• International Journal of Aeronautical and Space Sciences
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• 제15권2호
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• pp.183-189
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• 2014

Pseudo-spectral method typically converges at an exponential rate. However, it requires a special set of fixed collocation points (CPs) to get highly accurate formulas for partial integration and differentiation. In this study, computational nodes for defining the discrete variables of states and controls are built independently of the CPs. The state and control variables at each CP, which are required to transcribe an NOCP into the corresponding NLP, are interpolated, using those variables allocated at each node. Additionally, Lagrange interpolation and spline interpolation are investigated, to provide a guideline for selecting a favorable interpolation method. The proposed techniques are applied to the solution of an NOCP using equally spaced nodes, and the computed results are compared to those using the standard PS approach, to validate the usefulness of the proposed methods.

• 한국항공우주학회지
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• 제39권5호
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• pp.408-415
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• 2011

달착륙은 크게 궤도이탈 단계, 동력하강 단계로 구성되어지며, 동력하강단계는 Braking, Approach, Final landing phase의 세부 3단계로 나누어진다. 본 논문에서는 동력하강 세부 3단계의 최적경로를 통하여 달착륙선의 착륙 제어를 수행하기로 한다. 우선 Gauss pseudo-spectral 방법을 통하여 기준 궤적을 생성하였고, 고도와 각 방향의 속도오차를 이용하여 PID 제어기를 생성하였다. 마지막으로 Matlab의 Simulink를 이용하여 달착륙선의 착륙단계 시스템을 구성하고 이를 이용하여 시뮬레이션을 수행하였다.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제25권4호
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• pp.173-195
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• 2021

A new implicit discontinuous Galerkin spectral element method (DGSEM) based on the first order hyperbolic system(FOHS) is presented for solving elliptic type partial different equations, such as the Poisson problems. By utilizing the idea of hyperbolic formulation of Nishikawa[1], the original Poisson equation was reformulated in the first-order hyperbolic system. Such hyperbolic system is solved implicitly by the collocation type DGSEM. The steady state solution in pseudo-time, which is the solution of the original Poisson problem, was obtained by the implicit solution of the global linear system. The optimal polynomial orders of 𝒪(𝒽^𝑝+1)) are obtained for both the solution and gradient variables from the test cases in 1D and 2D regular grids. Spectral accuracy of the solution and gradient variables are confirmed from all test cases of using the uniform grids in 2D.

• Structural Engineering and Mechanics
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• 제18권6호
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• pp.791-806
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• 2004

The inverse pseudo excitation method is used in the identification of random loadings. For structures subjected to stationary random excitations, the power spectral density matrices of such loadings are identified experimentally. The identification is based on the measured acceleration responses and the structural frequency response functions. Numerical simulation is used in the optimal selection of sensor locations. The proposed method has been successfully applied to the loading identification experiments of three structural models, two uniform steel cantilever beams and a four-story plastic glass frame, subjected to uncorrelated or partially correlated random excitations. The identified loadings agree quite well with actual excitations. It is proved that the proposed method is quite accurate and efficient in addition to its ability to alleviate the ill conditioning of the structural frequency response functions.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제21권3호
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• pp.109-124
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• 2017

The numerical solution of the Stokes equation with discontinuous viscosity and singular force term is challenging, due to the discontinuity of pressure, non-smoothness of velocity, and coupled discontinuities along interface.In this paper, we give an efficient algorithm to solve this problem by employing spectral Legendre and Chebyshev approximations.First, we present the algorithm for a problem defined in rectangular domain with straight line interface. Then it is generalized to a domain with smooth curve boundary and interface by employing spectral element method. Numerical experiments demonstrate the accuracy and efficiency of our algorithm and its spectral convergence.

• The Journal of the Acoustical Society of Korea
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• 제29권3E호
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• pp.131-139
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• 2010

This paper proposes a novel spectral hole substitution technique for low bit-rate audio coding. The spectral holes frequently occurring in relatively weak energy bands due to zero bit quantization result in severe quality degradation, especially for harmonic signals such as speech vowels. The enhanced aacPlus (EAAC) audio codec artificially adjusts the minimum signal-to-mask ratio (SMR) to reduce the number of spectral holes, but it still produces noisy sound. The proposed method selectively predicts the spectral shapes of hole bands using either intra-band correlation, i.e. harmonically related coefficients nearby or inter-band correlation, i.e. previous frames. For the bands that have low prediction gain, only the energy term is quantized and spectral shapes are replaced by pseudo random values in the decoding stage. To minimize perceptual distortion caused by spectral mismatching, the criterion of the just noticeable level difference (JNLD) and spectral similarity between original and predicted shapes are adopted for quantizing the energy term. Simulation results show that the proposed method implemented into the EAAC baseline coder significantly improves speech quality at low bit-rates while keeping equivalent quality for mixed and music contents.

• Journal of Biosystems Engineering
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• 제16권2호
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• pp.111-117
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• 1991

An empirical model for diesel engine control was obtained using a system identification method. A pseudo-random binary sequence was used as an input signal. Spectral anaylsis was used to find the frequency response of system. Model parameters of transfer functions were obtained using nonlinear regression.

• 천문학회지
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• 제29권2호
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• pp.157-170
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• 1996

In order to determine the metallicity of a globuar cluster, M3,by using the spectral indices, a kind of index grid has been establshed by stars in globular clusters, M3, M15, M71 and old open cluster, NGC 188. The indices were measured from the medium resolution spectra of about $2{\AA}$. The summed indices were used to determine metallicity in order to increase signals. It is found that the core depth index is measured more accurately and leads result more accurate than the pseudo-equivalent width index. This method can be further improved by including many more calibration globular clusters of various metallicity to make finer grids. By this method, the metallicity of M3 is determined as $[Fe/H] = -1.46\pm0.15$.

• Structural Engineering and Mechanics
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• 제10권4호
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• pp.359-369
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• 2000

Random loading identification has long been a difficult problem for Multi-Input-Multi-Output (MIMO) structure. In this paper, the Pseudo Excitation Method (PEM), which is an exact and efficient method for computing the structural random response, is extended inversely to identify the excitation power spectral densities (PSD). This identified method, named the Inverse Pseudo Excitation Method (IPEM), resembles the general dynamic loading identification in the frequency domain, and can be used to identify the definite or random excitations of complex structures in a similar way. Numerical simulations are used to reveal the the difficulties in such problems, and the results of some numerical analysis are discussed, which may be very useful in the setting up and processing of experimental data so as to obtain reasonable predictions of the input loading from the selected structural responses.

• Kyungpook Mathematical Journal
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• 제52권3호
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• pp.327-346
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• 2012

In this paper, we present a simple explicit type numerical method for discretizations in time for solving one dimensional Burgers' equations. The proposed method does not need an iteration process that may be required in most implicit methods and have good convergence and efficiency in computational sense compared to other known numerical methods. For evidences, several numerical demonstrations are also provided.