• Journal of Astronomy and Space Sciences
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• 제30권2호
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• pp.79-82
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• 2013

We present the Hilbert-Huang transform (HHT) analysis on the quasi-periodic modulation of SMC X-1. SMC X-1, consisting of a neutron star and a massive companion, exhibits superorbital modulation with a period varying between ~40 d and ~65 d. We applied the HHT on the light curve observed by the All-Sky Monitor onboard Rossi X-ray Timing Explorer (RXTE) to obtain the instantaneous frequency of the superorbital modulation of SMC X-1. The resultant Hilbert spectrum is consistent with the dynamic power spectrum while it shows more detailed information in both the time and frequency domains. According to the instantaneous frequency, we found a correlation between the superorbital period and the modulation amplitude. Combining the spectral observation made by the Proportional Counter Array onboard RXTE and the superorbital phase derived in the HHT, we performed a superorbital phase-resolved spectral analysis of SMC X-1. An analysis of the spectral parameters versus the orbital phase for different superorbital states revealed that the diversity of $n_H$ has an orbital dependence. Furthermore, we obtained the variation in the eclipse profiles by folding the All Sky Monitor light curve with orbital period for different superorbital states. A dip feature, similar to the pre-eclipse dip of Her X-1, can be observed only in the superorbital ascending and descending states, while the width is anti-correlated with the X-ray flux.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제16권9호
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• pp.3087-3103
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• 2022

Nearest neighbor query in location-based services has become a popular application. Aiming at the shortcomings of the privacy protection algorithms of traditional ciphertext nearest neighbor query having the high system overhead because of the usage of the double Hilbert curves and having the inaccurate query results in some special circumstances, a privacy protection algorithm of ciphertext nearest neighbor query which is based on the single Hilbert curve has been proposed. This algorithm uses a single Hilbert curve to transform the two-dimensional coordinates of the points of interest into Hilbert values, and then encrypts them by the order preserving encryption scheme to obtain the one-dimensional ciphertext data which can be compared in numerical size. Then stores the points of interest as elements composed of index value and the ciphertext of the other information about the points of interest on the server-side database. When the user needs to use the nearest neighbor query, firstly calls the approximate nearest neighbor query algorithm proposed in this paper to query on the server-side database, and then obtains the approximate nearest neighbor query results. After that, the accurate nearest neighbor query result can be obtained by calling the precision processing algorithm proposed in this paper. The experimental results show that this privacy protection algorithm of ciphertext nearest neighbor query which is based on the single Hilbert curve is not only feasible, but also optimizes the system overhead and the accuracy of ciphertext nearest neighbor query result.

• Kyungpook Mathematical Journal
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• 제9권1_2호
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• pp.71-75
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• 1969

• 대한수학회논문집
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• 제16권3호
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• pp.371-383
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• 2001

In this survey article, we shall introduce the applications of the theory of reproducing kernels to inverse problems. At the same time, we shall present some operator versions of our fundamental general theory for linear transforms in the framework of Hilbert spaces.

• Communications for Statistical Applications and Methods
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• 제21권4호
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• pp.317-325
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• 2014

Consider a nonlinear transform ${\Phi}(x)$ of x in $\mathbb{R}^p$ to Hilbert space H and assume that the dot product between ${\Phi}(x)$ and ${\Phi}(x^{\prime})$ in H is given by < ${\Phi}(x)$, ${\Phi}(x^{\prime})$ >= K(x, x'). The aim of this paper is to propose a mathematical technique to take screen shots of the multivariate dataset mapped to Hilbert space H, particularly suited to Gaussian kernel $K({\cdot},{\cdot})$, which is defined by $K(x,x^{\prime})={\exp}(-{\sigma}{\parallel}x-x^{\prime}{\parallel}^2)$, ${\sigma}$ > 0. Several numerical examples are given.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2003년도 춘계학술대회논문집
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• pp.414-419
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• 2003

There are some methods fur extracting mode shapes from a continuously scanned data such as a modulation, Chebyshev polynomial, and Hilbert approach. In this paper, Chebyshev and Hilbert approaches were investigated through the numerical experiment first. As some experimental parameters were altered with small quantities, data were checked and plotted. From those results, the effects of unexpected parameters will be configured. And then, it will be actually helpful to select the proper method for specific testing environments.

• 한국지진공학회:학술대회논문집
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• 한국지진공학회 2002년도 춘계 학술발표회 논문집
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• pp.159-168
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• 2002

본 연구에서는 최근에 개발된 Hilbert-Huang 변환(HHT) 기법의 교각시스템에서 손상위치추정을 위한 적용성을 분석하였다. HHT기법으로 시계열의 순간주파수를 분석할 수 있음을 이용하여, 손상에 기인한 비선형 거동이 발생하는 때에 순간주파수의 변화를 분석함으로서, 손상부재와 위치를 추정하는 방법이다. 손상을 입은 교각 시스템에 대하여 수치모의실험을 수행하였는데, 이 때에 주파수가 점차로 증가하는 입력하중을 사용하였다. 연구결과로부터, HHT기법이 한정된 갯수의 가속도센서를 이용하여 계측오차가 포함된 조건하에서도 교각에 발생한 손상위치를 적절히 색출할 수 있다는 것을 알 수 있다.

• Smart Structures and Systems
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• 제16권5호
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• pp.919-935
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• 2015

The Hilbert-Huang transform (HHT) consists of empirical mode decomposition (EMD) and Hilbert spectral analysis. EMD has been successfully applied for identification of mode shapes of structures based on input-output approaches. This paper aims to extend application of EMD for output-only identification of mode shapes of linear structures. In this regard, a new simple and efficient method based on band-pass filtering and EMD is proposed. Having rather accurate estimates of modal frequencies from measured responses, the proposed method is capable to extract the corresponding mode shapes. In order to evaluate the accuracy and performance of the proposed identification method, two case studies are considered. In the first case, the performance of the method is validated through the analysis of simulated responses obtained from an analytical structural model with known dynamical properties. The low-amplitude responses recorded from the UCLA Factor Building during the 2004 Parkfield earthquake are used in the second case to identify the first three mode shapes of the building in three different directions. The results demonstrate the remarkable ability of the proposed method in correct estimation of mode shapes of the linear structures based on rather accurate modal frequencies.

• 한국인터넷방송통신학회논문지
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• 제17권2호
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• pp.179-190
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• 2017

Hand Accelerometer는 인간신체 운동 패턴을 실시간으로 파악하는데 널리 사용되고 있다. 그러므로 행동 유형을 정확하게 파악하는 것은 아주 중요하다. 이 과정에서 각 행동유형의 형태를 미리 정확하게 파악하는 것이 중요하다. 인간의 신체 행동은 센서를 통해 수집된 시계열 데이터로 표현된다. 이 데이터는 비안정적, 비선형적 성격을 가지고 있다. 그래서 이런 성격의 데이터의 유형을 효율적으로 추출하는 방법을 찾는 것은 매우 중요하다. 힐버트-황 변환은 비안정적 비선형적 요소를 시계열데이터에서 효율적으로 추출하는 방법이다. 이 방법을 위의 시계열 데이터에 적용한 결과 핵심패턴이 성공적으로 추출되었다.

• 한국공작기계학회논문집
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• 제16권2호
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• pp.112-119
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• 2007

In order to predict vibration trends occurred during vehicle drive, acceleration data was processed by using data processing algorithm with moving average and Hilbert transform. Specific mode constants of acceleration were obtained under various disturbance. Vehicle velocity, road condition, property of pointing structure were considered as factors which make change of vibration trend in vehicle dynamics. Results of signal processing were compared and analysed. Advanced performance of the timing selection algorithm from this study was verified by using simple equipment comparing with the deflection measurement laser system(Muzzle Reference System).