A Nonlinear Method for Robust Spectral Analysis

Li, Ta‐Hsin

doi:10.1109/tsp.2010.2042479

Cited by 53 publications

(24 citation statements)

References 26 publications

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“…Several signals, of different kinds (synthetic, acquired by IEEE test networks and real PMU data), were considered in order to establish if the p-value choice is affected by the signal typology. At the best of our simulation, we can confirm, as stated by Li [28], that the optimal p-value falls within the interval [1,2]; it is not possible to derive further practical considerations about the p-value choice with respect to the type of data analysed. The p-value of 1.5 can be reasonably conceived as a trade-off between the robustness of the Laplace periodogram ( p = 1) against the extreme heavy-tailed noise and the efficiency of the ordinary periodogram ( p = 2).…”

Section: Theoremmentioning

confidence: 59%

“…For this reason, a non-linear spectral analyser is employed for determining the bisecting frequencies, the L p periodogram, which can be interpreted as a direct extension of the Laplace periodogram, p = 1, and of the ordinary periodogram, p = 2: where n is the number of the samples of y(t). Li [28] shows how to design a harmonic regressor by employing p ∈ [1,2] in order to make the periodogram robust and efficient enough. In particular, by denoting with ||·|| the Euclidean norm, it is demonstrated that the following periodogram definition is well posed…”

Section: Theoremmentioning

confidence: 99%

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On Hilbert transform methods for low frequency oscillations detection

Lauria¹,

Pisani²

2014

IET Generation, Transmission & Distribution

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This study tackles the issue of electromechanical modes identification through a measurement-based methodology employing a novel signal decomposition theorem based upon the Hilbert transform. The methodology aims to answer in a simpler and more pragmatic manner to the main weaknesses of the Hilbert-Huang transform with respect to the major refinements in the relevant literature. These weak points are discussed with sufficient detailed degree in the study. The main contribution of this study consists in combining a recent signal decomposition theorem for separating an assigned signal into elemental ones, each of them characterised by a single frequency component and a robust preliminary non-linear spectral analyser, named Lp periodogram. This procedure's results are very appropriate for analysing some critical cases of electromechanical oscillations, because of the Lp periodogram robustness against heavy-tailed noise and also its intrinsic ability in estimating closely spaced frequency components. The proposed approach is found to be inherently simple, reliable and consistent in performance as well as characterised by low computational burden. Some numerical applications validate the methodology and assess its own performance on synthetic signals, near real-life signals acquired by IEEE test networks and on a real measured signal from a wide-area monitoring system currently in operation

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Section: Theoremmentioning

confidence: 59%

Section: Theoremmentioning

confidence: 99%

On Hilbert transform methods for low frequency oscillations detection

Lauria¹,

Pisani²

2014

IET Generation, Transmission & Distribution

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“…Moreover, the usually used robust estimator for impulsive noise, p -norm [14] is not an optimum algorithm for the mixture. Furthermore, although the conditional PDFs of each unknown parameters are known, the Gibbs sampling algorithm is not considered here since f (y|θ θ θ) is too complicate to sample from.…”

Section: Proposed Methodsmentioning

confidence: 99%

Estimation under additive Cauchy-Gaussian noise using Markov chain Monte Carlo

Chen

Kuruoğlu

2014

2014 IEEE Workshop on Statistical Signal Processing (SSP)

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In this paper, we consider an impulsive mixture noise process, which commonly comes across in applications such as multiuser radar communications, astrophysical imaging in the microwave range and kick detection in oil drilling. The mixture process is in the time domain, whose probability density function (PDF) corresponds to the convolution of the components' PDFs. In this work, we concentrate on the additive mixture of Gaussian and Cauchy PDFs, the convolution of which leads to a Voigt profile. Due to the complicated nature of the PDF, classical methods such as maximum likelihood estimation may be analytically not tractable; therefore, to estimate signals under such noise, we propose using a Markov chain Monte Carlo method, in particular the Metropolis-Hastings algorithm. For illustration, we study the estimation of a ramp function embedded in the Cauchy-Gauss mixture noise, which is motivated by the kick detection problem in oil drilling. Simulation results demonstrate that the mean square error performance of the proposed algorithm can attain the Cramer-Rao lower bound.

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“…Instead of fitting the models mentioned above by the popular least squares regression (see Table 2), RobPer also allows application of six robust regression techniques, see Table 3. Robust regression techniques like least absolute deviations, least trimmed squares (Rousseeuw and Yohai 1984) and M-regression (Huber and Ronchetti 1981) have already been used to fit sines (evaluating the squared amplitude) by Zhang and Chan (2005), Ahdesmäki et al (2007), Li (2009) and Li (2010). M-regression with the Huber function was applied to fit periodic splines by Oh et al (2004).…”

Section: Regression Techniques: Argument Regressionmentioning

confidence: 99%

RobPer: AnRPackage to Calculate Periodograms for Light Curves Based on Robust Regression

Thieler¹,

Fried²,

Rathjens³

2016

J. Stat. Soft.

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An important task in astroparticle physics is the detection of periodicities in irregularly sampled time series, called light curves. The classic Fourier periodogram cannot deal with irregular sampling and with the measurement accuracies that are typically given for each observation of a light curve. Hence, methods to fit periodic functions using weighted regression were developed in the past to calculate periodograms.We present the R package RobPer which allows to combine different periodic functions and regression techniques to calculate periodograms. Possible regression techniques are least squares, least absolute deviations, least trimmed squares, M-, S-and τ -regression. Measurement accuracies can be taken into account including weights. Our periodogram function covers most of the approaches that have been tried earlier and provides new model-regression-combinations that have not been used before.To detect valid periods, RobPer applies an outlier search on the periodogram instead of using fixed critical values that are theoretically only justified in case of least squares regression, independent periodogram bars and a null hypothesis allowing only normal white noise. Finally, the package also includes a generator to generate artificial light curves.

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A Nonlinear Method for Robust Spectral Analysis

Cited by 53 publications

References 26 publications

On Hilbert transform methods for low frequency oscillations detection

On Hilbert transform methods for low frequency oscillations detection

Estimation under additive Cauchy-Gaussian noise using Markov chain Monte Carlo

RobPer: AnRPackage to Calculate Periodograms for Light Curves Based on Robust Regression

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