Study of Uncertainties and Objective Function Modeling Effects on Probabilistic Optimization Results

2019 ◽  
Vol 5 (4) ◽  
Author(s):  
Oussama Braydi ◽  
Pascal Lafon ◽  
Rafic Younes
Keyword(s):  
Standard Deviation ◽  
Objective Function ◽  
Design Optimization ◽  
Robust Design ◽  
Optimization Design ◽  
Robust Design Optimization ◽  
Deterministic Case ◽  
Objective Functions ◽  
Design Problems ◽  
Probabilistic Optimization

Abstract In this work, we study the effect of uncertainties modeling and the choice of objective function on the results of optimization design problems in deterministic and probabilistic contexts. Uncertainties modeling are studied in two cases identified in the literature. The results show how the choice of two different objective functions, which lead to the same results in deterministic case, may lead to opposite results in probabilistic case. Also, the results show how the uncertainties modeling type can affect the antagonism between mean and standard deviation in the reliability-based robust design optimization (RBRDO) problems. Three mechanical applications chosen from the literature are used to illustrate these cases.

Robust Design Optimization Under Mixed Uncertainties With Stochastic Expansions

2013 ◽  
Vol 135 (8) ◽  
Author(s):  
Yi Zhang ◽  
Serhat Hosder
Keyword(s):  
Monte Carlo ◽  
Robust Optimization ◽  
Objective Function ◽  
Design Optimization ◽  
Robust Design ◽  
Optimization Technique ◽  
Response Surfaces ◽  
Robust Design Optimization ◽  
Stochastic Expansions ◽  
Mixed Uncertainties

The objective of this paper is to introduce a computationally efficient and accurate approach for robust optimization under mixed (aleatory and epistemic) uncertainties using stochastic expansions that are based on nonintrusive polynomial chaos (NIPC) method. This approach utilizes stochastic response surfaces obtained with NIPC methods to approximate the objective function and the constraints in the optimization formulation. The objective function includes a weighted sum of the stochastic measures, which are minimized simultaneously to ensure the robustness of the final design to both inherent and epistemic uncertainties. The optimization approach is demonstrated on two model problems with mixed uncertainties: (1) the robust design optimization of a slider-crank mechanism and (2) robust design optimization of a beam. The stochastic expansions are created with two different NIPC methods, Point-Collocation and Quadrature-Based NIPC. The optimization results are compared to the results of another robust optimization technique that utilizes double-loop Monte Carlo sampling (MCS) for the propagation of mixed uncertainties. The optimum designs obtained with two different optimization approaches agree well in both model problems; however, the number of function evaluations required for the stochastic expansion based approach is much less than the number required by the Monte Carlo based approach, indicating the computational efficiency of the optimization technique introduced.

Fuzzy-Robust Design Optimization of Dimension Tolerance Using the Improved Genetic Algorithm

2011 ◽  
Vol 55-57 ◽  
pp. 1502-1505
Author(s):  
Bo Zhong
Keyword(s):  
Genetic Algorithm ◽  
Design Optimization ◽  
Robust Design ◽  
Treatment Method ◽  
Robust Design Optimization ◽  
Continuous Variables ◽  
Discrete Variables ◽  
Improved Genetic Algorithm ◽  
Design Problems ◽  
Standard Genetic Algorithm

The standard genetic algorithm is improved by introducing the engineering treatment method of design vector in order to solve the optimization problem with mixed-discrete variables. A program of improved genetic algorithm has been designed. It can be used to solve the optimal design problems with continuous variables, discrete variables or mixed-discrete variables. For a dimension chain, the fuzzy-robust design of dimension tolerance is discussed and a model of fuzzy-robust design optimization is established. The solution of established model is achieved by using the improved genetic algorithm and the robustness of the dimension tolerance has been improved. The example shows that the proposed method is effective in engineering design.

Hybrid Discrete Variable Robust Design Optimization Based on the Intelligent Single Particle Algorithm

2013 ◽  
Vol 299 ◽  
pp. 143-147
Author(s):  
Mao Fu Liu ◽  
Hui Xian Han
Keyword(s):  
Design Optimization ◽  
Robust Design ◽  
Single Particle ◽  
Optimization Design ◽  
Robust Design Optimization ◽  
Position Vector ◽  
Engineering Practice ◽  
Discretization Method ◽  
Discrete Variable ◽  
Robust Optimization Design

Aiming to solve the problems of hybrid discrete variable robust design optimization in engineering practice, Particle position vector discretization method is applied toimprove intelligence single particle algorithm. A program written by MATLAB is designed for solving the problems of hybrid discrete variable robust design optimization. The paper verified the effectiveness and practicability of the method through an example of plane dimension chain’s discrete tolerance robust optimization design in the field of mechanical manufacturing.

Ship Robust Design Optimization Based on Polynomial Chaos Expansions

2020 ◽  
Vol 36 (03) ◽  
pp. 213-225
Author(s):  
Xiao Wei ◽  
Haichao Chang ◽  
Baiwei Feng ◽  
Zuyuan Liu
Keyword(s):  
Design Optimization ◽  
Robust Design ◽  
Optimization Design ◽  
Polynomial Chaos ◽  
Minimum Energy ◽  
Robust Design Optimization ◽  
Uncertain Variables ◽  
Polynomial Coefficients ◽  
Collocation Points ◽  
Polynomial Chaos Expansions

Considerable parameter perturbations occur owing to the influence of uncertain factors in actual ship transportation, resulting in a substantial decline in ship performance. These parameters should not be regarded as certain values but uncertain variables. Ship robust design optimization (RDO) is a method in which various uncertainties are fully considered in the early stages of ship design to ensure that the optimal case adapts to the perturbation of the uncertain parameters. In this study, instead of the commonly used Monte Carlo method, polynomial chaos expansions (PCEs) are adopted to quantify the uncertainty, and an improved probabilistic collocation method (PCM) based on the linear independence principle is proposed to select sample points for calculating polynomial coefficients of PCE, which not only reduces the number of collocation points compared with the traditional statistical sampling method but also avoids the problem that arises with the traditional PCM, which cannot maintain high calculation accuracy even with considerable collocation points. Finally, to ensure ship robustness, in comparison with deterministic optimization design, the proposed RDO framework is applied to minimum Energy Efficiency Design Index (EEDI) KRISO Container Ship hull form design.

Robust Design Optimization for Crashworthiness of Vehicle Side Impact

2017 ◽  
Vol 3 (3) ◽  
Author(s):  
Souvik Chakraborty ◽  
Tanmoy Chatterjee ◽  
Rajib Chowdhury ◽  
Sondipon Adhikari
Keyword(s):  
Design Optimization ◽  
New Product Development ◽  
Robust Design ◽  
Automobile Industry ◽  
Human Error ◽  
Differential Evolution Algorithm ◽  
Side Impact ◽  
Robust Design Optimization ◽  
Parameter Uncertainties ◽  
Design Engineers

Optimization for crashworthiness is of vast importance in automobile industry. Recent advancement in computational prowess has enabled researchers and design engineers to address vehicle crashworthiness, resulting in reduction of cost and time for new product development. However, a deterministic optimum design often resides at the boundary of failure domain, leaving little or no room for modeling imperfections, parameter uncertainties, and/or human error. In this study, an operational model-based robust design optimization (RDO) scheme has been developed for designing crashworthiness of vehicle against side impact. Within this framework, differential evolution algorithm (DEA) has been coupled with polynomial correlated function expansion (PCFE). An adaptive framework for determining the optimum basis order in PCFE has also been presented. It is argued that the coupled DEA–PCFE is more efficient and accurate, as compared to conventional techniques. For RDO of vehicle against side impact, minimization of the weight and lower rib deflection of the vehicle are considered to be the primary design objectives. Case studies by providing various emphases on the two objectives have also been performed. For all the cases, DEA–PCFE is found to yield highly accurate results.

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