Cyclostationary Signals Research Articles

An Improved Cyclic Modulation Spectral Analysis Based on the CWT and Its Application on Broken Rotor Bar Fault Diagnosis for Induction Motors

Induction motors (IMs) are widely used in many manufacturing processes and industrial applications. The harsh work environment, long-time enduring, and overloads mean that it is subjected to broken rotor bar (BRB) faults. The vibration signal of IMs with BRB faults consists of the reliable modulation information used for fault diagnosis. Cyclostationary analysis has been found to be effective in identifying and extracting fault feature. The estimators of cyclic modulation spectrum (CMS) and fast spectral correlation (FSC) based on the short-time fourier transform (STFT) have higher cyclic frequency resolution, which has proven efficient in demodulating second order cyclostationary (CS2) signals. However, these two estimators have limitations of processing the maximum cyclic frequency αmax that is smaller than Fs/2 (Fs is the sampling frequency) according to Nyquist’s Theorem. In addition, they have lower carrier frequency resolution due to the fixed window size used in STFT. In order to resolve the initial shortcomings of the CMS and FSC methods, in this paper, we extended the analysis of CMS algorithm based on the continuous wavelet transform (CWT), which enlarged the maximum cyclic frequency range to Fs/2 and provides higher carrier frequency resolution because the CWT has the advantage of multi-resolution analysis. The reliability and applicability of the proposed method for fault components localization were validated by CS2 simulation signals. Compared to CMS and FSC methods, the proposed approach shows better performance by analyzing vibration signals between healthy motor and faulty motor with one BRB fault under 0%, 20%, 40%, and 80% load conditions.

Efficient Cycle Frequency Acquisition of a Cyclostationary Signal with the FACA Method

Efficient Cycle Frequency Acquisition of a Cyclostationary Signal with the FACA Method

Low-complexity spectrum sensing for MIMO communication systems based on cyclostationarity

The problem of spectrum sensing in multiple-input multiple-output (MIMO) cognitive radio systems using the cyclostationarity property is considered. Since the noise is not a cyclostationary signal and the interference exhibits distinct cyclostationarity as primary user (PU) signals, spectrum sensing based on cyclostationarity is superior to traditional methods. To detect the presence of PU signals, cyclostationarity-based methods tend to use the second-order cyclostationarity property of cyclostationary signals. However, the computation of cyclostationary statistics is complicated. Thus, the complexity of conventional cyclostationary feature detection methods is challenging, especially for MIMO systems. A new improved algorithm that jointly utilizes the cyclostationarity property and the multiple antenna combining technique of MIMO systems is proposed in this paper. The proposed methods simplify the complexity of spectrum sensing and provide robust detection performance. The performance of the proposed schemes compared with conventional cyclic combining methods is evaluated via Monte-Carlo simulation. The simulation results indicate that the proposed method is preferred under some severe noise and interference presence scenarios.

Blind separation of complex-valued satellite-AIS data for marine surveillance: a spatial quadratic time-frequency domain approach

<p>In this paper, the problem of the blind separation of complex-valued Satellite-AIS data for marine surveillance is addressed. Due to the specific properties of the sources under consideration: they are cyclo-stationary signals with two close cyclic frequencies, we opt for spatial quadratic time-frequency domain methods. The use of an additional diversity, the time delay, is aimed at making it possible to undo the mixing of signals at the multi-sensor receiver. The suggested method involves three main stages. First, the spatial generalized mean Ambiguity function of the observations across the array is constructed. Second, in the Ambiguity plane, Delay-Doppler regions of high magnitude are determined and Delay-Doppler points of peaky values are selected. Third, the mixing matrix is estimated from these Delay-Doppler regions using our proposed non-unitary joint zero-(block) diagonalization algorithms as to perform separation.</p>

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.

Bearing fault diagnosis with nonlinear adaptive dictionary learning.

The monitoring of rotating machinery condition has been a critical component of the Industry 4.0 revolution in enhancing machine reliability and facilitating intelligent manufacturing. The introduction of condition-based monitoring has effectively reduced the catastrophic events and maintenance cost across various industries. One of the major challenges of the diagnosis remains as majority of the diagnostic model requires off-line analysis and human intervention. The offline analysis, which is normally done by previous experience, involves tuning model parameters to improve the performance of the diagnostic model. However, for newly developed models, the knowledge of the unknown parameters does not exist. One way to resolve this issue is through learning using adaptation. The adaptation algorithm adjusts itself by newly acquired data. Hence, improvement of the model performance is achieved. In this paper, a nonlinear adaptive dictionary learning algorithm is proposed to achieve early fault detection of bearing elements without using the conventional computation heavy algorithm to update the dictionary. Deterministic and random data separation is implemented using the autoregressive model to reduce the background noise. The filtered data is further analyzed by the Infogram to reveal the impulsiveness and cyclostationary signature of the vibration signal. The dictionary is initialized using random parameters. Instead of using the k means singular value decomposition algorithm to compute the dictionary for adaptation, the unscented Kalman filter (UKF) is implemented to update the dictionaries using the filtered signal from the Infogram. The updating algorithm does not require computation of the dictionary, and no previous knowledge of the dictionary's parameters is needed. The updated dictionary contains the detected fault signature from the Infogram and, therefore, is used for further fault analysis. The proposed algorithm has the advantage of self-adaptation, the capability to map the non-linear relationship of the signal and dictionary weights. The algorithm can be used in the various condition-based monitoring of rotating machineries to avoid additional human efforts and improve the performance of the diagnostic model.

Stochastic analysis of the LMS algorithm for cyclostationary colored Gaussian and non-Gaussian inputs

This paper studies the stochastic behavior of the LMS algorithm in a system identification framework for a cyclostationary colored input without assuming a Gaussian distribution for the input. The input cyclostationary signal is modeled by a colored random process with periodically time-varying power. The generation of the colored non-Gaussian random process is parametrized in novel manner by passing a Gaussian random process through a coloring filter followed by a zero memory nonlinearity. The unknown system parameters are fixed in most of the cases studied here. Mathematical models are derived for the behavior of the mean and mean-square-deviation (MSD) and the excess mean-square error (EMSE) of the adaptive weights as a function of the input cyclostationarity. The models display the dependence of the algorithm upon the input nonlinearity and coloration. Three nonlinearities that are studied in detail with Monte Carlo simulations provide strong support for the theory.

Maximally stationary window design for overlap-add based random vibration synthesis

Abstract The accurate synthesis of realistic waveforms conforming to certain specifications is a fundamental step in random vibration testing. Since real-time implementation of digital signal processing systems for random vibration and noise synthesis necessarily operates frame by frame, the overlap-add (OLA) method, by which frames are windowed and overlapped, is widely used in practice to avoid artifacts at frame boundaries. When a wide-sense stationary random signal is desired, however, the OLA method presents a shortcoming, because the inherent periodicity of the frame-by-frame process unavoidably produces a cyclostationary signal, i.e., its statistics present an undesired periodic behavior. We analyze the impact of the window coefficients in the cyclostationarity properties of the synthetic process, and then present algorithms for window design with the goal of maximizing a measure of its stationarity, considering both second- and fourth-order statistical properties. The proposed designs are shown to significantly improve the stationarity properties when compared to commonly used windows.

Cyclic Signals and Systems in Power Line Communications

This paper provides a comprehensive discussion about the characteristics of power line communication (PLC) channels related to its synchronization with the mains period. This fact constitutes an interesting and distinguishing feature of these kind of channels. Under the mains voltage presence, the behavior of some loads connected to the power network allows representing the transmission medium as a linear periodically time varying (LPTV) system. Some components in the received noise exhibit periodicity as well, in terms of impulsive waveforms synchronized with the mains period and other cyclostationary (CS) signals. This fact has been taken into account in the design of PLC systems, for instance by defining medium access control (MAC) frames synchronized with the mains period and by adapting the modulation to the cyclic signal-to-noise ratio (SNR) to improve the system performance. Hence, in PLC, it is of particular interest to describe the general relations of LPTV systems and CS signals when both have a common period, which is the purpose of this work. It is not aimed at providing new mathematical tools for the analysis of these cyclic signals and systems, which have been extensively developed over the last five decades, but to serve the readers of the PLC community more accessible mathematical relations that can be applied to the practical problems they have to face. A review of recent works dealing with the cyclic properties of PLC channels and transmission techniques aware of these strategies is included as well.

DOA Estimation Using Single or Dual Reception Channels Based on Cyclostationarity

This paper addresses the problem of direction-of-arrival (DOA) estimation for cyclostationary signals using less reception channel in comparison with the number of sensors. The system is considered to be realized by using the reception channel(s) to receive the signal reached each sensor in turn. Such simplification results in a cost reduction of the system and the effect of inconsistency among different channels are removed. However, non-synchronized sampling also makes the traditional DOA estimation algorithms ineffective. To cope with the problem, the signal models for DOA estimation using a single channel and dual channels are formulated based on signal cyclostationary, and the single channel cyclic MUSIC (SC-Cyclic-MUSIC) algorithm and the dual channels cyclic MUSIC (DC-Cyclic-MUSIC) algorithm are proposed correspondingly. This paper shows that both SC-Cyclic-MUSIC algorithm and DC-Cyclic-MUSIC algorithm work well when the switching interval is known, and a satisfied performance can also be obtained by DC-Cyclic-MUSIC algorithm when the uncertainty of the switching interval exists. Moreover, the proposed estimators are suitable for both narrow-band and wide-band signals. The computer simulations are provided to verify the effectiveness of the proposed algorithms.

Robust cyclic beamforming against cycle frequency error in Gaussian and impulsive noise environments

A robust cyclic array beamforming method is proposed for cyclostationary signals to counter against the cycle frequency error (CFE) in Gaussian and impulsive noise environments. In this approach, the maximum correntropy criterion (MCC) is employed as the cost function to compute an appropriate weight vector for performing cyclic adaptive array beamforming. We show that a closed form solution of weighting vector yields a weighted least-square-like formulation by using the MCC. The corresponding performances of unbiasedness and consistency are evaluated. Further, in order to solve the performance degradation caused by the CFE, an optimization method is developed based on the fact that the correntropy-based correlation (CRCO) function of the output signals will approach its maxima without any CFE. Finally, a robust iterative algorithm without the prior knowledge of the direction vector of the signal of interest (SOI) is proposed for robust adaptive array beamforming.

Multiple Cycle Frequencies Estimation Under Cochannel Interference

In this letter, two cycle frequencies estimation algorithms are proposed to estimate the number of weak cyclostationary signals and their cycle frequencies in the presence of higher power interferer signal. Both cycle frequencies estimation algorithms are eigenanalysis-based methods that use the cyclic autocorrelation function of the received signals. In particular, a new eigen-analysis cyclic null spectrum is introduced to determine the number of cyclostationary signals and estimate their cycle frequencies. The performances of the proposed cycle frequency estimation algorithms are demonstrated with numerical examples and compared with the existing cycle frequency estimation algorithms. It is shown that both the proposed cycle frequencies estimation algorithms have better accuracy than the existing methods and could work with small sample size for faster estimation.

Compressive Sensing for Detecting Ships With Second-Order Cyclostationary Signatures

Amplitude modulation of the broadband propeller noise as a result of the cavitation yields a second-order cyclostationary ship-radiated noise. The spectrum of the modulating signal, consisting of the so-called propeller (or cavitation) tonals, enables the detection and the classification of the submarines or surface ships. However, data acquisition for this purpose causes vast data sizes due to high sampling rates and multiple sensor deployment. To mitigate the negative effects of this acquisition process such as on energy efficiency, hardware complexity, and storage capacity, we propose a scheme for compressive sensing of propeller tonals. We show that the spectral correlation function of cyclostationary propeller noise is sparse and derive a linear relationship between the compressive and Nyquist-rate cyclic modulation spectra, i.e., the approximation of spectral correlation function that allows utilizing matrix representations required in compressive sensing. It also enables use of the cyclic modulation coherence, i.e., the normalized cyclic modulation spectrum, to demonstrate the effect of compressive sensing in terms of statistical detection. We compare the recovery and detection performance results of the sparse approximation algorithms based on the so-called iterative hard thresholding and compressive sampling matching pursuit. Results show that compression is achievable without affecting the detection performance negatively. The main challenges are the weak modulation, low signal-to-noise ratio, and nonstationarity of the ambient noise, all of which reduce the sparsity level, hence causing degraded recovery and detection performance.

Stochastic Analysis of the LMS and NLMS Algorithms for Cyclostationary White Gaussian and Non-Gaussian Inputs

This paper studies the stochastic behavior of the LMS and NLMS algorithms in a system identification framework for a cyclostationary white input without assuming a Gaussian distribution for the input. The input cyclostationary signal is modeled by a white random process with periodically time-varying power. The system parameters vary according to a random-walk. Mathematical models are derived for the mean and mean-square-deviation behavior of the adaptive weights as a function of the input cyclostationarity. Analytical models are first derived for the LMS and NLMS algorithms for cyclostationary white inputs. These models show the dependence of the two algorithms upon the kurtosis of the input. Significant differences are found between the behaviors of the two algorithms when the analysis is applied to non-Gaussian cases. Monte Carlo simulations provide strong support for the theory.

Performance analysis of LMS filters with non-Gaussian cyclostationary signals

Abstract The least mean-square (LMS) filter is one of the most common adaptive linear estimation algorithms. In many practical scenarios, e.g., digital communications systems, the signal of interest (SOI) and the input signal are jointly wide-sense cyclostationary. Previous works analyzing the performance of LMS filters for this important case assume Gaussian probability distributions of the considered signals. In this work, we provide a transient and steady-state performance analysis that applies to non-Gaussian cyclostationary signals. In the considered analysis, the SOI is modeled as a perturbed response of a linear periodically time-varying system to the input signal. We obtain conditions for convergence and derive analytical expressions for the non-asymptotic and steady-state mean-squared error. We then show how the theoretical analysis can be effectively applied for two common non-Gaussian classes of input distributions, the class of elliptical compound Gaussian distributions, and the broad class of Gaussian mixture distributions. The accuracy of our analysis is illustrated for system identification and signal recovery scenarios that involve linear periodically time variant systems and non-Gaussian inputs.

LMPIT-Inspired Tests for Detecting a Cyclostationary Signal in Noise With Spatio–Temporal Structure

In spectrum sensing for cognitive radio, the presence of a primary user can be detected by making use of the cyclostationarity property of digital communication signals. For the general scenario of a cyclostationary signal in temporally colored and spatially correlated noise, it has previously been shown that an asymptotic generalized likelihood ratio test (GLRT) and locally most powerful invariant test (LMPIT) exist. In this paper, we derive detectors for the presence of a cyclostationary signal in various scenarios with structured noise. In particular, we consider noise that is temporally white and/or spatially uncorrelated. Detectors that make use of this additional information about the noise process have enhanced performance. We have previously derived GLRTs for these specific scenarios; here, we examine the existence of LMPITs. We show that these exist only for detecting the presence of a cyclostationary signal in spatially uncorrelated noise. For white noise, an LMPIT does not exist. Instead, we propose tests that approximate the LMPIT, and they are shown to perform well in simulations. Finally, if the noise structure is not known in advance, we also present hypothesis tests using our framework.

Use of the correlated EEMD and time-spectral kurtosis for bearing defect detection under large speed variation

Vibration-based diagnosis is in common use for the health monitoring of rolling element bearing (REB). This paper is concerned with a new defect detection method of the REB under large speed variation by using the correlated ensemble empirical mode decomposition (EEMD) and time-spectral kurtosis (TSK), which are accomplished in two phases. During the first phase, vibration signals are decomposed into intrinsic mode functions (IMFs) with the EEMD, which are then correlated with the original signal in order to determine the shaft IMFs, and hence the distinct instantaneous rotation frequencies (IRFs). During the second phase, the TSK is adopted to determine the fault IMFs, which are further used to reconstruct the fault signal. As a result, the non-stationary signal in the time domain is transformed into the cyclostationary signal in the angular domain with respect to the IRFs by resampling with equal angle increments. Simulations and experiments are carried out to validate the feasibility of the proposed method. It is shown that proposed method offers a potential improvement over the conventional short time Fourier transform and order tracking-based method.

Support vector machine and higher‐order cumulants based blind identification for non‐linear Wiener models

A blind identification method for non-linear Wiener models is investigated. When the input signal of the system does not adopt a Gaussian random signal, the identification process with the input signal is changed into the one without input signal by using the first-order statistical properties of the cyclostationary input signal and the inverse mapping of the non-linear part of the model initially, moreover, all internal variables are recovered only based on the output signal. Then, the estimates of the order and parameters of the model are obtained by using the support vector machine regression theory and the higher-order cumulants principle. Finally, compared with other methods, the simulation results show the effectiveness of the proposed method for identifying non-linear Wiener models.

Reconstructing signal from quantized signal based on singular spectral analysis

Singular spectral analysis (SSA) is a nonparametric spectral estimation method for performing the time series analysis. It represents a signal as the sum of its components. In this manuscript, a nearly cyclostationary signal is considered. The signal is quantized and the SSA is employed to reconstruct the original signal based on the quantized signal. First, the reconstructed signal is modeled as the weighted sum of the SSA components. In order to estimate the weights, each quantization level is considered as a class. Different signal values are associated with different probabilities of the corresponding classes via the sigmoid functions defined based on the distances between the signal values and the corresponding quantized levels. Therefore, our proposed method provides the optimal estimate of a given signal in the minimum cross entropy sense. Computer numerical simulation results show that our proposed method can reduce the quantization error and reconstruct the original signal more accurately compared to some existing algorithms.

Extraction and imaging of aerodynamically generated sound field of rotor blades in the wind tunnel test

Abstract The acoustic beamforming has been widely applied in the imaging of flow-induced aeroacoustic sound sources. However, the measured signals of the rotor blades often accompanied with the unwanted interference from other components of the experimental setup in the wind tunnel test (for example, the rotor shaft and the stand), which results in the undistinguished sources in the beamforming result. In this paper, the signals of rotor blades are defined first as the cyclostationary process based on the Ffowcs Williams-Hawkings (FW-H) equation in the form of Wold-Cramer decomposition, which connects the statistical definition of rotor blades signals with the wave propagation model of moving sources. Then the developed cyclostationary signal processing tools of a second order, specifically the reduced-rank cyclic Wiener filter, can be applied in the wind tunnel test of rotor blades. The rotor blades signals can be extracted from the noisy measurements with other interferences, which aide to purify the image results of beamforming in the final experiment of wind tunnel test.