Keywords: stochastic, reliability, FORM, directional sampling, finite element analysis, industrial applications, approximation, simulation.

In this paper, a number of reliability methods are investigated with focus on the improvement of accuracy and efficiency, aiming at the application to large-scale industrial problems. These methods include approximation and simulation approaches, such as the widely known first-order reliability method (FORM) [1] and the directional sampling concept (DS) [1]. The methods are optimized, by increasing the robustness and keeping the computational cost to low levels, in order to enhance the applicability to a wide range of problems.

In the FORM framework, this is achieved by using variations of the method which improve its convergence. Therefore, different optimization algorithms [2] are considered for the solution of the underlying optimization problem of minimizing the distance from the limit state function to the origin of the standard normal space. These algorithms include the HL-RF [3,4] and improved HL-RF method [5], the gradient projection (GP) method [6] and a proposed improved GP method. The two improved versions of the methods presented a robust convergence behaviour, while the proposed method appeared to be more efficient than the improved HL-RF method, in the examples considered.

On the other hand, the DS method is combined with the use of a polynomial meta-model for the approximation of an adaptive response surface [7]. In addition, smart techniques that select an optimum sample (point-set) distribution, are utilized [8]. These include a geometric [9,10] and a physical approach [8]. It is shown that these improvements lead to more accurate solutions along with a reduction of the computational effort.

1

O. Ditlevsen, H.O. Madsen, "Structural Reliability Methods", Wiley, Chichester, United Kingdom, 1996.

2

P.-L. Liu, A. Der Kiureghian, "Optimization Algorithms for Structural Reliability", Structural Safety, 9, 161-177, 1991. doi:10.1016/0167-4730(91)90041-7

3

A. M. Hasofer, N. C. Lind, "Exact and Invariant Second Moment Code Format", Journal of Engineering Mechanics, 100, 111-121, 1974.

4

R. Rackwitz, B. Fiessler, "Structural Reliability under Combined Random Load Sequences", Computers and Structures, 9(5), 484-494, 1978. doi:10.1016/0045-7949(78)90046-9

5

Y. Zhang, A. Der Kiureghian, "Two Improved Algorithms for Reliability Analysis", in "Proceedings of the 6th IFIP WG7.5 Working Conference on Reliability and Optimization of Structural Systems", R. Rackwitz, G. Augusti, A. Borri, (Editors), Springer, Assisi, Italy, 297-304, 1995.

6

J. B. Rosen, "The Gradient Projection Method for Nonlinear Programming. Part II. Nonlinear Constraints", Journal of the Society for Industrial and Applied Mathematics, 9, 514-532, 1961. doi:10.1137/0109044

7

L. Schueremans, D. Van Gemert, "Benefit of Splines and Neural Networks in Simulation Based Structural Reliability Analysis", Structural Safety, 27, 246-261, 2005. doi:10.1016/j.strusafe.2004.11.001

8

J. Nie, B.R. Elingwood, "Directional Methods for Structural Reliability Analysis", Structural Safety, 22, 233-249, 2000. doi:10.1016/S0167-4730(00)00014-X

9

S. Katsuki, D.M. Frangopol, "Hyperspace Division Method for Structural Reliability", Journal of Engineering Mechanics, 120(11), 2405-2427, 1994. doi:10.1061/(ASCE)0733-9399(1994)120:11(2405)

10

L. Lovisolo, E.A.B. da Silva, "Uniform Distribution of Points on a Hypersphere with Applications to Vector Bit-plane Encoding", IEE Proceedings - Vision, Image and Signal Processing, 148, 187-193, 2001. doi:10.1049/ip-vis:20010361

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