Cyclostationary Processing Research Articles

Scattering moment matching-based interpretable domain adaptation for transfer diagnostic tasks

One significant fact familiar to the signal processing-based diagnostic community but generally ignored by the transfer learning-based diagnostic community is that the cyclostationarity of the monitored signal conveys the actual diagnostic information. Popular network architectures, e.g., ResNet, and domain discrepancy metrics, e.g., maximum mean discrepancy, in current transfer diagnostic research are generally borrowed from the transfer learning community yet do not explicitly consider machine fault physics. As Jérôme Antoni points out, signal processing and machine learning methods are not mutually exclusive but should complement each other. The current article aims to develop an interpretable domain adaptation method for transfer diagnostic tasks by simultaneously exploiting the ideas of cyclostationary signal processing and domain adaptation techniques. By taking NTScatNet as the network backbone and scattering moment distance as the domain discrepancy metric, the proposed scattering moment matching-based domain adaptation method is more interpretable and matches fault physics better than conventional deep transfer learning methods. Besides, the proposed method does not require target domain data during the training phase, thus relaxing the assumption of standard domain adaptation. The effectiveness and superiority of the proposed domain adaptation method were verified on four transfer diagnostic case studies, i.e., transfer diagnostic across bearing specifications, transfer diagnostic across escalator roller specifications, transfer diagnostic across transducers on bearing datasets, and transfer diagnostic across transducers on the gearbox datasets.

Fleet-based early fault detection of wind turbine gearboxes using physics-informed deep learning based on cyclic spectral coherence

The development of a reliable and automated condition monitoring methodology for the detection of mechanical failures in rotating machinery has garnered much interest in recent years. Thanks to the rise in popularity of machine learning techniques, the number of purely data-driven approaches that try to tackle the issue of vibration-based condition monitoring has also drastically improved. Instead of directly using the vibration measurement data as input to a machine learning model, this work first exploits the cyclostationary characteristics inherent to vibration waveforms originating from rotating machinery. The proposed methodology first estimates the two-dimensional cyclic spectral coherence map of a vibration signal in order to decompose the cyclic modulations on the cyclic and carrier frequency plane. While this provides an effective tool to visualize any potential modulation signatures of faulty gears or bearings, it does not allow for easy inspection over time due to its dimensions. To tackle this issue, this paper proposes an unsupervised deep learning approach to wield this vast amount of data as a tool for detecting persistent changes in the modulation characteristics of the vibration signals. In the first phase, a deep autoencoder learns to reconstruct predictions of the cyclic coherence maps based on unlabeled healthy vibration data and the machine operating conditions. Two post-processing steps improve the predictions by mitigating frequency shifts and outlier or noisy measurements. Lastly, the residual error between the predicted and the actual coherence map is then aggregated and employed for further alarming based on thresholds. The autoencoder model is trained using five years of gearbox vibration data from five different wind turbines. The methodology is then validated on two faulty and eight healthy turbines. The results confirm that the proposed approach can deliver clear indications of failure for the faulty turbine while being completely devoid of any significant alarm trends for the healthy turbines. Thanks to the combination of highly effective cyclostationary signal processing with deep learning while using the operating conditions, the proposed methodology can detect and track incipient mechanical faults from non-stationary vibration data of rotating machinery. Lastly, it is important to emphasize that the proposed method is capable of learning the healthy behavior on one turbine and predicting the expected behavior on another turbine.

LPI waveform design for radar system against cyclostationary analysis intercept processing

Low probability of intercept (LPI) property has provided the radar system with superior survivability on the practical battlefield. In this paper, we put forward a waveform design approach to enhance the LPI performance for radar systems by considering the intercept processing of the electronic reconnaissance (ER) systems. Based on this approach, an LPI waveform design problem against the typical cyclostationary analysis (CSA) widely performed by the ER systems is studied and further formulated as an optimization problem. In this problem, the deviation between the cyclic spectrum of the designed waveform and that of the Gaussian white noise is minimized to improve the LPI performance. Meanwhile, the optimal detection signal-to-noise ratio (SNR) restriction is enforced to ensure detection ability. The resulting optimization problem is shown to be a non-convex quartic programming that is intractable in general. To solve the problem efficiently, a structural sequential greedy optimization (S-SGO) algorithm is proposed. The proposed algorithm performs an ingenious reparameterization of the radar waveform vector and solves related problems in a polynomial-time based on the thought of alternation optimization. The convergence of the proposed S-SGO is also investigated. Numerical results verify the effectiveness of the proposed approach for the LPI waveform design as well as the proposed algorithm.

Cyclic correntropy: Properties and the application in symbol rate estimation under alpha-stable distributed noise

Over the past decades, cyclostationary signal processing has been considered one of the most critical theories in the field of nonstationary signal processing. Moreover, it has been widely adopted to handle practical problems, including signal parameter estimation, weak signal detection and pattern recognition. To improve the robustness of conventional methods under non-Gaussian noise, cyclic correntropy was recently proposed as the extension of correntropy in the cycle frequency domain. Due to the advantages inherited from both cyclostationary statistics and correntropy, cyclic correntropy has been employed in various applications involving co-channel interference and impulsive noise, such as carrier frequency estimation, direction of arrival (DOA) estimation, time difference of arrival (TDOA) estimation, automatic modulation classification and bearing fault diagnosis. Although cyclic correntropy has gained much attention, the related theoretical study is still insufficient, prohibiting further applications in other areas. To complete the theoretical framework, the existence condition of cyclic correntropy is first discussed in detail. Then, the relations among the cyclic correntropy spectrum, the symbol rate and the carrier frequency are addressed and proved mathematically. Besides, other properties of cyclic correntropy are also studied, involving symmetry, conjugation and time-shifting. These properties are studied for the first time and they fulfill the void of cyclic correntropy theory. Furthermore, a novel method is proposed for symbol rate estimation under non-Gaussian noise. Simulations are executed to validate the proposed method's superior robustness compared with other methods based on different cyclic spectra under the framework of cyclostationary signal processing. This method contributes to the application of cyclic correntropy, further highlighting the significance of the properties mentioned above.

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.

Robust time delay estimation with unknown cyclic frequency in co-channel interference and impulsive noise

Time delay estimation (TDE) has been an essential topic in both theoretical research and engineering practice. The effective models and solutions related to this work have been offered by pioneers, and preferable results are achieved. Nevertheless, in the environment of co-channel interference and impulsive noise, the traditional methods are degraded or even be unavailable. To solve these problems, a robust TDE method is proposed in this paper. On the one hand, the novel method designed in cyclostationary signal processing can suppress the co-channel interference effectively, and the cyclic frequencies of interference signals are not necessary. On the other hand, the novel method equipped with a nonlinear function can deal with impulsive noise and performs well compared to the traditional methods in Gaussian noise. In addition, theoretical analysis and comprehensive Monte Carlo simulations demonstrate the superiority of the proposed method compared to the existing competitive methods. It is believed that the robust TDE method could be fully utilized in more engendering fields, and the technologies involved could also be taken into consideration in other research.

Evidence for non-Rayleigh characteristics in ship underwater acoustic signatures.

This work examines ship underwater acoustic signature amplitude statistics and statistical distributions and explores the hypothesis that ship signatures exhibit amplitude fluctuations that are different from Rayleigh-distributed ambient ocean noise. Signature measurements from a small oceanographic ship conducting a variety of maneuvers are examined, focusing on those conditions where propeller cavitation and broadband signal modulation occur, specifically during maximum speed runs and turning maneuvers. A key difference for a ship signature is the amplitude modulation generated by propeller cavitation, and this is found to be associated with super-Rayleigh signal characteristics. Cyclostationary processing techniques are used to estimate propeller shaft- and blade-rate modulation. Under conditions of clearly observable propeller modulation, time-series statistics scintillation index and skewness showed values significantly in excess of Rayleigh-distributed values. Ship signature amplitude probability density functions were found to be better matched by a K-distribution model with small shape factor, indicating clearly non-Rayleigh behavior. Evidence for a secondary, high-amplitude, lognormally distributed sound generation mechanism was observed during maximum helm turns.

Hyperbolic tangent cyclic correlation and its application to the joint estimation of time delay and doppler shift

Gaussian distribution is a classic model for additive background noise in scientific research. By assuming and applying Gaussian noise, scholars in different fields can apply themselves to fundamental research and propose many innovative theories based upon Gaussianity. As the scope of engineering applications continues to expand, a single model of background noise cannot meet the more stringent conditions, and the errors caused by inappropriate noise models cannot be ignored. In this paper, alpha-stable distribution is utilized to model additive background noise because of the generality of this distribution. Correspondingly, a novel similarity measurement named hyperbolic tangent correlation (HTC) is proposed to replace the conventional correlation. Then, hyperbolic tangent cyclic correlation (HTCC) used in cyclostationary signal processing is proposed and thoroughly studied. HTC and HTCC emphasize preserving the signal of interest (SOI) rather than suppressing the noise, as traditionally practiced. In particular, they effectively process both the amplitude and phase information in the SOI. To demonstrate the superiority of HTCC in processing amplitude and phase information against background noise, a representative application in time-frequency analysis is presented, and the resulting performance is compared to that of the existing methods. Considering the beneficial mathematical properties of the hyperbolic tangent function, we hope that HTC and HTCC will have more applications in signal processing.

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.

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.

Cyclostationarity Based Sonar Signal Processing

This paper presents a reliable method for target vessel identification in passive sonar by exploiting the underlying periodicity of propeller noise signal, using the principles of cyclostationarity. In conventional signal processing methods, random signals are treated as statistically stationary and the parameters of the underlying physical mechanism that generates the signal would not vary in time. However, for most manmade signals, some parameters vary periodically with time and this requires that random signals be modeled as cyclostationary. In the field of sonar, the propeller noise signal generated by underwater vessels is cyclostationary. As a ship propagates in the sea, noise generated during the collapse of cavitation-induced bubbles are modulated by the rotating propeller shaft and this results in characteristic amplitude modulated random noise signal, which can be detected using passive sonar. Processing these signals, the number of blades and the shaft frequency of the propeller can be identified. In this work, cyclostationary processing technique is introduced for processing propeller noise signal and it is observed to provide better noise immunity. A detailed comparison with the conventional DEMON processing is also presented.

Noise and Disturbance Reduction for Heart Sounds in Cycle-Frequency Domain Based on Nonlinear Time Scaling

Through an investigation of various clinical cases, heart sounds are found to be quasi-cyclostationary. Nonlinear time scaling from cycle-to-cycle is proposed to enhance cyclic stationarity, where nonlinear time scaling is approximated by a piecewise linear function. The techniques of cyclostationary signal processing are employed in this paper to reduce noise and disturbance in the cycle-frequency domain. Heart sounds can be theoretically recovered in the presence of additive, zero mean noise, and disturbance (perhaps non-Gaussian, nonstationary, or colored). The experimental tests in various conditions confirm the theoretical results.

Cyclostationary Analysis based Fault Feature Extracting of Rolling Element Bearing

Many researches have proven that the vibration signal of rolling element bearing can be considered as a kind of cyclostationary signal (CS) since its periodically time various characteristics especially when fault occurs. In this paper, the basic theories of second-order cyclostationary signal processing is introduced. Then, a method so called slice analysis based on spectrum correlation density function is proposed, and it is employed in fault feature extracting to the vibration signal of rolling element bearing. Simulation and application results demonstrate that the slice analysis method is available and effective in fault diagnosis of rolling element bearing.

Acousto-optic cyclostationary signal processing

Cyclostationary signal-processing techniques implemented by means of acousto-optics are considered. Cyclic-processing methods are reviewed and motivated, such as the cyclic correlation and the cyclic spectrum. It is shown that the cyclic correlation can be computed at cycle frequencies of interest by use of one-dimensional time-integrating correlators in additive or multiplicative configurations. Detection of cycle frequencies is briefly considered, and a one-dimensional acousto-optic spectrum-analysis approach is described that is effective for amplitude-modulated signals. The problem of computing the two-dimensional cyclic correlation for all cycle frequencies and lags is then considered. This is accomplished by means of an acousto-optic triple-product processor configured in a manner similar to that used for ambiguity-function generation. The cyclic spectrum can be obtained in a postprocessing step by Fourier transformation of the cyclic correlation in one dimension. Higher-order extensions of the cyclic correlation are also discussed, and it is shown how a two-dimensional slice of the three-dimensional cyclic triple correlation can be computed by use of an acousto-optic four-product processor.