• Structural Engineering and Mechanics
• /
• 제55권6호
• /
• pp.1121-1137
• /
• 2015

High powered computers and engineering computer systems allow designers to routinely simulate complex physical phenomena. The presented work deals with the analysis of two finite element method optimization techniques (First Order Method-FOM and Subproblem Approximation Method-SAM) implemented in the individual Design Optimization module in the Ansys software to analyze the behavior of real problems. A design optimization is a difficult mathematical process, intended to find the minimum or maximum of an objective function, which is mostly based on iterative procedure. Using optimization techniques in engineering designs requires detailed knowledge of the analyzed problem but also an ability to select the appropriate optimization method. The methods embedded in advanced computer software are based on different optimization techniques and their efficiency is significantly influenced by the specific character of a problem. The efficiency, robustness and accuracy of the methods are studied through strictly convex two-dimensional optimization problem, which is represented by volume minimization of two bars' plane frame structure subjected to maximal vertical displacement limit. Advantages and disadvantages of the methods are described and some practical tips provided which could be beneficial in any efficient engineering design by using an optimization method.

• Nuclear Engineering and Technology
• /
• 제56권7호
• /
• pp.2610-2624
• /
• 2024

Liquid metal heat pipes play a critical role in various high-temperature applications, with their optimization being pivotal to achieving optimal thermal performance. In this study, a deep learning based genetic algorithm is suggested to optimize the operating conditions of liquid metal heat pipes. The optimization performance was investigated in both single and multi-variable optimization schemes, considering the operating conditions of heat load, inclination angle, and filling ratio. The single-variable optimization indicated reasonable performance for various conditions, reinforcing the potential applicability of the optimization method across a broad spectrum of high-temperature industries. The multi-variable optimization revealed an almost congruent performance level to single-variable optimization, suggesting that the robustness of optimization method is not compromised with additional variables. Furthermore, the generalization performance of the optimization method was investigated by conducting an experimental investigation, proving a similar performance. This study underlines the potential of optimizing the operating condition of heat pipes, with significant consequences in sectors such as high temperature field, thereby offering a pathway to more efficient, cost-effective thermal solutions.

• East Asian mathematical journal
• /
• 제31권3호
• /
• pp.371-377
• /
• 2015

We consider a nondifferentiable robust optimization problem, which has a maximum function of continuously differentiable functions and support functions as its objective function, continuously differentiable functions as its constraint functions. We prove optimality conditions for the nondifferentiable robust optimization problem. We formulate a Wolfe type dual problem for the nondifferentiable robust optimization problem and prove duality theorems.

• 한국CDE학회지
• /
• 제3권2호
• /
• pp.89-92
• /
• 1997

이 글에서 소개하는 topology optimization은 structural optimization의 한 분야로서 최근 10여년 동안 급격하게 발전되어 온 분야이다. Structural optimization은 오랜 역사(일반적으로 최초의 structural optimization은 17세기 Galileo에 의하여 되어졌다고 받아들임)를 가지고 발달되어 왔음에도 불구하고 아직도 최적화 방법론과 응용 관점에서 빠르게 발전되고 있다. 이 분야는 사회적인 요구(한정된 자원과 에너지, 안전도, 환경문제)와 컴퓨터 관련 학문(고성능 컴퓨터, computational geometry, finite element method)의 발달에 힘입어 최근 30년간 많은 진전이 있었다.

• East Asian mathematical journal
• /
• 제37권5호
• /
• pp.543-551
• /
• 2021

Recently, semidefinite optimization problems have been intensively studied since many optimization problem can be changed into the problems and the the problems are very computationable. In this paper, we consider a semidefinite linear vector optimization problem (VP) and we establish the optimality theorems for (VP), which holds without any constraint qualification.

• 한국추진공학회:학술대회논문집
• /
• 한국추진공학회 2008년 영문 학술대회
• /
• pp.130-135
• /
• 2008

An aerodynamic optimization design process of multistage axial turbine is presented in this article: first, applying quasi-three dimensional(Q3D) design methods to conduct preliminary design and then adopting modern optimization design methods to implement multistage local optimization. Quasi-three dimensional(Q3D) design methods, which mainly refer to S2 flow surface direct problem calculation, adopt the S2 flow surface direct problem calculation program of Harbin Institute of Technology. Multistage local optimization adopts the software of Numeca/Design3D, which jointly adopts genetic algorithm and artificial neural network. The major principle of the methodology is that the successive design evaluation is performed by using an artificial neural network instead of a flow solver and the genetic algorithms may be used in an efficient way. Flow computation applies three-dimensional viscosity Navier Stokes(N-S) equation solver. Such optimization process has three features: (i) local optimization based on aerodynamic performance of every cascade; (ii) several times of optimizations being performed to every cascade; and (iii) alternate use of coarse grid and fine grid. Such process was applied to optimize a three-stage axial turbine. During the optimization, blade shape and meridional channel were respectively optimized. Through optimization, the total efficiency increased 1.3% and total power increased 2.4% while total flow rate only slightly changed. Therefore, the total performance was improved and the design objective was achieved. The preliminary design makes use of quasi-three dimensional(Q3D) design methods to achieve most reasonable parameter distribution so as to preliminarily enhance total performance. Then total performance will be further improved by adopting multistage local optimization design. Thus the design objective will be successfully achieved without huge expenditure of manpower and calculation time. Therefore, such optimization design process may be efficiently applied to the aerodynamic design optimization of multistage axial turbine.

• 대한기계학회논문집A
• /
• 제31권11호
• /
• pp.1059-1068
• /
• 2007

Nonlinear response structural optimization is performed using equivalent loads (NROEL). Nonlinear response optimization is extremely cost because many nonlinear analyses are required. In NROEL, the external loads are transformed to the equivalent loads (EL) for linear static analysis and linear response optimization is carried out based on the EL in a cyclic manner until the convergence criteria are satisfied. EL is the load set which generates the same response field of linear analysis as that of nonlinear analysis. The primitive from of theory has been published. In this research, the theory is investigated with large scale example problems. Four examples are solved by using NROEL. Conventional optimization with sensitivity analysis using the finite difference method (FDM) is also applied to the same examples. Moreover, response surface optimization method is applied to the last two examples. The results of the optimizations are compared. In nonlinear response optimization of large scale problems, hundreds (or even thousands) of nonlinear analyses are expected to satisfy the convergence criteria. However, in nonlinear response optimization using equivalent loads, only tens of nonlinear analyses are required. The results are discussed and the usefulness of NROEL is presented.

• 한국전산유체공학회지
• /
• 제11권2호
• /
• pp.19-24
• /
• 2006

A research to evaluate the efficiency of design optimization was carried out for aerodynamic design optimization problem in distributed computing environment. The aerodynamic analyses which take most of computational work during design optimization were divided into several jobs and allocated to associated PC clients through network. This is not a parallel process based on domain decomposition in a single analysis rather than a simultaneous distributed-analyses using network-distributed computers. GBOM(gradient-based optimization method), SAO(Sequential Approximate Optimization) and RSM(Response Surface Method) were implemented to perform design optimization of transonic airfoils and evaluate their efficiencies. dimensional minimization followed by direction search involved in the GBOM was found an obstacle against improving efficiency of the design process in the present distributed computing system. The SAO was found fairly suitable for the distributed computing environment even it has a handicap of local search. The RSM is apparently the most efficient algorithm in the present distributed computing environment, but additional trial and error works needed to enhance the reliability of the approximation model deteriorate its efficiency from the practical point of view.

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

• 한국전산유체공학회지
• /
• 제21권3호
• /
• pp.39-47
• /
• 2016

We conducted a multi-stage optimization to secure the desired performance of a centrifugal fan for home appliance in an early stage of product development. In optimization, the static pressure at the outlet of the fan is chosen as an objective function that is to be maximized, providing the required flow rate at the operating point of the fan. The optimization procedure begins with parameters for an initial baseline fan design. The baseline design is optimized by using a commercial optimization package. Accordingly, the corresponding blade models with a set of geometrical parameters are generated. Flow through a fan is simulated by solving the Reynolds-averaged Navier-Stokes equations. A multi-stage optimization scheme is employed to determine the family of optimum values for the parameters, leading to the pressure increase at the outlet of the fan. To validate the numerically obtained optimal design parameters, we fabricated the three types of fans using rapid prototyping and assessed the performance using a fan tester. Experimental results show that the design parameters at each stage satisfy the goal of optimization. The multi-stage optimization process turned out to be a useful tool in the development of a centrifugal fan.