표준정규분포를 고려한 반응표면모델 기반 디스크 브레이크의 강건최적설계

이광기(Kwang Ki Lee),이용범(Yong Bum Lee),한승호(Seung Ho Han) 대한기계학회 2010 大韓機械學會論文集A Vol.34 No.9

복잡한 시스템 계의 설계정보를 효과적으로 추출하기 위해서 형상최적설계가 수행되는 경우, 일반적으로 유한요소해석 기법과 D-최적배열을 이용한 실험계획법이 연동된 반응표면모델을 구성하고 여기에 최적설계기법이 적용된다. 그러나, 설계변수에 형상공차와 같은 변동성이 존재하면 최적해의 강건성 확보를 위하여 설계변수의 형상공차를 확률론적인 변동성으로 고려한 추가적인 강건설계가 필요하다. 본 연구에서는 계산시간이 많이 소요되는 유한요소해석에 의한 강건설계문제에 설계변수의 표준정규분포를 고려한 반응표면모델을 구축하여 최적설계를 수행하므로서 손쉽게 강건최적값을 구하는 방법을 제안하였다. 승용차용 브레이크 디스크에 제안된 방법을 적용하여 열변형과 중량을 최소화하는 설계변수의 강건최적해를 구하고, 몬테카를로 시뮬레이션 추정결과와 비교하여 이의 적합성을 검증하였다. In a practical design process, the method of extracting the design space information of the complex system for verifying, improving, and optimizing the design process by taking into account the design variables and their shape tolerance is very important. Finite element analysis has been successfully implemented and integrated with design of experiment such as D-Optimal array; thus, a response surface model and optimization tools have been obtained, and design variables can be optimized by using the model and these tools. Then, to guarantee the robustness of the design variables, a robust design should be additionally performed by taking into account the statistical variation of the shape tolerance of the optimized design variables. In this study, a new approach based on the use of the response surface model is proposed; in this approach, the standard normal distribution of the shape tolerance is considered. By adopting this approach, it is possible to simultaneously optimize variables and perform a robust design. This approach can serve as a means of efficiently modeling the trade-off among many conflicting goals in the applications of finite element analysis. A case study on the robust optimal design of disc brakes under thermal loadings was carried out to solve multiple objective functions and determine the constraints of the design variables, such as a thermal deformation and weight.

표준정규분포를 고려한 반응표면모델 기반 디스크 브레이크의 강건최적설계

이광기(Kwang Ki Lee),이용범(Yong Bum Lee),한승호(Seung Ho Han) 대한기계학회 2010 대한기계학회 춘추학술대회 Vol.2010 No.5

복잡한 시스템 계의 설계정보를 효과적으로 추출하기 위해서 형상최적설계가 수행되는 경우, 일반적으로 유한요소해석 기법과 D-최적배열을 이용한 실험계획법이 연동된 반응표면모델을 구성하고 여기에 최적설계기법이 적용된다. 그러나, 설계변수에 형상공차와 같은 변동성이 존재하면 최적해의 강건성 확보를 위하여 설계변수의 형상공차를 확률론적인 변동성으로 고려한 추가적인 강건설계가 필요하다. 본 연구에서는 계산시간이 많이 소요되는 유한요소해석에 의한 강건설계문제에 설계변수의 표준정규분포를 고려한 반응표면모델을 구축하여 최적설계를 수행하므로서 손쉽게 강건최적값을 구하는 방법을 제안하였다. 승용차용 브레이크 디스크에 제안된 방법을 적용하여 열변형과 중량을 최소화하는 설계변수의 강건최적해를 구하고, 몬테카를로 시뮬레이션 추정결과와 비교하여 이의 적합성을 검증하였다. In the practical design process, it is very important how to extract the design space information of the complex system for verifying, improving and optimizing the design process to take into account of design variables with their shape tolerance. The finite element analysis has been successfully implemented and integrated with a design of experiment such as D-Optimal array providing a response surface model and optimization tools, so that optimized design variables can be found. Then, to ensure robustness of the design variables the robust design should be performed additionally, in which the statistical variation from shape tolerance of the design variables optimized is taken into account. In this study a new approach via the response surface model considering standard normal distribution of the shape tolerance is proposed that enables to perform both of the optimization and robust design. This approach can be utilized as an efficient means to rapidly model the trade-off among many conflicting goals existed in the finite element analysis applications. For the case study the robust optimal design of disc brake under thermal loadings was carried out to apply solving multiple objective functions and constraints of the design variables such as a thermal deformation and weight.

Quality Engineering Optimization of Robot Casting Considering Design Robustness: Comparison with Reliability

최하영,박준오,이종수 한국정밀공학회 2013 International Journal of Precision Engineering and Vol.14 No.12

The global business circumstances are rapidly changed so the design optimization which is related to quality engineering is needed than ever. In case of the robot casting the tolerance of material and variation of material property are the main cause of quality issues and such a reason quality based design optimization is urgently needed. Robust design gives robustness to the objective function considering tolerance and variation of material property while in the reliability based design, they are controlled by probability of constraint violation. In this study, two other quality engineering methods are done about same robot casting and compare with each other. During that process, some technical theory is applied. Sensitivity analysis with the design of experiments is used for reducing control design variable, approximation with central composite design is used to make objective and constraint functions. Genetic algorithm and search direction method is applied to make robust design optimization. For reliability based design optimization, the performance measure approach method is used. Comparing two other quality engineering method means that the robustness of objective and constraint functions which is resulted from robust design has certain results in aspect of reliability which is controlled by probability of constraint violation.

Theoretical and experimental study of robustness based design of single-layer grid structures

Wu, Hui,Zhang, Cheng,Gao, Bo-Qing,Ye, Jun Techno-Press 2014 Structural Engineering and Mechanics, An Int'l Jou Vol.52 No.1

Structural robustness refers to the ability of a structure to avoid disproportionate consequences to the original cause. Currently attentions focus on the concepts of structural robustness, and discussions on methods of robustness based structural design are rare. Firstly, taking basis in robust $H_{\infty}$ control theory, structural robustness is assessed by $H_{\infty}$ norm of the system transfer function. Then using the SIMP material model, robustness based design of grid structures is formulated as a continuum topology optimization problem, where the relative density of each element and structural robustness are considered as the design variable and the optimization objective respectively. Generalized elitist genetic algorithm is used to solve the optimization problem. As examples, robustness configurations of plane stress model and the rectangular hyperbolic shell model were obtained by robustness based structural design. Finally, two models of single-layer grid structures were designed by conventional and robustness based method respectively. Different interference scenarios were simulated by static and impact experiments, and robustness of the models were analyzed and compared. The results show that the $H_{\infty}$ structural robustness index can indicate whether the structural response is proportional to the original cause. Robustness based structural design improves structural robustness effectively, and it can provide a conceptual design in the initial stage of structural design.

Theoretical and experimental study of robustness based design of single-layer grid structures

Hui Wu,Cheng Zhang,Bo-qing Gao,Jun Ye 국제구조공학회 2014 Structural Engineering and Mechanics, An Int'l Jou Vol.52 No.1

Structural robustness refers to the ability of a structure to avoid disproportionate consequences to the original cause. Currently attentions focus on the concepts of structural robustness, and discussions onmethods of robustness based structural design are rare. Firstly, taking basis in robust H∞ control theory,structural robustness is assessed by H∞ norm of the system transfer function. Then using the SIMP material model, robustness based design of grid structures is formulated as a continuum topology optimization problem, where the relative density of each element and structural robustness are considered as the design variable and the optimization objective respectively. Generalized elitist genetic algorithm is used to solve the optimization problem. As examples, robustness configurations of plane stress model and the rectangular hyperbolic shell model were obtained by robustness based structural design. Finally, two models of single-layer grid structures were designed by conventional and robustness based method respectively. Different interference scenarios were simulated by static and impact experiments, and robustness of the models were analyzed and compared. The results show that the H∞ structural robustness index can indicate whether the structural response is proportional to the original cause. Robustness based structural design improves structural robustness effectively, and it can provide a conceptual design in the initial stage of structural design.

Uncertainty-based MDO for aircraft conceptual design

Park, Hyeong-Uk,Lee, Jae-Woo,Chung, Joon,Behdinan, Kamran Emerald Group Publishing Limited 2015 Aircraft engineering and aerospace technology Vol.87 No.4

<P><B>Purpose</B></P> <P> – The purpose of this paper is to study the consideration of uncertainty from analysis modules for aircraft conceptual design by implementing uncertainty-based design optimization methods. Reliability-Based Design Optimization (RBDO), Possibility-Based Design Optimization (PBDO) and Robust Design Optimization (RDO) methods were developed to handle uncertainties of design optimization. The RBDO method is found suitable for uncertain parameters when sufficient information is available. On the other hand, the PBDO method is proposed when uncertain parameters have insufficient information. The RDO method can apply to both cases. The RBDO, PBDO and RDO methods were considered with the Multidisciplinary Design Optimization (MDO) method to generate conservative design results when low fidelity analysis tools are used. </P> <P><B>Design/methodology/approach</B></P> <P> – Methods combining MDO with RBDO, PBDO and RDO were developed and have been applied to a numerical analysis and an aircraft conceptual design. This research evaluates and compares the characteristics of each method in both cases. </P> <P><B>Findings</B></P> <P> – The RBDO result can be improved when the amount of data concerning uncertain parameters is increased. Conversely, increasing information regarding uncertain parameters does not improve the PBDO result. The PBDO provides a conservative result when less information about uncertain parameters is available. </P> <P><B>Research limitations/implications</B></P> <P> – The formulation of RDO is more complex than other methods. If the uncertainty information is increased in aircraft conceptual design case, the accuracy of RBDO will be enhanced. </P> <P><B>Practical implications</B></P> <P> – This research increases the probability of a feasible design when it considers the uncertainty. This result gives more practical optimization results on a conceptual design level for fabrication. </P> <P><B>Originality/value</B></P> <P> – It is RBDO, PBDO and RDO methods combined with MDO that satisfy the target probability when the uncertainties of low fidelity analysis models are considered.</P>

Development of optimal water distribution system design and operation approach considering hydraulic and water quality criteria in many-objective optimization framework

Choi Young Hwan 한국CDE학회 2022 Journal of computational design and engineering Vol.9 No.2

Water distribution systems (WDSs) are major infrastructure, and it needs to consider economic, hydraulic stability, and water quality safety to optimal design and operation of WDSs. However, the previous studies related to WDS design and operation were focused on each field (i.e. design: optimal pipe diameter, pump sizing, and valve location; operation: optimal pump scheduling, etc.) even though the WDS design and operation have a correlation. Therefore, to achieve economic feasibility, hydraulic stability, and water quality safety under WDS design and operation process, this study develops an optimal WDS design and operation approach considering hydraulic and water quality criteria in the many-objective optimization framework. To consider design and operation, this study applies three objective functions to minimize the total design and operation cost (i.e. the pipe cost, pump construction, and pump operation cost), maximize system robustness, and minimize the amount of chlorine requisition simultaneously under the hydraulic and quality constraints. The proposed optimal WDS design and operation model was applied to the two-stage optimization procedures. The first process determined the optimal pipe diameter set. The second process determined the optimal pump construction and scheduling considering three objective functions such as the total pump cost, the system robustness, and the quantity of the required residual chlorine for determining optimally the available number of pumps, capacity, and scheduling. For the optimization, the self-adaptive multi-objective harmony search is used and a famous benchmark network for the optimal design and pump operation of WDSs is applied to verify the proposed approach. This study can provide a new perspective on WDS design and operation technique considering the essential design factors to the water utility.

Optimal design of pma-synrm for e-bike traction motor using adaptive interpolation robustness optimization algorithm

손지창,임동국 한국자동차공학회 2024 International journal of automotive technology Vol.25 No.1

This paper proposes an adaptive interpolation robustness optimization algorithm (AIROA) for the robust optimal design of a permanent magnet assisted synchronous reluctance motor for electric bicycle (EB) traction. The AIROA can drastically reduce the number of function calls to converge to an optimal solution by interpolating the problem regions. Especially, the AIROA eff ectively adjusts the number of generated samples using the diversifi cation strategy with novel initial sampling strategy. Moreover, in the intensive searching strategy, the calculation time for generating a surrogate model and the accuracy of the solutions of the surrogate model can be enhanced as the AIROA adjusts the resolution of the interpolation near the roughly found solutions. At the end of the algorithm, a robustness test strategy is conducted, and a robust optimal solution is determined considering the accuracy of the interpolated uncertainty band of both global and local solutions. The superior performance of the AIROA was verifi ed by two mathematical test functions. The applicability of the practical motor design was verifi ed by applying the AIROA to the optimal design of the EB traction motor and successfully deriving the robust optimum design. The prototype motor was manufactured, and further validation was conducted by comparing the experimental results.

A Study for Robustness of Objective Function and Constraints in Robust Design Optimization

Tae Won Lee 대한기계학회 2006 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.20 No.10

Since randomness and uncertainties of design parameters are inherent, the robust design has gained an ever increasing importance in mechanical engineering. The robustness is assessed by the measure of performance variability around mean value, which is called as standard deviation. Hence, constraints in robust optimization problem can be approached as probability constraints in reliability based optimization. Then, the FOSM (first order second moment) method or the AFOSM (advanced first order second moment) method can be used to calculate the mean values and the standard deviations of functions describing constraints and object. Among two methods, AFOSM method has some advantage over FOSM method in evaluation of probability. Nevertheless, it is difficult to obtain the mean value and the standard deviation of objective function using AFOSM method, because it requires that the mean value of function is always positive. This paper presented a special technique to overcome this weakness of AFOSM method. The mean value and the standard deviation of objective function by the proposed method are reliable as shown in examples compared with results by FOSM method.

ROBUST RELIABILITY DESIGN OF VEHICLE COMPONENTS WITH ARBITRARY DISTRIBUTION PARAMETERS

Zhang, Y.,He, X.,Liu, Q.,Wen, B. The Korean Society of Automotive Engineers 2006 International journal of automotive technology Vol.7 No.7

This study employed the perturbation method, the Edgeworth series, the reliability optimization, the reliability sensitivity technique and the robust design to present a practical and effective approach for the robust reliability design of vehicle components with arbitrary distribution parameters on the condition of known first four moments of original random variables. The theoretical formulae of the robust reliability design for vehicle components with arbitrary distribution parameters are obtained. The reliability sensitivity is added to the reliability optimization design model and the robust reliability design is described as a multi-objection optimization. On the condition of known first four moments of original random variables, the respective program can be used to obtain the robust reliability design parameters of vehicle components with arbitrary distribution parameters accurately and quickly.