Cyclic Spectral Analysis Research Articles

A coarse-to-fine demodulation frequency band selection strategy for multi-fault detection of rotating machinery

The most critical issue of envelope demodulation analysis for rotating machinery fault diagnosis is to identify the fault-induced informative frequency bands. However, the majority of currently used blind or targeted demodulation methods either only focus on selecting a single frequency band as the best (which may result in unexpected missed diagnosis in the case of multiple faults) or require prior fault knowledge (this is unfeasible for most blind cases). To address this issue, this study proposes a coarse-to-fine demodulation frequency band selection strategy for multi-fault detection of rotating machines. A reweighted Variational Mode Decomposition algorithm, aided by a new evaluation indicator coined fault information correlation index (CFII), is first proposed to coarsely select the useful frequency bands for signal initial denoising and reconstruction. Then, Cyclic Spectral Coherence (CSCoh), a powerful cyclic spectral analysis tool, is implemented to further process the reconstructed signal for fine demodulation analysis. To solve the problem of selecting the spectral frequency band of CSCoh, a practical guideline is established together with the cyclic-frequency-domain fault information index (αFII) for the automatic determination of informative frequency bands to be integrated. Benefiting from the above two stages and developed indicators, the proposed method can effectively detect features of incipient and multiple faults under complex interferences without requiring any prior candidate fault period. Its effectiveness and advancements over several commonly used demodulation techniques are validated using simulation and experimental scenarios involving multi-fault gears and bearings.

Gaussian-Distributed Spread-Spectrum for Covert Communications.

Covert communication techniques play a crucial role in military and commercial applications to maintain the privacy and security of wireless transmissions from prying eyes. These techniques ensure that adversaries cannot detect or exploit the existence of such transmissions. Covert communications, also known as low probability of detection (LPD) communication, are instrumental in preventing attacks such as eavesdropping, jamming, or interference that could compromise the confidentiality, integrity, and availability of wireless communication. Direct-sequence spread-spectrum (DSSS) is a widely used covert communication scheme that expands the bandwidth to mitigate interference and hostile detection effects, reducing the signal power spectral density (PSD) to a low level. However, DSSS signals possess cyclostationary random properties that an adversary can exploit using cyclic spectral analysis to extract useful features from the transmitted signal. These features can then be used to detect and analyse the signal, making it more susceptible to electronic attacks such as jamming. To overcome this problem, a method to randomise the transmitted signal and reduce its cyclic features is proposed in this paper. This method produces a signal with a probability density function (PDF) similar to thermal noise, which masks the signal constellation to appear as thermal white noise to unintended receivers. This proposed scheme, called Gaussian distributed spread-spectrum (GDSS), is designed such that the receiver does not need to know any information about the thermal white noise used to mask the transmit signal to recover the message. The paper presents the details of the proposed scheme and investigates its performance in comparison to the standard DSSS system. This study used three detectors, namely, a high-order moments based detector, a modulation stripping detector, and a spectral correlation detector, to evaluate the detectability of the proposed scheme. The detectors were applied to noisy signals, and the results revealed that the moment-based detector failed to detect the GDSS signal with a spreading factor, N = 256 at all signal-to-noise ratios (SNRs), whereas it could detect the DSSS signals up to an SNR of -12 dB. The results obtained using the modulation stripping detector showed no significant phase distribution convergence for the GDSS signals, similar to the noise-only case, whereas the DSSS signals generated a phase distribution with a distinct shape, indicating the presence of a valid signal. Additionally, the spectral correlation detector applied to the GDSS signal at an SNR of -12 dB showed no identifiable peaks on the spectrum, providing further evidence of the effectiveness of the GDSS scheme and making it a favourable choice for covert communication applications. A semi-analytical calculation of the bit error rate is also presented for the uncoded system. The investigation results show that the GDSS scheme can generate a noise-like signal with reduced identifiable features, making it a superior solution for covert communication. However, achieving this comes at a cost of approximately 2 dB on the signal-to-noise ratio.

Proportional Selection Scheme: A Frequency Band Division Tool for Rolling Element Bearing Diagnostics

The cyclic spectral coherence analysis has been proved to be a useful tool to reveal the hidden periodic or repetitive patterns, and how to determine an optimal demodulation band is crucial for characterizing the fault characteristic of the rolling element bearing (REB). Thus, a proportional selection scheme based on a bottom-up strategy is proposed in this study, which can determine an optimal demodulation band and realize bearing fault feature extraction under the conditions of poor frequency resolution and a lower signal-to-noise ratio (SNR). First, compared with conventional frequency division structures, such as the 1/3-binary tree structure, the finer frequency band groups with the same bandwidth in each division level can be obtained automatically and strictly under poor frequency resolution conditions. Second, the richness of the REB fault information of each divided frequency band can be evaluated by the improved diagnostic feature indicator under a lower SNR condition. By using the scheme, the fault characteristic of the REB can be exposed. The efficacy of the proposed scheme is supported by simulations and experiments under some tough conditions

Low-Rank Enforced Fault Feature Extraction of Rolling Bearings in a Complex Noisy Environment: A Perspective of Statistical Modeling of Noises

The fault feature extraction of rolling element bearings is of critical interest for fault diagnosis. The fault impulses are always buried in strong and complex background noise, which makes it hard to detect the fault characteristics and further diagnose the bearing. Many feature extraction techniques have been developed, which assumed that the noise obeys a single and straightforward Gaussian distribution. However, the noise is usually non-Gaussian and cannot be characterized by a single distribution in practical industrial scenarios. A fault feature extraction model for rolling bearings within complex noise is proposed in this article, where the complex noise is modeled by the Gaussian mixture model (GMM), thus highlighting the fault characteristics. The 2-D representation of the measurement is obtained by exploiting cyclic spectral analysis. Then, the measurement is further modeled as a low-rank faulty component and a complex noise component, where the noise is characterized by the GMM. Therefore, the model is named the GMM enable low-rank (GMM-LR) model. The variational Bayes inference method is employed to estimate the posterior of the proposed model, which can obtain the optimal solution to characterize the fault characteristics. Finally, the bearing fault features are detected by the enhanced envelope spectrum (EES). Both the synthetic and experimental signals are studied to demonstrate the efficacy of the proposed technique. The superiority is also validated by comparisons with envelope spectrum (ES), cyclic spectral analysis, spectral kurtosis (SK), and robust principal component analysis (RPCA).

Three-dimensional palatal rugae recognition based on cyclic spectral analysis

ObjectivePalatal rugae represent a new type of biometric characteristic that has a low cost and cannot be easily destroyed or forged. It can be used in forensic identification in special environments. However, prior research on palatal rugae recognition relied on the participation of forensic experts. In this study, a digital acquisition scheme of three-dimensional palatal rugae data is designed. MethodsAccording to the characteristics of palatal rugae, a cyclic spectrum is introduced as the recognition feature, and a k-nearest neighbor classifier is used to realize palatal rugae recognition. In addition, two strategies are utilized to reduce the computational complexity and information redundancy caused by the large dimension of three-dimensional data. Accordingly, isometric slicing is proposed to reduce the three-dimensional palatal rugae data dimension, and the cyclic spectral feature block partition scheme is then used to reduce the feature dimension. ResultsThe experimental results indicate that the accuracy of the proposed method is as high as 95 %. ConclusionThe proposed method uses pattern recognition technology to realize automatic palatal rugae recognition, which can reduce the dependence on forensic experts to achieve rapid forensic identification. SignificanceThis attempt is helpful in promoting the digitization of a forensic identification system based on palatal rugae.

A practical methodology for enhancement and detection of transient faults in a gearbox without prior fault feature information

Gear fault diagnosis has been the focus of research in both academia and industry in the past. Due to the complicated structures of gearboxes, the vibration signals collected from the gearbox casings are comprised of multiple sources, in which the fault-related components may be easily masked by the Gaussian and non-Gaussian noises (e.g. random external shocks and gear meshing harmonics). Moreover, fault feature frequencies of interest cannot always be obtained in advance in practical applications. Therefore, it is necessary to choose an appropriate signal processing method for gear fault diagnosis. In this study, a new practical methodology is proposed to extract the transient fault features from a gearbox vibration signal corrupted by complicated interference without prior fault feature information. In the proposed method, a modified self-adaptive noise cancellation (MSANC) algorithm is first developed for removing the interferences of gear meshing harmonics adaptively, which can overcome the shortcomings of the traditional SANC in parameter selection and convergence performance. Based on the de-noised signal, a cyclic spectral analysis tool called the fast spectral correlation and assisted by the multipoint optimal minimum entropy deconvolution adjusted algorithm is then applied to enhance and detect the certain and potential gear faults. The effectiveness of the proposed method is demonstrated by a numerical simulation and two experimental scenarios that are compared to an advanced blind optimal demodulation band selection technique. The results reveal that the proposed methodology has good capability to detect mono- and multiple gear faults under complicated interferences, and can be regarded as an efficient method for practical gear fault diagnosis, especially for applications where the fault feature frequencies are unknown in advance.

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.

New Analytical Channel Allocation Methodology for Multichannel Multi-Radio Wireless Networks

In wireless technologies, jamming attack is a main Research problem in multichannel multi-radio as they block communication in wireless networks. Malicious nodes block legitimate communication through jamming attacks that causes intentional interference. This paper presents the problem of jamming attack in multichannel multi-radio wireless network. First, Allocated the channel in Randomized manner and measure the Entropy rate. Second, defined the channel capacity. Third determined noiseless channel. Furthermore, Find the responses from channel and compare Response channel (H(S/R)) with Noise less channel (T). If H(S/R) ∈ T, Then to select the channel otherwise to reject the channel and assign (H(S/R)) = Attack. Finally, Based on the jammer detection algorithm, the result is compared with cyclic spectral analysis. But the proposed algorithm computation process is very simple than cyclic spectral analysis algorithm and Cyclostationary.Based jammer Detection Algorithm.

A deep learning method for bearing fault diagnosis based on Cyclic Spectral Coherence and Convolutional Neural Networks

Accurate fault diagnosis is critical to ensure the safe and reliable operation of rotating machinery. Data-driven fault diagnosis techniques based on Deep Learning (DL) have recently gained increasing attention due to theirs powerful feature learning capacity. However, one of the critical challenges lies in how to embed domain diagnosis knowledge into DL to obtain suitable features that correlate well with the health conditions and to generate better predictors. In this paper, a novel DL-based fault diagnosis method, based on 2D map representations of Cyclic Spectral Coherence (CSCoh) and Convolutional Neural Networks (CNN), is proposed to improve the recognition performance of rolling element bearing faults. Firstly, the 2D CSCoh maps of vibration signals are estimated by cyclic spectral analysis to provide bearing discriminative patterns for specific type of faults. The motivation for using CSCoh-based preprocessing scheme is that the valuable health condition information can be revealed by exploiting the second-order cyclostationary behavior of bearing vibration signals. Thus, the difficulty of feature learning in deep diagnosis model is reduced by leveraging domain-related diagnosis knowledge. Secondly, a CNN model is constructed to learn high-level feature representations and conduct fault classification. More specifically, Group Normalization (GN) is employed in CNN to normalize the feature maps of network, which can reduce the internal covariant shift induced by data distribution discrepancy. The proposed method is tested and evaluated on two experimental datasets, including data category imbalances and data collected under different operating conditions. Experimental results demonstrate that the proposed method can achieve high diagnosis accuracy under different datasets and present better generalization ability, compared to state-of-the-art fault diagnosis techniques.

A semi-supervised Support Vector Data Description-based fault detection method for rolling element bearings based on cyclic spectral analysis

The early and accurate detection of rolling element bearing faults, which is closely linked to the timely maintenance and repair before a sudden breakdown, is still one of the key challenges in the area of condition monitoring. Nowadays in the frames of research advanced signal processing techniques are combined with high level machine learning approaches, focusing towards automatic fault diagnosis and decision making. A plethora of Health Indicators (HIs) have been proposed to feed in machine learning models in orderto track the system degradation. Cyclic Spectral Analysis (CSA), including Cyclic Spectral Correlation (CSC) and Cyclic Spectral Coherence (CSCoh), has been proved as a powerful tool for rotating machinery fault detection. Due to the periodic mechanism of bearing fault impacts, the HIs extracted from the Cyclostationary (CS) domain can detect bearing defects even in premature stage. On the other hand, supervised machine learning approaches with labelled training and testing datasets cannot be yet realistically applied in industrial applications. In order to overcome this limitation, a novel semi-supervised Support Vector Data Description (SVDD) with negative samples (NSVDD) fault detection approach is proposed in this paper. The NSVDD model utilizes CS indicators to build the feature space, and fits a hyper-sphere to calculate the Euclidean distances in order to isolate the healthy and faulty data. An uniform object generation method is adopted to generate artificial outliers as negative samples for the NSVDD. A systematic fault detection decision strategy is proposed to estimate the bearing status simultaneously with the detection of fault initiation. Furthermore, a multi-level anomaly detection framework is built based on data at i) single sensor level, ii) machine level and iii) entire machine fleet level. Three run-to-failure bearing datasets including signals from twelve bearings are used to implement the proposed fault detection methodology. Results show that, the CS based indicators outperform time indicators and Fast Kurtogram (FK) based Squared Envelope Spectrum (SES) indicators. Moreover, the proposed NSVDD model show superior characteristics in anomaly detection compared to three classification methodologies, i.e. the Back-Propagation Neural Network, the Random Forest and the K-Nearest Neighbour.

Data Preprocessing Techniques in Convolutional Neural Network Based on Fault Diagnosis Towards Rotating Machinery

Rotating machinery plays a critical role in many significant fields. However, the unpredictable machinery faults may lead to the severe damage and losses. Hence, it is of great value to explore the precise approaches for fault diagnosis. With the development of the intelligent fault diagnosis methods based on deep learning, convolutional neural network (CNN) has aroused the attention of researchers in machinery fault diagnosis. In the light of the reduction of difficulty in feature learning and the improvement of final diagnosis accuracy, data preprocessing is necessary and crucial in CNN-based fault diagnosis methods. This review focuses on CNN-based fault diagnosis approaches in rotating machinery. Firstly, data preprocessing methods are overviewed. Then, we emphatically analyze and discuss several main techniques applied in CNN-based intelligent diagnosis, principally including the fast Fourier transform, wavelet transform, data augmentation, S-transform, and cyclic spectral analysis. Finally, the potential challenges and research objects are prospected on data preprocessing in intelligent fault diagnosis of rotary machinery.

Non-linear Phenomena Specific to Cyclic Dispersion in Laser-built Spark Plug Engines

This work presents procedures like correlation analysis and bi-spectral frequency analysis applied in order to highlight non-linear phenomena accompanying cyclic dispersion. The Liapounov exponent is highlighted as a non-linear phenomenon and its values are based on experimental data. The time-frequency analysis and cyclic spectral analysis of experimental data are used because these phenomena also have, in addition, a non-static character. Fractal-based mathematical models are established in the paper to ensure maximum modeling accuracy, since cyclic dispersion has a pronounced nonlinear as well as a non-static character. These models establish the equation between the indicated pressure and the amount of heat released during a thermodynamic cycle.

Fault Identification of Broken Rotor Bars in Induction Motors Using an Improved Cyclic Modulation Spectral Analysis

Induction motors (IMs) play an essential role in the field of various industrial applications. Long-time service and tough working situations make IMs become prone to a broken rotor bar (BRB) that is one of the major causes of IMs faults. Hence, the continuous condition monitoring of BRB faults demands a computationally efficient and accurate signal diagnosis technique. The advantage of high reliability and wide applicability in condition monitoring and fault diagnosis based on vibration signature analysis results in an improved cyclic modulation spectrum (CMS), which is one of the cyclic spectral analysis algorithms. CMS is proposed in this paper for the detection and identification of BRB faults in IMs at a steady-state operation based on a vibration signature analysis. The application of CMS is based on the short-time Fourier transform (STFT) and the improved CMS approach is attributed to the optimization of STFT. The optimal window is selected to improve the accuracy for identifying the BRB fault types and severities. The appropriate window length and step size are optimized based on the selected window function to receive a better calculation benefit through simulation and experimental analysis. Compared to other estimators, the improved CMS method provides better fault detectability results by analyzing vertical vibration signatures of a healthy motor, and damaged motors with 1 BRB and 2 BRBs under 0%, 20%, 40%, 60%, and 80% load conditions. Both synthetic and experimental investigations demonstrate the proposed methodology can significantly reduce computational costs and identify the BRB fault types and severities effectively.

The spectral amplitude modulation: A nonlinear filtering process for diagnosis of rolling element bearings

Rolling element bearings are the critical parts of every rotating machinery and their failure is one of the main reason of the machine downtime and even breakdown. For this reason, various methods have been proposed in the past for their early diagnosis. Among them, envelope analysis and cyclic spectral analysis (CSA) are the most effective and widely used approaches, working according to the principle of linear filtering process of signals to remove undesirable components. However, in many cases machine structures are excited in different frequency ranges by impacts generated when defects are engaged, hence, the signal should be filtered for multiple frequency bands to completely extract the defect signals. Also, finding the proper frequency bands for demodulation is not always a simple task. To overcome these challenges, in this paper an empirical and automated nonlinear filtering process will be proposed in which different components of a signal are decomposed based on their powers. Then, their squared envelope spectra are computed to seek the presence of bearings characteristic frequencies. Therefore, this method can be seen as complementary to the narrowband amplitude demodulation techniques. The phase of each filtered component is similar to the phase of the original signal but the magnitude is transformed. The idea is that reconstruction of a signal only by its phase preserves many useful features. A similar approach is employed by cepstrum pre-whitening for bearings diagnosis to reduce the effect of powerful exogenous sources which mask the bearings signals and, despite its simplicity, has achieved noteworthy outcomes. Finally, the performance of the proposed method is validated on real case data recorded from two test rigs. Also, its effectiveness is investigated under constant and variable speed regimes and in presence of various level of Gaussian and non-Gaussian (highly impulsive) background noise.

Characterization of cavitation and seal damage during pump operation by vibration and motor current signal spectra

Cyclic spectral analysis is conducted to extract the frequency characteristic components from nonstationary current signals under cavitation and seal damage conditions as indicators of fault characterization. Specifically, vibration and current signals are both acquired and pre-processed by envelope extraction and singular value decomposition methods, respectively. Since there are more noise waves in vibration power spectral density spectra in comparison with current signals, the cyclic spectral analysis is conducted for the current signal analysis. Cyclic autocorrelation functions of signals are firstly calculated then corresponding slices are extracted from the cyclic autocorrelation functions and processed by fast Fourier transform method. Consequently from the spectra, indicators for characterization are extracted to demonstrate the occurrence and severity of faults. Results show that the rotating frequency component shows obvious tendency as the flow rate deviates from the designed point without any faults. The indicators for seal damage characterization are 250 Hz and 350 Hz frequency components related with rotating frequency and blade passing frequency in the current signals. Meanwhile, the occurrence and development status of cavitation are indicated by the frequency component of 100 Hz in the slice spectra of cyclic autocorrelation functions. Additionally, the effect of instability caused by off-design, seal damage, as well as cavitation operation conditions is distinguished by cyclic spectral analysis. Characteristic components are innovatively extracted at specific frequencies to avoid the effect from modulated and noise components in the current signals. And the results about the recognition of different types of faults could provide important evidences for fault detection during pump operation.

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.

Interference Mitigation for the GPS Receiver Utilizing the Cyclic Spectral Analysis and RR-MSWF Algorithm

Interference Mitigation for the GPS Receiver Utilizing the Cyclic Spectral Analysis and RR-MSWF Algorithm

Cyclic spectral analysis of OFDM/OQAM signals

The orthogonal frequency division multiplexing signals based on the offset quadrature amplitude modulation (OFDM/OQAM) with pulse shaping are cyclostationary. Utilization of the cyclostationarity provides significant advantages in detection, identification, synchronization, and parameter estimation of these signals. In this paper, a matrix-based, stochastic method for the cyclic spectral analysis of OFDM/OQAM signals with pulse shaping, based on their aperiodic homogenous Markov chain representation, is proposed. Explicit expressions for the nonconjugate and conjugate cyclic spectrum of the complex envelope of these signals are derived by applying the proposed method. Cyclostationary characterizations of the nonconjugate and conjugate cyclic features at the cycle frequencies associated with the symbol rate and with the double carrier frequency, respectively, are performed. The final expression for the cyclic spectrum of the pulse shaping OFDM/OQAM signals is also derived. Some simulation results for the cyclic spectral analysis of these signals, based on the fast Fourier transform accumulation method (FAM), which confirm the theoretical results, are presented, as well.

Cyclic spectral analysis of electrocardiogram signals based on GARCH model

Abstract In this paper, the capability of Cyclic Spectral Density (CSD) is evaluated for ECG signal analyzing and a new feature generation method for them is presented. Although, the CSD presents a second-order statistical description in the frequency domain and reveals the hidden periodicity in EEG signals, it needs an efficient algorithm for calculating and also a suitable model for describing. By employing an efficient computational algorithm which is called the FFT accumulation method (FAM), the CSD of ECG signals can be computed. In this study, In order to choose an efficient statistical model for the Cyclic Spectral Analysis (CSA) coefficients of ECG signals, their statistical features are investigated at various regions of bi-frequency plane. It is revealed that the CSA coefficients are heteroscedastic and the Generalized Autoregressive Conditional Heteroscedasticity (GARCH) is a suitable model for them. Hence, The GARCH parameters of CSA sub-bands are calculated and are employed to classify the ECG using a support vector machine (SVM) classifier. Evidently, the results reveal that the performance of the new method in ECG classification outperforms the former studies.

Detection of gear cracks in a complex gearbox of wind turbines using supervised bounded component analysis of vibration signals collected from multi-channel sensors

In the complex gear transmission systems, in wind turbines a crack is one of the most common failure modes and can be fatal to the wind turbine power systems. A single sensor may suffer with issues relating to its installation position and direction, resulting in the collection of weak dynamic responses of the cracked gear. A multi-channel sensor system is hence applied in the signal acquisition and the blind source separation (BSS) technologies are employed to optimally process the information collected from multiple sensors. However, literature review finds that most of the BSS based fault detectors did not address the dependence/correlation between different moving components in the gear systems; particularly, the popular used independent component analysis (ICA) assumes mutual independence of different vibration sources. The fault detection performance may be significantly influenced by the dependence/correlation between vibration sources. In order to address this issue, this paper presents a new method based on the supervised order tracking bounded component analysis (SOTBCA) for gear crack detection in wind turbines. The bounded component analysis (BCA) is a state of art technology for dependent source separation and is applied limitedly to communication signals. To make it applicable for vibration analysis, in this work, the order tracking has been appropriately incorporated into the BCA framework to eliminate the noise and disturbance signal components. Then an autoregressive (AR) model built with prior knowledge about the crack fault is employed to supervise the reconstruction of the crack vibration source signature. The SOTBCA only outputs one source signal that has the closest distance with the AR model. Owing to the dependence tolerance ability of the BCA framework, interfering vibration sources that are dependent/correlated with the crack vibration source could be recognized by the SOTBCA, and hence, only useful fault information could be preserved in the reconstructed signal. The crack failure thus could be precisely identified by the cyclic spectral correlation analysis. A series of numerical simulations and experimental tests have been conducted to illustrate the advantages of the proposed SOTBCA method for fatigue crack detection. Comparisons to three representative techniques, i.e. Erdogan’s BCA (E-BCA), joint approximate diagonalization of eigen-matrices (JADE), and FastICA, have demonstrated the effectiveness of the SOTBCA. Hence the proposed approach is suitable for accurate gear crack detection in practical applications.