Introducing conjugate gradient optimization for modified HL-RF method

Purpose – Generally, iterative methods which have some instability solutions in complex structural and non-linear mechanical problems are used to compute reliability index. The purpose of this paper is to establish a non-linear conjugate gradient (NCG) optimization algorithm to overcome instability solution of the Hasofer-Lind and Rackwitz-Fiessler (HL-RF) method in first-order reliability analysis. The NCG algorithms such as the Conjugate-Descent (CD) and the Liu-Storey (LS) are used for determining the safety index. An algorithm is found based on the new line search in the reliability analysis. Design/methodology/approach – In the proposed line search for calculating the safety index, search direction is computed by using the conjugate gradient approach and the HL-RF method based on the new and pervious gradient vector of the reliability function. A simple step size is presented for the line search in the proposed algorithm, which is formulated by the Wolfe conditions based on the new and previous safet...

[1]  A. M. Hasofer,et al.  Exact and Invariant Second-Moment Code Format , 1974 .

[2]  R. Rackwitz,et al.  Structural reliability under combined random load sequences , 1978 .

[3]  R. Fletcher.  Practical Methods of Optimization , 1988 .

[4]  M. D. Stefano,et al.  Efficient algorithm for second-order reliability analysis , 1991 .

[5]  A. Kiureghian,et al.  Optimization algorithms for structural reliability , 1991 .

[6]  C. Storey,et al.  Efficient generalized conjugate gradient algorithms, part 1: Theory , 1991 .

[7]  R. Grandhi,et al.  Efficient safety index calculation for structural reliability analysis , 1994 .

[8]  Ramana V. Grandhi,et al.  Reliability based structural optimization - A simplified safety index approach , 1994 .

[9]  R. Grandhi,et al.  Safety index calculation using intervening variables for structural reliability analysis , 1996 .

[10]  Andrzej S. Nowak,et al.  Reliability of Structures , 2000 .

[11]  J. Beck,et al.  Estimation of Small Failure Probabilities in High Dimensions by Subset Simulation , 2001 .

[12]  Zhen-Jun Shi,et al.  Step-size estimation for unconstrained optimization methods , 2005 .

[13]  T. V. Santosh,et al.  Optimum step length selection rule in modified HL-RF method for structural reliability , 2006 .

[14]  Jinhua Guo,et al.  A new algorithm of nonlinear conjugate gradient method with strong convergence , 2008 .

[15]  Dixiong Yang,et al.  Chaos control of performance measure approach for evaluation of probabilistic constraints , 2009 .

[16]  Yunhai Xiao,et al.  Nonlinear Conjugate Gradient Methods with Sufficient Descent Condition for Large-Scale Unconstrained Optimization , 2009 .

[17]  Zengxin Wei,et al.  Globally convergent Polak-Ribière-Polyak conjugate gradient methods under a modified Wolfe line search , 2009, Appl. Math. Comput..

[18]  Dixiong Yang.  Chaos control for numerical instability of first order reliability method , 2010 .

[19]  Hiroshi Yabe,et al.  Nonlinear conjugate gradient methods with structured secant condition for nonlinear least squares problems , 2010, J. Comput. Appl. Math..