An Enhanced HL-RF Method for the Computation of Structural Failure Probability Based On Relaxed Approach

Document Type: Research Papers

Authors

Department of Civil Engineering, Faculty of Engineering, University of Sistan and Baluchestan

Abstract

The computation of structural failure probability is vital importance in the reliability analysis and may be carried out on the basis of the first-order reliability method using various mathematical iterative approaches such as Hasofer-Lind and Rackwitz-Fiessler (HL-RF). This method may not converge in complicated problems and nonlinear limit state functions, which usually shows itself in the form of periodic, bifurcation and chaos solution. In this paper, the HL-RF method has been improved based on the relaxed method to overcome these numerical instabilities. An appropriate relaxed coefficient has been defined, ranging between 0 and 1, to enhance the HL-RF method. This coefficient can be computed using the information from the new and previous iterations of the HL-RF algorithm based on second-order fitting. Capability, robustness and efficiency of the proposed algorithm have been studied by results of several examples compared to the HL-RF. Results illustrated that the proposed method is more efficient and robust in the computation of the failure probability compared to the HL-RF method.

Keywords


Choi, S.K., Grandhi, R.V. and Canfield, R.A. (2007). Reliability-based structural design, Springer-Verlag, London.

Elegbede, C. (2005). “Structural reliability assessment based on particles swarm optimization”, Structural Safety, 27(2), 171–186.

Hasofer, A.M. and Lind, N.C. (1974). “Exact and invariant second moment code format”, Journal of the Engineering Mechanics Division, 111(21), 111-121.

Lee, J.O., Yang, Y.S. and Ruy, W.S. (2002). “A comparative study on reliability-index and target-performance-based probabilistic structural design optimization”, Computers and Structures, 80(3-4), 257–269.

Liu, P.L. and Kiureghian, A.D. (1991). “Optimization algorithms for structural reliability”, Structural Safety, 9(3), 161–178.

Luo, Y., Zhan, K. and Li, A. (2009). “Structural reliability assessment based on probability and convex set mixed model”, Computers and Structures, 87(21), 1408–1415.

Naess, A., Leira, B.J. and Batsevych, O. (2009). “System reliability analysis by enhanced Monte Carlo simulation”, Structural Safety, 31(5), 349–355.

Nowak, A.S. and Collins, K.R. (2000). Reliability of Structures, McGraw-Hill, New York.

Rackwitz, R. and Fiessler, B. (1978). “Structural reliability under combined load sequences”, Computers and Structures, 9(8), 489–494.

Rao, S.S. (1996). “Engineering optimization, theory and practice”, Wiley, New York.

Santosh, T.V., Saraf, R.K., Ghosh, A.K. and Kushwaha, H.S. (2006). “Optimum step length selection rule in modified HL-RF method for structural reliability”, International journal of Pressure Vessels Piping, 83(10), 742–748.

Wang, L.P. and Grandhi, R.V. (1994). “Efficient safety index calculation for structural reliability analysis”, Computers and Structures, 52(1), 103–111.

Wang, L.P. and Grandhi, R.V. (1996). “Safety index calculation using intervening variables for structural reliability analysis”, Computers and Structures, 59(6), 1139–1148.

Yang, D. (2010). “Chaos control for numerical instability of first order reliability method”, Communications in Nonlinear Science and Numerical Simulation, 15(10), 3131–3141.

Yang, D., Li, G. and Cheng, G. (2006). “Convergence analysis of first order reliability method using chaos theory”, Computers and Structures, 84(8-9), 563–571.