Prediction of Compressive Strength of Concrete in Wet-Dry Environment by BP Artificial Neural Networks

Engineering structure degradation in the marine environment, especially the tidal zone and splash zone, is serious. +e compressive strength of concrete exposed to the wet-dry cycle is investigated in this study. Several significant influencing factors of compressive strength of concrete in the wet-dry environment are selected.+en, the database of compressive strength influencing factors is established from vast literature after a statistical analysis of those data. Backpropagation artificial neural networks (BPANNs) are applied to establish a multifactorial model to predict the compressive strength of concrete in the wet-dry exposure environment. Furthermore, experiments are done to verify the generalization of the BP-ANNmodel. +is model turns out to give a high accuracy and statistical analysis to confirm some rules in marine concrete mix and exposure. In general, this model is practical to predict the concrete mechanical performance.


Introduction
Marine environment tends to have a negative effect on concrete structures' performance, which has been investigated in many researches.Compressive strength is used to describe the mechanical performance of concrete.In the marine environment, especially tidal and splash zones, concrete structure degradation is quite serious and the compressive strength of that is descending with exposure age.It is investigated in either laboratory or actual marine condition that compressive strength degrades with time.
In the early 1980s, British academic Mangat and Gurusamy [1] did a research on mechanical properties of steel fiberreinforced concrete exposed to the marine splash zone and tidal zone in the Aberdeen beach, and the exposure age is up to three years (2000 wet-dry cycles).Results indicated that melt extract fibers are suitable for marine applications.In addition, another actual marine exposure experiment was done by Kuhail and Shihada [2] in the Gaza beach for a period of seven months.And it was found that the compressive strength of concrete shows a trend of rising early but declining later.Toutanji et al. [3] focused on studying the effect of different supplementary cementitious materials on strength and durability of concrete.ey found that proper mineral additives could improve the performance of concrete in the marine environment.Aye and Oguchi [4] investigated the effect of physical sulfate attack on the performance of plain and blended cement mortars.Specimens were exposed to 10% Na 2 SO 4 and MgSO 4 solutions for 24 months.MgSO 4 was found to be more damaging than Na 2 SO 4 considering chemical attack.However, Na 2 SO 4 was more harmful than MgSO 4 as far as the physical attack was considered.Jiang and Niu [5] also did a research on the effect of different types of sulfate solutions on concrete performance under wet-dry cycles.Results show that the deterioration degree of concrete in magnesium sulfate solution is more severe than that in the other sulfate solutions.Chloride ions in the composite solution help decrease the deterioration rate of concrete effectively.Chen [6] established a constitutive model for concrete in wet-dry cyclic sulfate attack.
In this research, compressive strength of concrete served in the marine tidal zone and splash zone or exposed to the wet-dry cycle environment was focused on.Database is established from existing researches.An artificial neural network (ANN) is applied in this study.e ANN has been widely adopted in construction material property prediction by many researches [8,9].For example, Tavakoli et al. [10] have predicted the energy absorption capability of fiberreinforced self-compacting concrete which contains nanosilica particles via an MLP-(multilayer perceptron-) type artificial neural network.Tavakoli et al. [11] simultaneously researched the mechanical properties of self-compacting concrete with nanosilica particles and various fibers via the MLP artificial neural network.In addition to that, many scholars utilized the ANN for concrete compressive strength prediction.Ni and Wang [12] utilized multilayer feed-forward neural networks (MFNNs) to predict the 28-day compressive strength of concrete, and the results conformed to some rules on mix of concrete.Lee [13] has developed the I-PreConS (Intelligent PREdiction system of CONcrete Strength) that provides in-place strength information of the concrete to facilitate concrete form removal and scheduling for construction based on the ANN.Alshihri et al. [14] have done a comparison on feed-forward backpropagation (BP) and cascade correlation (CC); CC is slightly better than BP, while both of them have good performance on light-concrete strength prediction.Öztas ¸et al. [15] have done a research on predicting compressive strength and slump of highstrength concrete.And the 187 sets of data used to establish a model come from literature.Except for that, Gaussian process regression (GPR) was applied by Hoang et al. [16], and it can well estimate the HPC strength.Nevertheless, those researches are mostly based on experimental data.Besides, these literature researches usually do not have a large database.
e backpropagation (BP) artificial neural network is selected in this research, for it has a mature application in various fields.e BP-ANN model is firstly put forward by Rumelhart and McClelland in 1986 [17].Based on the gradient descent algorithm, the BP neural network is an error backpropagation multiple-layer feed-forward network, focused on calculating the minimum of the mean square error of actual outputs of the network and the target outputs.Compared with the former multilayer perceptron, the BP neural model is capable of dealing with a complex nonlinear problem.Besides, compared with multilayer feed-forward neural networks (MFNNs) [18], it is equipped with a better ability of classifying random complex models [19].Moreover, good multidimensional function nonlinear versatile mapping capability and the flexible multilayer network structure are other two advantages of the BP neural model.After model development, experiments were done to validate the generalization of the prediction model.

Data Collection and Analysis
In order to establish a prediction model that can be widely used, the data were excerpted from large numbers of experiments carried out by researchers.2167 sets of data were collected in all, which cover over 80 articles from China, United States, Europe, and other regions, and they are presented in Table 1 in detail.

Database Establishment.
In this research, compressive strength of concrete in the wet-dry cycle exposure environment, as the target of prediction, is related to many factors, including material factors and environmental factors.Material factors include w/c, specimen sizes, initial strength, and fly ash dosage and slag dosage.Specific surface area is chosen to describe the specimen sizes.Environmental factors are various ion concentrations, including sodium, magnesium, chloride, and sulfate ions, exposure condition, and exposure age.Exposure condition contains five variables, including the wetting time, drying time, wetting temperature, drying temperature, and cycle period.
e detailed data of the factors mentioned above are excerpted from previous researches and are functioned as the database of the artificial neural network model.

Statistical Analysis.
Before establishing the model, a statistical analysis has been done on descriptive statistics of the database [7].Statistical analysis is a multiplex method that can be used to describe the regularity and distribution of the sample database, and the fluctuation of database can be seen according to some statistics such as variance, standard deviation, skewness, and kurtosis [20].Table 2 demonstrates some statistics of 1078 sets of data of factors influencing the compressive strength of concrete in the wet-dry environment.And those data were selected randomly from 2169 sets of data.
Table 2 mainly demonstrates six statistics of influencing factors.ey are, respectively, standard deviation, variance, skewness, kurtosis, minimum, and maximum.Standard deviation is used to reflect the fluctuation of a series of data, and the instability of a statistic is measured by its variance [21].In environmental factors, data of four types of solution ion concentrations share the similar discrete degree, so do the dosage of fly ash and slag in material factors.And compared to other factors, especially exposure age, variance and standard deviation of those six factors' data are much lower because almost the choice of ion concentration refers to seawater ion concentrations and the dosage of fly ash and slag is mainly concentrated at 0.3, which is considered as the optimum content.Nevertheless, the exposure age ranges from 2 days to several years, contributing to the high variance and standard deviation of exposure age.On top of this, the degree of dispersion and variation of initial strength is close to that of final strength.
Skewness and kurtosis are used to characterize the distribution of data [22,23].Normal distribution is the most common distribution.Skewness refers to the frequency distribution of asymmetric degree of skew direction.Deviation between normal distributions is often reflected by the coefficient of skewness.When the coefficient of skewness is higher than 0, the oblique direction of the distribution is right (positive); on the contrary, the oblique distribution is left (negative).Right oblique direction distribution has a thin and long tail on the left, which means that the data mainly focused on the small gures range.And taking a general observation of the data distribution of the factors, all of them are right oblique direction distributed.e coe cient of kurtosis indicates the shape of data distribution.It can be divided into spire distribution, standard distribution, and at distribution.When the coe cient of kurtosis is higher than 3, it belongs to spire distribution; conversely, it belongs to at distribution.roughout the statistics given above, it can be concluded that except for exposure age, the other factors' data are within normal limit.
e coe cient of skewness of variables is all above 0, and it means that all the variables' distribution directions show a positive oblique trend.Nevertheless, according to the results of coe cient of kurtosis, the four variables, respectively, y ash dosage, slag dosage, sodium ions, and sulfate ions, show the spire distribution and the ve variables, respectively, speci c surface area, initial strength, magnesium ions, chloride ions, and nal strength, show the at distribution.And due to the particularity of the distribution of exposure age, it belongs to neither spire nor at distribution.And initial strength shares a similar distribution with the nal strength.Figures 1 and 2 describe the distribution of initial strength and nal strength.Both of them are close to normal distribution.
In Table 3, the strength range is divided into 7 intervals and the distribution of values of initial strength and nal strength is demonstrated.It can be clearly seen that the samples whose values of initial strength are between 25 and 50 MPa account for the largest proportion.So are the nal strength of samples.Moreover, there is a decrease in the numbers of nal strength samples of high-strength concrete compared with that of initial strength samples of highstrength concrete.

Correlation Analysis.
On the basis of statistical analysis, correlation between nal strength and various in uencing factors is made in this research.e Pearson correlation coe cient, Kendall coe cient, and Spearman coe cient are commonly used.Nevertheless, the Pearson correlation coe cient is used in linear relationships [24].
e Kendall coe cient and Spearman coe cient belong to nonparametric statistics [25].In this study, Kendall and Spearman coe cients are used for a correlation analysis.e analysis results are demonstrated in Table 4.
e correlation coe cients calculated above are based on two di erent formulas, both of which can be adopted more widely in nonlinear relationships.e results are in absolute value.From the analysis results, it can be clearly seen that w/c and initial strength have a signi cant e ect on the nal strength.However, y ash dosage is more e ective than slag dosage.It is quite a complex relationship between mineral admixtures and compressive strength in the marine environment, and mineral admixtures are considered to have a positive in uence on concrete properties.e difference between those two correlations is attributed to the fact that data collected focused more on y ash dosage.Besides, seawater also plays a signi cant role in the evolution  Advances in Materials Science and Engineering of compressive strength.Nevertheless, the correlation coe cients calculated seem hard to re ect that.Taking an observation of data collected, ion data are based on marine hydrographic data and almost have no change.Hence, correlation coe cient calculation formulas are built on datachanging trends [26].Consequently, ion concentration seems to have a subtle e ect.
In general, the correlation analysis results can be used as a simple reference for construction of arti cial neural networks.

Construction of Artificial Neural Networks
Arti cial neural network (ANN) model is a prediction model that has been widely applied in many elds.Similar to human brains, which respond to external stimulus through connections and exchanging information among ten billions neurons, the arti cial neural network model is able to deal with the message inputted and realize result prediction [27].One important training rule of the ANN is the delta rule, which is based on the idea of gradient descent.e delta rule is applied to determine the fraction of di erence between the target and output [28].
e backpropagation (BP) neural network model is adopted in compressive strength in the research.
e BP algorithm underpins the delta rule to neural nets with hidden nodes.e whole operation is demonstrated in Figure 3.
e operation can be divided into six steps [29]. is is a quite complex process that detailed the calculated algorithm is invisible; Step 3: output nodes calculate outputs.Step 4: compare the outputs with targets and gure out the di erence; Step 5: adjust the model parameters on the basis of the training rule using the results of Step 4

Input layer
Hidden layer For example, Chen et al. [30] used 86% dataset for training and 14% dataset for testing to establish an ANN model to predict the strength of concrete.Hence, the conventional and widely recognized division ratio is 50% training set, 25% validation set, and 25% testing set [31].Prechelt has done a research on some benchmark rules and problems of the neural network model establishment and come up with a basic pattern classi cation.e division ruler is following the convention in the literature of using half of the images for training and half for testing.And he proved that this pattern classi cation method can well avoid the over tting of the model [32].Hence, in this research, 50% of the data are used as the training set, 25% are used as the testing set, and the rest 25% are used as the validation set to predict the compressive strength of concrete that is exposed to the wetdry environment.

Model Establishment.
e training and testing program is written and put into MATLAB.
e inner network structure is discussed.Ash used the DNC method to select the proper node parameters [33].DNC means dynamic node creation.DNC sequentially adds nodes one at a time to the hidden layer(s) of the network until the desired approximation accuracy is achieved.ere are six networks and they are discussed in Figure 4. Detailed structure information is given below, and Figure 4 presents the training results.Advances in Materials Science and Engineering improve or remains the same for max_fail epochs in a row.Test vectors are used as a further check that the network is generalizing well but does not have any e ect on training.

Prediction Results.
After the establishment of this prediction model, the prediction results are demonstrated in Figure 6.
In the training set, the correlation coe cient R is 0.9684 (Figure 6), and the training model is quite appropriate.en, the validation set is used to optimize the training set until it reaches the setting error value.And the nal correlation coe cient of the validation set is 0.92702.After the prediction model establishment, testing set data is to test the performance of the neural network model.e correlation coe cient of that is 0.94778.e general prediction is listed in Figure 7 (R 0.962).And this neural network model achieves a good prediction of 2169 sets of data.
In addition, the three error indexes, RMSE, MAPE, and MSE, of this model, respectively, are calculated in Table 5.
e MAE of training data, validation data, and testing data was all less than 4.05 MPa, the MAPE of training data, validation data, and testing data was all less than 5.5%, and

Comparison with the Linear Regression Model.
Relationship between multiple input variables (explanatory variables) and one output variable (a response variable) also can be expressed by the linear regression model [34][35][36].Linear regression model is a statistical model determined as follows: where Y is the output value and responds to compressive strength of concrete in this research; X i represents different influencing factors, such as w/c and initial strength; α i are the weighing coefficients of different influencing factors; and β is the error-modifying coefficient.Enter, stepwise, forward, and backward are four regression methods for ordinary least squares estimation.A linear model of compressive strength responding to various influencing factors is established through SPSS 22.0.
A stepwise method is chosen, and the fitting curve of outputs and targets of the linear model is shown in Figure 8.
e fitting result is obviously worse than that of the BP neural networks.And the MAE, RMSE, and MAPE are calculated in Table 6.From the comparison with the prediction results of the BP neural model, it is concluded that the BP neural model has a much better prediction performance.

Experiment Validation
In order to verify the generalization ability of this prediction model, a set of experiments were done.

Experiment Work and Data Collection
4.1.1.Raw Materials.Concrete specimens with three different strength grades were cast in the experiments.ree strength grades are, respectively, C30, C50, and C80.P52.5 Portland cement coming from Huaxin cement factory was chosen.Fine aggregates are fluvial sands and have a modulus of fineness of 2.7.e sediment content of the fluvial sands is 1%.Coarse aggregates are 5∼25 continuously graded limestones and the sediment content is 0. A water-reducing agent with a solid content of 30% is polycarboxylate highperformance water-reducing admixture, manufactured by Subote New Materials Co., Ltd.Advances in Materials Science and Engineering mechanical properties, and three specimens were prepared at every strength grade level.Table 7 shows the mix design of concrete specimens.Water-reducing admixture dosage is adjusted according to the rheological properties of fresh concrete in trial mix, and the nal mix design was determined.e specimens are curing according to GB/T50081-2002.Curing temperature is 20 ± 2 °C, and relative humidity is 95%.After curing for 90 days, cement hydration is almost completed, and the strength development reaches a plateau.e wet-dry cycle system is in accordance with GB/T50082-2009 but a little di erent from that.In this system, the specimens were immersed in solution for 16 hours, where the solution temperature is 20 °C.en, the specimens were put into the oven where the baking temperature is 50 °C for 8 hours.e whole process is treated as a complete cycle, and one wet-dry cycle takes one day.

Mix Proportions and Specimen
4.1.4.Testing Procedure.After mixing and standard curing, all hardened specimens from each group were tested to estimate the compressive strength.In order to achieve nondestructive testing of concrete, the ultrasonic method was chosen to measure compressive strength of concrete.Compressive strength at 90 days is regarded as initial strength.After 5, 10, 15, 20, and 25 wet-dry cycles, compressive strength was tested through the ultrasonic method.4.1.5.Experimental Results and Discussion. Figure 9 shows the compressive strength of cube specimens after wet-dry exposure.An assemble list including experiment results and in uencing factors is shown in Table 8, and lists A∼O are 15 in uencing parameters of nal compressive strength.

Consistency between Experiment Results and Prediction
Results.
e experimental parameters were brought into the input neurons of this model to test the di erence between prediction values and actual values.Figure 10 shows the prediction value and actual value.ese white dots are prediction values and red asterisks are actual values.It turns out to be a good compatibility.In order to assess the performance of this BP-ANN model, three statistical indictors are calculated.
Table 9 shows the detailed values and error percentages.A maximum error percentage is 3.93%, and all the errors are within acceptable range.e data tting is ideal.Hence, this model could be used for the wet-dry environment concrete compressive strength prediction.
e MAE of the prediction is 0.6356 MPa, the RMSE is 0.8144 MPa, and the average error percentage is 1.09%.From the calculation results of MAE and RMSE, it can be concluded that this model is quite accurate for predicting the strength.From the errors of the prediction values and true values in Table 10, the strength can be accurately predicted by this BP neural network model.However, because this BP neural network model is a four-layer structure, it may cost a long time to do the calculation.Besides, the influencing factors may not be considered totally, and this will have an effect on the prediction results.Last but not least, weighing coefficients could be calculated by some new method, such as Grey relational theory, in advance.It could shorten the running time and simplify the model structure.And this method is under exploration.

Conclusions
e BP artificial neural network was developed for compressive strength of concrete in wet-dry environment prediction.e following conclusions are obtained in this study: (1) Data collected to establish a prediction model are relatively representative in this research.However, data of some particular factors need more experiments to supplement, such as chloride ion and magnesium ion concentrations and slag dosage.
Step 1: input training factors.Fifteen in uencing factors are inputted into the model; Step 2: hidden nodes calculate the output.

Figure 6 :
Figure 6: Results of training, validation, and testing.

Figure 7 :
Figure 7: Fitting curve of outputs and targets.

Figure 8 :
Figure 8: Fitting curve of outputs and targets of the linear model.

4. 1 . 3 .
Details of Wet-Dry Exposure.Cube specimens are exposed to a wet-dry environment after 90-day standard curing.

Figure 9 :
Figure 9: Compressive strength of concrete exposed to cyclic numbers.

Table 1 :
Source of data collected.

Table 2 :
Statistical analysis of 1078 sets of data.

Table 3 :
Sample numbers of initial and nal strength distribution intervals.

Table 4 :
Kendall and Spearman correlation coe cients of in uencing factors.

Table 5 :
Prediction performance of different patterns of this model.

Table 6 :
Prediction performance comparison between LR and BP.

Table 7 :
Mix design of raw materials.

Table 8 :
Assemble list of influencing factors and results.

Table 10 :
Errors of the prediction values and true values.