1. Introduction

Artificial neural networks (ANNs) are computing systems inspired by the biological neural networks. They learn to do tasks by considering examples and are based on a collection of connected units called artificial neurons. Each connection between neurons can transmit a signal to another neuron. The receiving neuron can process the signal and then signal downstream neurons connected to it. Neurons are organized in layers. Signals travel from the input layer to the output layer after traversing the hidden layers. particle swarm optimization (PSO) is a method that optimizes a problem by iteratively trying to improve a candidate solution. It solves a problem by having a population of candidate solutions. The use of these soft computing methods studied by a lot of researchers in many fields of engineering. In Structural engineering, such approaches are very popular and used for prediction [1-3] or for FRP material [4]. ANN and PSO are useful method to for complex problems. In this paper, shear strength of fiber reinforced polymer reinforced concrete flexural members without stirrups was estimated by ANN-PSO based on experimental data which were published in literatures.

2. Experimental Data

For train the neural network, the author used 108 pairs of data which were published by researchers [5-21]. In addition, 92 data used for training and 16 remained data applied for testing the model. The ANN was created based on six inputs including compressive strength of concrete (MPa), flexural FRP reinforcement ratio, modulus of elasticity for FRP, shear span-to-depth ratio, member web width (mm) and member effective depth (mm), while the shear strength (N) was considered as the output.

3. Neural network based PSO for prediction

Based on six inputs and one output, a neural network with one hidden layer and ten neurons in this layer was considered. For transfer function, tangent sigmoid and purelin used for hidden and output layer respectively. Before training the model, the database was normalized and used randomly. For normalization of the dataset, the author used Eq. 1:

where  is the normalized value of a certain parameter,  is the experimental value,  and  are the minimum and maximum values in the database for this parameter, respectively.

4. Results of the ANN-PSO

Based on the training data (92 set), the model was trained. After training, it was test to examine the ability of the proposed model for the considered prediction by test data (16 data). The results presented in Fig. 1-2.

Figure 1. The results for train data

The regression plots for the train data presented in Fig. 3. It was clear from the figure that the proposed model trained successfully and the error was small. Also it can be underestand that the PSO algorithm as a optimezed algorithm can be able for modeling. The different between the real values and the predicted values can be acceptable with R2=0.98 and 0.96 for train and test respectively. The histogram plots for train and test phases of the system also presented in Fig. 4 and 5.

Figure 2. The results for test data

Figure 3. Regression plots for normal values

Figure 4. Histogram plot for train data (Normal values)

Figure 5. Histogram plot for test data (Normal values)

6. Conclusions

Artificial neural network based on particle swarm optimization algorithm used to predict the shear strength of fiber reinforced polymer reinforced concrete flexural members without stirrups in this paper. The proposed model had six inputs and one hidden layer with ten neurons. The weights and the biases values of the network optimized by PSO algorithm to fine the best values. The network trained based on experimental data and also the proposed final network was test. It was concluded that ANN-PSO with a suitable accuracy can be used for the considered estimation.