Optimum step length selection rule in modified HL–RF method for structural reliability

Santosh, T.V.; Saraf, R.K.; Ghosh, Ashish; Kushwaha, H.S.

doi:10.1016/j.ijpvp.2006.07.004

Cited by 68 publications

(38 citation statements)

References 8 publications

(21 reference statements)

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“…These methods may provide unstable results for highly nonlinear reliability problems [7,8,15,18]. However, the gradient and HL-RF method are FORM algorithms with a fast convergence rate because the step size in these approaches is selected equivalent to one, while the step size in the modified versions of FORMbased steepest descent search direction such as improved HL-RF [1,19], RHL-RF [11], and STM [8] is given less than 1 to achieve the stabilization. Hence, the improved versions of HL-RF may enhance the robustness of FORM formula compared to HL-RF for highly nonlinear problems but these approaches are computationally inefficient for moderately nonlinear or linear performance functions [7].…”

Section: Gradient Methodmentioning

confidence: 99%

“…The proposed MHL-RF method can be implemented for steel code calibration-based Iranian National Building code of strength and load in future, successfully. Figure 15 indicates the minimum reliability index based on the four failure modes in (16)- (19) of connection under various tensile forces. By increasing the load, the reliability index decreases.…”

Section: Connection Under Tensile Forcementioning

confidence: 99%

“…The HL-RF method was improved by Liu and der Kiureghian (1991) using a merit function to enhance the convergence properties. Santosh et al (2006) improved the HL-RF method based on Armijo rule. The convergence properties of HL-RF are improved based on the stability transformation method (STM) [8], the relaxed approach [10,11], conjugate search direction [7,[12][13][14], and sufficient descent condition [13].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Comparative Study of First-Order Reliability Method-Based Steepest Descent Search Directions for Reliability Analysis of Steel Structures

Makhduomi

Keshtegar

Shahraki

2017

Advances in Civil Engineering

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Three algorithms of first-order reliability method (FORM) using steepest descent search direction are compared to evaluate the reliability index of structural steel problems which are designed by the Iranian National Building code. The FORM formula is modified based on a dynamic step size which is computed based on the merit functions named modified Hasofer-Lind and Rackwitz-Fiessler (MHL-RF) method. The efficiency of the gradient, HL-RF, and MHL-RF method was compared for a bar structure under tensile capacity, a multispan beam under bending capacity, a connection under tension load, and a column under axial force. The results illustrated that the MHL-RF method is more efficient than the HL-RF and gradient method. The designed steel components by the Iranian National Building code showed good confidence levels with the reliability index in the range from 2.5 to 3.0.

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Section: Gradient Methodmentioning

confidence: 99%

Section: Connection Under Tensile Forcementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Comparative Study of First-Order Reliability Method-Based Steepest Descent Search Directions for Reliability Analysis of Steel Structures

Makhduomi

Keshtegar

Shahraki

2017

Advances in Civil Engineering

View full text Add to dashboard Cite

show abstract

“…Problem 7 [9]. The limit state function is hðxÞ ¼ x 3 1 þ x 3 2 À 18, the variables are statistically independent and normally distributed with parameters l 1 ¼ l 2 ¼ 10 and r 1 ¼ r 2 ¼ 5.…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…Santosh et al [9] presented an improvement to HLRF by using the same merit function of [7], combined with a linear search using the Armijo rule. Convergence proofs for the algorithm were not presented.…”

Section: Introductionmentioning

confidence: 99%

HLRF–BFGS optimization algorithm for structural reliability

Periçaro

Santos

Ribeiro

et al. 2015

Applied Mathematical Modelling

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a b s t r a c tIn this work we briefly discuss some concepts of structural reliability as well as the optimization algorithm that is commonly used in this context, called HLRF. We show that the HLRF algorithm is a particular case of the SQP method, in which the Hessian of the Lagrangian is approximated by an identity matrix. Motivated by this fact, we propose the HLRF-BFGS algorithm that considers the BFGS update formula to approximate the Hessian. The algorithm proposed herein is as simple as the HLRF algorithm, since it requires just one function and gradient evaluation at each iteration and the new iterate is given by a recursive formula. Comparative numerical experiments on a set of problems selected from the literature are presented to illustrate the performance of the algorithm and the results indicate that the HLRF-BFGS algorithm has the advantage of being more robust and efficient with respect to the function and gradient evaluation, than HLRF.

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Robust reliability‐based design approach by inverse FORM with adaptive conjugate search algorithm

Hanzo

Zhang

et al. 2023

Num Anal Meth Geomechanics

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The concept of reliability‐based design (RBD) of geotechnical works has seen great success in recent years, nevertheless, its application in real‐world engineering practice is still limited. This phenomenon could be mainly attributed to two aspects: the engineer's unfamiliarity of reliability algorithms even in their simplest forms, and the lack of direct connection between reliability algorithms and deterministic design tools. To promote the geotechnical RBD application, this study proposes an inverse first‐order reliability method (FORM) integrating adaptive conjugate direction search technique (RBD via conjugate FORM) to solve classical RBD problems where the number of (multiple) limit state functions is usually equal to the number of unknown design parameters. Notably, the RBD via conjugate FORM can readily back‐calculate those unknown design parameters subject to prescribed reliability index or probability of failure, by means of iterative evaluation of the parametric sensitivities. The proposed algorithm is first verified by several well‐documented examples. Comparative studies show that when the reliability problem to solve is highly nonlinear, the RBD results based on steepest descent search direction may fall in oscillation and non‐convergence, while the proposed RBD via conjugate FORM algorithm performs robustly and efficiently. It is then illustrated in combination with standalone numerical codes to conduct risk‐based optimization of unknown design parameters for two soil slope stability models. The first slope RBD model achieves designing the slope angle under specified reliability index, and the second slope RBD model is to optimize multiple design parameters of the stabilization pile, which can meet different slope reliability requirements under static and seismic loading conditions simultaneously.

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Optimum step length selection rule in modified HL–RF method for structural reliability

Cited by 68 publications

References 8 publications

A Comparative Study of First-Order Reliability Method-Based Steepest Descent Search Directions for Reliability Analysis of Steel Structures

A Comparative Study of First-Order Reliability Method-Based Steepest Descent Search Directions for Reliability Analysis of Steel Structures

HLRF–BFGS optimization algorithm for structural reliability

Robust reliability‐based design approach by inverse FORM with adaptive conjugate search algorithm

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