NEURAL NETWORK PREDICTION OF CONFINED PEAK STRESSES OF RC COLUMNS

The research presents ANN ("Artificial Neural Networks") estimation of confined peak strength for R.C columns. The modeling of the strength of reinforced concrete columns by uses of the (FEM) finite element method gets many difficulties, starting in geometric representation down to nonlinearities due to loads. The use of neural networks trained well can give us a model that can be utilized as an alternative and successful model for those columns. Experimental sets of data for concrete of square and circular concrete columns were gathered from many researches to develop an Artificial Neural Network formula as input data set parameters consist of ultimate strengths, size of mainly longitudinal and ties reinforcements, compressive concrete strength, thickness of concrete cover for reinforcement, specimen geometric dimension, and stirrup bars spacing. Confined Peaking Compressive Strength (CPCS) of square and circular concrete columns is predicted by neural networks technique and sorted with analytical models and found that they are scientifically accepted. The prediction was performed by package program (Mat Lap).


INTRODUCTION
The effectiveness of various parameters was studied on the CPCS. In many studies these analytical and empirical studies have been investigating by many researchers. Therefore many analytical approaches have been presented for predicting CPCS for columns. These analytical approaches were presented in the tables and references by means of stress-strain relationship models. These analytical models can be listed in the literature by Table 1:  Mander et al., 1988 "( f cc =f' co (-1.254+2.254(1+7.94f' l /f' co -2f' l /f' co ) 0.5 where, f' l = k e ρ s f yh /2, k e =(1-s/2d) n /(1-ρ cc ) and n=2 for circular hoops )" Sakai et al., 2000 "( f ' cc Table 2 as shown below presents the data sets used from the experimental studies presented by Mander et al. (1988b); Sakai et al. (200); and Sakai (2001). The values of the parameters are drawn:

EXPERIMENTAL DATABASE FOR NN MODEL
1. Compressive strength test of unconfined concrete for cylinder, f'c.
2. Compressive strength test of unconfined concrete specimen (similar in size and configuration of geometry), f'co.
3. Diameter of confined concrete of circular column, d.
5. Yield strength of ties reinforcement, f yh .
6. Ratio of volume of ties reinforcement to volume of concrete surrounding by tie, ρs.
7. Spacing between two tie bars or spiral pitch, s.
8. Ratio of main reinforcement to area of concrete surrounding by tie, ρcc, and.

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Luay M. Al-Shather 14 circular columns used in this research. The 6 specimens' that got from Mander et al. (1988) are 500 millimeter in diameter and 1,500 millimeter in rise. The effective diameters of the confined concrete area are 438 mm. All column specimens get ties (lateral) and main (longitudinal) bars with changing diameter of bars and the spacing between tie bars. The 4 specimens presented by Sakai et al. (2000) are of 180 millimeter in diameter and having 600 millimeter in rise, and having ties and main reinforcement (ten bars having 6.35 millimeter in diameter). The 4 tested specimens of Sakai (2001) have 300 millimeters in diameter (280 millimeter enclosed core diameters) and 900 millimeter specimen in rise. 16 main bars having approximated diameter of 10 millimeter were tested. Column's series C1 have one to three layers of tie reinforcement. 6 sets of experimental data tended to (square) RC column specimens have been collected from Yong et al. (1988). Geometric and mechanical properties of confined core of column specimens, tie reinforcement, and main bars were taken as different values for this research. These changed values represent concrete strength obtained from compressive strength from experimental tests, f'c , edge dimension of a cross section of square column, b, and specimen highness, H, concrete reinforcement cover, cc, yield strength of tie reinforcement, fyh, and main reinforcement, fyl, tie bar size, Dt, the bar diameter of main reinforcement, Dl, tie reinforcement spacing, s. The types of tie reinforcement configuration are given in Table 3.

NEURAL NETWORK ARCHITECTURE
Artificial neural networks ANNs are computer models of simulation of what happens between nerve cells (neurons) in the nervous system of human. The neurological unit called neuron is the main unit in the processing of information related to the neural network model. The nerve cell (neuron) consists of four parts as main parts can be shown in Fig. 1. The dendrites will collect the input data as signals from other neurons and get these data to another neuron (Ertekin Öztekin, 2012).
The process of replacing the transfer of signals using mathematical simulations, such as replacing input paths by connection weights, important activation functions, and output paths instead of the dendrite wires. A mathematical formulation in neuron calculates the sum of weighted of its input sets signals by using Equation 1, and it will give output signals by using activation function. A standard function of activation defined by Equation 2 was used in this research. These formulas will produce outputs sets by neurons that are either used as input data sets for next layer of neurons or used as results for final output (Andres et al., 2003 andErtekin Öztekin, 2012). (1) ( 2) Where: wij weight between neurons i and j, xi input for unit of neuron, uj summation of multi -inputs, bj the bias, and f(uj) output of neuron In this research can be use of (feed forward) multi-layer of NNs and (back propagation feed). A feed forward of ANNs and an artificial (neuron) can be seen in Fig. 1-a and in Fig. 1-b, respectively. A feed forward NN with multi-layer consist of an input data layer with one or multi-hidden layers and a targeted output layer. The input and output layers having the same numbers in neurons of variables and outputs case, respectively. There is a real difficulty in determining numbers of neurons and the quintets of layers in the hidden layer, and it's clear and visible in feed forward NN studies. This determination of the number of layers and neurons would be through the use of trial and error sequences of approach and depending on type of the problem. Bias values and Synaptic weights values can be fed at the beginning of the training phase of NN randomly with use of back propagation technic. After the neural network outputs provide the NN will determine the errors by comparing the outputs obtained with the desired outputs and returned account configuration process in the neural network to get to the outputs of convincing scientifically. Through the back propagation of network in the process of producing the Synaptic weights will be recalculated with new values (Ertekin Öztekin, 2012).

NEURON MODEL
A perceptron neuron, which uses in MATLAB Version 4.0 is hard-limit transfer function hardlim, is shown below.
w1j variable represents of the weight of each external input. The transfer function will collect sum of the input weights.
The transfer function (hard-limit) gives the ability to classify and evaluate the input vectors to isolate the input space available to the two regions. For example, outputs will be 0 if the net value of input n is less than (zero), or one if the net value of input n is (zero) or more in value. The hard limit neuron unit input space has the weights value (Howard and M. Beale): W1,1= -1 , W1,2= 1 and a bias = 1.

NETWORK VALIDATION AND ERROR ANALYSIS
The use of statistical measurement equations to estimate the level of the error in the outputs makes use of neural network model is valid and acquires accepted scientific confidence. So, it can be accomplished by the use of mean absolute error (MAE), root mean squared error (RMSE), and mean squared error (MSE). Mean absolute percent error (MAPE) equations are listed below. (3) The y The target output j

NETWORK DATA PREPARATION
Neural networks will be affected by the absolute magnitudes of the inputs and outputs because of its high sensitivity, so it's better to minimize this effect to control numerical overflow. Therefore all inputs data and outputs data to a NN were scaled; as shown in Table  4. Because of the sigmoidal function characteristic which is nearly to values (0 and 1), the derivative equal or near to values (0 and 1) will get a zero value in magnitude, and this will get to slow learning as a result of very small signal. Therefore, it's better to avoid the slow rate of NN learning close to the end points (output range); it is submitted to give range of the data between (0.1 and 0.9) as interval of scaled range (Teh, 1997). A submitted scaling equation presented by Tsoukalas and Uhrig (1997) for a variable limited to minimum (xmin) and maximum (xmax) values listed in Table 4 was used in this NN model and it's written as;  For square columns as shown in Fig. 2-b, the ANN models have eleven input nodes, one output nodes, and the hidden layer nodes will be varied in number and notified by experimentation. Connection weights between (0 and 1) were selected randomly by computer program in Mat lab software. Learning rate was 1. MAE, RMSE, MSE, and MAPE were employed for the checking of computation assessments of different NNs architecture. The trail code (9-1-2-1) architecture was chosen as the preferable ANNs architecture. The Selection of ANN architecture has 9-7-7-2 configuration as shown in Fig. 3.

TRAINING AND TESTING OF ANN MODEL
 14 data sets 4 confined materials of circular RC column data were chosen randomly for testing. Remaining 10 data sets can be used for training data sets. Training phase of the NN model showed Fig. 2-a was completed at the few seconds the epoch with 0.269 % error.
 6 data sets 2 confined materials of square RC column data were chosen randomly for testing. Remaining 4 data sets can be used as training data sets. Training phase of the NN model showed Fig. 2-b was completed at the few seconds the epoch with 0.395 % error, with a personal computer dell core I-7 for this NN architecture. The error of output was evaluated by use the mean squared error for each of the 5 seconds epochs during process of the training phase, and the NN outputs error graphic shown in Fig. 4 was evaluated at the end of training phase process. When the training phase processes were completed, the artificial neural networks model was tested and evaluated, and learning will be achieved with desired accuracy, see Table 3.

Square Concrete Columns:
Evaluation the values of confined concrete strength, fcc (model) by artificial neural networks model was contrasted with analytical experimental models offered by Yong et al. 1988. The comparison between the prediction and analytical results was achieved under the ratio of fcc(model) / fcc (by experiment) and the statistical characteristic values, which are defined previously ( MAE,RMSE,MSE,MAPE,and R2). The ratio of fcc (model) / fcc(experimental) for artificial neural networks model is shown in Fig. 5-a. As seen from this figure, the prediction of output values obtained by artificial neural networks model is mostly closer to the desired results (experimental). Computed for ANNs predictions output are lowest in the outcome than analytical models and the result can be corrected by improving the performance of the artificial neural networks model.

Circular Concrete Columns:
Predicted confined concrete strength values for circular concrete columns by ANNs were compared with analytical formulas given by Mander et al., 1988b;Sakai et al., 2000;and Sakai, 2001).  For a given transverse reinforcement (tie) spacing, s, the amount of reinforcement ratio, ρs , corresponding to tie reinforcement bars in (1 to 3) layer may be selected. As a result, an artificial neural model may be examined its demeanor due to changing of amount of reinforcement ratio, for fixed tie spacing (s). Fig. 6 shows the curves of peak confined concrete stresses for constant (tie) spacing, s, of the N 1-7-2 model for the circular columns. It is noticed that the peak confined concrete stress raises as the amount of tie reinforcement bars is increased for a fixed transvers reinforcement (tie) spacing, (for ρs = 2.5) the increase in f'cc =17.7 MPa, 87.2%).

 Varying Main Bars Steel Ratio
The both of circular and square columns spaceman's were examined for the NN 1-7-2 model when the main steel bars ratio, ρcc , is varied from 1.2% to 3%. All other needed input parameters were identified. In Fig. 7, the percentage value of f'cc was increased from (28.3 to 35) MPa, 4.37 % for (C1-20 to C1-60) columns. The number of longitudinal bars has a minor effect on confined stress. This fact was also noticed by Mander et al. (1988) in their works.

CONCLUSION
An artificial neural networks application technology used in this research to predict the confined concrete compressive strength of circular and square concrete column sections. The best result was obtained for many trail and evaluation of these results. These results were compared with both of the analytical and experimental works. The amendment artificial neural model estimated closer outputs to the many experimental and analytical model results. This conclusion comes to light the ability to use the developed NN model to estimate the confined compressive strength of reinforced concrete columns for high strength (f'c = 88.6 -93.5) MPa for square concrete columns and normal strength (f'c = 19.4 -31 MPa) for circular concrete columns. Many different types of confinement configurations were illustrated in this research. The percentage of errors given by (MAPE) of testing output sets was obtained 0.113334 and 0.132646, respectively. The final errors were computed below 12 % for testing sets.
Future study could develop a NN model to include other variables are set to study the effect of these variables in clear and them, like hooks in tie angle , modulus of elasticity of materials.
Where it is not used in this research.