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Concrete workability, quantified by concrete slump, is an important property of a concrete mixture. Concrete slump is generally known to affect the consistency, flowability, pumpability, compactibility, and harshness of a concrete mix. Hence, an accurate prediction of this property is a practical need of construction engineers. This research proposes a machine learning model for predicting concrete slump based on the Least Squares Support Vector Regression (LS-SVR). LS-SVR is employed to model the nonlinear mapping between the mix components and slump values. Since the learning process of the LS-SVR necessitates two hyperparameters, the regularization and the kernel parameters, the grid search method is employed search for the most desirable set of hyperparameters. Furthermore, to construct the hybrid model, this research collected a dataset including actual concrete slump tests from a hydroelectric dam construction project in Vietnam. Experimental results show that the proposed model is capable of predicting concrete slump accurately.

Concrete workability is defined as the effort required to manipulate a freshly mixed quantity of concrete with minimum loss of homogeneity [

The slump test is the most common method for assessing the flow properties of fresh concrete; the slump provides a measure of workability [

Concrete has been increasingly utilized in high-rise building and infrastructure development projects and special ingredients are often employed to make the material satisfy a specific set of performance requirements [

Due to the importance of the research topic, various studies have been dedicated to concrete slump prediction. Traditional statistical models and machine learning are prevailing approaches to tackle the problem at hand. Öztaş et al. [

Baykasoğlu et al. [

Due to the popularity of concrete in the construction industry, better alternatives for concrete slump prediction are of practical need for construction engineers in concrete mix design. This research contributes to the body of knowledge by proposing a new approach for improving the accuracy of concrete slump prediction which is based on the Least Squares Support Vector Regression (LS-SVR). LS-SVR is an advanced machine learning method which is designed for nonlinear modeling [

Furthermore, a dataset that contains slump test records, collected from a hydroelectric dam construction project in central Vietnam, is used to establish and verify the proposed approach. The rest of the article is organized as follows: the second section presents the research method. The proposed slump prediction model is described in the third section. The next section reports the experimental results. The conclusion of this study is stated in the final section.

This research recorded testing results of 95 concrete mixes during the construction progress of the Song Bung 2 hydroelectric dam construction project in central Vietnam (

Concrete slump test (image source:

In this study, the concrete slump conditioning factors are selected based on reviewing previous works [^{3}), natural sand (kg/m^{3}), crushed sand (kg/m^{3}), coarse aggregate (kg/m^{3}), water (liter/m^{3}), and superplasticizer (liter/m^{3}) are mix ingredients. For each mix design, the slump value obtained from the actual slump test experiment is recorded. Statistical descriptions of all specimens are shown in Table

Statistical description.

Factors | Notation | Min | Mean | Std. dev. | Max |
---|---|---|---|---|---|

Cement (kg/m^{3}) | | 201.0 | 338.6 | 62.3 | 446.3 |

Natural sand (kg/m^{3}) | | 384.0 | 690.1 | 154.2 | 827.0 |

Crushed sand (kg/m^{3}) | | 0.0 | 81.6 | 159.0 | 399.0 |

Coarse aggregate (kg/m^{3}) | | 1107.0 | 1155.7 | 33.0 | 1218.0 |

Water (liter/m^{3}) | | 164.0 | 174.2 | 6.4 | 186.0 |

Superplasticizer (liter/m^{3}) | | 1.0 | 3.1 | 0.9 | 4.5 |

Concrete slump (cm) | | 8.0 | 10.2 | 2.9 | 19.0 |

The dataset of concrete slump test.

Mix | | | | | | | |
---|---|---|---|---|---|---|---|

1 | 261.0 | 397.0 | 397.0 | 1200.0 | 176.0 | 1.3 | 8.0 |

2 | 248.0 | 399.0 | 399.0 | 1208.0 | 176.0 | 1.2 | 8.0 |

3 | 320.0 | 388.0 | 388.0 | 1154.0 | 179.0 | 3.2 | 9.0 |

4 | 304.0 | 391.0 | 391.0 | 1162.0 | 179.0 | 3.0 | 9.0 |

5 | 336.0 | 385.0 | 385.0 | 1148.0 | 178.0 | 3.4 | 9.5 |

6 | 356.0 | 769.0 | 0.0 | 1154.0 | 170.0 | 3.2 | 10.0 |

| | | | | | | |

90 | 339.0 | 765.0 | 0.0 | 1154.0 | 177.0 | 3.4 | 8.5 |

91 | 375.0 | 770.0 | 0.0 | 1144.0 | 167.0 | 3.4 | 10.0 |

92 | 393.0 | 757.0 | 0.0 | 1144.0 | 166.0 | 3.5 | 11.0 |

93 | 404.0 | 767.0 | 0.0 | 1124.0 | 166.0 | 4.0 | 9.0 |

94 | 378.0 | 751.0 | 0.0 | 1108.0 | 186.0 | 3.8 | 18.0 |

95 | 359.1 | 765.0 | 0.0 | 1111.0 | 186.0 | 3.6 | 19.0 |

LS-SVR, proposed by Suykens et al. [

To construct the prediction model, it is needed to prepare a dataset of slump test record in the form:

We aim to establish a mapping function

LS-SVR for concrete slump modeling.

In the training phase of LS-SVR, the learning objective can be formulated as the following optimization problem [

In order to solve the above optimization problem, the Lagrangian function is formulated as [

The Karush–Kuhn–Tucker conditions for optimality are used by differentiating the Lagrangian function

By solving linear system (

This section of the article describes the concrete slump prediction using LS-SVR (CSP-LSSVR). The prediction model relies on LS-SVR to discover the nonlinear mapping relationship between the concrete components and the slump. The flowchart of the CSP-LSSVR is demonstrated in Figure

Concrete slump prediction using LS-SVR (CSP-LSSVR).

Given the input data of concrete mix ingredients (the amounts of cement, natural sand, crushed sand, coarse aggregate, water, and superplasticizer), the first step of the model is to carry out the data normalization process within which the whole data is normalized into a (0, 1) range. This process can help prevent the circumstance in which inputs with greater magnitudes dominate those with smaller magnitudes. The function used for normalizing data is provided as follows:

The dataset, featuring six input factors and the output variable of concrete slump, is then randomly divided into a training set and a testing set. The training dataset is employed to establish the LS-SVR model. Since the LS-SVR with radial basis kernel function is employed, the learning process requires hyperparameters, the regularization parameter

In the grid search for tuning parameters, various pairs of (

When the training process finishes, the slump of concrete mix in the testing cases can be predicted by providing mixture components for the trained model. In the experiments, besides the proposed CSP-LSSVR, the Artificial Neural Network (ANN) and the multiple linear regression (MLR) are utilized as benchmark methods. In order to measure model performance, this research employs Root Mean Squared Error (RMSE), Mean Absolute Percentage Error (MAPE), and Coefficient of Determination (

The motivation for using these benchmark approaches is that the ANN is an effective tool for nonlinear modeling and has been successfully employed for predicting concrete slump [

To construct an ANN, the user needs to specify the network structure and the learning rate. Such parameters of the ANN model are usually selected via a trial-and-error process [

In the first experiment, the dataset is randomly divided into 2 sets: the training set that occupies 80% of the dataset and the testing set that includes 20% of the dataset. In detail, the training and testing sets consist of 76 and 19 mixes, respectively. The training and testing results of the CSP-LSSVR are illustrated in Figures

The CSP-LSSVR training results.

The CSP-LSSVR testing results.

The MLR model for predicting concrete slump based on the collected dataset is established via the Least Squares Estimation method [

The ANN model structure, which contains the input, hidden, and output layers, is illustrated in Figure

The ANN model structure.

It is noted that the weight matrices (

Table

Result comparison.

MLR | ANN | CSP-LSSVR | |
---|---|---|---|

| |||

RMSE | 1.23 | 0.94 | 0.46 |

MAPE (%) | 9.62 | 3.63 | 3.07 |

| 0.82 | 0.91 | 0.97 |

| |||

RMSE | 1.54 | 1.05 | 0.54 |

MAPE (%) | 12.08 | 5.96 | 3.68 |

| 0.28 | 0.83 | 0.96 |

The ANN and CSP-LSSVR models achieve much better performances; both models have the

Moreover, to avoid the randomness in selecting testing samples, the second experiment carries out a 10-fold cross-validation process. Using the cross-validation process, the whole dataset is randomly divided into 10 data folds in which each fold in turn serves as a testing set; and the performance of the model can be assessed by averaging results of the 10 folds. Because all of the subsamples are mutually exclusive, this experiment can evaluate the CSP-LSSVR more accurately.

Table

The result of the 10-fold cross-validation process.

Data fold | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | Avg. | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

CSP-LSSVR | | |||||||||||

RMSE | 0.46 | 0.32 | 0.24 | 0.30 | 0.25 | 0.29 | 0.29 | 0.26 | 0.69 | 0.29 | | |

MAPE | 3.15 | 1.37 | 0.65 | 1.13 | 0.68 | 0.90 | 0.88 | 0.96 | 5.21 | 0.92 | | |

| 0.97 | 0.99 | 0.99 | 0.99 | 0.99 | 0.99 | 0.99 | 0.99 | 0.94 | 0.99 | | |

| ||||||||||||

RMSE | 0.68 | 0.33 | 0.64 | 0.46 | 0.58 | 0.39 | 0.38 | 0.67 | 0.49 | 0.37 | | |

MAPE | 4.50 | 2.29 | 2.22 | 2.60 | 2.69 | 1.70 | 2.16 | 3.51 | 3.92 | 2.52 | | |

| 0.99 | 0.83 | 1.00 | 0.58 | 0.98 | 0.99 | 0.99 | 0.97 | 0.97 | 0.72 | | |

| ||||||||||||

ANN | | |||||||||||

RMSE | 0.56 | 0.47 | 0.48 | 0.74 | 0.57 | 0.61 | 0.36 | 0.50 | 0.44 | 0.46 | | |

MAPE | 4.27 | 3.13 | 3.45 | 3.00 | 3.78 | 4.25 | 1.56 | 3.43 | 2.56 | 2.36 | | |

| 0.96 | 0.97 | 0.96 | 0.94 | 0.96 | 0.96 | 0.98 | 0.97 | 0.98 | 0.97 | | |

| ||||||||||||

RMSE | 0.62 | 0.53 | 0.71 | 1.10 | 0.51 | 0.58 | 0.40 | 0.83 | 0.31 | 0.63 | | |

MAPE | 4.97 | 5.21 | 4.33 | 6.30 | 3.58 | 4.11 | 2.38 | 6.68 | 1.65 | 5.17 | | |

| 0.98 | 0.60 | 0.99 | 0.09 | 0.97 | 0.98 | 0.98 | 0.91 | 0.99 | 0.29 | | |

| ||||||||||||

MLR | | |||||||||||

RMSE | 1.23 | 1.25 | 1.19 | 1.20 | 1.27 | 1.21 | 1.25 | 1.27 | 1.29 | 1.23 | | |

MAPE | 9.26 | 9.56 | 9.07 | 9.29 | 9.73 | 9.16 | 9.80 | 9.85 | 10.12 | 9.62 | | |

| 0.79 | 0.81 | 0.75 | 0.83 | 0.80 | 0.79 | 0.79 | 0.79 | 0.79 | 0.82 | | |

| ||||||||||||

RMSE | 1.56 | 1.28 | 1.78 | 1.67 | 1.09 | 1.58 | 1.28 | 1.04 | 0.78 | 1.54 | | |

MAPE | 11.56 | 11.10 | 11.59 | 11.93 | 9.44 | 14.40 | 10.53 | 8.10 | 5.67 | 12.08 | | |

| 0.90 | 0.01 | 0.91 | 0.01 | 0.80 | 0.82 | 0.79 | 0.85 | 0.90 | 0.28 | |

Note: Avg. denotes the average result.

This study has established a new method for predicting concrete workability quantified by the slump values. The research extends the body of knowledge by investigating the capability of LS-SVR for concrete slump prediction. To establish the proposed CSP-LSSVR, a dataset consisting of actual concrete slump tests has been collected. From the experiments, the proposed model has achieved the most accurate prediction results.

The average MAPE of the method obtained from the cross-validation process is less than 3% which is very desirable because modeling concrete slump is known to be very complex and highly nonlinear. Since the tenfold cross-validation process is a very reliable way for model performance evaluation [

Nevertheless, in addition to the currently used six conditioning factors of concrete slump, other factors (e.g., the type, size, absorption, and the water amount of the fine and coarse aggregates) can be relevant and should be considered by the model. Furthermore, another limitation of the current study is that the employed dataset only consists of 95 data points. Thus, this dataset should be expanded in a future study to further enhance the generalization of the current model and better ensure the predictive accuracy of the model when dealing with new concrete mixes.

The authors declare that there is no conflict of interests regarding the publication of this manuscript.