• 대한수학회지
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• 제46권3호
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• pp.609-620
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• 2009

We establish some estimates on the hyper bilinear Hilbert transform on both Euclidean space and torus. We also use a transference method to obtain a Kenig-Stein's estimate on bilinear fractional integrals on the n-torus.

• 응용통계연구
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• 제24권6호
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• pp.995-1006
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• 2011

A time series can be decomposed into simple components with a multiscale method. Empirical mode decomposition(EMD) is a recently invented multiscale method in Huang et al. (1998). It is natural to apply a classical prediction method such a vector autoregressive(AR) model to the obtained simple components instead of the original time series; in addition, a prediction procedure combining a classical prediction model to EMD and Hilbert spectrum is proposed in Kim et al. (2008). In this paper, we suggest to adopt principal component analysis(PCA) to the prediction procedure that enables the efficient selection of input variables among obtained components by EMD. We discuss the utility of adopting PCA in the prediction procedure based on EMD and Hilbert spectrum and analyze the daily worm account data by the proposed PCA adopted prediction method.

• Earthquakes and Structures
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• 제18권4호
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• pp.507-517
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• 2020

This study aims to present new frequency-related seismic intensity parameters (SIPs) based on the Hilbert-Huang Transform (HHT) analysis. The proposed procedure is utilized for the processing of several seismic accelerograms. Thus, the entire evaluated Hilbert Spectrum (HS) of each considered seismic velocity time-history is investigated first, and then, a delimited area of the same HS around a specific frequency is explored, for the proposition of new SIPs. A first application of the suggested new parameters is to reveal the interrelation between them and the structural damage of a reinforced concrete frame structure. The index of Park and Ang describes the structural damage. The fundamental frequency of the structure is considered as the mentioned specific frequency. Two statistical methods, namely correlation analysis and multiple linear regression analysis, are used to identify the relationship between the considered SIPs and the corresponding structural damage. The results confirm that the new proposed HHT-based parameters are effective descriptors of the seismic damage potential and helpful tools for forecasting the seismic damages on buildings.

• 응용통계연구
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• 제22권3호
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• pp.499-513
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• 2009

An economic signal in the real world usually reflects complex phenomena. One may have difficulty both extracting and interpreting information embedded in such a signal. A natural way to reduce complexity is to decompose the original signal into several simple components, and then analyze each component. Spectral analysis (Priestley, 1981) provides a tool to analyze such signals under the assumption that the time series is stationary. However when the signal is subject to non-stationary and nonlinear characteristics such as amplitude and frequency modulation along time scale, spectral analysis is not suitable. Huang et al. (1998b, 1999) proposed a data-adaptive decomposition method called empirical mode decomposition and then applied Hilbert spectral analysis to decomposed signals called intrinsic mode function. Huang et al. (1998b, 1999) named this two step procedure the Hilbert-Huang transform(HHT). Because of its robustness in the presence of nonlinearity and non-stationarity, HHT has been used in various fields. In this paper, we discuss the applications of the HHT and demonstrate its promising potential for non-stationary financial time series data provided through a Korean stock price index.

• Smart Structures and Systems
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• 제17권5호
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• pp.753-771
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• 2016

This paper addresses the free and transient responses of a SDOF linear complex stiffness system by making use of the Hilbert transform and the convolution integral. Because the second-order differential equation of motion having the complex stiffness give rise to the conjugate complex eigen values, its time-domain analysis using the standard time integration scheme suffers from the numerical instability and divergence. In order to overcome this problem, the transient response of the linear complex stiffness system is obtained by the convolution integral of a green function which corresponds to the unit-impulse free vibration response of the complex system. The damped free vibration of the complex system is theoretically derived by making use of the state-space formulation and the Hilbert transform. The convolution integral is implemented by piecewise-linearly interpolating the external force and by superimposing the transient responses of discretized piecewise impulse forces. The numerical experiments are carried out to verify the proposed time-domain analysis method, and the correlation between the real and imaginary parts in the free and transient responses is also investigated.

• 천문학회보
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• 제40권2호
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• pp.55.4-56
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• 2015

The Hilbert-Huang Transform (HHT) is composed of the Empirical Mode Decomposition (EMD) and the Hilbert Spectral Analysis (HSA). The EMD decomposes any time series data into a small number of components called the Intrinsic Mode Functions (IMFs), compared to the Discrete Fourier Transform which decomposes a data into a large number of harmonic functions. Each IMF has varying amplitude and frequency with respect to time, which can be obtained by HSA. The time resolution of the modes in HHT is the same as that of the given time series, while in the Wavelet Transform, Constant Q Transform and Short-Time Fourier Transform, there is a tradeoff between the resolutions in frequency and time. Based on the time-dependent amplitudes of IMFs, we develop an Event Trigger Generator and demonstrate its efficiency by applying it to gravitational-wave data.

• 디지털융복합연구
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• 제14권4호
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• pp.277-283
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• 2016

본 논문에서는 가중 퍼지소속함수 기반 신경망(neural network with weighted fuzzy membership functions; NEWFM) 기반의 웨이블릿 변환(wavelet transform)과 힐버트 변환(Hilbert transform)에 의해 추출한 첨점(peak)을 사용하여 뇌파(EEG)로부터 정상 파형과 간질 파형을 분류하는 새로운 방안을 제안하였다. NEWFM의 입력을 추출하는데 다음과 같은 3개의 단계가 수행되었다. 첫 번째 단계에서는 뇌파로부터 잡음을 제거하기 위해서 웨이블릿 변환을 사용하였다. 두 번째 단계에서는 웨이블릿 계수로부터 첨점(peak)을 추출하기 위해서 힐버트 변환을 사용하였다. 또한 크기가 큰 첨점을 추출하기 위해서 첨점의 평균값보다 큰 첨점만을 선택하였다. 세 번째 단계에서는 통계적 방법을 이용하여 첨점으로부터 NEWFM의 입력으로 사용할 16개의 특징을 추출하였다. NEWFM은 이들 16개의 특징을 입력으로 사용하여 99.25%, 99.4%, 99%의 정확도, 특이도, 민감도를 각각 구하였다. 향후 연구에서는 특징선택을 이용하여 16개의 특징으로부터 좋은 특징을 선택하여 정확도를 향상시킬 계획이다.

• 한국추진공학회:학술대회논문집
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• 한국추진공학회 2012년도 제38회 춘계학술대회논문집
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• pp.555-561
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• 2012

Empirical Mode Decomposition(EMD)을 통한 Hilbert Huang Transform(HHT)은 시간-주파수 영역분석 방법 중 하나로 기존의 다른 분석 방법에 비해 비선형, 비정상 신호를 해석 가능하다는 등 여러가지 이점이 있다. 그러나 인접한 주파수를 분별하기 힘들고 잡음에 취약하다는 결점이 있다고 알려져 있다. 본 논문에서는 HHT와 정상신호 분석에 효과적인 Short-Time Fourier Transform(STFT)을 비교하여 각 방법의 장 단점을 분석하고 Rijke 튜브 실험에서 얻은 열음향학적 불안정 데이터에 적용하여 잡음에 취약한 점을 보완한 Improved HHT와 비교한다. 그 결과, EMD를 이용한 Original HHT보다 EEMD를 이용한 Improved HHT가 잡음의 영향을 적게 받아 보다 정확한 신호분석이 가능하다는 것을 알 수 있었다.

• Smart Structures and Systems
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• 제20권3호
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• pp.263-272
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• 2017

This paper presents the time response of a mixed vibration system with the viscous damping and the hysteretic damping. There are two ways to derive the time response of such a vibration system. One is an analytical method, using the contour integral of complex functions to compute the inverse Fourier transforms. The other is an approximate method in which the analytic functions derived by Hilbert transform are expressed in the state space representation, and only the effective eigenvalues are used to efficiently compute the transient response. The unit impulse responses of the two methods are compared and the change in the damping properties which depend on the viscous and hysteretic damping values is investigated. The results showed that the damping properties of a mixed damping vibration system do not present themselves as a linear combination of damping properties.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2002년도 가을 학술발표회 논문집
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• pp.453-458
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• 2002

A recently developed Hilbert-Huang transform (HHT) technique is applied to the detection of the damage locations of bridge structures. The HHT may be used to identify the locations of damages which exhibit nonlinear and non-stationary behavior, since the instantaneous frequency characteristics of the measured signal can be analyzed by the HHT. Numerical simulations were conducted on two bridge systems with damages using controlled excitations with sweeping frequency. Nonlinear plastic model using a gap element is employed to model the behavior of the cracked elements in the numerical simulations. The results indicate that the HHT method can reasonably identify the damage locations based on a limited number of acceleration sensors. Experimental study has been 실so carried out on a steel frame to confirm the applicability of the HHT to detect a structural connection with loosened bolts.