Linear Multi-Degree-of-Freedom System Stochastic Response by Using the Harmonic Wavelet Transform

2003 ◽  
Vol 70 (5) ◽  
pp. 724-731 ◽  
Author(s):  
P. Tratskas ◽  
P. D. Spanos
Keyword(s):  
Wavelet Transform ◽  
Linear System ◽  
Spectral Characteristics ◽  
Degree Of Freedom ◽  
Harmonic Wavelets ◽  
Time Frequency ◽  
The Family ◽  
Harmonic Wavelet ◽  
The Time Domain ◽  
System Frequency

The wavelet transform is used to capture localized features in either the time domain or the frequency domain of the response of a multi-degree-of-freedom linear system subject to a nonstationary stochastic excitation. The family of the harmonic wavelets is used due to the convenient spectral characteristics of its basis functions. A wavelet-based system representation is derived by converting the system frequency response matrix into a time-frequency wavelet “tensor.” Excitation-response relationships are obtained for the wavelet-based representation which involve linear system theory, spectral representation of the excitation and of the response vectors, and the wavelet transfer tensor of the system. Numerical results demonstrate the usefulness of the developed analytical procedure.

Using a Modified Harmonic Wavelet Transform to Characterize Mechanical Shock

2011 ◽  
Vol 54 (2) ◽  
pp. 85-102
Author(s):  
David Smallwood
Keyword(s):  
Wavelet Transform ◽  
Spectral Density ◽  
Estimation Error ◽  
Cross Product ◽  
Constant Time ◽  
Time Varying ◽  
Mechanical Shock ◽  
Time Frequency ◽  
Harmonic Wavelet

A modified harmonic wavelet transform is used to estimate a time varying spectral density. The resolution of the estimate has an approximate constant time-frequency product. The estimation error is directly related to this time-frequency product. Unwanted cross product terms are effectively minimized. Several examples are given: White random, two sine waves, chirps, impulses, sums of exponentially decaying sinusoids, and a pyroshock. It is also shown how realizations can be generated from the modified harmonic wavelet transform estimate of the time varying spectral density.

scholarly journals Detection of Patterns in Pressure Signal of Compressed Air System Using Wavelet Transform

2021 ◽  
pp. 61-67
Author(s):  
Mohamad Thabet ◽  
David Sanders ◽  
Nils Bausch
Keyword(s):  
Wavelet Transform ◽  
Wavelet Transforms ◽  
Compressed Air ◽  
Learning Tools ◽  
Time Frequency ◽  
Pressure Signal ◽  
Operating Modes ◽  
Air System ◽  
The Time Domain ◽  
Future Work

AbstractThis paper investigates detecting patterns in the pressure signal of a compressed air system (CAS) with a load/unload control using a wavelet transform. The pressure signal of a CAS carries useful information about operational events. These events form patterns that can be used as ‘signatures’ for event detection. Such patterns are not always apparent in the time domain and hence the signal was transformed to the time-frequency domain. Three different CAS operating modes were considered: idle, tool activation and faulty. The wavelet transforms of the CAS pressure signal reveal unique features to identify events within each mode. Future work will investigate creating machine learning tools for that utilize these features for fault detection in CAS.

scholarly journals SS-SWT and SI-CNN: An Atrial Fibrillation Detection Framework for Time-Frequency ECG Signal

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Hongpo Zhang ◽  
Renke He ◽  
Honghua Dai ◽  
Mingliang Xu ◽  
Zongmin Wang
Keyword(s):  
Atrial Fibrillation ◽  
Wavelet Transform ◽  
Morbidity And Mortality ◽  
High Morbidity ◽  
Ecg Signal ◽  
Time Frequency ◽  
Ecg Signals ◽  
Convolution Process ◽  
The Time Domain ◽  
Atrial Fibrillation Detection

Atrial fibrillation is the most common arrhythmia and is associated with high morbidity and mortality from stroke, heart failure, myocardial infarction, and cerebral thrombosis. Effective and rapid detection of atrial fibrillation is critical to reducing morbidity and mortality in patients. Screening atrial fibrillation quickly and efficiently remains a challenging task. In this paper, we propose SS-SWT and SI-CNN: an atrial fibrillation detection framework for the time-frequency ECG signal. First, specific-scale stationary wavelet transform (SS-SWT) is used to decompose a 5-s ECG signal into 8 scales. We select specific scales of coefficients as valid time-frequency features and abandon the other coefficients. The selected coefficients are fed to the scale-independent convolutional neural network (SI-CNN) as a two-dimensional (2D) matrix. In SI-CNN, a convolution kernel specifically for the time-frequency characteristics of ECG signals is designed. During the convolution process, the independence between each scale of coefficient is preserved, and the time domain and the frequency domain characteristics of the ECG signal are effectively extracted, and finally the atrial fibrillation signal is quickly and accurately identified. In this study, experiments are performed using the MIT-BIH AFDB data in 5-s data segments. We achieve 99.03% sensitivity, 99.35% specificity, and 99.23% overall accuracy. The SS-SWT and SI-CNN we propose simplify the feature extraction step, effectively extracts the features of ECG, and reduces the feature redundancy that may be caused by wavelet transform. The results shows that the method can effectively detect atrial fibrillation signals and has potential in clinical application.

A common-reflection-point gather random noise attenuation method based on the synchrosqueezing wavelet transform

2021 ◽  
pp. 1-81
Author(s):  
Xiaokai Wang ◽  
Zhizhou Huo ◽  
Dawei Liu ◽  
Weiwei Xu ◽  
Wenchao Chen
Keyword(s):  
Wavelet Transform ◽  
Frequency Domain ◽  
Seismic Data ◽  
Random Noise ◽  
Principal Component ◽  
Frequency Resolution ◽  
Reflection Point ◽  
Transform Method ◽  
Time Frequency ◽  
The Time Domain

Common-reflection-point (CRP) gather is one extensive-used prestack seismic data type. However, CRP suffers more noise than poststack seismic dataset. The events in the CRP gather are always flat, and the effective signals from neighboring traces in the CRP gather have similar forms not only in the time domain but also in the time-frequency domain. Therefore, we firstly use the synchrosqueezing wavelet transform (SSWT) to decompose seismic traces to the time-frequency domain, as the SSWT has better time-frequency resolution and reconstruction properties. Then we propose to use the similarity of neighboring traces to smooth and threshold the SSWT coefficients in the time-frequency domain. Finally, we used the modified SSWT coefficients to reconstruct the denoised traces for the CRP gather. Synthetic and field data examples show that our proposed method can effectively attenuate random noise with a better attenuation performance than the commonly-used principal component analysis, FX filter, and the continuous wavelet transform method.

Application of Harmonic Wavelet Analysis to Rubbing Vibration Signals for Rotating Machinery Fault Diagnosis

2013 ◽  
Vol 321-324 ◽  
pp. 1245-1248
Author(s):  
Xiang Wang ◽  
Yuan Zheng
Keyword(s):  
Wavelet Transform ◽  
Signal Analysis ◽  
Rotating Machinery ◽  
The Other ◽  
Vibration Signals ◽  
Time Frequency ◽  
Vibration Data ◽  
Turbo Generator ◽  
Harmonic Wavelet ◽  
Machinery Fault Diagnosis

Harmonic wavelet transform (HWT)and harmonic wavelet time-frequency profile plot (TFPP) is introduced firstly in practice to identify weak singularity in a signal with noise clearly. With TFPP method, emulational signal and vibration data of the rubbing of the large practical turbo-generator units are analyzed successfully, which prove that the method is effectively extract the rubbing signal feature which is can not gained by the other signal analysis methods, and the rubbing of the turbo-generator units is identified effectively.

Ridge and Phase Identification in the Frequency Analysis of Transient Signals by Harmonic Wavelets

1999 ◽  
Vol 121 (2) ◽  
pp. 149-155 ◽  
Author(s):  
D. E. Newland
Keyword(s):  
Frequency Analysis ◽  
Phase Identification ◽  
Computational Algorithms ◽  
High Definition ◽  
Diagnostic Features ◽  
Transient Signals ◽  
Phase Gradient ◽  
Harmonic Wavelets ◽  
Time Frequency ◽  
Harmonic Wavelet

It is difficult to generate high-definition time-frequency maps for rapidly changing transient signals. New details of the theory of harmonic wavelet analysis are described which provide the basis for computational algorithms designed to improve map definition. Features of these algorithms include the use of ridge identification and phase gradient as diagnostic features.

scholarly journals Application of Time-Frequency Analysis to Transient Data from Centrifuge Earthquake Testing

2000 ◽  
Vol 7 (4) ◽  
pp. 195-202 ◽  
Author(s):  
David E. Newland ◽  
Gary D. Butler
Keyword(s):  
Frequency Analysis ◽  
Good Method ◽  
Centrifuge Modeling ◽  
Transient Vibration ◽  
Time Frequency Analysis ◽  
Harmonic Wavelets ◽  
Time Frequency ◽  
Vibration Data ◽  
Harmonic Wavelet ◽  
Detailed Interpretation

Centrifuge model experiments have generated complex transient vibration data. New algorithms for time-frequency analysis using harmonic wavelets provide a good method of analyzing these data. We describe how the experimental data have been collected and show typical time-frequency maps obtained by the harmonic wavelet algorithm. Some preliminary comments on the interpretation of these maps are given in terms of the physics of the underlying model. Important features of the motion that are not otherwise apparent emerge from the analysis. Later papers will deal with their more detailed interpretation and their implications for centrifuge modeling.

scholarly journals Classification of Refrigerant Flow Noise of Air Conditioners Based on Continuous Wavelet Transform and Support Vector Machine

2020 ◽  
Vol 10 (11) ◽  
pp. 3959
Author(s):  
Un-Chang Jeong
Keyword(s):  
Support Vector Machine ◽  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Support Vector ◽  
Continuous Wavelet ◽  
Air Conditioner ◽  
Time Frequency ◽  
Flow Noise ◽  
The Time Domain

This study proposes a classification method that uses the continuous wavelet transform and the support vector machine approach to classify refrigerant flow noises generated in an air conditioner. The air conditioning noise was identified as an abnormal signal by the use of the first- and second-order moments. The start and end times of refrigerant flow noises were identified by detecting the singularities of the continuous wavelet transform coefficient in the time domain and by means of listening to the measured sounds. Further, the time-frequency characteristics of refrigerant flow noise were analyzed with the continuous wavelet transform. For the support vector machine-based classification of refrigerant flow noise in an air conditioner, the grid search method was used to determine kernel hyperparameters. Five-fold cross validation was employed for the application of the support vector machine to the classification of air conditioner refrigerant noise. In addition, measured sound sources were modified based on classified refrigerant flow noise to compare the classification accuracy of a jury test with the results of the support vector machine.

Spectral analysis of geomagnetically induced current and local magnetic field during the 17 March 2013 geomagnetic storm

2021 ◽  
Author(s):  
Wen-Hao Xu ◽  
Zan-Yang Xing ◽  
Nanan Balan ◽  
Li-Kai Liang ◽  
Yan-Ling Wang ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Wavelet Transform ◽  
Geomagnetic Storm ◽  
Spectral Characteristics ◽  
Low Frequency ◽  
High Energy ◽  
Local Magnetic Field ◽  
Induced Current ◽  
Geomagnetically Induced Current ◽  
Time Frequency

Abstract Geomagnetically induced current (GIC) is known to be closely related to the rate of change of local horizontal magnetic field (dBx/dt); and their spectra can give better insight into the relationship. We study the spectral characteristics of GIC measured in Finland and dBx/dt measured 30 km away during the 17 March 2013 intense geomagnetic storm (SymHMin = -132 nT). Two bursts of large GIC (up to 32A) and dBx/dt occurred at ~ 16 UT and 18 UT during the storm main phase, though their values were generally small. For the first time, the Cross Wavelet Transform (XWT) and Wavelet Coherence (WTC) techniques are used to investigate the correlation and phase relationship of GIC and dBx/dt in time-frequency domain. Their WTC correlation is strong (over 0.9) over the entire storm period, indicating dBx/dt is the main factor causing GIC and dBx/dt leading GIC. Their XWT spectra show two enclosed periods (8–42 min and 2–42 min) in the high energy region corresponding to the two bursts of activity in GIC and dBx/dt. Moreover, we use continuous wavelet transform (CWT) and discrete wavelet transform (DWT) to analyze the spectral characteristics of GIC and dBx/dt. It is found that the CWT and DWT spectra of the two are very similar, especially in the low frequency characteristics, without continuous periodicity. Wavelet coefficients become large when GIC and dBx/dT are large; and the third-order coefficient, which corresponds to low-frequency part, best reflects the disturbance of GIC and dBx/dt.

Joint Time-Frequency Analysis of Small Scale Ocean Storms via the Harmonic Wavelet Transform

2017 ◽  
Author(s):  
Valentina Laface ◽  
Felice Arena ◽  
Ioannis A. Kougioumtzoglou ◽  
Ketson Roberto Maximiano dos Santos
Keyword(s):  
Wavelet Transform ◽  
Frequency Analysis ◽  
Sea Surface ◽  
Surface Elevation ◽  
Scale Model ◽  
Small Scale ◽  
Ocean Engineering ◽  
Time Frequency Analysis ◽  
Time Frequency ◽  
Harmonic Wavelet

The paper focuses on utilizing the Harmonic Wavelet Transform (HWT) for estimating the evolutionary power spectrum (EPS) of sea storms. A sea storm is considered herein as a non-stationary stochastic process with a time duration of the order of days. The storm evolution can be represented in three stages: the growth, the peak and the decay. Specifically, during growth the intensity of the wave increases with time until reaching the apex, and then decreases. The analysis is carried out by processing the time series of the free surface elevation recorded at the Natural Ocean Engineering Laboratory of Reggio Calabria, Italy. A peculiarity of the NOEL lab is that a local wind from NNW often generates sea states consisting of pure wind waves that represent a small scale model, in Froude similarity, of ocean storms (www.noel.unirc.it). The main focus of the paper is, first, to acquire a joint time-frequency representation of the storm via estimating the associated EPS, and second, to explore the variability in time of the spectrum and of the dominant frequencies of the storm. The EPS is estimated by utilizing a non-stationary record of the sea surface elevation during a storm recorded at NOEL lab. Further, in this paper, the standard representation of sea storms is also considered. That is, the non-stationary process is represented as a sequence of stationary processes (sea states or buoy records), each of them characterized by an intensity defined by a significant wave height Hs and by a duration Δt. During the time interval Δt the sea surface elevation is considered stationary and the frequency spectrum may be computed via the Fast Fourier Transform (FFT). Results obtained following this procedure, which can be considered essentially as a brute-force application of the short-time FT, are compared with those obtained via a HWT based joint time-frequency analysis.

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