Cyclostationary Signals Research Articles

On the experimental full scale vibrational response analysis of a large pleasure yacht

This paper presents an experimental investigation carried out on a large pleasure yacht during a sea trial using vibration signal processing methods to characterize its dynamic operational behaviour and to identify contributions of the main sources acting on the system including the onset of the propeller cavitation phenomenon.Synchronous averages were computed to isolate vibration components associated with a specific source acting on the system. Their use jointly with variance computation allowed the detection of the rise of cavitation. Spectral Kurtosis analysis suggested optimal-bandwidth of the filter for system response demodulation and so better identify the rise of high frequency energy of bursting contents induced from cavitation strictly linked to propeller rotation.Cyclic modulation spectrum was also adopted, which allows to extract the modulation features of cyclostationary signals, shows the rise of an interaction between high frequency contents and blade passage phenomenon approaching cavitating condition.The results seem to provide an interesting solution based on the vessel vibrational response to define source contribution to the targets for a better identification of the dynamic system. Moreover, the proposed diagnostic methods reveal reliable tools for real time condition-based monitoring of the marine propeller to distinguish cavitation and wake energy contribution using vibrational response measured on the hull instead of hydrophone arrays.

Adaptive filter design for cyclostationary processes associated with sine-wave extraction operation

Cyclostationary signals have been generally used in condition monitoring and fault diagnosis of bearings, for which the adaptive filter is important in obtaining the signal-of-interest cyclostationary process from a disturbed signal. However, due to the nonstationarity of cyclostationary signals, their adaptive filters are usually time-varying and difficult to be implemented. In this study, a new optimum filter is obtained by converting the time-varying optimization function to be time-invariant using a sine-wave extraction (SE) operator, for which the adaptive implementation is designed and analyzed. The time-varying linear minimum mean-square error is converted to be time invariant using the SE operator, and its solution is time invariant but without explicit expression. Subsequently, an adaptive implementation, called the SE least mean square (SE-LMS), is introduced, for which the mean and weighted mean-square-deviation (MSD) are explicitly expressed. The scope of step size is determined to obtain a mean-convergent and mean-square-stable SE-LMS. The steady-state SE-operated excess mean-square-error is analyzed, and its explicit expression is obtained. The SE-LMS algorithm uses only a single cyclic frequency, based on which, the combined SE-LMS algorithm is introduced for a cyclostationary signal with multiple cyclic frequencies. Finally, several simulations are designed to verify the superiority of the proposed estimators over the time-average operator-based estimator.

Blind cyclostationary fault feature extraction in rolling bearings: a dual adaptive filtering approach

Extracting cyclostationary features from vibration signals is one of the most effective approaches in bearing fault diagnosis. However, current methods require prior knowledge of cycle-frequencies or other statistical information, which constrains their applicability across various scenarios. In this paper, we introduce a novel dual adaptive filtering method, incorporating cycle-frequency estimation to solve the existing problem. The method firstly employs an adaptive line enhancer (ALE) to isolate the first-order cyclostationary signal, thereby the cycle-frequencies can be effectively detected using an exhaustive estimation technique. Subsequently, an adaptive frequency-shift (FRESH) filter is further applied to extract the second-order cyclostationary features from the residual components. The proposed method successfully overcomes the challenge of separating cyclostationary signals without prior knowledge and can be tailored to real-time application scenarios. Besides, the approach distinguishes between the two cyclostationary signal types, effectively resolving any aliasing concerns inherent in their statistical characteristics. The effectiveness of the method is verified through simulation, experiments, and engineering data analysis. It is demonstrated that the method significantly enhances diagnostic accuracy and is more suitable for early fault diagnosis of rolling bearings by estimating spectral coherence on the extracted signals.

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.

Generalized spectrum analysis of Chirp Cyclostationary signals associate with linear canonical transform

A chirp cyclostationary (CCS) process is a nonstationary stochastic process, whose statistics have been defined and utilized in radar and communication signal processing. However, spectrum analysis of CCS signals, which provides a spectral view to characterize a signal, has not been performed. Classical spectrum analysis is based on the Fourier transform, which is not suitable for CCS signals because of the multiplicative chirp signals in a CCS model. In this study, we propose a generalized spectral representation of chirp cyclostationary signals associated with a linear canonical transform. The proposed representation shows that a CCS signal can be represented by a linear combination of a series of jointly stationary and equal-bandwidth processes, which bridge the nonstationary and stationary processes. Furthermore, the relationships between the second-order statistics of the CCS process and its stationary representations are introduced. Finally, based on the above observations, a linear time-varying Wiener filter was designed for CCS signal denoising and time-varying channel estimation. Finally, the relationships between the nonstationarity of the input and output and time-varying properties of the systems are discussed, which are helpful for determining the nonstationarity of the outputs or the time-varying property of a system.

Combined Weighted Envelope Spectrum: An enhanced demodulation framework for extracting characteristic frequency of rotating machinery

Envelope spectrum plays a pivotal role in the surveillance and diagnostics of rotating machinery. Two prevailing techniques for constructing this spectral quantity are narrowband demodulation and cyclostationary analysis. However, the former is susceptible to failure under low Signal-to-Noise Ratio (SNR) conditions or in the presence of non-Gaussian noise, while the latter exhibits sensitivity to cyclostationary noise, such as electromagnetic interferences. Notably, specific tasks determine the characteristic frequencies expected to be detected. More precisely, the determination of target component and noise interference depends on the mechanical part under scrutiny. Consequently, the envelope spectra provided by classical methods often manifest deficiencies when confronted with intricate monitoring signals from rotating machinery. To address this challenge, this paper proposes an enhanced demodulation framework—Combined Weighted Envelope Spectrum (CWES), tailored for extracting specific characteristic frequencies. First, a cyclostationary model for rotating machinery is presented, demarcating the target component as solely the cyclostationary signal caused by the mechanical element of concern. Second, the weighting functions with/without prior knowledge of characteristic frequency are elaborately designed, and the Adaptive Combined Weighted Envelope Spectrum (ACWES) and the Optimal Combined Weighted Envelope Spectrum (OCWES) are constructed correspondingly. Moreover, the indicator Characteristic peak-to-Noise peak Ratio (CNR) is proposed to evaluate the demodulation performance of different envelope spectra. Ultimately, the effectiveness of ACWES and OCWES is validated by simulation signals and experimental data from rolling bearing, centrifugal pump, and Francis turbine, and the comparison with the state-of-the-art demodulation methods verifies the superiority of the proposed enhanced demodulation framework.

Cyclostationarity of Communication Signals in Underwater Acoustic Channels

The effect of underwater acoustic propagation on the cyclostationary features of communication signals is modeled and analyzed. Two kinds of channels are considered: the multiscale-multilag channel, over which mobile and wideband acoustic systems usually communicate, and the dispersive channel resulting from low-frequency modal propagation in shallow water. It is shown that multiscale-multilag channels transform cyclostationary signals into a sum of velocity and acceleration-dependent time-warped cyclostationary processes. This time-warping is carefully taken into account to efficiently recover the cyclostationary features. On the other hand, it is found that low-frequency dispersive channels preserve the original periodicity but attenuate the shorter cycles and spread the correlations. To illustrate the theoretical results, applications with simulated and real data are also presented. Specifically, the problem of estimating time-varying Doppler scales is addressed for multiscale-multilag channels as well as the detection of signals with unique cyclostationary signatures. The example of blind symbol-rate estimation applied to covert communications in dispersive channels is also discussed. Special attention is paid to phase-shift keying (PSK), quadrature amplitude modulation (QAM), orthogonal frequency-division multiplexing (OFDM), and direct-sequence spread-spectrum (DSSS) signals. Accompanying supplementary material provides the MATLAB code used for the estimation and detection examples.

Cyclic Detectors in the Fraction-of-Time Probability Framework

The signal detection problem for cyclostationary signals is addressed within the fraction-of-time probability framework, where statistical functions are constructed starting from a single time series, without introducing the concept of stochastic process. Single-cycle detectors and quadratic-form detectors based on measurements of the Fourier coefficients of the almost-periodically time-variant cumulative distribution and probability density functions are proposed. The adopted fraction-of-time approach provides both methodological and implementation advantages for the proposed detectors. For single-cycle detectors, the decision statistic is a function of the received signal and the threshold is derived using side data under the null hypothesis. For quadratic-form detectors, the decision statistic can be expressed as a function of the received signal without using side data, at the cost of some performance degradation. The threshold can be derived analytically. Performance analysis is carried out using Monte Carlo simulations in severe noise and interference environments, where the proposed detectors provide better performance with respect to the analogous detectors based on second- and higher-order cyclic statistic measurements.

A Fourier-based explanation of 1D-CNNs for machine condition monitoring applications

Neural networks (NN) have generated extensive interest in the field of machine condition monitoring (MCM). Many applications are however adapting structures and approaches from fields where NNs are highly established (e.g., image classification). This is done despite many neural network layers presenting strong similarities to signal processing steps that are well established in MCM. This paper aims at providing a mathematical analysis of typical NN architectures and layers, with specific attention to similarities to common signal processing steps such as filtering, downsampling, and enveloping. The set of strong analogies between NN and traditional MCM tools enables this work to provide MCM-specific guidelines for the design and tuning of NN architectures for MCM-specific applications. Most MCM applications are often characterised by periodic and cyclostationary signals, a situation not frequently encountered in many other NN applications. Hence, the Fourier-based explanation of the typical NN layers will be specific to the solution of typical MCM problems (e.g., diagnostics of gears and bearings). The study is aligned with the current trends of explainable AI and physics informed neural networks (PINN), in the sense that it aims at producing mathematical rules for a rational design of the network, drawing on the expertise accumulated in decades of signal processing for MCM. This is however done without upsetting traditional NN architectures, but rather trying to provide clear reasons for the setting of network parameters. The analytical work will be verified with numerical tests, which will also enable practical considerations, and by application of the suggested guidelines to the popular Case Western Reserve University (CWRU) experimental dataset.

Electricity consumption simulation using random coefficient periodic autoregressive model

The concept of a continuous-time conditional linear random process involves a random kernel being integrated stochastically by a process with independent increments, which is often called a “generative process”. In cases where the “generative process” is Poisson, the resulting model represents an investigated signal as a sum of numerous stochastically dependent random impulses each of which occurs according to some inhomogeneous Poisson arrival process. This model can be applied to represent various processes related to energy consumption, such as electricity loads of electrical power systems, gas and water consumption, and other energy resources, while also considering the signals’ cyclostationarity, which is usually caused by the rhythmic nature of consumer behaviour. A member of the discretetime conditional linear cyclostationary random processes class is the random coefficient periodic autoregressive (RCPAR) model, which is appropriate for use in energy informatics, including estimation, forecasting, and computer simulation purposes. The primary objective of the paper is to establish a procedure for simulating the hourly electricity consumption of small and medium-sized enterprises using the RCPAR model, which has periodic parameters and creates cyclostationary properties while also accounting for the investigated process conditional heteroscedasticity. The statistical estimation step of the proposed procedure uses the general methodology for estimating the parameters of the RCPAR model and the methods of statistical analysis of cyclostationary signals. This step is used to identify the simulation characteristics. The simulation step is based on the methods of cyclostationary white noise generation and its transformation by a digital linear filter with random parameters. The last ones are obtained using the Gaussian random vectors computer simulation methods, taking into account the cyclostaionarity property.

Chirp cyclic moment for chirp cyclostationary processes: Definitions and estimators

In high-mobility wireless communications and radar systems, a higher carrier frequency and higher moving speed/acceleration of terminals enhance the impact of the time-varying Doppler effect. This effect alters the cyclostationarity of the transmitted signal and characterizes the received signal as a chirp cyclostationary (CCS) signal. The generalized cyclic statistics of CCS signals are defined based on Fourier analysis, which is either zero-value or non-bandlimited, and is thus inefficient. In this study, the linear canonical transform (LCT), a generalized form of the Fourier transform, was used to address these issues. The moment function is a k-dimensional variable comprising a single time variable and k−1 lag variables. The chirp cyclic moment and the time-varying canonical spectrum were designed as the LCT of the moment with respect to the time and lag variables, respectively. Furthermore, an estimator of the chirp cyclic moment was defined, which is demonstrated to be asymptotic unbiased, asymptotic mean-square-consistent and asymptotic complex normal. Applications of the chirp cyclic moment in radar parameter estimation and electrocardiogram signal characterization were verified using simulated and real-life data.

Fixed-point FPGA Implementation of the FFT Accumulation Method for Real-time Cyclostationary Analysis

The spectral correlation density (SCD) is an important tool in cyclostationary signal detection and classification. Even using efficient techniques based on the fast Fourier transform (FFT), real-time implementations are challenging because of the high computational complexity. A key dimension for computational optimization lies in minimizing the wordlength employed. In this article, we analyze the relationship between wordlength and signal-to-quantization noise in fixed-point implementations of the SCD function. A canonical SCD estimation algorithm, the FFT accumulation method (FAM) using fixed-point arithmetic, is studied. We derive closed-form expressions for SQNR and compare them at wordlengths ranging from 14 to 26 bits. The differences between the calculated SQNR and bit-exact simulations are less than 1 dB. Furthermore, an HLS-based FPGA design is implemented on a Xilinx Zynq UltraScale+ XCZU28DR-2FFVG1517E RFSoC. Using less than 25% of the logic fabric on the device, it consumes 7.7 W total on-chip power and has a power efficiency of 12.4 GOPS/W, which is an order of magnitude improvement over an Nvidia Tesla K40 graphics processing unit (GPU) implementation. In terms of throughput, it achieves 50 MS/sec, which is a speedup of 1.6 over a recent optimized FPGA implementation.

Deep-Learning-Based Classification of Digitally Modulated Signals Using Capsule Networks and Cyclic Cumulants.

This paper presents a novel deep-learning (DL)-based approach for classifying digitally modulated signals, which involves the use of capsule networks (CAPs) together with the cyclic cumulant (CC) features of the signals. These were blindly estimated using cyclostationary signal processing (CSP) and were then input into the CAP for training and classification. The classification performance and the generalization abilities of the proposed approach were tested using two distinct datasets that contained the same types of digitally modulated signals, but had distinct generation parameters. The results showed that the classification of digitally modulated signals using CAPs and CCs proposed in the paper outperformed alternative approaches for classifying digitally modulated signals that included conventional classifiers that employed CSP-based techniques, as well as alternative DL-based classifiers that used convolutional neural networks (CNNs) or residual networks (RESNETs) with the in-phase/quadrature (I/Q) data used for training and classification.

Modeling analysis of UAV communication cyclostationary signal based on virtual reality

In order to reduce the redundancy of the analysis process of UAV communication cyclostationary signal, a modeling and analysis method of UAV communication cyclostationary signal based on virtual reality technology is proposed. Using the VR technology, the 3D scene of UAV flight is reconstructed, and the mutual information and correlation dimension are obtained. Using the maximum negative entropy FastICA algorithm and non-cyclic stationary signal processing algorithm, the anti-jamming model of cyclic stationary signal processing is established by analyzing the signal compression performance and time delay of pseudo-random sequence. The experimental results show that there is no obvious signal fluctuation in the time domain of the oscillation signal and the reconstruction results of the oscillation signal, and the amplitude fluctuation is not large.

Toeplitz Cyclic-MUSIC Algorithms for DOA Estimation of the SOCS Correlated Signals

This letter addresses the problem of direction-of-arrival (DOA) estimation for cyclostationary signal when the second-order cyclic statistics (SOCS) of signals are correlated. We first present a Toeplitz Cyclic-MUSIC algorithm for multichannels receiver by exploiting signal cyclostationarity. Based on cyclic autocorrelation of the received signal, a new pesudocyclic covriance matrix, which is Toeplitz, is constructed. The rank of Toeplitz matrix is equal to the number of signals even if the SOCS of signals are correlated. So the MUSIC algorithm can be used to estimate the DOAs of sources. Moreover, a single channel Toeplitz Cyclic-MUSIC algorithm for the the single-channel receiver is proposed to avoid the affect of channel inconsistency. The effectiveness of the proposed algorithms is verified by computer simulation, and the performance of the proposed algorithms is compared with the existing algorithms correspondingly.

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.

Application of wireless network communication technology in interior decoration system and Commercialization of hospital buildings

In view of the low accuracy of signal perception caused by unbalanced task allocation of high-rise hospital building interior decoration system, a high-rise building interior decoration system is designed based on wireless network communication technology. Hardware part: the terminal node based on STM32 MCU is connected with the environment sensor, and the BC35-GNB-IOT communication module is set to ensure the anti-interference of the link. In the software part, the angular power spectrum is used to establish the indoor communication scene classification model of high-rise hospital buildings, the task is divided into several sub-tasks according to the time complexity, and the wireless network is used to realize the dynamic scheduling of tasks. The indoor environment sensing algorithm is designed to detect the performance of cyclostationary signals. It shows that the sensing accuracy of the system designed in this paper is higher than that of the system without a wireless network, which has good robustness and can improve the service quality of indoor environmental monitoring.

Minimum noise amplitude deconvolution and its application in repetitive impact detection

Blind deconvolution (BD) is an effective technology for rotating machinery fault detection because it significantly weakens noise and reduces the interference of the system transmission path. This paper analyses the possible shortcomings of several popular BDs in detecting repetitive impacts hidden in rotating machinery signals. Then a new index named periodic noise amplitude ratio (PNAR) is defined to measure the noise level of fault signals. Minimum noise amplitude deconvolution (MNAD) is a new BD algorithm based on PNAR minimization. Unlike the existing BDs, MNAD does not focus on the impacts with certain randomness in their moments of occurrence but enhances the repetitive impact characteristics by weakening the defined periodic noise. MNAD is particularly suitable for detecting repetitive impacts hidden in cyclostationary signals. Simulation analysis and experimental results show that MNAD adaptively determines one or more resonance bands generated by repetitive impacts and has a good suppression effect on the noise in the resonance bands. The implementation of MNAD is available in MATLAB community.

Linear time-varying matched filter for known and unknown SOI generalized cyclostationary signal with multiple cyclic frequencies

Chirp cyclic matched filter has been designed for chirp cyclostationary (CCS) signals, a kind of generalized cyclostationary signals, recently. However, it is designed based on statistical prior information and waveform of the signal-of-interest (SOI) CCS signal, which works only for CCS signal with a single chirp cyclic frequency. As known, the prior information of SOI signal may not be exactly known or the measured waveform of SOI signal is noised in practical applications, which decreases performance of the algorithm. In this study, by decomposing the imprecisely known SOI signal as the summation of SOI signal and an unknown additive disturbance, three kinds of chirp cyclic matched filters are designed according to the value of signal-to-noise ratio (SNR). Furthermore, noticing the CCS signal usually contains multiple chirp cyclic frequencies, three kinds of combined chirp cyclic matched filter are designed for known/unknown SOI CCS signals by linearly combining the chirp cyclic matched filter at every chirp cyclic frequency. Moreover, ramifications of the truncation process and complexity of the proposed algorithms are analyzed. Finally, simulation results validate the improvement of the chirp cyclic matched filter based on multiple chirp cyclic frequencies than on a single chirp cyclic frequency in different SNR situations.

Early warning of damaged wind turbine blades using spatial–temporal spectral analysis of acoustic emission signals

A spatial–temporal processing framework is proposed to forecast the wind turbine blade damage in the early stage. The sparse Bayesian learning beamforming (SBL) is applied to data received by a microphone array for enhancement of weak signals and suppressing interference of environmental noise. Then short-time Fourier transform (STFT) is utilized to create a time–frequency spectrum and analyze the nonstationarity of acoustic emission signals. The period of radiation energy change and the cyclic modulation spectrum (CMS) are respectively calculated from the time–frequency spectrum. Blade fault detection is performed based on whether or not the presence of the periodicity or cyclostationary signatures in acoustic emission signals. Numerical simulations have shown that the natural frequencies of acoustic emission signals tend to decrease when there is a hole on the blade surface. The experimental results have verified the effectiveness and robustness of the proposed blade damage detection method.