• 한국전산구조공학회논문집
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• 제26권4호
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• pp.223-231
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• 2013

본 논문에서는 물성이 균일하지 않은 반무한 고체영역의 탄성파속도 분포를 재구성하기 위한 시간영역 Gauss-Newton 전체파형 역해석 기법을 소개한다. 반무한 영역을 유한 계산영역으로 치환하기 위하여 유한영역의 경계에 수치적 파동흡수 경계조건인 perfectly-matched-layers(PMLs)를 도입하였다. 이 역해석 문제는 PML을 경계로 하는 영역에서의 탄성파동방정식을 구속조건으로 하는 최적화 문제로 성립되며, 표면에서 측정된 변위응답과 혼합유한요소법에 의해 계산된 응답간의 차이를 최소화함으로써 미지의 탄성파속도 분포를 결정한다. 이 과정에서 Gauss-Newton-Krylov 최적화 알고리즘과 정규화기법을 사용하여 탄성파속도의 분포를 반복적으로 업데이트하였다. 1차원 수치예제들을 통해 Gauss-Newton 역해석으로 부터 재구성된 탄성파속도의 분포가 목표값에 충분히 근사함을 보였으며, Fletcher Reeves 최적화 알고리즘을 사용한 기존의 역해석 결과에 비해 수렴율이 현저히 개선되고 계산 소요시간이 단축됨을 확인할 수 있었다.

• 한국생산제조학회지
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• 제23권4호
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• pp.337-344
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• 2014

While implicit integration methods such as Newton's method have excellent stability for the analysis of stiff and constrained mechanical systems, they have the drawback that the evaluation and LU-factorization of the system Jacobian matrix required at every time step are time-consuming. This paper proposes a Jacobian update-free Newton's method in order to overcome these defects. Because the motions of all bodies in a vehicle model are limited with respect to the chassis body, the equations are formulated with respect to the moving chassis-body reference frame instead of the fixed inertial reference frame. This makes the system Jacobian remain nearly constant, and thus allows the Newton's method to be free from the Jacobian update. Consequently, the proposed method significantly decreases the computational cost of the vehicle dynamic simulation. This paper provides detailed generalized formulation procedures for the equations of motion, constraint equations, and generalized forces of the proposed method.

• 한국산학기술학회논문지
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• 제14권10호
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• pp.4733-4738
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• 2013

본 연구에서는 구속조건을 가진 기계계의 동적 평형위치를 다물체 동역학 해석방법을 이용하여 계산하였다. 다물체계에서 얻어지는 시간 구속조건을 가진 구속조건식과 동역학식으로부터 독립좌표계로 이루어진 동적평형식을 유도하였다. 동적 평형식은 구속조건식과 함께 비선형 대수방정식의 형태로서 Newton-Raphson 방법을 이용하여 수치해를 구하였다. 제안된 동적 평형 계산 방법을 조속기에 적용하여 동적 평형위치를 구하였다. 해석결과는 상용 프로그램의 동역학해석을 통한 평형위치의 결과와 비교하여 타당성을 검증하였다. 조속기의 회전 각속도에 대한 평형위치를 계산하고 설계 파라미터에 대한 평형위치의 영향을 분석하였다.

• 대한수학회보
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• 제26권2호
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• pp.127-134
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• 1989

This paper proposes a deformation method for solving practical nonlinear programming problems. Utilizing the nonlinear parametric programming technique with Quasi-Newton method [6,7], the method solves the problem by imbedding it into a suitable one-parameter family of problems. The approach discussed in this paper was originally developed with the aim of solving a system of structural optimization problems with frequently appears in various kind of engineering design. It is assumed that we have to solve more than one structural problem of the same type. It an optimal solution of one of these problems is available, then the optimal solutions of thel other problems can be easily obtained by using this known problem and its optimal solution as the initial problem of our parametric method. The method of nonlinear programming does not generally converge to the optimal solution from an arbitrary starting point if the initial estimate is not sufficiently close to the solution. On the other hand, the deformation method described in this paper is advantageous in that it is likely to obtain the optimal solution every if the initial point is not necessarily in a small neighborhood of the solution. the Jacobian matrix of the iteration formula has the special structural features [2, 3]. Sectioon 2 describes nonlinear parametric programming problem imbeded into a one-parameter family of problems. In Section 3 the iteration formulas for one-parameter are developed. Section 4 discusses parametric approach for Quasi-Newton method and gives algorithm for finding the optimal solution.

• 한국자동차공학회논문집
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• 제5권1호
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• pp.154-161
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• 1997

This paper presents the method to eliminate the constraint reaction in the Lagrange multiplier form equation of motion by using a generalized coordinate driveder from the velocity constraint equation. This method introduces a matrix method by considering the m dimensional space spanned by the rows of the constraint jacobian matrix. The orthogonal vectors defining the constraint manifold are projected to null vectors by the tangential vectors defined on the constraint manifold. Therefore the orthogonal projection matrix is defined by the tangential vectors. For correcting the generalized position coordinate, the optimization problem is formulated. And this correction process is analyzed by the quasi Newton method. Finally this method is verified through 3 dimensional vehicle model.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2004년도 봄 학술발표회 논문집
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• pp.1-8
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• 2004

For the linearized differential algebraic equation of the nonlinear constrained system, exact initial values of the acceleration are needed to solve itself. It may be very troublesome to perform the inverse operation for obtaining the incremental quantities since the mass matrix contains the zero element in the diagonal. This fact makes the mass matrix impossible to be positive definite. To overcome this singularity phenomenon the mass matrix needs to be modified to allow the feasible application of predictor and corrector in the iterative computation. In this paper the proposed numerical algorithm based on the modified mass matrix combines the conventional implicit algorithm, Newton-Raphson method and Newmark method. The numerical example presents reliabilities for the proposed algorithm via comparisons of the 4th order Runge-kutta method. The proposed algorithm seems to be satisfactory even though the acceleration, Lagrange multiplier, and energy show unstable behaviour. Correspondingly, it provides one important clue to another algorithm for the enhancement of the numerical results.

• Journal of Mechanical Science and Technology
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• 제18권2호
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• pp.193-202
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• 2004

This paper presents a computer method for the dynamic analysis of a system of rigid bodies in plane motion. The formulation rests upon the idea of replacing a rigid body by a dynamically equivalent constrained system of particles. Newton's second law is applied to study the motion of the resulting system of particles without introducing any rotational coordinates. A velocity transformation is used to transform the equations of motion to a reduced set. For an open-chain, this process automatically eliminates all of the non-working constraint forces and leads to an efficient integration of the equations of motion. For a closed-chain, suitable joints should be cut and few cut-joints constraint equations should be included. An example of a closed-chain is used to demonstrate the generality and efficiency of the proposed method.

• Smart Structures and Systems
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• 제19권4호
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• pp.403-413
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• 2017

The present article encompasses a nonlinear finite element (FE) and genetic algorithm (GA) based optimal vibration energy harvesting from nonprismatic piezo-laminated cantilever beams. Three cases of cross section profiles (such as linear, parabolic and cubic) are modelled to analyse the geometric nonlinear effects on the output responses such as displacement, voltage, and power. The simultaneous effects of taper ratios (such as breadth and height taper) on the output power are also studied. The FE based nonlinear dynamic equation of motion has been solved by an implicit integration method (i.e., Newmark method in conjunction with the Newton-Raphson method). Besides this, a real coded GA based constrained optimization scheme has also been proposed to determine the best set of design variables for optimal harvesting of power within the safe limits of beam stress and PZT breakdown voltage.

• Communications for Statistical Applications and Methods
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• 제19권1호
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• pp.157-168
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• 2012

The EM algorithm is the most important tool to obtain the maximum likelihood estimator in finite mixture models due to its stability and simplicity. However, its convergence rate is often slow because the conventional EM algorithm is based on a large missing data space. Several techniques have been proposed in the literature to reduce the missing data space. In this paper, we review existing methods and propose a new EM algorithm for Gaussian mixtures, which reduces the missing data space while preserving the stability of the conventional EM algorithm. The performance of the proposed method is evaluated with other existing methods via simulation studies.

• 품질경영학회지
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• 제9권2호
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• pp.31-36
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• 1981

점증되고 있는 고신뢰성 제품의 설계에 있어 주어진 선형제약조건 내(內)에서 체계의 신뢰성을 최대화하는 방법을 소개하고 이를 해결하는 비선형계획법을 반복단계로 하여 Computer Programming을 하였다. 단, 본 논문에서 다루는 체계는 병렬중복구조를 갖는 직렬다단계 구조이다. 타당성 검토를 위한 예제를 해결하였으며 Computer Programming은 지면관계로 생략하였다.