Morlet Continuous Wavelet Transform Research Articles

A Time-Frequency Domain Feature Extraction Approach Enhanced by Computer Vision for Wire Arc Additive Manufacturing Monitoring Using Fourier and Wavelet Transform

Wire arc additive manufacturing (WAAM) is a rapidly growing technology that offers several advantages over traditional manufacturing methods, such as high deposition rates and the ability to build large components in a cost-effective manner. However, WAAM is also prone to the generation of defects, so the timely identification of anomalies is important to reduce the waste and get components of high quality. To develop anomaly detection application, the feature extraction process represents a key ingredient which allows machine learning systems to analyze big data. Waveform GMAW welding processes are typically used in WAAM to reduce the heat input supplied to the material and avoid defects such as excessive bending of parts and residual stress. These processes are based on the controlled dip transfer principle, so the waveforms should repeat themselves during deposition. This suggests that the frequency content of the voltage and current welding signals acquired during the process can provide important information about the process state. In this research, an experimental campaign was conducted to collect data for pulsed welding and surface tension transfer (STT) processes during the deposition of mild steel ER70S6, stainless steel 316L, Aluminum 4043, and Inconel 718 alloys. Welding voltage and current signals were acquired during the building processes, and a frequency domain analysis was conducted using the Fast Fourier transform (FFT) and discrete wavelet transform (DWT) with the aim to extract features from signals aiming to better separate the feature space, which means improve anomaly detection performance in detecting defects like arc instability, porosity, geometrical defect due to arc blow and humping. Furthermore, a methodology based on time-frequency analysis enhanced by Gabor filter for texture anomaly detection of scalograms obtained by Morlet Continuous Wavelet Transform is proposed, which showed an improvement of performance in separation between normal and anomalous deposition of several materials under different welding technologies.

A load spectrum editing method of time-frequency for rubber isolators based on the continuous wavelet transform

The load spectrum editing method of rubber isolator under the criterion of real damage retention was studied. A time-frequency editing method based on the continuous Morlet wavelet transform (CMWT) was proposed. In this method, the accumulative power spectral density (APSD) of strain-load spectrum was obtained using the CMWT method. Then an APSD threshold was set and time segments with small damage contribution in the load spectrum were identified and removed to obtain the edited load spectrum. For comparisons, the conventional time-domain editing method was used to edit the load spectrum. The obtained results show that the time compression of the proposed method is larger than that of the other editing method. The original and edited load spectra are consistent in terms of statistical parameters. Moreover, based on the mount fatigue analysis, the edited load spectrum was verified to have the same loading effect as the original load spectrum.

Motor Imagery EEG Signal Recognition Using Deep Convolution Neural Network.

Brain computer interaction (BCI) based on EEG can help patients with limb dyskinesia to carry out daily life and rehabilitation training. However, due to the low signal-to-noise ratio and large individual differences, EEG feature extraction and classification have the problems of low accuracy and efficiency. To solve this problem, this paper proposes a recognition method of motor imagery EEG signal based on deep convolution network. This method firstly aims at the problem of low quality of EEG signal characteristic data, and uses short-time Fourier transform (STFT) and continuous Morlet wavelet transform (CMWT) to preprocess the collected experimental data sets based on time series characteristics. So as to obtain EEG signals that are distinct and have time-frequency characteristics. And based on the improved CNN network model to efficiently recognize EEG signals, to achieve high-quality EEG feature extraction and classification. Further improve the quality of EEG signal feature acquisition, and ensure the high accuracy and precision of EEG signal recognition. Finally, the proposed method is validated based on the BCI competiton dataset and laboratory measured data. Experimental results show that the accuracy of this method for EEG signal recognition is 0.9324, the precision is 0.9653, and the AUC is 0.9464. It shows good practicality and applicability.

Rotor blade imbalance fault detection for variable-speed marine current turbines via generator power signal analysis

Marine hydrokinetic (MHK) turbines extract renewable energy from oceanic environments. However, due to the harsh conditions that these turbines operate in, system performance naturally degrades over time. Thus, ensuring efficient condition-based maintenance is imperative towards guaranteeing reliable operation and reduced costs for marine hydrokinetic power. This paper proposes a novel framework aimed at identifying and classifying the severity of rotor blade pitch imbalance faults experienced by marine current turbines (MCTs). In the framework, a Continuous Morlet Wavelet Transform (CMWT) is first utilized to acquire the wavelet coefficients encompassed within the 1P frequency range of the turbine's rotor shaft. From these coefficients, several statistical indices are tabulated into a six-dimensional feature space. Next, Principle Component Analysis (PCA) is employed on the resulting feature space for dimensionality reduction, and then the application of a K-Nearest Neighbor (KNN) machine learning algorithm is utilized for fault detection and severity classification. The effectiveness of the proposed framework is validated using a high-fidelity MCT numerical simulation platform, where results demonstrate that the presence of a pitch imbalance fault can be accurately detected 100% of the time and correctly classified based upon severity more than 97% of the time.

Chirp Analyzer for Estimating Amplitude and Latency of Steady-State Auditory Envelope Following Responses.

The envelope following response (EFR) is a clinically relevant evoked potential, reflecting the synchronization of the auditory pathway to the temporal envelope of sounds. Since there is no standard analysis of this potential, we here aim at contrasting the relative accuracy of known time-frequency methods and new strategies for the reliable estimation of the EFR amplitude and latency. The EFR was estimated using explicit time-frequency methods: the Short-Term Fourier Transform (STFT) and the Morlet Continuous Wavelet Transform (CWT). Furthermore, the Chirp Analyzer (CA) was introduced as a new tool for the reliable estimation of the EFR. The applicability of the methods was tested in animal and human recordings. Using simulated data for comparing the estimation performance by each method, we found that the CA is able to correctly estimate EFR amplitudes, without the typical bias observed in the STFT estimates. The CA is more robust to noise than the CWT method, although with higher sensitivity to the latency of the response. Thus, the estimation of the EFR amplitude with any of the methods, but especially with CA, should be corrected by using the estimated delay. Analysis of real data confirmed these results and showed that all methods offer estimated EFRs similar to those found in previous studies using the classical Fourier Analyzer. The CA is a potential valuable tool for the analysis of the EFR, which could be extended for the estimation of oscillatory evoked potentials of other sensory modalities.

Detecting Punctual Damage to Gears through the Continuous Morlet Wavelet Transform

In predictive maintenance, vibration signal analyses are frequently used to diagnose reducer failures because these analyses contain information about the conditions of the mechanical components. Reducer vibration signals are very noisy and the signal-to-noise ratio is so low that extracting information from the signal components is complex, especially in practical situations. Therefore, signal processing techniques are used to solve this problem and facilitate the retrieval of information. In this work, the adopted technique included noise-canceling technique, synchronous temporal mean (TSA), and continuous Morlet wavelet transform (CWT), designed to extract resources and diagnose local gear damage. These techniques are used in measured signals in an experimental workbench consisting of the gear pair coupled to a motor and a generator. The experiment was monitored according to the conditions of a gear pair throughout its useful life. The continuous wavelet transforms accurately identified faults in the gear teeth, and it was possible to detect in which tooth the fault was occurring.

Fault characteristic frequency analysis of elliptically shaped bearing

Elliptically shaped bearing (ESB) with complicated kinematics characteristic is easily damaged, there is not a theoretical formula for ESB fault characteristic frequency (FCF) due to its geometrical structure. A theoretical calculation method for ESB FCF based on analysis of the relationship between geometry and kinematics characteristics is proposed. The identification accuracy of fault type can be improved. The continuous Morlet wavelet transform (CMWT) combined with FFT-based Hilbert (FH) analysis (i.e., CMWT-FH) is utilized to extract the fault feature by suppressing the dominant rotational excitation of ESB against the FH method. Experiments are performed to verify the effectiveness of the proposed method. The experimental FCFs identified from the CMWT-FH spectrums of ESB signals are evidently close to the theoretical values calculated by using geometry and kinematics parameters of ESB (the errors are within 2%). The theoretical calculation method for ESB FCF has practical reference for the accurate detection in fault diagnosis.

MULTISCALE ENVIRONMENTAL MONITORING IN URBAN TOPOCLIMATE

Climate is a complex system subject to much natural and anthropogenic interference. Urban microclimates and topoclimates need effective methodologies to localize coexisting phenomena, including multiscale approaches that demonstrate their relational character. Air temperature, air relative humidity, and wind are microclimatic variables that can be evaluated with respect to their qualitative energy flow characteristics. The technical performance of this monitoring depends on a good estimate of the statistics of the digital signal assessed, which in turn represents greater care in the management and implementation of structural change indicators derived from frequency-domain modeling. Therefore, this study aimed to analyze the power spectra of the air temperature, air relative humidity and wind data series using the traditional Morlet Continuous Wavelet Transform (CWT) and the Cross Wavelet Transform (XWT), with Wavelet Coherence (WC) analysis. The daily, monthly and annual scales were studied, and the results demonstrated significant interrelationships between the variables. The WC values found were validated by the Monte Carlo method, scalograms and spectrograms, representing seasonal and daily cycle frequencies. The urban fractions presented behavior in accordance with the seasonality of tropical climates of the Cerrado, as well as of interference of the urban roughness. The CWT, XWT and WC tools are adequate for urban monitoring and planning analyses, qualitatively reflecting the urban dynamics of microenvironments

Time–frequency analysis for bearing fault diagnosis using multiple Q-factor Gabor wavelets

Rolling element bearings are key and also vulnerable machine elements in rotating machinery. Fault diagnosis of rolling element bearings is significant for guaranteeing machinery safety and functionality. To accurately extract bearing diagnostic information, a time–frequency analysis method based on continuous wavelet transform (CWT) and multiple Q-factor Gabor wavelets (MQGWs) (termed CMQGWT) is introduced in this paper. In the CMQGWT method, Gabor wavelets with multiple Q-factors are adopted and sets of the continuous wavelet coefficients for each Q-factor are combined to generate time–frequency map. By this way, the resolution of the CWT time–frequency map can be greatly increased and the diagnostic information can be accurately identified. Numerical simulation is carried out and verified the effectiveness of the proposed method. Case studies and comparisons with the continuous Morlet wavelet transform (CMWT) and the tunable Q-factor wavelet transform (TQWT) demonstrate the effectiveness and superiority of the CMQGWT for bearing diagnostic information extraction and fault identification.

Times Varying Spectral Coherence Investigation of Cardiovascular Signals Based on Energy Concentration in Healthy Young and Elderly Subjects by the Adaptive Continuous Morlet Wavelet Transform

ObjectiveThe aims of this study, to investigate the interaction among heart rate variability (HRV), respiratory, systolic arterial blood pressure variability (SABPV) and systolic arterial pressure interval variability (APIV) signals for understanding of cardiovascular control. MethodsIn this study, three methods referred as adaptive continuous Morlet wavelet transform (ADCMWT), adaptive Stockwell transform (ADST) and adaptive modified Stockwell transform (ADMST) was used to assess the accuracy (AC) of time-varying spectral coherence (TVSC). The adaptation of these estimators was based on maximum energy concentration measurement. The capability to correct temporal localization of time–frequency regions was validated on synthetic time series data modeled as dynamic characteristics of cardiovascular signals. ResultsThe results on synthetic simulated data show that the ADCMWT method allows for the temporal localization of the time–frequency regions with higher accuracy (AC > 96.074% for SNR ≥ 0 dB), compared to ADST (AC > 90.71% for SNR ≥ 0 dB) and ADMST (AC > 84.45% for SNR ≥ 5 dB). Further, the ADCMWT was applied to real cardiovascular data obtained from Fantasia standard data base and grouped as, 8 young subjects (4M + 4F, age range 23–32) and 8 elderly subjects (4M + 4F, age range 70–82) for estimating the TVSC in low frequency (LF) band (0.04 Hz–0.15 Hz) and high frequency (HF) band (0.15 Hz–0.4 Hz) of HRV spectrum. The global result depict that the median value of interquartile range of coherency between HRV-SABPV and HRV-APIV signals in LF and HF band were significantly (p=0.00001) lower in elderly group subjects compared to young group subjects. The coupling between HRV-Respiratory signals in LF band was not significantly affected with the aging of healthy subjects. However, this coupling in HF band significantly reduced in elderly compare to young group subjects (p=0.0125). ConclusionThe comparative study shows that the time-varying spectra and accurate localization of coupling between two physiological signals can be affected by energy concentration. The ADCMWT at w0=6, could be an alternative, possibly more suitable and highly accurate method for assessment and detection of time varying spectral and coherence components of cardiovascular time series.

Co-movement of stock exchange indices and exchange rates in Ghana: A wavelet coherence analysis

By means of the Continuous Morlet Wavelet Transform fostering covariance/correlation, lead-lag causal relationship as well as coherency via the wavelets analysis, we explore the two indices on the ...

Estimation of patterns in weaned piglets' activity using spectral analysis

The activity level of weaned piglets provides a useful tool for farmers to control animal welfare and pollutant emissions. In addition, data for weaned piglet activity can be used as an input signal in real-time ventilation control systems because of its relation to temperature and CO2 levels. This paper characterises the daily activity pattern of piglets from 6 to 20 kg live body mass based on data obtained by a passive infrared detector on a conventional farm. Activity level of piglets was at its maximum at the beginning of the experimental period and at its minimum at the end of the period. The analysis of the Fast Fourier Transform revealed an average pattern with two activity peaks, at 10:00 h and 18:00 h, described by three cosine waves with 24-, 12- and 8-h periodicity. The Continuous Morlet Wavelet Transform revealed variations in frequency spectrum with time between the first and second half of the cycle, defining two distinct activity periods. The predominant pattern during the first half was a single-peak pattern, whereas the predominant pattern during the second half was a two-peak pattern. Accordingly, two models for the prediction of piglet activity are proposed. Animal age and mass are essential to define behaviour patterns, which explains the existence of various models in the literature and the need to perform continuous measurements to establish accurate models for predicting activity in growing piglets. Passive infrared detectors are simple and cost-effective, and allow for the incorporation of animal activity into real-time control on conventional farms.

Time-Frequency Distribution of Seismocardiographic Signals: A Comparative Study.

Accurate estimation of seismocardiographic (SCG) signal features can help successful signal characterization and classification in health and disease. This may lead to new methods for diagnosing and monitoring heart function. Time-frequency distributions (TFD) were often used to estimate the spectrotemporal signal features. In this study, the performance of different TFDs (e.g., short-time Fourier transform (STFT), polynomial chirplet transform (PCT), and continuous wavelet transform (CWT) with different mother functions) was assessed using simulated signals, and then utilized to analyze actual SCGs. The instantaneous frequency (IF) was determined from TFD and the error in estimating IF was calculated for simulated signals. Results suggested that the lowest IF error depended on the TFD and the test signal. STFT had lower error than CWT methods for most test signals. For a simulated SCG, Morlet CWT more accurately estimated IF than other CWTs, but Morlet did not provide noticeable advantages over STFT or PCT. PCT had the most consistently accurate IF estimations and appeared more suited for estimating IF of actual SCG signals. PCT analysis showed that actual SCGs from eight healthy subjects had multiple spectral peaks at 9.20 ± 0.48, 25.84 ± 0.77, 50.71 ± 1.83 Hz (mean ± SEM). These may prove useful features for SCG characterization and classification.

Co-movement of real exchange rates in the West African Monetary Zone

AbstractIn three different ways of lead–lag causal relationship, covariance/correlation and coherence, we apply the wavelets analysis via the Continuous Morlet Wavelet Transform to delineate the significant frequency–time domain lead–lag relationships for the West African Monetary Zone member countries for real US dollar exchange rates and their absolute log returns from January 2001 to April 2015. The results indicate that lead–lag associations at different periodicities vary across the countries. No one country comes off as leading conveniently for both real and absolute returns of the exchange rates. Our results corroborate other evidences of non-convergence of exchange rates in the monetary zone, which hinders the eventual implementation of the single currency in the ECOWAS region.

Determining damping characteristics of railway-overhead-wire system for finite-element analysis

ABSTRACTIn order to investigate the damping characteristics of railway-overhead-wire systems, we propose herein an approach based on the continuous wavelet transform (CWT) and two existing formulas concerning Rayleigh damping coefficients (RDCs). In the proposed process, the displacement histories of a real catenary are first obtained by using a set of noncontact photogrammetric devices, following which an exclusive catenary damping ratio related to the first dominant modal component in the catenary response is identified through a complex Morlet CWT. Thereafter, iterative finite-element analysis is conducted to find the optimal RDCs, which involves using two related formulas and the similarity between the catenary displacements obtained by simulation and experimentation. The results of our study demonstrate that this combined approach is constructive, especially for structures with closely spaced modes, such as catenaries. For the case studied herein, the catenary modal damping ratio at 1.19 Hz is approximately 1%, and the mass and stiffness proportional Rayleigh damping coefficients are approximately 0.02845 and 0.00274, respectively.

Periodicity analysis of δ18O in precipitation over Central Europe: Time–frequency considerations of the isotopic ‘temperature’ effect

Summary In this paper the periodic patterns of the isotopic composition of precipitation (δ 18 O) for 22 stations located around Central Europe are investigated through sinusoidal models and wavelet analysis over a 23 years period (1980/01–2002/12). The seasonal distribution of δ 18 O follows the temporal variability of air temperature providing seasonal amplitudes ranging from 0.94‰ to 4.47‰; the monthly isotopic maximum is observed in July. The isotopic amplitude reflects the geographical dependencies of the isotopic composition of precipitation providing higher values when moving inland. In order to describe the dominant oscillation modes included in δ 18 O time series, the Morlet Continuous Wavelet Transform is evaluated. The main periodicity is represented at 12-months (annual periodicity) where the wavelet power is mainly concentrated. Stations (i.e. Cuxhaven, Trier, etc.) with limited seasonal isotopic effect provide sparse wavelet power areas at the annual periodicity mode explaining the fact that precipitation has a complex isotopic fingerprint that cannot be examined solely by the seasonality effect. Since temperature is the main contributor of the isotopic variability in mid-latitudes, the isotope–temperature effect is also investigated. The isotope–temperature slope ranges from 0.11‰/°C to 0.47‰/°C with steeper values observed at the southernmost stations of the study area. Bivariate wavelet analysis is applied in order to determine the correlation and the slope of the δ 18 O – temperature relationship over the time–frequency plane. High coherencies are detected at the annual periodicity mode. The time–frequency slope is calculated at the annual periodicity mode ranging from 0.45‰/°C to 0.83‰/°C with higher values at stations that show a more distinguishable seasonal isotopic behavior. Generally the slope fluctuates around a mean value but in certain cases (sites with low seasonal effect) abrupt slope changes are derived and the slope becomes strongly unstable.

Damage assessed by wavelet scale bands and b-value in dynamical tests of a reinforced concrete slab monitored with acoustic emission

The complex Morlet Continuous Wavelet Transform (CWT) was applied to acoustic emission (AE) signals from dynamic tests conducted on a reinforced concrete slab with a shaking table. The steel reinforcement bars did not yield during the tests, but a severe loss of bond between reinforcement bars and surrounding concrete was detected. Comparison of the evolution of the scale position of maximum values of CWT coefficients and the histories of response acceleration obtained in different seismic simulations allowed us to identify the (45–64kHz) frequency band corresponding to the fracture of concrete. The Cumulative Acoustic Emission Energy (CAE) obtained by reconstructing the AE signals in this scale (frequency) band was compared with the Cumulative Dissipated Energy (CDE) of the tested structure. The CDE is accepted as a good parameter for characterizing the mechanical damage in structures. A reasonably good agreement was found between the normalized histories of CAE and CDE. This made it possible to categorize the cracking of concrete as the main source of damage in the reinforced concrete slab. Conversely, the differences between the CAE and CDE curves observed for high levels of peak acceleration applied to the shaking table can be attributed to the deformation of the steel that formed the columns. The AE coming from the plastic deformation of the steel is not detected by CAE due to the threshold amplitude (45dB) used in the AE monitoring, but the strain energy dissipated by the steel through plastic deformations is included in the CDE. Further, a study of the evolution of the b-value in the successive seismic simulations revealed that the b-value can capture the inception of severe cracking in the concrete, which the tests described in this study attributed mainly to the loss of bond between reinforcing steel and surrounding concrete.

Purification and Compression of Continuous Morlet Wavelet Transform Based on Singular Value Decomposition

Purification and Compression of Continuous Morlet Wavelet Transform Based on Singular Value Decomposition

Time-frequency Techniques in Biomedical Signal Analysis

This review outlines the methodological fundamentals of the most frequently used non-parametric time-frequency analysis techniques in biomedicine and their main properties, as well as providing decision aids concerning their applications. The short-term Fourier transform (STFT), the Gabor transform (GT), the S-transform (ST), the continuous Morlet wavelet transform (CMWT), and the Hilbert transform (HT) are introduced as linear transforms by using a unified concept of the time-frequency representation which is based on a standardized analytic signal. The Wigner-Ville distribution (WVD) serves as an example of the 'quadratic transforms' class. The combination of WVD and GT with the matching pursuit (MP) decomposition and that of the HT with the empirical mode decomposition (EMD) are explained; these belong to the class of signal-adaptive approaches. Similarities between linear transforms are demonstrated and differences with regard to the time-frequency resolution and interference (cross) terms are presented in detail. By means of simulated signals the effects of different time-frequency resolutions of the GT, CMWT, and WVD as well as the resolution-related properties of the interference (cross) terms are shown. The method-inherent drawbacks and their consequences for the application of the time-frequency techniques are demonstrated by instantaneous amplitude, frequency and phase measures and related time-frequency representations (spectrogram, scalogram, time-frequency distribution, phase-locking maps) of measured magnetoencephalographic (MEG) signals. The appropriate selection of a method and its parameter settings will ensure readability of the time-frequency representations and reliability of results. When the time-frequency characteristics of a signal strongly correspond with the time-frequency resolution of the analysis then a method may be considered 'optimal'. The MP-based signal-adaptive approaches are preferred as these provide an appropriate time-frequency resolution for all frequencies while simultaneously reducing interference (cross) terms.

Wavelet-Based Analysis of Power System Low-Frequency Electromechanical Oscillations

This paper addresses the use of the continuous wavelet transform (CWT) in the study of power system low-frequency electromechanical oscillations (LFEOs). Based on a modified complex Morlet mother-wavelet function, an approach is proposed to exploit the relationship between system low-frequency oscillation features and the Morlet CWT of a system ringdown signal for detection of modal parameter changes as well as for modal frequency and damping computation. Also, several guidelines for selecting the center frequency and bandwidth parameters, the scaling factor and the translation factor, are proposed in order to provide reliable modal identification estimates. The efficiency of the proposed approach is confirmed by applying it to synthetic, simulated and measured signals.