• Structural Engineering and Mechanics
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• 제63권6호
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• pp.779-788
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• 2017

System identification and damage detection for structural health monitoring have received considerable attention. Various time domain analysis methodologies based on measured vibration data of structures have been proposed. Among them, recursive least-squares estimation of structural parameters which is also known as parametric Kalman filter (PKF) approach has been studied. However, the conventional PKF requires that all the external excitations (inputs) be available. On the other hand, structural uncertainties are inevitable for civil infrastructures, it is necessary to develop approaches for probabilistic damage detection of structures. In this paper, a parametric Kalman filter with unknown inputs (PKF-UI) is proposed for the simultaneous identification of structural parameters and the unmeasured external inputs. Analytical recursive formulations of the proposed PKF-UI are derived based on the conventional PKF. Two scenarios of linear observation equations and nonlinear observation equations are discussed, respectively. Such a straightforward derivation of PKF-UI is not available in the literature. Then, the proposed PKF-UI is utilized for probabilistic damage detection of structures by considering the uncertainties of structural parameters. Structural damage index and the damage probability are derived from the statistical values of the identified structural parameters of intact and damaged structure. Some numerical examples are used to validate the proposed method.

• 한국통신학회논문지
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• 제28권10C호
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• pp.1013-1022
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• 2003

본 논문은 연속적인 영상에 대해 비모수적 영상 처리 기법과 칼만 필터 기반의 동적 AR(2) 프로세스 기법을 적용하여 객체의 움직임을 적응적으로 추적하는 실시간 객체 추적 알고리즘을 구현하였다. 다양한 환경 조건에서 입력되는 영상에 대해 비모수적 영상 처리 기법을 이용하여 처리함으로써 효과적으로 움직임 객체를 추출하였으며, 객체의 움직임을 동적 AR(2) 프로세스 모형으로 모델링하고 동적으로 변하는 AR(2) 프로세스의 파라미터를 칼만 필터를 통해 추정함으로써 객체의 다변적인 움직임을 적응적으로 예측하여 추적할 수 있었다. 구현된 객체 추적 시스템을 실험한 결과, 기존의 선형 칼만 필터 기법을 이용한 추적 기법과 비교하여 추정 오차가 약 1/2.5∼1/50 만큼 더 적게 나와 객체의 움직임을 더 근사적으로 추적함을 알 수 있었다.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2002년도 합동 추계학술대회 논문집 정보 및 제어부문
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• pp.104-109
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• 2002

A new robust Kalman filter is designed for the linear discrete-time system with norm-bounded parametric uncertainties. Sum quadratic constraint, which describes the uncertainties of the system, is converted into an indefinite quadratic form to be minimized in indefinite inner product space. This minimization problem is solved by the new robust Kalman filter. Since the new filter is obtained by simply modifying the conventional Kalman filter, robust filtering scheme can be more readily designed using the proposed method in comparison with the existing robust Kalman filters. A numerical example demonstrates the robustness and the improvement of the proposed filter compared with the existing filters.

• 한국항행학회논문지
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• 제25권6호
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• pp.543-549
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• 2021

본 논문에서는 불확실성의 크기가 유한한 파라미터를 갖는 스트랩다운 관성항법시스템에 대한 강인한 전달정렬 기법을 제안하였다. 크레인 공간을 이용하면 에너지가 유한한 불확실성을 갖는 강인한 필터는 일반적인 칼만필터와 동일한 구조를 갖게 된다. 단지 측정 행렬과 측정 잡음의 공분산값을 수정하면 된다. 본 논문에서 제안한 강인한 전달정렬 기법의 성능을 분석하기 위해서 항체가 고기동 운항을 하면서 측정치에 시간 지연이 발생하는 경우를 가정하여 시뮬레이션을 수행하였고 제안한 기법의 강인성을 검증하였다.

• 대한전기학회논문지:전력기술부문A
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• 제48권5호
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• pp.560-570
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• 1999

This paper formulates the suboptimal robust Kalman filtering problem into two coupled Linear Matrix Inequality (LMI) problems by applying Lyapunov theory to the augmented system which is composed of the state equation in the uncertain linear system and the estimation error dynamics. This formulations not only provide the sufficient conditions for the existence of the desired filter, but also construct the suboptimal robust Kalman filter. The proposed filter can guarantee the optimized upper bound of the estimation error variance for uncertain systems with parametric uncertainties in both the state and measurement matrices. In addition, this paper shows how the problem of finding the minimizing solution subject to Quadratic Matrix Inequality (QMI), which cannot be easily transformed into LMI using the usual Schur complement formula, can be successfully modified into a generic LMI problem.

• 제어로봇시스템학회논문지
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• 제14권9호
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• pp.931-938
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• 2008

In this paper, a novel localization algorithm robust to the unmodeled systematic odometry errors is proposed for low-cost non-holonomic mobile robots. It is well known that the most pose estimators using odometry measurements cannot avoid the performance degradation due to the dead-reckoning of systematic odometry errors. As a remedy for this problem, we tty to reflect the wheelbase error in the robot motion model as a parametric uncertainty. Applying the Krein space estimation theory for the discrete-time uncertain nonlinear motion model results in the extended robust Kalman filter. This idea comes from the fact that systematic odometry errors might be regarded as the parametric uncertainties satisfying the sum quadratic constrains (SQCs). The advantage of the proposed methodology is that it has the same recursive structure as the conventional extended Kalman filter, which makes our scheme suitable for real-time applications. Moreover, it guarantees the satisfactoty localization performance even in the presence of wheelbase uncertainty which is hard to model or estimate but often arises from real driving environments. The computer simulations will be given to demonstrate the robustness of the suggested localization algorithm.

• 한국공간정보시스템학회:학술대회논문집
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• 한국공간정보시스템학회 2004년도 춘계 학술발표회 논문집 제1권1호(통권1호)
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• pp.29-36
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• 2004

In this paper, a study of damage detection for 2-Dimensional Truss Structures using the parametric projection filter theory is presented. Many researchers are interested in inverse problem and one of solution procedures for inverse problems that are very effective is the approach using the filtering algorithm in conjunction with numerical solution methods. In filtering algorithm, the Kalman filtering algorithm is well known and have been applied to many kind of inverse problems. In this paper, the Parametric projection filtering in conjunction with structural analysis is applied to the identification of damages in 2-D truss structures. The natural frequency and modes of damaged truss model are adopted as the measurement data. The effectiveness of proposed method is verified through the numerical examples.

• Structural Engineering and Mechanics
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• 제54권2호
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• pp.291-304
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• 2015

Compared with the identification of linear structures, it is more challenging to conduct identification of nonlinear structure systems, especially when the locations of structural nonlinearities are not clear in structural systems. Moreover, it is highly desirable to develop methods of parametric identification using partial measurements of structural responses for practical application. To cope with these issues, an identification method is proposed in this paper for the detection and parametric identification of structural nonlinear restoring forces using only partial measurements of structural responses. First, an equivalent linear structural system is proposed for a nonlinear structure and the locations of structural nonlinearities are detected. Then, the parameters of structural nonlinear restoring forces at the locations of identified structural nonlinearities together with the linear part structural parameters are identified by the extended Kalman filter. The proposed method simplifies the identification of nonlinear structures. Numerical examples of the identification of two nonlinear multi-story shear frames and a planar nonlinear truss with different nonlinear models and locations are used to validate the proposed method.

• 한국산학기술학회논문지
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• 제19권6호
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• pp.567-574
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• 2018

위험 관리는 1) 체계개발 프로젝트의 비용, 일정 및 목표 성능 달성에 부정적인 영향을 줄 수 있는 위험 요소를 식별하고, 2) 식별된 각 위험 요소에 영향도와 발생 가능성을 부여하고 이를 바탕으로 식별 위험 요소를 관리하는 방법을 의미한다. 위험 요소를 사전에 식별하고 이에 대처함으로써 프로젝트의 비용 및 일정 관리와 목표 성능을 효과적으로 수행하고 달성할 수 있기 때문에 다양한 분야에서 위험 관리를 적용하고 있으며 이에 대한 많은 연구가 현재 진행되고 있다. 본 논문에서는 칼만 필터를 이용한 위험 요소 영향도 추정 방안을 제시한다. 위험 요소 영향도는 위험 발생 시의 손실 비용 및 일정을 변수로 갖는 식으로 표현된다고 가정하였다. 위험 요소 영향도의 참 값과 추정 값 사이의 오차를 줄이기 위한 방안으로서 선형 칼만 필터가 사용되었으며, 결과적으로 이를 통해 위험 관리 절차에 투입되는 자원을 절약할 수 있다. 제시된 위험 요소 영향도 추정 프로세스 검증은 시뮬레이션을 통해 수행되었다.

• Smart Structures and Systems
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• 제14권6호
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• pp.1105-1129
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• 2014

The unscented Kalman filter (UKF) has been developed for nonlinear model parametric identification, and it assumes that the model parameters are symmetrically distributed about their mean values without any constrains. However, the parameters in many applications are confined within certain ranges to make sense physically. In this paper, a constrained unscented Kalman filter (CUKF) algorithm is proposed to improve accuracy of numerical substructure modeling in hybrid testing. During hybrid testing, the numerical models of numerical substructures which are assumed identical to the physical substructures are updated online with the CUKF approach based on the measurement data from physical substructures. The CUKF method adopts sigma points (i.e., sample points) projecting strategy, with which the positions and weights of sigma points violating constraints are modified. The effectiveness of the proposed hybrid testing method is verified by pure numerical simulation and real-time as well as slower hybrid tests with nonlinear specimens. The results show that the new method has better accuracy compared to conventional hybrid testing with fixed numerical model and hybrid testing based on model updating with UKF.