Document Type: Regular Article
Author
University of Wollongong, New South Wales, Australia
Abstract
Highlights
Keywords
Main Subjects
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.
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.
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:
|
(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.
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)
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.
[1] M. Mirrashid, "Earthquake magnitude prediction by adaptive neuro-fuzzy inference system (ANFIS) based on fuzzy C-means algorithm," Natural hazards, vol. 74, pp. 1577-1593, 2014.
[2] M. Mirrashid, M. Givehchi, M. Miri, and R. Madandoust, "Performance investigation of neuro-fuzzy system for earthquake prediction " Asian journal of civil enginering (BHRC), vol. 17, pp. 213-223, 2016.
[3] H. Naderpour and M. Mirrashid, "Compressive Strength of Mortars Admixed with Wollastonite and Microsilica," in Materials Science Forum, 2017, pp. 415-418.
[4] H. Naderpour and M. Mirrashid, "Application of Soft Computing to Reinforced Concrete Beams Strengthened with Fibre Reinforced Polymers: A State-of-the-Art Review," in Computational techniques for civil and structural engineering ed Stirlingshire, UK: Saxe-Coburg Publications, 2015, pp. 305-323.
[5] T. Alkhrdaji, M. Wideman, A. Belarbi, and A. Nanni, "Shear strength of RC beams and slabs. CCC2001, J. Figueiras, L. Juvandes, and R. Faria, eds," ed: AA Balkema Publishers, Netherlands, 2001.
[6] A. Ashour, "Flexural and shear capacities of concrete beams reinforced with GFRP bars," Construction and Building Materials, vol. 20, pp. 1005-1015, 2006.
[7] D. Deitz, I. Harik, and H. Gesund, "One-way slabs reinforced with glass fiber reinforced polymer reinforcing bars," Special Publication, vol. 188, pp. 279-286, 1999.
[8] N. Duranovic, K. Pilakoutas, and P. Waldron, "Tests on concrete beams reinforced with glass fibre reinforced plastic bars," Non-metallic (FRP) reinforcement for concrete structure, vol. 2, pp. 479-486, 1997.
[9] A. El-Sayed, E. El-Salakawy, and B. Benmokrane, "Shear strength of one-way concrete slabs reinforced with fiber-reinforced polymer composite bars," Journal of Composites for Construction, vol. 9, pp. 147-157, 2005.
[10] A. K. El-Sayed, E. F. El-Salakawy, and B. Benmokrane, "Shear capacity of high-strength concrete beams reinforced with FRP bars," ACI Structural Journal, vol. 103, p. 383, 2006.
[11] A. K. El-Sayed, E. F. El-Salakawy, and B. Benmokrane, "Shear strength of FRP-reinforced concrete beams without transverse reinforcement," ACI Structural Journal, vol. 103, p. 235, 2006.
[12] S. Gross, D. Dinehart, J. Yost, and P. Theisz, "Experimental tests of high-strength concrete beams reinforced with CFRP bars," in Proceedings of the 4th International Conference on Advanced Composite Materials in Bridges and Structures (ACMBS-4), Calgary, Alberta, Canada (quoted from Razaqpur and Isgor, 2006), 2004.
[13] S. P. Gross, J. R. Yost, D. W. Dinehart, E. Svensen, and N. Liu, "Shear strength of normal and high strength concrete beams reinforced with GFRP bars," in High performance materials in bridges, ed, 2003, pp. 426-437.
[14] A. Lubell, T. Sherwood, E. Bentz, and M. Collins, "Safe shear design of large wide beams," Concrete International, vol. 26, pp. 66-78, 2004.
[15] C. R. Michaluk, S. H. Rizkalla, G. Tadros, and B. Benmokrane, "Flexural behavior of one-way concrete slabs reinforced by fiber reinforced plastic reinforcements," ACI Structural Journal, vol. 95, pp. 353-365, 1998.
[16] Y. Mizukawa, Y. Sato, T. Ueda, and Y. Kakuta, "A study on shear fatigue behavior of concrete beams with FRP rods," Non-metallic (FRP) reinforcement for concrete structure, vol. 2, pp. 309-316, 1997.
[17] A. G. Razaqpur, B. O. Isgor, S. Greenaway, and A. Selley, "Concrete contribution to the shear resistance of fiber reinforced polymer reinforced concrete members," Journal of Composites for Construction, vol. 8, pp. 452-460, 2004.
[18] N. Swamy and M. Aburawi, "Structural implications of using GFRP bars as concrete reinforcement," in Proceedings of 3rd International Symposium, FRPRCS, 1997, pp. 503-510.
[19] M. Tariq and J. Newhook, "Shear testing of FRP reinforced concrete without transverse reinforcement," in Proceedings, Annual Conference of the Canadian Society for Civil Engineering, 2003, pp. 1330-1339.
[20] J. R. Yost, S. P. Gross, and D. W. Dinehart, "Shear strength of normal strength concrete beams reinforced with deformed GFRP bars," Journal of composites for construction, vol. 5, pp. 268-275, 2001.
[21] W. Zhao, K. Maruyama, and H. Suzuki, "Shear behavior of concrete beams reinforced by FRP rods as longitudinal and shear reinforcement," in RILEM PROCEEDINGS, 1995, pp. 352-352.
)