JILSA  Vol.6 No.4 , November 2014
Application of the Adaptive Neuro-Fuzzy Inference System for Optimal Design of Reinforced Concrete Beams
Using a genetic algorithm owing to high nonlinearity of constraints, this paper first works on the optimal design of two-span continuous singly reinforced concrete beams. Given conditions are the span, dead and live loads, compressive strength of concrete and yield strength of steel; design variables are the width and effective depth of the continuous beam and steel ratios for positive and negative moments. The constraints are built based on the ACI Building Code by considering the strength requirements of shear and the maximum positive and negative moments, the development length of flexural reinforcement, and the serviceability requirement of deflection. The objective function is to minimize the total cost of steel and concrete. The optimal data found from the genetic algorithm are divided into three groups: the training set, the checking set and the testing set for the use of the adaptive neuro-fuzzy inference system (ANFIS). The input vector of ANFIS consists of the yield strength of steel, compressive strength of concrete, dead load, span, width and effective depth of the beam; its outputs are the minimum total cost and optimal steel ratios for positive and negative moments. To make ANFIS more efficient, the technique of Subtractive Clustering is applied to group the data to help streamline the fuzzy rules. Numerical results show that the performance of ANFIS is excellent, with correlation coefficients between the three targets and outputs of the testing data being greater than 0.99.

Cite this paper
Yeh, J. and Yang, R. (2014) Application of the Adaptive Neuro-Fuzzy Inference System for Optimal Design of Reinforced Concrete Beams. Journal of Intelligent Learning Systems and Applications, 6, 162-175. doi: 10.4236/jilsa.2014.64013.
[1]   Holland, J.H. (1975) Adaptation in Natural and Artificial Systems. The University of Michigan Press, Ann Arbor.

[2]   Goldberg, D.E. (1989) Genetic Algorithms in Search, Optimization and Machine Learning. Addison Wesley, Reading.

[3]   Coello, C.C., Hernandez, F.S. and Farrera, F.A. (1997) Optimal Design of Reinforced Concrete Beams Using Genetic Algorithms. Expert Systems with Applications, 12, 101-108.

[4]   Coello, C.A. and Christiansen, A.D. (2000) Multiobjective Optimization of Trusses Using Genetic Algorithms. Computers and Structures, 75, 647-660.

[5]   Cheng, J. and Li, Q.S. (2008) Reliability Analysis of Structures Using Artificial Neural Network Based Genetic Algorithms. Computer Methods in Applied Mechanics and Engineering, 197, 3742-3750.

[6]   Belevi?ius, R. and ?e?ok, D. (2008) Global Optimization of Grillages Using Genetic Algorithms. Mechanika, 6, 38-44.

[7]   Sesok, D. and Belevicius, R. (2008) Global Optimization of Trusses with a Modified Genetic Algorithm. Journal of Civil Engineering Management, 14, 147-154.

[8]   Chan, C.M., Zhang, L.M. and Jenny, T.N. (2009) Optimization of Pile Groups Using Hybrid Genetic Algorithms. Journal of Geotechnical and Geoenvironmental Engineering, 135, 497-505.

[9]   McCulloch, W.S. and Pitts, W. (1943) A Logical Calculus of Ideas Immanent in Nervous Activity. Bulletin of Mathematical Biophysics, 5, 115-133.

[10]   Rumelhart, D.E., McClelland, J.L. and The PDP Research Group (1986) Parallel Distributed Processing: Explorations in the Microstructure of Cognition. Volume 1: Foundations. MIT Press, Cambridge.

[11]   Zadeh, L.A. (1965) Fuzzy Sets. Information and Control, 8, 338-353.

[12]   Klaua, D. (1965) über einen Ansatz zur mehrwertigen Mengenlehre. Monatsberichte der Deutschen Akademie der Wissenschaften zu Berlin, 7, 859-876.

[13]   Bezdek, J.C. and Harris, J.D. (1978) Fuzzy Partitions and Relations: An Axiomatic Basis for Clustering. Fuzzy Sets and Systems, 1, 111-127.

[14]   Kuzmin, V.B. (1982) Building Group Decisions in Spaces of Strict and Fuzzy Binary Relations. Nauka, Moscow.

[15]   De Cock, M., Bodenhofer, U. and Kerre, E.E. (2000) Modelling Linguistic Expressions Using Fuzzy Relations. Proceedings 6th International Conference on Soft Computing, Iizuka, 1-4 October 2000, 353-360.

[16]   Jang, J.S.R. (1993) ANFIS: Adaptive-Network-Based Fuzzy Inference System. IEEE Transactions on Systems, Man and Cybernetics, 23, 665-685.

[17]   Klir, G.J. and Yuan, B. (1995) Fuzzy Sets and Fuzzy Logic: Theory and Applications. Prentice-Hall International, Inc., Englewood Cliffs.

[18]   Chang, F.J. and Chang, Y.T. (2006) Adaptive Neuro-Fuzzy Inference System for Prediction of Water Level in Reservoir. Advances in Water Resources, 29, 1-10.

[19]   Valizadeh, N., El-Shafie, A., Mukhlisin, M. and El-Shafie, A.H. (2011) Daily Water Level Forecasting Using Adaptive Neuro-Fuzzy Interface System with Different Scenarios: Klang Gate, Malaysia. International Journal of the Physical Sciences, 6, 7379-7389.

[20]   Folorunsho, J.O., Iguisi, E.O., Mu’azu, M.B. and Garba, S. (2012) Application of Adaptive Neuro Fuzzy Inference System (Anfis) in River Kaduna Discharge Forecasting. Research Journal of Applied Sciences, Engineering and Technology, 4, 4275-4283.

[21]   Lin, L.C. and Chang, H.K. (2008) An Adaptive Neuro-Fuzzy Inference System for Sea Level Prediction Considering Tide-Generating Forces and Oceanic Thermal Expansion. Terrestrial Atmospheric and Oceanic Sciences, 19, 163-172.

[22]   Heydari, M. and Talaee, P.H. (2011) Prediction of Flow through Rockfill Dams Using a Neuro-Fuzzy Computing Technique. The Journal of Mathematics and Computer Science, 2, 515-528.

[23]   Wang, A.P., Liao, H.Y. and Chang, T.H. (2008) Adaptive Neuro-Fuzzy Inference System on Downstream Water Level Forecasting. 2008 Fifth International Conference on Fuzzy Systems and Knowledge Discovery, 3, 503-507.

[24]   Mukerji, A., Chatterjee, C. and Raghuwanshi, N.S. (2009) Flood Forecasting Using ANN, Neuro-Fuzzy and Neuro-GA Models. Journal of Hydrologic Engineering, 14, 647-652.

[25]   Kwong, C.K., Wong, T.C. and Chan, K.Y. (2009) A Methodology of Generating Customer Satisfaction Models for New Product Development Using a Neuro-Fuzzy Approach. Expert Systems with Applications, 36, 11262-11270.

[26]   Leung, K.F., Leung, F.H.F., Lam, H.K. and Ling, S.H. (2007) Application of a Modified Neural Fuzzy Network and an Improved Genetic Algorithm to Speech Recognition. Neural Computing and Applications, 16, 419-431.

[27]   Yeh, J.P. and Chang, Y.C. (2012) Comparison between Neural Network and Adaptive Neuro-Fuzzy Inference System for Forecasting Chaotic Traffic Volumes. Journal of Intelligent Learning Systems and Applications, 4, 247-254.

[28]   ACI (2008) Building Code Requirements for Structural Concrete (ACI 318-08) and Commentary (ACI 318R-08). American Concrete Institute, Farminton Hills.

[29]   The MathWorks Inc. (2012) Global Optimization Toolbox: User’s Guide. The MathWorks, Inc., Natick.

[30]   Conn, A.R., Gould, N.I.M. and Toint, Ph.L. (1991) A Globally Convergent Augmented Lagrangian Algorithm for Optimization with General Constraints and Simple Bounds. SIAM Journal on Numerical Analysis, 28, 545-572.

[31]   Conn, A.R., Gould, N.I.M. and Toint, Ph.L. (1997) A Globally Convergent Augmented Lagrangian Barrier Algorithm for Optimization with General Inequality Constraints and Simple Bounds. Mathematics of Computation, 66, 261-288.

[32]   Jang, J.S.R., Sun, C.T. and Mizutani, E. (1997) Neuro-Fuzzy and Soft Computing: A Computational Approach to Learning and Machine Intelligence. Prentice-Hall, Upper Saddle River.

[33]   Sugeno, M. (1985) Industrial Applications of Fuzzy Control. Elsevier Science Pub. Co., Amsterdam.

[34]   Chopra, S., Mitra, R. and Kumar, V. (2006) Analysis of Fuzzy PI and PD Type Controllers Using Subtractive Clustering. International Journal of Computational Cognition, 4, 30-34.

[35]   Chiu, S. (1994) Fuzzy Model Identification Based on Cluster Estimation. Journal of Intelligent and Fuzzy Systems, 2, 267-278.