• Communications for Statistical Applications and Methods
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• v.15 no.6
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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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• v.20 no.11
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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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• 2001.10a
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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.

• Proceedings of the KIEE Conference
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• 1997.11a
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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.

• Honam Mathematical Journal
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• v.16 no.1
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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.

• Proceedings of the KIEE Conference
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• 1998.07b
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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.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.48 no.3
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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.

• Journal of the Korean Institute of Intelligent Systems
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• v.8 no.3
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• pp.33-40
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• 1998

This paper presents an Modified Orthogonal Neural Network(MONN), new modified model of Orthogonal Neural Network(0NN) based on orthogonal functions, and applies it to nonlinear system approximator. ONN proposed by Yang and Tseng, doesn't have the problems of traditional multilayer feedforward neural networks such as the determination of initial weights and the numbers of layers and processing elements. And tranining of ONN converges rapidly. But ONN cannot adapt its orthogonal functions to a given system. The accuracy of ONN, in terms of the minimal possible deviation between system and approximator, is essentially dependent on the choice of basic orthogonal functions. In order to improve ability and effectiveness of approximate nonlinear systems, MONN has an input transformation layer to adapt its basic orthogonal functions to a given nonlinear system. The results show that MONN has the excellent performance of approximate nonlinear systems and the input transfnrmation makes the ability of MONN better than one of ONN.

• Kyungpook Mathematical Journal
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• v.48 no.1
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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.

• Proceedings of the KIEE Conference
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• 2005.07d
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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.