• Journal of Mechanical Science and Technology
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• 제15권8호
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• pp.1143-1155
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• 2001

In order to reduce the expensive CPU time for design sensitivity analysis in dynamic response optimization, this study introduces the design sensitivities approximated within estimated confidence radius in dynamic response optimization with ALM method. The confidence radius is estimated by the linear approximation with Hessian of quasi-Newton formula and qualifies the approximate gradient to be validly used during optimization process. In this study, if the design changes between consecutive iterations are within the estimated confidence radius, then the approximate gradients are accepted. Otherwise, the exact gradients are used such as analytical or finite differenced gradients. This hybrid design sensitivity analysis method is embedded in an in-house ALM based dynamic response optimizer, which solves three typical dynamic response optimization problems and one practical design problem for a tracked vehicle suspension system. The optimization results are compared with those of the conventional method that uses only exact gradients throughout optimization process. These comparisons show that the hybrid method is more efficient than the conventional method. Especially, in the tracked vehicle suspension system design, the proposed method yields 14 percent reduction of the total CPU time and the number of analyses than the conventional method, while giving similar optimum values.

• International Journal of Naval Architecture and Ocean Engineering
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• 제7권4호
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• pp.750-769
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• 2015

The geometry of engineering systems affects their performances. For this reason, the shape of engineering systems needs to be optimized in the initial design stage. However, engineering system design problems consist of multi-objective optimization and the performance analysis using commercial code or numerical analysis is generally time-consuming. To solve these problems, many engineers perform the optimization using the approximation model (response surface). The Response Surface Method (RSM) is generally used to predict the system performance in engineering research field, but RSM presents some prediction errors for highly nonlinear systems. The major objective of this research is to establish an optimal design method for multi-objective problems and confirm its applicability. The proposed process is composed of three parts: definition of geometry, generation of response surface, and optimization process. To reduce the time for performance analysis and minimize the prediction errors, the approximation model is generated using the Backpropagation Artificial Neural Network (BPANN) which is considered as Neuro-Response Surface Method (NRSM). The optimization is done for the generated response surface by non-dominated sorting genetic algorithm-II (NSGA-II). Through case studies of marine system and ship structure (substructure of floating offshore wind turbine considering hydrodynamics performances and bulk carrier bottom stiffened panels considering structure performance), we have confirmed the applicability of the proposed method for multi-objective side constraint optimization problems.

• 정보처리학회논문지B
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• 제14B권5호
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• pp.377-382
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• 2007

본 논문에서는 방사 기저함수 네트워크의 파라미터를 전 영역에서 최적화하는 학습 알고리즘을 제안한다. 기존의 학습 알고리즘들은 지역 최적화만을 수행하기 때문에 성능의 한계가 있고 최종 결과가 초기 네트워크 파라미터 값에 크게 의존하는 단점이 있다. 본 논문에서 제안하는 하이브리드 모의 담금질 기법은 모의 담금질 기법의 전 영역 탐색 능력과 경사 기반 학습 알고리즘의 지역 최적화 능력을 조합하여 전 파라미터 영역에서 해를 찾을 수 있도록 한다. 제안하는 기법을 함수 근사화 문제에 적용하여 기존의 학습 알고리즘에 비해 더 좋은 학습 및 일반화 성능을 보이는 네트워크 파라미터를 찾을 수 있으며, 초기 파라미터 값의 영향을 크게 줄일 수 있음을 보인다.

• 한국CDE학회논문집
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• 제21권4호
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• pp.443-452
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• 2016

This paper proposes a method for expensive black box optimization using radial basis functions (RBFs). The proposed algorithm is a computational strategy that uses a RBF model approximating the expensive black box function to predict an optimum. First, a RBF-based approximation technique is introduced and a sampling plan for estimation of the black box function is described. Then the proposed algorithm is explained, which presents the pseudo-codes for implementation and the detailed description of each step performed in the optimization process. In addition, numerical experiments will be given to analyze the performance of the proposed algorithm, by investigating computation accuracy, number of function evaluations, and convergence history. Finally, geometric distance problem as application example will be also presented for showing the algorithm applicability to different engineering problems.

• 한국CDE학회논문집
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• 제5권2호
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• pp.127-135
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• 2000

Emergent computing paradigms such as genetic algorithms have found increased use in problems in engineering design. These computational tools have been shown to be applicable in the solution of generically difficult design optimization problems characterized by nonconvexities in the design space and the presence of discrete and integer design variables. Another aspect of these computational paradigms that have been lumped under the bread subject category of soft computing, is the domain of artificial intelligence, knowledge-based expert system, and machine learning. The paper explores a machine learning paradigm referred to as teaming classifier systems to construct the high-quality global function approximations between the design variables and a response function for subsequent use in design optimization. A classifier system is a machine teaming system which learns syntactically simple string rules, called classifiers for guiding the system's performance in an arbitrary environment. The capability of a learning classifier system facilitates the adaptive selection of the optimal number of training data according to the noise and multimodality in the design space of interest. The present study used the polynomial based response surface as global function approximation tools and showed its effectiveness in the improvement on the approximation performance.

• 한국항공우주학회지
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• 제48권6호
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• pp.411-418
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• 2020

본 논문에서는 복합재 팬 블레이드의 구조적 성능에 대한 근사 및 최적설계 기법을 제안하였다. 그리고 이들을 활용하여 복합재 팬 블레이드의 질량 및 형상의 변화 없이 강성을 최대화하기 위한 적층 패턴의 최적설계를 수행하였다. 이 때 설계 변수 및 설계 영역을 축소하기 위하여 적층 파라미터를 도입하였고, 적층 파라미터의 특성을 활용하여 높은 적합도를 갖는 반응표면 근사모델을 생성하였다. 또한 효율적인 최적해 탐색을 위해 도함수 기반 방법과 유전자 알고리즘을 결합한 2단계 최적화 방법을 적용하였으며, 다양한 요구조건들을 고려한 다목적 최적설계를 수행하였다. 마지막으로는 초기 모델과 최적설계 모델의 유한요소해석 결과를 비교하여 적층 파라미터 기반의 근사 및 최적설계 기법을 검증하였다.

• 대한전자공학회논문지SD
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• 제43권3호
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• pp.15-20
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• 2006

본 논문은 Newton-Raphson 방법을 기반으로 하는 table-driven 알고리듬에 대해 연구되었다. 특히 본 논문에서는 Newton-Raphson 방법을 이용한 제곱근 근사에 중점을 두었다. Newton-Raphson방법에서 최적화된 초기근사해를 구하게 되면 제곱근 근사의 정확성을 높일 수 있으며, 연산 속도 또한 빨라지게 된다. 그러므로 Newton-Raphson 알고리듬에서 초기근사해를 어떻게 결정하느냐하는 것이 전체적인 알고리듬의 성능을 평가하게 되는 중요한 이슈이다. 본 논문에서는 Newton-Raphson 알고리듬의 초기 근사해를 기하평균을 기준으로 테이블에 저장, 연산의 속도와 최대 오차율을 줄일 수 있음을 확인하였다.

• Smart Structures and Systems
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• 제11권3호
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• pp.241-259
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• 2013

This paper presents the optimum load-speed diagram evaluation for a linear micromotor, including multitude cantilever piezoelectric bimorphs, briefly. Each microbeam in the mechanism can be actuated in both axial and flexural modes simultaneously. For this design, we consider quasi-static and linear conditions, and a relatively new numerical method called the smoothed finite element method (S-FEM) is introduced here. For this purpose, after finding an optimum volume fraction for piezoelectric layers through a standard numerical method such as quadratic finite element method, the relevant load-speed curves of the optimized micromotor are examined and compared by deterministic topology optimization (DTO) design. In this regard, to avoid the overly stiff behavior in FEM modeling, a numerical method known as the cell-based smoothed finite element method (CS-FEM, as a branch of S-FEM) is applied for our DTO problem. The topology optimization procedure to find the optimal design is implemented using a solid isotropic material with a penalization (SIMP) approximation and a method of moving asymptotes (MMA) optimizer. Because of the higher efficiency and accuracy of S-FEMs with respect to standard FEMs, the main micromotor characteristics of our final DTO design using a softer CS-FEM are substantially improved.

• Structural Engineering and Mechanics
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• 제45권6호
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• pp.759-777
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• 2013

In this paper, a topology optimization method based on the element independent nodal density (EIND) is developed for continuum solids with multiple load cases and multiple constraints. The optimization problem is formulated ad minimizing the volume subject to displacement constraints. Nodal densities of the finite element mesh are used a the design variable. The nodal densities are interpolated into any point in the design domain by the Shepard interpolation scheme and the Heaviside function. Without using additional constraints (such ad the filtering technique), mesh-independent, checkerboard-free, distinct optimal topology can be obtained. Adopting the rational approximation for material properties (RAMP), the topology optimization procedure is implemented using a solid isotropic material with penalization (SIMP) method and a dual programming optimization algorithm. The computational efficiency is greatly improved by multithread parallel computing with OpenMP to run parallel programs for the shared-memory model of parallel computation. Finally, several examples are presented to demonstrate the effectiveness of the developed techniques.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2008년도 정기 학술대회
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• pp.216-221
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• 2008

Shape design optimization for linear elasticity problem is performed using isogeometric analysis method. In many design optimization problems for real engineering models, initial raw data usually comes from CAD modeler. Then designer should convert this CAD data into finite element mesh data because conventional design optimization tools are generally based on finite element analysis. During this conversion there is some numerical error due to a geometry approximation, which causes accuracy problems in not only response analysis but also design sensitivity analysis. As a remedy of this phenomenon, the isogeometric analysis method is one of the promising approaches of shape design optimization. The main idea of isogeometric analysis is that the basis functions used in analysis is exactly same as ones which represent the geometry, and this geometrically exact model can be used shape sensitivity analysis and design optimization as well. In shape design sensitivity point of view, precise shape sensitivity is very essential for gradient-based optimization. In conventional finite element based optimization, higher order information such as normal vector and curvature term is inaccurate or even missing due to the use of linear interpolation functions. On the other hands, B-spline basis functions have sufficient continuity and their derivatives are smooth enough. Therefore normal vector and curvature terms can be exactly evaluated, which eventually yields precise optimal shapes. In this article, isogeometric analysis method is utilized for the shape design optimization. By virtue of B-spline basis function, an exact geometry can be handled without finite element meshes. Moreover, initial CAD data are used throughout the optimization process, including response analysis, shape sensitivity analysis, design parameterization and shape optimization, without subsequent communication with CAD description.