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Keywords = cyclostationary feature detection

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22 pages, 10320 KB  
Article
Adaptive Hoyer-L-Moment Envelope Spectrum: A Method for Robust Demodulation of Ship-Radiated Noise in Low-SNR Environments
by Ruizhe Zhang, Qingcui Wang and Shuanping Du
Sensors 2025, 25(24), 7434; https://doi.org/10.3390/s25247434 - 6 Dec 2025
Viewed by 579
Abstract
Propeller noise is the main source of ship-radiated noise. Extracting and analyzing the modulation characteristics from the propeller noise plays a crucial role in classifying and identifying vessel targets. Existing demodulation methods such as Detection of Envelope Modulation On Noise (DEMON), narrowband demodulation, [...] Read more.
Propeller noise is the main source of ship-radiated noise. Extracting and analyzing the modulation characteristics from the propeller noise plays a crucial role in classifying and identifying vessel targets. Existing demodulation methods such as Detection of Envelope Modulation On Noise (DEMON), narrowband demodulation, and cyclostationary analysis can be used to extract modulation features. However, capturing the modulation features on the envelope spectrum may be hard under low signal-to-noise ratio scenarios, since the envelope spectrum is contaminated by interference noise. To address this challenge, selecting an optimal frequency band rich in modulation information can significantly enhance demodulation performance. This paper proposes an Adaptive Hoyer-L-moment Envelope Spectrum (AHLES) method. The method first introduces an optimal frequency band selection method based on the golden section search strategy. A Hoyer-L-moment metric is then designed to quantify the modulation intensity within narrow frequency bands. Based on this metric, the optimal spectral coherence integration band is adaptively selected according to the signal’s inherent modulation characteristics, thereby enhancing demodulation performance. The effectiveness of the proposed method is validated through experiments on both simulated signals and merchant ship data. Full article
(This article belongs to the Section Physical Sensors)
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16 pages, 2860 KB  
Article
Maritime Spectrum Sensing Based on Cyclostationary Features and Convolutional Neural Networks
by Xuan Geng and Boyu Hu
Entropy 2025, 27(8), 809; https://doi.org/10.3390/e27080809 - 28 Jul 2025
Cited by 1 | Viewed by 895
Abstract
For maritime cognitive radio networks (MCRN), spectrum sensing (SS) is challenging due to the movement of the sea, channel interference, and unstable link quality. Besides the basic sensing capabilities that are required, SS in MCRN also requires the ability to adapt to complex [...] Read more.
For maritime cognitive radio networks (MCRN), spectrum sensing (SS) is challenging due to the movement of the sea, channel interference, and unstable link quality. Besides the basic sensing capabilities that are required, SS in MCRN also requires the ability to adapt to complex and dynamic environments. By transforming spectrum sensing into a classification problem and leveraging cyclostationary features and Convolutional Neural Networks (CNN), This paper proposes a classification-guided TC2NND (Transfer Cyclostationary- feature and Convolutional Neural Networks Detection) spectrum sensing algorithm, which regards the maritime spectrum sensing as a classification problem. The TC2NND algorithm first classifies the received signal features by extracting cycle power spectrum (CPS) features using the FFT (Fast Fourier Transform) Accumulation Method (FAM), and then makes a judgment using a variety of C2NND decision models. The experimental results demonstrate that the proposed TC2NND algorithm could achieve a detection probability of 91.5% with a false-alarm probability of 5% at SNR = −10 dB, which significantly outperforms the conventional methods. Full article
(This article belongs to the Special Issue Space-Air-Ground-Sea Integrated Communication Networks)
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18 pages, 608 KB  
Article
Blind Cyclostationary-Based Carrier Number and Spacing Estimation for Carrier-Aggregated Direct Sequence Spread Spectrum Cellular Signals
by Ali Görçin
Electronics 2024, 13(18), 3743; https://doi.org/10.3390/electronics13183743 - 20 Sep 2024
Cited by 1 | Viewed by 1673
Abstract
Automatic and blind parameter estimation based on the inherent features of wireless signals is a major research area due to the fact that these techniques lead to the simplification of receivers, especially in terms of coarse synchronization, and more importantly reduce the signaling [...] Read more.
Automatic and blind parameter estimation based on the inherent features of wireless signals is a major research area due to the fact that these techniques lead to the simplification of receivers, especially in terms of coarse synchronization, and more importantly reduce the signaling load at the control channels. Thus, in the literature, many techniques are proposed to estimate a vast set of parameters including modulation types and orders, data and chip rates, phase and frequency offsets, and so on. In this paper, a cyclostationary feature detection (CFD) based method is proposed to estimate the carrier numbers and carrier spacing of carrier-aggregated direct sequence spread spectrum (DSSS) cellular signals blindly. The particular chip rate of the signal is also estimated through the process jointly. The proposed CFD-based method unearths the inhered and hidden second-order periodicities of carrier-aggregated DSSS signals, particularly targeting repeated pseudorandom noise sequences of users over the carriers. Throughout the paper, after the proposed method is formulated, the measurement setup that is developed to collect the data for the validation of the method is introduced. The measurement results are post-processed for performance analysis purposes. To that end, the method is investigated in terms of signal-to-noise ratio (SNR) values, different channel conditions, and measurement durations. Furthermore, the performance of the proposed method is compared with that of energy detection. The measurement results indicate superior performance of the proposed method under significant wireless channel impairments and in low-SNR regions, e.g., for 0 dB the proposed method provides more than 0.9 detection performance for the case of 0.1 false alarm rate, while the performance of ED is 0.6 under the same wireless channel impairments. The raw outputs of the method can be utilized to train a convolutional neural network to eliminate the statistical estimation process in future work. Full article
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13 pages, 2191 KB  
Article
A Deep-Learning-Based Method for Spectrum Sensing with Multiple Feature Combination
by Yixuan Zhang and Zhongqiang Luo
Electronics 2024, 13(14), 2705; https://doi.org/10.3390/electronics13142705 - 10 Jul 2024
Cited by 16 | Viewed by 4194
Abstract
Cognitive radio networks enable the detection and opportunistic access to an idle spectrum through spectrum-sensing technologies, thus providing services to secondary users. However, at a low signal-to-noise ratio (SNR), existing spectrum-sensing methods, such as energy statistics and cyclostationary detection, tend to fail or [...] Read more.
Cognitive radio networks enable the detection and opportunistic access to an idle spectrum through spectrum-sensing technologies, thus providing services to secondary users. However, at a low signal-to-noise ratio (SNR), existing spectrum-sensing methods, such as energy statistics and cyclostationary detection, tend to fail or become overly complex, limiting their sensing accuracy in complex application scenarios. In recent years, the integration of deep learning with wireless communications has shown significant potential. Utilizing neural networks to learn the statistical characteristics of signals can effectively adapt to the changing communication environment. To enhance spectrum-sensing performance under low-SNR conditions, this paper proposes a deep-learning-based spectrum-sensing method that combines multiple signal features, including energy statistics, power spectrum, cyclostationarity, and I/Q components. The proposed method used these combined features to form a specific matrix, which was then efficiently learned and detected through the designed ‘SenseNet’ network. Experimental results showed that at an SNR of −20 dB, the SenseNet model achieved a 58.8% spectrum-sensing accuracy, which is a 3.3% improvement over the existing convolutional neural network model. Full article
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19 pages, 713 KB  
Article
Machine-Learning-Assisted Cyclostationary Spectral Analysis for Joint Signal Classification and Jammer Detection at the Physical Layer of Cognitive Radio
by Tassadaq Nawaz and Ali Alzahrani
Sensors 2023, 23(16), 7144; https://doi.org/10.3390/s23167144 - 12 Aug 2023
Cited by 18 | Viewed by 4852
Abstract
Cognitive radio technology was introduced as a possible solution for spectrum scarcity by exploiting dynamic spectrum access. In the last two decades, most researchers focused on enabling cognitive radios for managing the spectrum. However, due to their intelligent nature, cognitive radios can scan [...] Read more.
Cognitive radio technology was introduced as a possible solution for spectrum scarcity by exploiting dynamic spectrum access. In the last two decades, most researchers focused on enabling cognitive radios for managing the spectrum. However, due to their intelligent nature, cognitive radios can scan the radio frequency environment and change their transmission parameters accordingly on-the-fly. Such capabilities make it suitable for the design of both advanced jamming and anti-jamming systems. In this context, our work presents a novel, robust algorithm for spectrum characterisation in wideband radios. The proposed algorithm considers that a wideband spectrum is sensed by a cognitive radio terminal. The wideband is constituted of different narrowband signals that could either be licit signals or signals jammed by stealthy jammers. Cyclostationary feature detection is adopted to measure the spectral correlation density function of each narrowband signal. Then, cyclic and angular frequency profiles are obtained from the spectral correlation density function, concatenated, and used as the feature sets for the artificial neural network, which characterise each narrowband signal as a licit signal with a particular modulation scheme or a signal jammed by a specific stealthy jammer. The algorithm is tested under both multi-tone and modulated stealthy jamming attacks. Results show that the classification accuracy of our novel algorithm is superior when compared with recently proposed signal classifications and jamming detection algorithms. The applications of the algorithm can be found in both commercial and military communication systems. Full article
(This article belongs to the Special Issue Security and Privacy in Wireless Communications and Networking)
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18 pages, 3312 KB  
Article
Gaussian-Distributed Spread-Spectrum for Covert Communications
by Ismail Shakeel, Jack Hilliard, Weimin Zhang and Mark Rice
Sensors 2023, 23(8), 4081; https://doi.org/10.3390/s23084081 - 18 Apr 2023
Cited by 9 | Viewed by 4330
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Section Communications)
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14 pages, 4106 KB  
Article
Sustainable Non-Cooperative User Detection Techniques in 5G Communications for Smart City Users
by Shayla Islam, Anil Kumar Budati, Mohammad Kamrul Hasan, Hima Bindu Valiveti and Sridhar Reddy Vulupala
Sustainability 2023, 15(1), 118; https://doi.org/10.3390/su15010118 - 21 Dec 2022
Cited by 1 | Viewed by 2272
Abstract
The 4G network is not sufficient for achieving the high data requirements of smart city users. The 5G network intends to meet these requirements and overcome other application issues, such as fast data transmission, video buffering, and coverage issues, providing excellent mobile data [...] Read more.
The 4G network is not sufficient for achieving the high data requirements of smart city users. The 5G network intends to meet these requirements and overcome other application issues, such as fast data transmission, video buffering, and coverage issues, providing excellent mobile data services to smart city users. To allocate a channel or spectrum to a smart city user for error-free transmission with low latency, the accurate information of the spectrum should be detected. In this study, we determined the range of non-cooperative detection techniques, such as matched filter detection with inverse covariance approach (MFDI), cyclostationary feature detection with inverse covariance approach (CFDI), and hybrid filter detection with inverse covariance approach (HFDI); based on the results of these methods, we provided highly accurate spectrum information for smart city users, enabling sustainable development. To evaluate the performance of the proposed detection techniques, the following parameters are used: probability of detection (PD), probability of false alarms (Pfa), probability of miss detection (Pmd), sensing time, and throughput. The simulation results revealed that the HFDI detection method provided sustainable results at low signal-to-noise ratio ranges and improved channel detection and throughput of approximately 17% and 10%, respectively. Full article
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15 pages, 3383 KB  
Article
Data Augmentation in 2D Feature Space for Intelligent Weak Fault Diagnosis of Planetary Gearbox Bearing
by Rui Yang, Zenghui An, Weiling Huang and Rijun Wang
Appl. Sci. 2022, 12(17), 8414; https://doi.org/10.3390/app12178414 - 23 Aug 2022
Cited by 4 | Viewed by 2294
Abstract
Quickly detecting and accurately diagnosing early bearing faults is the key to ensuring the stable operation of high-precision equipment. In actual industrial applications, it is common to face the issues of big data and poor fault identification accuracy. To accurately and automatically realize [...] Read more.
Quickly detecting and accurately diagnosing early bearing faults is the key to ensuring the stable operation of high-precision equipment. In actual industrial applications, it is common to face the issues of big data and poor fault identification accuracy. To accurately and automatically realize the diagnostics of rolling bearings, a convolutional neural network algorithm and fault feature enhancement method is proposed. A two-dimensional space feature extraction method based on the Cyclostationary theory and wavelet transform shows good results in noise suppression. Firstly, the cyclic demodulation of wavelet transform coefficients is performed on bearing vibration signals to convert one-dimensional vibration data into a two-dimensional spectrogram for enhancing the weak fault feature. Secondly, the image segmentation theory is introduced, which can obtain more data and improve the calculation accuracy and efficiency on the basis of data dimension reduction. Finally, the augmented 2D spectrograms are inputted into a convolutional neural network. Through the analysis of the actual planetary gearbox bearing data, and compared with other mainstream intelligence algorithms, the effectiveness and superiority of this method are verified. Full article
(This article belongs to the Special Issue Intelligent Fault Diagnosis and Health Detection of Machinery)
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20 pages, 489 KB  
Article
Signal Folding for Efficient Classification of Near-Cyclostationary Biological Signals
by Tianxiang Zheng and Pavel Loskot
Mathematics 2022, 10(2), 192; https://doi.org/10.3390/math10020192 - 8 Jan 2022
Cited by 1 | Viewed by 2331
Abstract
The classification of biological signals is important in detecting abnormal conditions in observed biological subjects. The classifiers are trained on feature vectors, which often constitute the parameters of the observed time series data models. Since the feature extraction is usually the most time-consuming [...] Read more.
The classification of biological signals is important in detecting abnormal conditions in observed biological subjects. The classifiers are trained on feature vectors, which often constitute the parameters of the observed time series data models. Since the feature extraction is usually the most time-consuming step in training a classifier, in this paper, signal folding and the associated folding operator are introduced to reduce the variability in near-cyclostationary biological signals so that these signals can be represented by models that have a lower order. This leads to a substantial reduction in computational complexity, so the classifier can be learned an order of magnitude faster and still maintain its decision accuracy. The performance of different classifiers involving signal folding as a pre-processing step is studied for sleep apnea detection in one-lead ECG signals assuming ARIMA modeling of the time series data. It is shown that the R-peak-based folding of ECG segments has superior performance to other more general, similarity based signal folding methods. The folding order can be optimized for the best classification accuracy. However, signal folding requires precise scaling and alignment of the created signal fragments. Full article
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34 pages, 1185 KB  
Article
UGRansome1819: A Novel Dataset for Anomaly Detection and Zero-Day Threats
by Mike Nkongolo, Jacobus Philippus van Deventer and Sydney Mambwe Kasongo
Information 2021, 12(10), 405; https://doi.org/10.3390/info12100405 - 30 Sep 2021
Cited by 31 | Viewed by 9062
Abstract
This research attempts to introduce the production methodology of an anomaly detection dataset using ten desirable requirements. Subsequently, the article presents the produced dataset named UGRansome, created with up-to-date and modern network traffic (netflow), which represents cyclostationary patterns of normal and abnormal classes [...] Read more.
This research attempts to introduce the production methodology of an anomaly detection dataset using ten desirable requirements. Subsequently, the article presents the produced dataset named UGRansome, created with up-to-date and modern network traffic (netflow), which represents cyclostationary patterns of normal and abnormal classes of threatening behaviours. It was discovered that the timestamp of various network attacks is inferior to one minute and this feature pattern was used to record the time taken by the threat to infiltrate a network node. The main asset of the proposed dataset is its implication in the detection of zero-day attacks and anomalies that have not been explored before and cannot be recognised by known threats signatures. For instance, the UDP Scan attack has been found to utilise the lowest netflow in the corpus, while the Razy utilises the highest one. In turn, the EDA2 and Globe malware are the most abnormal zero-day threats in the proposed dataset. These feature patterns are included in the corpus, but derived from two well-known datasets, namely, UGR’16 and ransomware that include real-life instances. The former incorporates cyclostationary patterns while the latter includes ransomware features. The UGRansome dataset was tested with cross-validation and compared to the KDD99 and NSL-KDD datasets to assess the performance of Ensemble Learning algorithms. False alarms have been minimized with a null empirical error during the experiment, which demonstrates that implementing the Random Forest algorithm applied to UGRansome can facilitate accurate results to enhance zero-day threats detection. Additionally, most zero-day threats such as Razy, Globe, EDA2, and TowerWeb are recognised as advanced persistent threats that are cyclostationary in nature and it is predicted that they will be using spamming and phishing for intrusion. Lastly, achieving the UGRansome balance was found to be NP-Hard due to real life-threatening classes that do not have a uniform distribution in terms of several instances. Full article
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16 pages, 5843 KB  
Article
Time–Frequency Envelope Analysis for Fault Detection of Rotating Machinery Signals with Impulsive Noise
by Dong-Hyeon Lee, Chinsuk Hong, Weui-Bong Jeong and Sejin Ahn
Appl. Sci. 2021, 11(12), 5373; https://doi.org/10.3390/app11125373 - 9 Jun 2021
Cited by 21 | Viewed by 6705
Abstract
Envelope analysis is a widely used tool for fault detection in rotating machines. In envelope analysis, impulsive noise contaminates the measured signal, making it difficult to extract the features of defects. This paper proposes a time–frequency envelope analysis that overcomes the effects of [...] Read more.
Envelope analysis is a widely used tool for fault detection in rotating machines. In envelope analysis, impulsive noise contaminates the measured signal, making it difficult to extract the features of defects. This paper proposes a time–frequency envelope analysis that overcomes the effects of impulsive noises. Envelope analysis is performed by dividing the signal into several sections through a time window. The effect of impulsive noises is eliminated by using the frequency characteristics of the short time rectangular wave. The proposed method was verified through simulation and experimental data. The simulation was conducted by mathematically modeling a cyclo-stationary process that characterizes rotating machinery signals. In addition, the effectiveness of the method was verified by the measured data of normal and defective air-conditioners produced on the actual assembly line. This simple proposed method is effective enough to detect the faults. In the future, the approaches of big data and deep learning will be required for the development of the prognostic health-management framework. Full article
(This article belongs to the Section Mechanical Engineering)
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19 pages, 2007 KB  
Article
Cyclostationary-Based Vital Signs Detection Using Microwave Radar at 2.5 GHz
by Fatima Sekak, Kawtar Zerhouni, Fouzia Elbahhar, Madjid Haddad, Christophe Loyez and Kamel Haddadi
Sensors 2020, 20(12), 3396; https://doi.org/10.3390/s20123396 - 16 Jun 2020
Cited by 10 | Viewed by 3900
Abstract
Non-contact detection and estimation of vital signs such as respiratory and cardiac frequencies is a powerful tool for surveillance applications. In particular, the continuous wave bio-radar has been widely investigated to determine the physiological parameters in a non-contact manner. Since the RF-reflected signal [...] Read more.
Non-contact detection and estimation of vital signs such as respiratory and cardiac frequencies is a powerful tool for surveillance applications. In particular, the continuous wave bio-radar has been widely investigated to determine the physiological parameters in a non-contact manner. Since the RF-reflected signal from the human body is corrupted by noise and random body movements, traditional Fourier analysis fails to detect the heart and breathing frequencies. In this effort, cyclostationary analysis has been used to improve the radar performance for non-invasive measurement of respiratory rate and heart rate. However, the preliminary works focus only on one frequency and do not include the impact of attenuation and random movement of the body in the analysis. Hence in this paper, we evaluate the impact of distance and noise on the cyclic features of the reflected signal. Furthermore, we explore the assessment of second order cyclostationary signal processing performance by developing the cyclic mean, the conjugate cyclic autocorrelation and the cyclic cumulant. In addition, the analysis is carried out using a reduced number of samples to reduce the response time. Implementation of the cyclostationary technique using a bi-static radar configuration at 2.5 GHz is shown as an example to demonstrate the proposed approach. Full article
(This article belongs to the Section Electronic Sensors)
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23 pages, 8221 KB  
Article
Multi-objective Informative Frequency Band Selection Based on Negentropy-induced Grey Wolf Optimizer for Fault Diagnosis of Rolling Element Bearings
by Xiaohui Gu, Shaopu Yang, Yongqiang Liu, Rujiang Hao and Zechao Liu
Sensors 2020, 20(7), 1845; https://doi.org/10.3390/s20071845 - 26 Mar 2020
Cited by 17 | Viewed by 5106
Abstract
Informative frequency band (IFB) selection is a challenging task in envelope analysis for the localized fault detection of rolling element bearings. In previous studies, it was often conducted with a single indicator, such as kurtosis, etc., to guide the automatic selection. However, in [...] Read more.
Informative frequency band (IFB) selection is a challenging task in envelope analysis for the localized fault detection of rolling element bearings. In previous studies, it was often conducted with a single indicator, such as kurtosis, etc., to guide the automatic selection. However, in some cases, it is difficult for that to fully depict and balance the fault characters from impulsiveness and cyclostationarity of the repetitive transients. To solve this problem, a novel negentropy-induced multi-objective optimized wavelet filter is proposed in this paper. The wavelet parameters are determined by a grey wolf optimizer with two independent objective functions i.e., maximizing the negentropy of squared envelope and squared envelope spectrum to capture impulsiveness and cyclostationarity, respectively. Subsequently, the average negentropy is utilized in identifying the IFB from the obtained Pareto set, which are non-dominated by other solutions to balance the impulsive and cyclostationary features and eliminate the background noise. Two cases of real vibration signals with slight bearing faults are applied in order to evaluate the performance of the proposed methodology, and the results demonstrate its effectiveness over some fast and optimal filtering methods. In addition, its stability in tracking the IFB is also tested by a case of condition monitoring data sets. Full article
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20 pages, 21948 KB  
Article
Fault Detection in a Multistage Gearbox Based on a Hybrid Demodulation Method Using Modulation Intensity Distribution and Variational Mode Decomposition
by Chaofan Hu, Yanxue Wang, Jianwei Yang and Suofeng Zhang
Appl. Sci. 2018, 8(5), 696; https://doi.org/10.3390/app8050696 - 1 May 2018
Cited by 5 | Viewed by 4257
Abstract
It is critical to detect hidden, periodically impulsive signatures caused by tooth defects in a gearbox. A hybrid demodulation method for detecting tooth defects has been developed in this work based on the variational mode decomposition algorithm combined with modulation intensity distribution. An [...] Read more.
It is critical to detect hidden, periodically impulsive signatures caused by tooth defects in a gearbox. A hybrid demodulation method for detecting tooth defects has been developed in this work based on the variational mode decomposition algorithm combined with modulation intensity distribution. An original multi-component signal is first non-recursively decomposed into a number of band-limited mono-components with specific sparsity properties in the spectral domain using variational mode decomposition. The hidden meaningful cyclostationary features can be clearly identified in the bi-frequency domain via the modulation intensity distribution (MID) technique. Moreover, the reduced frequency aliasing effect of variational mode decomposition is evaluated as well, which is very useful for separating noise and harmonic components in the original signal. The influences of the spectral coherence density and the spectral correlation density of the modulation intensity distribution on the demodulation were also investigated. The effectiveness and noise robustness of the proposed method have been well-verified using a simulated signal compared with the empirical mode decomposition algorithm associated with modulation intensity distribution. The proposed technique is then applied to detect four different defects in a multi-stage gearbox. The results demonstrated that the demodulated numerical information and pigmentation directly illustrated in the bi-frequency plot of the modulation intensity distribution can be successfully used to quantitatively differentiate the four gear defects. Full article
(This article belongs to the Special Issue Fault Detection and Diagnosis in Mechatronics Systems)
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