Al-Qadisiyah Journal For Engineering Sciences, Vol. 10……No. 1….2017 11 PREDICTION OF ULTIMATE LOAD OF CONCRETE BEAMS REINFORCED WITH FRP BARS USING ARTIFICIAL NEURAL NETWORKS Ahmed Sagban Saadoon, Basrah Univ., Civil Eng. Dept., ahmsag@gmail.com Hawraa Sami Malik Basrah Univ., Civil Eng. Dept., wesamsalm85@gmail.com Received on 09 October 2016 Accepted on 22 December 2016 Abstract Artificial neural networks (ANN) were used in this study to predict ultimate load of simply supported concrete beams reinforced with FRP bars under four point loading. A proposed neural model was used to predict the ultimate load of these beams. A total number of (199) beams (samples) were collected as data set and it was decided to use eight input variables, representing the dimensions of beams and properties of concrete and FRP bars, while the output variable was only the ultimate load of these beams. It was found that the use of 11 and 10 nodes in the two hidden layers was very efficient for predicting the ultimate load. The obtained results were compared with available experimental results and with the ACI 440.1R specifications. The proposed neural model gave very good predictions and more accurate results than the ACI 440.1R approach. The overall average error, in the value of the predicted ultimate load, was 3.6% and 21.7% for the proposed neural model and the ACI 440.1R approach, respectively. Key words: FRP bars, flexural behavior, artificial neural networks. تقدیر الحمل األقصى للعتبات الخرسانیّة المسلّحة بقضبان بولیمیریّة باستخدام الشبكات العصبیّة االصطناعیّة ahmsag@gmail.comجامعة البصرة، العراق، ,قسم الھندسة المدنیة ,احمد صكبان سعدون wesamsalm85@gmail.comعراق، ال ,جامعة البصرة ,قسم الھندسة المدنیة , حوراء سامي مالك الخالصة لقد تّم استخدام الشبكات العصبیّة االصطناعیّة في ھذه الدراسة لتقدیر الحمل األقصى للعتبات الخرسانیّة بسیطة اإلسناد والمسلّحة الحمل األقصى لھذه بقضبان تسلیح بولیمیریّة والمعّرضة الى تحمیل نقطي رباعي. حیث تّم إقتراح وتطویر شبكة عصبیّة لتقدیر ) نموذج كقاعدة بیانات. وقد تقّرر أْن یكون عدد متغیّرات اإلدخال لھذه الشبكة ھو ثمان متغیّرات ١٩٩العتبات وقد ُجمعت نتائج ( تمثّل أبعاد العتبات وخواص الخرسانة وقضبان التسلیح، في حین كان ھناك متغیّراً وحیداً ھو الحمل األقصى كمتغیّر إخراج. لقد عقد في الطبقة الثانیة كان فّعاالً جّداً في تقدیر ١٠عقدة (خلیّة عصبیّة) في الطبقة المخفیّة االولى من الشبكة و ١١ُوجد بأّن اختیار ACI 440.1Rقیمة الحمل األقصى. وقد قُورنت النتائج المستحصلة مع نتائج عملیّة متوفّرة ومع مواصفات المدّونة األمریكیّة لشبكة المقترحة نتائج أكثر دقّة من المدّونة األمریكیّة، إذ كان مقدار معّدل الخطأ الكلّي في قیمة الحمل األقصى المقّدر حیث أعطت ا % باستخدام المدّونة األمریكیّة.٢١.٧% باستخدام الشبكة المقترحة بینما كان مقداره ٣.٦ھو Nomenclature a Shear span (mm) a Summation function Af Area of FRP bar (mm 2 ) Al-Qadisiyah Journal For Engineering Sciences, Vol. 10……No. 1….2017 12 ACI American Concrete Institute ANN Artificial neural network b Width of beam (mm) or bias Ef FRP elasticity modulus (MPa) f Activation function f’c Compressive strength of concrete (MPa) fu FRP tensile strength (MPa) FOV Fraction of variance FRP Fiber reinforcement polymer h Beam’s depth (mm) L Beam’s length (mm) Logsic Logistic sigmoidal function m Shear span ratio (a/L) MAE Mean absolute error MAPE Mean absolute percentage error MSE Mean square error N Number of input samples (vectors) P Ultimate load (kN) PACI Ultimate load predicated by ACI code (kN) PANN Ultimate load predicated by neural network (kN) Pexp Experimental ultimate load (kN) Purelin Linear function R Coefficient of correlation RMSE Root mean squared error tansig Hyperbolic tangent function u Actual value v Predicted value u Mean of the actual values w Weight vector x Neural input y Neural output 1 General The ultimate strength in reinforcing members is depending on the type of reinforcement materials. Due to durability and corrosion problem of steel reinforcement under aggressive conditions, other materials, like fiber reinforcement polymers (FRP), have appeared to be an alternative reinforcement material. The FRP reinforcing bars are a composite materials made of reinforcing fibers and a matrix (resin). FRP composites are used in many types of engineering structures and can be used for enhancing requirements of performance due to their advantageous properties. FRP composites are utilized in rehabilitation, formwork, and reinforcement for seismic design [Jain and lee, 2012]. FRP reinforced concrete members started to be used all over the world, specifically in areas like flexural behavior, bond performance, column behavior and shear behavior. In structural applications, FRP are available as plates, strips or sheets, and reinforcing bars. The use of FRP can be either as an alternative reinforcing instead of steel or for retrofitting to strengthening existing structures. FRP are used as internal or external reinforcement to strengthen columns, slabs, and beams. The strength of these members can be increased even after their damage due to subjected loading. Al-Qadisiyah Journal For Engineering Sciences, Vol. 10……No. 1….2017 13 Many experimental and theoretical investigations [6, 11, 15, 18, and 29] were performed to study the structural and flexural behavior of FRP reinforced concrete beams. These beams are expected to undergo larger deformations than corresponding steel reinforced beams, since the modulus of elasticity of FRP bars is low. FRP bars have high ultimate strength and a linear stress- strain response. This would lead to an almost linear load-deflection response beyond the crack formation phase, up to failure. In this study, an attempt is made to get and predict the ultimate load of FRP reinforced concrete beams using artificial neural networks. 2 Artificial Neural Networks (Ann) ANNs are computational networks which simulating a biological neural network. Due to this, they allow using simple and basic operations to solve nonlinear or complex problems [Graupe, 2007]. Neural networks are considered good for regression and classification tasks in practical cases [Begg et al., 2006]. This makes ANN a very efficient tool to solve and deal with many structural and civil engineering problems [see 21, 24, and 31], particularly in problems having complex or insufficient data. Basically, all ANNs have the same structure or topology, the most common arrangement of the neurons by using a series of layers as shown in Figure (1). The first layer is the layer of input. The input units at this layer is dictated by the number of independent variables or feature values and the input data are taken either directly from electronic sensors or from input files. The final layer is the output layer which its units depend on the number of values or classes to be predicated and it sends information to the outside world or other devices like a mechanical control system, or a secondary computer system. The intermediate layers are called the hidden layers which contain many neurons in different interconnection structures. Figure (2) shows the scheme of a model of an artificial neuron. The shown model has N number of input and one output. The body of neuron contains the summing junction (∑) and the activation function f. The following parameters and variables are used in the artificial neurons. Every input has its own weight, which gives it the effect that it requires to process elements summation function. The node's internal bias (b) is a constant component represents the magnitude offset that affects the activation of the node output. The input vector and the weights vector can be represented as (x1, x2, ….., xN) and (w1, w2, ……, wN), respectively. The summation function can be calculated by multiplying of vector x and w and then adding up the products: å += = N 1i ii b)x(wa , (1) The result will be as a single number. This weighted sum, from summation function, is transformed to the working output though an algorithmic process called transfer function. When neurons are sufficiently activated its output will take a value of 1, but it take zero when the neuron is not sufficiently activated. There are many activation functions used in neural networks which specify the neuron output to a given input. 3 Development Of Proposed Neural Model An artificial neural model is proposed to predict the ultimate load of simply supported FRP reinforced concrete beams under four point loading as shown in Figure (3). The neural network program that is implemented in MATLAB version 8.3.0.532 (R2014a) is used for performing the neural network in this study. This program has many advantages such as containing several types of networks and implementing many different training algorithms. Al-Qadisiyah Journal For Engineering Sciences, Vol. 10……No. 1….2017 14 Back-propagation neural networks are proposed to study the relations between the input variables and the output variables by using the feed-forward back-propagation algorithm. The trial and error process is used to configure and train the neural networks for their indeterminate parameters such as the hidden layers and their nodes, learning patterns, and training parameters. 3.1 Selection Of Data Set The purpose of training a network is to allow it to produce accurate answers and generalize future data. The experimental data used in modeling the proposed neural model are subdivided into two groups; training and testing group. The network uses the training group to updating values of the nodes’ biases and weights in order to minimize the training error. In other words, it uses this group to get the relationship between the input and output variables. While the network uses the testing group to check the generalization ability of the proposed model. The total actual (experimental) data used in the proposed neural model are those obtained from available open literature [1, 2, 4-13, 15-18, 20, 22, 25-30, and 32-40]. A total number of (199) beams (samples) were collected as data set. The training group must contain the extreme values of the different input parameters of the total data set. For estimating the generalization capacity of the training process, the testing set is either selected rotationally from the total data set, or is selected randomly by the computer. In this study, the testing group comprises of approximately (20)% of the collected data and is selected randomly over the entire region of data set. Accordingly, the training group is decided to comprise of (159) samples, while the testing group is comprised of (40) samples. 3.2 Defining Of Input And Output Variables The problem’s nature is the effective factor that state the defining of the input and output variables (parameters). Selection of the input variables is important to get an efficient network, while the selection of the output variables depends on what required from the network to know. In this study, the dimensions and properties of concrete and FRP bars are chosen as candidate input variables. While the output variable is only the ultimate load (P) of the considered concrete beams. For the proposed neural model, it is decided to use the following eight variables as input variables: the cross sectional width (b) of beams, cross sectional depth (h) of beams, cylinder concrete compressive strength (f’c), cross sectional area of FRP bars (Af), FRP bars tensile strength (fu), FRP bars elasticity modulus (Ef), effective span length (L) of beams, and shear span ratio (m). To minimize the input variables several attempts are tried to choose their proper number to represent the properties of the considered beams. In one attempt, the gross cross sectional area of concrete is used instead of its width and depth. Also in another attempt, the reinforcement ratio of FRP bars is used as an input variable. Although good performance in training is found, but the generalization is very poor. Therefore, it is decided to use the above eight input variables for the proposed model. So, eight nodes in the input layer and (1) node in the output layer are used in the proposed neural model. The ranges of all variables are given in Table (1). 3.3 Hidden Layers And Their Nodes determining of hidden layers and their nodes depends on the network application. There is no rules available to find out their exact number. Once start with small number and then is increased until the wanted value from the model (network) is reached. This number is chosen by a trial and error process. If the nodes number is large, the operation of network will be slow and may cause overfitting in the testing group performance. And if this number is very small then the network may be unable to learn well. The suitable number will be selected by a trial and error process to get the network of the minimum error (the best performance) for both training and testing group. Al-Qadisiyah Journal For Engineering Sciences, Vol. 10……No. 1….2017 15 Firstly, a proposed Levenberg-Marquardt back-propagation neural network is investigated with different configurations to choose the best network. Many different trial networks are trained and the optimal topology is determined by choosing the best performed network (of the less training error). Trial networks with single and multi hidden layers and nodes and with a various activation functions (hyperbolic tangent (tansig), logistic sigmoidal (logsig), and linear (purelin) function) are tested. The results show that, the (11-10) two hidden layered model gives best performance with least error in the output variable. This network, with ten nodes in the first hidden layers and twelve nodes in the second and with tansig function for hidden layers and purelin function for the output layer, gives the best performance with MSE of (0.000445) for the training group and (0.001069) for the testing group and number of epochs of (616). Thus, this configuration (topology) is adopted to the proposed network. The topology of this neural network are shown in Figure (4). While the properties of this proposed model are shown in Table (2). 4. Results And Discussion A regression analysis between the obtained (predicted) results and the actual values is performed to investigate the accuracy of the proposed network. The regression coefficient of correlation (R) is used as an index in this analysis. If (R) is close to a value of one, then there is an excellent correlation between the obtained (predicted) loads and the actual loads. Figure (5) shows the correlation analysis of the proposed model output and the experimental values for the training group, while Figure (6) shows this analysis for the testing and group. From Figure (5), which represents the regression analysis for the training data, the correlation coefficient (R) is (0.9988), the interception with y-axis is (0.307) and the slope is (0.997). While for the testing data, Figure (6), the correlation coefficient (R) is (0.9961), interception with y-axis is (0.863) and the slope is (0.991). These analyses certify good agreement between the obtained results and the actual results. 5. Comparative Study The proposed neural model is used to obtain and predict the ultimate load of the FRP reinforced concrete beams that used in the selected testing set of this study. A comparison between the experimental and predicted ultimate loads obtained by the proposed model (PANN) and those obtained from using the ACI 440.1R approach [3] (PACI) is presented in Table (3). As can be noticed from this table, for almost specimens the proposed network gives more accurate results as compared with those predicted by the ACI 440.1R approach. The ACI 440.1R approach underestimates ultimate loads up to approximately 50% (beam number 17) and overestimates ultimate loads up to approximately 24% (beam number 27). While the proposed neural model underestimates ultimate loads up to approximately 12% (beam number 17) and overestimates ultimate loads up to approximately 8% (beam number 10). A statistical comparison between the actual and predicted loads is also performed to check the accuracy of the proposed network and the ACI 440.1R approach of ultimate load calculation as shown in Table (4). Four indices are used in this study to comparative evaluation of the behavior of the proposed network and the calculated ultimate loads using the ACI 440.1R specifications. These indices are the mean absolute error (MAE), root mean squared error (RMSE), mean absolute percentage error (MAPE), and fraction of variance (FOV). and they are given, respectively, as: å -= = n 1i vu n 1 MAE , (2) Al-Qadisiyah Journal For Engineering Sciences, Vol. 10……No. 1….2017 16 2 n 1i )vu( n 1 RMSE -å= = , (3) 100u/)vu( n 1 MAPE n 1i ´å -= ú û ù ê ë é = , (4) )uu(/)vu(1FOV n 1i 2 n 1i -å-å-= == , (5) where u is the actual value, v is the predicted value, u is the mean of the actual values, and n is number of specimens. If MAE is 0, RMSE is 0, MAPE is 0, and FOV is 1, then the used model will be excellent. As can be noticed from Table (4), the MAE, RMSE, MAPE, and FOV for the ultimate load prediction of the proposed neural model are (4.4, 5.7, 3.6, and 0.992), respectively. While these values for the ACI 440.1R approach are (31.4, 41.7, 21.7, and 0.582), respectively. These values proved that the proposed neural model prediction is satisfactory indicating that, an excellent agreement with the experimental data is obtained and hence the proposed network can obtain and predict loads very well and better than ACI 440.1R approach. In Figure (7), the predicted ultimate loads obtained by the proposed model (PANN) and the ACI 440.1R approach (PACI) are plotted against the actual loads. From this Figure, it is obvious that in general the ACI approach underestimates the value of the ultimate load. The coefficient of correlation R = 0.9961 and 0.7629 for PANN and PACI, respectively. These values show that the proposed neural model predicts loads much better than the ACI approach. Therefore, with an overall average error of 3.6%, it is concluded that the developed network could be used efficiently in obtaining the ultimate loads and that the ANN provided an alternative procedure to the costly test procedures for the ultimate load prediction of FRP reinforced concrete beams. 6. Conclusions The main important points that can be concluded from this study are as follows: 1. The artificial neural networks (ANN) have been proved its capability in predicting the ultimate load of FRP reinforced concrete beams, and it could be used this procedure as a reliable alternative to other complex or costly test procedures. 2. The proposed neural model, in the current study, has been found to be very excellent for prediction of the ultimate load of FRP reinforced concrete beams. 3. The configuration (11-10) for the proposed neural model was found to be very typical for prediction of the ultimate load of FRP reinforced concrete beams. 4. The overall average error, in ultimate load prediction, was 3.6% and 21.7% for the proposed neural model and the ACI 440.1R approach, respectively. So the proposed neural model gave more accurate results than the ACI 440.1R specifications and it could be used efficiently in predicting the ultimate load FRP reinforced concrete beams. Al-Qadisiyah Journal For Engineering Sciences, Vol. 10……No. 1….2017 17 5. The ACI 440.1R approach was shown to give, in general, an underestimated value for the ultimate load. References 1. Abdalla H. A., 2002, ''Evaluation of Deflection in Concrete Members Reinforced With Fibre Reinforced Polymer (FRP) Bars'', Composite Structures, 56, P. 63–71. 2. Abdul Hamid N. A., Thamrin R., and Ibrahim A., 2013, ''Shear Capacity of Non- Metallic (FRP) Reinforced Concrete Beams with Stirrups'', IACSIT International Journal of Engineering and Technology, Vol. 5, No. 5, P. 593-598. 3. 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Table (1) Input And Output Variables Variable Range Input variables: Width of beam, b, (mm) 80 – 500 Depth of beam, h, (mm) 100 – 590 Concrete compressive strength, f'c, (MPa) 13.7 – 85.6 Area of FRP bars, Af, (mm 2 ) 39.3 – 19635 FRP bars tensile strength, fu, (MPa) 126.2 – 2250 FRP bars elasticity modulus, Ef, (MPa) 30000 – 200000 Length of beam, L, (mm) 400 – 4200 Shear span ratio, m 0.273 – 0.47 Output variable: Ultimate load, P, (kN) 16 – 365.4 Table (2) Properties Of The Proposed Neural Model Network Nodes in 1 st hidden layer Nodes in 2 nd hidden layer Nodes in output layer Epochs MSE for training set MSE for testing set 11 – 10 11 10 1 616 0.000445 0.001069 Table (3) Actual And Predicted Ultimate Load Beam No. Type of FRP bars Concrete Compressive Strength, f’c (MPa) FRP reinforcement ratio to balanced ratio, (ef / ebf ) Ultimate load (kN) PANN /PEXP PACI /PEXP Actual PEXP Predicted By By Al-Qadisiyah Journal For Engineering Sciences, Vol. 10……No. 1….2017 21 ANN PANN ACI PACI 1 GFRP 24.5 2.67 75.2 74.2 42.5 0.987 0.565 2 GFRP 30.0 1.99 96.0 96.3 79.2 1.003 0.825 3 GFRP 27.6 0.42 33.7 33.9 31.6 1.006 0.938 4 GFRP 27.6 0.69 51.2 53.4 62.5 1.043 1.221 5 GFRP 38 4.05 40.7 40.5 34.7 0.995 0.853 6 GFRP 27.6 4.30 41.6 41.2 33.4 0.990 0.803 7 GFRP 27.6 3.44 127.4 118.6 75.4 0.931 0.592 8 GFRP 59.8 3.68 143.4 150.2 89.5 1.047 0.624 9 GFRP 56.3 5.58 169.8 164.6 102.8 0.969 0.605 10 GFRP 55.2 4.43 85.1 92.3 55.7 1.085 0.655 11 GFRP 39.6 3.38 134.9 140.5 82.2 1.042 0.609 12 BFRP 61.7 3.23 200.0 209.8 164.1 1.049 0.821 13 CFRP 40.1 1.76 170.5 162.7 162.0 0.954 0.950 14 CFRP 40.4 2.52 178.7 180.0 158.2 1.007 0.885 15 GFRP 39.3 3.36 162.3 161.9 127.4 0.998 0.785 16 GFRP 32.5 1.19 185.5 187.3 211.7 1.010 1.141 17 GFRP 41.4 1.28 154.1 134.9 77.9 0.875 0.506 18 GFRP 41.4 1.71 106.4 100.9 55.4 0.948 0.521 19 GFRP 29.8 1.67 80.0 76.0 70.0 0.950 0.875 20 GFRP 29.8 6.26 118.0 110.0 117.8 0.932 0.998 21 CFRP 29.8 0.76 76.0 74.0 63.8 0.974 0.839 22 CFRP 29.8 1.14 105.0 100.0 100.5 0.952 0.957 23 CFRP 29.8 1.81 125.0 123.0 117.2 0.984 0.938 24 GFRP 40.6 1.09 76.0 80.0 79.7 1.053 1.048 25 GFRP 40.0 5.74 112.0 118.0 138.4 1.054 1.236 26 CFRP 47.0 0.67 70.0 75.0 75.5 1.071 1.079 27 CFRP 44.7 1.34 100.0 101.0 124.4 1.010 1.244 28 CFRP 44.0 3.18 120.0 125.0 145.1 1.042 1.209 29 GFRP 30.0 3.61 123.2 127.8 129.1 1.037 1.048 30 CFRP 30.0 3.13 135.0 139.9 132.3 1.036 0.980 31 GFRP 48.0 4.89 135.0 130.7 104.3 0.968 0.773 32 GFRP 48.0 4.80 138.6 134.6 119.9 0.971 0.865 33 CFRP 48.0 4.25 155.0 144.8 107.3 0.934 0.692 34 GFRP 24.0 1.21 92.8 99.0 79.6 1.067 0.858 35 GFRP 24.0 1.82 125.6 132.1 93.2 1.052 0.742 Al-Qadisiyah Journal For Engineering Sciences, Vol. 10……No. 1….2017 22 36 GFRP 29.3 1.06 207.0 209.5 137.1 1.012 0.662 37 GFRP 29.3 2.28 307.0 302.7 192.6 0.986 0.627 38 GFRP 29.9 2.44 229.7 228.0 162.7 0.993 0.708 39 GFRP 36.5 2.12 227.0 228.0 177.4 1.004 0.781 40 GFRP 29.9 5.12 331.3 332.8 230.9 1.005 0.697 Average 1.001 0.844 Standard deviation 0.007 0.032 Table (4) Statistical comparison Norm Proposed neural model (NN1) ACI approach Mean absolute error (MAE) 4.4 31.4 Root mean squared error (RMSE) 5.7 41.7 Mean absolute percentage error (MAPE) 3.6 21.7 Fraction of variance (FOV) 0.992 0.582 Connection WeightsNodes Hidden Layer Output Layer Input Layer Input Signal Output Signal Figure (1) Architecture Of A Neural Network Al-Qadisiyah Journal For Engineering Sciences, Vol. 10……No. 1….2017 23 Figure (2) Artificial Neuron Model Figure (3) Four Point Loading Beam Figure (4) Proposed Neural Model Topology (m=a/L) Al-Qadisiyah Journal For Engineering Sciences, Vol. 10……No. 1….2017 24 Figure (5) Regression Analysis For Training Group Figure (6) Regression Analysis For Testing Group Al-Qadisiyah Journal For Engineering Sciences, Vol. 10……No. 1….2017 25 Figure (7) Comparison Between Predicted And Actual Loads