• Proceedings of the KSME Conference
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• 2000.04a
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• pp.566-572
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• 2000

The System identification is the process of developing or improving a mathematical model of a physical system using experimental data of the input, output and noise relationship. The field of system identification has been an important discipline within the automatic control area. The reason is the requirement that mathematical models having a specified accuracy must be used to apply modem control methods. In this paper, it is confirmed that we can obtain transfer function of flexible beam that is expressed in the forms of identified state-space system matrix A, B, C, D and identified observer gain G using Eigensystem Realization Algorithm including singular value decomposition. And these matrices can be applied to the automatic control. In addition to, it is also confirmed that transfer function can express a system using identified observer gain G, in spite of a noisy data or a periodic disturbance.

• Structural Engineering and Mechanics
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• v.34 no.5
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• pp.625-634
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• 2010

The objective of this paper is to apply a new proposed accuracy indicator to quantify the true and false modes for Eigensystem Realization Algorithm using output-based responses. First, a discrete mass-spring system and a simply supported continuous beam were modelled using finite element method. Then responses are simulated under random excitation. Natural Excitation Technique using only response measurements is applied to compute the impulse responses. Eigensystem Realization Algorithm is employed to identify the modal parameters on the simulated responses. A new accuracy indicator, Normalized Occurrence Number-NON, is developed to quantitatively partition the realized modes into true and false modes so that the false portions can be disregarded. Numerical simulation demonstrates that the new accuracy indicator can determine the true system modes accurately.

• Structural Engineering and Mechanics
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• v.63 no.6
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• pp.743-750
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• 2017

Modal parameter identification plays a key role in the structural health monitoring (SHM) for civil engineering. Eigensystem realization algorithm (ERA) is one of the most popular identification methods. However, the complex environment around civil structures can introduce the noises into the measurement from SHM system. The spurious modes would be generated due to the noises during ERA process, which are usually ignored and be recognized as physical modes. This paper proposes an improved stabilization diagram method in ERA to distinguish the spurious modes. First, it is proved that the ERA can be performed by any two Hankel matrices with one time step shift. The effect of noises on the eigenvalues of structure is illustrated when the choice of two Hankel matrices with one time step shift is different. Then, a moving data diagram is proposed to combine the traditional stabilization diagram to form the improved stabilization diagram method. The moving data diagram shows the mode variation along the different choice of Hankel matrices, which indicates whether the mode is spurious or not. The traditional stabilization diagram helps to determine the concerned truncated order before moving data diagram is implemented. Finally, the proposed method is proved through a numerical example. The results show that the proposed method can distinguish the spurious modes.

• Journal of Electrical Engineering and Technology
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• v.11 no.1
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• pp.9-19
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• 2016

Accurate models of the characteristics of typical inverse-time overcurrent (OC) protective devices play an important role in the protective coordination schemes. This paper presents a novel approach to determine the OC protective device parameters. The approach is based on the Eigensystem Realization Algorithm which generates a state space model to fit the characteristics of OC protective devices. Instead of the conventional characteristic curves, the dynamic state space model gives a more exact fit of the OC protective device characteristics. This paper demonstrates the feasibility of decomposing the characteristic curve into smooth components and oscillation components. 19 characteristic curves from 13 typical and 6 non-typical OC protective devices are chosen for curve-fitting. The numbers of fitting components required are determined by the maximum absolute values of errors for the fitted equation. All fitted equations are replaced by a versatile equation for the characteristics of OC protective devices which represents the characteristic model of a novel flexible OC relay, which in turn may be applied to improve the OC coordination problems in the sub-transmission and distribution systems.

• Structural Engineering and Mechanics
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• v.17 no.3_4
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• pp.445-466
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• 2004

In this paper, several modal identification techniques for output-only structural systems are extensively investigated. The methods considered are the power spectral method, the frequency domain decomposition method, the Ibrahim time domain method, the eigensystem realization algorithm, and the stochastic subspace identification method. Generally, the power spectral method is most widely used in practical area, however, the other methods may give better estimates particularly for the cases with closed modes and/or with large measurement noise. Example analyses were carried out on typical structural systems under three different loading cases, and the identification performances were examined throught the comparisons between the estimates by various methods.

• Structural Monitoring and Maintenance
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• v.1 no.2
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• pp.231-247
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• 2014

This paper focuses on the dynamic behaviour of Mirandola City Hall (a XV century Renaissance Palace) that was severely damaged during May 2012 Emilia earthquake in Northern Italy. Experimental investigations have been carried out on this monumental building. Firstly, detailed investigations have been carried out to identify the identification of the geometry of the main constructional parts as well as the mechanical features of the constituting materials of the palace. Then, Ambient Vibration Tests (AVT) have been applied, for the detection of the main dynamic features. Three output-only identification methods have been compared: (i) the Frequency Domain Decomposition, (ii) the Random Decrement (RD) and the (iii) Eigensystem Realization Algorithm (ERA). The modal parameters of the Palace were difficult to be identified due to the severe structural damage; however the two bending modes in the perpendicular directions were identified. The comparison of the three experimental techniques showed a good agreement confirming the reliability of the three identification methods.

• Structural Engineering and Mechanics
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• v.42 no.3
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• pp.425-448
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• 2012

In this paper, a new damage detection and quantification method has been presented to perform detection and quantification of structural damage under ambient vibration loadings. To extract modal properties of the structural system under ambient excitation, natural excitation technique (NExT) and eigensystem realization algorithm (ERA) are employed. Sensitivity matrices of the dynamic residual force vector have been derived and used in the parameter subset selection method to identify multiple damaged locations. In the sequel, the steady state genetic algorithm (SSGA) is used to determine quantified levels of the identified damage by minimizing errors in the modal flexibility matrix. In this study, performance of the proposed damage detection and quantification methodology is evaluated using a finite element model of a truss structure with considerations of possible experimental errors and noises. A series of numerical examples with five different damage scenarios including a challengingly small damage level demonstrates that the proposed methodology can efficaciously detect and quantify damage under noisy ambient vibrations.

• 제어로봇시스템학회:학술대회논문집
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• 1998.10a
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• pp.289-294
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• 1998

The distributed-parameter structures expressed with the partial differential equations are considered as the infinite-dimensional dynamic system. For implementation of a controller in multivariate systems, it is necessary to derive the state-space reduced order model. By the eigensystem realization algorithm, we can yield tile subspace system with the Markov parameters derived from the measured frequency response function by the inverse discrete Fourier transformation. We also review the necessary conditions for the convergence of the approximation system and the error bounds in terms of the singular values of Markov-parameter matrices. To determine the natural frequencies and modal damping ratios, the modal coordinate transformation is applied to the realization system. The vibration test for a smart structure is performed to provide the records of frequency response functions used in the subspace system realization.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2006.05a
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• pp.1334-1337
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• 2006

System identification is the field of modeling dynamic systems from experimental data. As a modeling technique, we can mention finite element method (FEM). In addition, we are able to measure modal data as the experimental data. The system can be generally categorized into a gray box and black box. In the gray box, we know mathematical model of a system, but we don't know structural parameters exactly, so we need to estimate structural parameters. In the black box, we don't know a system completely, so we need to identify system from nothing. To date, various system identification methods have been developed. Among them, we introduce system realization theory which uses Hankel matrix and Eigensystem Realization Algorithm (ERA) that enable us to identify modal parameters from noisy measurement data. Although we obtain noise-free data, however, we are likely to face difficulties in identifying a structure with hidden modes. Hidden modes can be occurred when the input or output position comes to a nodal point. If we change a system using a mode decoupling controller, the hidden modes can be revealed. Because we know the perturbation quantities in a closed loop system with the controller, we can realize an original system by subtracting perturbation quantities from the closed loop system. In this paper, we propose a novel method to identify a structure with hidden modes using the mode decoupling controller and the associated example is given for illustration.

• Journal of the Korean Statistical Society
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• v.25 no.1
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• pp.49-66
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• 1996

The singular value decomposition is one of the most useful methods in the area of matrix computation. It gives dimension reduction which is the centeral idea in many multivariate analyses. But this method is not resistant, i.e., it is very sensitive to small changes in the input data. In this article, we derive the resistant version of singular value decomposition for principal component analysis. And we give its statistical applications to biplot which is similar to principal component analysis in aspects of the dimension reduction of an n x p data matrix. Therefore, we derive the resistant principal component analysis and biplot based on the resistant singular value decomposition. They provide graphical multivariate data analyses relatively little influenced by outlying observations.