A Study for robustness of objective function and constraints in robust design optimization

2006 ◽  
Vol 20 (10) ◽  
pp. 1662-1669 ◽  
Author(s):  
Tae Won Lee
Keyword(s):  
Objective Function ◽  
Design Optimization ◽  
Robust Design ◽  
Robust Design Optimization

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.

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 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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