Prediction of the Frost Resistance of Iron Ore Tailings Concrete Based-BP Neural Network

Fu, Chun; Li, Xiaohong; Han, Jie; Li, Haijun; Wu, Haotian; Liu, Songyang

doi:https://doi.org/10.1155/2023/5525182

Journal of Sensors

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

Research Article | Open Access

Volume 2023 | Article ID 5525182 | https://doi.org/10.1155/2023/5525182

Prediction of the Frost Resistance of Iron Ore Tailings Concrete Based-BP Neural Network

Chun Fu,^1,2Xiaohong Li,^1,2Jie Han ,^1,2Haijun Li,^1,2Haotian Wu,^1,3and Songyang Liu^1,2

Academic Editor: Yunchao Tang

Received23 Mar 2023

Revised23 Jul 2023

Accepted02 Aug 2023

Published12 Oct 2023

Abstract

In order to predict the relative dynamic elastic modulus (RDEM), which is used to reflect the frost resistance of iron ore tailings concrete, the backpropagation neural network (BPNN) was used in this study. Here, one hidden layer was chosen in the structure of BPNN. It is well known that the number of neurons in the hidden layer is the key of BPNN; hence, checking the features of overfitting was chosen in this paper to determine the number of neurons in the hidden layer. According to the actual conditions of freeze–thaw cycle test, a BPNN model of 2D input vector and 1D output vector was established. Thirty datasets from the test were used for training and test the proposed ANN. The results showed that the predicted values were in good agreement with the measured ones, and the correlation coefficient between them reached 0.9505. It showed that the BPNN, with the ability to solve nonlinear problems, had great advantages in predicting RDEM, and it can be used as reliable and simple forecasting tools for the prediction of frost resistance of iron ore tailings concrete.

1. Introduction

With the rapid development of the global economy, the amount of construction projects in the world continues to increase, and the amount of concrete rises sharply, coupled with the overexploitation of river sand, resulting in concrete aggregates becoming a globally scarce resource [1]. At the same time of the rapid development of contemporary industry, tailings, as the waste of industrial production, not only occupy a large amount of land but also cause great harm and burden to the surrounding ecological environment. Therefore, it is necessary to comprehensively recover and utilize the tailings resources and incorporate them into the production of concrete as aggregates, which can not only alleviate the current situation of the shortage of concrete aggregates but also have positive significance for the protection of the environment. Iron tailings concrete has become a hot research issue [2–4].

In order to promote the application of iron tailings concrete in a seasonal area, as an important evaluation index of the durability of concrete under freeze–thaw cycles, the dynamic elastic modulus is of great significance to evaluate and predict it [5]. Previous experience tells us the prediction of the freezing resistance of ordinary concrete can save a lot of experimental costs. Therefore, many scholars have conducted a lot of research on the prediction of freezing resistance of concrete and achieved a lot of corresponding results, such as the theoretical model based on classical theory and the empirical model supported by test data. The establishment of a theoretical model requires the theoretical knowledge of materials science, mechanics, chemistry, and other disciplines, as well as the combination of submicro and macro perspectives to study. The difficulty of establishing a theoretical model can be imagined [6, 7]. On the other hand, most of the empirical models take freeze–thaw mechanism as the macroscopic guidance, considered the main factors affecting the frost resistance of concrete and conduct regression analysis based on the test data to establish the empirical model, but the practicability of the model remains to be discussed [8].

In recent years, many scholars have studied the mechanical properties of concrete prepared by iron tailing sand, and there are many reports on the preparation of high-performance concrete by iron tailing powder [9–11]. However, there are few studies on freeze–thaw properties of iron tailings concrete and few reports on the prediction of freeze–thaw resistance of iron tailings concrete [12–15]. Obviously, the frost resistance of concrete is a complicated and controversial problem that is affected by many factors and involves many uncertain factors. Compared with ordinary concrete, various properties of the concrete have changed to varying degrees due to the incorporation of iron tail ore into the concrete, which makes the problem of frost resistance and durability more complex and makes it more difficult to establish a theoretical model [16–20]. Therefore, it is necessary to find new forecasting methods.

In recent years, with the rapid development of artificial neural network (ANN), its application scope is gradually expanding, and its characteristics such as information distribution, fault tolerance, and self-adaptability have attracted more and more attention [21, 22]. Because of its powerful nonlinear mapping ability and adaptive learning and memory, ANN model is very suitable for solving a series of durability problems such as carbonation resistance, chemical erosion resistance, and frost resistance prediction of concrete. Machine learning has been widely used in classification and prediction by scholars because it can dig out intrinsic relationships from large amounts of historical data for classification or prediction. Such as, deep learning [23, 24], random forest (RF) [25], support vector machine (SVM) [26] and backpropagation neural network (BPNN) [27, 28], and so on, have been gradually applied to prediction in various engineering fields because of its good accuracy. A comparative study was made by Liu et al. [29] on the prediction of frost resistance of recycled concrete by using three methods, including ANN, Gaussian process regression, and multivariate adaptive regression spline; the results showed that, among the three methods, the prediction accuracy of ANN model is the best. Wu et al. [30] proposed a hybrid prediction approach based on the RF algorithm and recursive feature elimination to predict the frost resistance of concrete; the results showed that the frost resistance of concrete can be accurately predicted by the RF model. Deng et al. [31] Proposed a compressive strength prediction model of recycled concrete based on deep learning; the results showed that the proposed prediction model can get higher precision and higher efficiency than traditional ANN. In order to predict and analyze the compressive strength of recycled aggregate thermal insulation concrete, a GA-BP optimization network was proposed by Tu et al. [32]. Zhang et al. [21] established an ANN model based on BPNN to predict yield performance and failure mode of reinforced concrete columns; the results indicated that, compared with traditional methods, BPNN had better prediction accuracy and had a good agreement with the experimental results. Peng and Unluer [33] used three machine learning algorithms (BPNN, SVM, and extreme learning machine) to predict the feasibility of 28 day strength of geopolymer concrete through mix ratio and precuring conditions and compared their differences. The results show that the number of cases with error rates of BPNN model within ±20% is the largest. Tang et al. [34] carried out a low cyclic loading test on 23 recycled aggregate concrete-filled steel tube columns and three ordinary concrete-filled steel tube columns and used artificial intelligence technology (RF with hyperparameters tuned by firefly algorithm) to estimate the influence of parameter changes (such as slenderness ratio, axial compression ratio, etc.) on the seismic performance of concrete columns, and obtained satisfactory prediction results. In order to quantify the axial properties of fiber reinforced polymer (FRP)-confined recycled aggregate concrete columns, Zhao et al. [35] introduced a synthetic data generator, the tabular generative adversarial network, to supplement the limited training data. Experimental results show that the model outperforms existing empirical equations and several baseline machine learning models. Zhang et al. [36] established three prediction methods for shear strength and failure mode of beam-column nodes based on BPNN, radial basis function neural network (RBFNN), and generalized regression neural network (GRNN). The experimental prediction results show that the BPNN, RBFNN, and GRNN models can be used as suitable tools to estimate the shear strength and failure modes of beam–column joints during structural predesign. Jiang et al. [37] proposed a data-driven neural network prediction model based on the ultimate working conditions and stress–strain constitutive relationships of FRP-constrained concrete. Experimental prediction results show that the developed data-driven neural network prediction model can provide rapid prediction and design for FRP-constrained composites. Moreover, some researchers [38–40] also used machine learning methods to predict the strength and self-healing behavior of concrete and have obtained good prediction results.

Therefore, in this paper, BPNN is applied to the freeze–thaw related change law of concrete in this study, which is mainly used to predict the relative dynamic elastic modulus f(RDEM) of freeze–thaw iron tailings concrete based on sample data, which provides a basis for the design of iron tailings concrete With good frost-resistance. The rest of this article is organized as follows: Section 2 describes the sample data set or prediction. Section 3 introduces the basic principle of BPNN model. In Section 4, the results predicted by BPNN are introduced and analyzed, and the last part is the conclusion.

2. Mix Proportion and RDEM

2.1. Mix Proportion

According to Han et al. [16], iron ore tailings from Dandong Iron Mine in Liaoning of China are used instead of natural sand, and ordinary Portland cement P.O32.5 produced by Fushun Cement Co., Ltd. of China is used. The C30 concrete used in freeze–thaw cycle test was prepared by replacing natural sand with iron ore tailings sand with 0%, 20%, 40%, 60%, and 80%, respectively. Five different mix ratios were used in the experiment, as shown in Table 1. The details are shown in Table 1.

2.2. RDEM [16]

According to Han et al. [16], the dynamic elastic modulus of iron ore tailings concrete after freeze–thaw was calculated by Equation (1), and the RDEM can be calculated by Equation (2).where means dynamic elastic modulus of concrete (MPa), α means the width of the specimen (a = 100 mm), means the length of the specimen (L = 400 mm), means the mass of specimen (the actual measured mass), f_n means the measured transverse fundamental frequency (Hz), is the correction coefficient (K = 1.4).where P_n means the RDEM after n freezing–thawing cycles, n is the number of freezing–thawing, .

3. BP Neural Network

3.1. Theory

ANN is composed of a large number of simple neurons connected to each other and has the ability to self-learning and self-adaptation. ANN can analyze and grasp the potential rules between the input and output data provided in advance and finally use the new input data to calculate the output result according to these rules.

Among many types of neural networks, BP neural network [27, 28], as a typical representative of multilayer feedforward network, is the most widely used. The BP neural network trains the network according to the error backpropagation algorithm. The whole processing process consists of two parts, one is the forward propagation of information, and the other is the backpropagation of error. BP neural network includes input layer, intermediate layer (hidden layer), and output layer, as shown in Figure 1. The function of the input layer is to receive information from the outside world and pass it to the intermediate layer. The role of the intermediate layer is to transform the information. The intermediate layer can be a single hidden layer or multiple hidden layers, depending on the need. When the information transmitted from the last hidden layer to the output layer is processed, a positive learning propagation and processing is completed, and the processing results are transmitted to the outside world by the output layer. When the output value is inconsistent with the expected value, the network begins to enter the error backpropagation stage. The error corrects the weight and threshold of each layer by the way of error gradient descent through the output layer and then reverses layer by layer to the hidden layer and the input layer. This is the whole process of BP neural network learning and training. When the network output error is reduced to an acceptable value or the learning times reach the preset upper limit, the network will stop training.

It can be seen from Figure 1 that the essence of BPNN is a nonlinear mapping relationship between each layer of a network, (X₁, X₂, …, X_n) and (Y₁, Y₂, …, Y_m) are the input values, and the predicted values of the BPNN, respectively, where, W_ij and W_jk represent connection weights. Assuming that l is the number of nodes in the hidden layer, the initial threshold of the hidden layer and output layer are a and b, respectively. The output of the hidden layer is H,

The predicted output of the BPNN is O,

The network prediction error is

Then, updating the weights and thresholds of the network as follows, η is learning rate,

3.2. BP Network Modeling

3.2.1. Network Input, Output, and Samples

In this study, the replacement rate of iron tailing sand and the number of freeze–thaw cycles are taken as the input values of BP neural network, and the RDEM is taken as the output values of the network. The samples are selected from the study of Han et al. [16], as shown in Table 2.

3.2.2. Network Structure and Parameters

In this paper, a three-layer BPNN structure was established, in which there were two nodes in the input layer, including iron ore tailing sand replace rate and the number of freeze–thaw cycles; at the meantime, there was a node in output layer, that is the RDEM. MATLAB neural network toolbox was used to calculate BPNN in this study; all its operations were in matrix form, so that its training was simple and fast (as shown in Figure 2).

It is well known that the number of hidden layer nodes affects the accuracy of the network model. For a long time, the selection of nodes in the hidden layer of neural networks has attracted much attention [21, 32]. A large number of experiments showed that it is difficult to get good prediction results when the number of hidden layer nodes is too large or too small. If the number of hidden layer nodes is too small, it is difficult for the network to acquire the necessary learning ability and information processing ability. Whereas, if the number of nodes in the hidden layer is too large, the complexity of the network structure will be increased, which will lead to the local minimum in the learning process of the network and sacrifice the learning speed of the network. Therefore, trying to determine the number of hidden layer nodes according to the task is very difficult. This was because of the complexity of network mapping and many uncertainties in completing the training process. So in this paper, through repeated training and comparison, the final number of hidden layer nodes of the network was determined as 18 according to the minimum values of mean square error (MSE), which avoided overfitting. The “satlins” function was used as the activation function, the “purelin” function was used as the activation function in the output layer, and the “traingdx” algorithm was used for training. The model parameters of BPNN are summarized in Table 3.

4. The Results and Discussion

According to Han et al. [16], as the number of freeze–thaw cycles increased, the corresponding freeze–thaw performance parameters, such as the mass loss rate and the RDEM loss rate also changed, which indicated that the internal structure was gradually damaging and deteriorating. Since the mass loss rate cannot be measured reasonably in practical engineering, it is difficult to ensure the accuracy, while the RDEM can be measured exactly, so as to evaluate the deterioration degree of the concrete structure after freeze–thaw cycle. RDEM of iron ore tailings concrete is mainly related to two main factors, namely the replacement rate of natural sand and the number of freeze–thaw cycles. Therefore, this study took the RDEM of concrete as the training object, listed data can be found in Table 4; it is also can be found in the study of Han et al. [16], and collected a total of 30 sets of test data, which are divided into two groups, i.e., the asterisks are for testing data, and the rest are for training data.

In order to unify the units of different inputs, the data shown in Table 2 should be normalized first so that each input variable was within the range of [0,1]. The normalization formula is shown in Equation (10):where x_min is the minimum value of the data, x_max is the maximum value of the data, x_n is the normalized results of the data. x is the value before data normalization.

The best validation performance and training status tracking of BPNN are shown in Figures 3 and 4, respectively; Table 4 shows the connection weights of each layer, and the threshold of each neuron of the BP NN model used in this paper is obtained. It can be seen that, from Figures 3 and 4, the training of BPNN reached very high accuracy in step 228.

It can be seen from Figure 3, in the BPNN validation steps for predicting RDEM, the minimum MSE value appeared at the 228th training iteration; after that, the network training continued until the network error converged in the testing process; at this point, the network training terminated. As can be seen from Figure 4, the BPNN finished the network training after the 228th training iteration, which essentially avoided the problem of overfitting.

Figure 5 shows the relationship between the measured value of RDEM and the simulated output value of network training and testing. It can be seen from Figure 5 that there was basically a 1 : 1 linear relationship between the simulated and measured values of the designed BP neural network for training and testing; the correlation coefficients reached 0.99859 and 0.9505, respectively. It indicated that the designed BPNN had good performance after training. From Figure 6, it can be seen that the proposed BPNN model had good accuracy.

(a)

(b)

(a)

(b)

Then, the trained BPNN was used to predict RDEM, and the results are shown in Table 2. It can be seen from Table 2 that the prediction results of BPNN were in good agreement with the test data, and the prediction accuracy was high. It showed that the BPNN, with the ability to solve nonlinear problems, had great advantages in predicting RDEM.

As shown in Equations (11)–(14), mean absolute error (MAE), MSE, root mean square error (RMSE), and correlation coefficient (R²) are usually used to evaluate the prediction performances of BPNN. MAE and MSE are the average of the absolute error and the average of the square of the absolute error, respectively. Which is between the target and the predicted values. RMSE is the sample standard deviation of the difference between the predicted and observed values (called the residual). RMSE is used to illustrate the degree of dispersion of the sample. The smaller MAE, MSE, and RMSE are, the larger R² is, which indicates that the prediction effect of BPNN is better.where E_i represents the ith experimental value, represents the average of the experimental values, P_i represents the ith predicted value, represents the average of the predicted values.

MAE, MSE, RMSE, and R² values of RDEM are shown in Table 5. It can be seen that the error MAE, MSE, and RMSE between the predicted and the measured values was very small, and R² was 0.9505; as previously mentioned, the smaller MAE, MSE, and RMSE are, the larger R² is, which indicates that the prediction effect of BPNN is better, namely, BPNN had very high accuracy in predicting the RDEM of iron ore tailings concrete.

5. Conclusion

Iron ore tailings concrete is the same as normal concrete; the influencing factors of RDEM after freeze–thaw are complex and changeable. Therefore, the dispersion degree of sample data obtained by experiment or engineering observation is large, which leads to unsatisfactory prediction accuracy in statistical analysis. Therefore, there are few research reports on the prediction of frost resistance of iron ore tailings concrete. In this study, an ANN prediction model for RDEM of iron ore tailings concrete was established, and the relevant conclusions were as follows:(1)The RDEM of iron ore tailings concrete with different iron ore tailings sand replacement rates under different freeze–thaw cycles is predicted, so as to reflect the frost resistance of the same source of iron ore tailings concrete.(2)A BPNN model with the replace rate of iron ore tailing sand and the number of freeze–thaw cycles as in input factors was established in this paper, the prediction results of BPNN showed that the proposed BPNN had high accuracy, and the nonlinear mapping relationship between the two input parameters and RDEM was well-reflected.(3)Compared with the traditional method, BPNN can effectively avoid the errors caused by human factors, and the accurate prediction results showed that BPNN provided a new method to predict the RDEM of iron ore tailings concrete after freeze–thaw.(4)In the case of a small number of samples, the proposed BPNN in this paper still got satisfactory prediction results; the correlation coefficient between testing data and prediction results was 0.9505. It should be noted that a complete and higher quality database is needed in order to build a more accurate forecasting model. In the following research, the main work is to extend the database, and more factors related to concrete freeze–thaw durability were introduced to further improve the generalization ability of the model.

It should be pointed out that BP neural network can learn more fully in the case of large samples, thus showing better performance. Therefore, based on the results of this study, it can be seen that if more data of iron tailings concrete can be collected and then network model can be established, better prediction results can be obtained. Moreover, the determination of the number of hidden layer neurons is still an urgent problem to be solved, and the number of hidden layer neurons directly affects the accuracy of BPNN prediction results, so it will be a key issue in future research. In conclusion, BPNN provides a reliable method for predicting the frost resistance of iron tailings concrete.

Data Availability

Data supporting this research article are available from the corresponding author on reasonable request.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Acknowledgments

We are thankful to Liaoning Key Lab of Petro-chemical Special Building Materials, and this research was supported by the General Project of Education Department of Liaoning Province: Study on freeze–thaw cycle failure mechanism and strengthening mechanism of iron tailing concrete in Fushun area (L2019030) and Basic Scientific Research Project of Education Department of Liaoning Province (LJKMZ20220750).

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