• 대한수학회보
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• 제59권2호
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• pp.507-528
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• 2022

We propose a path integral method to construct a time stepwise local volatility for the stock index market under Dupire's model. Our method is focused on the pricing with the Monte Carlo Method (MCM). We solve the problem of randomness of MCM by applying numerical integration. We reconstruct this task as a matrix equation. Our method provides the analytic Jacobian and Hessian required by the nonlinear optimization solver, resulting in stable and fast calculations.

• Steel and Composite Structures
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• 제27권1호
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• pp.13-25
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• 2018

The main objective of this study is to develop a dual approach for geometrically nonlinear finite element analysis of plane truss structures. The geometric nonlinearity is considered using the Total Lagrangian formulation. The nonlinear solution is obtained by introducing and minimizing an objective function subjected to displacement-type constraints. The proposed method can fully trace the whole equilibrium path of geometrically nonlinear plane truss structures not only before the limit point but also after it. No stiffness matrix is used in the main approach and the solution is acquired only based on the direct classical stress-strain formulations. As a result, produced errors caused by linearization and approximation of the main equilibrium equation will be eliminated. The suggested algorithm can predict both pre- and post-buckling behavior of the steel plane truss structures as well as any arbitrary point of equilibrium path. In addition, an equilibrium path with multiple limit points and snap-back phenomenon can be followed in this approach. To demonstrate the accuracy, efficiency and robustness of the proposed procedure, numerical results of the suggested approach are compared with theoretical solution, modified arc-length method, and those of reported in the literature.

• Smart Structures and Systems
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• 제24권2호
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• pp.209-221
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• 2019

The classical Kalman filter (KF) provides a practical and efficient way for state estimation. It is, however, not applicable when the external excitations applied to the structures are unknown. Moreover, it is known the classical KF is only suitable for linear systems and can't handle the nonlinear cases. The aim of this paper is to extend the classical KF approach to circumvent the aforementioned limitations for the joint estimation of structural states and the unknown inputs. On the basis of the scheme of the classical KF, analytical recursive solution of an improved KF approach is derived and presented. A revised form of observation equation is obtained basing on a projection matrix. The structural states and the unknown inputs are then simultaneously estimated with limited measurements in linear or nonlinear systems. The efficiency and accuracy of the proposed approach is verified via a five-story shear building, a simply supported beam, and three sorts of nonlinear hysteretic structures. The shaking table tests of a five-story building structure are also employed for the validation of the robustness of the proposed approach. Numerical and experimental results show that the proposed approach can not only satisfactorily estimate structural states, but also identify unknown loadings with acceptable accuracy for both linear and nonlinear systems.

• 한국지능시스템학회논문지
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• 제26권1호
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• pp.50-55
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• 2016

본 논문은 특이섭동을 포함한 비선형 시스템을 위한 샘플치 제어 기법을 논한다. 비선형 시스템은 타카기--수게노(Takagi--Sugeno: T--S) 퍼지모델 형태로 표현됨을 가정한다. 새로운 리아푸노프 함수와 추가적인 항등식을 이용하여 선형행렬부등식 형태의 샘플치 폐루프 T--S 퍼지시스템의 점근적 안정도 조건을 제시한다. 분석결과에 대한 몇 가지 논의점을 언급한다. 모의실험에 의하여 제안된 기법의 타당성을 보인다.

• 전산구조공학
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• 제11권1호
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• pp.217-226
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• 1998

본 논문은 변위제약모드를 갖는 트러스구조물의 형태해석을 목적으로 하였으며, 이를 위하여 해의 존재조건과 무어-펜로즈(Moore-Penrose) 일반역행렬을 이용하였다. 또한, 수치해석과정에서의 변위제약모드로는 호몰로지변형(homologous deformation)을 고려하여 해석하였고, 다음으로 다양한 변위제약모드와 절점에 작용하는 하중비를 만족하는 구조물의 형태를 구하였다. 본 논문에서의 형태해석문제는 지정된 변위를 만족하는 구조물의 형태를 찾는 일종의 역문제(inverse problem)로서 일반적인 구조해석과정과는 반대되는 입장에서 접근하였다. 또한, 본 논문에서는 수치해석과정에서 근사해의 정도를 향상시키기 위하여 뉴튼-랩슨법을 사용하였고, 수치해석예제로서 부재의 배열형태에 따라 3가지모델을 선택하였으며, 이들 모델을 통하여 적용한 해석기법의 정확성과 효율성을 검증하였다.

• Journal of Electrical Engineering and Technology
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• 제6권5호
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• pp.697-705
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• 2011

In this paper, a closed-loop system constructed with a linear plant and nonlinearity in the feedback connection is considered to argue against its planar orbital stability. Through a state space approach, a main result that presents a sufficient stability criterion of the limit cycle predicted by solving the harmonic balance equation is given. Preliminarily, the harmonic balance of the nonlinear feedback loop is assumed to have a solution that determines the characteristics of the limit cycle. Using a state-space approach, the nonlinear loop equation is reformulated into a linear perturbed model through the introduction of a residual operator. By considering a series of transformations, such as a modified eigenstructure decomposition, periodic averaging, change of variables, and coordinate transformation, the stability of the limit cycle can be simply tested via a scalar function and matrix. Finally, the stability criterion is addressed by constructing a composite Lyapunov function of the transformed system.

• Journal of Mechanical Science and Technology
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• 제16권8호
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• pp.1072-1078
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• 2002

The constrained motion requires the determination of constraint force acting on unconstrained systems for satisfying given constraints. Most of the methods to decide the force depend on numerical approaches such that the Lagrange multiplier method, and the other methods need vector analysis or complicated intermediate process. In 1992, Udwadia and Kalaba presented the generalized inverse method to describe the constrained motion as well as to calculate the constraint force. The generalized inverse method has the advantages which do not require any linearization process for the control of nonlinear systems and can explicitly describe the motion of holonomically and/or nongolonomically constrained systems. In this paper, an explicit equation to describe the constrained motion is derived by minimizing the performance index, which is a function of constraint force vector, with respect to the constraint force. At this time, it is shown that the positive-definite weighting matrix in the performance index must be the inverse of mass matrix on the basis of the Gauss's principle and the derived differential equation coincides with the generalized inverse method. The effectiveness of this method is illustrated by means of two numerical applications.

• 전자공학회논문지S
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• 제36S권12호
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• pp.20-26
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• 1999

본 논문에서는 신호 부공간을 이용하여 표적들의 방위각 이노베이션을 구함으로써, 별도의 데이터연관 기법이 필요 없으며 간단한 구조의 효율적인 다중표적 방위각 추적 알고리즘을 제안하였다. 신호 부공간은 PAST와 같은 신호 부공간 추적 알고리즘을 이용하여 추정된다. 추정된 신호 부공간과 방위각 이노베이션이 만족시키는 비선형 행렬방정식을 유도하고, 이를 Taylor 급수 전개하여 선형근사화 한다. 이렇게 선형근사화하여 얻은 선형 행렬방정식으로부터 최소제곱법을 이용하여 방위각 이노베이션을 구한다. 다양한 컴퓨터 시뮬레이션을 통하여 제안한 알고리즘의 효율적이고 우수한 성능을 확인하였다.

• Structural Monitoring and Maintenance
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• 제11권3호
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• pp.219-234
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• 2024

The strength reduction factor spectrum is traditionally obtained from a single-degree-of-freedom (SDOF) system with a constant damping coefficient. However, according to the principle of Rayleigh damping, the damping coefficient matrix of a system changes with the stiffness matrix, and the damping coefficient of an equivalent SDOF system changes with the tangent stiffness coefficient. In view of that, this study proposes an equivalent SDOF system with an adaptive damping coefficient and derives a standardized reaction balance equation. By iteratively adjusting the strength reduction factor, the corresponding spectrum with an equivalent ductility factor is obtained. In addition, the ratio between the strength reduction factor that considers adaptive damping and the traditional strength reduction factor, denoted by η, is determined, and the η-μ-T relationship is obtained. Seismic records of Classes C, D, and E sites are selected as excitations. Moreover, a nonlinear response time-history analysis is performed to establish the relationship between the η and T values for the equivalent ductility factor μ. Further, by exploring the effects of the site class, ductility factor, second-order stiffness coefficient, and period T on the mean value of η, a simplified calculation equation of mean η is derived, and η is used as a modified value for the traditional strength reduction factor R spectrum.

• 한국산학기술학회논문지
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• 제21권6호
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• pp.634-639
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• 2020

일반적으로 비선형 시스템은 1차와 2차 시스템의 곱으로 선형화할 수 있기 때문에 시스템은 2차 시스템의 중근, 복소근, 서로 다른 두 실근과 1차 시스템의 근을 극점으로 가진다. 이런 극점의 위치 변경으로 시스템의 안정성과 응답특성을 개선할 수 있어서 다양한 방법으로 극점을 이동시키는 제어기를 설계한다. 여러 방법 중에서 LQ 제어는 이득여유와 위상여유의 안정성을 보장한다. 그런데 시행착오 방법으로 가중행렬을 선택하여 원하는 응답특성을 얻기 때문에 극점의 위치를 임의로 지정하기 어렵다. 이 논문은 조단블록을 가진 다중 중근을 원하는 실근으로 이동시키는 LQ 제어의 가중행렬을 선택하는 방법에 관한 것이다. 대각행렬 형태의 제어가중행렬과 ρ_d와 ϕ_d의 2개 변수 상태가중행렬을 갖는 해밀토니안 시스템의 특성방정식에서 중근과 가중행렬의 관계식을 유도한다. 그리고 상태가중행렬이 양의 준정부호 행렬이 될 조건에서 실근으로 이동할 중근의 이동범위를 구하고, 좌표평면에 표현한다. 이 범위에서 극점을 선택하고, 관계식으로 가중행렬을 계산하는 방법을 제안한다. 그리고 예제를 통해 조단블록을 갖는 4개의 중근을 원하는 서로 다른 실근으로 이동시키는 가중행렬과 제어법칙의 계산과정을 통해 제안한 방법의 유용성을 확인하였다.