• 소성∙가공
• /
• 제27권1호
• /
• pp.28-36
• /
• 2018

Electromagnetic forming is a type of high-speed forming process to deform a workpiece through a Lorentz force. As the high strain rate in an electromagnetic-forming simulation causes infeasibility in determining constitutive parameters, we employed inverse parameter estimation in the previous study. However, the inverse parameter estimation process required us to spend considerable time, which leads to an increase in computational cost. To overcome the computational obstacle, in this research, we applied two types of surrogate modeling methods and compared them to each other to evaluate which model is best for the electromagnetic-forming simulation. We exploited an artificial neural network and we reduced-order modeling methods. During the construction of a reduced-order model, we extracted orthogonal bases with proper orthogonal decomposition and predicted basis coefficients by utilizing an artificial neural network. After the construction of the surrogate models, we verified the artificial neural network and reduced-order models through training and testing samples. As a result, we determined the artificial neural network model is slightly more accurate than the reduced-order model. However, the construction of the artificial neural network model requires a considerably larger amount of time than that of the reduced-order model. Thus, a reduced order modeling method is more efficient than an artificial neural network for estimating the electromagnetic forming and for the rapid approximation of structural simulations which needs repetitive runs.

• 한국전산응용수학회:학술대회논문집
• /
• 한국전산응용수학회 2003년도 KSCAM 학술발표회 프로그램 및 초록집
• /
• pp.1-1
• /
• 2003

In this talk, a reduced-order modeling methodology based on centroidal Voronoi tessellations (CVT's)is introduced. CVT's are special Voronoi tessellations for which the generators of the Voronoi diagram are also the centers of mass (means) of the corresponding Voronoi cells. The discrete data sets, CVT's are closely related to the h-means clustering techniques. Even with the use of good mesh generators, discretization schemes, and solution algorithms, the computational simulation of complex, turbulent, or chaotic systems still remains a formidable endeavor. For example, typical finite element codes may require many thousands of degrees of freedom for the accurate simulation of fluid flows. The situation is even worse for optimization problems for which multiple solutions of the complex state system are usually required or in feedback control problems for which real-time solutions of the complex state system are needed. There hava been many studies devoted to the development, testing, and use of reduced-order models for complex systems such as unsteady fluid flows. The types of reduced-ordered models that we study are those attempt to determine accurate approximate solutions of a complex system using very few degrees of freedom. To do so, such models have to use basis functions that are in some way intimately connected to the problem being approximated. Once a very low-dimensional reduced basis has been determined, one can employ it to solve the complex system by applying, e.g., a Galerkin method. In general, reduced bases are globally supported so that the discrete systems are dense; however, if the reduced basis is of very low dimension, one does not care about the lack of sparsity in the discrete system. A discussion of reduced-ordering modeling for complex systems such as fluid flows is given to provide a context for the application of reduced-order bases. Then, detailed descriptions of CVT-based reduced-order bases and how they can be constructed of complex systems are given. Subsequently, some concrete incompressible flow examples are used to illustrate the construction and use of CVT-based reduced-order bases. The CVT-based reduced-order modeling methodology is shown to be effective for these examples and is also shown to be inexpensive to apply compared to other reduced-order methods.

• East Asian mathematical journal
• /
• 제34권5호
• /
• pp.661-681
• /
• 2018

In this paper, we discuss a reduced-order modeling for the Benjamin-Bona-Mahony-Burgers (BBMB) equation and its application to a distributed feedback control problem through the centroidal Voronoi tessellation (CVT). Spatial distcritization to the BBMB equation is based on the finite element method (FEM) using B-spline functions. To determine the basis elements for the approximating subspaces, we elucidate the CVT approaches to reduced-order bases with snapshots. For the purpose of comparison, a brief review of the proper orthogonal decomposition (POD) is provided and some numerical experiments implemented including full-order approximation, CVT based model, and POD based model. In the end, we apply CVT reduced-order modeling technique to a feedback control problem for the BBMB equation.

• Journal of Electrical Engineering and information Science
• /
• 제2권4호
• /
• pp.92-98
• /
• 1997

This paper presents a new approach to obtaining a reduced-order model for multi-module converters. The proposed approach can be used to derive the reduced-order model for a wide class of multi-module converters including pulse-width-modulated (PWM) converters, soft-switched PWM converters, and resonant converters. The reduced-order model has the structure of a conventional single-module converter while preserving the dynamics of the original multi-module converter. Derivation procedures and the use of the reduced-order model is demonstrated using a three-module boost converter.

• 한국소음진동공학회:학술대회논문집
• /
• 한국소음진동공학회 2011년도 춘계학술대회 논문집
• /
• pp.339-344
• /
• 2011

In the past much effort has been made to utilize advanced computational fluid dynamic (CFD) programs for aeroelastic simulations and analysis. However, it is limited in the field of unsteady aeroelasticity due to enormous size of computer memory and unreasonably long CPU time. Recently, AAEMS(Aerodynamics is Aeroelasticity minus Structure) was developed for linear time-invariant, coupled fluid-structure systems. In this paper, to demonstrate further the efficiency and accuracy of the new model reduction method, we successfully examine AGARD 445.6 wing modeled by FLUENT CFD, FSIPRO3D and NASTRAN FEM(Finite Element Method) programs. Using the ROM(Reduced Order Modeling) one can predict flutter boundary as a function of the dynamic pressure.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제19권2호
• /
• pp.123-135
• /
• 2015

In this paper, a reduced-order modeling(ROM) of Burgers equations is studied based on pseudo-spectral collocation method. A ROM basis is obtained by the proper orthogonal decomposition(POD). Crank-Nicolson scheme is applied in time discretization and the pseudo-spectral element collocation method is adopted to solve linearlized equation based on the Newton method in spatial discretization. We deliver POD-based algorithm and present some numerical experiments to show the efficiency of our proposed method.

• Interaction and multiscale mechanics
• /
• 제6권4호
• /
• pp.395-409
• /
• 2013

Molecular dynamics (MD) systems are highly nonlinear and nonlocal, and the conventional model order reduction methods are ineffective for MD systems. The RBF-POD method (Lee and Chen, 2013) employed a radial basis function (RBF) approximated potential energies and inter-atomic forces of MD systems under the framework of the proper orthogonal decomposition (POD) method for the reduced-order modeling of MD systems. In this work, we focus on the numerical procedures of the RBF-POD method and demonstrate how to apply this approach to the modeling of ds-DNA molecules under stretching and bending conditions.

• Journal of applied mathematics & informatics
• /
• 제25권1_2호
• /
• pp.293-304
• /
• 2007

In this paper, we present a Krylov subspace based projection method for reduced-order modeling of large scale bilinear multi-input multi-output (MIMO) systems. The reduced-order bilinear system is constructed in such a way that it can match a desired number of moments of multi-variable transfer functions corresponding to the kernels of Volterra series representation of the original system. Numerical examples report the effectiveness of this method.

• Journal of Mechanical Science and Technology
• /
• 제17권12호
• /
• pp.1844-1854
• /
• 2003

This paper discusses details of modeling and robust control of an AMB (active magnetic bearing) spindle, and part I presents a modeling and validation process of the AMB spindle. There are many components in AMB spindle : electromagnetic actuator, sensor, rotor, power amplifier and digital controller. If each component is carefully modeled and evaluated, the components have tight structured uncertainty bounds and achievable performance of the system increases. However, since some unknown dynamics may exist and the augmented plant could show some discrepancy with the real plant, the validation of the augmented plant is needed through measuring overall frequency responses of the actual plant. In addition, it is necessary to combine several components and identify them with a reduced order model. First, all components of the AMB spindle are carefully modeled and identified based on experimental data, which also render valuable information in quantifying structured uncertainties. Since sensors, power amplifiers and discretization dynamics can be considered as time delay components, such dynamics are combined and identified with a reduced order. Then, frequency responses of the open-loop plant are measured through closed-loop experiments to validate the augmented plant. The whole modeling process gives an accurate nominal model of a low order for the robust control design.

• 한국항공우주학회지
• /
• 제50권3호
• /
• pp.147-155
• /
• 2022

항공기 및 철도차량 운용 중 발생하는 착빙 및 착설 현상은 공력 성능 감소와 주요 부품의 파손을 야기하기 때문에 시간에 따른 얼음 증식을 예측하는 것이 운용 안전 측면에서 매우 중요하다. 결빙수치해석은 실험적 방법에 비해 경제적으로 저렴하고 상사성 문제로부터 자유롭다는 점에서 결빙 형상을 예측하기 위한 수단으로 널리 사용되고 있다. 그러나 결빙수치해석은 착빙노출시간을 multi-step으로 나누어 매 단계별로 정상상태를 가정하는 준정상상태(quasi-steady) 가정을 이용한다. 이러한 방법은 효율적인 해석이 가능하지만 연속적인 결빙 형상을 얻지 못한다는 단점을 가지고 있다. 본 연구에서는 차원축소기법을 활용하여 결빙 형상 데이터를 보간함으로써 시간에 따른 결빙 형상을 연속적으로 예측할 수 있는 모델을 만드는 것을 목적으로 한다. 서로 다른 100개의 결빙 조건에서 형성된 결빙 데이터에 대하여 차원축소모델을 적용하였으며, 학습 데이터의 수와 결빙 조건이 차원축소모델의 예측 오차에 미치는 영향을 분석하였다.