A Hybrid Loop Approach Using the Sufficient Descent Condition for Accurate, Robust, and Efficient Reliability-Based Design Optimization

2016 ◽  
Vol 138 (12) ◽  
Author(s):  
Behrooz Keshtegar ◽  
Peng Hao
Keyword(s):  
Design Optimization ◽  
Nonlinear Problems ◽  
Performance Measure ◽  
Reliability Based Design Optimization ◽  
Nonlinear Constraint ◽  
Sufficient Descent Condition ◽  
Reliability Based Design ◽  
Highly Nonlinear ◽  
Sufficient Descent ◽  
Descent Condition

For reliability-based design optimization (RBDO) problems, single loop approaches (SLA) are very efficient but prone to converge to inappropriate point for highly nonlinear constraint functions, and double loop approaches (DLA) are proven to be accurate but require more iterations to achieve stable results. In this paper, an adjusted advanced mean value (AAMV) method is firstly proposed to improve the robustness and efficiency of performance measure approach. The global convergence of the AAMV is guaranteed using sufficient descent condition for the reliability loop in RBDO. Then, a hybrid RBDO method is developed to improve the efficiency of DLA and accuracy of SLA, on the basis of sufficient descent condition and AAMV method, named as hybrid single and double loops (HSD) method. Three nonlinear concave and convex performance functions are used to illustrate the efficiency and robustness of the AAMV method; then the accuracy, robustness, and efficiency of the proposed HSD method are compared to current SLA and DLA through another three benchmark nonlinear RBDO examples. Results show that the AAMV is more robust and efficient than the existing reliability analysis methods. The HSD is more accurate than the SLA for highly nonlinear problems, and also exhibits a better performance than the DLA from the point of view of both robustness and efficiency.

An Investigation of Nonlinearity of Reliability-Based Design Optimization Approaches

2002 ◽  
Author(s):  
Kyung K. Choi ◽  
Byeng D. Youn
Keyword(s):  
Design Optimization ◽  
Reliability Analysis ◽  
Probability Distributions ◽  
Performance Measure ◽  
Probabilistic Constraints ◽  
Random Parameters ◽  
Reliability Based Design Optimization ◽  
Reliability Based Design ◽  
Highly Nonlinear ◽  
Standard Normal

Deterministic optimum designs that are obtained without consideration of uncertainty could lead to unreliable designs, which call for a reliability approach to design optimization, using a Reliability-Based Design Optimization (RBDO) method. A typical RBDO process iteratively carries out a design optimization in an original random space (X-space) and reliability analysis in an independent and standard normal random space (U-space). This process requires numerous nonlinear mapping between X- and U-spaces for a various probability distributions. Therefore, the nonlinearity of RBDO problem will depend on the type of distribution of random parameters, since a transformation between X- and U-spaces introduces additional nonlinearity to reliability-based performance measures evaluated during the RBDO process. Evaluation of probabilistic constraints in RBDO can be carried out in two different ways: the Reliability Index Approach (RIA) and the Performance Measure Approach (PMA). Different reliability analysis approaches employed in RIA and PMA result in different behaviors of nonlinearity of RIA and PMA in the RBDO process. In this paper, it is shown that RIA becomes much more difficult to solve for non-normally distributed random parameters because of highly nonlinear transformations involved. However, PMA is rather independent of probability distributions because of little involvement of the nonlinear transformation.

An Investigation of Nonlinearity of Reliability-Based Design Optimization Approaches

2003 ◽  
Vol 126 (3) ◽  
pp. 403-411 ◽  
Author(s):  
Byeng D. Youn ◽  
Kyung K. Choi
Keyword(s):  
Design Optimization ◽  
Reliability Analysis ◽  
Probability Distributions ◽  
Performance Measure ◽  
Probabilistic Constraints ◽  
Random Parameters ◽  
Reliability Based Design Optimization ◽  
Reliability Based Design ◽  
Highly Nonlinear ◽  
Standard Normal

Because deterministic optimum designs obtained without taking uncertainty into account could lead to unreliable designs, a reliability-based approach to design optimization is preferable using a Reliability-Based Design Optimization (RBDO) method. A typical RBDO process iteratively carries out a design optimization in an original random space (X-space) and a reliability analysis in an independent and standard normal random space (U-space). This process requires numerous nonlinear mappings between X- and U-spaces for various probability distributions. Therefore, the nonlinearity of the RBDO problem will depend on the type of distribution of random parameters, since a transformation between X- and U-spaces introduces additional nonlinearity into the reliability-based performance measures evaluated during the RBDO process. The evaluation of probabilistic constraints in RBDO can be carried out in two ways: using either the Reliability Index Approach (RIA), or the Performance Measure Approach (PMA). Different reliability analysis approaches employed in RIA and PMA result in different behaviors of nonlinearity for RIA and PMA in the RBDO process. In this paper, it is shown that RIA becomes much more difficult to solve for non-normally distributed random parameters because of the highly nonlinear transformations that are involved. However, PMA is rather independent of probability distributions because it only has a small involvement with a nonlinear transformation.

scholarly journals Efficient optimum safety factor approach for system reliability-based design optimization with application to composite yarns

2019 ◽  
Vol 19 (3) ◽  
pp. 221-230 ◽  
Author(s):  
Gh. Kharmanda ◽  
I. R. Antypas
Keyword(s):  
Design Optimization ◽  
Safety Factor ◽  
Reliability Index ◽  
Performance Measure ◽  
Alternative Methods ◽  
Reliability Based Design Optimization ◽  
Implementation Framework ◽  
Reliability Level ◽  
Reliability Based Design ◽  
Convergence Stability

Introduction. The integration of reliability and optimization concepts seeks to design structures that should be both economic and reliable. This model is called Reliability-Based Design Optimization (RBDO). In fact, the coupling between the mechanical modelling, the reliability analyses and the optimization methods leads to very high computational cost and weak convergence stability. Materials andMethods. Several methods have been developed to overcome these difficulties. The methods called Reliability Index Approach (RIA) and Performance Measure Approach (PMA) are two alternative methods. RIA describes the probabilistic constraint as a reliability index while PMA was proposed by converting the probability measure to a performance measure. An Optimum Safety Factor (OSF) method is proposed to compute safety factors satisfying a required reliability level without demanding additional computing cost for the reliability evaluation. The OSF equations are formulated considering RIA and PMA and extended to multiple failure case.Research Results. Several linear and nonlinear distribution laws are applied to composite yarns studies and then extended to multiple failure modes. It has been shown that the idea of the OSF method is to avoid the reliability constraint evaluation with a particular optimization process.Discussion and Conclusions. The simplified implementation framework of the OSF strategy consists of decoupling the optimization and the reliability analyses. It provides designers with efficient solutions that should be economic satisfying a required reliability level. It is demonstrated that the RBDO compared to OSF has several advantages: small number of optimization variables, good convergence stability, small computing time, satisfaction of the required reliability levels.

Reliability-Based Design Optimization of Robotic System Dynamic Performance

2006 ◽  
Vol 129 (4) ◽  
pp. 449-454 ◽  
Author(s):  
Alan P. Bowling ◽  
John E. Renaud ◽  
Jeremy T. Newkirk ◽  
Neal M. Patel ◽  
Harish Agarwal
Keyword(s):  
Design Optimization ◽  
Reference Point ◽  
High Reliability ◽  
Dynamic Performance ◽  
Performance Measure ◽  
Robotic System ◽  
Reliability Based Design Optimization ◽  
End Effector ◽  
Reliability Based Design ◽  
Reliable Design

In this investigation a robotic system’s dynamic performance is optimized for high reliability under uncertainty. The dynamic capability equations (DCE) allow designers to predict the dynamic performance of a robotic system for a particular configuration and reference point on the end effector (i.e., point design). Here the DCE are used in conjunction with a reliability-based design optimization (RBDO) strategy in order to obtain designs with robust dynamic performance with respect to the end-effector reference point. In this work a unilevel performance measure approach is used to perform RBDO. This is important for the reliable design of robotic systems in which a solution to the DCE is required for each constraint call. The method is illustrated on a robot design problem.

A New Study on Reliability-Based Design Optimization

1999 ◽  
Vol 121 (4) ◽  
pp. 557-564 ◽  
Author(s):  
J. Tu ◽  
K. K. Choi ◽  
Y. H. Park
Keyword(s):  
Design Optimization ◽  
Reliability Index ◽  
Performance Measure ◽  
Probabilistic Constraints ◽  
Probabilistic Constraint ◽  
Reliability Based Design Optimization ◽  
Performance Measure Approach ◽  
Reliability Based Design ◽  
Index Approach ◽  
Special Cases

This paper presents a general approach for probabilistic constraint evaluation in the reliability-based design optimization (RBDO). Different perspectives of the general approach are consistent in prescribing the probabilistic constraint, where the conventional reliability index approach (RIA) and the proposed performance measure approach (PMA) are identified as two special cases. PMA is shown to be inherently robust and more efficient in evaluating inactive probabilistic constraints, while RIA is more efficient for violated probabilistic constraints. Moreover, RBDO often yields a higher rate of convergence by using PMA, while RIA yields singularity in some cases.

Reliability-based design optimization of fluid–solid interaction problems

2013 ◽  
Vol 228 (10) ◽  
pp. 1724-1742 ◽  
Author(s):  
Hong-Lae Jang ◽  
Hyunkyoo Cho ◽  
Kyung K Choi ◽  
Seonho Cho
Keyword(s):  
Design Optimization ◽  
Incompressible Flows ◽  
Variational Equation ◽  
Optimization Method ◽  
Programming Algorithm ◽  
Reliability Based Design Optimization ◽  
Reliability Based Design ◽  
Highly Nonlinear ◽  
Fluid Solid Interaction ◽  
Interaction Problem

Using a sampling-based reliability-based design optimization method, we present a shape reliability-based design optimization method for coupled fluid–solid interaction problems. For the fluid–solid interaction problem in arbitrary Lagrangian–Eulerian formulation, a coupled variational equation is derived from a steady state Navier–Stokes equation for incompressible flows, an equilibrium equation for geometrically nonlinear solids, and a traction continuity condition at interfaces. The fluid–solid interaction problem is solved using the finite element method and the Newton–Raphson scheme. For the fluid mesh movement, we formulated and solved a pseudo-structural sub-problem. The shape of the solid is modeled using the Non-Uniform Rational B-Spline (NURBS) surface, and the coordinate components of the control points are selected as random design variables. The sensitivity of the probabilistic constraint is calculated using the first-order score functions obtained from the input distributions and from the Monte Carlo simulation on the surrogate model constructed by using the Dynamic Kriging method. The sequential quadratic programming algorithm is used for the optimization. In two numerical examples, the proposed optimization method is applied to the shape design problems of solid structure which is loaded by prescribed fluid flow, and this proves that the sampling-based reliability-based design optimization can be successfully utilized for obtaining a reliable optimum design in highly nonlinear multi-physics problems.

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