected, the highest compressive strength value was obtained for the sample preserved in water; its curing condition was noted as CC1. The older the sample, the higher the compressive strength value obtained. However, the compressive strength value equivalent to that of the reference sample of 60 MPa could not be obtained with the addition of granite powder, but the minimum value of compressive strength increased with increasing granite powder content (from about 20 MPa to 28 MPa) due to the filling effect of the powder. for 10% granite powder to replace cement and 25 MPa for 20% granite powder to replace cement). This effect is very promising for the design of low-quality cement composite mixtures.

Modeling compressive strength with an ensemble model

As mentioned above, there is no strong correlation between variables that are components of mixture ratio, curing conditions, or test age and compressive strength. Therefore, it is reasonable to use more sophisticated techniques such as ensemble models for numerical analysis.

These decision tree-based models are considered supervised machine learning algorithms capable of solving regression and classification problems.The structure of this decision tree consists of nodes that make binary decisions, and this division continues until the point where the algorithm cannot separate the data in the nodes33. This node, called the leaf of the tree, provides the solution to the problem. The advantage of using this algorithm is that the model obtained is simple. However, this is also a disadvantage in comparison, as it can lead to overfitting of the algorithm.Decision trees are accurate and perform well on datasets where variables vary widely and the number of records is not large34.

This problem can be solved by using the random forest algorithm, which uses many decision trees to obtain a solution to a problem.Each tree in the forest is constructed from a random training set, at each node, divided according to randomly selected input variables35.

However, in some cases, the performance of the random forest algorithm is not accurate, and efforts should be made to improve it. For this reason, among various ensemble learning algorithms, the adaptive boosting (AdaBoost) algorithm is the most typical and widely used algorithm.36. The algorithm works because the next tree in the algorithm is modified based on the accuracy of the previous tree, enhancing the learning ability.Structural scheme for decision trees, where the input variables represent XA generation and the output variable is represented as YesA generation,as the picture shows. 4 Combining random forest and AdaBoost algorithm scheme.

Figure 4
Figure 4

Integrated model scheme: (One) decision tree, (b) random forest and (C) AdaBoost.

The accuracy level of the model is evaluated using several parameters, according to37can include linear correlation coefficients (R), the mean absolute error (Stomach), root mean square error (RMSE), and mean percent error (map). These parameters are calculated as follows:

$$ R = sqrt {1 – frac{{sum left( {y – hat{y}} right)^{2} }}{{sum left( {y – overline{y }} right)^{2} }}} $$


$$ MAE = frac{1}{n}sum left| {y – hat{y}} right| $$


$$ RMSE = sqrt {frac{{sum left( {y – hat{y}} right)^{2} }}{n}} $$


$$ MAP = frac{1}{n}sum left| {frac{{y – hat{y}}}{y}} right| cdot $100


Where Yesmeasurements from experimental tests; (hat{y})The predicted value of the analysis; (overline{y})average; OneThe number of data samples in the process.

Note that a R Values ​​close to 1 correspond to better predictions by the algorithm.Conversely, lower values Stomach and root mean square error and map Means that the algorithm predicts the output variable better than other algorithms.Furthermore, to avoid overfitting, according to38,as the picture shows. 5.

Figure 5
Figure 5

The division of cross-validation folds.

Based on the division of the dataset shown in Figure 1. 5. Carry out numerical analysis. The performance of each fold was evaluated and shown in Figure 1. 6 In terms of value R, MAE, RMSE and map. In addition, the relationship between the experimentally measured compressive strength values ​​and the compressive strength values ​​obtained using the machine learning algorithm is shown in Fig. 1. 7 Combine the error distribution in Figure 7. 8.

Image 6
Image 6

Depend on (One) linear correlation coefficient, (b) average error, (C) root mean square error and (d) mean percent error.

Figure 7
Figure 7

Relationship between measured compressive strength and predicted compressive strength (One) decision tree, (b) random forest and (C) AdaBoost algorithm.

Figure 8
Figure 8

Prediction error distribution: (One) value and (b) percentage.

According to Fig. As shown in Figures 6, 7 and 8, all the studied ensemble models are very accurate in predicting the compressive strength of mortars containing waste granite.This is evidenced by the very high values ​​obtained for the linear dependence of the coefficients R, close to 1.0. The performance accuracy is also supported by very low error values, as shown in Figure 1. 7. Less than 4%. In addition, according to Fig. 8, the proposed model accurately predicts the compressive strength value and fails to correctly predict the strength of only a few samples (percentage error is higher than 10%).

The proposed model is also accurate compared to other machine learning algorithms used to predict the compressive strength of green cement composites containing different admixtures. In addition to the results obtained by the model proposed in this work, some selected works are listed in Table 4.

Table 4 Comparison of algorithms used to predict the compressive strength of green cement composites with different admixtures.

Analysis of the results in Table 4 shows a very high level of accuracy for the compressive strength of green cement composites using the machine learning algorithm. Furthermore, in this work, a very accurate model was constructed for predicting the compressive strength of green cement composites containing different admixtures, compared with the models studied previously.

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