• 제목/요약/키워드: Higher order polynomial

검색결과 115건 처리시간 0.028초

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

  • 박태훈;최승억;박동철
    • 대한전기학회:학술대회논문집
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    • 대한전기학회 1996년도 하계학술대회 논문집 B
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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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Estimation of Covariance Functions for Growth of Angora Goats

  • Liu, Wenzhong;Zhang, Yuan;Zhou, Zhongxiao
    • Asian-Australasian Journal of Animal Sciences
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    • 제22권7호
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    • pp.931-936
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    • 2009
  • Body weights of 862 Angora goats between birth and 36 months of age, recorded on a semiyearly basis from 1988 to 2000, were used to estimate genetic, permanent environmental and phenotypic covariance functions. These functions were estimated by fitting a random regression model with 6th order polynomial for direct additive genetic and animal permanent environmental effects and 4th and 5th order polynomial for maternal genetic and permanent environmental effects, respectively. A phenotypic covariance function was estimated by modelling overall animal and maternal effects. The results showed that the most variable coefficient was the intercept for both direct and maternal additive genetic effects. The direct additive genetic (co)variances increased with age and reached a maximum at about 30 months, whereas the maternal additive genetic (co)variances increased rapidly from birth and reached a maximum at weaning, and then decreased with age. Animal permanent environmental (co)variances increased with age from birth to 30 months with lower rate before 12 months and higher rate between 12 and 30 months. Maternal permanent environmental (co)variances changed little before 6 months but then increased slowly and reached a maximum at about 30 months. These results suggested that the contribution of maternal additive genetic and permanent environmental effects to growth variation differed from those of direct additive genetic and animal permanent environmental effects not only in expression time, but also in action magnitude. The phenotypic (co)variance estimates increased with age from birth to 36 months of age.

유량제어밸브 개방형태가 선형펌프 방식 수중사출 시스템에 미치는 영향에 관한 수치적 연구 (Numerical Investigation of Effect of Opening Pattern of Flow Control Valve on Underwater Discharge System using Linear Pump)

  • 이선주
    • 한국군사과학기술학회지
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    • 제22권2호
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    • pp.255-265
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    • 2019
  • In the present study, the effect of opening patterns of a flow control valve on underwater discharge systems using a linear pump was investigated numerically. For that, a improved mathematical model was developed. The improvement is to separate a middle tank from a water cylinder because the cross-section area of the inlet of the middle tank is an important parameter. To validate the improved model, calculation results were compared with a previous study. The results showed that $2^{nd}$ order or more polynomial opening patterns had an advantage over ramp opening patterns. Higher an order of polynomial resulted in wider operating limits. An escape velocity and a maximum acceleration of underwater vehicle were affected by time derivative of the cross-section area of the flow control valve. Besides, as a velocity profile of the vehicle got closer to linearity, the escape velocity got faster and the maximum acceleration got smaller. And velocities of the vehicle and piston had similar variation trend.

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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    • 제55권4호
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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.

SOLUTIONS OF STURM-LIOUVILLE TYPE MULTI-POINT BOUNDARY VALUE PROBLEMS FOR HIGHER-ORDER DIFFERENTIAL EQUATIONS

  • Liu, Yuji
    • Journal of applied mathematics & informatics
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    • 제23권1_2호
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    • pp.167-182
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    • 2007
  • The existence of solutions of the following multi-point boundary value problem $${x^{(n)}(t)=f(t,\;x(t),\;x'(t),{\cdots}, x^{(n-2)}(t))+r(t),\;0 is studied. Sufficient conditions for the existence of at least one solution of BVP(*) are established. It is of interest that the growth conditions imposed on f are allowed to be super-linear (the degrees of phases variables are allowed to be greater than 1 if it is a polynomial). The results are different from known ones since we don't apply the Green's functions of the corresponding problem and the method to obtain a priori bounds of solutions are different enough from known ones. Examples that can not be solved by known results are given to illustrate our theorems.

Static analysis of singly and doubly curved panels on rectangular plan-form

  • Bahadur, Rajendra;Upadhyay, A.K.;Shukla, K.K.
    • Steel and Composite Structures
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    • 제24권6호
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    • pp.659-670
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    • 2017
  • In the present work, an analytical solution for the static analysis of laminated composites, functionally graded and sandwich singly and doubly curved panels on the rectangular plan-form, subjected to uniformly distributed transverse loading is presented. Mathematical formulation is based on the higher order shear deformation theory and principle of virtual work is applied to derive the equations of equilibrium subjected to small deformation. A solution methodology based on the fast converging finite double Chebyshev series is used to solve the linear partial differential equations along with the simply supported boundary condition. The effect of span to thickness ratio, radius of curvature to span ratio, stacking sequence, power index are investigated. The accuracy of the solution is checked by the convergence study of non-dimensional central deflection and moments. Present results are compared with those available in the literature.

음향 센서 배열 형상 추정을 위한 가중 다항 근사화 기법 (Weighted polynomial fitting method for estimating shape of acoustic sensor array)

  • 김동관;김용국;최창호
    • 한국음향학회지
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    • 제39권4호
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    • pp.255-262
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    • 2020
  • 현대의 수동소나 시스템에서는 자함 소음의 영향을 최소화하고 더 높은 신호대잡음비를 얻기 위한 목적으로 예인형 선배열 센서를 운용한다. 얇고 긴 예인형 선배열 센서는 예인선의 기동에 따라 비선형 형태로 유도될 수 있다. 이러한 배열 형상의 변화가 고려되지 않는다면 빔형성기의 성능이 저하될 수 있다. 따라서 예인형 선배열 센서를 이용한 빔형성 시 센서 배열에 대한 정확한 형상의 추정이 필요하다. 선배열 형상 추정에는 다양한 기법이 존재한다. 그 중 방위센서를 이용한 기법의 경우, 방위센서 잡음의 영향으로 추정성능이 감소할 수 있다. 이러한 잠재적 오류를 제거하기 위해 가중 다항 근사화 기반 배열 형상 추정 기법을 제안하였다. 제안 기법의 성능 검증을 위하여 컴퓨터 시뮬레이션을 수행하였다. 그 결과 제안 기법의 성능이 기존 기법에 비해 잡음에 강인함을 확인하였다.

크라운 곡면 형성 (The construction of a crowned surface)

  • 김회섭
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • 제10권2호
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    • pp.49-52
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    • 2006
  • 요즈음 디스플레이가 평판 제품인 PDP, LCD등으로 급속히 대체됨으로써 브라운관도 두께가 점점 얇아지고 있다. 따라서 새도우마스크 부품도 점점 평평해진다. 평평한 곡면은 진동이나 충격에 약하기 때문에 곡면을 크라운하게 설계하는 방법을 제시한다.

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ON CONSTRUCTING A HIGHER-ORDER EXTENSION OF DOUBLE NEWTON'S METHOD USING A SIMPLE BIVARIATE POLYNOMIAL WEIGHT FUNCTION

  • LEE, SEON YEONG;KIM, YOUNG IK
    • 충청수학회지
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    • 제28권3호
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    • pp.491-497
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    • 2015
  • In this paper, we have suggested an extended double Newton's method with sixth-order convergence by considering a control parameter ${\gamma}$ and a weight function H(s, u). We have determined forms of ${\gamma}$ and H(s, u) in order to induce the greatest order of convergence and established the main theorem utilizing related properties. The developed theory is ensured by numerical experiments with high-precision computation for a number of test functions.

고급 뉴로퍼지 다항식 네트워크의 해석과 설계 (The Analysis and Design of Advanced Neurofuzzy Polynomial Networks)

  • 박병준;오성권
    • 전자공학회논문지CI
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    • 제39권3호
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    • pp.18-31
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    • 2002
  • 본 연구는 뉴로퍼지 네트워크와 다항식 뉴럴네트워크를 합성한 하이브리드 모델링 구조인 고급 뉴로퍼지 다항식 네트워크(Advanced neurofuzzy polynomial networks ; ANFPN)를 제안한다. 제안된 네트워크 구조는 높은 비선형 규칙 기반 모델로, CI(Computational Intelligence)의 기술, 즉 퍼지집합, 뉴럴네트워크, 유전자 알고리즘에 의해 설계되어진다. 뉴로퍼지 네트워크는 ANFPN 구조의 전반부를, 다항식 뉴럴네트워크는 후반부를 구성한다. ANFPN의 전반부에서, 뉴로퍼지 네트워크는 간략추론, 오류역전파 학습 규칙을 이용한다. 멤버쉽함수의 파라미터, 학습율, 모멘텀 계수는 유전자 최적화를 이용하여 조절된다. ANFPN의 후반부 구조로서 다항식 뉴럴네트워크는 학습을 통해 생성되는(전개되는) 유연한 네트워크 구조이다. 특히 다항식 뉴럴네트워크의 층과 노드 수는 고정되어 있지 않고 동적으로 생성된다. 본 연구에서는, 2가지 형태의 ANFPN 구조를 제안한다. 즉 기본 구조와 변형된 구조이다. 여기서 기본 구조와 변형된 구조는 다항식 뉴럴네트워크 구조의 각 층에서 입력변수의 수와 회귀다항식의 차수에 의존한다. 두 결합 구조의 특징 때문에 공정 시스템의 비선형적인 특성을 고려할 수 있고 보다 우수한 예측능력을 가진 좋은 출력선응을 얻을 수 있게 한다. ANFPN의 유용성과 실용성은 2개의 수치 예제를 통해 논의된다. 제안된 ANFPN은 기존의 모델보다 높은 정밀도와 예측능력을 가진 모델을 생성함을 보인다.