An empirical signal separation algorithm for multicomponent signals based on linear time-frequency analysis

Empirical mode decomposition (EMD) is a powerful tool for the non-stationary and nonlinear signal analysis and has attracted considerable attention recently. However, one of primary problems existing in the EMD is the mode mixing, which makes the physical meaning of decomposition results obscure. The ensemble EMD (EEMD) is presented to alleviate the shortcoming. The EEMD is a noise-added method and can extract the components with truly physical meaning from the signal. Firstly, a simulation signal is used to test the performance of the EEMD; compared with the EMD, the EEMD illustrates the superiority over the EMD. Then, the fault diagnosis method based on the EEMD is applied to diagnose the faults of the gearbox with multiple faults and successfully extracts the multiple faults information from the collected signal. The results show that the fault diagnosis method based on the EEMD is a promising method for the fault diagnosis of gearboxes.

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 primary objective of this paper is to develop output only modal identification and structural damage detection. Identification of multi-degree of freedom (MDOF) linear time invariant (LTI) and linear time variant (LTV—due to damage) systems based on Time-frequency (TF) techniques—such as short-time Fourier transform (STFT), empirical mode decomposition (EMD), and wavelets—is proposed. STFT, EMD, and wavelet methods developed to date are reviewed in detail. In addition a Hilbert transform (HT) approach to determine frequency and damping is also presented. In this paper, STFT, EMD, HT and wavelet techniques are developed for decomposition of free vibration response of MDOF systems into their modal components. Once the modal components are obtained, each one is processed using Hilbert transform to obtain the modal frequency and damping ratios. In addition, the ratio of modal components at different degrees of freedom facilitate determination of mode shape. In cases with output only modal identification using ambient/random response, the random decrement technique is used to obtain free vibration response. The advantage of TF techniques is that they are signal based; hence, can be used for output only modal identification. A three degree of freedom 1:10 scale model test structure is used to validate the proposed output only modal identification techniques based on STFT, EMD, HT, wavelets. Both measured free vibration and forced vibration (white noise) response are considered. The secondary objective of this paper is to show the relative ease with which the TF techniques can be used for modal identification and their potential for real world applications where output only identification is essential. Recorded ambient vibration data processed using techniques such as the random decrement technique can be used to obtain the free vibration response, so that further processing using TF based modal identification can be performed.

A method of and a system for speech enhancement consists of Hilbert spectrum and wavelet packet analysis is studied. We implement ISA to separate speech and interfering signals from single mixture and wavelet packet based soft-thresholding algorithm to enhance the quality of target speech. The mixed signal is projected onto time-frequency (TF) space using empirical mode decomposition (EMD) based Hilbert spectrum (HS). Then a finite set of independent basis vectors are derived from the TF space by applying principal component analysis (PCA) and independent component analysis (ICA) sequentially. The vectors are clustered using hierarchical clustering to represent the independent subspaces corresponding to the component sources in the mixture. However, the speech quality of the separation algorithm is not enough and contains some residual noises. Therefore, in the next stage, the target speech is enhanced using wavelet packet decomposition (WPD) method where the speech activity is monitored by updating noise or unwanted signals statistics. The mode mixing issue of traditional EMD is addressed and resolved using ensemble EMD. The proposed algorithm is also tested using short-time Fourier transform (STFT) based spectrogram method. The simulation results show a noticeable performance in the field of audio source separation and speech enhancement.

Knock is one of the major constraints to improve the performance and thermal efficiency of spark ignition (SI) engines. It can also result in severe permanent engine damage under certain operating conditions. Based on the ensemble empirical mode decomposition (EEMD), this paper proposes a new approach to determine the knock characteristics in SI engines. By adding a uniformly distributed and finite white Gaussian noise, the EEMD can preserve signal continuity in different scales and therefore alleviates the mode-mixing problem occurring in the classic empirical mode decomposition (EMD). The feasibilities of applying the EEMD to detect the knock signatures of a test SI engine via the pressure signal measured from combustion chamber and the vibration signal measured from cylinder head are investigated. Experimental results show that the EEMD-based method is able to detect the knock signatures from both the pressure signal and vibration signal, even in initial stage of knock. Finally, by comparing the application results with those obtained by short-time Fourier transform (STFT), Wigner–Ville distribution (WVD) and discrete wavelet transform (DWT), the superiority of the EEMD method in determining knock characteristics is demonstrated.

Empirical mode decomposition (EMD) is a fully unsupervised and data-driven approach to the class of nonlinear and non-stationary signals. A new approach is proposed, namely PHEEMD, to image analysis by using Peano–Hilbert space filling curves to transform 2D data (image) into 1D data, followed by ensemble EMD (EEMD) analysis, i.e., a more robust realization of EMD based on white noise excitation. Tests’ results have shown that PHEEMD exhibits a substantially reduced computational cost compared to other 2D-EMD approaches, preserving, simultaneously, the information lying at the EMD domain; hence, new perspectives for its use in low computational power devices, like portable applications, are feasible.

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.

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%.

Adaptive short-time Fourier transform and synchrosqueezing transform for non-stationary signal separation

Empirical mode decomposition (EMD) is an adaptive, data-driven algorithm that decomposes any time series into its intrinsic modes of oscillation, which can then be used in the calculation of the instantaneous phase and frequency. Ensemble EMD (EEMD), where the final EMD is estimated by averaging numerous EMD runs with the addition of noise, was an advancement introduced by Wu and Huang (2008) to try increasing the robustness of EMD and alleviate some of the common problems of EMD such as mode mixing. In this work, we test the performance of EEMD as opposed to normal EMD, with emphasis on the effect of selecting different stopping criteria and noise levels. Our results indicate that EEMD, in addition to slightly increasing the accuracy of the EMD output, substantially increases the robustness of the results and the confidence in the decomposition.

A building, a central location of human activities, is equipped with many devices that consume a lot of electricity. Therefore, predicting the energy consumption of a building is essential because it helps the building management to make better energy management policies. Thus, predicting energy consumption of a building is very important, and this study proposes a forecasting framework for energy consumption of a building. The proposed framework combines a decomposition method with a forecasting algorithm. This study applies two decomposition algorithms, namely the empirical mode decomposition and wavelet transformation. Furthermore, it applies the long short term memory algorithm to predict energy consumption. This study applies the proposed framework to predict the energy consumption of 20 buildings. The buildings are located in different time zones and have different functionalities. The experiment results reveal that the best forecasting algorithm applies the long short term memory algorithm with the empirical mode decomposition. In addition to the proposed framework, this research also provides the recommendation of the forecasting model for each building. The result of this study could enrich the study about the building energy forecasting approach. The proposed framework also can be applied to the real case of electricity consumption.

A Hilbert–Huang transform (HHT) is a time–frequency technique and has been widely applied to analyzing vibration signals in the field of fault diagnosis of rotating machinery. It analyzes the vibration signals using intrinsic mode functions (IMFs) extracted using empirical mode decomposition (EMD). However, EMD sometimes cannot reveal the signal characteristics accurately because of the problem of mode mixing. Ensemble empirical mode decomposition (EEMD) was developed recently to alleviate this problem. The IMFs generated by EEMD have different sensitivity to faults. Some IMFs are sensitive and closely related to the faults but others are irrelevant. To enhance the accuracy of the HHT in fault diagnosis of rotating machinery, an improved HHT based on EEMD and sensitive IMFs is proposed in this paper. Simulated signals demonstrate the effectiveness of the improved HHT in diagnosing the faults of rotating machinery. Finally, the improved HHT is applied to diagnosing an early rub-impact fault of a heavy oil catalytic cracking machine set, and the application results prove that the improved HHT is superior to the HHT based on all IMFs of EMD.

Emotion feature extraction is the key to speech emotional recognition. And ensemble empirical mode decomposition(EEMD) is a newly developed method aimed at eliminating emotion mode mixing present in the original empirical mode decomposition(EMD). To evaluate the performance of this new method, this paper investigates the effect of a parameters pertinent to EEMD: speech emotional envelope. Firstly, a speaker emotional envelope features extraction based on EEMD is proposed in the paper. Using the piecewise power function in speech emotional envelope has a better effect in emotional identification. At the same time, the proposed technique has been utilized for classification of fo ur kinds of emotional(angry, happy, sad and neutral) speech signals. Emotional intrinsic mode functions(IMFe) are obtained by empirical mode decomposition on emotional speech signals, the fast fourier transform(FFT) of each intrinsic mode function is extracte d as the emotional feature coefficient which is used in speaker emotional identification applying by vector quantization. MATLAB is used to ca lculate the characteristic of emotional speech signals using empirical mode decomposition (EEMD). We obtain an emotional envelope by transforming the IMFe of emotional speech signals, and obtain a new method of emotion recognition according to different emotional envelop feature vectors. The results indicate the proposed method works well in speaker emotional identification.

Wind turbine blades are the most critical components of wind turbines. Full-scale blade fatigue testing is required to verify that the blades possess the strength and service life specified in the design. Unfortunately, the test must be run for a long time period. This problem led the blade testing laboratories to accelerate fatigue testing time. To achieve the objective, this thesis proposes two novel methods called STFT- and WT-based fatigue damage part extracting methods which are based on short-time Fourier transform (STFT) and wavelet transform (WT), respectively. For WT, different wavelet functions which are Morl, Meyr, Dmey, Mexh and DB30 are studied.
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\nAn aerodynamic computer code, HAWTsimulator, based on blade element momentum theory has been developed. This code is used to generate the sets of aerodynamic loads acting along the span of a ‘SERI-8 wind turbine blade’ in the range of wind speed from cut-in to cut-out. SERI-8 blades are installed on 65 kW wind turbines. Each set of aerodynamic loads is applied on the finite element model of the SERI-8 blade in structural software (ANSYS) to generate a plot of von Mises stress at the critical point on the blade versus wind speed. By relating this relationship to the wind speed data, the stress-time history at the critical point on the SERI-8 blade can be generated. It has the same sampling rate and length as the wind speed data.
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\nA concept of applying accumulative power spectral density (AccPSD) distribution with time to identify fatigue damage events contained in the stress-time history has been introduced in this thesis. For STFT, AccPSD is the sum of power spectral density (PSD) of each frequency band at each time interval in the spectrogram. For WT, AccPSD is the sum of PSD of wavelet coefficients of each scale at each time interval in the scalogram. It has been found that the locations of AccPSD spikes imply where the fatigue damage events are. Based on an appropriate AccPSD level called a cutoff level, the fatigue damage events can be identified at time location of the stress-time history.
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\nA fatigue computer code, HAWTfatigue, based on stress-life approach and Miner’s linear cumulative damage rule has been developed. Basically, the code is used for evaluating the fatigue damage and service lifetime of horizontal axis wind turbine blade. In addition, the author has implemented STFT- and WT-based fatigue damage part extracting methods into the code. Fatigue damage parts are extracted from the stress time history and they are concatenated to form the edited stress-time history. The effectiveness of STFT- and WTbased algorithms is performed by comparing the reduction in length and the difference in fatigue damage per repetition of the edited stress-time histories generated by STFT and WT to those of the edited stress-time history generated by an existing method, Time Correlated Fatigue Damage (TCFD) used by commercial software.
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\nThe findings of this research project are as follows:
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\n1. The comparison of the reduction in length of the edited stress-time histories generated by TCFD, STFT and WT indicates that WT with the Mexh wavelet has the maximum reduction of 20.77% in length with respect to the original length, followed by Meyr (20.24%), Dmey (19.70%), Morl (19.66%), DB30 (19.19%), STFT (15.38%), and TCFD (10.18%), respectively.
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\n2. The comparison of the retained fatigue damage per repetition in the edited stress-time histories generated by TCFD, STFT and WT indicates that TCFD has the retained fatigue damage per repetition less than the original fatigue damage per repetition by 0.076%, followed by Mexh (0.068%), DB30 (0.063%), STFT (0.045%), Meyr (0.032%), Dmey (0.014%), and Morl (0.013%), respectively.
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\n3. Both comparison of reduction in length and comparison in the retained fatigue damage per repetition of the edited stress-time histories suggest that WT is the best method for extracting fatigue damage parts from the given stress-time history. It has also been indicated that not only do STFT and WT improve accuracy of fatigue damage per repetition retained in the edited stress-time histories, but also they provide the length of the edited stress-time histories shorter than TCFD does. Thus, STFT and WT are useful methods for performing accelerated fatigue tests.
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\n4. It has been found that STFT is controlled by two main factors which are window size and cutoff level. Also, WT is controlled by three main factors which are wavelet decomposition level, cutoff level and wavelet type.
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\nTo conclude, the edited stress-time history can be used by blade testing laboratories to accelerate fatigue testing time. STFT- and WT-based fatigue damage part extracting methods proposed in this thesis are suggested as alternative methods in accelerating fatigue testing time, especially for the field of wind turbine engineering.

This paper presents the methodology, properties and processing of the time-frequency techniques for non-stationary signals, which are frequently used in biomedical, communication and image processing fields. Two classes of time-frequency analysis techniques are chosen for this study. One is short-time Fourier Transform (STFT) technique from linear time-frequency analysis and the other is the Wigner-Ville Distribution (WVD) from Quadratic time-frequency analysis technique. Algorithms for both these techniques are developed and implemented on non-stationary signals for spectrum analysis. The results of this study revealed that the WVD and its classes are most suitable for time-frequency analysis.