AM-FM Components Research Articles

Power quality disturbance detection based on IEWT

With the continuous development of distributed generation, power quality problems are more complex. In order to ensure that the power quality of the active distribution network meets the requirements of users, it is of great significance to accurately obtain the power quality disturbance parameters. For the problem that the traditional empirical wavelet transform needs to manually select the number of frequency bands when analyzing unknown power quality disturbances, this paper proposes an improved empirical wavelet transform (IEWT) algorithm. The algorithm uses the Piecewise Cubic Hermite Interpolation (PCHIP) method and the improvement of the transition region to achieve adaptive frequency band division and noise interference reduction, and different amplitude (AM) and pitch (FM) components can be obtained. Then the Normalized Direct Quadrature (NDQ) algorithm and Singular Value Decomposition (SVD) algorithm are used to extract frequency, amplitude and time parameters of the AM-FM components. Simulation and experimental results show that the power quality disturbance parameters extracted by the proposed method are more accurate and less affected by noise.

A local modulation signal bispectrum for multiple amplitude and frequency modulation demodulation in gearbox fault diagnosis

This paper proposes a novel multiple amplitude modulation and frequency modulation (AM–FM) demodulation method based on local modulation signal bispectrum (LMSB), which can demodulate the fault features of different components from the gearbox signal with multi-mesh frequency bands and multi-modulation components. Firstly, the collected measurement signal is decomposed into a series of sub-band signals, and the generated sub-band signals are demodulated by modulation signal bispectrum (MSB), which realizes the simultaneous demodulation of multi-mesh frequency bands and multi-modulation components. Subsequently, each sub-band signal resulting from MSB demodulation is synchronously averaged to generate the LMSB, which removes random noise and interference frequencies from the sub-band signals. Finally, the periodic modulation intensity (PMI) is utilized to evaluate the ability of the LMSB to demodulate multi-component signals with AM–FM components. The effectiveness of LMSB in processing multi-component signals with AM–FM components is demonstrated by numerical simulation signals and experimental analysis. Analysis results demonstrate the superiority of LMSB in multiple AM–FM demodulation compared with MSB, envelope analysis (EA) and Teager energy operator (TEO). This research provides a novel perspective for gearbox fault detection.

High-order synchroextracting transform for characterizing signals with strong AM-FM features and its application in mechanical fault diagnosis

In this paper, a novel time–frequency analysis (TFA) technique termed High-order Synchroextracting Transform (HSET), is proposed to better characterize the changing dynamics of multi-component signals with strong AM-FM components. Synchroextracting Transform (SET) is a TFA method has been developed recently. As a post-processing technology, unlike the parameterized TFA methods that requires different demodulation operators to be designed according to different types of signals, SET can generate high-quality time–frequency representation (TFR) only on the basis of short-time Fourier transform (STFT). However, since the core of SET is based on the assumption that the signal is composed of pure harmonics, SET cannot accurately extract the time-varying characteristics of signal with strong AM-FM components. To construct a method to well characterize the time-varying laws of strong AM-FM signals, this paper uses high-order Taylor expansion to estimate the time varying laws of the signal to obtain a more accurate frequency estimation operator, which we call high-order Synchroextracting operator (HSEO), and then HSET can be constructed through Dirichlet function to generate TFR with high TF resolution. Good reconstruction quality can be achieved through the inverse transformation of HSET while signal reconstruction operation can be completed concisely. In addition, this paper applies HSET to the processing of the measured vibration signals and feature extraction of gravitational-wave (GW) signal. Compared with other advanced TFA technologies, the effectiveness and competitiveness of the proposed method can be demonstrated.

A Novel Wave Decomposition for Oscillatory Signals

Oscillatory systems arise in the different science fields. Complex mathematical formulations with differential equations have been proposed to model the dynamics of these systems. While they have the advantage of having a direct physiological meaning, they are not useful in practice as a result of the parameter adjustment complexity and the presence of noise. In this paper, a novel decomposition approach in AM-FM components, competing with Fourier and other decompositions is presented. Several interesting theoretical properties are derived including the ordinary differential equations describing the signal. Furthermore, the usefulness in real practice is demonstrated to analyse signals associated to neuron synapses and by addressing other questions in neuroscience.

Vibration signal fusion using improved empirical wavelet transform and variance contribution rate for weak fault detection of hydraulic pumps

This paper presents a novel vibration signal fusion algorithm using improved empirical wavelet transform and variance contribution rate to fuse three-channel vibration signals for weak fault detection of hydraulic pumps. Firstly, empirical wavelet transform (EWT) is utilized to decompose the three-channel signals into several AM–FM components. Then in accordance with the statistical characteristics of these component data, variance contribution rate is defined to measure the weight of component data points. A series of fusion coefficients are computed and assigned to every component point. Finally, these component points are fused into one single signal and Hilbert transform is conducted to demodulate the fault characteristic frequency for weak fault detection. Moreover, to address the issue of improper EWT spectrum segmentation, we introduce Density-Based Spatial Clustering of Applications with Noise (DBSCAN) to improve EWT in the full space and the frequencies corresponding to outlier points are taken as the boundaries of spectrum segmentation. Therefore, the number of boundaries is more reasonable and the AM–FM components are more consistent with inherent components existing in the vibration signals of pumps. Results of simulation and experiment analysis demonstrate the good performance of the exhibited fusion algorithm in weak fault detection of hydraulic pumps.

Fault feature extraction method based on EWT-SMF and MF-DFA for valve fault of reciprocating compressor

According to the nonlinearity and nonstationarity characteristics of reciprocating compressor vibration signal, a fault feature extraction method of reciprocating compressor based on the empirical wavelet transform (EWT) and state-adaptive morphological filtering (SMF) is proposed. Firstly, an adaptive empirical wavelet transform was used to divide the Fourier spectrum by constructing a scale-space curve, and an appropriate orthogonal wavelet filter bank was constructed to extract the AM-FM component with a tightly-supported Fourier spectrum. Then according to the impact characteristic of the reciprocating compressor vibration signal, the morphological structural elements were constructed with the characteristics of the signal to perform state-adaptive morphological filtering on the partitioned modal functions. Finally, the MF-DFA method of the modal function was quantitatively analyzed and the fault identification was performed. By analyzing the experimental data, it can be shown that the method can effectively identify the fault type of reciprocating compressor valve.

The Instantaneous Spectrum: A General Framework for Time-Frequency Analysis

This paper is a contribution to the old problem of representing a signal in the coordinates of time and frequency. We review the fundamental Hilbert transform relationship in systems analysis and argue that the dual relationship assumed in signal analysis, i.e. spectral single-sidedness is not necessarily justifiable. Therefore, we abandon the analytic signal and utilize a carefully parameterized signal model composed of a superposition of complex, AM–FM components that enables rigorous definition of instantaneous amplitude and instantaneous frequency. We then propose the instantaneous spectrum (IS) and prove that it exactly localizes signal components in an instantaneous bandwidth sense. The relation of the IS to traditional time-frequency distributions is discussed and comparative examples are provided. It is shown that under certain conditions the IS specializes to the Fourier spectrum and properties of the IS, similar to standard Fourier transform properties, are given.

An adaptive thresholding technique for QRS-complex detection in ECG signal based on empirical wavelet transform

Since the QRS complex varies with different cardiac health conditions, therefore efficient and automatic detection of QRS complex and is essential for reliable health condition monitoring. In this work an empirical wavelet transform (EWT)-based algorithm has been used for accurate detection of QRS complex. EWT is one of the adaptive time-frequency data analysis method. In the first step, this method decomposes the ECG signal into set of the AM-FM components called modes. Later, adaptive thresholding is applied to its last mode to detection of QRS-complexes. Last mode is nearly the same as that of the original signal if we look at it visually. The proposed algorithm has been tested on the standard. The performance of proposed method has been measured on the basis of statistical parameters and gives the positive predictivity 99.82%, sensitivity 99.93%, and error rate 0.24%. The proposed method is also tested on self-recorded dataset and achieves 100% sensitivity and positive predictivity and zero error rates.

Analysis of the Hilbert Spectrum for Text-Dependent Speaker Verification

This work explores the utility of the Hilbert Spectrum (HS) of the speech signal, constructed from its AM-FM components, or Intrinsic Mode Functions (IMFs), in characterizing speakers for the task of Text-Dependent Speaker Verification (TDSV). The IMFs of the speech signal are obtained using a non-linear and non-stationary data analysis technique called Modified Empirical Mode Decomposition (MEMD). The HS, which is a representation of the instantaneous frequencies and instantaneous energies of the IMFs, is processed in short time-segments to generate features, which are then experimented for the task of TDSV. Two databases – the RSR2015 and the IITG – are utilized in this work, for validating the experimental findings. The performances of the TDSV system are evaluated for the individual features, and their combinations with the 39-dimensional Mel Frequency Cepstral Coefficients (MFCCs). To assess the practical utility of the features, they are tested not only for clean speech, but also for speech corrupted by low-frequency (Babble) noise, and environmental noise. The experiments reveal that the features obtained from the HS, in combination with the MFCCs, enhances the performance of the TDSV system. Further, the features extracted are effective at very low dimensions. Moreover, the features extracted from the HS are found to be consistently more effective than cepstral/energy feature obtained from the raw IMFs, under noisy conditions.

An optimum allocation sampling based feature extraction scheme for distinguishing seizure and seizure-free EEG signals.

Epileptic seizure is the common neurological disorder, which is generally identified by electroencephalogram (EEG) signals. In this paper, a new feature extraction methodology based on optimum allocation sampling (OAS) and Teager energy operator (TEO) is proposed for detection of seizure EEG signals. The OAS scheme selects the finite length homogeneous sequence from non-homogeneous recorded EEG signal. The trend of selected sequence by OAS is still non-linear, which is analyzed by non-linear operator TEO. The TEO convert non-linear but homogenous EEG sequence into amplitude-frequency modulated (AM-FM) components. The statistical measures of AM-FM components used as input features to least squares support vector machine classifier for classification of seizure and seizure-free EEG signals. The proposed methodology is evaluated on a benchmark epileptic seizure EEG database. The experimental results demonstrate that the proposed scheme has capability to effectively distinguish seizure and seizure-free EEG signals.

Adaptive multimode signal reconstruction from time-frequency representations.

This paper discusses methods for the adaptive reconstruction of the modes of multicomponent AM–FM signals by their time–frequency (TF) representation derived from their short-time Fourier transform (STFT). The STFT of an AM–FM component or mode spreads the information relative to that mode in the TF plane around curves commonly called ridges. An alternative view is to consider a mode as a particular TF domain termed a basin of attraction. Here we discuss two new approaches to mode reconstruction. The first determines the ridge associated with a mode by considering the location where the direction of the reassignment vector sharply changes, the technique used to determine the basin of attraction being directly derived from that used for ridge extraction. A second uses the fact that the STFT of a signal is fully characterized by its zeros (and then the particular distribution of these zeros for Gaussian noise) to deduce an algorithm to compute the mode domains. For both techniques, mode reconstruction is then carried out by simply integrating the information inside these basins of attraction or domains.

Research on Speech Enhancement Algorithm Based on EMD in Noisy Environments

This paper presents a new technique for speech enhancement in a noisy environment based on the empirical mode decomposition (EMD) algorithm and spectral subtraction. With the EMD, the noise speech signals can be decomposed into a sum of the band-limited function called intrinsic mode functions (IMFs), which is a zero-mean AM-FM component. Then spectral subtraction of the IMF components with noise can be used to eliminate the effect of the noise for speech enhancement. Experimental results demonstrate the advantage of using the proposed simultaneous detection and estimation approach with the proposed algorithm, which facilitate suppression of transient noise with a controlled level of speech distortion.

An unconstrained optimization approach to empirical mode decomposition

Empirical mode decomposition (EMD) is an adaptive (data-driven) method to decompose non-linear and non-stationary signals into AM-FM components. Despite its well-known usefulness, one of the major EMD drawbacks is its lack of mathematical foundation, being defined as an algorithm output. In this paper we present an alternative formulation for the EMD method, based on unconstrained optimization. Unlike previous optimization-based efforts, our approach is simple, with an analytic solution, and its algorithm can be easily implemented. By making no explicit use of envelopes to find the local mean, possible inherent problems of the original EMD formulation (such as the under- and overshoot) are avoided. Classical EMD experiments with artificial signals overlapped in both time and frequency are revisited, and comparisons with other optimization-based approaches to EMD are made, showing advantages for our proposal both in recovering known components and computational times. A voice signal is decomposed by our method evidencing some advantages in comparison with traditional EMD and noise-assisted versions. The new method here introduced catches most flavors of the original EMD but with a more solid mathematical framework, which could lead to explore analytical properties of this technique.

Speech Enhancement Based on EMD and Wavelet Threshold in Noisy Environments

Speech enhancement is crucial for speech recognition accuracy. How to eliminate the effect of the noise constitutes a challenging problem in speech processing. This paper presents a new technique for speech enhancement in a noisy environment based on the empirical mode decomposition (EMD) algorithm and wavelet threshold. With the EMD, the noise speech signals can be decomposed into a sum of the band-limited function called intrinsic mode functions (IMFs), which is a zero-mean AM-FM component. Then wavelet threshold of the IMF components can be used to eliminate the effect of the noise for speech enhancement. Experimental results show that the proposed speech enhancement by de-noising algorithm is possible to achieve an excellent balance between suppresses noise effectively and preserves as many target characteristics of original signal as possible.

On the behavior of EMD and MEMD in presence of symmetric $\alpha$-stable noise

Empirical Mode Decomposition (EMD) and its extended versions such as Multivariate EMD (MEMD) are data-driven techniques that represent nonlinear and non-stationary data as a sum of a finite zero-mean AM-FM components referred to as Intrinsic Mode Functions (IMFs). The aim of this work is to analyze the behavior of EMD and MEMD in stochastic situations involving non-Gaussian noise, more precisely, we examine the case of Symmetric α-Stable (SαS) noise. We report numerical experiments supporting the claim that both EMD and MEMD act, essentially, as filter banks on each channel of the input signal in the case of SαS noise. Reported results show that, unlike EMD, MEMD has the ability to align common frequency modes across multiple channels in same index IMFs. Further, simulations show that, contrary to EMD, for MEMD the stability property is well satisfied for the modes of lower indices and this result is exploited for the estimation of the stability index of the SαS input signal.

Time-Varying Bandpass Filter Based on Assisted Signals for AM-FM Signal Separation: A Revisit

In this paper, a new signal separation method mainly for AM-FM components blended in noises is revisited based on the new derived time-varying bandpass filter (TVBF), which can separate the AM-FM components whose frequencies have overlapped regions in Fourier transform domain and even have crossed points in time-frequency distribution (TFD) so that the proposed TVBF seems like a “soft-cutter” that cuts the frequency domain to snaky slices with rational physical sense. First, the Hilbert transform based decomposition is analyzed for the analysis of nonstationary signals. Based on the above analysis, a hypothesis under a certain condition that AM-FM components can be separated successfully based on Hilbert transform and the assisted signal is developed, which is supported by representative experiments and theoretical performance analyses on a error bound that is shown to be proportional to the product of frequency width and noise variance. The assisted signals are derived from the refined time-frequency distributions via image fusion and least squares optimization. Experiments on man-made and real-life data verify the efficiency of the proposed method and demonstrate the advantages over the other main methods.

Speech Endpoint Detection Based on EMD and Spectral Entropy in Noisy Environments

Accurate endpoint detection is crucial for speech recognition accuracy. A novel approach that finds robust features for endpoint detection based on the empirical mode decomposition (EMD) algorithm and spectral entropy in a noisy environment is proposed. With the EMD, the noise signals can be decomposed into different numbers of sub-signals called intrinsic mode functions (IMFs), which is a zero-mean AM-FM component. Then spectral entropy can be used to extract the desired feature for IMF components. In order to show the effectiveness of the proposed method, we present examples showing that the new measure is more effective than traditional measures. The experiments show that the proposed algorithm can suppress different noise types with different SNR, and the algorithm is robust in the real signal tests.

Fast-varying AM–FM components extraction based on an adaptive STFT

A new method is proposed in this article for fast-varying AM-FM components extraction. There are two prominent characteristics in this method. Firstly, a new evaluation method for the instantaneous bandwidth is established, which is based on the instantaneous slope of the time-frequency curve with respect to the AM-FM component. Secondly, a new adaptive STFT algorithm is established, which adjusts the window width by adapting to the instantaneous bandwidth at each frequency position. In order to extract multiple AM-FM components from a signal, the width of the reconstruction area is required to be determined efficiently to avoid the interference caused by adjacent components. Simulations are given in the end, which show that the proposed method has good performance for fast-varying AM-FM components extraction from noisy signals.

Time–frequency signal analysis for gearbox fault diagnosis using a generalized synchrosqueezing transform

The vibration data, especially those collected during the system run-up and run-down periods, contain rich information for gearbox condition monitoring. Time–frequency (TF) signal analysis is an effective tool to detect gearbox faults under varying shaft speed. However, the feature of the amplitude modulated–frequency modulated (AM–FM) gearbox fault signal usually cannot be directly extracted from the blurred time–frequency representation (TFR) caused by the time-varying frequency and noisy multicomponent measurement. As such, we propose to use a generalized synchrosqueezing transform (GST)-based TF method to detect and diagnose gearbox faults. With this method, the original vibration signal is first mapped into another analytical signal to facilitate synchrosqueezing of the TF picture. A time-scale domain restoration process is then applied to recover the instantaneous frequency profile with concentrated TFR. The gearbox fault, if any, can then be detected by observing the presence of the meshing frequency and sideband components in the TFR. The faulty gear can be identified via frequency relation analysis of AM–FM components. The proposed method is evaluated using both simulated and experimental gearbox vibration signals. The results show that the proposed approach is effective for gearbox condition monitoring.

Teager-Huang Analysis Applied to Sonar Target Recognition

� Abstract—In this paper, a new approach for target recognition based on the Empirical mode decomposition (EMD) algorithm of Huang et al. (11) and the energy tracking operator of Teager (13)-(14) is introduced. The conjunction of these two methods is called Teager- Huang analysis. This approach is well suited for nonstationary signals analysis. The impulse response (IR) of target is first band pass filtered into subsignals (components) called Intrinsic mode functions (IMFs) with well defined Instantaneous frequency (IF) and Instantaneous amplitude (IA). Each IMF is a zero-mean AM-FM component. In second step, the energy of each IMF is tracked using the Teager energy operator (TEO). IF and IA, useful to describe the time-varying characteristics of the signal, are estimated using the Energy separation algorithm (ESA) algorithm of Maragos et al .(16)- (17). In third step, a set of features such as skewness and kurtosis are extracted from the IF, IA and IMF energy functions. The Teager- Huang analysis is tested on set of synthetic IRs of Sonar targets with different physical characteristics (density, velocity, shape,… ). PCA is first applied to features to discriminate between manufactured and natural targets. The manufactured patterns are classified into spheres and cylinders. One hundred percent of correct recognition is achieved with twenty three echoes where sixteen IRs, used for training, are free noise and seven IRs, used for testing phase, are corrupted with white Gaussian noise. Keywords—Target recognition, Empirical mode decomposition, Teager-Kaiser energy operator, Features extraction.