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.

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.

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.

Comparison of the robustness-based optimal designs of water distribution systems in three different formulations

Jung, Donghwi,Kang, Doosun,Chung, Gunhui,Kim, Joong Hoon IWA Publishing 2013 Journal of hydroinformatics Vol.15 No.4

<P>Robustness is generally defined as a system's ability to stay within satisfactory bounds against variations in system factors. Recently, robustness has been indicated to be a useful objective function for the optimal design of water distribution systems (WDSs). While various formulations are possible to represent WDS robustness, few efforts have been made to compare the performances of these formulations. This study examined three potential formulations for quantifying system robustness to provide guidelines on the usage of a robustness index. Giustolisi <I>et al</I>.'s robustness index (see Giustolisi <I>et al.</I> (2009) ‘Deterministic versus stochastic design of water distribution networks’, <I>J. Water Resour. Plann. Manage.</I> <B>135</B> (2), 117–127) was adopted to calculate nodal robustness, while the system robustness was defined using three different formulations: (1) minimum among nodal robustness values; (2) total sum of nodal robustness; and (3) sum of nodal robustness at multiple critical nodes. The three proposed formulations were compared through application to identify the most appropriate one for enhancing system robustness in general; three representative benchmark networks were optimally designed to minimize the economic cost while maximizing the system robustness.</P>

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.

건설안전분야 : 다목적 시스템식별을 이용한 모우드 불확실성이 있는 구조물의 강인 최적 감쇠기 설계

정성운 ( Seong Woon Jeong ),옥승용 ( Seung Yong Ok ),박원석 ( Won Suk Park ),고현무 ( Hyun Moo Koh ) 한국안전학회(구-한국산업안전학회) 2012 한국안전학회지 Vol.27 No.1

This paper proposes a robust damper design technique for adjacent structures against model uncertainty. This approach introduces multi-objective optimization based system identification using measurement information which enables reasonable selection of the perturbation range in the robust design. Moreover, in order to improve the numerical efficiency in sampling the structural models required for the robust design of large structures, we define new objective functions which enable us to minimize the number of candidate models suitable to the purpose of the robust design. In addition, the performance index is newly employed to evaluate the robust performance of the sampled structural models, and the robust design has been performed according to the performance index. As a numerical example to demonstrate the efficiency of the proposed method, 5-story and 10-story two adjacent buildings are taken into account, and the existing and newly proposed robust design approaches are compared with each other. The results demonstrate that the proposed approach can guarantee more robust damper system only using small number of samples of the structural models because of using the measurement information which leads to improvement in the numerical efficiency, compared with the existing robust design methods

설계자 선호도를 고려한 동적 시스템의 강건설계법

김경모 ( Kim Gyeong Mo ) 한국품질경영학회 2003 품질경영학회지 Vol.31 No.4

Dynamic robust design has been regarded as the most powerful design methodology for improving product quality. Dynamic SN ratio adopted in dynamic robust design combines two major quality attributes, the variability around the linear function and the slope of the linear function, into a single design metric. The principal shortcoming associated with the dynamic SN ratio is that the metric is independent of designer`s preferences for the quality attributes due to priori sets of attribute tradeoff values inherent in it. Therefore, a more rigorous preference-based design metric to accurately capture designer s intent and preference is needed. A new design metric that can be used in dynamic robust design is proposed. The effectiveness of the proposed design metric is examined with the aid of a demonstrative case study and the results are discussed.

다 특성 설계 최적화를 위한 새로운 호감도 함수 적용 다구치 법

조재훈,이지호,박종필,남윤의 한국산업경영시스템학회 2022 한국산업경영시스템학회 학술대회 Vol.2022 No.추계

현대 사회가 복잡해지고 기술이 진보하면서 하나의 제품을 설계할 때 단일 특성이 아닌 다 특성을 갖는 제품을 설계하는 것이 요구되고 있다. 다 특성 설계 최적화 문제에서는 설계 변수의 최적값이 특성별로 다르게 되는 현상이 발생하고 이에 따라 하나의 특성에 대한 결과값이 좋아지면 다른 특성에 대한 결과값이 나빠지는 경우에 대해서 trade-off가 필요하다. 따라서 다 특성을 갖는 제품 설계 시 각각의 특성에 대한 성능을 최대화할 수 있는 효율적인 설계 방법의 필요성이 중요한 문제로 떠오르고 있다. 다 특성을 갖는 제품을 설계하는 연구는 오래전부터 중요한 문제로 인식되어 왔는데, 단일 특성에 대해 성능을 최대화하며 강건한 설계를 할 수 있는 다구치 기법과 다기준/다특성 의사 결정 방법인 TOPSIS(Technique for Order of Preference by Similarity to Ideal Solution), GRA(Grey relational analysis), PCA(Principle Component Analysis), Fuzzy Logic System을 통합한 연구들이 진행되어 왔다. 하지만 기존 연구들은 각각의 설계 대안들에 대해 다 특성 결과값에 대한 점수를 통합하여 종합 점수를 비교해 최적의 설계안을 도출할 뿐 설계자의 호감도에 대한 정보는 설계에 반영하지 못한다. 따라서 본 연구에서는 다구치 기법을 기반으로 각각의 특성들에 대한 설계자의 서로 다른 호감도를 함수로써 표현하여 강건성과 함께 설계자의 호감도를 동시에 설계에 반영할 수 있는 방법을 제안한다. As a modern society becomes complicated and technology advances, it is required to design products with multiple characteristics, not a single characteristic, when designing a product. In a multi-characteristic optimization design problem, an optimum value of design variables can be different for each characteristic. Accordingly, if a performance of one characteristic improves, performance of another characteristic can be deteriorated. So-called trade-off can occur. Therefore, when designing products with multiple characteristics, the need for an efficient design method that can maximize a performance for each characteristic is emerging as an important issue. Study on designing products with multiple characteristics has been recognized as an important issue for a long time, and studies that integrate the Taguchi method that maximizes performance for a single characteristic and makes a robust design possible with techniques for order of preference by ideal solution (TOPSIS), gray relational analysis (GRA), principal component analysis (PCA), fuzzy logic system which are multi-criteria/characteristic decision-making method have been conducted. However, existing studies just compare the overall score of the multi-characteristic results for each design alternative to obtain an optimal design solution, do not reflect information on the designer’s desirability in design. Therefore, in this study, based on the Taguchi method, we propose a design method that can reflect the designer’s desirability as well as robustness in the design by expressing the designer’s desirability for each characteristic as a function.

A Flexible and Robust Approach for Preliminary Engineering Design Based on Designer's Preference

Nahm, Yoon-Eui,Ishikawa, Haruo,Yang, Young-Soon Sage Publications 2007 Concurrent Engineering Vol.15 No.1

<P>This study proposes a new set-based design approach for preliminary engineering design that intrinsically contains various sources of uncertainties. The goal is to achieve design flexibility and robustness while capturing designer's preference. The proposed design approach includes three computational methods: (1) set representation method to specify the varying degree of desirability of a ranged set of design solutions and performance requirements, thereby enabling the manipulation of uncertain design solutions and requirements based on designer's preference structure; (2) set propagation method to obtain performance possibilities achievable by uncertain design solutions, thus exploring a broader design possibilities; (3) set narrowing method to generate a ranged set of feasible solutions (i.e., robust and flexible solution set) instead of single point solution that satisfies changing sets of performance requirements by eliminating infeasible and inferior subsets of solutions, thus allowing designs to be readily adapted to changing conditions. Finally, the proposed design approach is illustrated with a successful implementation of real industrial design problem (i.e., vehicle side-door structure design) in the simulation-based design environment.</P>