• Journal of the Korean Institute of Telematics and Electronics
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• v.25 no.12
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• pp.1625-1632
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• 1988

This paper aims not only to introduce the concept of linear singular systems, geometric structure, and feedback but also to provide applications of the multivariable linear singular system theories to electric circuits which may appear in some electronic equipments. The impulsive or discontinuous behavior which is not desirable can be removed by the set of admissible initial conditions. The output-nulling supremal (A,E,B) invariant subspace and the singular system structure algorithm are applied to this double-input double-output electric circuit. The Weierstrass form of the pencil (s E-A) is related to the output-nulling supremal (A,E,B) invariant subspace from which the time domain solutions of the finite and the infinite subsystems are found. The generalized Lyapunov equation for this application with feedback is studied and finally, the use of orthogonal functions in singular systems is discussed.

• Proceedings of the Korean Institute of Navigation and Port Research Conference
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• v.1
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• pp.133-138
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• 2006

Singular value decomposition (SDV) approach is applied to the observability analysis of GPS/INS in this paper. A measure of observability for a subspace is introduced. It indicates the minimum size of perturbation in the information matrix that makes the subspace unobservable. It is shown that the measure has direct connections with observability of systems, error covariance, and singular structure of the information matrix. The observability measure given in this paper is applicable to the multi-input/multi-output time-varying systems. An example on the observability analysis of GPS/INS is given. The measure of observability is confirmed to be less sensitive to system model perturbation. It is also shown that the estimation error for the vertical component of gyro bias can be considered unobservable for small initial error covariance for a constant velocity horizontal motion.

• Communications for Statistical Applications and Methods
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• v.23 no.2
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• pp.93-103
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• 2016

In the paper, we discuss dimension reduction of predictors ${\mathbf{X}}{\in}{{\mathbb{R}}^p}$ in a regression of $Y{\mid}{\mathbf{X}}$ with a notion of sufficiency that is called sufficient dimension reduction. In sufficient dimension reduction, the original predictors ${\mathbf{X}}$ are replaced by its lower-dimensional linear projection without loss of information on selected aspects of the conditional distribution. Depending on the aspects, the central subspace, the central mean subspace and the central $k^{th}$-moment subspace are defined and investigated as primary interests. Then the relationships among the three subspaces and the changes in the three subspaces for non-singular transformation of ${\mathbf{X}}$ are studied. We discuss the two conditions to guarantee the existence of the three subspaces that constrain the marginal distribution of ${\mathbf{X}}$ and the conditional distribution of $Y{\mid}{\mathbf{X}}$. A general approach to estimate them is also introduced along with an explanation for conditions commonly assumed in most sufficient dimension reduction methodologies.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1995.10a
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• pp.299-303
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• 1995

This paper charcterizes dynamics of cold tandem minns, and constructs it state-space model of which are linear time invariant, using subspace method. Step responses particularly show the influence on mass transfer delay. Input-output data set are obtained form nonlinear differential equations including mass transfer delay and nonlinearity. It is shown that the identified state-apace model well approximates the original systems dynamics.

• Journal of the Korean Mathematical Society
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• v.33 no.4
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• pp.1069-1099
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• 1996

Let X be a smooth, simply connected and oriented closed fourmanifold such that the dimension $b_{2}^{+}(X)$ of a maximal positive subspace for the intersection form is greater than or equal to 3.

• Smart Structures and Systems
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• v.10 no.4_5
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• pp.331-351
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• 2012

In this study an output-only system identification technique for civil structures under ambient vibrations is carried out, mainly focused on using the Stochastic Subspace Identification (SSI) based algorithms. A newly developed signal processing technique, called Singular Spectrum Analysis (SSA), capable to smooth a noisy signal, is adopted for preprocessing the measurement data. An SSA-based SSI algorithm with the aim of finding accurate and true modal parameters is developed through stabilization diagram which is constructed by plotting the identified system poles with increasing the size of data matrix. First, comparative study between different approaches, with and without using SSA to pre-process the data, on determining the model order and selecting the true system poles is examined in this study through numerical simulation. Finally, application of the proposed system identification task to the real large scale structure: Canton Tower, a benchmark problem for structural health monitoring of high-rise slender structures, using SSA-based SSI algorithm is carried out to extract the dynamic characteristics of the tower from output-only measurements.

• Smart Structures and Systems
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• v.11 no.1
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• pp.19-34
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• 2013

The objective of this paper is to develop on-line system parameter estimation and damage detection technique from the response measurements through using the Recursive Covariance-Driven Stochastic Subspace identification (RSSI-COV) approach. To reduce the effect of noise on the results of identification, discussion on the pre-processing of data using recursive singular spectrum analysis (rSSA) is presented to remove the noise contaminant measurements so as to enhance the stability of data analysis. Through the application of rSSA-SSI-COV to the vibration measurement of bridge during scouring experiment, the ability of the proposed algorithm was proved to be robust to the noise perturbations and offers a very good online tracking capability. The accuracy and robustness offered by rSSA-SSI-COV provides a key to obtain the evidence of imminent bridge settlement and a very stable modal frequency tracking which makes it possible for early warning. The peak values of the identified $1^{st}$ mode shape slope ratio has shown to be a good indicator for damage location, meanwhile, the drastic movements of the peak of $2^{nd}$ mode slope ratio could be used as another feature to indicate imminent pier settlement.

• Journal of information and communication convergence engineering
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• v.5 no.1
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• pp.12-16
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• 2007

In this paper, a new method is proposed for tracking the direction-of-arrival (DOA) of the wideband moving source incident on uniform linear array sensors. DOA is estimated by focusing transformation matrices. To update focusing matrices along with new data snap shots, we use the FAST (Fast Approximate Subspace Tracking) method. Present focusing matrices are constructed by previous signal and its orthogonal basis vectors as well as present signal and its orthogonal basis vectors, which are the left and right singular vectors of the inner product of two approximated matrices. Simulation results are shown to illustrate the performance of the proposed method.

• Smart Structures and Systems
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• v.26 no.4
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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.

• Journal of the Korean Mathematical Society
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• v.48 no.2
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• pp.397-420
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• 2011

In this paper we study the structure of closed weakly dense ideals in Privalov spaces $N^p$ (1 < p < $\infty$) of holomorphic functions on the disk $\mathbb{D}$ : |z| < 1. The space $N^p$ with the topology given by Stoll's metric [21] becomes an F-algebra. N. Mochizuki [16] proved that a closed ideal in $N^p$ is a principal ideal generated by an inner function. Consequently, a closed subspace E of $N^p$ is invariant under multiplication by z if and only if it has the form $IN^p$ for some inner function I. We prove that if $\cal{M}$ is a closed ideal in $N^p$ that is dense in the weak topology of $N^p$, then $\cal{M}$ is generated by a singular inner function. On the other hand, if $S_{\mu}$ is a singular inner function whose associated singular measure $\mu$ has the modulus of continuity $O(t^{(p-1)/p})$, then we prove that the ideal $S_{\mu}N^p$ is weakly dense in $N^p$. Consequently, for such singular inner function $S_{\mu}$, the quotient space $N^p/S_{\mu}N^p$ is an F-space with trivial dual, and hence $N^p$ does not have the separation property.