A hybrid relaxed first-order reliability method for efficient structural reliability analysis

Keshtegar, Behrooz; Meng, Zeng

doi:10.1016/j.strusafe.2017.02.005

Cited by 113 publications

(36 citation statements)

References 26 publications

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“…Select an idealized system. For the simplicity of the linear system in solving vibration reliability problems, in this paper, an equivalent linear system is selected as the idealized system, and the design point of this linear system is obtained by (12) and is taken as the initial iteration value u (0) i of the real system design point. At the time constant t, the acceleration response of the idealized linear system is G c , that is, € x…”

Section: Model Correction Factor Methods Formentioning

confidence: 99%

“…A variety of methods for nonlinear stochastic dynamic analysis have been explored and presented. In the structural reliability field, first-and second-order reliability methods (FORM and SORM) [11,12] have been proven to be effective methods, for their simplicity and efficiency. e mirror image excitation method presented by Koo et al [13] provided an approximate method for the nonlinear system failure probability estimation, and the solution of this method does not require the finding of the design point and response gradient; however, this method is restricted to the displacement first passage of single-degreeof-freedom problems.…”

Section: Introductionmentioning

confidence: 99%

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Acceleration Response First Passage Failure Probability Analysis Method for Nonlinear Package

Zhu

2018

Shock and Vibration

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e acceleration response first passage failure problem of the nonlinear package base excited by Gaussian white noise is analyzed. e model correction factor method (MCFM) is implemented in conjunction with the first-order reliability method (FORM) to analyze the first passage failure probability of the nonlinear package. e white noise is discretized in standard normal space, and an iterative algorithm is proposed to find the design point of the packaging system. On the design point, the hypersurface representing the limit-state function of the nonlinear package is replaced approximately by a hyperplane representing the limitstate function of an equivalent linear system, and the FORM is employed to calculate the failure probability of the packaging system. e accuracy of this method is verified by crude Monte Carlo simulations. Numerical simulations are carried out to observe the effects of system parameters variations on failure probability which can be used for the improvement of packaging design.

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Section: Model Correction Factor Methods Formentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Acceleration Response First Passage Failure Probability Analysis Method for Nonlinear Package

Zhu

2018

Shock and Vibration

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“…Meng et al presented chaos control method to performance measure approach for the inverse reliability analysis, and the robustness and efficiency were increased obviously . Recently, improved HL‐RF, stability transformation method, directional stability transformation method, adaptive finite step length, hybrid relaxed HL‐RF, conjugate HL‐RF, limited and enriched Fletcher‐Reeves method, chaos control, adaptive and relaxed conjugate FORM, and hybrid conjugate FORM were developed to increase the robustness and efficiency of FORM during the process of searching the most probable failure point and the reliability index.…”

Section: Introductionmentioning

confidence: 99%

Structural reliability assessment by salp swarm algorithm–based FORM

Zhong

Wang

Dang

et al. 2020

Quality & Reliability Eng

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The first-order reliability method (FORM) is well recognized as an efficient approach for reliability analysis. Rooted in considering the reliability problem as a constrained optimization of a function, the traditional FORM makes use of gradient-based optimization techniques to solve it. However, the gradient-based optimization techniques may result in local convergence or even divergence for the highly nonlinear or high-dimensional performance function. In this paper, a hybrid method combining the Salp Swarm Algorithm (SSA) and FORM is presented. In the proposed method, a Lagrangian objective function is constructed by the exterior penalty function method to facilitate meta-heuristic optimization strategies. Then, SSA with strong global optimization ability for highly nonlinear and high-dimensional problems is utilized to solve the Lagrangian objective function. In this regard, the proposed SSA-FORM is able to overcome the limitations of FORM including local convergence and divergence. Finally, the accuracy and efficiency of the proposed SSA-FORM are compared with two gradient-based FORMs and several heuristic-based FORMs through eight numerical examples. The results show that the proposed SSA-FORM can be generally applied for reliability analysis involving low-dimensional, high-dimensional, and implicit performance functions. KEYWORDS first-order reliability method, high-dimensional problem, meta-heuristic algorithm, reliability analysis, Salp Swarm Algorithm 1224

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“…In probability theory, uncertain parameters are represented by random variables, which are quantified by distribution function and correlation coefficient. Many probabilistic analysis methods that are based on probability models have been well developed, such as the Monte Carlo method [1,2], full factorial numerical integration [3], univariate dimension reduction [4], first-order reliability method [5,6], and Bayesian approach [7,8]. For the uncertainty analysis of structures, the probabilistic theory and the finite element method are combined to generate stochastic finite element analysis (SFEM) [9].…”

Section: Introductionmentioning

confidence: 99%

Probabilistic Analysis for Structures with Hybrid Uncertain Parameters

Xiao

Zhao

Wen

et al. 2020

Mathematical Problems in Engineering

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In practical engineering problems, the distribution parameters of random variables cannot be determined precisely due to limited experimental data. e hybrid uncertain model of interval and probability can deal with the problem, but it will produce extensive computation and it is difficult to meet the requirement of the complex engineering problem analysis. In this scenario, this paper presents a vertex method for the uncertainty analysis of the hybrid model. By combining the traditional finite element method, it can be applied to the structural uncertainty analysis. e key of this method is to demonstrate the monotonicity between expectation and variance of the function and distribution parameters of random variables. Based on the monotonicity analysis, interval bounds of the expectation and variance are directly calculated by means of vertex of distribution parameter intervals. Two numerical examples are used to evaluate the effectiveness and accuracy of the proposed method. e results show the vertex method is computationally more efficient than the common interval Monte Carlo method under the same accuracy. Two practical engineering examples are to show that the vertex method makes the engineering application of the hybrid uncertain model easy.

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A hybrid relaxed first-order reliability method for efficient structural reliability analysis

Cited by 113 publications

References 26 publications

Acceleration Response First Passage Failure Probability Analysis Method for Nonlinear Package

Acceleration Response First Passage Failure Probability Analysis Method for Nonlinear Package

Structural reliability assessment by salp swarm algorithm–based FORM

Probabilistic Analysis for Structures with Hybrid Uncertain Parameters

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