HLRF–BFGS optimization algorithm for structural reliability

Periçaro, Gislaine Aparecida; Santos, Sérgio Rodrigo Quadros dos; Ribeiro, Ademir A.; Matioli, Luiz Carlos

doi:10.1016/j.apm.2014.10.024

Cited by 66 publications

(20 citation statements)

References 20 publications

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“…This HLRF-based method was found to have a fast convergence as demonstrated by the numerical examples considered by Der Kiureghian et al [11]. However, when the limit state function is highly nonlinear, this method may converge slowly [18].…”

Section: Mathematical Problems In Engineeringmentioning

confidence: 98%

“…In inverse-FORM, the HLRF-based algorithm, the Hessian of the Lagrangian is approximated by the identity matrix for every iteration as shown by Periçaro et al [18]. However, the proposed hybrid method uses the BFGS update formula in some iterations to calculate the Hessian of the Lagrangian.…”

Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

“…Note that, in (18) and (19), the Hessian of the Lagrangian for the th iteration is given by the BFGS matrix B . The BFGS matrix in each iteration is updated using the BFGS update formula shown in (20).…”

Section: Inverse-form Algorithmmentioning

confidence: 99%

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HLRF‐BFGS‐Based Algorithm for Inverse Reliability Analysis

Ramesh

Mirza

Kang

2017

Mathematical Problems in Engineering

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This study proposes an algorithm to solve inverse reliability problems with a single unknown parameter. The proposed algorithm is based on an existing algorithm, the inverse first-order reliability method (inverse-FORM), which uses the Hasofer Lind Rackwitz Fiessler (HLRF) algorithm. The initial algorithm analyzed in this study was developed by modifying the HLRF algorithm in inverse-FORM using the Broyden-Fletcher-Goldarb-Shanno (BFGS) update formula completely. Based on numerical experiments, this modification was found to be more efficient than inverse-FORM when applied to most of the limit state functions considered in this study, as it requires comparatively a smaller number of iterations to arrive at the solution. However, to achieve this higher computational efficiency, this modified algorithm sometimes compromised the accuracy of the final solution. To overcome this drawback, a hybrid method by using both the algorithms, original HLRF algorithm and the modified algorithm with BFGS update formula, is proposed. This hybrid algorithm achieves better computational efficiency, compared to inverse-FORM, without compromising the accuracy of the final solution. Comparative numerical examples are provided to demonstrate the improved performance of this hybrid algorithm over that of inverse-FORM in terms of accuracy and efficiency.

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Section: Mathematical Problems In Engineeringmentioning

confidence: 98%

Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

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HLRF‐BFGS‐Based Algorithm for Inverse Reliability Analysis

Ramesh

Mirza

Kang

2017

Mathematical Problems in Engineering

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“…The CHL-RF algorithm can generally improve the convergence rate, but its performance depends strongly on the choice of the conjugate gradient factor and step length. In addition, there are other algorithms similar to the FORM, such as the first-order saddlepoint approximation methods [35], HLRF-BFGS algorithm [36], and hybrid particle swarm optimization algorithm [37].…”

Section: Introductionmentioning

confidence: 99%

A Novel Algorithm for Structural Reliability Analysis Based on Finite Step Length and Armijo Line Search

Huang

2019

Applied Sciences

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This paper presents a novel algorithm for structural reliability analysis based on the finite step length and Armijo line search to remove the drawbacks of the Hasofer–Lind and Rakwitz–Fiessler (HL-RF) algorithm that may be subjected to non-convergence in the first-order reliability method (FORM). Initially, the sensitivity factor with finite step length is introduced for preventing the iterative process of the algorithm from entering a periodic loop. Subsequently, an optimization method based on the sufficient descent condition with the Armijo line search technique is proposed. With that, the initial step length and adjusting coefficient are optimized to enhance the applicability of the algorithm emphatically for highly nonlinear functions. A comparison analysis is carried out between the proposed algorithm and existing FORM-based algorithms to validate the robustness and efficiency of the proposed algorithm. The results of this demonstrate that the proposed algorithm is superior to the HL-RF algorithm in terms of robustness and surpass the other existing FORM-based algorithms in connection to efficiency.

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“…Among the various existing algorithms, HLRF algorithm (see Appendix), proposed by Hasofer and Lind [64] and Rackwitz and Fiessler [65], was employed. The algorithm requires least amount of storage, has lower number of computations and converges fast for most situations [66]. The HLRF algorithm was improved in this paper and combined with iHLRF algorithm that was developed by Zhang and Kiureghian [67] by introducing a non-differentiable merit function and an Armijo rule to select the step size in the linear search.…”

Section: Assembly Simulation and Optimizationmentioning

confidence: 99%

Tolerance analysis — Form defects modeling and simulation by modal decomposition and optimization

Homri

Goka

Levasseur

et al. 2017

Computer-Aided Design

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is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. Tolerance analysis aims on checking whether specified tolerances enable functional and assembly requirements. The tolerance analysis approaches discussed in literature are generally assumed without the consideration of parts' form defects. This paper presents a new model to consider the form defects in an assembly simulation. A Metric Modal Decomposition (MMD) method is henceforth, developed to model the form defects of various parts in a mechanism. The assemblies including form defects are further assessed using mathematical optimization. The optimization involves two models of surfaces: real model and difference surface-base method, and introduces the concept of signed distance. The optimization algorithms are then compared in terms of time consumption and accuracy. To illustrate the methods and their respective applications, a simplified over-constrained industrial mechanism in three dimensions is also used as a case study.

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HLRF–BFGS optimization algorithm for structural reliability

Cited by 66 publications

References 20 publications

HLRF‐BFGS‐Based Algorithm for Inverse Reliability Analysis

HLRF‐BFGS‐Based Algorithm for Inverse Reliability Analysis

A Novel Algorithm for Structural Reliability Analysis Based on Finite Step Length and Armijo Line Search

Tolerance analysis — Form defects modeling and simulation by modal decomposition and optimization

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