Improvement Of Second‐Order Reliability Estimates by Importance Sampling

Hohenbichler, M.; Rackwitz, R.

doi:10.1061/(asce)0733-9399(1988)114:12(2195)

Cited by 331 publications

(164 citation statements)

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“…(10)) is thus approximated by Pr[g L (u) , 0] in FORM and Pr[g Q (u) , 0] in SORM. These ®rst-order (P F,1 ) and second-order (P F,2 ) estimates are given by [21,22] …”

Section: First-and Second-order Reliability Methodsmentioning

confidence: 99%

“…(8) involves a multidimensional probability integration for its evaluation. In this study, standard reliability methods, such as FORM/SORM [21], and Monte Carlo with importance sampling (MCIS) [22]were used to compute these probabilities. These standard reliability methods are brie¯y described here to compute the probability of failure P F in Eq.…”

Section: Structural Reliability Analysismentioning

confidence: 99%

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Probabilistic fracture mechanics for nonlinear structures

Rahman

Kim

2001

International Journal of Pressure Vessels and Piping

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“…(10)) is thus approximated by Pr[g L (u) , 0] in FORM and Pr[g Q (u) , 0] in SORM. These ®rst-order (P F,1 ) and second-order (P F,2 ) estimates are given by [21,22] …”

Section: First-and Second-order Reliability Methodsmentioning

confidence: 99%

Section: Structural Reliability Analysismentioning

confidence: 99%

Probabilistic fracture mechanics for nonlinear structures

Rahman

Kim

2001

International Journal of Pressure Vessels and Piping

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“… is the upper limit of the acceleration, which is set 30g herein. 10 sample size. It can be seen that both the two methods converge to the same point (0.0500, 0.3325), which verifies that the proposed method has the same accuracy as MCS-SAP.…”

Section: Honeycomb Crashworthiness Design Applicationmentioning

confidence: 99%

“…First-order reliability method (FORM) [5,9,28] and second-order reliability method (SORM) [10] are the most commonly used analytical methods. FORM/SORM involves linear or second-order Taylor expansion of the performance constraint at the most probable point (MPP) [32].…”

Section: Introductionmentioning

confidence: 99%

An Efficient Moving Optimal Radial Sampling Method for Reliability-Based Design Optimization

Li¹

2017

IJPE

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Reliability-based design optimization (RBDO) plays an essential role in structure and system design. However, its application in practical engineering is hindered by the huge computational cost in performance function evaluation. In this paper, a moving optimal radial sampling (MORS) method is proposed for RBDO problems to substantially improve the computational efficiency of Monte Carlo simulation (MCS). In MORS, the failure probability and its gradient are calculated using radius based importance sampling (RBIS) method. The initial radius is selected according to the target reliability, which can also be used to check the feasibility of probabilistic constraints afterwards. The arc search scheme in enhanced performance measure approach (PMA+) and linear interpolation scheme are used to calculate the optimal radius of RBIS. After the failure probability and its gradient are calculated, the optimal design is obtained using sequential approximation programming (SAP). The computational capability of the proposed MORS method is demonstrated using a honeycomb crashworthiness design application, a nonlinear mathematical problem and a speed reducer design. The comparison results show that the proposed MORS-SAP method is very efficient and accurate.

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“…The simulation techniques have their origin in Monte Carlo simulation (MCS) method, which generates a large sample set of limit state evaluations and approximates the true value of the probability of failure by = , where is the number of samples lying in the failure region and S the total number of samples. In order to further improve the computational efficiency of MCS, many variance reduction techniques have been proposed [9], including importance sampling ( [10], [11]), directional simulation [12] or subset simulation ( [13], [14]). Despite these improvements, the MCS method is still timeconsuming and further development is crucial.…”

Section: Introductionmentioning

confidence: 99%