Cyclostationary Method Research Articles

Study on the Extraction Method for Track-Side Acoustic Features Based on Cyclic Stationary Analysis

Because of its non-contact measurement characteristics, trackside acoustic technology is now utilized for train bearing fault diagnosis. However, the collected acoustic signal produces Doppler distortions that can impact the accuracy of bearing fault diagnosis. Additionally, when a fault occurs in the train bearing, it is analyzed using cyclostationary methods. In this study, we combine bearing fault characteristics with Doppler distortion correction and cyclostationary analysis methods. The trackside acoustic test platform is employed to collect and test the fault signals from bearings. These signals are processed and analyzed using Doppler distortion correction algorithms and cyclostationary techniques. A comparison between time domain maps and power spectrum maps before and after correction reveals an increase in SNR (signal to noise ratio) and a more concentrated energy distribution within the fault signals—at least a 50% improvement is observed. To further validate our method’s effectiveness, we select existing TADS equipment from a depot to collect bearing signals for analysis and processing using our proposed bearing fault diagnosis method. Comparison of time domain maps and power spectrum maps before and after correction shows clearer overall images and amplitude increase of nearly 125%. Therefore, we have successfully developed a stepwise method for bearing fault diagnosis based on cyclostationary Doppler distortion correction.

An enhanced cyclostationary method and its application on the incipient fault diagnosis of induction motors

The cyclostationary analysis techniques have been extensively explored for the purpose of fault detection in rotating machinery. However, there are still huge challenges because of both limited detection frequency range and low fault identification accuracy. This paper proposes an improved cyclostationary method to enhance incipient fault features. Firstly, the continuous wavelet transform is used to accurately locate important frequency bands, and the fault modulation mechanism or fast kurtogram can be adopted to design the optimal wavelet transform scale factor. Secondly, the Teager-Kaiser energy operator is improved to be used in the frequency domain for the weak fault feature enhancement. Finally, fault features are presented in the cyclic frequency domain through spectral coherence and enhanced envelope spectrum. The proposed method is verified through both numerical simulation and experiments, including incipient half-broken rotor bar, and rolling bearing outer race faults in induction motors.

Holo-hilbert square spectral analysis: A new fault diagnosis tool for rotating machinery health management

The Holo-Hilbert spectral analysis (HHSA) is an emerging analysis tool for rotating machinery fault diagnosis. It has an excellent performance in reflecting the cross-scale coupling relationship in the nonlinear and non-stationary vibration signals, by combining the two-layer empirical mode decomposition structure. However, the random phase shift involved in the envelope signal analysis limits the wide application of HHSA and may lead to an inaccurate instantaneous frequency estimation. To solve the aforementioned problem and acquire an accurate modulation relationship between amplitude-modulated (AM) and frequency-modulated (FM) characteristics, a novel non-stationary signal analysis method, namely Holo-Hilbert square spectral analysis (HHSSA), is put forward in this paper by combing the square envelope analysis. The proposed HHSSA is integrated to compute a new quantity called the AM-marginal spectrum to reveal the separation efficiency of fault characteristics. Moreover, the relationships between HHSSA with the commonly used second-order cyclostationary methods (Cyclic Modulation Spectrum and Fast Spectral Correlation) are further investigated. Furthermore, the analysis of simulation, experimental data, and industrial data are conducted to demonstrate the high resolution and superior modulation relationship recognition capability of HHSSA. The analysis results further prove that the proposed HHSSA-based AM-marginal spectrum has the best fault identification performance and robustness compared with traditional methods.

Blind Symbol-Rate Estimation for Short and Bursty Communications

The design of a blind receiver for unsynchronized bursty communications is a challenging task, especially when the data burst duration is very short and the over-sampling ratio (OSR) at the receiver is a non-integer value. In this article, the problem of blind symbol-rate estimation for bursty communications is studied. A cyclostationary method with bias removal (CS-BR) is proposed to improve the accuracy of the “OSR peak” detection in cyclostationary method when the length of signal burst is very short. Factors which affect the accuracy of the proposed blind symbol-rate estimation are thoroughly analyzed. Both field measurement data simulations and Monte Carlo simulations show that by using our proposed CS-BR method, the accuracy of blind symbol-rate estimation can be significantly improved, and the root-mean-square-error of the estimated OSR can be reduced to as small as <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$10^{-4}$</tex-math></inline-formula> even if each short data burst consists of only tens of symbols.

Cyclostationary modeling for the aerodynamically generated sound of helicopter rotors

Helicopter rotor aerodynamic noise research has become essential as helicopters’ reliability and comfort requirements have increased. Significant progress has been made in modeling the aerodynamically generated sound of helicopter rotors. The cyclostationary signal processing methods have been widely used for machine fault diagnosis, machinery system identification and mechanical source separation. However, the lack of a generally accepted formal definition of cyclostationarity based on the basic aerodynamic theory and wave propagation model limits cyclostationary methods’ application to the helicopter rotor aerodynamic noise. A formal cyclostationary modeling process to the helicopter rotor aerodynamic noise based on aerodynamic and wave propagation theory is proposed in this paper for subsequent cyclostationary signal processing. The rotor blade noise is mathematically formulated as a cyclostationary process by imposing the periodic Green’s function based on the Wold–Cramer decomposition form of the Ffowcs Williams–Hawkings (FW–H) equation, and the formal definition of the rotor blade noise cyclostationary process is derived. Then, the cyclostationarity is defined for both the tonal noise and the broadband noise of rotor aerodynamic noise, respectively. Furthermore, a periodic amplitude modulation (PAM) signal model is proposed to approximate the measured rotor aerodynamic noise signal. The proposed signal model is validated by the measurement in the wind tunnel test.

A Wideband 5G Cyclostationary Spectrum Sensing Method by Kernel Least Mean Square Algorithm for Cognitive Radio Networks

This brief proposes a new cyclostationary method on the basis of the Gaussian Kernel Least Mean Square (KLMS) algorithm for wideband spectrum sensing in the upcoming 5G mobile networks. To focus on a special fragment of the 5G network frequency spectrum, the KLMS algorithm uses a set of inaccurate cyclic frequencies of low complexity belonging to the signal of the primary user (PU). A suboptimal detector is designed on the basis of the KLMS weights and the performance of the proposed detector is measured and compared with other recent spectrum sensing techniques. The method is very easy to implement and less complex to compute than other spectrum-sensing counterparts. Analytical and simulation results have been verified by an experimental 5G communication setup which shows the effectiveness of the proposed method.

Estimation of Modulation Parameters of LPI Radar Using Cyclostationary Method

Low Probability of intercept (LPI) radars work on the principle of low peak-power and wide bandwidth. To achieve this, the LPI radars use special type of modulated waveforms which are difficult to intercept. The main tasks of intercept receivers are to detect, estimate and classify LPI signals even in the presence of high noise. Accurate estimation of the modulation parameters also provides information about threat to radar so that necessary counter measures could be initiated against the enemy radars. In the present work, Cyclo-stationary (CS) method is used to estimate the parameters of Polytime coded LPI signals. CS method is efficient for the analysis of periodic waveforms like LPI signals and finds applications in many fields such as array signal processing, estimation of direction of arrival, signal detection. Cyclic auto correlation function and the spectral correlation density function (SCD) which are the basis for CS analysis are computed for all the four types of polytime codes. Generation of all the four types of Polytime codes and computation of SCD coefficients are carried out using MATLAB. From the contour plot of SCD function, the parameters carrier frequency, bandwidth and code rate are measured. It is assumed that the received signal is not corrupted with any noise. The simulation results are compared with the values available in the literature. The maximum error of estimation is well within ± 6% for all the codes in the proposed method whereas the maximum error reported in the literature is 25.7%. Hence the proposed method is better. Since CS method is sensitive to sampling frequency, the analysis is repeated for three different sampling frequencies and in all cases, the estimation error is less than 6%.

Analysis of Covariance Ratio Based Detection Techniques for Cognitive Radio Networks

The conventional method of spectrum sensing such as Energy detection, matched filter and cyclostationary methods require prior knowledge of primary user. Also, these methods are highly vulnerable to noise uncertainty. In this paper statistical covariance based matrix methods such as CVD, CFN, MME, EME and MSEE are analysed. These methods employ the sample covariance matrix for obtaining the test statistic and threshold. Moreover these methods are robust to noise uncertainty and also perform well at low SNR.

Cyclic Frequency Estimation by Compressed Cyclic Correntropy Spectrum in Impulsive Noise

Non-Gaussianity of noises and non-stationarity of signals have been the two crucial considerations in the fields of signal processing and communications. Correspondingly, many denoising and cyclostationary methods have been published to deal with the relevant problems, respectively. Recently, a novel method named cyclic correntropy or cyclostationary correntropy was proposed to deal with the two problems simultaneously. Thanks to the symmetry and sparsity of cyclic correntropy spectrum, the compressed spectrum obtained by compressive sensing can be used to complete the task in certain situations. In this letter, a novel method to estimate the cyclic frequency by compressed cyclic correntropy spectrum is proposed to reduce computational complexity and storage cost. To reveal the proposed method's effectiveness and robustness to impulsive noise, a number of numerical experiments are carried out to compare with existing cyclostationary methods. As cyclostationary signal processing and compressive sensing are the two great theories, through in-depth study, they can have more collaborative work opportunities and meanings.

Determining the parameters of chirp signals using cyclostationary method in presence of the interference

This paper deals with the problems of detecting a chirp signal of motion target against a strong undesired signal from the transmitter in radar. We use Generalized Almost- Cyclostationary (GACS) signal processing method to determine the rate and initial frequency of the chirp signal in presence of the strong undesired signal. This technique which exploits the second order cyclostationary to detect features of the chirp signal in low SNR has desirable properties. The study utilized a method to determine and characterize signals for highly adverse signal to interference plus noise and explain how using cyclostationary properties can extract features of chirp signal from the mixture received signal. The theory and simulation of this method indicated that the chirp rate depends on the lag parameter and the cycle frequency. Keywords : Chirp Signal, Cyclostationary, initial frequency, Chirp rate.

Sparse Representation for Blind Spectrum Sensing in Cognitive Radio: A Compressed Sensing Approach

Cognitive radios enable opportunistic transmission for secondary users (SUs) without interfering the primary user (PU). Cyclo-stationary-based spectrum sensing methods are better than the energy detection methods in negative signal-to-noise (SNR) decibel (dB) regime, in which case the noise variance cannot be exactly estimated. However, blind cyclo-stationary methods require a large number of symbols (and hence measurements). This paper aims to reduce the number of measurements in a blind sensing method (using a combination of linear prediction and QR decomposition), by employing compressed sensing at the receiver front-end, so as to reduce the A/D requirements needed with a large number of measurements, along with oversampling the received signal. Till now, compressed sensing has not been investigated at very low negative SNR (dB), e.g., $$-$$-12 dB, which is very crucial in spectrum sensing. The novel algorithm, in this paper, overcomes this shortcoming, and its simulation results show that the SU is able to detect the PU signal, using much less measurements, even at very low negative SNR (dB). The proposed method also investigates the effect of joint and individual measurement matrices at multiple oversampled branches.

Cognitive (LabVIEW) on FPGA–a novel approach for dynamic spectrum sensing

The spectrum allotted for communications has been distributed to various service providers, who maintain and manage their portion of the spectrum by accommodating as many users as possible through spectral management techniques. Static spectrum management has been replaced by dynamic spectrum management to meet the vastly increasing number of users. Although dynamic spectrum management techniques have enabled the efficient assignment of channels to the user, it has been statistically observed that a huge part of the communications spectrum is scarcely used at all times. Cognitive radio is a useful tool for efficient dynamic spectrum management. The cognitive radio is adaptive in nature and is most effective because of its ability to monitor the spectrum, sense the channel occupancy and mobilise the secondary user to an unused primary user channel, as well as to relocate the secondary user if the primary user wishes to communicate. In this work, the energy-detection method and the cyclostationary method, which are the methods to sense the spectrum, are analysed and the results are compared. Simulation is done using a LabVIEW tool (National Instruments, Bangalore, India) and finally the implementation is done on a Field Programmable Gate Array.

Symbol Rate Estimation Method for Digital Signal Based on Square Timing

In this paper, aiming at the poor performance of the existing symbol rate estimation methods when SNR is low, we proposed a method based on the timing square which can be simply calculated and applied to MASK/MPSK/MQAM modulated signal, improved the performance of signal symbol rate estimation compared with the existing method. Based on the principle of the timing square, the signal modules were squared to calculate the fourier coefficient modulus corresponding to different sampling ratios. Then the characteristic line was searched in the transform spectrum which contains symbol rate information and obtained an estimation of the symbol rate. The impact of the roll-off factor and the carrier wave was analyzed and solution was proposed in this paper. Simulation results show that the performance of symbol rate estimation of the improved method is better than the original method, the wavelet transform method and the cyclostationary method in low SNR and low roll-off factor environment.

Application of the cyclostationairity for the cutting tool diagnosis

This work is interested to the analysis of the vibratory signals coming from a milling operation. The objective is the detection of cutting tool breakage using the cyclostationary tools. Initially, we will show that the vibration signals captured from the milling operation are cyclostationary. The proposed cyclostationary methods are the first and second order synchronous statistics and the spectral correlation. A test rig, composed of a milling machine (cutter with 5 teeth) and a workpiece, is used to extract the vibration signals that are angular sampled in the free fault case and one broken tooth case. This test rig is instrumented with three accelerometers, installed in the three directions, and an optical encoder that allows the angular sampling. Then we will see that the angular sampling of the signals captured from a milling operation is essential to preserve the cyclostationary properties destroyed, in the case of the temporal sampling, by speed fluctuations. The proposed method capacity to detect the broken tooth is shown. The synchronous statistics of order 1 and order 2 detect the broken tooth presence and its emplacement. The spectral correlation analysis distinguishes the broken tooth presence, but is not practical for the diagnosis. For that, an indicator based on the spectral correlation is proposed.

Cyclostationarity approach for monitoring chatter and tool wear in high speed milling

Detection of chatter and tool wear is crucial in the machining process and their monitoring is a key issue, for: (1) insuring better surface quality, (2) increasing productivity and (3) protecting both machines and safe workpiece. This paper presents an investigation of chatter and tool wear using the cyclostationary method to process the vibrations signals acquired from high speed milling. Experimental cutting tests were achieved on slot milling operation of aluminum alloy. The experimental set-up is designed for acquisition of accelerometer signals and encoding information picked up from an encoder. The encoder signal is used for re-sampling accelerometers signals in angular domain using a specific algorithm that was developed in LASPI laboratory. The use of cyclostationary on accelerometer signals has been applied for monitoring chatter and tool wear in high speed milling. The cyclostationarity appears on average properties (first order) of signals, on the energetic properties (second order) and it generates spectral lines at cyclic frequencies in spectral correlation. Angular power and kurtosis are used to analyze chatter phenomena. The formation of chatter is characterized by unstable, chaotic motion of the tool and strong anomalous fluctuations of cutting forces. Results show that stable machining generates only very few cyclostationary components of second order while chatter is strongly correlated to cyclostationary components of second order. By machining in the unstable region, chatter results in flat angular kurtosis and flat angular power, such as a pseudo (white) random signal with flat spectrum. Results reveal that spectral correlation and Wigner Ville spectrum or integrated Wigner Ville issued from second-order cyclostationary are an efficient parameter for the early diagnosis of faults in high speed machining, such as chatter, tool wear and bearings, compared to traditional stationary methods. Wigner Ville representation of the residual signal shows that the energy corresponding to the tooth passing decreases when chatter phenomenon occurs. The effect of the tool wear and the number of broken teeth on the excitation of structure resonances appears in Wigner Ville presentation.

Neural Network Aided Enhanced Spectrum Sensing in Ognitive Radio

Wireless communication applications are increasing day-by-day. As a consequence efficient spectrum utilization becomes a key task. Cognitive radio is a booming technique for efficient spectrum utilization. Spectrum sensing is a key technology of cognitive radio and it is the first step in cognitive cycle to find out the spectrum availability. The three spectrum sensing methods are matched filter detection, energy detection and cyclostationary. Matched filter method should have the prior knowledge about the primary users signal and it will not be an optimal choice. But no prior information is needed for cyclostationary method and it can extract information about the primary signal waveform. But this method is complex to implement and it is under research. Energy detection is the most common spectrum sensing techniques because this method does not require any prior knowledge about the unknown signal .It is less complex and it takes less sensing time but at the same time it is susceptible to uncertainty in noise power and it cannot differentiate between primary user and secondary user signal. This paper focuses on all three methods and in order to improve the performance of energy detection under heavy noise scenario double threshold technique is also proposed. The presence of primary is determined by three criteria, i.e., probability of detection, probability of miss-detection and probability of false alarm. Simulation results prove that the double threshold method is better than the single threshold.

Cyclic Spectrum Analysis on Rolling-Element Bearing with Inner-Race Point Defect

Vibration signal of rolling-element bearing is random cyclostationarity when a fault develops, the proper analysis of which can be used for condition monitor. Cyclic spectrum is a common cyclostationary analysis method and has a great many algorithms which have distinct efficiency in different application circumstance, two common algorithms (SSCA and FAM) are compared in the paper. The FAM is recommended to be used in diagnosing rolling-element bearing fault via calculation of simulation signal in different signal to noise ratio. The cyclic spectrum of practice signal of rolling-element bearing with inner-race point defect is analyzed and a new characteristic extraction method is put forward. The preferable result is acquired verify the correctness of the analysis and indicate that the cyclic spectrum is a robust method in diagnosing rolling-element bearing fault.

Enhanced Detection of Visual-Evoked Potentials in Brain-Computer Interface Using Genetic Algorithm and Cyclostationary Analysis

We propose a novel framework to reduce background electroencephalogram (EEG) artifacts from multitrial visual-evoked potentials (VEPs) signals for use in brain-computer interface (BCI) design. An algorithm based on cyclostationary (CS) analysis is introduced to locate the suitable frequency ranges that contain the stimulus-related VEP components. CS technique does not require VEP recordings to be phase locked and exploits the intertrial similarities of the VEP components in the frequency domain. The obtained cyclic frequency spectrum enables detection of VEP frequency band. Next, bandpass or lowpass filtering is performed to reduce the EEG artifacts using these identified frequency ranges. This is followed by overlapping band EEG artifact reduction using genetic algorithm and independent component analysis (G-ICA) which uses mutual information (MI) criterion to separate EEG artifacts from VEP. The CS and GA methods need to be applied only to the training data; for the test data, the knowledge of the cyclic frequency bands and unmixing matrix would be sufficient for enhanced VEP detection. Hence, the framework could be used for online VEP detection. This framework was tested with various datasets and it showed satisfactory results with very few trials. Since the framework is general, it could be applied to the enhancement of evoked potential signals for any application.

Application of Degree of Cyclostationarity in Rolling Element Bearing Diagnosis

Minor and random slip between rolling elements and races in rolling element bearings makes vibration signals have periodically time-varying ensemble statistics, which is known as cyclostationarity. Two second-order cyclostationary methods, the spectral correlation density (SCD) and the degree of cyclostationarity (DCS), are talked about in this paper based on a statistical model of rolling element bearings. The SCD provides redundant information in bi-frequency plane and cyclic frequency domain embodies the majority of it, which is a series of non-zero discrete cyclic frequencies completely reflecting the fault characters of rolling element bearings. The DCS has virtues of less computation and clearer representation, at the same time keeps the same characters with SCD in cyclic frequency domain. And the DCS is also proved to be resistant to the additive and multiplicative stationary noise. Simulation and experiential results from three rolling element bearing faults: outer race defect, inner race defect and rolling element defect, indicate practicability of the DCS analysis in rolling element bearing condition monitoring and fault diagnosis.