Measurement of the Compressive Strength of Concrete Using Modeling of Deep Hybrid Forest Regression

Rajprasad, J.; Priya Rachel, P.; Arulselvan, S.; Arul, D.; Ramesh Kumar, G.; Pallavi, H. J.; Sivaraja, M.; Singh, Vinay Kumar; Gebreamlak, Getachew

doi:https://doi.org/10.1155/2023/3766214

Advances in Materials Science and Engineering

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Abstract Introduction Literature Review Discussion Conclusion Data Availability Conflicts of Interest References Copyright Related Articles

Research Article | Open Access

Volume 2023 | Article ID 3766214 | https://doi.org/10.1155/2023/3766214

Measurement of the Compressive Strength of Concrete Using Modeling of Deep Hybrid Forest Regression

J. Rajprasad,¹P. Priya Rachel,²S. Arulselvan,³D. Arul,³G. Ramesh Kumar,⁴H. J. Pallavi,⁵M. Sivaraja,⁶Vinay Kumar Singh,⁷and Getachew Gebreamlak⁸

Academic Editor: Sachin Salunkhe

Received30 Dec 2022

Revised12 May 2023

Accepted05 Jun 2023

Published01 Jul 2023

Abstract

The paper proposes a deep hybrid forest regression-based modeling method for measuring the compressive strength (CS) of concrete. Then, the reduced feature vector is used as input to train multiple subforest models (SFM), the predicted values are selected from multiple subforests via the KNN (K-nearest neighbor) method to combine them to obtain the layer regression vector (LRV), and it is combined with the reduced feature vector to obtain the improved LRV, then the output of this layer is taken; second, the regression vector (RV) of the input layer enhancement layer is used as input to obtain the output of the second layer FM, and the steps are repeated until the output of the input layer FM is complete. Finally, the output of the FM of the first layer is obtained. Several SFMs are trained and the result is obtained. The final prognosis is obtained by arithmetically averaging the forecast results of the SFMs of this layer.

1. Introduction

Mechanical strength is a very important property of concrete and is translated into compressive, tensile, bending, and shear strength. It is the strength that allows concrete structural elements to withstand high loads in service without collapsing [1]. Several factors can significantly influence the mechanical strength of concrete in the hardened state. Concrete is as requisite material in modern construction engineering, and its compressive strength (CS) is the most important index of concrete. In concrete structural engineering, the strength of concrete is checked and evaluated by the results of the CS test of concrete specimens. Due to the inability to measure the real-time data of the concrete compressive strength online, it is difficult to achieve optimal control of the concrete production process. The parameters of concrete CS usually require a long period of offline laboratory analysis to obtain. Limited to complex physical/chemical production processes such as unclear mechanism, nonlinearity, and strong coupling, the key process parameters that characterize the product quality and environmental protection indicators of this type of process are usually called difficult-to-measure parameters [2]. Such parameters are manually sampled at regular intervals and then analyzed offline in the laboratory (such as concrete CS, dioxin concentration emitted from urban solid waste incineration pollution, and grinding particle size that characterizes the quality of grinding) or rely on excellent fields. It is estimated by experts at the production site based on experience (such as the mill load that characterizes the grinding efficiency). The abovementioned inaccurate and long-lag detection method has become one of the main bottlenecks restricting the production process to achieve operation optimization and feedback control. Combining the production process mechanism and empirical knowledge, it is one of the effective ways to solve this problem by using offline easy-to-detect process variables to establish soft-sensing models for difficult-to-measure parameters [3].

2. Literature Review

In recent years, the development of increasingly powerful computers has contributed to the increased use of computational modeling techniques using ML in very different areas of engineering and research. These tools can substantially improve any proposed previous model. In the area of civil engineering, there have been many applications of ML techniques, such as monitoring the service life of structures, predicting different mechanical properties of concrete, optimizing design of structural elements, and mixing concrete with alternative materials [4].

Data-based ML techniques prove to be successful in predicting the mechanical properties of concrete produced with alternative materials such as construction and demolition and industrial and mining waste [5–8]. However, the amount of existing research on ML in the study of concrete with mining waste is still small.

In order to explore the main ML techniques applied in predicting the mechanical strength of concrete, a scientific mapping was carried out through a bibliometric review of the literature [9–11].

The hardening process of Portland cement-based concrete is very long and can last for years. Increasing age allows it to gain resistance, that is, increases its capacity for mechanical resistance. In 28 days, the concrete acquires 75% to 90% of its final resistance and it is based on this value, obtained through tests, that the concrete elements are designed [12]. Curing is a procedure used to promote cement hydration by controlling the temperature and movement of water into and out of the concrete. In this way, it directly influences the moisture and temperature of the concrete at early ages, ensuring that the mechanical strength properties of the concrete are achieved [13]. As the main branch of machine learning, ensemble learning has been widely used in the field of hard-to-measure parameter soft-sensing in industrial processes. As a basic learner of ensemble learning, decision tree (DT) can not only deal with classification problems but also can deal with regression problems, the most representative of which is classification and regression tree (CART) [14]. The method of integrating DT is called forest algorithm (FM), among which the random forest (RF) [15] algorithm proposed by Breiman is the most representative. The deep neural network learning algorithm [16] makes traditional machine learning methods lose their competitiveness in many fields, but it is essentially a “black box” model, which has many hyperparameters and difficult training problems. The authors [17] analyzed the internal reasons for the success of DNN, proposed a deep forest (DF) structure consisting of multigrained scanning and cascading forests, and conducted research on deep learning of nonneural network structures composed deep model. Although similar related research is gradually increasing, its research fields mainly deal with classification problems, and its main contribution is to use the class distribution vector as a feature representation method for transfer between layers. For the continuous numerical data of industrial processes, literature [17] introduced a deep Boltzmann machine (DBM) to convert the original features into 2-D vectors before multigrained scanning and then used the DF method to construct a classifier and used industrial process fault diagnosis.

All proposed soft sensor modeling methods based on ensemble learning [18–20] realized online soft sensor of concrete CS. However, the structure of the concrete CS soft sensor model in the above research literature is complex, and the representation learning of features is not considered between modules, and there are problems such as low prediction accuracy of the concrete CS soft sensor value [21–36].

3. Overview of the Proposed Work

The difficult-to-detect quality indicators or environmental protection index parameters of complex industrial processes usually require long-term offline assay analysis to obtain, and in order to realize the operation optimization control of these processes, online real-time measurement of these difficult parameters is usually required. The mechanistic complexity of industrial processes involving multiple physical and chemical principles makes it difficult to construct interpretable mapping models between high-dimensional input features and difficult-to-measure parameters.

For the abovementioned problems, the present work proposes a kind of modeling method based on depth hybrid forest regression (DHFR) for measuring concrete CS and comprises: adopt dimension reduction module to pass through adopting the dimension reduction that is suitable for industrial process. The reduction strategy preprocesses the original high-dimensional features to obtain the reduced feature vector. This vector is given as input to the input layer of forest module to train multiple SFMs and selects the predicted values of several subforests through the KNN (K-nearest neighbor) method combined to obtain the LRV. This vector is combined with the reduced feature vector to obtain the enhancement LRV, and then, the output of this layer is obtained. This vector is given as input to the input layer of the middle layer forest module containing the K − 2 layer, to obtain the output of the second layer FM in the same way as the input layer forest module and repeat in sequence until the output of the K − 1 layer FM is completed and the output of the K − 1 layer intermediate FM is obtained in the output layer of the forest module. This output is used as the input of the FM module of the output layer K, and multiple SFMs are trained, and the final prediction result is calculated by performing arithmetic mean on the prediction output of the SFMs of this layer. The effectiveness of the current method is evaluated by the concrete CS data simulation in UCI platform.

Our study combines deep learning, random forest, and regression as a single algorithm. This novelty is not presented so far.

3.1. Characterization of Concrete Components

The results of the characterization of the constituent materials of the concrete are shown in Table 1.

3.2. Mixture and Dosage of Concrete

To carry out the concrete dosage, the characteristic strengths of 10 MPa and standard deviation of Dp = 4.0 MPa were adopted for concrete with a w/c ratio of 0.7, and 20 MPa and standard deviation of Dp = 5.5 MPa for concrete with a w/c ratio of 0.5. The slump of the adopted truncated cone was 80 ± 20 mm. The traits obtained through the calculations proposed by the Brazilian Portland Cement Association (ABCP) are shown in Table 2.

3.3. Concrete in the Fresh State

The average value of concrete consistency in the fresh state (slump test) of the replacement concretes (0, 25, 50, 75, and 100%) correspond to three different measurements collected and are presented in Table 3 together with the moisture values relative air and temperature in the laboratory during molding.

Making a comparative analysis between the concretes that have the same w/c ratio of 0.5 and 0.7, the results of the measurements of the slump of the concretes corresponded to the expected being within the foreseen limits and presenting workable conditions facilitating the molding.

4. Implementation of the Proposed Work

The present work proposes a kind of modeling method based on deep hybrid forest regression (DHFR) for measuring concrete CS, by dimension reduction module, input layer forest module, intermediate layer forest module, and output layer The forest module implements DHFR modeling, where the number of decision trees in each SFM is J (Figure 1).

In Figure 1, represents original high-dimensional feature vector, and it comprises eight process measurement values such as concrete content, blast furnace slag powder content, fly ash content, water content, water reducing agent content, coarse aggregate content, fine aggregate content, and concrete placement days. represents the reduced feature vector after dimensionality reduction (the input feature vector of the input layer), that is to reduce the dimensionality of the 8 features of the concrete CS; means that in the soft measurement of the concrete CS, the t^th SFM of the input layer FM represents the t^th subforest of the input layer FM Model , the predicted value vector of concrete CS generated by J decision trees of t (•); represents the predicted mean value (pmv) of the t^th predicted value vector in the input layer FM represents the value obtained from the input layer using kNN In the t^th predicted value vector in the layer FM, the RV composed of concrete CS prediction values near the pmv is the LRV composed of T RVs of the input layer FM in series; represents the enhanced LRV composed of the reduced feature vector and the LRV of the input layer FM in series, which is also the input feature vector of the middle layer (layer 2) in the concrete CS soft sensor model.

indicates the enhancement LRV composed of the input feature vector and the LRV of the k − 1^th layer FM in series, which is the input feature vector of the k^th layer FM in the concrete CS soft sensor model; k = 1, 2, …, K, K represents the number of layers (depth) of DHFR; represents the t^th SFM in the k^th layer FM in the soft sensor model of concrete CS, indicates the predicted value vector of concrete CS generated by J decision trees of the t^th SFM in the K^th layer FM. represents the t^th predicted value vector in the K^th layer forest . The pmv of represents the DHFR final concrete CS prediction output value.

The abovementioned modules and their functions are described as follows: dimensionality reduction module adopt dimensionality reduction method to carry out preprocessing to the original high-dimensional feature vector in concrete CS data and obtain reduction feature vector. Input layer FM module accepts reduction eigenvector as input, build T SFMs that are made up of J decision trees to form input layer FM, and select in the predicted value vector of each SFM. The predicted values are combined into a LRV and then combined with the reduction vector to form an enhancement LRV, and then, the input of the intermediate layer FM module is obtained. Middle layer FM module accepts the enhancement LRV obtained by input layer FM is used as input and continues training K − 2 layer FM with the same mode of training input layer FM.

Output layer FM module: take the output of the K − 1^th layer FM as the input of the output layer (K^th layer) FM module, train the K^th layer FM, and then transfer the T predictions in the K^th layer FM to true. The arithmetic mean of the values is obtained to obtain the final prediction result of concrete CS.

The concrete process of dimension reduction module is the complex physical/chemical production process generally has characteristics such as strong coupling and nonlinearity, resulting in many redundant features in the process data, which are easy to form problems such as the curse of dimensionality in modeling [13]. Consider using dimensionality reduction algorithm to reduce high-dimensional original feature vectors to limited dimensions before model training. Dimensionality reduction can be used to deal with the curse of dimensionality and to improve algorithm efficiency, model interpretability, and data visualization. Since the output in the regression problem is a continuous real-valued variable, many reduction methods that work well in the classification problem cannot achieve the optimal effect. Various linear and nonlinear dimension reduction methods for regression problems are available. When using the method proposed in this application, the corresponding dimension reduction method can be selected according to the characteristics of different data sets to obtain the feature vector of dimension reduction [15–27].

The concrete process of input layer FM module is the subforest in the DHFR structure can adopt the regression FM of various forms such as random forest and complete random forest. Self-sampling (bootstrap) and random subspace method (RSM) were used to analyze the eight process measurement values. The training set of eight features such as the number of days of concrete placement and the detection value of concrete CS is used for random sampling of samples and features to Increase the diversity of subforests.

4.1. Construction Process of the Input Layer Subforest

The training set D of the CS detection value is randomly sampled, taking the J training subset.

of the t^th SFM in the input layer FM as an example, the generation process iswhere D represents in the concrete CS soft measurement model, the training set of eight features; J indicates the number of bootstrap and also indicates the number of decision trees of each SFM in the input layer FM.

indicates the j^th training subset of the t^th subforest in the input layer FM, where indicates that the j^th training subset selects from eight features, y^j represents the actual detection value of concrete CS; m = 1, …, , represents the feature selected from the 8 features of the j^th training set of the t^th subforest in the input layer FM Quantity, usually << M; t = 1,2, …, T, t is the t^th SFM in the input layer FM.

With the abovementioned J training subset , we build J decision trees in the t^th subforest in the concrete CS soft sensor model and obtain the t^th SFM in the input layer (Figure 2).

The process of constructing the SFM is detailed in literature [28]. By repeating the abovementioned steps T times, you can get the set of input layer FM .

4.2. Enhancement of the LRV Generation Process of the Input Layer FM

For the t^th SFM in the input layer FM, each decision tree model will produce a concrete CS prediction value to the concrete process measurement value sample , then we obtain the predicted value of J concrete CS , a vector of predictors consisting of .

Calculate the pmv of the t^th SFM in the input layer FM,

Select concrete CS prediction values near the pmv through kNN to form the RV of the t^th subforest. The abovementioned steps are T times repeated to obtain the LRVs of T SFMs in the input layer FM,

Then, the reduced feature vector and the LRV are combined in series to obtain the enhanced LRV output by the input layer FM, which is concrete input for the intermediate layer FM (layer 2) of the CS soft sensor model. Its generation process iswhere represents to select the concrete CS predictive value quantity near the pmv.

4.3. The Concrete Processing Process of Middle Layer FM Module

We take the k^th layer FM as an example to introduce the construction process of the middle layer FM module.

The training data set of the k^th layer FM is the combination of the enhancement LRV output by the k − 1 layer FM and the detection value of concrete CS, and the features include: concrete content, blast furnace slag content, pulverized coal Ash content, water content, water reducing agent content, coarse aggregate content, fine aggregate content, days of concrete placement, and other eight features and LRV . The representation process iswhere y represents the concrete CS true value vector in the training set D; N represents the sample size of the training set D; and represents the LRV of the k − 1 layer FM and will be to the concrete CS 8 Dimension reduction. The simplified reduced feature vector is the RV of the enhancement layer after concatenation; , represents the input training set of the k^th layer FM, where x_k and i represent the i^th layer containing eight process measurement values and LRV training samples, y_i represents the i^th CS of concrete

The actual detection value is . It means that the FM of the k^th layer includes eight process measurement values, the training data set D_k, and the LRV and the detection value of the concrete CS.

Then, we adopt bootstrap and RSM to include eight characteristics, the LRV and the training data set D_k of the concrete CS detection value are randomly sampled for samples and features, and the training subset can be expressed as follows:where represents the jth training subset of the t^th SFM in the k^th layer FM, and represents the eight process measurement values in the jth training subset. The eight features, and the training samples of m_k features selected from the LRV: represent the actual detection value of concrete CS . The number of features selected from the 8 features and LRV of the jth training set of the t^th SFM in the k^th layer FM, usually there is .

Construct J decision trees of the t^th SFM in the k^th layer FM in the concrete CS soft sensor model with the abovementioned J training subset and obtain the t^th SFM in the k^th layer FM.

We repeat abovementioned steps T times and obtain the collection of the k^th layer FM .

Next, we describe the enhancement LRV generation process of the k^th layer FM.

In the k^th layer FM, the t^th SFM, each decision tree model produces a concrete CS predictive value to input , J predictive values of concrete CS can be obtained . A vector of predictors consisting of .

Calculate the prediction mean value of the t^th SFM in the k^th layer,

Select concrete CS prediction values near the pmv through KNN to form the RV of the t^th SFM. Repeat the abovementioned steps T times to obtain the RVs of T SFMs. After combination, the first SFM is obtained.

The LRV of the k^th layer FM .

Then, the reduced feature vector after dimensionality reduction of the 8 features of concrete CS is combined in series with the LRV to obtain the enhanced LRV output by the k^th layer FM, which is the k^th + 1 input for layer FMs. Its generation process can be expressed as follows:

4.4. The Specific Processing Process of the Output Layer FM Module

The training data set of the K^th layer FM is the combination of the enhancement LRV and the concrete CS detection value that the K − 1 layer FM outputs, wherein feature includes: eight features and LRV . The expression process is

Among them, means the training set of the k^th layer FM, where means the i^th one contains the eight process measurement values. The training samples of eight features and LRV, y_i represents the actual detection value of the i^th concrete CS; indicates that the K^th layer contains eight features and LRVs including eight process measurement values and the number of features of the training data set D_K for concrete CS detection values. Then, adopt bootstrap and RSM to include eight process measurement values, the LRV and the training data set DK of the concrete CS detection value are used for random sampling of samples and features, and the generation process of J training subsets of the t^th SFM in the K^th layer FM can be expressed as follows:where represents the j^th training subset of the t^th SFM in the K^th layer FM, where represents the j^th training subset from the eight process measurement values and a training sample of a feature selected from layer regression vector, where , represent the actual detection value of concrete CS; represents the K^th layer and the j^th training set of the t^th SFM in the layer FM is selected from 8 features and the number of features of the LRV , usually there exists .

Construct J decision trees of the t^th SFM in the K^th layer with the abovementioned J training subsets and obtain the t^th SFM of the K^th layer. The abovementioned steps are T times repeated to get the model of the K^th layer forest module.

In the t^th SFM in the K^th layer, each decision tree model will produce a concrete CS predictive value and then obtain the predictive value vector that J concrete CS predictive value forms and calculate in the K^th layer. The mean value of the t^th SFM predicted,

The abovementioned steps are T times repeated to obtain the prediction output set of T SFMs. Finally, the predicted values of the concrete CS of the T SFMs are arithmetically averaged,where represents the final concrete CS prediction output of the DHFR model.

5. Experimental Description

The concrete CS data set contains 1030 samples, and the first columns are input (eight process measurement values); the ninth column is the output, that is, the CS of the concrete. In this paper, half of the 1030 samples are used as training samples, quarter are used as verification samples, and the remaining quarter samples are used as test samples.

According to the characteristic attribute of concrete CS data set, the following model will carry out the model of dimensionality reduction module expressed as DHFR-D_red and the model without dimensionality reduction module is denoted as DHFR-NoD_red. The initial parameter setting in the experiment is that the number of subforests in the forest layer in the concrete CS soft sensor model is set to T = 8, which includes 4 random forests and 4 complete random forests, and the predicted value of the concrete CS selected by KNN The number = 1.

5.1. Experimental Result with Dimensionality Reduction Module

Eight process measurement values and concrete CS in concrete are analyzed. The statistical results of the linear correlation coefficient of the true value of the strength (Figure 3), and the absolute values of the correlation coefficients between the eight features and the CS of concrete (Figure 3), and the eight features are divided into two parts with 0.2 as the dividing line part. Among them, the characteristics greater than 0.2 are: concrete content, water content, water reducing agent content, and concrete storage days. Therefore, the four features of concrete content, water content, water reducing agent content, and concrete placement days are selected from the eight features of concrete CS data through the dimensionality reduction module as the training set.

With the mean value of 50 times operation as final result, parameter is set to K = 50, M^j = 4, = 1, T = 8, and J = 500, wherein M^j = 4 represents concrete content in concrete CS data set, Four features are randomly selected from the four features of water content, water reducing agent content, concrete placement days, and the LRV. Test the relationship between the training sample threshold θ_Forest of the decision tree leaf node and the RMSE of the concrete CS soft sensor model DHFR-D_red in the verification set (Figure 4).

As can be seen from Figure 4, when the training sample threshold θ_DT = 10 of the leaf node, the RMSE (7.1736) value of the verification set reaches the minimum, and when the θ_DT increases again, the RMSE also increases thereupon. Therefore, the training sample threshold θ_DT = 10 of the leaf nodes of the decision tree is selected. Then, test the relationship between the number J of the decision tree of the SFMs in the forest layer model and the RMSE of the concrete CS soft sensor model DHFR-D_red in the verification set (Figure 5).

As can be seen from Figure 5, the RMSE (6.9979) value of verification set reaches minimum when the quantity J = 100 of the decision tree in the subforest of forest layer in the concrete CS soft sensor model DHFR-D_Red.

The parameter of final concrete CS soft measurement model DHFR- D_Red is determined as T = 8, = 1, K = 50, θ_DT = 10, M^j = 4, and J = 100.

5.2. Method Comparison

Adopt complete random forest method (CRF) and random forest (RF) to compare with method DHFR-D_red mentioned herein, where CRF parameter is set to θ_DT = 10, M^j = 4, and J = 100 and RF parameter setting is set to θ_DT = 10, M^j = 4, and J = 100. The accuracy of the prediction curves of all methods are shown in Figures 6–8. Figure 9 shows the correlation between the predicted and experimental values of the CS of concrete for the three models. The comparisons of the different methods are shown in Table 4.

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The result of Figures 6–8 and Table 4 shows that CRF has maximum prediction error in predicting concrete CS because of its inherent randomness, and test set error is 9.3488. Also, RF uses the minimum average error rule to split the nodes of the decision tree, making its prediction performance in concrete CS stronger than CRF, and the error of the test set is 7.5390; both the verification set and the test set have the best predictive performance on the prediction of concrete CS, the error of the test set is 7.2320, and the number of layers K = 3.

5.3. Experimental Result without Dimensionality Reduction Module

Taking the mean of 50 runs as the final result, the parameters are set as K = 50, M^j = 4, = 1, T = 8, and J = 500, where M^j = 4 means 8 features and layers from the concrete CS data set four of the RVs are randomly selected as input features. Test the relationship between the training sample threshold θ_Forest of the decision tree leaf node and the RMSE of the concrete CS soft sensor model DHFR-Nodimred in the verification set (Figure 10).

The relationship between the RMSE of NoD_red in the validation set (Figure 10). As can be seen from Figure 10, when the training sample threshold θ_DT = 10 of the leaf node, the RMSE (7.4893) value of the verification set reaches the minimum, and when the θ_DT increases again, the RMSE also increases thereupon. Therefore, the training sample threshold θ_DT = 10 of the leaf nodes of the decision tree is selected. Then, test the relationship between the number J of the decision tree of the SFM in the forest layer model and the RMSE of the concrete CS soft sensor model DHFR-NoD_red in the verification set (Figure 10).

It can be seen from Figure 11, the RMSE (7.4771) value of the verification set reaches the minimum when the number J = 200 of the decision tree in the subforest of the forest layer in the concrete CS soft sensor model DHFR-NoD_red.

The parameter of final concrete CS soft measurement model DHFR-NoD_red is determined as T = 8, = 1, K = 50, θ_DT = 10, M^j = 4, andJ = 200.

5.4. Method Comparison

Adopt complete random forest method (CRF) and random forest (RF) to compare with method DHFR-NoD_red mentioned herein, where CRF parameter is set to θ_DT = 10, M^j = 4, and J = 200 and RF parameter is set to θ_DT = 10, M^j = 4, and J = 200. The accuracy of the prediction curves of all methods are shown in Figures 12–14, and their statistical results are as shown in Table 5. Figure 15 shows the correlation between the predicted and experimental values of the CS of concrete for the three models.

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The results of Figures 11–13 and Tables 4 and 5 show that (1) after omitting the dimension reduction module, the DHFR- NoD_red method proposed in this paper can predict the compressive strength of concrete in the training set, verification set, and test set, All have the best prediction performance: the test set error is 6.4018 and the number of layers K = 3; (2) compared with DHFR- D_red red for dimensionality reduction, DHFR- NoD_red is better than DHFR- D_red in predicting the compressive strength of concrete in the verification set and test set, which shows that the deep forest structure proposed in this paper is effectiveness. Therefore, the deep integrated forest regression model proposed by the method proposed in this paper has the best predictive performance in the soft measurement of concrete compressive strength. Aiming at the soft sensor modeling of difficult-to-measure parameters in industrial processes, the present invention proposes a modeling method based on deep integrated forest regression. The main contributions are as follows: for the first time, it solved the feature representation method between levels in the deep integrated forest in the regression problem and realized the application of the deep forest structure in the regression modeling problem for the first time. The effectiveness of the proposed method is verified by the simulation of concrete compressive strength data on the UCI platform.

6. Discussion

In the instance, it is seen in Table 5 that all of the models, RF and CNN, provide good forecasts compared to CRF. Table 6 depicts the relationship between experimental and anticipated values for several models; all models exhibit a positive association between experimental and predicted values. Finally, Table 5 shows the prediction accuracy of the models, indicating that DHFR outperforms the other models.

6.1. Comparison of ML Models

This study examines the performance of CRF, RF, and DHFR models to evaluate its performance in predicting the CS of concrete. In this work, DHFR has highest correlation and lowest performance metrics (MSE = 1.708; RMSE = 1.309; MSLE = 0.005; RMSLE = 0.07.8; MAE = 1.130.; R² = 0.809.). The prediction of the CS shows that CHFR gives the best results. Compared to other works, our work predicts the CS with three models; however, other studies ([4–11, 37]) used ANN and found good results; in contrast, this paper used DHFR and provided comparison between with (DHFR- D_red) and without (DHFR- NoD_red) dimensionality reduction. DHFR- NoD_red is better than DHFR- D_red in predicting the compressive strength of concrete in the verification set and test set, which shows that the deep forest structure proposed in this paper is effectiveness.

7. Conclusion

The proposed work presented an approach using different artificial intelligence techniques to predict the mechanical strength of concrete produced with niobium waste. Three ML techniques (CRF, RF, and DHFR) were tested in order to verify the prediction of CS of concrete. The CS was evaluated from the metrics R², MAE, MSE, and RMSE. After executing the proposed approach, the best results for data tested were presented.

It was found that the models found for each method achieve a good approximation of the real values ranging from 85% to 98% of accuracy and MAE values (mean absolute error) ranging from 0.005 to 1.708. The values found by the metrics are consistent with the results of other works found in the literature that aim to obtain predictions of concrete properties, showing that the proposal, despite being applied in a different database, managed to obtain satisfactory results in the prediction of CS. Finally, it is important to reinforce that the present study brings important scientific contributions to the application of computational techniques in the study of concretes, making it possible to minimize the costs and time spent in a complex experimental study, in which it is necessary to carry out an extensive work of production and characterization of the materials.

Data Availability

The data used to support the findings of this study are included within the article.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

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