불확실 변수에 대한 구배 최소화를 이용한 강건 최적 설계와 마이크로 자이로스코프에의 응용

한정삼,곽병만,Han, Jeong-Sam,Gwak, Byeong-Man 대한기계학회 2002 大韓機械學會論文集A Vol.26 No.9

In this paper a formulation of robust optimization is presented and illustrated by a design example of vibratory micro gyroscopes in order to reduce the effect of variations due to uncertainties in MEMS fabrication processes. For the vibratory micro gyroscope considered it is important to match the resonance frequencies of the vertical (sensing) and lateral (driving) modes as close as possible to attain a high sensing sensitivity. A deterministic optimization in which the difference of both the sensing and driving natural frequencies is minimized as an objective function results in highly enhanced performance but apt to be very sensitive to fabrication errors. The formulation proposed is to attain robustness of the performance by including the sensitivity of the response with respect to uncertain variables as a term of objective function to be minimized. This formulation is simple and practically applicable since no detail statistical information on fabrication errors is required. The geometric variables, beam width, length and thickness of vibratory micro gyroscopes are adopted as design variables and at the same time considered as uncertain variables because here occur the fabrication errors. A robustness test in terms of a percentage yield by using the Monte Carlo simulation has shown that the robust optimum produces twice more acceptable designs than the deterministic optimum. Improvement of robustness becomes bigger as the amount of fabrication errors is assumed larger. Considering that the magnitude of fabrication errors and uncertainties in a MEMS structure are comparatively large, the present method is illustrated to be a viable approach for a robust MEMS design.

Comparison of model order reductions using Krylov and modal vectors for transient analysis under seismic loading

한정삼 국제구조공학회 2020 Structural Engineering and Mechanics, An Int'l Jou Vol.76 No.5

Generally, it is necessary to perform transient structural analysis in order to verify and improve the seismic performance of high-rise buildings and bridges against earthquake loads. In this paper, we propose the model order reduction (MOR) method using the Krylov vectors to perform seismic analysis for linear and elastic systems in an efficient way. We then compared the proposed method with the mode superposition method (MSM) by using the limited numbers of modal vectors (or eigenvectors) calculated from the modal analysis. In the calculation, the data of the El Centro earthquake in 1940 were adopted for the seismic loading in the transient analysis. The numerical accuracy and efficiency of the two methods were compared in detail in the case of a simplified high-rise building.

Krylov 벡터를 이용한 모델차수축소법

한정삼,Han, Jeong-Sam 한국전산구조공학회 2012 전산구조공학 Vol.25 No.4

고충격 미소가속도계의 압저항-구조 연성해석 및 최적설계

한정삼,권순재,고종수,한기호,박효환,이장우,Han, Jeong-Sam,Kwon, Soon-Jae,Ko, Jong-Soo,Han, Ki-Ho,Park, Hyo-Hwan,Lee, Jang-Woo 한국군사과학기술학회 2011 한국군사과학기술학회지 Vol.14 No.1

A micromachined silicon accelerometer capable of surviving and detecting very high accelerations(up to 200,000 times the gravitational acceleration) is necessary for a high impact accelerometer for earth-penetration weapons applications. We adopted as a reference model a piezoresistive type silicon micromachined high-shock accelerometer with a bonded hinge structure and performed structural analyses such as stress, modal, and transient dynamic responses and sensor sensitivity simulation for the selected device using piezoresistive-structural coupled-field analysis. In addition, structural optimization was introduced to improve the performances of the accelerometer against the initial design of the reference model. The design objective here was to maximize the sensor sensitivity subject to a set of design constraints on the impact endurance of the structure, dynamic characteristics, the fundamental frequency and the transverse sensitivities by changing the dimensions of the width, sensing beams, and hinges which have significant effects on the performances. Through the optimization, we could increase the sensor sensitivity by more than 70% from the initial value of $0.267{\mu}V/G$ satisfying all the imposed design constraints. The suggested simulation and optimization have been proved very successful to design high impact microaccelerometers and therefore can be easily applied to develop and improve other piezoresistive type sensors and actuators.

모델차수축소법을 이용한 효율적인 진동해석

한정삼 대한기계학회 2006 大韓機械學會論文集A Vol.30 No.3

Efficient frequency response and its direct sensitivity analyses for large-size finite element models using Krylov subspace-based model order reduction

한정삼 대한기계학회 2012 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.26 No.4

In this paper, we examine an efficient calculation of the approximate frequency response (FR) for large-size finite element (FE) models using the Krylov subspace-based model order reduction (MOR) and its direct design sensitivity analysis with respect to design variables for sizing. Information about both the FR and its design sensitivity is necessary for typical gradient-based optimization iterations;therefore, the problem of high computational cost may occur when FRs of a large-size FE models are involved in the optimization problem. In the method suggested in this paper, reduced order models, generated from the original full-order FE models through the Arnoldi process, are used to calculate both the FR and FR sensitivity. This maximizes the speed of numerical computation of the FR and its design sensitivity. Assuming that the Krylov basis vectors remain constant with respect to the perturbation of a design variable, the FR sensitivity analysis is performed in a more efficient manner. As numerical examples, a car body with 535,992 degrees of freedom (DOF)and a 6 × 6 micro-resonator array with 368,424 DOF are adopted to demonstrate the numerical accuracy and efficiency of the suggested approach. Using the reduced-order models, we found that the FR and FR sensitivity are in a good agreement with those using the fullorder FE model. The reduction in computation time is also found to be significant because of the use of Krylov subspace-based reduced models.

4중 안정성 일체형 메커니즘의 설계, 해석 및 제작

한정삼 대한기계학회 2007 大韓機械學會論文集A Vol.31 No.5

축소된 유한요소모델을 이용한 하드디스크 구동부의 고유치 및 주파수응답 해석

한정삼 대한기계학회 2007 大韓機械學會論文集A Vol.31 No.5

Krylov subspace-based model order reduction for Campbell diagram analysis of large-scale rotordynamic systems

한정삼 국제구조공학회 2014 Structural Engineering and Mechanics, An Int'l Jou Vol.50 No.1

This paper focuses on a model order reduction (MOR) for large-scale rotordynamic systems by using finite element discretization. Typical rotor-bearing systems consist of a rotor, built-on parts, and a support system. These systems require careful consideration in their dynamic analysis modeling because they include unsymmetrical stiffness, localized nonproportional damping, and frequency-dependent gyroscopic effects. Because of this complex geometry, the finite element model under consideration may have a very large number of degrees of freedom. Thus, the repeated dynamic analyses used to investigate the critical speeds, stability, and unbalanced response are computationally very expensive to complete within a practical design cycle. In this study, we demonstrate that a Krylov subspace-based MOR via moment matching significantly speeds up the rotordynamic analyses needed to check the whirling frequencies and critical speeds of large rotor systems. This approach is very efficient, because it is possible to repeat thedynamic simulation with the help of a reduced system by changing the operating rotational speed, which canbe preserved as a parameter in the process of model reduction. Two examples of rotordynamic systems show that the suggested MOR provides a significant reduction in computational cost for a Campbell diagram analysis, while maintaining accuracy comparable to that of the original systems.

Calculation of design sensitivity for large-size transient dynamic problems using Krylov subspace-based model order reduction

한정삼 대한기계학회 2013 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.27 No.9

Nowadays, transient dynamic responses of a large-size finite element (FE) model can be solved within a reasonable computation time owing to rapid improvement in both numerical schemes and computing resources. However, increasing demands for accurate simulation and complicated modeling have led to larger and more complex finite element models, which consequently result in considerably high computational cost. In addition, when structural optimizations include transient responses such as displacement, velocity, and acceleration,the optimizations often do not end within a reasonable process time because the large-size simulation must be repeated many times. In order to reduce the computational cost in this respect, model order reduction (MOR) for the original full-order model (FOM) can be used for the transient response simulation. In this paper, a transient dynamic response analysis using Krylov subspace-based MOR and its design sensitivity analysis with respect to sizing design variables is suggested as an approach to the handling of large-size finite element models. Large-size finite element models can incur the problem of a long computation time in gradient-based optimization iterations because of the need for repeated simulation of transient responses. In the suggested method, the reduced order models (ROMs) generated from the original FOMs using implicit moment-matching via the Arnoldi process are used to calculate the transient response and its design sensitivity. As a result, the speed of numerical computation for the transient response and its design sensitivity is maximized. Newmark’s time integration method is employed to calculate transient responses and their design sensitivities. In the case of the transient sensitivity analysis, we apply a temporal discretization scheme to the design sensitivity equation derived by directly differentiating the governing equation with respect to design variables. This methodology has been programmed on the MATLAB with the FE information extracted from the FE package ANSYS. Two application examples are provided to demonstrate the numerical accuracy and efficiency of the suggested approach. The relative errors of transient response and design sensitivity between the FOMs and ROMs are also compared according to the orders of the reduced model. Calculation of transient dynamic responses and their sensitivities using Krylov subspacebased MOR shows a sizeable reduction in computation time and a good agreement with those provided by the FOM.