Time-frequency Energy Distribution Research Articles

Chatter identification in end milling process using wavelet packets and Hilbert–Huang transform

Chatter detection is an important task to improve productivity and part quality in the machining process. Since measured signals from sensors are usually contaminated by background noise and other disturbances, it is necessary to find efficient signal processing algorithms to identify the chatter as soon as possible. This paper presents an effective chatter identification method for the end milling process based on the study of two advanced signal processing techniques, i.e., wavelet package transform (WPT) and Hilbert–Huang transform (HHT). The WPT works as a preprocessor to denoise the measured signals and hence the performance of the HHT is enhanced. The proposed method consists of four steps. First, the measured signals are decomposed by the WPT, so that the chatter signals are allocated in a certain frequency band. Secondly, wavelet packets with rich chatter information are selected and are used to reconstruct new signals. Thirdly, the reconstructed signals are analyzed with HHT to obtain a Hilbert–Huang spectrum, which is a full time–frequency–energy distribution of the signals. Finally, the mean value and standard deviation of the Hilbert–Huang spectrum are calculated to detect the chatter and identify its levels as well. The proposed method is applied to the end milling process and the experimental results prove that the method can identify the chatter effectively.

Feature extraction of AC square wave SAW arc characteristics using improved Hilbert–Huang transformation and energy entropy

In order to extract the arc feature information related to welding quality in alternating current square wave submerged arc welding (AC Square Wave SAW), an improved Hilbert–Huang transform (HHT) is put forward to investigate the time–frequency distribution of arc current, and the energy entropy is employed to quantitatively judge the arc characteristics. The empirical mode decomposition (EMD) is used to decompose the collected current signal into a number of Intrinsic Mode Functions (IMFs). The method for removing the high frequency and undesirable low-frequency IMFs is proposed by using the correlation coefficient of the IMF and the original signal as criterion, and the valid IMFs are selected for the Hilbert transform and energy entropy calculation. The improved HHT combining with energy entropy can quantitatively describe the time–frequency energy distribution characteristics of the arc current signal at different duty cycle, frequency and welding speed. Experimental results are provided to confirm the effectiveness of this approach to extract the arc physical information related to welding quality.

Thermal variability of the Indo-Pacific warm pool

The Indo-Pacific warm pool (IPWP) over the Indian Ocean and the Pacific Ocean is the largest warm pool in the global oceans. Its thermal variability and trend between 1982 and 2011 are extracted from the Ensemble Empirical Mode Decomposition method. Time–frequency energy distributions using the Hilbert–Huang transform are computed to evaluate the thermal spectrum-energy. From the SST variability and the heat storage anomaly, we find that the thermal variability is strongly influenced by the Pacific Decadal Oscillation (PDO). The size, increasing trend in the IPWP, calculated from the SST data is (0.18±0.01)×106km2/decade. Besides, the magnitude of increasing rate during the positive phase of the PDO is couple times higher than that during the negative phase. Furthermore, the SST trend is also associated with 1999/2000 climate shift. The heat increases in the IPWP from 1993 to 2011 implied an average warming rate of 1.41Wm−2. The thermal variations in the IPWP are controlled by interannual to decadal variabilities mostly related to the PDO in the Pacific Ocean sector and by annual variability in the Indian Ocean sector.

Characterization and Classification of Modes in Acoustic Emission Based on Dispersion Features and Energy Distribution Analysis

Acoustic Emission (AE) techniques are used for the structural health monitoring of civil, aeronautic and aerospace structures. Recently, these structures are made of composite materials due to their advantages over traditional materials, but this increases the interpretation complexity of the failure modes present. Therefore, in order to make AE a trustworthy technique, reliable source location and damage mechanism characterization must be accomplished. On that account, this work proposes a novel approach based on a chirplet atomic decomposition, time-frequency energy distribution and dispersion analysis, where the failure-emitted signals are separated from extraneous noise and the detected modes are analyzed according to their dispersive behaviour and angular dependence characteristics. Dispersion relations are obtained by the use of a higher order plate theory on a non-absorbing anisotropic plate model, and then used in conjunction with the previous methodologies for mode identification and localization. The proposed methodology and model are validated, and the capability of the method to overcome practical issues encountered in AE testing is demonstrated experimentally.

Characterization and Classification of Modes in Acoustic Emission Based on Dispersion Features and Energy Distribution Analysis

Acoustic Emission (AE) techniques are used for the structural health monitoring of civil, aeronautic and aerospace structures. Recently, these structures are made of composite materials due to their advantages over traditional materials, but this increases the interpretation complexity of the failure modes present. Therefore, in order to make AE a trustworthy technique, reliable source location and damage mechanism characterization must be accomplished. On that account, this work proposes a novel approach based on a chirplet atomic decomposition, time-frequency energy distribution and dispersion analysis, where the failure-emitted signals are separated from extraneous noise and the detected modes are analyzed according to their dispersive behaviour and angular dependence characteristics. Dispersion relations are obtained by the use of a higher order plate theory on a non-absorbing anisotropic plate model, and then used in conjunction with the previous methodologies for mode identification and localization. The proposed methodology and model are validated, and the capability of the method to overcome practical issues encountered in AE testing is demonstrated experimentally.

Illusory continuity without sufficient sound energy to fill a temporal gap: Examples of crossing glide tones.

The gap transfer illusion is an auditory illusion where a temporal gap inserted in a longer glide tone is perceived as if it were in a crossing shorter glide tone. Psychophysical and phenomenological experiments were conducted to examine the effects of sound-pressure-level (SPL) differences between crossing glides on the occurrence of the gap transfer illusion. We found that the subjective continuity-discontinuity of the crossing glides changed as a function of the relative level of the shorter glide to the level of the longer glide. When the relative level was approximately between -9 and +2 dB, listeners perceived the longer glide as continuous and the shorter glide as discontinuous, that is, the gap transfer illusion took place. The glides were perceived veridically below this range, that is, gap transfer did not take place, whereas above this range the longer glide and the shorter glide were both perceived as continuous. The fact that the longer glide could be perceived as continuous even when the crossing shorter glide was 9 dB weaker indicates that the longer glide's subjective continuity cannot be explained within the conventional framework of auditory organization, which assumes reallocation of sound energy from the shorter to the longer glide. The implicated mechanisms are discussed in terms of the temporal configuration of onsets and terminations and the time-frequency distribution of sound energy.

Variability of sea surface temperature and warm pool area in the South China Sea and its relationship to the western Pacific warm pool

Sea surface temperature (SST) data derived from satellite and in situ measurements are used to study the thermal variability in the South China Sea (SCS). Time–frequency–energy distributions, periods of variability, and trends are computed by the Hilbert–Huang transform method. The SST trend from 1982 to 2005 is 0.276°C per decade in the SCS which is higher than 0.144°C per decade in the western Pacific warm pool (WPWP). The warm pool (SST ≥ 28°C) area in the SCS has increased by 0.20 × 106 km2 per decade. The SST and area of the warm pool in the SCS are strongly correlated, respectively, with the SST and area of the WPWP with a time lag of 1 month, suggestive of a strong connection between these two warm pools. Once the annual cycle is eliminated, decadal oscillations dominate the variability of SST and warm pool area in the SCS.

Time–frequency energy distribution of phrenic nerve discharges during aspiration reflex, cough and quiet inspiration

Aspiration reflex (AspR) represents a specific inspiratory motor behavior expressed by short, powerful inspiratory activity without subsequent active expiration and characterized by the ability to interrupt strong tonic inspiratory activity, as well as hypoxic apnea and several other functional disorders. Multiresolution analysis-based determination of spectral features arising during AspR has not yet been satisfactorily investigated. The time–frequency energy distribution of phrenic nerve electrical activity was compared during the AspR, inspiratory phase of tracheobronchial cough and quiet inspiration. Data obtained from 16 adult cats anesthetized with chloralose or pentobarbital were analyzed using a wavelet transformation, a sensitive method suitable for processing of the non-stationary respiratory output signal. Phrenic nerve energy was accumulated within lower frequency bands in AspR bursts. In AspR, higher frequencies contributed less to the total power, when compared to cough inspiration. Moreover, AspR indicated a stable time–frequency energy distribution, regardless of which of the two types of anesthesia were used. Chloralose anesthesia induced a decrease of parameters in cough and quiet inspiration related to the quantity of energy. The results indicate a specific method of information processing during generation of AspR, underlying its powerful ability to influence various severe functional disorders with potential implications for model experiments and clinical practice.

Time–frequency analysis of time-varying modulated signals based on improved energy separation by iterative generalized demodulation

Energy separation algorithm is good at tracking instantaneous changes in frequency and amplitude of modulated signals, but it is subject to the constraints of mono-component and narrow band. In most cases, time-varying modulated vibration signals of machinery consist of multiple components, and have so complicated instantaneous frequency trajectories on time–frequency plane that they overlap in frequency domain. For such signals, conventional filters fail to obtain mono-components of narrow band, and their rectangular decomposition of time–frequency plane may split instantaneous frequency trajectories thus resulting in information loss. Regarding the advantage of generalized demodulation method in decomposing multi-component signals into mono-components, an iterative generalized demodulation method is used as a preprocessing tool to separate signals into mono-components, so as to satisfy the requirements by energy separation algorithm. By this improvement, energy separation algorithm can be generalized to a broad range of signals, as long as the instantaneous frequency trajectories of signal components do not intersect on time–frequency plane. Due to the good adaptability of energy separation algorithm to instantaneous changes in signals and the mono-component decomposition nature of generalized demodulation, the derived time–frequency energy distribution has fine resolution and is free from cross term interferences. The good performance of the proposed time–frequency analysis is illustrated by analyses of a simulated signal and the on-site recorded nonstationary vibration signal of a hydroturbine rotor during a shut-down transient process, showing that it has potential to analyze time-varying modulated signals of multi-components.

Opto-Current-Clamp Actuation of Cortical Neurons Using a Strategically Designed Channelrhodopsin

BackgroundOptogenetic manipulation of a neuronal network enables one to reveal how high-order functions emerge in the central nervous system. One of the Chlamydomonas rhodopsins, channelrhodopsin-1 (ChR1), has several advantages over channelrhodopsin-2 (ChR2) in terms of the photocurrent kinetics. Improved temporal resolution would be expected by the optogenetics using the ChR1 variants with enhanced photocurrents.Methodology/Principal FindingsThe photocurrent retardation of ChR1 was overcome by exchanging the sixth helix domain with its counterpart in ChR2 producing Channelrhodopsin-green receiver (ChRGR) with further reform of the molecule. When the ChRGR photocurrent was measured from the expressing HEK293 cells under whole-cell patch clamp, it was preferentially activated by green light and has fast kinetics with minimal desensitization. With its kinetic advantages the use of ChRGR would enable one to inject a current into a neuron by the time course as predicted by the intensity of the shedding light (opto-current clamp). The ChRGR was also expressed in the motor cortical neurons of a mouse using Sindbis pseudovirion vectors. When an oscillatory LED light signal was applied sweeping through frequencies, it robustly evoked action potentials synchronized to the oscillatory light at 5–10 Hz in layer 5 pyramidal cells in the cortical slice. The ChRGR-expressing neurons were also driven in vivo with monitoring local field potentials (LFPs) and the time-frequency energy distribution of the light-evoked response was investigated using wavelet analysis. The oscillatory light enhanced both the in-phase and out-phase responses of LFP at the preferential frequencies of 5–10 Hz. The spread of activity was evidenced by the fact that there were many c-Fos-immunoreactive neurons that were negative for ChRGR in a region of the motor cortex.Conclusions/SignificanceThe opto-current-clamp study suggests that the depolarization of a small number of neurons wakes up the motor cortical network over some critical point to the activated state.

Exploring time variants for short-term passenger flow

Passenger flow is a fundamental element in a transportation system. It is important to explore the time variants of short-term passenger flow for transportation planning and operation. When the data are sufficiently analyzed, transportation planners not only can make better decisions, but also enhance the performance of transportation systems. The data of short-term passenger flow may be difficult to analyze due to its exotic oscillation. Hilbert–Huang transform (HHT) has recently been developed for analyzing non-linear and non-stationary data. In this paper, the proposed time variants exploration method includes two stages: empirical mode decomposition (EMD) and Hilbert spectral analysis (HSA). A real passenger flow dataset is collected from Taipei rapid transit corporation (TRTC) to investigate the viability of the proposed time variants exploration approach. The intrinsic mode functions (IMFs) extracted by EMD can represent the local characteristics of passenger flow and imply its meaningful time variants such as peak period pattern, semi-service period pattern, semi-daily pattern and daily pattern. By comparing the results of HHT with that of fast Fourier transform (FFT), it indicates that HHT can obtain the narrower frequency band, accurately capture time–frequency–energy distribution, and help to enhance the performance of transportation systems. The results show that HHT is an effective approach for exploring the time variants of short-term passenger flow in a metro system.

Control algorithms for adaptive time-frequency test signal synthesis for architectural acoustics measurements during music concerts.

A system was proposed by G. Ren et al. [158th Meeting of the ASA (2009)] to perform field acoustics measurements during ongoing music concerts. It addresses the long-standing problem of performing architectural acoustic measurements with an audience present. In this system, an adaptive time-frequency synthesis algorithm was employed to generate test signals with time-frequency energy distributions that conform to predicted “masked measurement vacancies” to ensure that the acoustic response of the test signals can be separated from the music and that the test signals are inaudible to the audience by taking advantage of auditory masking phenomena. In the present paper, approaches utilizing higher-level structure of music are exploited to reduce the number of conflicts between the test signals and the music. Three approaches are described: a music theory based probabilistic prediction algorithm, using prior knowledge of the score, and the third exploits the availability of previous recordings of the music being performed. These control algorithms are adapted to architectural acoustic measurement procedures conforming to ISO3382-1/2(2009). The proposed system achieves similar performance compare to conventional acoustic test procedures, which emit loud test signals in empty music halls.

Wavelet Analysis of Electrical Activities from Respiratory Muscles during Coughing and Sneezing in Anaesthetized Rabbits

Despite high behavioural similarity, some differences in the central neural control of the cough and sneeze reflexes have been suggested. The main aim of our study was to analyze and compare characteristics of electromyographic (EMG) activities of the respiratory muscles during these two behaviours. Data were taken from eight adult rabbits under pentobarbital anaesthesia. We compared diaphragm EMG activities in tracheobronchial cough, sneeze, and quiet breathing during inspiration. Electromyograms were read from the abdominal muscles during the expiratory phases of coughing and sneezing. Due to the non-stationary character of electromyographic signals, we used wavelet analysis to determine the time-frequency distribution of energy during the behaviours. Inspiratory durations of all above mentioned behaviours were similar. The maximum inspiratory power occurred later in sneeze than during quiet inspiration (P < 0.05). The total inspiratory power during sneeze was higher compared to that in cough (P < 0.05) and quiet inspiration (P < 0.01). Lower frequencies contributed to this increase significantly more in sneeze compared to cough (less than 287.5 Hz, P < 0.05; 287.5 Hz up to 575 Hz, P < 0.01). We found similar energy distribution for coughing and quiet inspiration. Its maximum occurred at lower frequency in quiet inspiration compared to sneezing (P < 0.01). The abdominal burst during cough was longer than that in sneezing (P < 0.001). Our results support the concept that both cough and eupnoeic inspiration are generated by similar neuronal structures. A non-specific mechanism producing expiratory activity during tracheobronchial cough and sneeze is suggested.

Comparative Analysis of Spectral Approaches to Feature Extraction for EEG-Based Motor Imagery Classification

The quantification of the spectral content of electroencephalogram (EEG) recordings has a substantial role in clinical and scientific applications. It is of particular relevance in the analysis of event-related brain oscillatory responses. This work is focused on the identification and quantification of relevant frequency patterns in motor imagery (MI) related EEGs utilized for brain-computer interface (BCI) purposes. The main objective of the paper is to perform comparative analysis of different approaches to spectral signal representation such as power spectral density (PSD) techniques, atomic decompositions, time-frequency (t-f) energy distributions, continuous and discrete wavelet approaches, from which band power features can be extracted and used in the framework of MI classification. The emphasis is on identifying discriminative properties of the feature sets representing EEG trials recorded during imagination of either left- or right-hand movement. Feature separability is quantified in the offline study using the classification accuracy (CA) rate obtained with linear and nonlinear classifiers. PSD approaches demonstrate the most consistent robustness and effectiveness in extracting the distinctive spectral patterns for accurately discriminating between left and right MI induced EEGs. This observation is based on an analysis of data recorded from eleven subjects over two sessions of BCI experiments. In addition, generalization capabilities of the classifiers reflected in their intersession performance are discussed in the paper.

Parametric adaptive time-frequency representation based on time-sheared Gabor atoms

Abstract A localized parametric time-sheared Gabor atom is derived by convolving a linear frequency modulated factor, modulating in frequency and translating in time to a dilated Gaussian function, which is the generalization of Gabor atom and is more delicate for matching most of the signals encountered in practice, especially for those having frequency dispersion characteristics. The time-frequency distribution of this atom concentrates in its time center and frequency center along energy curve, with the curve being oblique to a certain extent along the time axis. A novel parametric adaptive time-frequency distribution based on a set of the derived atoms is then proposed using a adaptive signal subspace decomposition method in frequency domain, which is non-negative time-frequency energy distribution and free of cross-term interference for multicomponent signals. The results of numerical simulation manifest the effectiveness of the approach in time-frequency representation and signal de-noising processing.

Hilbert–Huang transform based signal analysis for the characterization of gas–liquid two-phase flow

This paper reports the application of the Hilbert–Huang Transform (HHT) to the dynamic characterization of gas–liquid two-phase flow in a horizontal pipeline. A differential pressure fluctuation signal of gas–liquid two-phase flow is adaptively decomposed into Intrinsic Mode Functions (IMFs) through the use of Empirical Mode Decomposition (EMD) methods. Based on the EMD, the associated time–frequency–energy distribution, i.e., the Hilbert spectrum, is obtained for the analysis of the differential pressure fluctuation signal and subsequent identification of its corresponding energy characteristics. The relationship between the energy distribution of the signal and the flow pattern is established. In order to assess the effectiveness of the approach, the results obtained using the HHT are compared with those from Fourier analysis and wavelet based methods. It is found that the extracted energy characteristics give a good indication of the dynamic state of the gas–liquid two-phase flow and thus can be used for flow pattern recognition. The proposed method is a useful tool for the in-depth understanding and subsequent quantitative characterization of gas–liquid two-phase flow.

A New Study of the Mediterranean Outflow, Air–Sea Interactions, and Meddies Using Multisensor Data

Abstract Previous studies of the Mediterranean Sea outflow and meddies (O&M) were limited by the poor spatial and temporal resolution of conventional in situ observations as well as the confinement of satellite observations to the ocean’s surface. Accordingly, little is known about the formation and transport of meddies and the spatial and temporal variation of O&M trajectories, which are located, on average, at a depth of 1000 m. However, a new remote sensing method has been developed by the authors to observe and study the O&M through unique approaches in satellite multisensor data integration analyses. Satellite altimeter, scatterometer, infrared satellite imagery, and XBT data were used to detect and calculate the trajectories and the relative transport of the O&M (January 1993–December 2002). Two experiments [covering 1993–95: A Mediterranean Undercurrent Seeding Experiment (AMUSE) and Structures des Echanges Mer–Atmosphère, Propriétés des Hétérogénéités Océaniques: Recherche Expérimentale (SEMAPHORE)] and XBT temperature measurements were used to directly validate the method presented herein. The monthly mean features derived from floats and XBTs for multiple meddies and the results of the presented method were significantly correlated based on a statistical chi-square test. In addition, the complex singular value decomposition method was used to identify the propagating features and their phase speeds. It was found that saltier water from the Mediterranean Sea was transported into the North Atlantic Ocean over the Strait of Gibraltar in boreal spring and summer relative to boreal autumn and winter. Streamfunctions using altimetry, and time–frequency energy distributions using the Hilbert–Huang transform, were computed to evaluate the meddy interactions with the sea surface variation. Since the O&M play a significant role in carrying salty water from the Mediterranean Sea into the Atlantic, such new knowledge about their trajectories, transport, and life histories is important to the understanding of their mixing and interaction with North Atlantic water. This may lead to a better understanding of the global ocean circulation and global climate change.

Identification of Transition Velocities in Fluidized Beds Using Wavelet Analysis

Recently, the wavelet transform analysis based on the localized functions has been utilized to effectively analyze the pressure fluctuation signals. The pressure fluctuation signals can be decomposed into its approximations and details at different resolutions. By the wavelet transform, the time-frequency distribution of energy was described by the multi-resolution method. The result from the maximum energy of the approximations by wavelet transform analysis agreed with the result of the standard deviation analysis of pressure fluctuations. As seen from this study, the wavelet analysis in comparison with the standard deviation analysis, power spectral density function (PSDF), and the energy of PSDF enabled us to obtain the transition velocities, Uc and Uk, in characterizing the flow regimes of the fluidized bed.

Analysis of spontaneous electrochemical oscillations by energy distribution technique

Analysis of non-stationary electrochemical oscillations emerges utilization of the techniques allowing an observation of time evolution of their parameters such as instantaneous frequency, amplitude or frequency band. An algorithm of extraction of these parameters can be based on one of linear or quadratic time–frequency representations of oscillations record. In this paper, the authors present representatives of such transformations (Choi–Williams and Cone-shaped) originating from one of the most popular joint time–frequency energy distribution—Wigner–Ville distribution. Short introduction to the mathematics of the topic discussed is provided, then the authors present an example of application in the analysis of current oscillations of copper dissolution process.

Discriminant feature extraction using empirical probability density estimation and a local basis library

The authors previously developed the so-called local discriminant basis (LDB) method for signal and image classification problems. The original LDB method relies on differences in the time–frequency energy distribution of each class: it selects the subspaces where these energy distributions are well separated by some measure such as the Kullback–Leibler divergence. Through our experience and experiments on various datasets, however, we realized that the time–frequency energy distribution is not always the best quantity to analyze for classification. In this paper, we propose to use the discrimination of coordinates based, instead, on empirical probability densities. That is, we estimate the probability density of each class in each coordinate in the wavelet packet/local trigonometric bases after expanding signals into such bases. We then evaluate a power of discrimination of each subspace by selecting the m most discriminant coordinates in terms of the “distance” among the corresponding densities (e.g., by the Kullback–Leibler divergence among the densities). This information is then used for selecting a basis for classification. We will demonstrate the capability of this algorithm using both synthetic and real datasets.