• 전기학회논문지
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• 제57권8호
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• pp.1434-1439
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• 2008

Numerical methods for solving the state feedback control problem of linear time invariant system are presented in this paper. The methods are based on Haar wavelet approximation. The properties of Haar wavelet are first presented. The operational matrix of integration and its inverse matrix are then utilized to reduce the state feedback control problem to the solution of algebraic matrix equations. The proposed methods reduce the computation time remarkably. Finally a numerical example is illustrated to demonstrate the validity and applicability of the proposed methods.

• 제어로봇시스템학회논문지
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• 제14권12호
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• pp.1270-1277
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• 2008

A Haar wavelet based numerical method for solving singularly perturbed linear time invariant system is presented in this paper. The reduced pure slow and pure fast subsystems are obtained by decoupling the singularly perturbed system and differential matrix equations are converted into algebraic Sylvester matrix equations via Haar wavelet technique. The operational matrix of integration and its inverse matrix are utilized to reduce the computational time to the solution of algebraic matrix equations. Finally a numerical example is given to demonstrate the validity and applicability of the proposed method.

• 제어로봇시스템학회논문지
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• 제14권10호
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• pp.977-982
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• 2008

In this paper Haar functions are developed to approximate the solutions of continuous time linear system. Properties of Haar functions are first presented, and an explicit expression for the inverse of the Haar operational matrix is presented. Using the inverse of the Haar operational matrix the full order Stein equation should be solved in terms of the solutions of pure algebraic matrix equations, which reduces the computation time remarkably. Finally a numerical example is illustrated to demonstrate the validity of the proposed algorithm.

• Structural Engineering and Mechanics
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• 제45권1호
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• pp.95-110
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• 2013

In the recent decade, practical of wavelet technique is being utilized in various domain of science. Particularly, engineers are interested to the wavelet solution method in the time series analysis. Fundamentally, seismic responses of structures against time history loading such as an earthquake, illustrates optimum capability of systems. In this paper, a procedure using particularly discrete Haar wavelet basis functions is introduced, to solve dynamic equation of motion. In the proposed approach, a straightforward formulation in a fluent manner is derived from the approximation of the displacements. For this purpose, Haar operational matrix is derived and applied in the dynamic analysis. It's free-scaled matrix converts differential equation of motion to the algebraic equations. It is shown that accuracy of dynamic responses relies on, access of load in the first step, before piecewise analysis added to the technique of equation solver in the last step for large scale of wavelet. To demonstrate the effectiveness of this scheme, improved formulations are extended to the linear and nonlinear structural dynamic analysis. The validity and effectiveness of the developed method is verified with three examples. The results were compared with those from the numerical methods such as Duhamel integration, Runge-Kutta and Wilson-${\theta}$ method.

• Computers and Concrete
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• 제4권3호
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• pp.243-257
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• 2007

A novel method for recognition, characterization, and quantification of deterioration in bridge components and laboratory concrete samples is presented in this paper. The proposed scheme is based on grey level co-occurrence matrix texture analysis using Haar's discrete wavelet transform on concrete imagery. Each image is described by a subset of band-filtered images containing wavelet coefficients, and then reconstructed images are employed in characterizing the texture, using grey level co-occurrence matrices, of the different types and degrees of damage: map-cracking, spalling and steel corrosion. A comparative study was conducted to evaluate the efficiency of the supervised maximum likelihood and unsupervised K-means classification techniques, in order to classify and quantify the deterioration and its extent. Experimental results show both methods are relatively effective in characterizing and quantifying damage; however, the supervised technique produced more accurate results, with overall classification accuracies ranging from 76.8% to 79.1%.

• 디지털콘텐츠학회 논문지
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• 제16권5호
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• pp.805-813
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• 2015

Compressive sensing 및 희소 복원 문제(sparse recovery problem)는 기존 디지털 기술의 한계를 극복할 수 있는 새로운 이론으로 많은 관심을 받고 있다. 그러나 신호 재구성에서 l1 norm 최적화 문제 해결에 많은 연산이 수행되며 따라서 병렬 처리 기법이 필요하다. 이 과정에서 무작위 행렬과 벡터 연산을 통한 변환 연산이 전체 과정 중에서 많은 부분을 차지하는데, 특히 원본 신호의 크기로 인해 이 과정에서 필요한 무작위 행렬을 메모리에 저장하기 곤란하며 계산 시 무작위 행렬의 절차적(procedural) 처리 방식이 필수적이다. 본 논문에서는 이 문제에 대한 해결책으로 단일 명령 다중 스레드(SIMT) 병렬 플랫폼 상에서 무작위 부분적 Haar 웨이블릿 변환을 절차적으로 계산할 수 있는 새로운 병렬 알고리듬을 제안한다.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2007년도 심포지엄 논문집 정보 및 제어부문
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• pp.281-282
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• 2007

We address a new representation of DCT/DFT/Wavelet matrices via one hybrid architecture. Based on an element inverse matrix factorization algorithm, we show that the OCT, OFT and Wavelet which based on Haar matrix have the similarrecursive computational pattern, all of them can be decomposed to one orthogonal character matrix and a special sparse matrix. The special sparse matrix belongs to Jacket matrix, whose inverse can be from element-wise inverse or block-wise inverse. Based on this trait, we can develop a hybrid architecture.

• 대한수학회논문집
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• 제15권4호
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• pp.587-595
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• 2000

We contain a simple construction for the sparse n x n connected orthogonal matrices which have a row of p nonzero entries with 2$\leq$p$\leq$n. Moreover, we study the analogous sparsity problem for an m x n connected row-orthogonal matrices.

• 한국콘텐츠학회:학술대회논문집
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• 한국콘텐츠학회 2004년도 추계 종합학술대회 논문집
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• pp.348-351
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• 2004

본 논문은 Haar 웨이브릿 변환과 2D PCA를 이용한 얼굴 인식 방법에 대하여 제안한다. 기존의 PCA는 1 차원 벡터들로 공분산 행렬을 구하는 반면에 2D PCA는 2 차원 영상을 직접적으로 이용하여 공분산 행렬을 구한 후 그것의 고유값에 따른 고유벡터를 구하여 특징 벡터들을 추출하였다. 제안 방법은 얼굴 데이터를 낮은 차원과 강건한 특징을 가지는 얼굴 영상을 얻기 위해 웨이브릿 변환을 이용하여 LL 대역의 영상 데이터로 2D PCA 방법을 적용하여 얼굴을 인식한다. 실험결과는 원래 크기의 얼굴 영상에 2D PCA를 적용한 인식률보다 웨이브릿 변환의 LL 대역의 얼굴 영상에 2D PCA를 적용한 얼굴 인식률이 더 좋음을 보여준다.