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.

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 3D orthogonal woven composite automobile shock tower

2021 ◽  
pp. 002199832110476
Author(s):  
Zhao Liu ◽  
Lei Zhang ◽  
Ping Zhu ◽  
Mushi Li
Keyword(s):  
Design Optimization ◽  
Composite Structures ◽  
Optimization Design ◽  
Optimization Procedure ◽  
Woven Composite ◽  
Reliability Based Design Optimization ◽  
Multi Scale ◽  
Reliability Based Design ◽  
Design Variables ◽  
3D Orthogonal Woven

Three-dimensional orthogonal woven composites are noted for their excellent mechanical properties and delamination resistance, so they are expected to have promising prospects in lightweight applications in the automobile industry. The multi-scale characteristics and inherent uncertainty of design variables pose great challenges to the optimization procedure for 3D orthogonal woven composite structures. This paper aims to propose a reliability-based design optimization method for guidance on the lightweight design of 3D orthogonal woven composite automobile shock tower, which includes design variables from material and structure. An analytical model was firstly set up to accurately predict the elastic and strength properties of composites. After that, a novel optimization procedure was established for the multi-scale reliability optimization design of composite shock tower, based on the combination of Monte Carlo reliability analysis method, Kriging surrogate model, and particle swarm optimization algorithm. According to the results, the optimized shock tower meets the requirements of structural performance and reliability, with a weight reduction of 37.83%.

scholarly journals Reliability-Based Design Optimization of Structures Using Complex-Step Approximation with Sensitivity Analysis

2021 ◽  
Vol 11 (10) ◽  
pp. 4708
Author(s):  
Junho Chun
Keyword(s):  
Sensitivity Analysis ◽  
Structural Optimization ◽  
Design Optimization ◽  
Optimization Problems ◽  
Probabilistic Constraints ◽  
Reliability Based Design Optimization ◽  
Step Size ◽  
First Derivative ◽  
Step Approximation ◽  
Reliability Based Design

Structural optimization aims to achieve a structural design that provides the best performance while satisfying the given design constraints. When uncertainties in design and conditions are taken into account, reliability-based design optimization (RBDO) is adopted to identify solutions with acceptable failure probabilities. This paper outlines a method for sensitivity analysis, reliability assessment, and RBDO for structures. Complex-step (CS) approximation and the first-order reliability method (FORM) are unified in the sensitivity analysis of a probabilistic constraint, which streamlines the setup of optimization problems and enhances their implementation in RBDO. Complex-step approximation utilizes an imaginary number as a step size to compute the first derivative without subtractive cancellations in the formula, which have been observed to significantly affect the accuracy of calculations in finite difference methods. Thus, the proposed method can select a very small step size for the first derivative to minimize truncation errors, while achieving accuracy within the machine precision. This approach integrates complex-step approximation into the FORM to compute sensitivity and assess reliability. The proposed method of RBDO is tested on structural optimization problems across a range of statistical variations, demonstrating that performance benefits can be achieved while satisfying precise probabilistic constraints.

Reliability-based robust design optimization using anchored ANOVA expansion and truncated Edgeworth series approximation

2017 ◽  
Vol 232 (4) ◽  
pp. 408-417
Author(s):  
Hao Lu ◽  
Zhencai Zhu
Keyword(s):  
Design Optimization ◽  
Robust Design ◽  
Moment Method ◽  
Optimization Procedure ◽  
Robust Design Optimization ◽  
Reliability Based Design Optimization ◽  
Reliability Based Design ◽  
Edgeworth Series ◽  
Reliability Sensitivity ◽  
The Moment

Based on the basic concept of reliability-based design optimization and robust design optimization, a reliability-based robust design optimization is achieved with the moment method in this work. At the first step, two methods, i.e. the anchored ANOVA expansion and truncated Edgeworth series approximation, are combined to solve the reliability constraints in the optimization procedure. The computational effort of the reliability analysis involved in the reliability-based design optimization is then reduced by the moment method. The reliability-based robust design optimization is then formulated by introducing the reliability sensitivity into the reliability-based design optimization as a sub-objective function, which is derived based on the truncated Edgeworth series expansion. The numerical examples illustrate the effectiveness and applicability of the proposed methodology and that the moment-based reliability-based robust design optimization satisfies (1) the reliability target of each constraint and (2) the minimum reliability sensitivity with respect to the mean value of the input random variables. The proposed reliability-based robust design optimization procedure could be applied to the product design under uncertain environment.

A Hybrid Reliability Approach for Reliability-Based Design Optimization

2010 ◽  
Author(s):  
Po Ting Lin ◽  
Yogesh Jaluria ◽  
Hae Chang Gea
Keyword(s):  
Design Optimization ◽  
Reliability Index ◽  
Optimization Problems ◽  
Performance Measure ◽  
Accurate Solution ◽  
Probabilistic Constraints ◽  
Reliability Based Design Optimization ◽  
Reliability Based Design ◽  
Index Approach ◽  
Hybrid Reliability

Reliability-based Design Optimization problems have been solved by two well-known methods: Reliability Index Approach (RIA) and Performance Measure Approach (PMA). RIA generates first-order approximate probabilistic constraints using the measures of reliability indices. For infeasible design points, the traditional RIA method suffers from inaccurate evaluation of the reliability index. To overcome this problem, the Modified Reliability Index Approach (MRIA) has been proposed. The MRIA provides the accurate solution of the reliability index but also inherits some inefficiency characteristics from the Most Probable Failure Point (MPFP) search when nonlinear constraints are involved. In this paper, the benchmark examples have been utilized to examine the efficiency and stability of both PMA and MRIA. In our study, we found that the MRIA is capable of obtaining the correct optimal solutions regardless of the locations of design points but the PMA is much efficient in the inverse reliability analysis. To take advantages of the strengths of both methods, a Hybrid Reliability Approach (HRA) is proposed. The HRA uses a selection factor that can determine which method to use during optimization iterations. Numerical examples from the proposed method are presented and compared with the MRIA and the PMA.

scholarly journals RELIABILITY-BASED DESIGN OPTIMIZATION USING OPTIMUM SAFETY FACTORS FOR LARGE-SCALE PROBLEMS

2018 ◽  
Vol 18 (3) ◽  
pp. 271-279
Author(s):  
Gh. Kharmanda ◽  
I. R. Antypas
Keyword(s):  
Design Optimization ◽  
Large Scale ◽  
Failure Modes ◽  
Computing Time ◽  
Computational Time ◽  
Reliability Based Design Optimization ◽  
Numerical Application ◽  
Direct Evaluation ◽  
Implementation Framework ◽  
Reliability Based Design

Introduction. Reliability-Based Design Optimization (RBDO) model reduces the structural weight in uncritical regions, does not only provide an improved design but also a higher level of confidence in the design.Materials and Methods. The classical RBDO approach can be carried out in two separate spaces: the physical space and the normalized space. Since very many repeated researches are needed in the above two spaces, the computational time for such an optimization is a big problem. An efficient method called Optimum Safety Factor (OSF) method is developed and successfully put to use in several engineering applications. Research Results. A numerical application on a large scale problem under  fatigue  loading  shows  the  efficiency of the developed RBDO method relative to the Deterministic Design Optimization (DDO). The efficiency of the OSF method is also extended to multiple failure modes to control several out-put parameters, such as structural volume and damage criterion.Discussion and Conclusions. The simplified implementation framework of the OSF strategy consists of a single optimization problem to evaluate the design point, and a direct evaluation of the optimum solution considering OSF formulations. It provides designers with efficient solutions that should be economic, satisfying a required reliability level with a reduced computing time.

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