Journal of the Korea Academia-Industrial cooperation Society Vol. 16, No. 6 pp , ISSN 197

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1 Journal of the Korea cademia-industrial cooperation Society Vol. 16, No. 6 pp , ISSN / eissn MDO 에서적용가능한근사기법의활용에관한연구 박창규 1* 1 전주비전대학교조선해양과 Study on an pproximation Technique using MDO Chang-Kyu Park 1* 1 Dept. of Ship & Ocean, VISION University, College of Jeonju 요약본논문은 MDO에서적용가능한근사기법의활용에관한연구를수행하였다. MDO 통합설계시스템을구축하는데있어서, 최적화과정에서발생하는수많은반복계산, 광범위한다분야간설계및 CD/CE 와의연계를고려함으로써발생하는방대한계산량및데이터의정보량으로인해수반되는계산비용을현저히줄이지않고는통합설계시스템을실제로구축한다해도그효용성은비현실적일수밖에없게된다. 따라서본연구에서는 MDO 통합설계시스템프레임워크의목적을위해, 필수적으로선행되어야하는다양한근사기법의적절한활용을통해 MDO에서적용가능한근사기법의활용에대한연구를수행하였다. bstract The paper describes the integrated design system using MDO and approximation technique. In MDO related research, final target is an integrated and automated MDO framework systems. However, in order to construct the integrated design system, the prerequisite condition is how much save computational cost because of iterative process in optimization design and lots of data information in CD/CE integration. Therefore, this paper presents that an efficient approximation method, daptive approximation, is a competent strategy via MDO framework systems. Key Words : daptive approximation, pproximation technique, CD/CE integration, MDO(Multidisciplinary Optimization), Optimization design 1. 서론다기능, 고성능, 다목적, 고부가가치의제품의설계를위해서는다수의공학적현상이연관된다분야해석및설계기술이필요하다. 즉, 다양한공학적원리, 지식, 기술등을동시에고려하여균형있고유기적인방법으로최적의설계를결정하는체계적인설계자동화기술인다분야통합최적설계 (Multidisciplinary Optimization, MDO) 기술이요구된다. 최근각분야별해석기술의눈부신발전으로인해점차그정밀도는높아졌으나, 이에따른설계의복잡성의증대로인해설계의체계적인다분야통합설계기술이절실히요구되고있다. 특히, 산업현장의설계프로세스에있어서, 세부적인 분야로의편중된연구와각분야만을위한적정설계로인한분야간상충현상이발생하게되는것을볼수있는데, 이러한분야간혹은부서간의설계타협을효율적으로해결하며, 관련분야간설계요소를동시에고려하는설계의통합화및자동화를구현해줄수있는 MDO 기술을도입함으로써, 제품설계에있어서고효율및균형있는생산을가능케해준다. 즉, 조선, 기계, 항공분야와같이복잡한시스템의효율적인설계기법으로대두되고있는 MDO 관련연구분야에있어서연구의최종목표는다분야설계를통합화, 자동화시킬수있는즉, MDO 통합설계프레임워크를구축 [Fig. 1] 하고자하는것이다. MDO 프레임워크를구축하기위해서는최적화요소 * Corresponding uthor : Chang-Kyu Park(VISION University, College of Jeonju) Tel: ckpark@jvision.ac.kr Received May 21, 2015 ccepted June 11, 2015 Revised June 10, 2015 Published June 30,

2 한국산학기술학회논문지제 16 권제 6 호, 2015 기법, 시스템통합기술, 이러한최적화기법과시스템통합기술의응용기술구축이필수적이다. 그러나, MDO 통합설계시스템을구축하는데있어서, 최적화과정에서발생하는수많은반복계산, 광범위한다분야간설계및 CD/CE와의연계를고려함으로써발생하는방대한계산량및데이터의정보량으로인해수반되는계산비용을현저히줄이지않고는통합설계시스템을실제로구축한다해도그효용성은비현실적일수밖에없게된다. 따라서, 본연구에서는 MDO 통합설계시스템프레임워크의목적을위해, 필수적으로선행되어야하는다양한근사기법 (pproximation) 의적절한활용을통해 MDO에서적용가능한근사기법의활용에대한연구를수행하였다. 2.2 MDO프레임워크국내외개발연구동향 MDO 프레임워크에관한연구는미래지향적핵심기술로분류하여국가적지원을받고있는미국을중심으로, 항공우주와관련된산업체, 대학, 자동차및정부기관연구소등에서수행되어왔다 [3]. 특히 1990년대중반이후많은 MDO 프레임워크가개발되어사용되고있다. 그중에서대표적으로 Engineous.com의 isight[4] 및 Phoenix Integration[5] 의 ModelCenter 및한양대학교최적설계신기술연구센터 (idot)[1] 에서개발된 EMDIOS 의 MDO 프레임워크의특성을비교하였다 [Table 1]. Table 1은주로이러한 MDO 프레임워크에서사용된각각의최적화기법, 근사기법, 샘플링기법, 품질공학기법및 MDO 방법론의관점을통해비교하였다. 또한, 특이할만한사항은 isight 및 ModelCenter는자체적으로 MDO 방법론 (Methodology), 즉, MDF(Multi Disciplinary Feasible), IDF(Individual Discipline Feasible), CO(Collaborative Optimization)[6] 등이내재되어있지않고사용자 (User) 가이러한필요한 MDO 방법론을직접 Formulation해야하는어려운문제점이내재되어있다는것이다. Table 1. Research trend in MDO Framework Fig. 1. n integrated and automated MDO framework 2. 통합설계시스템을위한 MDO 프레임워크 2.1 국내연구동향국내에서통합설계시스템을위한 MDO 관련연구는기계및항공분야를중심으로활발히진행되고있다. 기계분야는한양대학교최적설계신기술연구센터 [1] 를중심으로최적화기술, 정보기술, 통합설계기술및기존 CD/CE도구를통합하여 MDO 프레임워크를구축하고있으며, 항공분야는 DD 비행체기술특화연구센터를 [2] 중심으로공력 / 구조연계설계기법, 스텔스기술의 MDO 적용기법, 불확정성을고려한비행체구조설계기법, 초음속무인비행체최적형상설계기법및로터특성을고려한 MDO 기법을연구하고있다. Development Optimization Technique isight ModelCenter EMDIOS Engineous.com Phoenix Integration idot Exterior Penalty Hooke-Jeeves MMFD DS Tool MFD SLP DOT Tool SLP, SQP SQP G G, S RSM based Gradient-based pproximation Robust Reliability - - nalysis pproximation RSM RSM Quality Engineering MDO Methodology User Defined Formulation User Defined Formulation MDF, IDF, CO 2.3 MDO 통합설계시스템 - Basic Concept 본연구에서제안하고자하는 MDO 통합설계시스템의기본개념은 Fig. 2와같이개략적으로나타낼수있는데, 기본개념은기본설계 (Basic ), 상세설계 (Detail ), 생산설계 (Production ) 및생산 (Production) 의설계전반적인과정전체를통합하는것이다. 3662

3 MDO 에서적용가능한근사기법의활용에관한연구 Integrated Overall More fast process More convenience MDO Based Basic Detail X2 1 Production Construction Original Problem Screening using DOE pproximation Fig. 2. n integrated and automated MDO framework - Basic Concept 또한, MDO와최적설계의본질적인수많은반복과정및설계 / 해석연계, 즉, CD/CE 와의연계를통해설계해의반복과정탐색과정에서발생하는다량의설계정보의부담및계산시간의부담을최소화하기위해 DOE( Of Experiment) 를기반으로설계영역을 Screening하여적절한근사기법을적용하여, 보다빠르고편리한, 통합설계시스템을구축하는것이다. X1 FOSM(dvanced First-Order Second-Moment) 기법 [8] 이며, 결과를 Table 2에나타내었다. Table 2에는유한요소해석없이 FOSM과보이론에서유도된식을이용한 nalysis 1, FOSM과해석프로그램 (nsys) 과연계한 nalysis 2 및 FOSM과해석프로그램 (nsys) 의과도한계산시간을효과적으로줄이기위해 RSM의근사기법을연계한 nalysis 3의각각의반복 (Iteration) 횟수, 계산시간 (Computing time) 및파괴확률 (Probability of Failure, P f) 의결과를나타내었다. nalysis 2의결과에서알수있듯이총 40회의반복계산을무려 3일동안수행하여중간에실행을정지할수밖에없었고 nalysis 3에서는해석과정에서발생하는계산시간을효율적으로줄이기위해근사기법인 RSM을이용하여한계상태식 (Limit State Equation, LSE) 을몇번의탐색과정을통해근사화하여최종결과를얻을수있었다. 이상의결과에서알수있듯이해석과정과의연계로인해발생하는계산시간의증가는피할수없지만적절한근사기법을적용함으로써현저하게계산비용의부담을줄일수있음을확인할수있었다. 3. MDO 통합설계시스템에서 근사기법의활용 3.1 MDO통합설계시스템에서근사기법의필요성최적설계에있어서많은제약조건을만족시키고좀더우수한설계점을찾기위해서는크고작은반복과정은피할수없다. 특히, MDO 통합설계시스템에서는단순히최적설계뿐만아니라설계 / 해석정보의통합화로인해반복적인탐색과정의증가가불가피하게된다. 해석과정, 즉, 유한요소해석 (FEM) 에있어서해석모델수행은과도한계산시간이필연적으로수반될수밖에없다. 본연구에서는실제로이러한해석과정에서얼마나많은반복계산의부담이될수있는지규명하고실제로이러한 MDO 통합설계시스템에서근사기법의필요성을설명하기위해화재에의한보 (Beam) 요소의구조강도평가에있어서파괴확률 (Probability of Failure) 을구하는예 [Fig. 4] 를제시한다 [7]. Fig. 3에적용된보요소의모델및범용유한요소해석프로그램 (nsys) 과확률적기법 (Probabilistic pproach) 과의연계를도시하였다. 본예제에서적용된확률적기법은 Hasofer-Lind의 Fig. 3. Fire Safety nalysis Example Table 2. Comparisons of Fire Safety nalysis Example nalysis 1 (FOSM + Beam Theory) nalysis 2 (FOSM + nalysis Interface) More than 40 times nalysis 3 (RSM + nalysis Interface) # of Iteration Computing Time(sec) days after Stop Probability of Failure, P f 따라서, 선박, 기계, 항공등과같은대규모설계시스템의경우에있어서는, 다량의설계변수와제약조건을만족하기위한반복계산과정및, 설계 / 해석과의연계로 3663

4 한국산학기술학회논문지제 16 권제 6 호, 2015 인해계산시간을얼마나줄일수있느냐가중요한관건이될수밖에없다. 3.2 적응적근사모델기법일반적으로근사기법 (pproximation Method) 은크게 NN(Neural Network), GP(Genetic Programming) 와같은전역근사기법 (Global pproximation) 과 RSM(Response Surface Method) 과같은국부근사기법 (Local pproximation) 으로분류되며본연구에서는이러한근사기법들에비해효율성을부가하여해의정확성을보장하기위한근사기법으로전역근사와국부근사가조합된적응적근사모델 (daptive pproximation) 이다. 적응적근사모델은관심영역의계속적인수정을통해정확도를향상시킴으로써고성능 (High-fidelity) 함수의효율적인평가를통해정확한최적점으로의수렴을목적으로한다. 기존의근사기법은실제로평가해본결과제한조건을위배한다거나실제최적점과는거리가먼, 해로서부적합한경우마땅히대처할일반적전략이없게된다. 반면적응적근사모델의경우, 최적화모듈에고성능 (High-fidelity) 모델에대한정보를제공하고, 반대로최적화는근사모델에새롭게추가될표본점에대한정보를제공하는상호보완적인과정을포함한다. 즉, 근사계산및해석계산의과정에서일괄적인근사를하지않고근사계산과해석계산의계속적인수정을하게된다. 이두기법은단일목적 [Fig. 4] 및다목적최적화 [Fig. 5] 과정에서근사모델의계속적인개선 (Update) 을통해고성능 (High-fidelity) 근사해석을수행함으로써최적점을얻을수있는가능성을부가한기법이다 [9,10]. Pareto set System Optimizer Search using MultiObjective Opt. MultiObjective by MOG Opt. by MOG Select a few points among Pareto set Single Objective Single Opt. by Objective S Opt. by S Discipline s Discipline s Optimization for given coupling points Update Re-fitting including new poin Fig. 5. MO(daptive pproximation in Multi- Objective Optimization) 3.3 MDO에서근사기법의활용앞절에서최적화과정에서많은계산을요하는해석에의존한최적화문제에서근사기법을효과적으로관리하는방안을제시했다. 그목적은계산비용과시간을줄임과동시에거의정확한최적점에도달하도록하는데있다. 그방안들은근사모델을사용한최적화를통해얻은정보를이용해근사모델을재구성하는과정을반복하게된다. 이로써그러한재구성과정이없이단순하게근사모델을이용하는최적화에비해더적은표본점으로더정확히최적점에다다를수있게된다. 본연구에서제안하고자하는 daptive pproximation in Multi-Disciplinary Optimization, MDO)[Fig. 6] 는 MDO기법중에서 CO[6] 의시스템단계의최적화에이기법을적용하게하는것이다. Search using System Optimizer Search using Optimizer Optimizer MultiObjective Opt. MultiObjective by MOG Opt. by MOG Single Objective Single Opt. by Objective S Opt. by S Evaluate predicted a predicted predictive capability High-fidelity nalysis High-fidelity nalysis Update Re-fitting including new x Fig. 4. SO(daptive pproximation in Single Objective Optimization) Pareto set Select a few points among Pareto set Discipline s Discipline s Optimization for given coupling points Update Re-fitting including new points Fig. 6. MDO(daptive pproximation in MDO) 3664

5 MDO 에서적용가능한근사기법의활용에관한연구 이로써최적화에필요한하위분야의최적화의회수를줄이면서동시에정확한최적점이나 Pareto set에최대한근접할수있게된다. 결과가 Weighting method로다목적을처리한 Standard Optimization 과 CO의결과와일치하는것을보여주고있다. Q b cm h t 3 b 2 R P Load Case 2: 135 kn-cm 150 cm 45 o P Load Case 1: 100 kn Fig. 7. Two-member hub frame[11] t 1 t 2 Translational Displacement (cm) SO (Weighting Method, Time = 86 sec) MDO (MOG, Time = 69 sec) CO (Weighting Method, Time = 164 sec) Volume (cm 3 ) Fig. 9. Result of two-member hub frame problem 4. 결론 본연구에서는 MDO 통합설계프레임워크를구축하기위해 MDO와관련된국내기계, 항공분야의연구센터를통해향후 MDO 통합설계프레임워크를구축하기위해필요한기술이무엇인지를살펴보았고, 국내외에서개발된다양한 MDO 프레임워크의개별적인특성을살펴보았다. MDO 프레임워크에서는본질적으로다양한 CD/CE와의연계를구축해야하므로최적화및 MDO의반복계산과 Fig. 8. MDO(CO) formulation for two-member hub frame problem 3.4 MDO에서근사기법의적용예본예제는 Fig. 7과같은 two-member hub frame의단면치수를결정하는것이며 MDO(CO) 정식화는 Fig.8 과같다. 세분야간의연성변수중부재 PQ와 PR의부재력은분야 0을분야 1, 2 보다선행수행함으로써제거될수있다 [11]. 목적함수로는전체부피와절점 P에서의병진변위를최소화하는것이다. 설계제한조건으로는 P에서의변위제한조건과각부재의허용응력과좌굴에대한조건이있다. 절점 P에서의병진변위와각분야의제한조건위배량인 d 1 과 d 2 는각각네연성변수, 즉두부재의단면적 ( 1, 2 ) 과 2 차관성모멘트 ( I 1, I 2 ) 의함수로근사된다. Fig. 9 는 MDO 방법에의한 정및설계 / 해석정보에서발생하는과도한계산시간을효율적으로줄이는것이무엇보다도중요한기반기술이됨을보요소의화재시구조강도평가방법을근거로확인할수있었다. 또한, MDO에서이러한근사기법을효율적으로적용하기위한일환으로적응적근사기법을적용한 MDO의활용을 two-member hub frame의단면치수를결정하는예를통해증명하였다. MDO 프레임워크를단지학계만의연구가아닌실제로산업현장에서응용할수있을정도로구축하기위해서는아직도해결해야될문제점이산적한데그중의하나가다분야전문지식을효과적으로교환하고응용될수있도록지원하는협동설계작업환경, 즉, 분산설계구현기술과인터넷환경에적합하며, 분산된다양한플랫폼및다른언어로개발된프로그램들을통합하고, 기업내의부서간또는기업간의협업설계를위한웹기반 MDO 프레임워크의기술이향후필요할것으로기대된다. 3665

6 한국산학기술학회논문지제 16 권제 6 호, 2015 References [1] idot Homepage, vailable From: [2] FVRC Homepage, vailable From:, [3] S. O. Cho, J. Y. Hwang, et al, Overview of Framework and Databese Deveopment for Multidisciplinary Interated Environment, Journal of KSS, Vol. 29, pp , [4] Engineous.com Homepage, [5] Phonex Integration Homepage, vailable From:, [6] Braun, R., D., Collaborative Optimization: n rchitecture for Large-Scale Distributed, Ph.D. Dissertation, Stanford University, [7] S. Y. Lee, Study of Structural Strength ssessment under Fire Situation, MS Thesis, Seoul National University, [8] Y. S. Yang, Y. S. Seo, J. O. Lee, Structural Reliability Engineering, Seoul National University Press, [9] Y. S. Yang, B. S. Jang et al, Managing approximation models in Multiobjective optimization, Structural and multidisciplinary Optimization, Vol. 24, [10] B. S. Jang, Managing pproximation Model in Collaborative Optimization, Ph.D. Dissertation, Seoul National University, [11] Balling, R. J., and Sobieszczanski-Sobieski, J., n lgorithm for Solving the System-Level Problem in Multilevel Optimization, Structural Optimization, vol. 9, pp , DOI: 박창규 (Chang-Kyu Park) [ 정회원 ] 2007년 8월 : 서울대학교조선해양공학과 ( 공학박사 ) 2007년 9월 ~ 2008년 8월 : 서울대학교해양시스템공학연구소선임연구원 2008년 11월 ~ 2009년 2월 : LG 전자선임연구원 2009년 3월 ~ 현재 : 전주비전대학교조선해양과교수 < 관심분야 > 선박설계, 다분야통합최적설계 (MDO), CD/CE 3666

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