• 제목/요약/키워드: Taylor expansion

검색결과 190건 처리시간 0.026초

Smart System Identification of Super High-Rise Buildings using Limited Vibration Data during the 2011 Tohoku Earthquake

  • Ikeda, A.;Minami, Y.;Fujita, K.;Takewaki, I.
    • 국제초고층학회논문집
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    • 제3권4호
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    • pp.255-271
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    • 2014
  • A method of smart system identification of super high-rise buildings is proposed in which super high-rise buildings are modeled by a shear-bending system. The method is aimed at finding the story shear and bending stiffnesses of a specific story only from the horizontal floor accelerations. The proposed method uses a set of closed-form expressions for the story shear and bending stiffnesses in terms of the limited floor accelerations and utilizes a reduced shear-bending system with the same number of elements as the observation points. A difficulty of prediction of an unstable specific function in a low frequency range can be overcome by introducing an ARX model and discussing its relation with the Taylor series expansion coefficients of a transfer function. It is demonstrated that the shear-bending system can simulate the vibration records with a reasonable accuracy. It is also shown that the vibration records at two super high-rise buildings during the 2011 Tohoku (Japan) earthquake can be simulated with the proposed method including a technique of inserting degrees of freedom between the vibration recording points. Finally it is discussed further that the time-varying identification of fundamental natural period and stiffnesses can be conducted by setting an appropriate duration of evaluation in the batch least-squares method.

대변위 밀 대회전을 고려한 편심된 격하 보요소의 기하학적 비선형해석 (A Geometrically Nonlinear Analysis for the Eccentric Degenerated Beam Element Considering Large Displacements and Large Rotations)

  • 이재욱;양영태
    • 대한조선학회논문집
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    • 제29권4호
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    • pp.227-233
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    • 1992
  • 3차원 편심 보요소의 기하학적 비선형 해석에서 증분 평형식을 유도하는 일반적인 방법의 대부분은 비선형을 고려한 가상일의 평형방정식을 선형화하는 방법으로, 회전증분이 미소하다는 가정에 의해서 선형화된 증분 평형식을 유도하고, 구조물의 변형이 일어나는 동안에 발생하는 유한회전의 영향은 반복계산의 과정에서 고려하는 방법이다. 그리고 유한회전을 고려하는 개선된 방법으로 Surana와 Onate 등에 의해서 개발되었는데, Surana는 비선형 절점함수를 가정하였고, Onate는 회전행렬의 관계식을 이차항까지 고려하여 비선형 증분 평형식을 유도하였다. 본 논문에서는 비선형 해석의 증분이론(incremental theory)을 도입, $^{t+dt}U_i$ 변위증분을 Talyer 급수로 2차항까지 전개하므로서 1차 선형항($U_L$)과 2차 유한회전항($U_R$)으로 표시하여 연속체운동의 비선형 증분평형식에서 유한회전의 영향을 고려하는 방법을 사용하였다. 이상의 해석방법에 따른 수치해석 결과는 Surana와 Onate등에 의하여 다루어진 예제와 비교 하였다.

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강인한 제어를 위한 수중이동시스템의 상태추정에 대한 연구 (The State Estimation by Unknown Disturbance Observer of Underwater Vehicle System for Robust Control)

  • 이진우;김환성;안영주
    • 한국안전학회지
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    • 제18권4호
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    • pp.169-175
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    • 2003
  • 본 연구에서는 외부의 알 수 없는 외란을 포함한 수중이동시스템의 상태를 추정하는 추정방법을 제시하였다. 우선, 수중이동시스템의 동력학적 운동방정식을 수직평면과 수평평면에 대하여 확장 테일러 전개법에 의하여 각각 유도하였다. 수중이동시스템에서 바다표면의 파랑, 주류, 바람 등과 같이 측정하기 어려운 외력을 시스템의 외란으로 간주하였으며, 이러한 외란을 시스템에 대한 외부 입력으로 고려하였다. 본 연구에서는 위와 같은 외부에서 가해지는 잘 알려지지 않은 외란 등에 대해 전혀 영향을 받지 않는 미지외란 관측기를 제안하였으며, 제안된 관측기가 미지외란에 대해서 영향을 받지 않음을 증명하였다. 또한, 수중이동시스템의 강인한 제어를 위해 수치적인 시뮬레이션을 통하여 본 미지 외란 관측기의 유효성을 확인하였다.

Performance Analysis of Distributed Antenna Systems with Antenna Selection over MIMO Rayleigh Fading Channel

  • Yu, Xiangbin;Tan, Wenting;Wang, Ying;Liu, Xiaoshuai;Rui, Yun;Chen, Ming
    • KSII Transactions on Internet and Information Systems (TIIS)
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    • 제8권9호
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    • pp.3016-3033
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    • 2014
  • The downlink performance of distributed antenna systems (DAS) with antennas selection is investigated in Rayleigh fading multicell environment, and the corresponding system capacity and bit error rate (BER) analysis are presented. Based on the moment generating function, the probability density function (PDF) and cumulative distribution function (CDF) of the effective signal to interference plus noise ratio (SINR) of the system are first derived, respectively. Then, with the available CDF and PDF, the accurate closed-form expressions of average channel capacity and average BER are further derived for exact performance evaluation. To simplify the expression, a simple closed-form approximate expression of average channel capacity is obtained by means of Taylor series expansion, with the performance results close to the accurate expression. Besides, the system outage capacity is analyzed, and an accurate closed-form expression of outage capacity probability is derived. These theoretical expressions can provide good performance evaluation for DAS downlink. It can be shown by simulation that the theoretical analysis and simulation are consistent, and DAS with antenna selection outperforms that with conventional blanket transmission. Moreover, the system performance can be effectively improved as the number of receive antennas increases.

Stochastic fracture behavior analysis of infinite plates with a separate crack and a hole under tensile loading

  • Khubi Lal Khatri;Kanif Markad
    • Computers and Concrete
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    • 제32권1호
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    • pp.99-117
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    • 2023
  • The crack under the influence of the higher intensities of the stresses grows and the structure gets collapsed with the time when the crack length reaches to critical value. Therefore, the fracture behavior of a structure in terms of stress intensity factors (SIF) becomes important to determine the remaining fracture strength and capacity of material and structure for avoiding catastrophic failure, increasing safety and further improvement in the design. The robustness of the method has been demonstrated by comparing the numerical results with analytical and experimental results of some problems. XFEM is used to model cracks and holes in structures and predict their strength and reliability under service conditions. Further, XFEM is extended with a stochastic method for predicting the sensitivity in terms of output COVs and fracture strength in terms of mean values of stress intensity factors (SIFs) of a structure with discontinuities (cracks and holes) under tensile loading condition with input individual and combined randomness in different system parameters. In stochastic technique, the second order perturbation technique (SOPT) has been used for the predicting the fracture behavior of the structures. The stochastic/perturbation technique is also known as Taylor series expansion method and it provides the reliable results if the input randomness is less than twenty percentage. From the present numerical analysis it is observed that, the crack tip near to the hole is under the influence of the stress concentration and the variational effect of the input random parameters on the crack tip in terms of the SIFs are lesser so the COVs are the less sensitive. The COVs of mixed mode SIFs are the most sensitive for the crack angles (α=45° to 90°) for all the values of c1 and d1. The plate with the shorter distance between hole and crack is the most sensitive with all the crack angles but the crack tip which is much nearer to the hole has the highest sensitivity.

Combination resonances of porous FG shallow shells reinforced with oblique stiffeners subjected to a two-term excitation

  • Kamran Foroutan;Liming Dai;Haixing Zhao
    • Steel and Composite Structures
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    • 제51권4호
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    • pp.391-406
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    • 2024
  • The present research investigates the combination resonance behaviors of porous FG shallow shells reinforced with oblique stiffeners and subjected to a two-term excitation. The oblique stiffeners considered in this research reinforce the shell internally and externally. To model the stiffeners, Lekhnitskii's smeared stiffeners technique is utilized. According to the first-order shear deformation theory (FSDT) and stress functions, a nonlinear model of the oblique stiffened shallow shell is established. With regard to the FSDT and von-Kármán nonlinear geometric assumptions, the stress-strain relationships for the present shell system are developed. Also, in order to discretize the nonlinear governing equations, the Galerkin method is implemented. To obtain the required relations for investigating the combination resonance theoretically, the method of multiple scales is applied. For verifying the results of the present research, generated results are compared with previous research. Additionally, a comparison with the P-T method is conducted to increase the validity of the generated results, as this method has illustrated advantages over other numerical methods in terms of accuracy and reliability. In this method, the piecewise constant argument is used jointly with the Taylor series expansion, which is why it is named the P-T method. The effects of stiffeners with different angles, and the effects of material parameters on the combination resonance behaviors of the present system are addressed. With the findings of this research, researchers and engineers in this field may use them as benchmarks for their design and research of porous FG shallow shells.

불량률 최소화를 통한 강건 최적화의 확률제한조건 처리 (Solving Probability Constraint in Robust Optimization by Minimizing Percent Defective)

  • 이광기;박찬경;김근연;이권희;한상욱;한승호
    • 대한기계학회논문집A
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    • 제37권8호
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    • pp.975-981
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    • 2013
  • 강건 최적화 기법은 설계 초기 단계부터 설계변수의 변동이 목적함수에 미치는 효과를 최소화할 수 있는 유일한 방법이다. 강건 최적화의 정식화를 위해서는 분산을 정확히 예측하고 확률제한조건을 정식화하는 것이 가장 중요한 과정이 된다. 분산 및 확률제한조건을 예측하고 정식화하기 위한 방법으로 공정능력지수 및 식스시그마 기법과 같은 여러 가지 방법이 적용되고 있으나, 실제 공정에서 널리 적용되는 불량률을 이용한 확률제한조건 처리 기법에 대한 연구는 아직까지 전무한 상태이다. 본 연구에서는 자동차 로워암의 무게와 최대응력의 평균과 표준편차에 대한 설계영역을 탐색하고, 이후 로워암의 강건 최적화를 수행하였다. 변동을 예측하기 위한 표준편차의 계산은 2 차 테일러 전개를 통해 수치적인 정확도를 기하였다. 강건 최적화는 설계변수의 불연속성을 고려하기 위하여 최적화 과정에서 미분 정보를 적용하지 않은 심플렉스 알고리즘을 적용하였다.

네트워크형 터널의 환기해석 방법에 대한 기초연구-비 Hardy-Cross 방법을 중심으로 (A fundamental study on the ventilation analysis method for the network-type tunnel - focused on the none hardy-cross method)

  • 김효규;최판규;류지오;이창우
    • 한국터널지하공간학회 논문집
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    • 제18권3호
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    • pp.291-303
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    • 2016
  • 최근 도시부 지하도로 건설에 따른 터널내 다양한 형태의 분기부가 설계되고 있으며, 이는 기존의 일자형 터널에서의 환기해석 방법과는 다른 해석방법을 요구하고 있다. 그러나 국내외 터널환기 해석방법중 네트워크형 터널에 대한 환기해석에 대한 방법은 설계기준으로 제시되지 않고 있으며, 주로 네트워크용 수치해석 프로그램에 의존하여 설계가 진행되고 있다. 본 연구에서는 수치해석적 방법이 아닌 특성화 방정식에 기초한 네트워크형 터널에 대한 환기해석 방법 중 설계기준으로 적합한 네트워크 모형을 고찰하였다. 기존의 Hardy-Cross 방법은 계산방법이 비교적 간단하고 수계산이 가능한 장점이 있어, 광산통기 및 터널환기 분야에서 폭넓게 적용되어 왔다. 그러나 Tayler 정리에 따른 절단오차 문제 및 대규모 네트워크 환경에서 mesh의 선택 알고리즘에 따른 수렴성 문제가 보고되고 있다. 따라서 본 연구에서는 비 hardy-cross 방법 중 mesh의 구성이 없이도 유량과 압력을 동시에 해석할 수 있는 gradient method로 네트워크형 터널에 대한 환기해석의 적용성을 고찰하였고, 더불어 네트워크형 터널에 대한 환기해석이 가능한 간편한 방법을 제시하는데 그 목적이 있다.

Adaptable Center Detection of a Laser Line with a Normalization Approach using Hessian-matrix Eigenvalues

  • Xu, Guan;Sun, Lina;Li, Xiaotao;Su, Jian;Hao, Zhaobing;Lu, Xue
    • Journal of the Optical Society of Korea
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    • 제18권4호
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    • pp.317-329
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    • 2014
  • In vision measurement systems based on structured light, the key point of detection precision is to determine accurately the central position of the projected laser line in the image. The purpose of this research is to extract laser line centers based on a decision function generated to distinguish the real centers from candidate points with a high recognition rate. First, preprocessing of an image adopting a difference image method is conducted to realize image segmentation of the laser line. Second, the feature points in an integral pixel level are selected as the initiating light line centers by the eigenvalues of the Hessian matrix. Third, according to the light intensity distribution of a laser line obeying a Gaussian distribution in transverse section and a constant distribution in longitudinal section, a normalized model of Hessian matrix eigenvalues for the candidate centers of the laser line is presented to balance reasonably the two eigenvalues that indicate the variation tendencies of the second-order partial derivatives of the Gaussian function and constant function, respectively. The proposed model integrates a Gaussian recognition function and a sinusoidal recognition function. The Gaussian recognition function estimates the characteristic that one eigenvalue approaches zero, and enhances the sensitivity of the decision function to that characteristic, which corresponds to the longitudinal direction of the laser line. The sinusoidal recognition function evaluates the feature that the other eigenvalue is negative with a large absolute value, making the decision function more sensitive to that feature, which is related to the transverse direction of the laser line. In the proposed model the decision function is weighted for higher values to the real centers synthetically, considering the properties in the longitudinal and transverse directions of the laser line. Moreover, this method provides a decision value from 0 to 1 for arbitrary candidate centers, which yields a normalized measure for different laser lines in different images. The normalized results of pixels close to 1 are determined to be the real centers by progressive scanning of the image columns. Finally, the zero point of a second-order Taylor expansion in the eigenvector's direction is employed to refine further the extraction results of the central points at the subpixel level. The experimental results show that the method based on this normalization model accurately extracts the coordinates of laser line centers and obtains a higher recognition rate in two group experiments.

산사태 위험도 추정을 위한 간극수압 예측에 관한 연구(II) -산사면에서의 지하수위 예측 모델의 개발- (Porewater Pressure Predictions on Hillside Slopes for Assessing Landslide Risks (II) Development of Groundwater Flow Model)

  • 이인모;박경호;임충모
    • 한국지반공학회지:지반
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    • 제8권2호
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    • pp.5-20
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    • 1992
  • The physical-based and lumped-parameter hydrologic groundwater flow model for predicting the rainfall-triggered rise of groundwater levels in hillside slopes is developed in this paper to assess the risk of landslides. The developed model consists of a vertical infiltration model for unsaturated zone linked to a linear storage reservoir model(LSRM) for saturated zone. The groundwater flow model has uncertain constants like soil depttL slope angle, saturated permeability, and potential evapotranspiration and four free model parameters like a, b, c, and K. The free model parameters could be estimated from known input-output records. The BARD algorithm is uses as the parameter estimation technique which is based on a linearization of the proposed model by Gauss -Newton method and Taylor series expansion. The application to examine the capacity of prediction shows that the developed model has a potential of use in forecast systems of predicting landslides and that the optimal estimate of potential 'a' in infiltration model is the most important in the global optimum analysis because small variation of it results in the large change of the objective function, the sum of squares of deviations of the observed and computed groundwater levels. 본 논문에서는 가파른 산사면에서 산사태의 발생을 예측하기 위한 수문학적 인 지하수 흐름 모델을 개발하였다. 이 모델은 물리적인 개념에 기본하였으며, Lumped-parameter를 이용하였다. 개발된 지하수 흐름 모델은 두 모델을 조합하여 구성되어 있으며, 비포화대 흐름을 위해서는 수정된 abcd 모델을, 포화대 흐름에 대해서는 시간 지체 효과를 고려할 수 있는 선형 저수지 모델을 이용하였다. 지하수 흐름 모델은 토층의 두께, 산사면의 경사각, 포화투수계수, 잠재 증발산 량과 같은 불확실한 상수들과 a, b, c, 그리고 K와 같은 자유모델변수들을 가진다. 자유모델변수들은 유입-유출 자료들로부터 평가할 수 있으며, 이를 위해서 본 논문에서는 Gauss-Newton 방법을 이용한 Bard 알고리즘을 사용하였다. 서울 구로구 시흥동 산사태 발생 지역의 산사면에 대하여 개발된 모델을 적용하여 예제 해석을 수행함으로써, 지하수 흐름 모델이 산사태 발생 예측을 위하여 이용할 수 있음을 입증하였다. 또한, 매개변수분석 연구를 통하여, 변수 a값은 작은 변화에 대하여 목적함수값에 큰 변화를 일으키므로 a의 값에 대한 최적값을 구하는 것이 가장 중요한 요소라는 결론을 얻었다.

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