ANN prediction of cement mortar compressive strength, influence of cement strength class

Construction and Building Materials 138 (2017) 1–11

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ANN prediction of cement mortar compressive strength, influence of cement strength class Hamid Eskandari-Naddaf ⇑, Ramin Kazemi Department of Civil Engineering, Hakim Sabzevari University, Sabzevar, Iran

h i g h l i g h t s

g r a p h i c a l a b s t r a c t


The effect of cement strength class on

80 70 60 50 40 30 20 10 0

Fc Experimental (MPa)

2.5

i n f o

Article history: Received 30 July 2016 Accepted 27 January 2017

Keywords: Cement mortar Cement strength class Artificial neural networks Compressive strength prediction

Considering Cement strength class

Fc 14

2.75 S/C

3

Neglecting Cement strength class

Training R2 = 0.9431

70 60 50 40 30 20 10 0

Fc (MPa)

Experimental Peredicted

30

60

90 120 150 180 210 240 270 Row number

Training R2 = 0.738

70 60 50 40 30 20 10 0

Experimental Peredicted

0

30

60

90 120 150 180 210 240 270 Row number

a b s t r a c t An artificial neural network (ANN) study is presented to predict the compressive strength (Fc) of mortar mixtures containing different cement strength classes of CME 32.5, 42.5, and 52.5 MPa. For this purpose, 54 mixtures considering six water/cement ratios (W/C) (0.25, 0.3, 0.35, 0.4, 0.45, and 0.5) and three sand/ cement ratios (S/C) (2.5, 2.75, and 3) along with the abovementioned three types of cement strength classes have been constructed, and the results for a total of 810 specimens have been obtained. A comparative investigation was performed on two conditions of with and without considering the cement strength class as an input parameter in developed ANN-I and ANN-II models in order to obtain the optimum state. The comparison of the proposed idealized ANN model with two other existing models indicates good precision and accuracy of the developed ANN model in predicting the compressive strength of the mortar and the deficiency of these existing models in situations where cement strength class is present as an input parameter. Ó 2017 Elsevier Ltd. All rights reserved.

1. Introduction According to the British Standard [1], Sika Concrete Handbook [2], and Indian Standard plain and reinforced concrete code of

⇑ Corresponding author. E-mail address: [email protected] (H. Eskandari-Naddaf). http://dx.doi.org/10.1016/j.conbuildmat.2017.01.132 0950-0618/Ó 2017 Elsevier Ltd. All rights reserved.

Fc 21 Fc 3

Compressive strength

0

a r t i c l e

Fc 28 Fc 7

Relation of Fc and S/C ratios for W/C = 0.3 with cement strength classs of 52.5 (MPa).

Fc (MPa)

the compressive strength of cement mortar is examined.
ANN model accurately predicted compressive strength of cement mortar.
The results between ANN model and experiments results show a good agreement.
The performance of ANN model show improved with cement strength class considered.

practice [3], the compressive strength of cement is one of main factors that affects the compressive strength of a mortar and concrete, which needs to be considered during the cement-producing process. Recently, cement strength classes of 32.5, 42.5, and 52.5 MPa have been applied in various types of constructions with the same conditions of constructing, curing, testing, and so on and result in different values of compressive strength. Moreover, parameters such as water/cement ratio (W/C) [4,5], sand/cement

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H. Eskandari-Naddaf, R. Kazemi / Construction and Building Materials 138 (2017) 1–11

ratio (S/C) [6], age [7,8] and shape [9,10] of specimens cause various effects [11]. The application of analytical models to represent the influences of each of these parameters on compressive strength is very complicated, but such predicting tools can be sufficient for solving these objects. In this regard, several researchers have predicted the compressive strength of cementations materials using extrapolation method, electrical resistivity measurement, regression analysis methods, genetic algorithm, fuzzy logic, ultrasonic pulse velocity and artificial neural network (ANN) approaches [12–25]. However, among all mentioned approaches, ANN is a more popular and efficient way due to its ability to classify the data and learn the input and output relation for any complex problem [26,27]. In recent years, several works were reported wherein ANN was used for estimating the compressive strength of many concrete-involved problems such as issues related to high performance [28–31], high strength [32], FRP-confined [33,34], selfcompacting [35–37], self-stressing [38] and lightweight [39–41] concretes, sulfate resistance in concrete [42–44], concrete exposed to high temperatures [45] and applying admixtures in concrete [46–48]. In addition, some attempts have been made in applying neural networks in cement mortars. Onal and Ozturk [49] studied the relation among the microstructural properties of cement mortars by studying digital image processing to predict compressive strengths using ANN analysis. Microstructural phase formation on the mechanical properties of cement mortars was obtained at different time periods (1, 2, 7, 28, and 90 days), and the findings were predicted with the proposed model. The results indicated that a good agreement between the microstructural properties of cement mortar and compressive strengths is established by using ANN as the non-linear statistical data modeling tool. Moreover, Sarıdemir [50] predicted the compressive strength of mortars containing metakaolin at the age of 3, 7, 28, 60, and 90 days by ANN, and the data for training and testing was from the available experimental results for 179 specimens produced with 46 different mixture proportions. The results illustrated that the ANN model is a practical method for these kinds of predictions. Although these previous studies typically have had successful experiences in predicting with their intelligent ANN models, some studies have had very large errors in a few of their predictions when they predicted the cement type effect on demanded results. Ni and Wang [51] in their research on predicting the Fc of concrete considered the class of cement on total strength and concluded that the mixture with higher cement class leads to greater concrete strength. Furthermore, Duan, Kou [52] applied the ANN in predicting the Fc of recycled aggregate concrete where some of their networks did not fit well and they concluded that these large errors may be related to not considering the cement type as an input parameter. In another study, predicting the compressive strength of cement mortar was done by Akkurt, Ozdemir [53] in which the sensitivity analysis was implemented in various physical and chemical cement properties as input parameters of the ANN model. Their results showed that change in levels of some materials such as SO3, C2S, and C3A cause such important influences in the final concrete compressive strength, which emphasizes again the significant role of cement strength class in achieving desirable consequences due to existing different amounts of these parameters in various cement types. However, in none of these described studies, cement strength class has been considered as an independent input parameter in ANN modeling and predictions. Thus, the aim of this paper is to investigate and estimate the effect of the cement strength class on the cement mortar properties. The experimental work was planned so that 54 mix designs including 15 specimens in each mixture were constructed. A total 810 specimens applying three types of cement strength class of 32.5, 42.5, and 52.5 MPa and various mix parameters have been tested, and compressive strength results of 3, 7, 14, 21, and

28-day ages were obtained. Likewise, two ANN models with and without considering the cement strength class as an input parameter were developed, and analyses were implemented with training and error in order to achieve the most appropriate model. Afterward, the predicted results were compared with experimental results of this study and two other studies to validate the established model. 2. Experimental plan 2.1. Materials Three types of cements (CEM 32.5, 42.5, and 52.5 MPa) were proposed, which their physical and chemical properties are listed in Table 1. Sand was passed through a 4.75 mm sieve with a specific gravity of 2.6 and the fineness modulus of 2.48 was also used in mixtures and the High range water reducing (HRWR) admixture was based on poly carboxylic technology (Structuro 100). HRWR is different from conventional superplasticizers. HRWR is based on a unique carboxylic ether polymer. Also, HRWR is a high performance superplasticizer intended for applications where increased early and ultimate compressive strengths are required. 2.2. Mix design, sample preparation and testing The mortar used consists of 1 part cement and various values of 2.5, 2.75, and 3 parts of sand proportioned by mass. Portland cements with three cement strength class types of 32.5, 42.5, and 52.5 MPa are mixed at specified W/C ratios of 0.25, 0.3, 0.35, 0.4, 0.45, and 0.5. Details of all 54 mix proportions are listed in Table 2. HRWR content for various mixtures is sufficient to obtain a flow of 110 ± 5 in 25 drops of the flow table. The 50-mm test cubes are compacted by tamping in two layers for each mixture. The cubes are cured one day in the molds and stripped and immersed in water until tested according to ASTM C109 [54]. There are 15 specimens for each mix design by means of 3 ones at each age of 3, 7, 14, 21, and 28 days, equaling 810 tested specimens and obtaining the Fc results. Fig. 1 shows the construction and testing procedures of many specimens. 3. Experimental results Relations of Fc and S/C ratio for various ages of specimens (3, 7, 14, 21, and 28 days) considering different W/C ratios (0.25, 0.3, 0.35, 0.4, 0.45, and 0.5) are depicted in Fig. 2 so parts (a–c) of the figures are related respectively to 32.5, 42.5, and 52.5 MPa as cement compressive strength classes. Fig. 2 shows the relation of Fc and S/C ratios for W/C = 0.25 with cement strength classes of 32.5 (a), 42.5 (b) and 52.5 (c) MPa. The S/C ratio initially changed from 2.5 to 2.75 and increased the mortar Fc for the 32.5 MPa cement strength class, but decreased the mortar Fc in both 42.5 and 52.5 MPa classes. After the S/C increased past 2.75 these trends for the 32.5 and 52.5 MPa classes changed reversely, which shows that the 2.75 S/C ratio might be a critical value, but the 42.5 MPa class continues as previous with a negative slope. Indeed, the maximum amounts of Fc occurred in 28 days age of specimens and with an S/C ratio of 2.5 for 42.5 and 52.5 MPa classes and a ratio of 2.75 for 32.5 MPa cement class with Fc values of 30, 42, and 50 MPa for 32.5, 42.5, and 52.5 MPa cement strength classes. Accordingly, a constant S/C ratio amount would be an effective parameter in the ultimate strength of mortar, because these cement strength classes are so noticeable. Moreover, these trends approximately have been followed similarly for whole ages of specimens. In Fig. 3 the curves have been plotted for W/C of 0.3, which typically shows similar trends to previous ones. However, this curves

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H. Eskandari-Naddaf, R. Kazemi / Construction and Building Materials 138 (2017) 1–11 Table 1 Properties of Portland cement. Cement strength class

Chemical analysis (%) SiO2

Al2O3

Fe2O3

CaO

MgO

SO3

Na2O

K2O

LOI

F.CaO

C3A

C3S

Specific Gravity (ton/m3)

Sieve residue on 90 mm (%)

Blaine test (cm2/gr)

C 325 C 425 C 525

20.4 20.2 21

4.56 4.6 4.7

3.4 3.5 3.52

64.12 64 64.18

1.93 1.94 1.93

2.3 2.4 2.53

0.32 0.35 0.32

0.7 0.7 0.65

2.2 2.7 1.2

1.3 1.3 1.2

6.33 6.27 6.5

63.94 64.27 57.85

3.13 3.13 3.15

0.9 0.8 0.1

3000 3050 3600

Physical analysis

Table 2 Mix proportions of various specimens of cement mortar. No.

CSC (MPa)

C (kg)

S/C

W/C

HRWR (ml)

No.

CSC (MPa)

C (kg)

S/C

W/C

HRWR (ml)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

32.5 42.5 52.5 32.5 42.5 52.5 32.5 42.5 52.5 32.5 42.5 52.5 32.5 42.5 52.5 32.5 42.5 52.5 32.5 42.5 52.5 32.5 42.5 52.5 32.5 42.5 52.5

2.85 2.85 2.85 2.67 2.67 2.67 2.5 2.5 2.5 2.85 2.85 2.85 2.67 2.67 2.67 2.5 2.5 2.5 2.85 2.85 2.85 2.67 2.67 2.67 2.5 2.5 2.5

2.5 2.5 2.5 2.75 2.75 2.75 3 3 3 2.5 2.5 2.5 2.75 2.75 2.75 3 3 3 2.5 2.5 2.5 2.75 2.75 2.75 3 3 3

0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35

90 40 40 90 95 90 95 85 50 40 30 30 45 35 40 90 35 35 17 17 12 22 17 17 22 17 30

28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54

32.5 42.5 52.5 32.5 42.5 52.5 32.5 42.5 52.5 32.5 42.5 52.5 32.5 42.5 52.5 32.5 42.5 52.5 32.5 42.5 52.5 32.5 42.5 52.5 32.5 42.5 52.5

2.85 2.85 2.85 2.67 2.67 2.67 2.5 2.5 2.5 2.85 2.85 2.85 2.67 2.67 2.67 2.5 2.5 2.5 2.85 2.85 2.85 2.67 2.67 2.67 2.5 2.5 2.5

2.5 2.5 2.5 2.75 2.75 2.75 3 3 3 2.5 2.5 2.5 2.75 2.75 2.75 3 3 3 2.5 2.5 2.5 2.75 2.75 2.75 3 3 3

0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

7 5 5 10 7 5 15 10 12 3 3 3 3 3 3 3 3 3 2 2 2 2 2 2 2 2 2

Cement strength class = CSC, Cement = C, Sand = S, Water = W, High range water reducer = HRWR.

Fig. 1. Construction and testing process of the specimens.

only show a similar trend in the part (c), which is related to a 52.5 MPa cement strength class. Additionally, the contours slope after the 2.75 S/C ratio and is negative in the all curves. Due to this fact, a cement class of 52.5 MPa in mixtures, which includes S/C ratio of 3, should be better to keep the W/C ratio up to 0.25 and have an optimum total Fc. Furthermore, among all amounts of

W/C ratios, the maximum values of Fc have been achieved in ratio of 0.3 as 42, 54, and 65 MPa for cement classes of 32.5, 42.5, and 52.5 MPa which shows these are the most appropriate values in order to obtain the optimal design in compressive strength. In the same way, Fig. 4 represents the previous relations but with lower maximum amounts of Fc for each three classes of cement strength. Additionally, in this W/C ratio the slopes of contours after S/C of 2.75 changes to be positive. This makes the extreme points for curves related to part (b), namely the cement strength class of 42.5 MPa, increase. This increase continued in Fig. 5 by getting to the maximum value of 56 MPa and after that decreased gradually in Figs. 6 and 7. After these detailed explanations, comparing all experimental results indicates that each cement strength class could be executable in various particular conditions depending on different specified ends and requirements. Overall, the optimal amount of Fc is achieved, by designing the mixtures with a W/C ratio equal to 0.3 using the cement strength class of 52.5 MPa. In other words, it is an important point to remember that the cement strength class could play a very significant role in all concrete designing problems and must be paid more attention especially in such sensitive situations. 4. Artificial neural networks ANNs are non-linear statistical data modeling tools for relations between input and output data, which can be an adaptive system that changes its structure based on information that flows through

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H. Eskandari-Naddaf, R. Kazemi / Construction and Building Materials 138 (2017) 1–11

40

Fc 28

Fc 21

Fc 14

Fc 7

(a)

Fc 3

Fc Experimental (MPa)

Fc Experimental (MPa)

(a)

30 20 10

2.5

Fc 14

Fc 7

Fc 3

30 20 10 2.5

(b)

50 Fc 28

Fc 21

Fc 14

Fc 7

Fc 3

40 30 20 10

2.5

60

2.75 S/C Fc 28

Fc 21

Fc 14

Fc 7

50 40 30 20 10 0 2.5

2.75 S/C

3

Fig. 2. Relation of Fc and S/C ratios for W/C = 0.25 with cement strength classes of 32.5 (a), 42.5 (b) and 52.5 (c) MPa.

the network during the learning phase. Feed-forward networks have their neurons arranged in layers. All the neurons in the different layers are connected to each other; however, there are no connections between neurons in the same layer. The first layer known as the input layer, which includes the ANN input parameters and the same number of neurons as inputs, and the last layer is entitled the output layer, which contains the results of the ANN, with the same number of neurons as problem outputs. The other layers that are between these two are named the hidden layers. The number of hidden layers and the number of neurons in each hidden layer may not be identified beforehand due to depending on the problem under investigation [55–57]. The Element ANN has a loop from the output of the hidden layer to the input layer. In this study, the multilayer feed-forward type of neural networks, as shown in Fig. 8, is considered. 4.1. Data preprocessing and ANN preparation A multilayered feed-forward neural network is used in the present study. The nonlinear function is used in the hidden layer and the neuron outputs at the output layer. The neural network architecture developed in this research has been done for both conditions of with and without considering cement strength class as ANN-I and ANN-II respectively. Due to this fact, ANN-I model consists of 1 more input node than ANN-II model. One neuron in

3

60 Fc 28

Fc 21

Fc 14

Fc 7

Fc 3

50 40 30 20 10 2.5

(c)

Fc 3

2.75 S/C

0

3

Fc Experimental (MPa)

Fc Experimental (MPa)

Fc 21

40

3

Fc Experimental (MPa)

Fc Experimental (MPa)

2.75 S/C

0

(c)

Fc 28

50

0

0

(b)

60

80 70 60 50 40 30 20 10 0

2.75 S/C Fc 28

2.5

Fc 21

Fc 14

2.75 S/C

3

Fc 7

Fc 3

3

Fig. 3. Relation of Fc and S/C ratios for W/C = 0.3 with cement strength classes of 32.5 (a), 42.5 (b) and 52.5 (c) MPa.

the output layer and a hidden layer, which consists of four neurons, is used in the architecture of multilayer feed-forward neural network. Quality of ANN result depends on data accuracy. Therefore, in composite materials like mortar the more appropriate work for making the prediction more precise may be expressing the various effective variables in such ratios like W/C, S/C, and Fine Aggregate/ powder against considering individual parameters such as amount of water, cement, sand, and others. For input functions of the network, both hyperbolic tangent (tanh) and logistic transfer functions are adopted, but for the output, just the tanh function has been applied with the learning rate of 0.01 and iteration number of 2000. These functions are nonlinear and it becomes essential to normalize the original data before training the network. The Outputs from a tanh function range are between 1 and 1, as shown in Fig. 9 [58]. Furthermore, linear transformation viz. Eq. (1) is considered as the input and output vectors as the following:

Xi ¼

1:6ðXio  Xmin Þ  0:8 Xmax  Xmin

And

Yi ¼

1:6ðYio  Ymin Þ  0:8 Ymax  Ymin

ð1Þ

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H. Eskandari-Naddaf, R. Kazemi / Construction and Building Materials 138 (2017) 1–11

(a)

50

Fc 28

Fc 21

Fc 14

Fc 7

Fc 3

50

Fc Experimental (MPa)

Fc Experimental (MPa)

(a)

40 30 20 10

2.5

Fc 7

Fc 3

20 10

2.5

(b)

60

Fc 28

Fc 21

Fc 14

Fc 7

Fc 3

50 40 30 20 10 2.5

70

2.75 S/C

Fc 28

Fc 21

Fc 14

Fc 7

50 40 30 20 10 0 2.5

2.75 S/C

3

Fig. 4. Relation of Fc and S/C ratios for W/C = 0.35 with cement strength classes of 32.5 (a), 42.5 (b) and 52.5 (c) MPa.

Xio and Xi are the ith components of the input vector before and after being normalized, respectively, and Yio and Yi are the ith components of the output vector before and after being transformed, respectively. The Xmax, Xmin, Ymax, and Ymin are the maximum and minimum values of all the components of the input and output vectors before the normalization, respectively [58]. The 70% of input values are considered as training, 15% as validating, and the remaining 15% as testing data, which are used in the ANN model in the arranged format of five input parameters, viz. the age of specimen, W/C and S/C ratios, type of cement strength class, and HRWR. Considering these five input nodes, the target node was the compressive strength of specimens. The network architecture used in this study was called ANN 5-n-1, where the first character is the number of input nodes, n is the number of hidden nodes, and third character is the number of outputs. The input data with a range of hidden nodes from 4 to 20 have been tested by mentioned transformation functions, which results related to regression values have been shown in Figs. 10 and 11. Correlation coefficients, which have values closer to one, revealed the more exact estimate and better performance compared to those with a greater difference. On the other hand, if the coefficients of training, validating, and testing data in each network were closer to each other, the network includes less error and may be more reliable. Another investigation of the networks for selecting the best number of the hidden layer nodes was implemented due to the

Fc 28

Fc 21

Fc 14

Fc 7

Fc 3

60 50 40 30 20 10 2.5

(c)

Fc 3

3

0

3

60

2.75 S/C

70

Fc Experimental (MPa)

Fc Experimental (MPa)

Fc 14

30

3

Fc Experimental (MPa)

Fc Experimental (MPa)

2.75 S/C

0

(c)

Fc 21

0

0

(b)

Fc 28

40

80 70 60 50 40 30 20 10 0

2.75 S/C

Fc 28

2.5

Fc 21

Fc 14

2.75 S/C

3

Fc 7

Fc 3

3

Fig. 5. Relation of Fc and S/C ratios for W/C = 0.4 with cement strength classes of 32.5 (a), 42.5 (b) and 52.5 (c) MPa.

maximum absolute errors appeared in the networks (Fig. 12). It can be perceived that almost all networks were well trained for both functions. Considering all of these significant issues, the most appropriate network would be chosen as ANN 5-16-1 and ANN 511-1 from tanh and logistic functions, respectively. In order to make it single, the best model could be selected as ANN 5-11-1 due to containing low maximum squared error and good correlation between data. Likewise, the Mean Squared Error (MSE) between the experimental and predicted amounts of Fc as target and output parameters, respectively, has been obtained according to the Eq. (2) and the results have been depicted in Fig. 13 where the observations are the validation of choosing the network ANN 5-11-1 as the idealized model.

MSE ¼

N 1X ðt i  pi Þ2 N i¼1

ð2Þ

where N is total number of data, ti is the experimental value, and pi is the predicted value of compressive strength. The proposed ANN-I model is illustrated in Fig. 14. In this regard, the network ANN 4-11-1 can be considered for ANN-II model where the cement strength class eliminated from network in order to perform the sensitivity analysis on this parameter.

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H. Eskandari-Naddaf, R. Kazemi / Construction and Building Materials 138 (2017) 1–11

(a)

40

Fc 28

Fc 21

Fc 14

Fc 7

Fc 3

Fc Experimental (MPa)

Fc Experimental (MPa)

(a)

30 20 10

40

70

2.75 S/C

Fc 3

10

Fc 28

Fc 21

Fc 14

3

Fc 7

2.5

(b)

Fc 3

Fc Experimental (MPa)

Fc Experimental (MPa)

Fc 7

20

60 50 40 30 20 10 2.5

2.75 S/C

Fc 21

Fc 14

Fc 7

50 40 30 20 10

Fc 14

Fc 7

Fc 3

30 20 10

2.5

(c)

Fc 3

Fc 21

0

Fc Experimental (MPa)

Fc 28

60

Fc 28

3

40

3

70

2.75 S/C

50

0

Fc Experimental (MPa)

Fc 14

0 2.5

(c)

Fc 21

30

0

(b)

Fc 28

2.75 S/C

60

Fc 28

Fc 21

3

Fc 14

Fc 7

Fc 3

50 40 30 20 10 0

0 2.5

2.75 S/C

2.5

3

Fig. 6. Relation of Fc and S/C ratios for W/C = 0.45 with cement strength classes of 32.5 (a), 42.5 (b) and 52.5 (c) MPa.

2.75 S/C

Fig. 7. Relation of Fc and S/C ratios for W/C = 0.5 with cement strength classes of 32.5 (a), 42.5 (b) and 52.5 (c) MPa.

Feed-forward

5. Evaluation of experimental results and ANN predictions The comparison of experimental and predicted results of the multilayer feed-forward neural network for 3, 7, 14, 21, and 28 days Fc are given in Fig. 15. The outcomes indicated that the proposed neural network was successful in learning the relation between the different input parameters and the output parameter via compressive mortar strength. Fig. 15 shows that there are three major parts in it, which are related to various types of 32.5, 42.5, and 52.5 MPa cement strength classes, which include 0–90, 90– 180, and 180–270 row numbers respectively. Each of these three parts involves the various ages of specimens from 3 to 28 days, which shows growth in results by increasing in ages of specimens too. It can be observed that improving the cement strength class results in enhancing the total Fc of mortar. The performance in predicting the compressive strength of the training mixture in Fig. 16 is satisfactory with R2 = 0.94. Evaluations of predicted and target values using ANN-II model have been depicted in Fig. 17. As seen, the error between actual and predicted data is almost high in comparison of the ANN-I model, which may be caused by neglecting the cement strength class as an input parameter. For better understanding, paying more attention to this fact that the cement is commonly used in mortars and also concrete mixtures as cohesive material, and it is so

3

1

Input

Output

Output layer Input layer

Hidden layer Fig. 8. The artificial neuron model.

obvious that omitting this important material from input parameters of predicting network can cause a significant effect in predicted results. The similar trend can be observed in Fig. 18 that the performance in predicting the Fc of the training mixture is satisfactory with R2 = 0.74, which could not be acceptable as a suitable prediction. To validate the recommended ANN model, a comparison procedure with the prediction works of Siddique, Aggarwal [37] and Sarıdemir [50] has been performed. For this purpose, data sets of

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0.014 Logistic

Maximum Squared Error

1 -------------------------------------------0 F(net) = Tanh

-------------------------------------------1

0.012

Hyperbolic tangent

0.01 0.008 0.006 0.004 0.002 0 4

Fig. 9. Output activation function.

Training

Validation

Test

5

6

7

8

9 10 11 12 13 14 15 16 17 18 19 20

Networks with Different Numbers of Hidden Nodes Total Data

Fig. 12. Maximum squared error versus number of hidden layer neurons for Logistic and Tanh input function.

1 0.8

0.035

0.7

Logistic

0.03

0.6 0.5 0.4 0.3 0.2 0.1 0 4

5

6

7

8

9 10 11 12 13 14 15 16 17 18 19 20

Networks with Different Numbers of Hidden Nodes Fig. 10. Correlation coefficient versus ANN 5-n-1 using Hyperbolic tangent input function.

Mean Squared Error

Correlation Coefficient

0.9

Hyperbolic tangent

0.025 0.02 0.015 0.01 0.005 0 4

5

6

7

8

9 10 11 12 13 14 15 16 17 18 19 20

Networks with Different Numbers of Hidden Nodes Training

Validation

Test

Total Data

1

Correlation Coefficient

0.9

Fig. 13. Mean squared error (MSE) versus number of hidden layer neurons for Logistic and Tanh input functions.

where the achieved coefficient of determination could not be satisfactory due to representing almost large errors (Fig. 20). The R2 and root mean squared error (RMSE) for whole states of prediction are listed in Table 3 showing that the errors of estimating the Siddique et al. and Saridemir data with ANN-I model are less than what they predicted with their offered models. Finally, this comparison shows that their offered ANN models to be impractical in such works, which suggest cement strength class significance in the final compressive strength of mortars and consider it as an input parameter in the models.

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 4

5

6

7

8

9 10 11 12 13 14 15 16 17 18 19 20

Networks with Different Numbers of Hidden Nodes Fig. 11. Correlation coefficient versus ANN 5-n-1 using Logistic input function.

the mentioned studies were collected and then utilized in the ANN study so that the cement strength classes they used in experimental works were considered as an input parameter and predicted with the proposed ANN-I model. The results suggest a better coefficient of determination of 0.97 and 0.993 for Siddique et al. and Saridemir data, respectively, which may confirm the validity of the suggested ANN model (Fig. 19). Also, the offered ANN models of these two studies have been applied for estimating the experimental data of current work

6. Conclusions In this study, a total of 810 specimens of 50-mm cubes were constructed in order to implementing the compressive strength test. The results illustrate that increasing the cement strength class caused improved mortar compressive strength values. Additionally, the maximum Fc was obtained for cement class of 52.5 MPa with W/C and S/C ratios of 0.3 and 2.5, respectively. To predict these empirical results, the ANN analysis was performed. After training the 17 neural networks with various numbers of hidden neurons and also two different nonlinear input activation functions as Tanh and Logistic, the ANN 5-11-1 network with Logistic function was chosen as ANN-I by considering the performance of the networks (R2 and MSE). Eliminating cement strength class from

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H. Eskandari-Naddaf, R. Kazemi / Construction and Building Materials 138 (2017) 1–11

Input layer

Hidden layer

Output layer

1 1

Age of specimen (day)

2

2 1

3 Cement strength class

4

HRWR

5

Compressive Strength

10 11

Fig. 14. ANN-I architecture for prediction the Fc of cement mortar.

70 Experimental 60

Peredicted

Fc (MPa)

50 40 30 20 10 0 0

15

30

45

60

75

90 105 120 135 150 165 180 195 210 225 240 255 270

Row number Fig. 15. Evaluation of experimental and predicted compressive strength by ANN-I.

60

Peredicted Fc (MPa)

R² = 0.9431 50 40 30 20 10 0 0

10

20

30

40

50

60

Experimental Fc (MPa) Fig. 16. Neural network training regression model ANN-I.

input parameters led the ANN-II model to be similar to architecture ANN 4-11-1 to specify the influence of cement strength class in such estimations. From these ANN investigations, the following conclusions were made: 1. The coefficient of determination for proposed ANN-I model appears to lie in an acceptable range of R2 = 0.94, but for ANN-II the amount of R2 = 0.74 may not be satisfactory for such that predictions.

2. In order to verify the performance of the network, the ANN-I model was examined with the data set of two existing models, and the results measured by the R2 and RMSE show better correlations and lower errors than that have been obtained in mentioned researches. 3. Moreover, data set of this study was applied in the two existing models; the results show the coefficient determination lower than 0.9, which may not be good agreements and can be related to non-arrival of cement strength class in the models.

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H. Eskandari-Naddaf, R. Kazemi / Construction and Building Materials 138 (2017) 1–11

70 Experimental 60

Peredicted

Fc (MPa)

50 40 30 20 10 0 0

15

30

45

60

75

90 105 120 135 150 165 180 195 210 225 240 255 270

Row number Fig. 17. Evaluation of experimental and predicted compressive strength by ANN-II.

60 R² = 0.738

Peredicted Fc (MPa)

50 40 30 20 10 0 0

10

20

30

40

50

60

Experimental Fc (MPa) Fig. 18. Neural network training regression model ANN-II.

80

80 Experimental

70 Fc (MPa)

Peredicted Fc (MPa)

Peredicted

60 50 40 30 20 10 0 0

10

20

30

40

50

60

70

60 50 40 30 20 10 0

80

0

(a)

Row number 80

10

20 30 40 50 60 Experimental Fc (MPa)

70

80

60 Experimental

70

R² = 0.993 Peredicted Fc (MPa)

Peredicted

60 Fc (MPa)

R² = 0.97

70

50 40 30 20 10 0 0

10

20

30 Row number

40

50

50 40 30 20

60

20

(b)

30

40

50

60

Experimental Fc (MPa)

Fig. 19. Performance of neural network for ANN-I model with data set collected from (a) Siddique et al. and (b) Saridemir.

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H. Eskandari-Naddaf, R. Kazemi / Construction and Building Materials 138 (2017) 1–11

70

60 Experimental

60

Peredicted Fc (MPa)

Peredicted

Fc (MPa)

50 40 30 20 10 0

40 30 20 10 0

0

54

108

162

216

0

270

70

20

30

40

50

60

50

60

Experimental Fc (MPa) 60

Experimental

60

10

(a)

Row number

Peredicted Fc (MPa)

Peredicted

50 Fc (MPa)

R² = 0.8566

50

40 30 20 10 0

R² = 0.8963

50 40 30 20 10 0

0

54

108

162

216

270

0

(b)

Row number

10

20

30

40

Experimental Fc (MPa)

Fig. 20. Performance of neural network for models of (a) Siddique et al. and (b) Saridemir with data set collected from experimental results of current study.

Table 3 Summary of coefficients for investigated neural network models. Data set

Predicting model

R2

RMSE

Results of current study

ANN-I Siddique et al. Saridemir

0.9431 0.8566 0.8963

2.74 4.33 3.7

Results of Siddique et al.

Siddique et al. ANN-I

0.9188 0.97

5.557 2

Results of Saridemir

Saridemir ANN-I

0.9887 0.993

1.13 0.8

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