FIRST OREDR RELIABILITY METHOD OF STRACTURS USINGA IMPRVED HARMONY SEARCH OPTIMIZATION

Document Type : Research Paper

Author

Abstract

The first order reliability method (FORM) is widely used to estimate the failure probability of structures. Appropriate evaluation of the reliability index is more important to estimate the failure probability in FORM. Generally, the iterative mathematical formula of FORM (i.e. Hasofer and Lind- Rackwitz and Fiessler (HL-RF)) was shown the instable solution of reliability index in highly nonlinear problems. The harmony search algorithm can be estimated the reliability index for concave and convex reliability problems due to capability and not need the gradient vector of random variables. In this paper, a global-best harmony search (GHS) algorithm with small harmony memory was proposed. In proposed GHS, a dynamical bandwidth, which is computed based on number of random variables, is proposed to adjust the harmony memory by a random generation with Normal distribution function. Accuracy and robustness of the proposed GHS have been compared with the HL-RF and stability transformation method (STM) through several limit state functions to that have been taken from. The results indicate that the HL-RF formula of FORM was not converged in several nonlinear examples. The proposed GHS was converged as similar as the STM results but it is more efficient )there is required less iterations to converge than STM). The GHS algorithm has top performance both of accuracy fast convergence rate.

Keywords

References

 
[1].      Keshtegar, B., Miri, M. (2013). “An enhanced HL-RF Method for the computation of structural failure probability based on relaxed approach”. Civil Engineering Infrastructures, Vol. 1(1), pp. 69-80.
[2].      کشته گر، ب. میری، م. (1393). "ارائه روشی جدید برای ارزیابی قابلیت اعتماد سازه‌ها". مجله مدل‌سازی در مهندسی، سال 12، شماره 36، ص. 29-42.
[3].      Santosh, T.V., Saraf, R.K., Ghosh, A.K., Kushwaha, H.S. (2006). “Optimum step lengthselection rule in modified HL-RF method for structural reliability”. International Journal of Pressure Vessels Piping, Vol. 83)10(, pp. 742-748.
[4].      Keshtegar, B., Miri, M. (2014). “Introducing Conjugate gradient optimization for modified HL-RF method”. Engineering Computations, Vol. 31(4), pp. 775-790.
[5].      Naess, A., Leira, B.J., Batsevych, O. (2009). “System reliability analysis by enhanced Monte Carlo simulation”. Structural Safety, Vol. 31, pp. 349–355.
[6].      Hasofer, A.M., Lind, N.C. (1974). “Exact and invariant second moment code format”. journal of engineering mechanics, Vol. 100(1), pp. 111-121.
[7].      Rackwitz, R., Fiessler, B. (1978). “Structural reliability under combined load sequences”. Computers and Structures, Vol. 9, pp.489–494.
[8].      Liu P.L., Derkiureghian, A. (1991). “Optimization algorithms for structural reliability”. Structural Safety, Vol. 9 (3), pp. 161–78.
[9].      Yang, D. (2010). “Chaos control for numerical instability of first order reliability method”. Communications in Nonlinear Science and Numerical Simulation, Vol. 5(10), pp. 3131-3141.
[10].  Gong, J.X., Yi, P. (2011). “A robust iterative algorithm for structural reliability analysis”. Structural and Multidisciplinary Optimization, Vol. 43(4), pp. 519–527.
[11].  Elegbede, C. (2005). “Structural reliability assessment based on particles swarm optimization”, Structural Safety, Vol. 27(2), pp. 171–186.
[12].  Geem, Z.W., Kim, J.H., Loganathan, G.V. (2001). “A new heuristic optimization algorithm: harmony search”. International Transactions of the Society for Modeling and Simulation, Vol. 76(2), pp. 60–68.
[13].  Mahdavi, M., Fesanghary, M., Damangir, E. (2007). “An improved harmony search algorithm for solving optimization problems”. Applied Mathematics and Computation, Vol. 188, pp. 1567–1579.
[14].  Kattan, A., Abdullah, R. (2013). “A dynamic self-adaptive harmony search algorithm for continuous optimization problems”. Applied Mathematics and Computation, Vol. 219, pp. 8542–8567.
[15].  Lee, K.S., Geem, Z.W. (2005). “A new meta-heuristic algorithm for continuous engineering optimization: harmony search theory and practice”. Computer Methods Applied Mechanic Engineering, Vol. 194(36-38), pp.3902–3933.
[16].  Sinsuphan, N., Leeton U., Kulworawanichpong, T. (2013). “Optimal power flow solution using improved harmony search method”. Applied Soft Computing, Vol. 13, pp. 2364–2374.
[17].  Ricart, J., H¨uttemann, G., Lima, J., Bar´an, B. (2011). “Multi-objective Harmony Search Algorithm Proposals”. Electronic Notes in Theoretical Computer Science, Vol. 281, pp. 51–67.
[18].  Omran, M.G.H., Mahdavi, M. (2008). “Global-best harmony search”. Applied Mathematics and Computation, Vol. 198, 643–656.
[19].  El-Abd, M. (2013). “An improved global-best harmony search algorithm”. Applied Mathematics and Computation, Vol. 222, pp. 94–106.
[20].  Zhao, Y.G., Lu, Z.H., (2007).” Fourth-Moment standardization for structural reliability assessment, Journal of Structural Engineering, Vol. 133(7), pp. 916–924,
[21].  Derkiureghian, A., Stefano, M.D. (1991). “Efficient algorithm for second-order reliability analysis”. Journal of Engineering Mechanics, Vol. 117(12), pp. 2904-2923.
 
Journal of Modeling in Engineering
Volume 15, Issue 51
October 2017
Pages 15-27

Files

History

  • Receive Date: 24 August 2014
  • Accept Date: 03 February 2016

Share

How to cite

Statistics