Cyclostationary Theory Research Articles

Multi-parameter estimation resistant to the random polarization effect for coherent optical receivers.

Optical parameter estimation based on the data obtained by coherent optical receivers is critical for optical performance monitoring (OPM) and the stable operation of the receiver digital signal processing (DSP). A robust multi-parameter estimation is intricate due to the interference of various system effects. By resorting to the cyclostationary theory, we are able to formulate a chromatic dispersion (CD), frequency offset (FO), and optical signal-to-noise ratio (OSNR) joint estimation strategy that is resistant to the random polarization effect, including polarization mode dispersion (PMD) and polarization rotation. The method uses data directly after the DSP resampling and matched filtering. Both numerical simulation and field optical cable experiment validate our method.

Data Augmentation in 2D Feature Space for Intelligent Weak Fault Diagnosis of Planetary Gearbox Bearing

Quickly detecting and accurately diagnosing early bearing faults is the key to ensuring the stable operation of high-precision equipment. In actual industrial applications, it is common to face the issues of big data and poor fault identification accuracy. To accurately and automatically realize the diagnostics of rolling bearings, a convolutional neural network algorithm and fault feature enhancement method is proposed. A two-dimensional space feature extraction method based on the Cyclostationary theory and wavelet transform shows good results in noise suppression. Firstly, the cyclic demodulation of wavelet transform coefficients is performed on bearing vibration signals to convert one-dimensional vibration data into a two-dimensional spectrogram for enhancing the weak fault feature. Secondly, the image segmentation theory is introduced, which can obtain more data and improve the calculation accuracy and efficiency on the basis of data dimension reduction. Finally, the augmented 2D spectrograms are inputted into a convolutional neural network. Through the analysis of the actual planetary gearbox bearing data, and compared with other mainstream intelligence algorithms, the effectiveness and superiority of this method are verified.

Blind deconvolution criterion based on Fourier–Bessel series expansion for rolling element bearing diagnostics

In the last years, Blind Deconvolution methods demonstrated their effectiveness for the diagnostics of rotating machines through the extraction of impulsive signatures directly from noisy observations. Recently, in this scenario the explicit combination between Blind Deconvolution and cyclostationary theory strongly improved the fault detection ability of this diagnostic tool. This work presents a novel criterion based on the Fourier–Bessel series expansion instead of the common Fourier transform. This idea comes from the comparison between the mathematical nature of the Fourier–Bessel and the Fourier series, based on modulated and constant amplitude sinusoidal functions, respectively. The two criteria are compared through the analysis of both simulated and real vibration signals of faulty bearings. The results highlight the ability of the proposed criterion to detect the fault-related source with a lower number of characteristic cyclic frequency harmonics, strongly reducing the computational time required by the algorithm.

A study on the feature separation and extraction of compound faults of bearings based on casing vibration signals

The autocorrelation function is combined with wavelet transform and cyclostationary theory (WT-AF-CT) in place of threshold denoising, and meanwhile the mean power ratio (MPR) is calculated by the proposed method. Furthermore, extracted characteristic as well as calculated MPR is used to identify compound faults of rolling bearings in aero-engine based on casing vibration acceleration signal-including the ones of common rolling bearing (inner race rotates and outer race is constant) and intershaft bearing (co-rotates with outer and inner race). A comparative analysis was carried out between conventional researches (cyclostationary theory (CT) or wavelet transform combined with threshold value denoising (WT-TD)) and proposed WT-AF-CT method. Additionally, the effect of sensors installation direction for feature separation and extraction of compound faults is considered. The results indicate that the proposed WT-AF-CT method can separate and extract characteristics of compound faults exactly and identify fault types of bearings precisely, no matter sensors are installed horizontally or vertically, while CT or WT cannot.

A study on the extraction of characteristics of compound faults of rolling bearings based on ITD-AF-CAF

In view of the cyclostationary characteristics of vibration signals from aero-engine, the combination of cyclic autocorrelation function and intrinsic timescale decomposition (ITD) has been proposed. According to the proposed method, vibration signals are decomposed by ITD algorithm to obtain the autocorrelation function of proper rotation components (PRC), based on which characteristic extraction and identification of compound faults of rolling bearings is made possible. To validate the effectiveness of method, an analysis has been given to the vibration signals of rolling bearings collected by sensors of different positions in different compound fault modes. As shown by results, the method combining ITD and cyclostationary theory can precisely and effectively extract the characteristic frequency relative to the type of faults and identify the compound faults.

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.

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.

Multiple Discolored Cyclic Harmonic Ratio Diagram Based on Meyer Wavelet Filters for Rotating Machine Fault Diagnosis

Rotating machines are widely used in industry, and occurrence of failures may cause severe economic losses and social impacts. Hence, this paper conducts an investigation on rotating machine fault diagnosis, and a novel method based on the structure of fast kurtogram is proposed. On one hand, a novel index is constructed that makes use of both the second order cyclostationary theory and the threshold of statistical test based on hypothesis of coloured noise. In order to reduce impact of outliers on the proposed method, information of fault characteristic frequency of rotating machine to be diagnosed is involved in the definition of index. On the other hand, the Meyer wavelet filters of empirical wavelet transform are employed to replace the filters of fast kurtogram, mainly considering the Meyer basis’ properties of good time and frequency localization, good spectrum partitioning capability, and similarity with gear and bearing vibration signal. In the case study, an acoustic emission signal of planetary gearbox and a vibration signal of rolling bearing are used to validate the proposed method compared with the fast kurtogram and Gini-based method.

GPGPU Based Parallel Implementation of Spectral Correlation Density Function

In this study, the parallelization of a critical statistical feature of communication signals called the spectral correlation density (SCD) is investigated. The SCD is used for synchronization in OFDM-based systems such as LTE and Wi-Fi, but is also proposed for use in next-generation wireless systems where accurate signal classification is needed even under poor channel conditions. By leveraging cyclostationary theory and classification results, a method for reducing the computational complexity of estimating the SCD for classification purposes by 75% or more using the Quarter SCD (QSCD) is proposed. We parallelize the SCD and QSCD implementations by targeting general purpose graphics processing unit (GPU) through architecture specific optimization strategies. We present experimental evaluations on identifying the parallelization configuration for maximizing the efficiency of the program architecture in utilizing the threading power of the GPU architecture. We show that algorithmic and architecture specific optimization strategies result with improving the throughput of the state of the art GPU based SCD implementation from 120 signals/second to 3300 signals/second.

Development of a generalized chatter detection methodology for variable speed machining

Abstract Regenerative chatter is one of the most deleterious phenomena affecting machining operations. It affects the integrity of the tool and the achievement of the targeted performance both for what concerns the material removal rate MRR and the quality of the processed surfaces. The majority of the chatter detection algorithms found in literature were not conceived for machining operations performed in non-stationary conditions although, it was demonstrated, that a continuous modulation of the spindle speed (spindle speed variation SSV) is one of the most profitable chatter suppression methodologies. This limitation represents an obstacle to the development of chatter controller systems that need to rely on effective and robust chatter monitoring procedures. In the present research, a chatter detection algorithm, specifically suitable for dealing with variable speed machining, was thus developed. More in details, the cutting stability assessment, performed in the spindle angular domain, is carried out through the real-time computation of a normalized chatter indicator that refers to the cyclostationary theory. Before computing the chatter indicator, the order tracking and the synchronous averaging methodologies are adopted for pre-processing the vibrational signals and the data coming from the spindle encoder. The devised chatter monitoring methodology was successfully validated executing real milling operations in which both constant and variable speed machining (SSV) were carried out. It was observed that the developed algorithm is capable of fast and robustly detecting chatter in all the tested cutting conditions.

Rolling element bearing weak fault diagnosis based on optimal wavelet scale cyclic frequency extraction

Rolling element bearing fault characteristic information is within the second-order cyclic stationary signal. However, it is susceptible to noise interference. In this article, a new method is proposed for rolling element bearing early fault characteristic extraction according to the cyclic periodogram method. The wavelet transform coefficients are processed and analyzed using the cyclostationary theory. As a result, the implicit cyclic characteristics are contained in wavelet transform coefficients. Therefore, using the modulus or envelope of wavelet transform coefficients instead of the calculation of the cyclic statistics can avoid the window function length selection while maintaining the computation rate. In addition, the calculation of correlated kurtosis is introduced into frequency domain to select optimal wavelet scales. The larger the correlated kurtosis, the stronger the cycle impact characteristic in wavelet coefficients. Calculating the cyclic frequency in the optimal wavelet scale range can accurately extract the weak fault characteristic information. The data processing results demonstrated that the proposed method outperforms existing cyclostationary signal analysis methods in weak fault feature extraction for rolling element bearing.

Cyclic Spectral Analysis of Vibration Signals for Centrifugal Pump Fault Characterization

Seal damage and cavitation are common faults during centrifugal pump operation. The characterization and recognition of these faults are investigated in this paper to improve the efficiency and reliability of pumps. A time-frequency signal analysis method based on the cyclostationary theory is adopted to extract the frequency characteristic components from non-stationary vibration signals under cavitation and seal damage conditions. Specifically, the signal analysis was conducted preliminarily based on the calculation of cyclic autocorrelation functions (CAFs) for various signals. Corresponding slices are extracted from the CAFs and processed by fast Fourier transform (FFT) method. Consequently from the FFT spectra, indicators for characterization are extracted to demonstrate the occurrence and severity of faults. Results show that the indicators for seal damage characterization are 100 and 600-Hz frequency components in slice $\alpha =600$ Hz of CAF corresponding to shaft and blade passing frequency in the frequency domain of vibration signals. Meanwhile, the occurrence and development status of cavitation are indicated by the frequency component of 200 Hz in slice $\alpha =600$ Hz of CAF. Additionally, the effect of instability caused by off-design, seal damage, and cavitation operation conditions are distinguished by cyclic spectra analysis. Characteristic components are innovatively extracted at specific frequencies to avoid the effect from modulated and noise components in vibration signals. And the results about recognition of different types of faults could provide important evidences for fault detection during pump operation.

Characteristic extraction of rolling bearing compound faults of aero-engine

Rolling bearing’s fault mode usually shows compound faults in aero-engine. The compound faults characteristics are more complex than single one, and many signal analysis methods have rather great limitation for compound fault characteristic extraction which leads to the difficulty to monitor the running state of rolling bearing in aero-engine. Based on above analysis, a method of combining wavelet transform with cyclostationary theory, autocorrelation function and Hilbert transform is proposed and applied to extract characteristic frequency of rolling bearing from compound faults mode only according to single-channel vibration acceleration signal of aero-engine. Meanwhile, a consideration is given to the influence of sensor installation position, compound fault types in the extraction of compound faults characteristics. The result indicates that the proposed new method can effectively monitor rolling bearing running state in four different compound fault modes just according to single-channel vibration acceleration signal no matter sensors are installed in horizontal or vertical direction.

A new characteristic analysis method for aero-engine rotor–stator rubbing

Aero-engine fault diagnosis is often studied according to casing signal owing to the inconvenience of assembly and structural limitations. Satisfactory result by cyclic statistics alone is difficult to obtain because casing signal is weak and complex. Based on this, a cyclostationary theory combined with autocorrelation function and Hilbert transform is applied to extract the characteristics of aero-engine rotor–stator rubbing fault according to the aero-engine structure and rotating features with regard to of single-point rubbing and local rubbing. Signal autocorrelation function is analyzed by cyclic autocorrelation function and Hilbert transform, in order to extract rubbing characteristics based on casing signal of aero-engine and reduce inconsistent frequency in the frequency spectrum between time-delay signal of cyclic frequency slice position and original signal. Meanwhile, consideration is given to the influence of rubbing position and sensor installation position in the extraction of rubbing characteristics. Finally, the Hilbert envelope spectrum is compared and analyzed between normal running and occurrence of the rubbing faults of aero-engines. The result indicates that the different cyclic frequency positions slice signal's Hilbert envelop spectrum of signal autocorrelation function, but not original acceleration signal which has outstanding characteristic frequency for rubbing frequency (product between blade numbers and rotating frequency) and its twice frequency when rubbing fault occurs not only in single rubbing but also in local partial rubbing. Meanwhile, when compared with the original vibration signal slice, inconsistent frequency of the autocorrelation function slice in the Hilbert envelope spectrum is decreased considerably.

Vibration-based fault detection of meshing shafts

In this article, vibration-based monitoring of cracked shafts is addressed in the context of mechanical transmission of helicopters. The approach developed is based on the detection of cyclostationary components produced by a crack. The cyclostationary theory is first presented on a mechanical point of view. Then a signal processing indicator, the spectral coherence, is introduced in order to quantify the second order cyclostationary content of a signal. The characteristics of the vibration produced in the faulty case are explained from a mechanical model of a cracked shaft. It is then shown that small variations in the structural parameters of the crack creates cyclostationary modulations around the meshing frequencies. This justifies the spectral coherence as a relevant indicator to monitor the crack. The spectal coherence is successful applied on bench data reproducing a crack propagation on an actual helicopter shaft.

A Blind Symbol Rate Estimation of Weak Signal Based on Cyclic Spectrum and Wavelet Transform

In the paper, we propose a new blind symbol rate estimation of weak signal with fixed sampling rate based on cyclic spectrum and wavelet transform. Firstly, the FFT characteristics is used to estimate the carrier frequency and the received signal is moved to the baseband by Digital Down Converter (DDC). Then, the wavelet transform is used for pre-estimating the symbol rate. Thirdly, the symbol rate estimation is proposed on the basis of cyclostationary theory and pre-estimated symbol rate. Simulation results verified the correctness of this method with MPSK signal. When the Signal to Noise Ratio (SNR) is −10 db, the approach proposed in this paper can accurately estimate the varied symbol rate with fixed sampling rate.

Estimation of micro-motion parameters based on cyclostationary analysis

A method to describe and estimate the characteristics of target with micro-motions based on cyclostationary theory is proposed in this study. The radar signal returned from a target with vibration or rotation can be modelled as cyclostationary, and a method based on cyclic statistics is designed to estimate the frequency and amplitude of the vibration or rotation. The experiments showed the performance of the proposed method under different signal noise ratios with simulated radar data.

Diagnostics of Gear Systems Using the Spectral Correlation Density of the Vibration Signal

This paper is devoted to gear diagnostics using a new technique based on cyclostationary theory. Fonnulation of the method and calculation of the Spectral Correlation Density (SCD) are presented. The Spectral Correlation Function may be seen as a parameter measuring the 'link' between harmonic components. This technique is demonstrated on simulated example, and used to analyse real vibration signals measured on an industrial like gear system. SCD is compared to classical (but powerful) phase modulation technique for the diagnostics of spalling in gear teeth. The results show that SCD may detect this fault in an early stage.