Reliability Based Design Optimization Using First, Second and Quasi-Second Order Saddlepoint Approximations

2018 ◽  
Author(s):  
Dimitrios Papadimitriou ◽  
Dionysios Panagiotopoulos ◽  
Zissimos Mourelatos
Keyword(s):  
Design Optimization ◽  
Second Order ◽  
Reliability Based Design Optimization ◽  
Saddlepoint Approximations ◽  
Reliability Based Design

A hybrid sequential approximate programming method for second-order reliability-based design optimization approach

2017 ◽  
Vol 228 (5) ◽  
pp. 1965-1978 ◽  
Author(s):  
Zeng Meng ◽  
Huanlin Zhou ◽  
Gang Li ◽  
Hao Hu
Keyword(s):  
Design Optimization ◽  
Second Order ◽  
Programming Method ◽  
Optimization Approach ◽  
Reliability Based Design Optimization ◽  
Reliability Based Design

A second order SAP algorithm for risk and reliability based design optimization

2019 ◽  
Vol 190 ◽  
pp. 106499 ◽  
Author(s):  
A.J. Torii ◽  
R.H. Lopez ◽  
L.F.F. Miguel
Keyword(s):  
Design Optimization ◽  
Second Order ◽  
Reliability Based Design Optimization ◽  
Reliability Based Design

scholarly journals Reliability-Based Design Optimization of Structures Using the Second-Order Reliability Method and Complex-Step Derivative Approximation

2021 ◽  
Vol 11 (11) ◽  
pp. 5312
Author(s):  
Junho Chun
Keyword(s):  
Sensitivity Analysis ◽  
Design Optimization ◽  
Optimization Problems ◽  
Second Order ◽  
Probabilistic Constraints ◽  
Reliability Based Design Optimization ◽  
Step Size ◽  
Reliability Based Design ◽  
Reliability Method ◽  
Derivative Approximation

This paper proposes a reliability-based design optimization (RBDO) approach that adopts the second-order reliability method (SORM) and complex-step (CS) derivative approximation. The failure probabilities are estimated using the SORM, with Breitung’s formula and the technique established by Hohenbichler and Rackwitz, and their sensitivities are analytically derived. The CS derivative approximation is used to perform the sensitivity analysis based on derivations. Given that an imaginary number is used as a step size to compute the first derivative in the CS derivative method, the calculation stability and accuracy are enhanced with elimination of the subtractive cancellation error, which is commonly encountered when using the traditional finite difference method. The proposed approach unifies the CS approximation and SORM to enhance the estimation of the probability and its sensitivity. The sensitivity analysis facilitates the use of gradient-based optimization algorithms in the RBDO framework. The proposed RBDO/CS–SORM method is tested on structural optimization problems with a range of statistical variations. The results demonstrate that the performance can be enhanced while satisfying precisely probabilistic constraints, thereby increasing the efficiency and efficacy of the optimal design identification. The numerical optimization results obtained using different optimization approaches are compared to validate this enhancement.

Sensitivity Analyses of FORM-Based and DRM-Based Performance Measure Approach for Reliability-Based Design Optimization

2008 ◽  
Author(s):  
Ikjin Lee ◽  
Kyung K. Choi ◽  
Liu Du ◽  
David Gorsich
Keyword(s):  
Design Optimization ◽  
Performance Measure ◽  
Second Order ◽  
Probabilistic Constraints ◽  
Sensitivity Analyses ◽  
Probabilistic Constraint ◽  
Reliability Based Design Optimization ◽  
Performance Measure Approach ◽  
Reliability Based Design ◽  
Reliability Method

In a gradient-based design optimization, it is necessary to know sensitivities of the constraint with respect to the design variables. In a reliability-based design optimization (RBDO), the constraint is evaluated at the most probable point (MPP) and called the probabilistic constraint, thus it requires the sensitivities of the probabilistic constraints at MPP. This paper presents the rigorous analytic derivation of the sensitivities of the probabilistic constraint at MPP for both First Order Reliability Method (FORM)-based Performance Measure Approach (PMA) and Dimension Reduction Method (DRM)-based PMA. Numerical examples are used to demonstrate that the analytic sensitivities agree very well with the sensitivities obtained from the finite difference method (FDM). However, since the sensitivity calculation at the true DRM-based MPP requires the second-order derivatives and additional MPP search, the sensitivity derivation at the approximated DRM-based MPP, which does not require the second-order derivatives and additional MPP search to find the DRM-based MPP, is proposed in this paper. A convergence study illustrates that the sensitivity at the approximated DRM-based MPP converges to the sensitivity at the true DRM-based MPP as the design approaches the optimum design. Hence, the sensitivity at the approximated DRM-based MPP is proposed to be used for the DRM-based RBDO to enhance the efficiency of the optimization.

Second-Order Reliability Method Based on Edgeworth Expansion With Application to Reliability-Based Design Optimization

2019 ◽  
Author(s):  
Rami Mansour ◽  
Mårten Olsson
Keyword(s):  
Design Optimization ◽  
Limit State ◽  
Probability Of Failure ◽  
Second Order ◽  
State Function ◽  
Reliability Based Design Optimization ◽  
First Order ◽  
Reliability Based Design ◽  
Statistical Measures ◽  
Reliability Method

Abstract In the Second-Order Reliability Method, the limit-state function is approximated by a hyper-parabola in standard normal and uncorrelated space. However, there is no exact closed form expression for the probability of failure based on a hyper-parabolic limit-state function and the existing approximate formulas in the literature have been shown to have major drawbacks. Furthermore, in applications such as Reliability-based Design Optimization, analytical expressions, not only for the probability of failure but also for probabilistic sensitivities, are highly desirable for efficiency reasons. In this paper, a novel Second-Order Reliability Method is presented. The proposed expression is a function of three statistical measures: the Cornell Reliability Index, the skewness and the Kurtosis of the hyper-parabola. These statistical measures are functions of the First-Order Reliability Index and the curvatures at the Most Probable Point. Furthermore, analytical sensitivities with respect to mean values of random variables and deterministic variables are presented. The sensitivities can be seen as the product of the sensitivities computed using the First-Order Reliability Method and a correction factor. The proposed expressions are studied and their applicability to Reliability-based Design Optimization is demonstrated.

A robust method for the reliability-based design optimization of shape memory alloy actuator

2021 ◽  
pp. 1-19
Author(s):  
Ahmed Yaich ◽  
Fatma Abid ◽  
Tarek Merzouki ◽  
Abdelkhalak El Hami ◽  
Lassaad Walha ◽  
...  
Keyword(s):  
Shape Memory Alloy ◽  
Shape Memory ◽  
Design Optimization ◽  
Robust Method ◽  
Reliability Based Design Optimization ◽  
Shape Memory Alloy Actuator ◽  
Reliability Based Design
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