• Smart Structures and Systems
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• v.17 no.3
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• pp.363-389
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• 2016

Deficient modes that cannot be always identified from different sets of measurement data may exist in the application of operational modal analysis such as the stochastic subspace identification techniques in large-scale civil structures. Based on a recent work using the long-term ambient vibration measurements from an instrumented cable-stayed bridge under different wind excitation conditions, a benchmark problem is launched by taking the same bridge as a test bed to further intensify the exploration of mode identifiability. For systematically assessing this benchmark problem, a recently developed SSI algorithm based on an alternative stabilization diagram and a hierarchical sifting process is extended and applied in this research to investigate several sets of known and blind monitoring data. The evaluation of delicately selected cases clearly distinguishes the effect of traffic excitation on the identifiability of the targeted deficient mode from the effect of wind excitation. An additional upper limit for the vertical acceleration amplitude at deck, mainly induced by the passing traffic, is subsequently suggested to supplement the previously determined lower limit for the wind speed. Careful inspection on the shape vector of the deficient mode under different excitation conditions leads to the postulation that this mode is actually induced by the motion of the central tower. The analysis incorporating the tower measurements solidly verifies this postulation by yielding the prevailing components at the tower locations in the extended mode shape vector. Moreover, it is also confirmed that this mode can be stably identified under all the circumstances with the addition of tower measurements. An important lesson learned from this discovery is that the problem of mode identifiability usually comes from the lack of proper measurements at the right locations.

• The Journal of Korea Institute of Information, Electronics, and Communication Technology
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• v.15 no.1
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• pp.1-7
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• 2022

It has been found through physiological experiments that the visual neurons constituting the human visual cortex do not respond to all visual stimuli, but to a visual stimuli with specific conditions. In order to interpret such physiological experiments, a model that can simulate the firing characteristics of neurons including a linear filter with random gain was proposed. It has been proven through experiments that subspaces are formed. To verify the validity of the implemented model, the distribution of values for two pixels randomly extracted from four different visual stimulus data was observed. The difference between the two distributions was confirmed by extracting the central coordinate value, that is, the coordinate value with the most values, from the distribution of the total stimulus data and the spike ignition stimulus data. In the case of the entire set, it was verified through experiments that the stimulus data generating spikes is a subset or subspace of the entire stimulus data. This study can be used as a basic study related to the mechanism of spikes in response to visual stimuli.

• Smart Structures and Systems
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• v.20 no.2
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• pp.115-126
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• 2017

The modal identification of large civil structures such as bridges under the ambient vibrational conditions has been widely investigated during the past decade. Many operational modal analysis methods have been proposed and successfully used for identifying the dynamic characteristics of the constructed bridges in service. However, there is very limited research available on reliable criteria for the robustness of these identified modal parameters of the bridge structures. In this study, two time-domain operational modal analysis methods, the data-driven stochastic subspace identification (SSI-DATA) method and the covariance-driven stochastic subspace identification (SSI-COV) method, are employed to identify the modal parameters from field recorded ambient acceleration data. On the basis of the SSI-DATA method, the modal contribution indexes of all identified modes to the measured acceleration data are computed by using the Kalman filter, and their applicability to evaluate the robustness of identified modes is also investigated. Here, the benchmark problem, developed by Hong Kong Polytechnic University with field acceleration measurements under different excitation conditions of a cable-stayed bridge, is adopted to show the effectiveness of the proposed method. The results from the benchmark study show that the robustness of identified modes can be judged by using their modal contributions to the measured vibration data. A critical value of modal contribution index of 2% for a reliable identifiability of modal parameters is roughly suggested for the benchmark problem.

• Communications for Statistical Applications and Methods
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• v.18 no.3
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• pp.267-275
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• 2011

According to recent studies, Bayesian information criteria(BIC) is proposed to determine the structural dimension of the central subspace through sliced inverse regression(SIR) with high-dimensional predictors. The BIC may be useful in K-means clustering inverse regression(KIR) with high-dimensional predictors. However, the direct application of the BIC to KIR may be problematic, because the slicing scheme in SIR is not the same as that of KIR. In this paper, we present empirical penalty term studies of BIC in KIR to identify the most appropriate one. Numerical studies and real data analysis are presented.

• Communications for Statistical Applications and Methods
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• v.22 no.3
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• pp.305-312
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• 2015

We extend a generalized partially linear single-index model and newly define a generalized partially double-index model (GPDIM). The philosophy of sufficient dimension reduction is adopted in GPDIM to estimate unknown coefficient vectors in the model. Subsequently, various combinations of popular sufficient dimension reduction methods are constructed with the best combination among many candidates determined through a bootstrapping procedure that measures distances between subspaces. Distinguishing values are newly defined to match the estimates to the corresponding population coefficient vectors. One of the strengths of the proposed model is that it can investigate the appropriateness of GPDIM over a single-index model. Various numerical studies confirm the proposed approach, and real data application are presented for illustration purposes.

• Korean Journal of Mathematics
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• v.8 no.2
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• pp.163-172
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• 2000

Let $\mathcal{S}^{\prime}(\mathbb{R})$ be the dual of the Schwartz spaces $\mathcal{S}(\mathbb{R})$), A be a self-adjoint operator in $L^2(\mathbb{R})$ and ${\Gamma}(A)^*$ be the adjoint operator of ${\Gamma}(A)$ which is the second quantization operator of A. It is proven that under a suitable condition on A there exists a nuclear subspace $\mathcal{S}$ of a fundamental space $\mathcal{S}_A$ of Hida's type on $\mathcal{S}^{\prime}(\mathbb{R})$) such that ${\Gamma}(A)\mathcal{S}{\subset}\mathcal{S}$ and $e^{-t{\Gamma}(A)}\mathcal{S}{\subset}\mathcal{S}$, which enables us to show that a stochastic differential equation: $$dX(t)=dW(t)-{\Gamma}(A)^*X(t)dt$$, arising from the central limit theorem for spatially extended neurons has an unique solution on the dual space $\mathcal{S}^{\prime}$ of $\mathcal{S}$.

• Communications for Statistical Applications and Methods
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• v.25 no.5
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• pp.513-521
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• 2018

The goal of sufficient dimension reduction (SDR) is to replace original p-dimensional predictors with a lower-dimensional linearly transformed predictor. The sliced inverse regression (SIR) (Li, Journal of the American Statistical Association, 86, 316-342, 1991) is one of the most popular SDR methods because of its applicability and simple implementation in practice. However, SIR may yield different dimension reduction results for different numbers of slices and despite its popularity, is a clear deficit for SIR. To overcome this, a fused sliced inverse regression was recently proposed. The study shows that the dimension-reduced predictors is robust to the numbers of the slices, but it does not investigate how robust its dimension determination is. This paper suggests a permutation dimension determination for the fused sliced inverse regression that is compared with SIR to investigate the robustness to the numbers of slices in the dimension determination. Numerical studies confirm this and a real data example is presented.

• Communications for Statistical Applications and Methods
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• v.28 no.3
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• pp.267-279
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• 2021

A regression with multi-dimensional responses is quite common nowadays in the so-called big data era. In such regression, to relieve the curse of dimension due to high-dimension of responses, the dimension reduction of predictors is essential in analysis. Sufficient dimension reduction provides effective tools for the reduction, but there are few sufficient dimension reduction methodologies for multivariate regression. To fill this gap, we newly propose two fused slice-based inverse regression methods. The proposed approaches are robust to the numbers of clusters or slices and improve the estimation results over existing methods by fusing many kernel matrices. Numerical studies are presented and are compared with existing methods. Real data analysis confirms practical usefulness of the proposed methods.

• Communications for Statistical Applications and Methods
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• v.28 no.2
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• pp.205-215
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• 2021

Sufficient dimension reduction is useful dimension reduction tool in regression, and sliced inverse regression (Li, 1991) is one of the most popular sufficient dimension reduction methodologies. In spite of its popularity, it is known to be sensitive to the number of slices. To overcome this shortcoming, the so-called fused sliced inverse regression is proposed by Cook and Zhang (2014). Unfortunately, the two existing methods do not have the direction application to large p-small n regression, in which the dimension reduction is desperately needed. In this paper, we newly propose seeded sliced inverse regression and seeded fused sliced inverse regression to overcome this deficit by adopting iterative projection approach (Cook et al., 2007). Numerical studies are presented to study their asymptotic estimation behaviors, and real data analysis confirms their practical usefulness in high-dimensional data analysis.

• Smart Structures and Systems
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• v.22 no.1
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• pp.41-55
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• 2018

Damping ratio and frequency have influence on dynamic serviceability or instability such as vortex-induced vibration and displacement amplification due to earthquake and critical flutter velocity, and it is thus important to make determination of damping ratio and frequency accurate. As bridges are getting longer, small scale model test considering similitude law must be conducted to evaluate damping ratio and frequency. Analysis conditions modified by similitude law are applied to experimental test considering different scale ratios. Generally, Nyquist frequency condition based on natural frequency modified by similitude law has been used to determine sampling rate for different scale ratios, and total time length has been determined by users arbitrarily or by considering similitude law with respect to time for different scale ratios. However, Nyquist frequency condition is not suitable for multimode system with noisy signals. In addition, there is no specified criteria for determination of total time length. Those analysis conditions severely affect accuracy of damping ratio. The focus of this study is made on the determination of minimum analysis conditions for different scale ratios. Influence of signal to noise ratio is studied according to the level of noise level. Free initial value problem is proposed to resolve the condition that is difficult to know original initial value for free vibration. Ambient and free vibration tests were used to analyze the dynamic properties of a system using data collected from tests with a two degree-of-freedom section model and performed on full bridge 3D models of cable stayed bridges. The free decay is estimated with the stochastic subspace identification method that uses displacement data to measure damping ratios under noisy conditions, and the iterative least squares method that adopts low pass filtering and fourth order central differencing. Reasonable results were yielded in numerical and experimental tests.