A simulation-based method for reliability based design optimization problems with highly nonlinear constraints

2014 ◽  
Vol 47 ◽  
pp. 24-36 ◽  
Author(s):  
Mohsen Rashki ◽  
Mahmoud Miri ◽  
Mehdi Azhdary Moghaddam
Keyword(s):  
Design Optimization ◽  
Optimization Problems ◽  
Nonlinear Constraints ◽  
Reliability Based Design Optimization ◽  
Reliability Based Design ◽  
Highly Nonlinear ◽  
Simulation Based

scholarly journals A decoupling algorithm with first-order asymptotic integration for reliability-based design optimization

2018 ◽  
Vol 10 (9) ◽  
pp. 168781401879333 ◽  
Author(s):  
Zhiliang Huang ◽  
Tongguang Yang ◽  
Fangyi Li
Keyword(s):  
Design Optimization ◽  
Reliability Analysis ◽  
Optimization Problems ◽  
Asymptotic Integration ◽  
Probabilistic Constraints ◽  
Reliability Based Design Optimization ◽  
First Order Reliability Method ◽  
First Order ◽  
Reliability Based Design ◽  
Reliability Method

Conventional decoupling approaches usually employ first-order reliability method to deal with probabilistic constraints in a reliability-based design optimization problem. In first-order reliability method, constraint functions are transformed into a standard normal space. Extra non-linearity introduced by the non-normal-to-normal transformation may increase the error in reliability analysis and then result in the reliability-based design optimization analysis with insufficient accuracy. In this article, a decoupling approach is proposed to provide an alternative tool for the reliability-based design optimization problems. To improve accuracy, the reliability analysis is performed by first-order asymptotic integration method without any extra non-linearity transformation. To achieve high efficiency, an approximate technique of reliability analysis is given to avoid calculating time-consuming performance function. Two numerical examples and an application of practical laptop structural design are presented to validate the effectiveness of the proposed approach.

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.

Reliability-based design optimization for vertical vibrations of a modified electric vehicle using fourth-moment polynomial standard transformation method

2020 ◽  
Vol 234 (10-11) ◽  
pp. 2649-2664
Author(s):  
Sheng Wang ◽  
Lin Hua ◽  
Xinghui Han ◽  
Zhuoyu Su
Keyword(s):  
Design Optimization ◽  
Electric Vehicle ◽  
Optimization Problems ◽  
Computing Time ◽  
Optimization Procedure ◽  
Transformation Method ◽  
Vertical Vibration ◽  
Fourth Moment ◽  
Reliability Based Design Optimization ◽  
Reliability Based Design

This article presents a new reliability-based design optimization procedure for the vertical vibration issues raised by a modified electric vehicle using fourth-moment polynomial standard transformation method. First, the fourth-moment polynomial standard transformation method with polynomial chaos expansion is used to obtain the reliability index of uncertain constraints in the reliability-based design optimization which is highly precise and saves computing time compared with other common methods. Next, the half-car model with nonlinear suspension parameters for the modified electric vehicle is investigated, and the response surface methodology is adopted to approximate the complex and time-consuming vertical vibration calculation to the polynomial expressions, and the approximation is validated for reliability-based design optimization results within permissible error level. Then, reliability-based design optimization results under both deterministic and uncertain load parameters are shown and analyzed. Unlike the traditional vertical vibration optimization that only considers one or several sets of load parameters, which lacks versatility, this article presents the reliability-based design optimization with uncertain load parameters which is more suitable for engineering. The results show that the proposed reliability-based design optimization procedure is an effective and efficient way to solve vertical vibration optimization problems for the modified electric vehicle, and the optimization statistics, including the maximum probability interval, can provide references for other suspension dynamical optimization.

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.

A Hybrid Reliability-Based Design Optimization Approach with Adaptive Chaos Control Using Kriging Model

2016 ◽  
Vol 13 (01) ◽  
pp. 1650006 ◽  
Author(s):  
Gang Li ◽  
Zeng Meng ◽  
Peng Hao ◽  
Hao Hu
Keyword(s):  
Design Optimization ◽  
Chaos Control ◽  
Pso Algorithm ◽  
Kriging Model ◽  
Target Point ◽  
Optimization Approach ◽  
Reliability Based Design Optimization ◽  
Local Optima ◽  
Reliability Based Design ◽  
Highly Nonlinear

Traditional reliability-based design optimization (RBDO) approaches are computationally expensive for complicated problems. To cope with this challenge, a surrogate-based hybrid RBDO approach for the problems with highly nonlinear constraints and multiple local optima is proposed in this study. Specifically, the adaptive chaos control (ACC) method is used to ensure the robustness of the most probable target point (MPTP) search process, and the particle swarm optimization (PSO) algorithm is utilized to conquer the barrier caused by multiple local optima. Three illustrative benchmark examples together with a 3 m diameter orthogrid stiffened shell for current launch vehicles are employed to demonstrate the efficiency and robustness of the proposed method.

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