• Management Science and Financial Engineering
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• 제21권2호
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• pp.25-30
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• 2015

This short article compares different solution methods for a basic RBC model (Hansen, 1985). We solve and simulate the model using two main algorithms: the methods of perturbation and projection, respectively. One novelty is that we offer a type of the hybrid method: we compute easily a second-order approximation to decision rules and use that approximation as an initial guess for finding Chebyshev polynomials. We also find that the second-order perturbation method is most competitive in terms of accuracy for standard RBC model.

• 대한기계학회논문집A
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• 제26권12호
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• pp.2631-2635
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• 2002

The semi-analytic sensitivity analysis using Pade approximation is presented for linear elastic structures. Although the semi-analytic method has several advantages, accuracy of the method prevents it from practical application. One of promising remedies is the use of geometric series for the matrix inversion. Though series expansion of order three has been successfully applied to the calculation of the structural sensitivity in the most range of the design perturbation, it is prone to have a slow convergence for large perturbation. To overcome this shortage, Pade approximation is introduced so that it can broaden the trust region of the perturbation without adding expansion terms. Numerical results show that the confident sensitivity can be obtained with tiny expenses of computation effort.

• Journal of Electrical Engineering and Technology
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• 제3권1호
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• pp.14-19
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• 2008

The paper presents an intelligent time series model to predict uncertain electricity market price in the deregulated industry environment. Since the price of electricity in a deregulated market is very volatile, it is difficult to estimate an accurate market price using historically observed data. The parameter of an intelligent time series model is obtained based on the simultaneous perturbation stochastic approximation (SPSA). The SPSA is flexible to use in high dimensional systems. Since prediction models have their modeling error, an error compensator is developed as compensation. The SPSA based intelligent model is applied to predict the electricity market price in the Pennsylvania-New Jersey-Maryland (PJM) electricity market.

• International Journal of Control, Automation, and Systems
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• 제6권4호
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• pp.506-514
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• 2008

This paper presents an intelligent model; named as free model, approach for a closed-loop system identification using input and output data and its application to design a power system stabilizer (PSS). The free model concept is introduced as an alternative intelligent system technique to design a controller for such dynamic system, which is complex, difficult to know, or unknown, with input and output data only, and it does not require the detail knowledge of mathematical model for the system. In the free model, the data used has incremental forms using backward difference operators. The parameters of the free model can be obtained by simultaneous perturbation stochastic approximation (SPSA) method. A linear transformation is introduced to convert the free model into a linear model so that a conventional linear controller design method can be applied. In this paper, the feasibility of the proposed method is demonstrated in a one-machine infinite bus power system. The linear quadratic regulator (LQR) method is applied to the free model to design a PSS for the system, and compared with the conventional PSS. The proposed SPSA-based LQR controller is robust in different loading conditions and system failures such as the outage of a major transmission line or a three phase to ground fault which causes the change of the system structure.

• Journal of the Korean Data and Information Science Society
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• 제14권3호
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• pp.623-630
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• 2003

Recently, Tanaka(1988) derived two influence functions related to an eigenvalue problem $(A-\lambda_sI)\upsilon_s=0$ of real symmetric matrix A and used them for sensitivity analysis in principal component analysis. In this paper, we deal with the perturbation expansions up to quadratic terms of the same functions and discuss the application to sensitivity analysis in principal component regression analysis(PCRA). Numerical example is given to show how the approximation improves with the quadratic term.

• Journal of applied mathematics & informatics
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• 제28권5_6호
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• pp.1227-1237
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• 2010

In this paper, a Klein-Gordon equation is solved by using the homotopy analysis method (HAM), homotopy perturbation method (HPM) and modified homotopy perturbation method (MHPM). The approximation solution of this equation is calculated in the form of series which its components are computed easily. The uniqueness of the solution and the convergence of the proposed methods are proved. The accuracy of these methods are compared by solving an example.

• 한국음향학회지
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• 제28권3호
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• pp.174-186
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• 2009

경계면이 존재하는 해양에서의 수중 음파 전달 모델링 시 일반적으로 평평한 경계면을 가정하고 Rayleigh가 제안했던 반사계수를 이용해 반사파를 계산할 수 있다. 하지만 해수면이나 해저면과 같은 실제 해양의 경계면은 불규칙적인 거칠기를 가진다. 이러한 경계면에서의 반사 손실은 실험식이나 산란 이론에 기반한 간섭 반사 계수를 계산하여 구할 수 있다. 본 논문에서는 섭동 이론, Kirchhoff 근사법, 작은 가지 근사법과 같은 산란 이론을 이용하여 유체-유체 경계면에 대한 간섭 반사 계수를 각각 유도한다. 이를 이용하여 임의의 거칠기를 가지는 해수면과 해저면에 대한 각 산란 이론의 간섭 반사계수를 계산하며, 이 결과를 Rayleigh 반사 계수와 비교하여 경계면의 거칠기에 따른 반사 손실을 분석한다. 또한, 섭동 이론과 Kirchhoff 근사법의 결과를 일반적으로 적용 범위가 넓은 작은 기울기 근사법의 결과와 비교하여 각 이론의 유효범위에 대해 고찰한다.

• Structural Engineering and Mechanics
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• 제10권5호
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• pp.427-440
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• 2000

The formulas for the perturbation analysis with modes of close eigenvalues are derived in this paper. Emphasis is made on the consistency of the straightforward perturbation process, given the complete terms of perturbations in the zeroth-order, which is a form of Rayleigh quotient, and in the higher-orders. By dividing the perturbation of eigenvector into two parts, the first-order perturbation with respect to the modes of close eigenvalues is moved into the zeroth-order perturbation. The normality condition is employed to compute the higher-order perturbations of eigenvector. The algorithm can be condensed to a single mode with a distinct eigenvalue, and this can accelerate the convergence of the perturbation analysis. The example confirms that the perturbation approximation obtained from the suggested procedure is in a good accuracy on the eigenvalues, eigenvectors, and normality.

• 터널과지하공간
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• 제13권5호
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• pp.389-396
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• 2003

본 연구는 정상류 Navier-Stokes 방정식에 섭동(perturbation) 이론을 적용하여 주기함수 간극에 대한 삼승법칙의 수정에 대해 논하였다. 이를 위해, 주기함수를 진폭과 파장에 대한 무차원 함수로 전환한 뒤 미소 계수에 대한 무차원 유동함수와 연속 방정식을 적용하였다. 이러한 과정을 통해 정상류 Navier-Stokes 방정식의 섭동 근사해를 구하였으며 이를 유한 차분법에 적용하였다. 단일 절리 모델에 대한유한 차분 수치해석을 통해, 수정된 삼승 법칙이 주기함수 간극의 유체 유동에 대한 정상류 Navier-Stokes 방정식의 섭동 근사해와 잘 일치하는 것으로 나타났다. 이를 통해 본 연구에서 제시된 삼승 법칙이 간극 분포에 따른 유체 유동의 평가에 있어 유용하게 적용될 수 있는 것으로 나타났다.

• Journal of applied mathematics & informatics
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• 제23권1_2호
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• pp.141-152
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• 2007

In this paper a numerical method is presented to solve singularly perturbed two points boundary value problems for second order ordinary differential equations consisting a discontinuous source term. First, in this method, an asymptotic expansion approximation of the solution of the boundary value problem is constructed using the basic ideas of a well known perturbation method WKB. Then some initial value problems and terminal value problems are constructed such that their solutions are the terms of this asymptotic expansion. These initial value problems are happened to be singularly perturbed problems and therefore fitted mesh method (Shishkin mesh) are used to solve these problems. Necessary error estimates are derived and examples provided to illustrate the method.