• 제목/요약/키워드: stochastic matrices

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프레임 구조물의 확률론적 동적 민감도 해석에 관한 연구 (A Study on the Stochastic Sensitivity Analysis in Dynamics of Frame Structure)

  • 부경대학교
    • 수산해양기술연구
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    • 제35권4호
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    • pp.435-447
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    • 1999
  • It is main objective of this approach to present a method to analyse stochastic design sensitivity for problems of structural dynamics with randomness in design parameters. A combination of the adjoint variable approach and the second order perturbation method is used in the finite element approach. An alternative form of the constant functional that holds for all times is introduced to consider the time response of dynamic sensitivity. The terminal problem of the adjoint system is solved using equivalent homogeneous equations excited by initial velocities. The numerical procedures are shown to be much more efficient when based on the fold superposition method: the generalized co-ordinates are normalized and the correlated random variables are transformed to uncorrelated variables, whereas the secularities are eliminated by the fast Fourier transform of complex valued sequences. Numerical algorithms have been worked out and proved to be accurate and efficient : they can be readily adapted to fit into the existing finite element codes whose element derivative matrices can be explicitly generated. The numerical results of two cases -2 dimensional portal frame for the comparison with reference and 3-dimensional frame structure - for the deterministic sensitivity analysis are presented.

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The combined deterministic stochastic subspace based system identification in buildings

  • Bakir, Pelin Gundes
    • Structural Engineering and Mechanics
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    • 제38권3호
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    • pp.315-332
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    • 2011
  • The Combined Deterministic Stochastic Subspace based System Identification Technique (CDSSSIT) is a powerful input-output system identification technique which is known to be always convergent and numerically stable. The technique determines a Kalman state sequence from the projection of the output-input data. The state space matrices are determied subsequently from this Kalman state sequence using least squares. The objective of this paper is to examine the efficiency of the CDSSSIT in identifying the modal parameters (frequencies and mode shapes) of a stiff structure. The results show that the CDSSSIT predicts the modal parameters of stiff buildings quite accurately but is very sensitive to the location of sensors.

System identification of a super high-rise building via a stochastic subspace approach

  • Faravelli, Lucia;Ubertini, Filippo;Fuggini, Clemente
    • Smart Structures and Systems
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    • 제7권2호
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    • pp.133-152
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    • 2011
  • System identification is a fundamental step towards the application of structural health monitoring and damage detection techniques. On this respect, the development of evolved identification strategies is a priority for obtaining reliable and repeatable baseline modal parameters of an undamaged structure to be adopted as references for future structural health assessments. The paper presents the identification of the modal parameters of the Guangzhou New Television Tower, China, using a data-driven stochastic subspace identification (SSI-data) approach complemented with an appropriate automatic mode selection strategy which proved to be successful in previous literature studies. This well-known approach is based on a clustering technique which is adopted to discriminate structural modes from spurious noise ones. The method is applied to the acceleration measurements made available within the task I of the ANCRiSST benchmark problem, which cover 24 hours of continuous monitoring of the structural response under ambient excitation. These records are then subdivided into a convenient number of data sets and the variability of modal parameter estimates with ambient temperature and mean wind velocity are pointed out. Both 10 minutes and 1 hour long records are considered for this purpose. A comparison with finite element model predictions is finally carried out, using the structural matrices provided within the benchmark, in order to check that all the structural modes contained in the considered frequency interval are effectively identified via SSI-data.

쉘 구조물의 확률적 동적 민감도 해석에 관한 연구 (A Study on the Stochastic Sensitivity Analysis in Dynamics of Shell Structure)

  • 배동명;이창훈
    • 수산해양기술연구
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    • 제34권3호
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    • pp.328-338
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    • 1998
  • It is main objective of this approach to present a method to analyse stochastic design sensitivity for problems of structural dynamics with randomness in design parameters. A combination of the adjoint variable approach and the second oder perturbation method is used in the finite element approach. An alternative form of the constant functional that holds for all times is introduced to consider the time response of dynamic sensitivity. The terminal problem of the adjoint system is solved using equivalent homogeneous equations excited by initial velocities. The numerical procedures are shown to be much more efficient when based on the fold superposition method : the generalized co-ordinates are normalized and the correlated random variables are transformed to uncorrelated variables, where as the secularities are eliminated by the fast Fourier transform of complex valued sequences. Numerical algorithms have been worked out and proved to be accurate and efficient : they codes whose element derivative matrices can be explicitly generated. The numerical results of two cases - 2-dimensional portal frame and 3/4-cylindrical shell structure - for the deterministic and stochastic sensitivity analysis illustrates in this paper.

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Modal tracking of seismically-excited buildings using stochastic system identification

  • Chang, Chia-Ming;Chou, Jau-Yu
    • Smart Structures and Systems
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    • 제26권4호
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    • pp.419-433
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    • 2020
  • Investigation of structural integrity has been a critical issue in the field of civil engineering for years. Visual inspection is one of the most available methods to explore deteriorative components in structures. Still, this method is not applicable to invisible damage of structures. Alternatively, system identification methods are capable of tracking modal properties of structures over time. The deviation of these dynamic properties can serve as indicators to access structural integrity. In this study, a modal tracking technique using frequency-domain system identification from seismic responses of structures is proposed. The method first segments the measured signals into overlapped sequential portions and then establishes multiple Hankel matrices. Each Hankel matrix is then converted to the frequency domain, and a temporal-average frequency-domain Hankel matrix can be calculated. This study also proposes the frequency band selection that can divide the frequency-domain Hankel matrix into several portions in accordance with referenced natural frequencies. Once these referenced natural frequencies are unavailable, the first few right singular vectors by the singular value decomposition can offer these references. Finally, the frequency-domain stochastic subspace identification tracks the natural frequencies and mode shapes of structures through quick stabilization diagrams. To evaluate performance of the proposed method, a numerical study is carried out. Moreover, the long-term monitoring strong motion records at a specific site are exploited to assess the tracking performance. As seen in results, the proposed method is capable of tracking modal properties through seismic responses of structures.

NUMERICAL METHODS FOR SOME NONLINEAR STOCHASTIC DIFFERENTIAL EQUATIONS

  • El-Borai, Mahmoud M.;El-Nadi, Khairia El-Said;Mostafa, Osama L.;Ahmed, Hamdy M.
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • 제9권1호
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    • pp.79-90
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    • 2005
  • In this paper we study the numerical solutions of the stochastic differential equations of the form $$du(x,\;t)=f(x,\;t,\;u)dt\;+\;g(x,\;t,\;u)dW(t)\;+\;\sum\limits_{|q|\leq2m}\;A_q(x,\;t)D^qu(x,\;t)dt$$ where $0\;{\leq}\;t\;{\leq}\;T,\;x\;{\in}\;R^{\nu}$, ($R^{nu}$ is the $\nu$-dimensional Euclidean space). Here $u\;{\in}\;R^n$, W(t) is an n-dimensional Brownian motion, $$f\;:\;R^{n+\nu+1}\;{\rightarrow}\;R^n,\;g\;:\;R^{n+\nu+1}\;{\rightarrow}\;R^{n{\times}n},$$, and $$A_q\;:\;R^{\nu}\;{\times}\;[0,\;T]\;{\rightarrow}\;R^{n{\times}n}$$ where ($A_q,\;|\;q\;|{\leq}\;2m$) is a family of square matrices whose elements are sufficiently smooth functions on $R^{\nu}\;{\times}\;[0,\;T]\;and\;D^q\;=\;D^{q_1}_1_{\ldots}_{\ldots}D^{q_{\nu}}_{\nu},\;D_i\;=\;{\frac{\partial}{\partial_{x_i}}}$.

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상호 상관관계가 있는 다중 재료상수의 불확실성에 의한 평면구조의 확률론적 거동 (Probabilistic Behavior of In-plane Structure due to Multiple Correlated Uncertain Material Constants)

  • 노혁천
    • 한국전산구조공학회논문집
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    • 제18권3호
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    • pp.291-302
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    • 2005
  • 구조응답에 기여하는 중요성으로 인하여 추계론적 해석에서는 재료탄성계수의 불확실성에 의한 응답변화도에 대한 연구가 주로 진행되어 왔다. 그러나 추계론적 해석이 의미있는 값을 제공하기 위해서는 가능한 많은 인수에 대한 불확실성을 동시에 고려하여야 한다. 본 연구에서는 구조재료의 중요한 두 인수인 탄성계수와 포아송비에 나타나는 불확실성을 고려한 추계론적 해석을 위한 정식화를 평면문제에 대하여 제안하였다. 이를 위하여 이들 두 인수의 함수로 주어지는 구성행렬의 각 요소에 대한 다항식 전개를 채용하였으며, 두 인수의 불확실성에 따라 나타나는 자기 및 상호상관함수는 n-차 모멘트에 대한 일반식을 적용하여 구성하였다. 다항식 전개에 따라 부행렬의 무한합으로 변형된 구성행렬은 계산상의 편의를 위하여 요구되는 정확도 내에서 절삭하여 사용하였다. 제안된 방법의 검증을 위하여 단순 평면구조를 예제로 택하여 해석하었으며, 해석결과는 국부평균법을 채용한 고전적인 몬테카를 해석 결과와 비교하였다.

주기적 확률외란을 갖는 DC 전동기의 적응형 상태궤환 제어시스템 (Adaptive State Feedback Control System of DC Motors with Periodic Random Disturbance)

  • 정상철;김준수;조현철;이형기
    • 전기학회논문지
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    • 제57권6호
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    • pp.1036-1041
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    • 2008
  • Periodic disturbance is practically occurred in several engineering applications, especially in data storage systems. However, recently addressed controls for such problem were mostly dealt with its deterministic nature, which is rarely practical in real-time implementation. We present an adaptive control approach for DC motor systems with periodic stochastic disturbance whose frequency and magnitude are both random variables. We establish adaptive state feedback control which is linearly composed of nominal and corrective control parameter matrices. The former is derived from a nominal system model voiding disturbance and the latter is constructed from a disturbed system model by using Lyapunov stability theory. We carry out computer simulation to evaluate the proposed control methodology and compare to the recently addressed control method to demonstrate its superiority.

Tracking Filter Design for a Maneuvering target Using Jump Processes

  • Lim, Sang-Seok
    • Journal of Electrical Engineering and information Science
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    • 제3권3호
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    • pp.373-384
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    • 1998
  • This paper presents a maneuvering target model with the maneuver dynamics modeled as a jump process of Poisson-type. The jump process represents the deterministic maneuver(or pilot commands) and is described by a stochastic differential equation driven by a Poisson process taking values a set of discrete states. Employing the new maneuver model along with the noisy observations described by linear difference equations, the author has developed a new linear, recursive, unbiased minimum variance filter, which is structurally simple, computationally efficient, and hence real-time implementable. Futhermore, the proposed filter does not involve a computationally burdensome technique to compute the filter gains and corresponding covariance matrices and still be able to track effectively a fast maneuvering target. The performance of the proposed filter is assessed through the numerical results generated from the Monte-Carlo simulation.

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수학적 모형화 기법이 GPS 기준점 측량 정확도 표현에 미치는 영향 (Impact of Mathematical Modeling Schemes into Accuracy Representation of GPS Control Surveying)

  • 이흥규;서완수
    • 한국측량학회지
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    • 제30권5호
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    • pp.445-458
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    • 2012
  • GPS 기준점 측량은 관측과 데이터 처리를 통해 측지계에 대한 물리적인 표지의 위치를 목표 정확도 범위 이내로 결정하기 위해 실시하며, 이러한 이유로 측량 정확도를 실제와 유사하게 표현하는 것이 매우 중요한 문제이다. 망조정을 통해 산정되는 기준점 성과의 정확도는 사용되는 수학적 모형에 민감한 영향을 받는 추정좌표의 분산-공분산 행렬에 의해 정량적으로 표현된다. 본 연구는 GPS 망조정에 사용되는 함수모형과 통계모형이 기준점 위치 추정과 정확도 표현에 미치는 영향을 연구하여 향후 정확도 표현의 표준화를 위한 기초자료 확보를 위해 실시하였다. 이를 위하여 단일기선해석 다중세션 망조정 이론과 절차와 방법을 실제 관측데이터 처리를 통한 수치적 분석을 병행한 연구를 수행 하였다. 그 결과 절대정확도와 상대정확도를 보다 현실적으로 반영하여 표현하기 위해서는 잔존하는 관측오차의 모형화가 가능한 경험적 통계모형을 사용하는 다점가중제약조정이 GPS 기준점 성과산정을 위한 수학적 모형으로 보다 타당한 것으로 분석되었다.