Cyclostationary Analysis Research Articles

Infogram performance analysis and its enhancement for bearings diagnostics in presence of non-Gaussian noise

Local damage detection in rotating machines is a well-established field of study, however, some new challenges have recently appeared. They are associated with the presence of strongly non-Gaussian noise related to harsh environments or technological processes. Searching for cyclic impulses in the presence of noncyclic, high amplitude impulses becomes difficult. Cyclostationary analysis may be the answer to such a problem. However, it does not recognize the impulsive nature of the signal. Thus, the concept of infogram, a tool that investigates diagnostic information both in the time and frequency domain, seems ideally suited for such an application. It uses the negentropy to measure the impulsiveness of the squared envelope (SE infogram) and the periodicity in the spectral domain (SES infogram) to finally get the combined information on impulsiveness and periodicity as the average of the SE and SES infograms, called average infogram or just infogram. The purpose of this study is to examine the performance of the infogram for several benchmark signals i.e. Gaussian noise, signals with cyclic impulses and non-cyclic impulses and the mixture of all of them. Finally, the enhancement of the classical infogram is proposed. It is shown that replacing simple averaging of partial infograms with the logarithmic mean, geometric mean, or normalizing of partial infograms, improves the robustness of the classical infogram in the presence of strongly non-Gaussian noise. As an illustration, two real signals are considered. The first one isthe vibration signal from the ore crusher used in the raw materials’ industry, for mechanical fragmentation of rock oversized pieces. The second one is an acoustic signal from bearing installed in an idler in a belt conveyor. In both cases the impulses occurring in this signal (from the crushing process or interaction between a moving belt joint and coating of idler) make the classical diagnosis very difficult. The proposed modified infogram can deal with such a problem successfully.

Condition Monitoring in a Wind Turbine Planetary Gearbox Using Sensor Fusion and Convolutional Neural Network

To meet the requirements of reducing operations and maintenance costs of wind turbines, we present a machine learning framework for early damage detection in gearboxes based on the cyclostationary analysis of sensor data. The application focus is the condition monitoring of wind turbine gearboxes under varying load scenarios, in particular turbulent wind conditions. Faults in the rotating components in the gearbox can leave their signature in the vibrations that can be measured by accelerometers. We analyze data stemming from a simulated vibration response of a 5MW multibody wind turbine model in a healthy and damaged scenarios and under different wind conditions. With cyclostationary analysis applied on acquired sensor data, we generate cyclic spectral coherence maps that highlight signatures related to the fault damage and enable its identification. These maps are used to train convolutional neural networks that then identify faults, including those of small magnitude, in test data with a high accuracy. Benchmark test cases inspired by an NREL study are tested and faults successfully detected.

Parametric simulator of cyclic and non-cyclic impulsive vibration signals for diagnostic research applications

In recent years cyclostationary analysis of vibration signals is considered to be one of the most potent approaches for diagnostics of machines with rotating components. However, it is a subject of an extensive research towards extending its robustness due to its significant inefficiency in the presence of non-cyclic impulsive components in measured data. This problem is especially visible in datasets measured on machines such as ore crushers, where the high-energy impacts are a natural phenomenon. Unfortunately, due to practical inaccessibility, real-life datasets necessary to properly study this problem are extremely difficult to obtain. To address this issue, the authors propose an easy to use simulator of impulsive components. It covers both cyclic components that can describe various types of fault signatures, and non-cyclic ones that can represent impacts occurring naturally due to the nature of machine operation. Simulated signals have been compared with real ones to ensure a high similarity degree, which in turn guarantees a relatively high level of realism.

Improved cyclostationary analysis method based on TKEO and its application on the faults diagnosis of induction motors

Cyclostationary analysis has been strongly recognized as an effective demodulation tool in identifying fault features of rotating machinery based on vibration signature analysis. This study improves two current mature cyclostationary approaches, cyclic modulation spectrum (CMS) and fast spectral correlation (Fast-SC), combined with the novel frequency-domain application of Teager Kaiser energy operator (TKEO). They can enhance fault feature identification with the lower computational burden. Firstly, the raw vibration signal is transformed into the time–frequency domain through the short-time Fourier transform (STFT) to realize the conversion of the multi-carrier signal to a multiple signal-carrier signal. Secondly, the TKEO is utilized to enhance the fault feature by taking full advantage of demodulating the mono-component. Finally, the spectral coherence and enhanced envelope spectrum (EES) are calculated to effectively exhibit fault features. The superiority of the proposed methods is successfully validated by the simulation study and diagnosing the broken rotor bar (BRB) and bearing outer race faults of induction motors (IMs) under various operating conditions.

Comparative study between objective and subjective methods for identifying the gravity of single and multiple gear defects in case of noisy signals

This paper aims to compare two approaches for the identification of gear defects in a very noisy environment. The first one, called subjective, is based on sound perception using paired comparison test; the second, objective, is based on vibration analysis using three advanced signal processing methods. The first part of the paper determines a correlation between the sound perception obtained by the listeners and the scalar indicators calculated for different gravities of gear defects (simple and/or double). The perception test was carried out on sounds obtained directly by converting the measured vibratory signals. The study is conducted in a two-dimensional proximity space. The results obtained allowed the determination of mathematical models that correlate between the objective and subjective aspects and highlight the important relationship between the vibratory indicators and the distances between the sounds in the perceptual space. The correlation ratios obtained for the first dimension (DIM1) prove to be very significant. In the second part of the paper, the same signals are processed by three methods, known to be powerful tools in vibratory signal processing, namely Optimized Wavelet Multi-Resolution Analysis (WMRA), cyclostationary analysis, and a hybrid approach based on an improved version of the Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (ICEEMDAN) and multivariate denoising by wavelets and PCA (Principal Component Analysis). For all three methods considered, a demodulation approach is performed to obtain an envelope spectrum as a final result. In the case of very noisy signals, the subjective method allows a better assessment of the evolution of the severity of the gear defects compared to the objective methods used. In our opinion, this is due to the high sensitivity of the human ear to identify the existence of a defect and to assess its degree of severity, far better than the most sophisticated objective signal processing methods, which remain limited in the case of very noisy signals.

Methods of Hidden Periodicity Discovering for Gearbox Fault Detection.

It is shown that the models of gear pair vibration, proposed in literature, are particular cases of the bi-periodically correlated random processes (BPCRPs), which describe its stochastic recurrence with two periods. The possibility of vibration and analysis within the framework of BPCRP approximation, in the form of periodically correlated random processes (PCRPs), is grounded and the implementation of vibration processing procedures using PCRP techniques, which are worked out by the authors, is given. Searching for hidden periodicities of the first and the second orders was considered as the main issue of this approach. The estimation of the non-stationary period (basic frequency) allowed us to carry out a detailed analysis of the deterministic part, the covariance structure of the stochastic part, and to form, using their parameters, the sensitive indicators for fault detection. The results of the processing of the wind turbine gearbox vibration signals are presented. The amplitude spectra of the deterministic oscillations and the time changes of the stochastic part power for different fault stages are analyzed. The most efficient indicators, which are formed using the amplitude spectra for practical applications, are proposed. The presented approach was compared with known in literature cyclostationary analysis and envelope techniques, and its advantages are shown.

Alternative Measures of Dependence for Cyclic Behaviour Identification in the Signal with Impulsive Noise—Application to the Local Damage Detection

The local damage detection procedures in rotating machinery are based on the analysis of the impulsiveness and/or the periodicity of disturbances corresponding to the failure. Recent findings related to non-Gaussian vibration signals showed some drawbacks of the classical methods. If the signal is noisy and it is strongly non-Gaussian (heavy-tailed), searching for impulsive behvaior is pointless as both informative and non-informative components are transients. The classical dependence measure (autocorrelation) is not suitable for non-Gaussian signals. Thus, there is a need for new methods for hidden periodicity detection. In this paper, an attempt will be made to use alternative measures of dependence used in time series analysis that are less known in the condition monitoring (CM) community. They are proposed as alternatives for the classical autocovariance function used in the cyclostationary analysis. The methodology of the auto-similarity map calculation is presented as well as a procedure for a “quality” or “informativeness” assessment of the map is proposed. In the most complex case, the most resistant to heavy-tailed noise turned out the proposed techniques based on Kendall, Spearman and Quadrant autocorrelations. Whereas in the case of the local fault disturbed by the Gaussian noise, the most efficient proved to be a commonly-known approach based on Pearson autocorrelation. The ideas proposed in the paper are supported by simulation signals and real vibrations from heavy-duty machines.

Identifying ENSO-related interannual and decadal variability on terrestrial water storage

We apply two statistical techniques to satellite measurements to identify a relationship between terrestrial water storage (TWS) and El Niño-Southern Oscillation (ENSO). First, we modified and used the least-squares regression of a previous study using longer records. Second, we applied a cyclostationary empirical orthogonal function analysis (CSEOF). Although the CSEOF technique is distinct from the least-squares regression in that it does not consider proxies, each method produces two modes (decadal and interannual), showing consistency with each technique in spatial pattern and its evolution amplitudes. We also compared the results obtained by the two methods for thirty watersheds, of which five watersheds were compared with previous studies. The combination of the two modes explains the total variance in most watersheds showing the role that interannual and decadal ENSO-related signals in understanding terrestrial water storage variability. The results show that the decadal mode, along with the interannual mode, also plays an important role in describing the local TWS.

Cyclostationary Analysis of Fan Noise Influenced by an Inflow Control Device

Acoustic data measured in a fan test facility with and without an inflow control device (ICD) over the inlet were analyzed using the cyclostationary analysis technique, which separates the total power into a rotor-locked and a fluctuating component. Measurements were taken with an inlet mode detection ring upstream of the rotor and with far-field microphones for configurations with subsonic and with supersonic fan blade tip speeds. The ICD reduces the fluctuating component and stabilizes the rotor-locked component of the frequency spectrum at the blade passing frequency and its harmonics in the way that the mode amplitudes of the Tyler–Sofrin modes increase, whereas neighboring mode orders are suppressed. The mode distribution and intermode coherence in the inlet are also changed, which changes the far-field directivity when an ICD is installed. It is demonstrated that cyclostationary analysis is a powerful tool to investigate the acoustic effect of an ICD on turbofan noise, revealing more details about the temporal and spatial structures of the generated sound field than a classical spectral analysis.

A Review on Vibration-Based Fault Diagnosis Techniques for Wind Turbine Gearboxes Operating Under Nonstationary Conditions

Numerous studies on vibration-based techniques for fault diagnosis of wind turbine gearboxes operating under nonstationary conditions have been reported. In spite, a review on vibration-based condition monitoring and fault diagnosis techniques for gearboxes of wind turbines operating under nonstationary conditions is unavailable. Thus, the objective of this review is to discuss filtering, decomposition, entropy, and cyclostationary analysis techniques, as well as summarizing the remaining issues. This review will discuss various vibration-based diagnostic approaches developed for wind turbine gearboxes under nonstationary conditions, including both simulation and experimental approaches. Studies on dynamic models of gear systems and advanced signal-processing techniques developed for nonstationary conditions are reviewed. Additionally, the importance of multi-sensor and cointegration based approaches is discussed, and intelligent classification methods that have been used to distinguish healthy and faulty gear systems are also reviewed. Finally, the remaining research challenges are outlined.

Cyclostationary Analysis of Irregular Statistical Cyclicity and Extraction of Rotating Speed for Bearing Diagnostics With Speed Fluctuations

Mechanical fault diagnosis under nonstationary conditions is one of the hotspots in the condition monitoring research field, presenting still several difficulties. Vibration signals of faulty bearings exhibit second-order cyclostationarity when rotating speed and load are constant. Due to the time-varying rotating speed, the original cyclostationary signal becomes a special type of nonstationary signal. Considering the superiority of cyclostationary analysis in bearing fault diagnosis, it is interesting to extend the cyclostationary paradigm to make it suitable for particular signals that show irregular statistical cyclicity (ISC). Modeling bearing vibrations with speed fluctuation, however, is a controversial topic, which further sparked a debate on how to process bearing signals with ISC. Therefore, in this article, a detailed comparison of two signal models is made, the pace irregularity and the time warping, to illustrate the advantages and disadvantages of the modeling ideas. Based on these models, two novel tacholess diagnostic methods, the synchronization-sequence method and the dewarping method, are proposed for bearing diagnosis in nonstationary operations. By identifying the impact points with the same cyclic feature, the synchronization-sequence method shifts the impulse patches to the same interval, so the signal becomes cyclostationary. Using another strategy, the dewarping method recovers the regular statistical property by maximizing the squared modulus of the cyclic autocorrelation of specific feature points. The results show that both models can help diagnose local bearing faults, and the classical cyclostationary diagnostic tools become more powerful when extending to nonstationary operation conditions. In addition, the speed fluctuation curve can also be estimated by the two methods without using a tachometer. The characteristic of the proposed methods for speed estimation is that only the second-order cyclostationary information is utilized. Besides, the methods are robust to noise, so they are suitable for processing bearing data in the incipient failure stage. Numerical simulations and experimental data analyses corroborate the theoretical results.

Casing vibration signal characteristic extractions and applications in rolling bearing

A method of combining autocorrelation function with cyclostationary theory and Hilbert envelope analysis is proposed and applied to extract characteristic frequency of rolling bearing. Meanwhile, mean power ratio is calculated and used to identify the fault types of aero-engine rolling bearing based on single-channel casing vibration signal. To verify the effectiveness of proposed method, a comparing analysis is carried out between traditional studies and proposed new method. Furthermore, the influences on the extraction of characteristics and calculation of mean power ratio are taken into account, including the ones of sensor installation position, fault types, type of experiment rigs, failure mode and rotational speed of rolling bearing. The result shows that the proposed method can diagnose running conditions and identify fault types of rolling bearing accurately and effectively just by single-channel casing vibration signal.

Influence of non-Gaussian noise on the effectiveness of cyclostationary analysis – Simulations and real data analysis

Cyclostationary analysis is a useful approach in diagnostics of the machinery with rotating components. It allows indicating the cyclic modulations in the signal via analysis of a bi-frequency map called Cyclic Spectral Coherence (CSC). A non-zero CSC value at two frequencies means the presence of the cyclic process. Unfortunately, we have found that for some cyclostationary signals CSC provides difficult to interpret information. These disturbances in the CSC map have been linked to the presence of non-Gaussian noise. To prove it an original procedure has been proposed. Using simulations covering the model of signal, α-stable distribution, and Monte Carlo simulations it has been shown that indeed increasing presence of non-Gaussian noise makes worse the quality of diagnostic information extracted from CSC map. It has been recalled that the Cyclic Spectral Coherence is based on the autocovariance function of a given signal, thus it is properly defined for data coming from the distribution with the finite second moment.Finally, the authors selected three real examples that confirm the simulation-based findings. The main conclusion is before using the CSC analysis for cyclostationary signal one should validate the type of the noise. If noise is Gaussian — the CSC will bring optimal results. For the increasing level of impulsive non-cyclic noise, the CSC map becomes more and more disturbed and the detection of periodic excitation is difficult. Performed simulations on a very generic model some guidelines have been formulated regarding the acceptable level of non-Gaussian noise.

Cyclostationary Analysis towards Fault Diagnosis of Rotating Machinery

In the light of the significance of the rotating machinery and the possible severe losses resulted from its unexpected defects, it is vital and meaningful to exploit the effective and feasible diagnostic methods of its faults. Among them, the emphasis of the analysis approaches for fault type and severity is on the extraction of useful components in the fault features. On account of the common cyclostationarity of vibration signal under faulty states, fault diagnosis methods based on cyclostationary analysis play an essential role in the rotatory machine. Based on it, the fundamental definition and classification of cyclostationarity are introduced briefly. The mathematical principles of the essential cyclic spectral analysis are outlined. The significant applications of cyclostationary theory are highlighted in the fault diagnosis of the main rotating machinery, involving bearing, gear, and pump. Finally, the widely-used methods on the basis of cyclostationary theory are concluded, and the potential research directions are prospected.

Comparative study between cyclostationary analysis, EMD, and CEEMDAN for the vibratory diagnosis of rotating machines in industrial environment

The aim of this paper is to propose a comparative study between three advanced signal processing methods for the vibratory diagnosis of rotating machines working in industrial conditions. Cyclostationary analysis, empirical mode decomposition (EMD), and complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) are then applied for the detection of mechanical defects of a turbofan machine in the biggest fertilizer company in Algeria. These methods proved their efficiency for the diagnosis of specific defects, like rolling bearing and gear defects in laboratory test rigs, but their application in industrial field remains limited. The application of these methods on vibratory signals measured in low, medium, and high-frequency range allowed determining the efficiency of each method to diagnose the occurrence of different defects manifested in the three considered frequency ranges. The great advantage of the modulation intensity distribution (MID), and its integration (IMID), obtained from the cyclostationary analysis, is proven compared to the envelope spectra performed from the EMD or the CEEMDAN approaches, especially for defects inducing modulation phenomena. Finally, the main result of this paper is that the advanced signal processing tools can be easily applied on signals measured in industrial environment, and can be extended to detect mechanical defects in real running conditions, more real than those simulated on laboratory test rigs.

Cyclostationary-Based Vital Signs Detection Using Microwave Radar at 2.5 GHz.

Non-contact detection and estimation of vital signs such as respiratory and cardiac frequencies is a powerful tool for surveillance applications. In particular, the continuous wave bio-radar has been widely investigated to determine the physiological parameters in a non-contact manner. Since the RF-reflected signal from the human body is corrupted by noise and random body movements, traditional Fourier analysis fails to detect the heart and breathing frequencies. In this effort, cyclostationary analysis has been used to improve the radar performance for non-invasive measurement of respiratory rate and heart rate. However, the preliminary works focus only on one frequency and do not include the impact of attenuation and random movement of the body in the analysis. Hence in this paper, we evaluate the impact of distance and noise on the cyclic features of the reflected signal. Furthermore, we explore the assessment of second order cyclostationary signal processing performance by developing the cyclic mean, the conjugate cyclic autocorrelation and the cyclic cumulant. In addition, the analysis is carried out using a reduced number of samples to reduce the response time. Implementation of the cyclostationary technique using a bi-static radar configuration at 2.5 GHz is shown as an example to demonstrate the proposed approach.

Learning-Aided Physical Layer Attacks Against Multicarrier Communications in IoT

Internet-of-Things (IoT) devices that are limited in power and processing are susceptible to physical layer (PHY) spoofing (signal exploitation) attacks owing to their inability to implement a full-blown protocol stack for security. The overwhelming adoption of multicarrier techniques such as orthogonal frequency division multiplexing (OFDM) for the PHY layer makes IoT devices further vulnerable to PHY spoofing attacks. These attacks which aim at injecting bogus/spurious data into the receiver, involve inferring transmission parameters and finding PHY characteristics of the transmitted signals so as to spoof the received signal. Non-contiguous (NC) OFDM systems have been argued to have low probability of exploitation (LPE) characteristics against classic attacks based on cyclostationary analysis, and the corresponding PHY has been deemed to be secure. However, with the advent of machine learning (ML) algorithms, adversaries can devise data-driven attacks to compromise such systems. It is in this vein that PHY spoofing performance of adversaries equipped with supervised and unsupervised ML tools are investigated in this paper. The supervised ML approach is based on deep neural networks (DNN) while the unsupervised one employs variational autoencoders (VAEs). In particular, VAEs are shown to be capable of learning representations from NC-OFDM signals related to their PHY characteristics such as frequency pattern and modulation scheme, which are useful for PHY spoofing. In addition, a new metric based on the disentanglement principle is proposed to measure the quality of such learned representations. Simulation results demonstrate that the performance of the spoofing adversaries highly depends on the subcarriers' allocation patterns. Particularly, it is shown that utilizing a random subcarrier occupancy pattern secures NC-OFDM systems against ML-based attacks.

Utilisation of Ensemble Empirical Mode Decomposition in Conjunction with Cyclostationary Technique for Wind Turbine Gearbox Fault Detection

In this paper the application of cyclostationary signal processing in conjunction with Ensemble Empirical Mode Decomposition (EEMD) technique, on the fault diagnostics of wind turbine gearboxes is investigated and has been highlighted. It is shown that the EEMD technique together with cyclostationary analysis can be used to detect the damage in complex and non-linear systems such as wind turbine gearbox, where the vibration signals are modulated with carrier frequencies and are superimposed. In these situations when multiple faults alongside noisy environment are present together, the faults are not easily detectable by conventional signal processing techniques such as FFT and RMS.

Vibration-Based Condition Monitoring of Helicopter Gearboxes Based on Cyclostationary Analysis

Abstract The core of a helicopter drivetrain is a complex planetary main gearbox (MGB), which reduces the high input speed generated by the engines in order to provide the appropriate torque to the main rotors and to other auxiliary systems. The gearbox consists of various shafts, planetary gears, and bearings, and operates under varying conditions under excessive friction, heat, and high mechanical forces. The components are vulnerable to fatigue defects and therefore health and usage monitoring systems (HUMS) have been developed in order to monitor the health condition of the gearbox, focusing toward early, accurate, and on-time fault detection with limited false alarms and missed detections. The main aim of a HUMS is by health monitoring to enhance the helicopters' operational reliability, to support the maintenance decision-making, and to reduce the overall maintenance costs. The importance and the need for more advanced and accurate HUMS have been emphasized recently by the postaccident analysis of the helicopter LN-OJF, which crashed in Norway in 2016. During the last few decades, various methodologies and diagnostic indicators/features have been proposed for the monitoring of rotating machinery operating under steady conditions but still there is no global solution for complex structures. A new tool called improved envelope spectrum via feature optimization-gram (IESFOgram) has been recently proposed by the authors, based on cyclostationary analysis, focusing on the accurate selection of a filtering band, under steady and varying speed conditions. Moreover, the cyclic spectral coherence (CSCoh) is integrated along the selected frequency band leading to an improved envelope spectrum (IES). In this paper, the performance of the tool is tested on a complex planetary gearbox, with several vibration sources. The method is tested, evaluated, and compared to state-of-the-art methods on a dataset captured during experimental tests under various operating conditions on a Category A Super Puma SA330 main planetary gearbox, presenting seeded bearing defects of different sizes.

Design of Wavelet-Encoded Symbol Constellations for Cyclostationary Spectrum Sensing

In mobile communication systems, the signals propagate through multipath over time-varying channels, which are subject to distortion caused by fading and Doppler shifts. In order to minimize such distortions, coding techniques and transmission diversity can be employed, e.g., wavelet coding. In this work, the wavelet coding is investigated in scenarios of cognitive radio systems with dynamic spectrum access. Cognitive radio systems with dynamic spectrum access should be able to sense unoccupied frequency bands for opportunistic transmissions, as well as detect the presence of primary users when they occupy their licensed spectrum. Therefore, an essential element for the accurate operation of cognitive radio systems encoded by wavelet coding is the ability to sense the signals encoded by this technique. It is effectively demonstrated that the possibility of sensing such signals is associated with a suitable design of the signal constellation used in the modulation of the coded symbols. The constellation design of these is performed via genetic algorithms using a multiobjective optimization approach. The developed system is evaluated according to the robustness to time-varying flat fading through a bit error probability (BER) versus Eb/N0 analysis. The spectral sensing ability is also addressed employing the cyclostationary analysis. The results denote the feasibility of using wavelet coding in radio scenarios with dynamic spectrum access, with good performance in terms of BER and signal detection rates.