Multiple-view time–frequency distribution based on the empirical mode decomposition

Detection of Subtle Damage in Structures through Smart Signal Reconstruction

This paper considers the blind separation of nonstationary sources in the underdetermined case, when there are more sources than sensors. A general framework for this problem is to work on sources that are sparse in some signal representation domain. Recently, two methods have been proposed with respect to the time-frequency (TF) domain. The first uses quadratic time-frequency distributions (TFDs) and a clustering approach, and the second uses a linear TFD. Both of these methods assume that the sources are disjoint in the TF domain; i.e., there is, at most, one source present at a point in the TF domain. In this paper, we relax this assumption by allowing the sources to be TF-nondisjoint to a certain extent. In particular, the number of sources present at a point is strictly less than the number of sensors. The separation can still be achieved due to subspace projection that allows us to identify the sources present and to estimate their corresponding TFD values. In particular, we propose two subspace-based algorithms for TF-nondisjoint sources: one uses quadratic TFDs and the other a linear TFD. Another contribution of this paper is a new estimation procedure for the mixing matrix. Finally, then numerical performance of the proposed methods are provided highlighting their performance gain compared to existing ones

A relationship between Intrinsic Mode Functions (IMFs), derived from the Empirical Mode Decomposition (EMD), and the slow-flow model of a no nlinear dynamical system has been exploited in the development of the Slow Flow Model Identification (SFMI) method for strongly nonlinear systems, in which the physical parameters of such systems are identified from experimental data. Both the slow flows and IMFs provide the means to expand a general multicomponent signal in terms of a series of simpler, dominant, monocomponent signals. The slow flows are obtained analytically, for example through application of the method of complexification and averaging (CxA), which transforms the equations of motion into a set of approximate equations in amplitude and phase for each modeled frequency component. In contrast, the EMD characterizes a signal through the envelope and phase of its elemental components, the IMFs. Thus, between nonlinear transitions, the equations derived using the CxA method govern the amplitude and phase of the modeled IMFs. Application of SFMI has, until now, been limited to low-dimensional systems subjected to impulsive excitation. Herein, the method is extended to identificatio n of a planar rigid airfoil

This paper presents a novel method of detecting and classifying the power system faults of voltage sags based on Empirical Mode Decomposition (EMD). A technique employed for analyzing power system fault data in terms of voltage sags is required. Also, provides information about the underlying event i.e. the fault type. EMD is to method which decomposes a non stationary signal into mono component and symmetric component signals called Intrinsic Mode Functions (IMFs). Further the Hilbert Transform (HT) of IMF provides magnitude and phase angle information. The characteristic features of the first three IMFs of each phase are used as inputs to the classifier Probabilistic Neural Network (PNN) for identification of fault type. Four types of shunt faults are taken for classification. A comparison is also made with wavelet Transform (WT). Simulation results show that the classification accuracy is better for EMD, which proves that the method is efficient in classifying the faults.

Wigner-Ville distribution (WVD) is a joint time-frequency analysis for non-stationary signals. The main difficulty with the WVD is its bilinear characteristic which leads to cross terms in the time-frequency domain. Recently the technique of empirical mode decomposition (EMD) has been proposed as a novel tool for the analysis of nonlinear and non-stationary data. In this paper, key elements of the numerical procedure and principles of EMD are introduced. Wigner-Ville distribution based on EMD is applied in the research of the faults diagnosis of the bearing. Firstly, the original time series data is decomposed in intrinsic mode functions (IMFs) using the empirical mode decomposition. Then, the Wigner-Ville distribution for selected IMF is calculated. The signal simulation and experimental results show that Wigner-Ville distribution based on EMD can not only successfully eliminate the cross terms but also effectively diagnosis the faults of the bearing.

Sleep disorders has a vital effect on mental depression and many other diseases of human body. Diagnosing the sleep disorder in an early curable stage may help to provide better treatment and save the life. The EEG (Electroencephalogram) signal is one of the most uses bio signal for capturing brain activities to detect and diagnosis the sleep disorders. Empirical mode decomposition (EMD) is an efficient time-frequency data analysis technique for diagnosing disease by analyzing EEG signal. However, it is a challenging issue to select the optimal intrinsic mode functions (IMFs) of Empirical mode decomposition (EMD) for extracting discriminant properties of EEG signals to diagnosis the sleep disorder. From this point of view, this paper presents a model to select optimal IMF of EMD for diagnosing the sleep disorder using EEG brain signal. In this proposed model, EMD is applied to decompose and analyze EEG signal for extracting biomarker/feature of sleep disorders. During the EMD decomposition process, different levels of IMF are extracted and features, i.e., Shannon Entropy, Spectral Entropy, Standard deviation, Skewness and Kurtosis are calculated from those IMFs for detecting the sleep disorders. In identification process, the multiclass support vector machine (MC-SVM) classification algorithm is used and sleep disorders are classified based on trained knowledge. Finally, the performance of proposed model is evaluated for different IMFs of EMD and find the optimal IMF for sleep disorder diagnosis. For evaluating the proposed model, a benchmark dataset including 4 types of data such as Apnea, REM, PLM and healthy subjects are used in experiment. According to the experimental result, the proposed model achieves the optimal classification performance for IMF 8, i.e., 93.24% average classification accuracy.

Using filter bank property to simplify the calculations of Empirical Mode Decomposition

In this paper, we propose a novel method for the detection of road accidents by analyzing audio streams for road surveillance application. In the last decade, due to the increase in a number of people and transportation vehicles, traffic accidents have become one of a major public issue worldwide. The vast number of injuries and death due to road traffic accident reveals the story of a global crisis of road safety. A total of 52,160 road traffic accidents (RTA), 1130 injuries and 85 fatalities were registered during the year 2000, in the state of Qatar. An increase in the number of transportation vehicles around cities has risen the need for more security and safety in public environments. The most obvious reason for a person's death during accidents is the absence or prolong response time of the first aid facility, which is due to the delay in the information of the accident being reached to the police, hospital or ambulance team. In the last couple of years, several surveillance systems have been proposed based on image and video processing for automatically detecting road accidents and car crashes to ensure a quick response by emergency teams. However, in some situations such as adverse weather conditions or cluttered environments, the visual information is not sufficient enough, whereas analyzing the audio tracks can significantly improve the overall reliability of surveillance systems. In this paper we propose a novel method that automatically identifies hazardous situations such as tire skidding and car crashes in presence of background noises, by analyzing the audio streams. Previous studies show that methods for the detection, estimation, and classification of nonstationary signals can be enhanced by utilizing the time-frequency (TF) characteristics of such signals. The TF-based techniques have been proved to outperform classical techniques based on either time or frequency domains, in analyzing real-life nonstationary signals. Time-frequency distributions (TFDs) give additional information about signals that cannot be extracted from either the time domain or frequency domain representations, i.e. the instantaneous frequency of the components of a signal. In order to utilize this extra information provided by TF domain representation, the proposed approach extracts TF image features from quadratic time-frequency distributions (QTFDs), for the detection of audio anomalies. The extended modified-B distribution (EMBD) is utilized to transform a 1-dimensional audio signal into 2-dimensional TF representation which is interpreted as an image. The image descriptors based features are then extracted from the TF representation to classify visually the audio signals into background or abnormal activity patterns in the TF domain. The proposed features are based on Haralick's texture features extracted from the TF representation of audio signals considered and processed as a textured image. These features are used to characterize and hence classify audio signals into M classes. This research study demonstrates that a TF image pattern recognition approach offers significant advantages over standard signal classification methods that utilize either t-domain only or f-domain only features. The proposed method has been experimentally validated on a large open source database of sounds, including several kinds of background noise. The events to be recognized are superimposed on different background sounds of roads and traffic jam. The obtained results are compared with a recent study, utilizing the same large and complex data set of audio signals, and the same experimental setup. The overall classification results confirm the superior performance of the proposed approach with accuracy improvement up to 6%.

Primal sketch performs an important role in early vision. In this paper, we propose a novel method to obtain the primal sketch of natural images by integrating empirical mode decomposition (EMD) techniques and image gradient. 2D EMD approach can decompose the image into a finite number of intrinsic mode functions (IMF), and each one represents the original image in a different scale, with the 1st IMF representing the finest scale. To enhance the information represented by the IMF, we multiply the 1st IMF by the image gradient. This enhanced IMF highlights intensity changes in the image. By linking all the maximal points in the enhanced IMF, we obtain a primal sketch of the original image. Compared with the existed primal sketch extraction methods, our method is fully driven by the image data, and it needs neither to choose filters nor to learn the image bases. The experiment results show that our method is fast and effective.

Signal is a non-linear and non- stationary signal, the empirical mode decomposition (EMD) can decompose the signal into several intrinsic mode functions(IMF), the IMF can reflect the characteristic in frequency changing of logging data along depth, IMF curves of different steps might reveal cycle characteristics of different scale, which are in correspondence with geological cycles o different scales, so that different scale sequences might be detected clearly from IMF curves. Empirical mode decomposition method is used to demarcat stratigraphic sequence and stratigraphic correlation in this paper ,the result show that EMD method can better show the internal vibration of logging signal and reflect the characteristics of the stratigraphic sequence ,and EMD method can provide technical support for stratigraphic correlation.

In this paper, a statistical analysis of electroencephalogram (EEG) signals is carried out in the empirical mode decomposition (EMD) domain using a publicly available benchmark EEG database. First, the intrinsic mode functions (IMF) are extracted from the EEG signals in the EMD domain. Next, the investigation was carried whether the Bessel k-form (BKF) probability density function (pdf) can appropriately model the IMFs extracted in EMD domain of the EEG signals. It is shown that on an average, the BKF pdf is a suitable prior to model the first five IMFs extracted from various types of EEG recordings. After that, it is shown that the BKF parameters can distinguish among the EEG signals at those five IMF levels quite well. The analysis is further confirmed through the p-values obtained by one way analysis of variance (ANOVA). Thus, the BKF parameters in the EMD domain may be used to characterize EEG signals and help the electroencephalographers in developing fast and effective classifiers for seizure seizure detection.

Various faults inevitably occur in mechanical systems and may result in unexpected failures. Hence, fault detection is critical to reduce unscheduled downtime and costly breakdowns. Empirical mode decomposition (EMD) is an adaptive time-frequency domain signal processing method, potentially suitable for nonstationary and/or nonlinear processes. However, the EMD method suffers from several problems such as mode mixing, defined as intrinsic mode functions (IMFs) with incorrect scales. In this paper, an ensemble noise-reconstructed EMD method is proposed to ameliorate the mode mixing problem and denoise IMFs for enhancing fault signatures. The proposed method defines the IMF components as an ensemble mean of EMD trials, where each trial is obtained by sifting signals that have been reconstructed using the estimated noise present in the measured signal. Unlike traditional denoising methods, the noise inherent in the input data is reconstructed and used to reduce the background noise. Furthermore, the reconstructed noise helps to project different scales of the signal onto their corresponding IMFs, instrumental in alleviating the mode mixing problem. Two critical issues concerned in the method, i.e., the noise estimation strategy and the number of EMD trials required for denoising are discussed. Furthermore, a comprehensive noise-assisted EMD method is proposed, which includes the proposed method and ensemble EMD (EEMD). Numerical simulations and experimental case studies on accelerometer data collected from an industrial shaving process are used to demonstrate and validate the proposed method. Results show that the proposed method can both detect impending faults and isolate multiple faults. Hence, the proposed method can act as a promising tool for mechanical fault detection.

The Empirical Mode Decomposition (EMD) is a signal analysis method that separates multi-component signals into single oscillatory modes called intrinsic mode functions (IMFs). These IMFs can generally be associated to a physical meaning of the process from which the signal is obtained. When the phenomena of mode mixing occurs, as a result of the EMD sifting process, the IMFs may lose their physical meaning hindering the interpretation of the results of the analysis. Previous research presents a rigorous mathematical analysis that shows how EMD behaves in the case of a composite two-components signal, explaining the roots of the mode mixing problem. Also, the frequency-amplitude region within which a good separation is achieved with EMD is well identified and discussed. However, a solution that offers good IMF separation when components reside within the same octave is not yet available. In this paper, a method to separate spectral components that reside within the same octave, is presented. This method is based on reversing the conditions by which mode mixing occurs presented in the paper One or Two frequencies? The Empirical Mode Decomposition Answers, in [3]. Numerical experiments with signals containing spectral components within the same octave shows the effective separation of modes that EMD can perform after this principle is applied. This separation technique has potential application for identifying the cause of different oscillatory modes with spectral proximity present in the smart grid.

Time-frequency analysis is of necessity for wrist pulse signal due to its complexity, among which, empirical mode decomposition (EMD) algorithm and its improved noise-assisted versions (such as ensemble EMD, noise-assisted multivariate EMD (NA-MEMD) and very recently median EMD) are deemed to be the most representative ones. In this study, we provide an in-depth evaluation of these well-established noise-assisted EMD algorithms in computational pulse analysis for the first time. In particular, we compare the performance of the different algorithms systematically and quantitatively based on objective quantitative criteria: number and central frequency of intrinsic mode function (IMF) components, total orthogonality index and mode mixing. Rather than using synthetic signals with visual inspection in most existing literature, the wrist pulse signals used in the evaluation are real recorded samples acquired from both healthy and patient subjects. Through extensive experiments, we found that: 1) Advanced EMD algorithm that has the best performance in other areas may not be the most suitable method for pulse signal analysis, which indicates its high dependence on the type of signal to be analyzed; 2) Adding noise can significantly improve algorithm performance, but tends to produce physiologically not relevant components, which however are usually neglected throughout the intelligent pulse diagnosis literature. Therefore, excluding redundant components and then extracting features is expected to improve performance further. Together, currently NA-MEMD achieves a better performance consistently, potential to become a powerful tool for computational pulse analysis, which in itself have not been applied in wrist pulse analysis before. We believe our works can bring up a new perspective to application of EMD-like algorithms in computational pulse analysis/diagnosis with effective information and guidance. Additionally, considering the similarity between physiological signals, especially such as photoplethysmogram/electrocardiogram, our research can be extended to wearable health monitoring technologies, including smart watches and fitness trackers, and their potential future applications, such as in heart rate estimation and evaluate various cardiovascular-related diseases. The present study underscored the necessity of evaluation noise-assisted EMDs or other adaptive decomposition algorithms based on real recorded signals with more objective measures. Especially, caution the possible redundant components that are introduced.

Complex nonlinear and nonstationary signals can be adaptively analyzed by the Hilbert–Huang transform through empirical mode decomposition and the Hilbert transform to generate the instantaneous energy. The instantaneous energy was able to display the local characteristics of the signals and had good time–frequency analysis capability, it is therefore widely applied to the analysis of vibration signals in the field of gear fault diagnosis. However, only a few extracted intrinsic mode functions through empirical mode decomposition can reflect fault feature or closely related to the faults but others are irrelevant. Therefore, the fault feature of the instantaneous energy for all intrinsic mode functions was not obvious and the accuracy of diagnosis was low. Aimed at solving this problem, a fault leading rate evaluation algorithm was proposed that can select those intrinsic mode functions, which reflect fault features (it was called the dominant intrinsic mode function) from all intrinsic mode functions. In the paper, this algorithm was applied to gear fault feature extraction. By calculating the instantaneous energy of the dominant intrinsic mode function the method could accurately extract gear fault feature and improve the accuracy of diagnosis. Both simulated signals and experimental signals of a Klingelnberg bevel gear were analyzed to verify the effectiveness and correctness of the algorithm.