Time-frequency Techniques Research Articles

Axisymmetric bodies with fixed and free separation: Base-pressure and near-wake fluctuations

The fluctuations of the base pressure and of the near-wake velocity are experimentally characterized for a constant-diameter axisymmetric blunt-based body with different boundary-layer thicknesses and for boat-tailed bodies with various extents of flow separation. The tests are carried out at Re=u∞D/ν=9.6×104. The analysis is performed through time-frequency techniques based on the wavelet and Hilbert transforms.Two frequencies are detected: a higher frequency, which corresponds to the shedding of hairpin vortices, and a lower one, associated with the pulsation of the recirculation region. The shedding occurs with a preferential vertical symmetry plane due to the presence of the support and the corresponding frequency becomes dominant downstream of the recirculation region and over the base contour. The lower frequency is present in the pressure signals from the central region of the base and in the adjacent velocity field. The two icdominant frequencies decrease with increasing boundary-layer thickness and significantly increase with decreasing boat-tail diameter ratio. Despite the differences in geometry and flow conditions, the lower frequency is always found equal to 1/3 of the higher one. Furthermore, a Strouhal number based on the wake width and the velocity defect at a suitable cross section downstream of the recirculation region remains practically constant.

A Jointed Signal Analysis and Convolutional Neural Network Method for Fault Diagnosis

Fault diagnosis plays a vital role in the modern industry. In this research, a joint vibration signal analysis and deep learning method for fault diagnosis is proposed. The vibration signal analysis is a well-established technique for condition monitoring, and deep learning has shown its potential in fault diagnosis. In the proposed method, the time-frequency technique, named as S transform, is applied to transfer the vibration signals to images, and then an improved convolutional neural network (CNN) is applied to classify these images. The results show the proposed method has achieved the significant improvement.

Numerical and experimental diagnosis of complex rotor system by time-frequency techniques

This paper describes the application of Discrete Wavelet Transform (DWT) to identify various types of nonlinear damage caused by, unbalance, rotor-stator contact and a breathing crack in rotating machinery. Multiple faults have been investigated based on numerical and experimental signal analysis using Fast Fourier Transform (FFT) and DWT. A four degree of freedom fully coupled model of the rotor-stator system that includes the nonlinear damage in the rotor vibrations was established using Energy principles. Existence of high system nonlinearity could not allow exhaustive discrimination of rub and crack by classical FFT. Therefore, the DWT was employed. The results provide detailed feature analysis of the fault signals. Practical vibration measurements through a data acquisition system interfaced with Rotor Kit-4 and crack simulator provided the test data. Experimental Time-Frequency analysis gave more realistic faults responses with variable faults features. Irregularity of orbit, harmonic peaks in the presence of rub and crack were unique and distinguished periodic motion from other types of motion. The presence of a crack shifted the critical speed location and exhibited sub-harmonic components, which were more prominent with rub in vibration response. The detailed decomposition signal by DWT method established inherent feature patterns that effectively discriminated the multiple faults.

Discrete Time-Frequency Signal Analysis and Processing Techniques for Non-Stationary Signals

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.

Automated and High Accuracy Out-Of-Hospital Heart Diseases Early Detection System

Background: ECG measurement and analysis being performed in-hospital normally check patients with obvious symptoms. Asymptomatic patients, for example, those with silent ischemia, paroxysmal atrial fibrillation and Brugada syndrome are very difficult to detect using in-hospital ECG system. To make matter worst, conventional ECG analysis techniques only focuses in time domain that limits the sensitivity, specificity and accuracy of the interpretation due to ECG signals non-stationary nature. Most recent researches have proposed linear joint time-frequency analysis to overcome these limitations, however, their linear methods limit their accuracy. Objective: The main objective is to enable automated and high accuracy out-of-hospital ECG analysis for early detection of heart disease. Materials & Methods: MIT-BIH ECG databases are used to test the performance of the proposed system. The data is pre-processed for amplitude normalization and frequency resampling. The pre-processed output is then fed to the non-linear joint time-frequency algorithm for analysis. The outcome of the analysis is further classified by the machine learning algorithm. Before the classification can be performed, the intelligent classifier is trained using control data that contains 52 normal and 148 patients data. After that, it is used for classifying 40 normal and 88 patients with ischaemia. The entire processes is automated inside a computer. The main disadvantage of the proposed non-linear joint time-frequency technique together with the intelligent classification is that it requires huge amount of computing system resources (big data problem). To solve this issue the system can be connected to the cloud to further enhance the performance and the accuracy of the system. Results: The analysis is performed on 421632 normal and 863282 patients ECG beats. The results obtained show that the system gives high performance of accuracy, sensitivity and specificity with values of 99.03%, 99.59% and 99.57%, respectively. Conclusions: The proposed method operates in joint time-frequency in non-linear fashion. Hence it produces more accurate interpretation compared to the conventional time domain and the more recent linear time-frequency techniques. The high accuracy together with the automated capability of the system can help detect heart problems at the early stages even before the patients pay visit to the hospital.

Biomedical Signals Analysis Using the Empirical Mode Decomposition and Parametric and non Parametric Time-Frequency Techniques

In this paper, the Empirical mode decomposition (EMD) technique is used, in a first time, to separate the artifact from the biomedical signals. The biomedical signals treated are electroencephalogram (EEG) and Electrocardiogram (ECG) for normal and abnormal patients. Analysis of EEG and ECG signals is a challenging problem due to the fact that the signals are multi-component and very non-stationary. Due to the nature of these signals, the time-frequency analysis is an important tool for representing the evolution of the frequential components of these biomedical signals over time. The time-frequency techniques used are the parametric, Periodogram and Capon methods, and non-parametric Smoothed Pseudo Wigner-Ville method. As a first step of analysis, the EMD technique is applied to eliminate the artifact from these signals after that the parametric and non-parametric time-frequency techniques are processed to the results signals to present the non-stationary multicomponent of these signals in function of time. The results show that the EMD technique associated to the Periodogram method give a good localization of the transient abnormal ECG and the energies of the EEG signals as compared to others time-frequency methods associated to the EMD technique.

Midterm Periodicity Analysis of the Mount Wilson Magnetic Indices Using the Synchrosqueezing Transform

Abstract A novel time–frequency technique, called the synchrosqueezing transform (SST), is used to investigate the midterm periodic variations of magnetic fields on the solar surface. The Magnetic Plage Strength Index (MPSI) and the Mount Wilson Sunspot Index (MWSI), measured daily by the Mount Wilson Observatory between 1970 January 19 and 2012 January 22, are selected. Short-, mid, and longer-term periodicities are represented and decomposed by the SST with hardly any mode mixing. This demonstrates that the SST is a useful time–frequency analysis technique to characterize the periodic modes of helioseismic data. Apart from the fundamental modes of the annual periodicity, ∼27 day rotational cycle and ∼11 year solar cycle, the SST reveals several midterm periodicities in the two magnetic activity indices, specifically, ∼157 days (i.e., Rieger-type periodicity), and ∼1.3 and 1.7 years. The periodic modes, with 116.4 and 276.2 day periodicity in the MPSI, 108.5 and 251.6 day periodicity in the MWSI, and 157.7 day periodicity in the two indices, are in better accord with those significant periodicities derived from the Rossby waves theoretical model. This study suggests that the modes are caused by Rossby waves. For the 1.30 and 1.71 year periodicity of the MPSI, and the 1.33 and 1.67 year periodicity of the MWSI, our analysis infers that they are related to those periodicities with the same timescale in the interior of the Sun and in the high atmospheric layers.

Period Estimation of an Almost Periodic Signal Using Persistent Homology With Application to Respiratory Rate Measurement

Time-frequency techniques have difficulties in yielding efficient online algorithms for almost periodic signals. We describe a new topological method to find the period of signals that have an almost periodic waveform. Proposed method is applied to signals received from a pyro-electric infrared sensor array for the online estimation of the respiratory rate (RR) of a person. Time-varying analog signals captured from the sensors exhibit an almost periodic behavior due to repetitive nature of breathing activity. Sensor signals are transformed into two-dimensional point clouds with a technique that allows preserving the period information. Features, which represent the harmonic structures in the sensor signals, are detected by applying persistent homology and the RR is estimated based on the persistence barcode of the first Betti number. Experiments have been carried out to show that our method makes reliable estimates of the RR.

Structural health monitoring under random flow loading

The aim of the work is the analysis of fluid-structure systems, when excited by a flow consisting of an incompressible potential fluid with embedded vortexes. In fact, in many problems of relevant application interests, the monitoring and the potentially detection of structural damages in structures undergoing loads in operative conditions is important. The present method tries to identify simultaneously the load characteristics together with the structural damage. The flow is characterized by the average velocity of the fluid conveying the vortexes and by the position and intensity of the conveyed vortexes. A method for the identification of these flow parameters, based on vibration signals measured at the elastic fluid-structure interface, is proposed. Vibration signals are numerically generated and then processed with time-frequency techniques, such as the ensemble empirical mode decomposition and the normalized Hilbert transform. The sensitivity of the algorithm to the measurement position and to sing...

A Comparison of Techniques for Fault Detection in Inverter-Fed Induction Motors in Transient Regime

Fault detection in induction motors operating in non-stationary regimes has become a need in today’s industry. Most of the works published deal with line-fed motors. Nevertheless, the number of inverter-fed induction motors has significantly increased in recent years. Therefore, several fault detection techniques have been proposed lately for this type of motors, based mainly on an adequate input signal processing to obtain fault signatures in the time-frequency domain. In this paper, a comparison of time-frequency techniques applied to fault detection in inverter-fed induction motors in a transient state is presented. For that purpose, the techniques are applied to two current signals acquired from two induction motors with two types of faults: bar breakage and mixed eccentricity. The paper shows the particularities and special difficulties of diagnosing under this type of feeding, reviewing the works related to each technique. The strengths and weaknesses of these techniques are discussed with the goal of providing a criterion for its application in an industrial environment and guidance for future developments in this field.

Time-frequency techniques for modal parameters identification of civil structures from acquired dynamic signals

A major trust of modal parameters identification (MPI) research in recent years has been based on using artificial and natural vibrations sources because vibration measurements can reflect the true dynamic behavior of a structure while analytical prediction methods, such as finite element models, are less accurate due to the numerous structural idealizations and uncertainties involved in the simulations. This paper presents a state-of-the-art review of the time-frequency techniques for modal parameters identification of civil structures from acquired dynamic signals as well as the factors that affect the estimation accuracy. Further, the latest signal processing techniques proposed since 2012 are also reviewed. These algorithms are worth being researched for MPI of large real-life structures because they provide good time-frequency resolution and noise-immunity.

Dynamic analysis of gearbox behaviour in milling process: Non-stationary operations

Dynamic behaviour of gearbox transmitting power to milling tool in a milling process application is considered in this paper. The gearbox is subjected to variable cutting torque induced by the milling operation. This variability will lead to fluctuating speed. The dynamic behaviour of the system should be investigated according to this non-stationary operating condition. To achieve this objective, a simple model of motor-gearbox-milling tool system is developed. The influence of variable cutting torque on driving motor speed is taken into account. The gearmesh function which describes the meshing phenomena is modified according to this specific operating condition. Simulations of the dynamic behaviour of the gearbox show a simultaneous frequency and amplitude modulation. These modulations are highlighted using time frequency representation which is necessary to implement so that it is possible to achieve a correct diagnosis of the transmission. Simulations in presence of tooth crack defect confirmed the necessity to implement time frequency techniques to characterize time varying systems.

Radar detection of high-energy cosmic rays in non-Gaussian background using a time-frequency technique

Cosmic rays are the highest-energy observable particles in the universe. Their study opens a new frontier for scientists to better understand the nature of the universe. This paper reports our study of a bistatic radar approach that is being developed for remote sensing of cosmic-ray induced air showers. In this context, we propose a robust detection technique based on time-frequency domain for the received radar echoes. These echoes are modeled as linear-downward chirp signals, characterized by very short sweep periods, low energies, and corrupted by non-stationary and non-Gaussian background noise. In addition, the related parameters of the received echoes are variable within some expected ranges, determined by the physical parameters of the air showers. In this paper, we explore the performance of the proposed detection method through an extensive theoretical analysis. We derive formulae for probability of the correct detection, as well as false-alarm rate. Numerical simulations and experimental results that corroborate our analysis are also presented.

Development of Ventricular Fibrillation Diagnosis Method Based on Neuro-fuzzy Systems for Automated External Defibrillators

The aim of this study is to develop an embedded method for automatic diagnosis of ventricular fibrillation (VF) using a neuro-fuzzy system embedded in an automated external defibrillator (AED). To diagnose VF using AEDs, we use the neural network with weighted fuzzy membership functions (NEWFM), a wavelet transform (WT), a sequential increment method (SIM), and phase-space reconstruction (PSR) in order to classify normal sinus rhythm (NSR) and VF of electrocardiogram (ECG) episodes. This study has the following key points. The first contribution is the extraction of peaks from ECG episodes by the use of the WT and SIM by a time–frequency technique. The second contribution is that NSR and VF are distinguished by means of three-dimensional (3D) PSR based on a 3D graphic model. The third contribution is the identification of feature differences between NSR and VF by the use of graphical characteristics of weighted fuzzy membership functions (WFMs) supported by the NEWFM. The final contribution is the development of a neuro-fuzzy system for automatic diagnosis of VF using the WFMs embedded in the AED. The following four preprocessing steps are implemented to extract features from ECG episodes. In the first step, the WT is used for multi-scale representation and analysis and wavelet coefficients are then generated from the ECG episodes. In the second step, the SIM is used to extract peaks from the wavelet coefficients. In the third step, successive peaks are plotted in a 3D phase-space diagram by performing 3D PSR. In the final step, the distance between the origin (0, 0, 0) and the successive peaks plotted in a 3D phase-space diagram is calculated; then, 20 features are extracted from the calculated distances using statistical methods, including frequency distributions and their variability. The 20 extracted features are applied as inputs to the NEWFM, and the result is that the classification accuracy of the NEWFM is 100 %.

Vital-Sign Extraction Using Bootstrap-Based Generalized Warblet Transform in Heart and Respiration Monitoring Radar System

In biomedical Doppler radar applications, the return signal is a nonlinear frequency-modulation (NLFM) random process whose phase conveys heart and respiration vital-sign information. These signatures modulate the phase of the signal as two oscillating components with frequencies less than a few hertz. Due to the nonstationary nature of these signals, their analysis by 1-D techniques, temporal and spectral, may not be very useful, and time-frequency techniques may be incapable of accurately extracting their instantaneous frequency (IF) trajectory. In this paper, we present a bootstrap-based generalized warblet transform (GWT) signal processing method. The presented signal processing tool is a parametric method that has a kernel with Fourier-series components. The coefficients of the kernel are estimated by an iteration procedure that converges to the IF of the radar signal. We show theoretically and experimentally that the bootstrap-based GWT can extract the amplitude and frequency of the two vital-sign components at a range of 3 m in the face of low signal-to-noise ratio and in the presence of phase noise and body motion artifacts, achieving an accuracy that is potentially better than conventional methods can provide.

Detection and Parameter Extraction of Low Probability of Intercept Radar Signals using the Hough Transform

Digital intercept receivers are currently moving away from Fourier-based analysis and towards classical time-frequency analysis techniques, such as the Wigner-Ville distribution, Choi-Williams distribution, spectrogram, and scalogram, for the purpose of analyzing low probability of intercept radar signals (e.g. triangular modulated frequency modulated continuous wave and frequency shift keying). Although these classical time-frequency techniques are an improvement over the Fourier-based analysis, they still suffer from a lack of readability, due to cross-term interference, and a mediocre performance in low SNR environments. This lack of readability may lead to inaccurate detection and parameter extraction of these radar signals. In this paper, the use of the Hough transform, because of its ability to suppresscross-term interference, separate signals from cross-terms, and perform well in the presence of noise, is proposed as an improved signal analysis technique. With these qualities, the Hough transform has the potential to produce better readability and consequently, more accurate signal detection and parameter extraction metrics.

Improved Signal Characterization via Empirical Mode Decomposition to Enhance in-line Quality Monitoring

The machine tool industry is facing the need to increase the sensorization of production systems to meet evolving market demands. This leads to the increasing interest for in-process monitoring tools that allow a fast detection of faults and unnatural process behaviours during the process itself. Nevertheless, the analysis of sensor signals implies several challenges. One major challenge consists of the complexity of signal patterns, which often exhibit a multiscale content, i.e., a superimposition of both stationary and non-stationary fluctuations on different time-frequency levels. Among time-frequency techniques, Empirical Mode Decomposition (EMD) is a powerful method to decompose any signal into its embedded oscillatory modes in a fully data-driven way, without any ex-ante basis selection. Because of this, it might be used effectively for automated monitoring and diagnosis of manufacturing processes. Unfortunately, it usually yields an over-decomposition, with single oscillation modes that can be split into more than one scale (this effect is also known as “mode mixing”). The literature lacks effective strategies to automatically synthetize the decomposition into a minimal number of physically relevant and interpretable components. This paper proposes a novel approach to achieve a synthetic decomposition of complex signals through the EMD procedure. A new criterion is proposed to group together multiple components associated to a common time-frequency pattern, aimed at summarizing the information content into a minimal number of modes, which may be easier to interpret. A real case study in waterjet cutting is presented, to demonstrate the benefits and the critical issues of the proposed approach.

Chapter I: The Time-Frequency Approach: Essence and Terminology

This chapter starts the introductory tutorial that constitutes Part I of the book. It provides the basic insights needed to understand time-frequency (t, f) fundamental principles, techniques, methods, and algorithms; it also provides the background material required to do the (t, f) toolbox tutorial in Chapter 17. Time-frequency signal processing (TFSP) is a set of signal processing (SP) methods, techniques, and algorithms in which the two natural variables time (t) and frequency (f) are used concurrently. This contrasts with traditional SP methods in which either time t or frequency f is used exclusively and independently of the other. TFSP has become a standard digital signal processing (DSP) technology with applications found in all traditional areas of DSP and beyond. This chapter presents the essential concepts on which the field of TFSP is built. It uses simple language, describes the most important concepts in qualitative terms and illustrates them with examples. An understanding of these basic (t, f) concepts and terminology is a prerequisite for comprehending, mastering, and using the more specialized methods reported in the other chapters.The choice of the contents, style, and organization of this chapter is motivated by the desire toprovide a nonspecialist with:• a bridge or stepping stone to the key fundamental (t, f) concepts presented in Chapter 1;• a step-by-step approach to conceptually grasp the complexities of the field and be able to representa signal in a 2D (t, f) space;• a framework that relates general and generic TFSP principles to those more specific methods andtechniques applicable in typical situations;• a presentation of TFSP using examples that are familiar to students, engineers, and researchers inrelated fields;• an insight into key characteristic features that are (t, f) specific, such as instantaneous frequency(IF), spectral delay (SD), and instantaneous bandwidth.Finally, a brief overview of the following chapters is provided at the end of this chapter.

High-resolution Spectral-analysis for Fundamental Frequency Estimation of High-rise Buildings subjected to Earthquakes

Accurate estimation of the fundamental frequency of civil structures is crucial for many applications; in particular, this estimation becomes more important when it helps to avoid or minimize human, economic, and structural damages as the case of the design and analysis of high-rise buildings subjected to earthquakes. Although many techniques have been proposed for this task, several aspects such as accuracy, noise immunity, and suitable time-frequency resolution have not been adequately addressed. In this work, the short-time multiple signal classification (ST-MUSIC), a high-resolution spectral-analysis technique, is proposed to estimate the fundamental frequency of high-rise buildings using vibration signals. The proposal is validated and tested using synthetic signals and real measurements. In the latter, the fundamental frequency of a high-rise building, 1:20 scale model, is estimated before-, during-, and after-seismic excitation through the analysis of the generated vibrations. For comparison purposes, the short-time Fourier transform (STFT), a conventional time-frequency technique, is also used. The obtained results show a high accuracy and noise immunity in the analysis, which makes the proposal a suitable and reliable tool for this task.

Fault detection in rotor bearing systems using time frequency techniques

Faults such as misalignment, rotor cracks and rotor to stator rub can exist collectively in rotor bearing systems. It is an important task for rotor dynamic personnel to monitor and detect faults in rotating machinery. In this paper, the rotor startup vibrations are utilized to solve the fault identification problem using time frequency techniques. Numerical simulations are performed through finite element analysis of the rotor bearing system with individual and collective combinations of faults as mentioned above. Three signal processing tools namely Short Time Fourier Transform (STFT), Continuous Wavelet Transform (CWT) and Hilbert Huang Transform (HHT) are compared to evaluate their detection performance. The effect of addition of Signal to Noise ratio (SNR) on three time frequency techniques is presented. The comparative study is focused towards detecting the least possible level of the fault induced and the computational time consumed. The computation time consumed by HHT is very less when compared to CWT based diagnosis. However, for noisy data CWT is more preferred over HHT. To identify fault characteristics using wavelets a procedure to adjust resolution of the mother wavelet is presented in detail. Experiments are conducted to obtain the run-up data of a rotor bearing setup for diagnosis of shaft misalignment and rotor stator rubbing faults.