• Communications for Statistical Applications and Methods
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• 제15권6호
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• pp.837-842
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• 2008

Students taking linear model courses have difficulty in determining which parametric functions are estimable when the design matrix of a linear model is rank deficient. In this note a special form of estimable functions is presented with a linear combination of some orthogonal estimable functions. Here, the orthogonality means the least squares estimators of the estimable functions are uncorrelated and have the same variance. The number of the orthogonal estimable functions composing the special form is equal to the rank of the design matrix. The orthogonal estimable functions can be easily obtained through the singular value decomposition of the design matrix.

• Journal of Mechanical Science and Technology
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• 제20권11호
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• pp.1790-1800
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• 2006

Dynamic behavior of flexural-torsional coupled vibration of rotating beams using the Rayleigh-Ritz method with orthogonal polynomials as basis functions is studied. Performance of various orthogonal polynomials is compared to each other in terms of their efficiency and accuracy in determining the required natural frequencies. Orthogonal polynomials and functions studied in the present work are: Legendre, Chebyshev, integrated Legendre, modified Duncan polynomials, the special trigonometric functions used in conjunction with Hermite cubics, and beam characteristic orthogonal polynomials. A total of 5 cases of beam boundary conditions and rotation are studied for their natural frequencies. The obtained natural frequencies and mode shapes are compared to those available in various references and the results for coupled flexural-torsional vibrations are especially compared to both previously available references and with those obtained using NASTRAN finite element package. Among all the examined orthogonal functions, Legendre orthogonal polynomials are the most efficient in overall CPU time, mainly because of ease in performing the integration required for determining the stiffness and mass matrices.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2001년도 ICCAS
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• pp.26.1-26
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• 2001

In this paper, we will expand and generalize the orthogonal functions as basis functions for dynamical system representations. The orthogonal functions can be considered as generalizations of, for example, the pulse functions, Laguerre functions, and Kautz functions, and give rise to an alternative series expansion of rational transfer functions. It is shown row we can exploit these generalized basis functions to increase the speed of convergence in a series expansion. The set of Kautz functions is discussed in detail and, using the power-series equivalence, the truncation error is obtained. And so we will present the influence of noises to use Kautz function on the identification accuracy.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1997년도 추계학술대회 논문집 학회본부
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• pp.142-145
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• 1997

This paper presents an modified orthogonal neural network(MONN) based on orthogonal functions and applies the network to nonlinear system control. The accuracy of orthogonal neural network is essentially dependent on the choice of basic orthogonal functions. Modified orthogonal neural network is modified model of orthogonal neural network with input transformation to adapt its basic orthogonal functions. The results show that the modified orthogonal neural network has the excellent performance of approximating and controlling nonlinear systems and the input transformation make the ability of modified orthogoneural neural network better than one of orthogonal neural network.

• 호남수학학술지
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• 제16권1호
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• pp.47-54
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• 1994

We present a generating function and three semi-orthogonal relations for a class of hypergeometric functions. We employ semi-orthogonal relations to generate a theory concerning finite series expansions involving our hypergeometric functions.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1998년도 하계학술대회 논문집 B
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• pp.468-470
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• 1998

We have studied system identification model reduction method, optimal control by orthogonal functions. This paper presents the easy method that solves algebra equations instead of differential equations using Walsh, Haar, Block pulse function of orthogonal functions in state equation. The proposed algorithm is verified through some examples.

• 대한전기학회논문지:전력기술부문A
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• 제48권3호
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• pp.263-269
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• 1999

In this paper, an unifying design algorithm is presented for efficient digital implementation of continuous PID controller using general discrete orthogonal functions. The proposed algorithm is an algebraic method to determine controller parameters, which can unify controller design procedures divided into three ways. A set of linear equations for the controller design are derived from simple algebraic transformation based on general discrete orthogonal functions. By solving these equations, all of the controller parameters can be determined directly and simultaneously, which thus makes the design procedure systematic and straightforward. It does not involve any trial and error procedure, hence the difficulty of conventional approach can be avoided. The simulation results and discussions are given to demonstrate the efficiency of the proposed method.

• 한국지능시스템학회논문지
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• 제8권3호
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• pp.33-40
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• 1998

최근 Yang과 Tseng이 제안한 직교 신경망(ONN)은 직교 함수를 이용하여 신경망을 구성한 것으로서, 다층 신경망이 가지는 층의 구조에 대한 어려움이 없이 전체 구조를 결정할 수 있다는 장점을 가지고 있다. 또한 요구되는 정확성을 기준으로 직교 함수의 급수를 증가시키므로써 학습하는 동안에 전제 구조를 변형하는 것이 가능하고 가중치의 직？ 함수의급수를 증가시키므로써 학습하는 동안에 전체 구조를 변형하는 것이 가능하고 가중치의 학습 알고리듬이 오차 역전파법 학습 알고리듬에 비해 간단하며 수렴 속도가 빠르다는 장점도 있다. 그러나 이러한 직교 신경망은 구조의 골격이 디ㅗ는 직교 함수를 변형할 수 없는 구조를 가진다는 문제점이 있다. 본 논문에서는 입력 변환을 이용하여 직교함수를 학습할 수 있는 구조를 가지는 수정된 직교 신경망(MONN)을 제안한다. 제안한 수정된 지？ 신경망을 이용하여 비선형 시스템을 식별하기 위해 식별기 구조를 설정하고 목적을 달성하기 위한 수정된 직교 신경망의 학습 알고리듬을 유도한다.사례연구른 통하여 본 논문에서 제안한 수정된 직교 신경망의 비선형 시스템 모형화 능력, 입력 변환의 유용성을 다충 신경망, 직교 신경망과 비교하여 검증한다.

• Kyungpook Mathematical Journal
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• 제48권1호
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• pp.155-163
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• 2008

This is an extended version of the paper [K] of the author. The average formulas on the circles and disks around arbitrary points of Nevanlinna counting functions of holomorphic self-maps of the unit disk, given in terms of the boundary values of the selfmaps, are shown to give another characterization of the whole class or a special subclass of inner functions in terms of Nevanlinna counting function in addition to the previous applications to Rudin's orthogonal functions.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2005년도 제36회 하계학술대회 논문집 D
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• pp.2543-2545
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• 2005

It is well known that the orthogonal function is a very useful to estimate an unknown inputs in the linear dynamic systems for its recursive algebraic algorithm. At this aspects, derivative operation(matrix) of orthogonal functions(walsh, block pulse and haar) are introduced and shown how it can useful to design an UIO(unknown inputs observer) design.