5,776 research outputs found
Automatic Kalman-filter-based wavelet shrinkage denoising of 1D stellar spectra
We propose a non-parametric method to denoise 1D stellar spectra based on wavelet shrinkage followed by adaptive Kalman thresholding. Wavelet shrinkage denoising involves applying the discrete wavelet transform (DWT) to the input signal, 'shrinking' certain frequency components in the transform domain, and then applying inverse DWT to the reduced components. The performance of this procedure is influenced by the choice of base wavelet, the number of decomposition levels, and the thresholding function. Typically, these parameters are chosen by 'trial and error', which can be strongly dependent on the properties of the data being denoised. We here introduce an adaptive Kalman-filter-based thresholding method that eliminates the need for choosing the number of decomposition levels. We use the 'Haar' wavelet basis, which we found to provide excellent filtering for 1D stellar spectra, at a low computational cost. We introduce various levels of Poisson noise into synthetic PHOENIX spectra, and test the performance of several common denoising methods against our own. It proves superior in terms of noise suppression and peak shape preservation. We expect it may also be of use in automatically and accurately filtering low signal-to-noise galaxy and quasar spectra obtained from surveys such as SDSS, Gaia, LSST, PESSTO, VANDELS, LEGA-C, and DESI
Time-varying parametric modelling and time-dependent spectral characterisation with applications to EEG signals using multi-wavelets
A new time-varying autoregressive (TVAR) modelling approach is proposed for nonstationary signal processing and analysis, with application to EEG data modelling and power spectral estimation. In the new parametric modelling framework, the time-dependent coefficients of the TVAR model are represented using a novel multi-wavelet decomposition scheme. The time-varying modelling problem is then reduced to regression selection and parameter estimation, which can be effectively resolved by using a forward orthogonal regression algorithm. Two examples, one for an artificial signal and another for an EEG signal, are given to show the effectiveness and applicability of the new TVAR modelling method
Forecasting interest rates: A Comparative assessment of some second generation non-linear model
Modelling and forecasting of interest rates has traditionally proceeded in the framework of linear stationary models such as ARMA and VAR, but only with moderate success. We examine here four models which account for several specific features of real world asset prices such as non-stationarity and non-linearity. Our four candidate models are based respectively on wavelet analysis, mixed spectrum analysis, non-linear ARMA models with Fourier coefficients, and the Kalman filter. These models are applied to weekly data on interest rates in India, and their forecasting performance is evaluated vis-…-vis three GARCH models (GARCH (1,1), GARCH-M (1,1) and EGARCH (1,1)) as well as the random walk model. The Kalman filter model emerges at the top, with wavelet and mixed spectrum models also showing considerable promise.Interest rates, wavelets, mixed spectra, non-linear ARMA, Kalman filter, GARCH, Forecast encompassing
FORECASTING INTEREST RATES - A COMPARATIVE ASSESSMENT OF SOME SECOND GENERATION NON-LINEAR MODELS
Modelling and forecasting of interest rates has traditionally proceeded in the framework of linear stationary models such as ARMA and VAR, but only with moderate success. We examine here four models which account for several specific features of real world asset prices such as non-stationarity and non-linearity. Our four candidate models are based respectively on wavelet analysis, mixed spectrum analysis, non-linear ARMA models with Fourier coefficients, and the Kalman filter. These models are applied to weekly data on interest rates in India, and their forecasting performance is evaluated vis--vis three GARCH models (GARCH (1,1), GARCH-M (1,1) and EGARCH (1,1)) as well as the random walk model. The Kalman filter model emerges at the top, with wavelet and mixed spectrum models also showing considerable promise.interest rates, wavelets, mixed spectra, non-linear ARMA, Kalman filter, GARCH, Forecast encompassing.
Online Bearing Remaining Useful Life Prediction Based on a Novel Degradation Indicator and Convolutional Neural Networks
In industrial applications, nearly half the failures of motors are caused by
the degradation of rolling element bearings (REBs). Therefore, accurately
estimating the remaining useful life (RUL) for REBs are of crucial importance
to ensure the reliability and safety of mechanical systems. To tackle this
challenge, model-based approaches are often limited by the complexity of
mathematical modeling. Conventional data-driven approaches, on the other hand,
require massive efforts to extract the degradation features and construct
health index. In this paper, a novel online data-driven framework is proposed
to exploit the adoption of deep convolutional neural networks (CNN) in
predicting the RUL of bearings. More concretely, the raw vibrations of training
bearings are first processed using the Hilbert-Huang transform (HHT) and a
novel nonlinear degradation indicator is constructed as the label for learning.
The CNN is then employed to identify the hidden pattern between the extracted
degradation indicator and the vibration of training bearings, which makes it
possible to estimate the degradation of the test bearings automatically.
Finally, testing bearings' RULs are predicted by using a -support
vector regression model. The superior performance of the proposed RUL
estimation framework, compared with the state-of-the-art approaches, is
demonstrated through the experimental results. The generality of the proposed
CNN model is also validated by transferring to bearings undergoing different
operating conditions
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A mission synthesis algorithm for fatigue damage analysis
This paper presents a signal processing based algorithm, the Mildly Nonstationary Mission Synthesis
(MNMS), which produces a short mission signal from long records of experimental data. The
algorithm uses the Discrete Fourier Transform, Orthogonal Wavelet Transform and bump reinsertion
procedures. In order to observe the algorithm effectiveness a fatigue damage case study was
performed for a vehicle lower suspension arm using signals containing tensile and compressive
preloading. The mission synthesis results were compared to the original road data in terms of both the
global signal statistics and the fatigue damage variation as a function of compression ratio. Three
bump reinsertion methods were used and evaluated. The methods differed in the manner in which
bumps (shock events) from different wavelet groups (frequency bands) were synchronised during the
reinsertion process. One method, based on time synchronised section reinsertion, produced the best
results in terms of mission signal kurtosis, crest factor, root-mean-square level and power spectral
density. For improved algorithm performance, bump selection was identified as the main control
parameter requiring optimisation
AN INVESTIGATION OF SEISMIC ATTENUATION IN MARINE SEDIMENTS
There have been relatively few investigations into the attenuation properties of
unconsolidated sediments using marine surface seismic data.
Several methods of measuring attenuation were assessed for reliability in a noise-free
case and with the addition of noise using a set of synthetically absorbed and dispersed
wavelets. Wavelet modelling proved to be superior to the other techniques, followed by
spectrum modelling and the spectral ratios method. Complex trace analysis using the
analytical signal proved to be unreliable for non-sinusoidal wavelets, whilst the risetime
method was found to be very susceptible to noise for practical purposes.
Numerical modelling was carried out to assess the spectral effects of layering on a
propagating pulse. The thin layer / peg-leg phenomenon has varying filtering effects on the
propagating pulse. In particular, layers which are less than the "tuning thickness" of the
propagating pulse have a low-pass effect.
The quality factor, Q, was measured in two case studies. In the first, the mean Q
was determined from wavelet and spectrum modelling and found to be 60 for fine sands and
47 for coarse sands in the 1 kHz to 3 kHz frequency band. In the second, Q was
determined as 59 for poorly sorted sandy diamicts in the 100 Hz to 240 Hz frequency band.
The close fit between synthesised spectra and wavelets and observed data showed that a
constant- Q mechanism would account for the spectral changes between the seabed and the
deeper target reflection events in the two case studies. The spectra of the target reflection
events in both case studies were lacking in low frequencies which is likely to be due to low-pass
filtering from composite reflection events due to thin bed layering. For practical
purposes, the determination of Q from a mean normalised seismic trace yielded the same
result as measuring a mean Q from individual traces.
In a third case study, the seabed multiple was compared to the seabed reflection
using wavelet and spectrum modelling. A lack of low frequencies in the seabed multiple
showed that the seabed can act as a low-pass filter to an incident pulse. As the numerical
methods rely on the seabed as having a white reflection and transmission response, the low-pass
effect will result in erroneous estimates of the quality factor, Q
Detection of the ISW effect and corresponding dark energy constraints made with directional spherical wavelets
Using a directional spherical wavelet analysis we detect the integrated
Sachs-Wolfe (ISW) effect, indicated by a positive correlation between the
first-year Wilkinson Microwave Anisotropy Probe (WMAP) and NRAO VLA Sky Survey
(NVSS) data. Detections are made using both a directional extension of the
spherical Mexican hat wavelet and the spherical butterfly wavelet. We examine
the possibility of foreground contamination and systematics in the WMAP data
and conclude that these factors are not responsible for the signal that we
detect. The wavelet analysis inherently enables us to localise on the sky those
regions that contribute most strongly to the correlation. On removing these
localised regions the correlation that we detect is reduced in significance, as
expected, but it is not eliminated, suggesting that these regions are not the
sole source of correlation between the data. This finding is consistent with
predictions made using the ISW effect, where one would expect weak correlations
over the entire sky. In a flat universe the detection of the ISW effect
provides direct and independent evidence for dark energy. We use our detection
to constrain dark energy parameters by deriving a theoretical prediction for
the directional wavelet covariance statistic for a given cosmological model.
Comparing these predictions with the data we place constraints on the
equation-of-state parameter and the vacuum energy density .
We also consider the case of a pure cosmological constant, i.e. . For
this case we rule out a zero cosmological constant at greater than the 99.9%
significance level. All parameter estimates that we obtain are consistent with
the standand cosmological concordance model values.Comment: 16 pages, 13 figures; replaced to match version accepted by MNRA
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