• Title, Summary, Keyword: Higher order polynomial

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UNIVARIATE LEFT FRACTIONAL POLYNOMIAL HIGH ORDER MONOTONE APPROXIMATION

  • Anastassiou, George A.
    • Bulletin of the Korean Mathematical Society
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    • v.52 no.2
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    • pp.593-601
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    • 2015
  • Let $f{\in}C^r$ ([-1,1]), $r{\geq}0$ and let $L^*$ be a linear left fractional differential operator such that $L^*$ $(f){\geq}0$ throughout [0, 1]. We can find a sequence of polynomials $Q_n$ of degree ${\leq}n$ such that $L^*$ $(Q_n){\geq}0$ over [0, 1], furthermore f is approximated left fractionally and simulta-neously by $Q_n$ on [-1, 1]. The degree of these restricted approximations is given via inequalities using a higher order modulus of smoothness for $f^{(r)}$.

Identification of Anisotropic Bearing Non-linearity

  • Han, Dong-Ju
    • International Journal of Aeronautical and Space Sciences
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    • v.5 no.2
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    • pp.35-42
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    • 2004
  • Among other critical conditions in rotor svstems the large non-linearvibration excited by bearing non-linearity causes the rotor failure. For reducing thiscatastrophic failure and predictive analysis of this phenomena the identificationanalysis of bearing non-linearity in an anisotropic rotor system using the higherorder dFRFs are developed and are shown to be theoretically feasible as innon-rotating structures. For the identification of the anisotropic rotor withanisotropic bearing non-linearity expressed by the displacement in polynomial form,the higher order dFRFs based upon the Volterra series are investigated and depicttheir features by using the simple forms of the normal and reverse dFRFs. Theyproduce additional sub-harmonic resonant peaks, which indicate the existence ofhigher order non-linearties, and show the energy transfer such that the modes fornormal and reuerse dFRFs are exchanged, which are the fundamental differencesfrom what we can expect in linear ones.

A New Economic Dispatch Algorithm Considering Any Higher Order Generation Cost Functions (고차 발전 비용 함수를 고려한 새로운 경제급전 알고리즘)

  • 박정도;문영현
    • The Transactions of the Korean Institute of Electrical Engineers A
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    • v.51 no.12
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    • pp.603-610
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    • 2002
  • In this paper, a new economic dispatch algorithm for unit commitment is proposed to improve both the accuracy of the final solution and the calculation speed of economic dispatch. By using the inverse incremental cost functions, economic dispatch can be transformed into a simple optimization problem associated with an n-th order polynomial equation. The proposed method remarkably reduces the computation time with adaptability to any higher order generation cost functions. The proposed method is tested with sample system, which shows that the proposed algorithm yields more accurate and economical generation scheduling results with high computation speed.

Higher order impact analysis of sandwich panels with functionally graded flexible cores

  • Fard, K. Malekzadeh
    • Steel and Composite Structures
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    • v.16 no.4
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    • pp.389-415
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    • 2014
  • This study deals with dynamic model of composite sandwich panels with functionally graded flexible cores under low velocity impacts of multiple large or small masses using a new improved higher order sandwich panel theory (IHSAPT). In-plane stresses were considered for the functionally graded core and face sheets. The formulation was based on the first order shear deformation theory for the composite face sheets and polynomial description of the displacement fields in the core that was based on the second Frostig's model. Fully dynamic effects of the functionally graded core and face-sheets were considered in this study. Impacts were assumed to occur simultaneously and normally over the top and/or bottom of the face-sheets with arbitrary different masses and initial velocities. The contact forces between the panel and impactors were treated as internal forces of the system. Nonlinear contact stiffness was linearized with a newly presented improved analytical method in this paper. The results were validated by comparing the analytical, numerical and experimental results published in the latest literature.

Parametric Sensitivity Analyses of Linear System relative to the Characteristic Ratios of Coefficient (I) : A General Case (계수의 특성비에 대한 선형계의 파라미터적 감도해석(I): 일반적인 경우)

  • 김영철;김근식
    • Journal of Institute of Control, Robotics and Systems
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    • v.10 no.3
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    • pp.205-215
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    • 2004
  • The characteristic ratio assignment (CRA) method〔1〕 is new polynomial approach which allows to directly address the transient responses such as overshoot and speed of response time in time domain specifications. The method is based on the relationships between time response and characteristic ratios($\alpha_i$ ) and generalized time constant (T), which are defined in terms of coefficients of characteristic polynomial. However, even though the CRA can apply to developing a linear controller that meets good transient responses, there are still some fundamental questions to be explored. For the purpose of this, we have analyzed several sensitivities of a linear system with respect to the changes of coefficients itself and $\alpha_i$ of denominator polynomial. They are (i) the unnormalized root sensitivity : to determine how the poles change as $\alpha_i$ changes, and (ii) the function sensitivity to determine the sensitivity of step response to the change of o, and to analyze the sensitivity of frequency response as o, changes. As an other important result, it is shown that, under any fixed T and coefficient of the lowest order of s in denominator, the step response is dominantly affected merely by $\alpha_1, alpha_2 and alpha_3$ regardless of the order of denominator higher than 4. This means that the rest of the$\alpha_i$ s have little effect on the step response. These results provide some useful insight and background theory when we select $\alpha_i$ and T to compose a reference model, and in particular when we design a low order controllers such as PID controller.

K-Means-Based Polynomial-Radial Basis Function Neural Network Using Space Search Algorithm: Design and Comparative Studies (공간 탐색 최적화 알고리즘을 이용한 K-Means 클러스터링 기반 다항식 방사형 기저 함수 신경회로망: 설계 및 비교 해석)

  • Kim, Wook-Dong;Oh, Sung-Kwun
    • Journal of Institute of Control, Robotics and Systems
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    • v.17 no.8
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    • pp.731-738
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    • 2011
  • In this paper, we introduce an advanced architecture of K-Means clustering-based polynomial Radial Basis Function Neural Networks (p-RBFNNs) designed with the aid of SSOA (Space Search Optimization Algorithm) and develop a comprehensive design methodology supporting their construction. In order to design the optimized p-RBFNNs, a center value of each receptive field is determined by running the K-Means clustering algorithm and then the center value and the width of the corresponding receptive field are optimized through SSOA. The connections (weights) of the proposed p-RBFNNs are of functional character and are realized by considering three types of polynomials. In addition, a WLSE (Weighted Least Square Estimation) is used to estimate the coefficients of polynomials (serving as functional connections of the network) of each node from output node. Therefore, a local learning capability and an interpretability of the proposed model are improved. The proposed model is illustrated with the use of nonlinear function, NOx called Machine Learning dataset. A comparative analysis reveals that the proposed model exhibits higher accuracy and superb predictive capability in comparison to some previous models available in the literature.

Fuzzy Polynomial Neural Network Algorithm using GMDH Mehtod and its Application to the Wastewater Treatment Process (GMDH 방법에 의한 FPNN 일고리즘과 폐스처리공정에의 응용)

  • Oh, Sung-Kwon;Hwang, Hyung-Soo;Ahn, Tae-Chon
    • Journal of the Korean Institute of Intelligent Systems
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    • v.7 no.2
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    • pp.96-105
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    • 1997
  • In this paper, A new design method of fuzzy modeling is presented for the model identification of nonlinear complex systems. The proposed FPNN(Fuzzy Polynomial Neural Network) modeling implements system structure and parameter identification using GMDH(Group Method of Data Handling) method and linguistic fuzzy implication rules from input and output data of processes. In order to identify premise structure and parameter of fuzzy implication rules, GMDH method and regression polynomial fuzzy reasoning method are used and the least square method is utilized for the identification of optimum consequence parameters. Time series data for gas furnace and those for wastewater treatment process are used for the purpose of evaluating the performance of the proposed FPNN modeling. The results show that the proposed method can produce the fuzzy model with higher accuracy than other works achieved previously.

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A Preliminary Result on Electric Load Forecasting using BLRNN (BiLinear Recurrent Neural Network) (쌍선형 회귀성 신경망을 이용한 전력 수요 예측에 관한 기초연구)

  • Park, Tae-Hoon;Choi, Seung-Eok;Park, Dong-Chul
    • Proceedings of the KIEE Conference
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    • pp.1386-1388
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    • 1996
  • In this paper, a recurrent neural network using polynomial is proposed for electric load forecasting. Since the proposed algorithm is based on the bilinear polynomial, it can model nonlinear systems with much more parsimony than the higher order neural networks based on the Volterra series. The proposed Bilinear Recurrent Neural Network(BLRNN) is compared with Multilayer Perceptron Type Neural Network(MLPNN) for electric load forecasting problems. The results show that the BLRNN is robust and outperforms the MLPNN in terms of forecasting accuracy.

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GA-based Feed-forward Self-organizing Neural Network Architecture and Its Applications for Multi-variable Nonlinear Process Systems

  • Oh, Sung-Kwun;Park, Ho-Sung;Jeong, Chang-Won;Joo, Su-Chong
    • KSII Transactions on Internet and Information Systems (TIIS)
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    • v.3 no.3
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    • pp.309-330
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    • 2009
  • In this paper, we introduce the architecture of Genetic Algorithm(GA) based Feed-forward Polynomial Neural Networks(PNNs) and discuss a comprehensive design methodology. A conventional PNN consists of Polynomial Neurons, or nodes, located in several layers through a network growth process. In order to generate structurally optimized PNNs, a GA-based design procedure for each layer of the PNN leads to the selection of preferred nodes(PNs) with optimal parameters available within the PNN. To evaluate the performance of the GA-based PNN, experiments are done on a model by applying Medical Imaging System(MIS) data to a multi-variable software process. A comparative analysis shows that the proposed GA-based PNN is modeled with higher accuracy and more superb predictive capability than previously presented intelligent models.

New enhanced higher order free vibration analysis of thick truncated conical sandwich shells with flexible cores

  • Fard, Keramat Malekzadeh;Livani, Mostafa
    • Structural Engineering and Mechanics
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    • v.55 no.4
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    • pp.719-742
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    • 2015
  • This paper dealt the free vibration analysis of thick truncated conical composite sandwich shells with transversely flexible cores and simply supported boundary conditions based on a new improved and enhanced higher order sandwich shell theory. Geometries were used in the present work for the consideration of different radii curvatures of the face sheets and the core was unique. The coupled governing partial differential equations were derived by the Hamilton's principle. The in-plane circumferential and axial stresses of the core were considered in the new enhanced model. The first order shear deformation theory was used for the inner and outer composite face sheets and for the core, a polynomial description of the displacement fields was assumed based on the second Frostig's model. The effects of types of boundary conditions, conical angles, length to radius ratio, core to shell thickness ratio and core radius to shell thickness ratio on the free vibration analysis of truncated conical composite sandwich shells were also studied. Numerical results are presented and compared with the latest results found in literature. Also, the results were validated with those derived by ABAQUS FE code.