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Keywords = energy kurtosis mean filtering

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18 pages, 1998 KB  
Article
Experimental Study on Time-Frequency Analysis of Vibration Signals from an Active De-Icing Exciter on Transmission Lines
by Dongwang Fan, Bin Zhao, Mengxuan Li, Hao Wang and Lei Ding
Sensors 2026, 26(13), 4128; https://doi.org/10.3390/s26134128 - 30 Jun 2026
Viewed by 412
Abstract
In traditional mechanical de-icing technologies, the time-frequency evolution and spatial propagation mechanisms of transient high-frequency impact signals in flexible transmission lines remain unclear. To address this issue, transient impact responses were experimentally investigated using a full-scale transmission line model. An active de-icing exciter, [...] Read more.
In traditional mechanical de-icing technologies, the time-frequency evolution and spatial propagation mechanisms of transient high-frequency impact signals in flexible transmission lines remain unclear. To address this issue, transient impact responses were experimentally investigated using a full-scale transmission line model. An active de-icing exciter, featuring controllable impact energy and the potential for sustained online operation, was independently developed. High-frequency transient acceleration signals were acquired at multiple measurement points on a 20 m single-span line. The spatial distribution and time-frequency attenuation characteristics of the impact energy were quantitatively evaluated by extracting high-order time-domain statistical features, including root mean square, kurtosis, and crest factor, together with frequency-domain analyses based on Fast Fourier Transform (FFT) and wavelet entropy. The results indicate that: (1) The exciter generated highly impulsive transient responses, with a kurtosis up to 795.3 and a crest factor approaching 40. This suggests a strong local concentration of impact energy at the excitation source, which provides a dynamic basis for analyzing potential localized stress concentration and dynamic responses of the conductor system. (2) The transmission line structure exhibited a significant low-pass filtering effect on transient high-frequency shock waves. As the shock wave propagated towards the distal end, its high-frequency components above 30 Hz were substantially attenuated, likely due to internal dry friction within the stranded conductor. Consequently, the dominant frequency decreased to a low-frequency macroscopic sway of approximately 12 Hz, indicating a reduced risk of transmitting high-frequency shock loads to distal fittings and towers. (3) Under geometric nonlinear coupling, the vertical impact energy was partially transferred to the longitudinal and lateral directions during propagation, leading to sustained out-of-plane swaying. This study reveals the signal evolution characteristics of transient impacts in overhead transmission lines and provides experimental evidence for optimizing excitation parameters and assessing the engineering safety of active impact de-icing technologies. Full article
(This article belongs to the Section Electronic Sensors)
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26 pages, 4162 KB  
Article
A Priori Study of Inter-Scale Kinetic Energy Transfer and Energy Exchange in a Turbulent Premixed Flame
by Vladimir A. Sabelnikov and Andrei N. Lipatnikov
Energies 2026, 19(3), 822; https://doi.org/10.3390/en19030822 - 4 Feb 2026
Viewed by 732
Abstract
Velocity, pressure, and density fields computed in earlier three-dimensional direct numerical simulations of a statistically stationary, planar, one-dimensional, low-Mach-number hydrogen–air flame propagating in small-scale, moderately intense, spatially decaying turbulence are filtered out using top-hat filters of four different widths. Certain source/sink filtered terms [...] Read more.
Velocity, pressure, and density fields computed in earlier three-dimensional direct numerical simulations of a statistically stationary, planar, one-dimensional, low-Mach-number hydrogen–air flame propagating in small-scale, moderately intense, spatially decaying turbulence are filtered out using top-hat filters of four different widths. Certain source/sink filtered terms in the transport equations for resolved and subfilter-scale kinetic energies are analyzed. These are (i) the rate of inertial transfer of kinetic energy between resolved and subfilter scales, (ii) baropycnal work, (iii) subfilter-scale velocity–pressure–gradient term, and (iv) subfilter-scale pressure–dilatation term. These filtered terms are averaged over transverse planes and time or conditioned to the filtered combustion progress variable. Results show that terms (i) and (ii) work to transfer kinetic energy from smaller to larger scales (backscatter) and from larger to smaller scales, respectively, with the baropycnal work dominating the former term. These trends are observed for mean and conditional terms. The mean velocity–pressure–gradient term is positive and works to increase subfilter-scale kinetic energy due to combustion-induced thermal expansion. The pressure–dilatation term changes its sign from negative to positive at the leading and trailing edges, respectively, of the turbulent flame brush. Under conditions of the present study, the magnitudes of the mean velocity–pressure–gradient and pressure–dilatation terms are smaller when compared to the baropycnal work. Probability Density Functions (PDFs) for the explored filtered terms exhibit long tails, are highly skewed, and are characterized by a large kurtosis, thus implying significant intermittency of inter-scale energy transfer and energy exchange between internal and kinetic energy in the flame. These PDFs indicate that the intermittency of the inter-scale energy transfer and energy exchange depends substantially on mechanisms and scales of energy injection. Full article
(This article belongs to the Section A: Sustainable Energy)
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31 pages, 25297 KB  
Article
AET-FRAP—A Periodic Reshape Transformer Framework for Rock Fracture Early Warning Using Acoustic Emission Multi-Parameter Time Series
by Donghui Yang, Zechao Zhang, Zichu Yang, Yongqi Li and Linhuan Jin
Sensors 2025, 25(24), 7580; https://doi.org/10.3390/s25247580 - 13 Dec 2025
Viewed by 813
Abstract
The timely identification of rock fractures is crucial in deep subterranean engineering. However, it remains necessary to identify reliable warning indicators and establish effective warning levels. This study introduces the Acoustic Emission Transformer for FRActure Prediction (AET-FRAP) multi-input time series forecasting framework, which [...] Read more.
The timely identification of rock fractures is crucial in deep subterranean engineering. However, it remains necessary to identify reliable warning indicators and establish effective warning levels. This study introduces the Acoustic Emission Transformer for FRActure Prediction (AET-FRAP) multi-input time series forecasting framework, which employs acoustic emission feature parameters. First, Empirical Mode Decomposition (EMD) combined with Fast Fourier Transform (FFT) is employed to identify and filter periodicities among diverse indicators and select input channels with enhanced informative value, with the aim of predicting cumulative energy. Thereafter, the one-dimensional sequence is transformed into a two-dimensional tensor based on its predominant period via spectral analysis. This is coupled with InceptionNeXt—an efficient multiscale convolution and amplitude spectrum-weighted aggregate—to enhance pattern identification across various timeframes. A secondary criterion is created based on the prediction sequence, employing cosine similarity and kurtosis to collaboratively identify abrupt changes. This transforms single-point threshold detection into robust sequence behavior pattern identification, indicating clearly quantifiable trigger criteria. AET-FRAP exhibits improvements in accuracy relative to long short-term memory (LSTM) on uniaxial compression test data, with R2 approaching 1 and reductions in Mean Squared Error (MSE), Root Mean Squared Error (RMSE), and Mean Absolute Error (MAE). It accurately delineates energy accumulation spikes in the pre-fracture period and provides advanced warning. The collaborative thresholds effectively reduce noise-induced false alarms, demonstrating significant stability and engineering significance. Full article
(This article belongs to the Section Electronic Sensors)
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18 pages, 1705 KB  
Article
Enhanced Epileptic Seizure Detection through Wavelet-Based Analysis of EEG Signal Processing
by Sebastián Urbina Fredes, Ali Dehghan Firoozabadi, Pablo Adasme, David Zabala-Blanco, Pablo Palacios Játiva and Cesar Azurdia-Meza
Appl. Sci. 2024, 14(13), 5783; https://doi.org/10.3390/app14135783 - 2 Jul 2024
Cited by 44 | Viewed by 5686
Abstract
Epilepsy affects millions worldwide, making timely seizure detection crucial for effective treatment and enhanced well-being. Electroencephalogram (EEG) analysis offers a non-intrusive solution, but its visual interpretation is prone to errors and requires a lot of time. Many existing works focus solely on achieving [...] Read more.
Epilepsy affects millions worldwide, making timely seizure detection crucial for effective treatment and enhanced well-being. Electroencephalogram (EEG) analysis offers a non-intrusive solution, but its visual interpretation is prone to errors and requires a lot of time. Many existing works focus solely on achieving competitive levels of accuracy without considering processing speed or the computational complexity of their models. This study aimed to develop an automated technique for identifying epileptic seizures in EEG data through analysis methods. The efforts have been primarily focused on achieving high accuracy results by operating exclusively within a narrow frequency band of the signal, while also aiming to minimize computational complexity. In this article, a new automated approach is presented for seizure detection by combining signal processing and machine learning techniques. The proposed method comprises four stages: (1) Preprocessing: Savitzky–Golay filter to remove the background noise. (2) Decomposition: discrete wavelet transform (DWT) to extract spontaneous alpha and beta frequency bands. (3) Feature extraction: six features (mean, standard deviation, skewness, kurtosis, energy, and entropy) are computed for each frequency band. (4) Classification: a support vector machine (SVM) method classifies signals as normal or containing a seizure. The method was assessed using two publicly available EEG datasets. For the alpha band, the highest achieved accuracy was 92.82%, and for the beta band it was 90.55%, which demonstrates adequate capability in both bands for accurate seizure detection. Furthermore, the obtained low computational cost suggests a potentially valuable application in real-time assessment scenarios. The obtained results indicate its capacity as a valuable instrument for diagnosing epilepsy and monitoring patients. Further research is necessary for clinical validation and potential real-time deployment. Full article
(This article belongs to the Special Issue AI-Based Biomedical Signal Processing)
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29 pages, 15293 KB  
Article
Parameter-Adaptive TVF-EMD Feature Extraction Method Based on Improved GOA
by Chengjiang Zhou, Zenghui Xiong, Haicheng Bai, Ling Xing, Yunhua Jia and Xuyi Yuan
Sensors 2022, 22(19), 7195; https://doi.org/10.3390/s22197195 - 22 Sep 2022
Cited by 17 | Viewed by 3338
Abstract
In order to separate the sub-signals and extract the feature frequency in the signal accurately, we proposed a parameter-adaptive time-varying filtering empirical mode decomposition (TVF-EMD) feature extraction method based on the improved grasshopper optimization algorithm (IGOA). The method not only improved the local [...] Read more.
In order to separate the sub-signals and extract the feature frequency in the signal accurately, we proposed a parameter-adaptive time-varying filtering empirical mode decomposition (TVF-EMD) feature extraction method based on the improved grasshopper optimization algorithm (IGOA). The method not only improved the local optimal problem of GOA, but could also determine the bandwidth threshold and B-spline order of TVF-EMD adaptively. Firstly, a nonlinear decreasing strategy was introduced in this paper to adjust the decreasing coefficient of GOA dynamically. Then, energy entropy mutual information (EEMI) was introduced to comprehensively consider the energy distribution of the modes and the dependence between the modes and the original signal, and the EEMI was used as the objective function. In addition, TVF-EMD was optimized by IGOA and the optimal parameters matching the input signal were obtained. Finally, the feature frequency of the signal was extracted by analyzing the sensitive mode with larger kurtosis. The optimization experiments of 23 sets of benchmark functions showed that IGOA not only enhanced the balance between exploration and development, but also improved the global and local search ability and stability of the algorithm. The analysis of the simulation signal and bearing signal shows that the parameter-adaptive TVF-EMD method can separate the modes with specific physical meanings accurately. Compared with ensemble empirical mode decomposition (EEMD), variational mode decomposition (VMD), TVF-EMD with fixed parameters and GOA-TVF-EMD, the decomposition performance of the proposed method is better. The proposed method not only improved the under-decomposition, over-decomposition and modal aliasing problems of TVF-EMD, but could also accurately separate the frequency components of the signal and extract the included feature information, so it has practical significance in mechanical fault diagnosis. Full article
(This article belongs to the Section Physical Sensors)
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24 pages, 6683 KB  
Article
A FCEEMD Energy Kurtosis Mean Filtering-Based Fault Feature Extraction Method
by Chengjiang Zhou, Ling Xing, Yunhua Jia, Shuyi Wan and Zixuan Zhou
Coatings 2022, 12(9), 1337; https://doi.org/10.3390/coatings12091337 - 14 Sep 2022
Cited by 6 | Viewed by 2489
Abstract
Aiming at the problem that fault feature extraction is susceptible to background noises and burrs, we proposed a new feature extraction method based on a new decomposition method and an effective intrinsic mode function (IMF) selection method. Firstly, pairs of white noises with [...] Read more.
Aiming at the problem that fault feature extraction is susceptible to background noises and burrs, we proposed a new feature extraction method based on a new decomposition method and an effective intrinsic mode function (IMF) selection method. Firstly, pairs of white noises with opposite signs were introduced to neutralize the residual noises in ensemble empirical mode decomposition (EEMD) and suppress mode mixing. Both the reconstruction error (1.8445 × 10−17) and decomposition time (0.01 s) were greatly reduced through fast, complementary ensemble empirical mode decomposition (FCEEMD). Secondly, we integrated the energy and kurtosis of the IMF and proposed an effective IMF selection method based on energy kurtosis mean filtering, and the background noise of the signal was greatly suppressed. Finally, the periodic impacts were extracted from the IMF reconstruction signal by multipoint optimal minimum entropy deconvolution adjusted (MOMEDA). The fault frequencies were extracted from the periodic impacts through Hilbert demodulation, and the relative errors between the measured values and the theoretical values were all less than 0.05. The experimental results show that the proposed method can extract fault features more efficiently and provide a novel method for the fault diagnosis of rotating machinery. Full article
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20 pages, 3628 KB  
Article
Application of Compressed Sensing Based on Adaptive Dynamic Mode Decomposition in Signal Transmission and Fault Extraction of Bearing Signal
by Zhixin Cai, Zhang Dang, Ming Wen, Yong Lv and Haochun Duan
Machines 2022, 10(5), 353; https://doi.org/10.3390/machines10050353 - 9 May 2022
Cited by 8 | Viewed by 3358
Abstract
Bearings are widely used in mechanical equipment; nevertheless, potential dangers are also widespread, making bearing fault detection very important. For large equipment, the amount of collected signals tends to be huge, which challenges both signal transmission and storage. To solve this problem, compressed [...] Read more.
Bearings are widely used in mechanical equipment; nevertheless, potential dangers are also widespread, making bearing fault detection very important. For large equipment, the amount of collected signals tends to be huge, which challenges both signal transmission and storage. To solve this problem, compressed sensing (CS), based on specific dynamic modes of adaptive truncated rank dynamic mode decomposition (ADMD), is adopted to achieve the purpose of compressing and transmitting the signal, as well as extracting fault features. Firstly, this paper has proposed a new fitness function, which is called the synthetic envelope kurtosis characteristic energy difference ratio, and adopted the improved particle swarm optimization algorithm (IPSO) to select the best truncated rank adaptively. Then, the historical signal attempts to be decomposed into a series of temporal and spatial coherent modes, through ADMD, and those modes are filtered and cascaded into a highly self-adaptive dictionary, the DMD dictionary, which approximates the original signal with some error. Next, CS is employed to compress and reconstruct the signal, in order to reduce storage space and improve transmission efficiency. Finally, signals of high quality can be reconstructed through orthogonal matching pursuit (OMP) algorithm. Compared with traditional dictionaries, the DMD dictionary, based on the mode structure generated by ADMD decomposition, ass proposed in this paper, can better represent the original signal in the simulation signal and have good noise reduction performance. The correlation coefficient (CORR) between the reconstructed signal and noise signal is 0.8109, between the reconstructed signal and non-noise signal is 0.9278, and the root mean square error (RMSE) is 0.0659 and 0.0351, respectively. Compared with the traditional SVD and EMD denoising methods, ADMD-CS has better noise reduction performance. In this paper, the signal-to-noise ratio (SNR) is taken as the quantitative indicator of denoising performance. It is found that the SNR of simulation signal and experimental signal processed by ADMD-CS is higher than that of the traditional denoising methods, which is 0.3017 and 0.8407, respectively. The storage space of the signal is quite smaller than traditional methods, and the compression ratios (CR) of the simulation and experimental signals are 66.16% and 59.08%, respectively. In conclusion, ADMD-CS has a good application prospect in signal transmission, storage, and feature extraction. Full article
(This article belongs to the Section Machines Testing and Maintenance)
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19 pages, 5121 KB  
Article
Time-Varying Spectral Kurtosis: Generalization of Spectral Kurtosis for Local Damage Detection in Rotating Machines under Time-Varying Operating Conditions
by Jacek Wodecki
Sensors 2021, 21(11), 3590; https://doi.org/10.3390/s21113590 - 21 May 2021
Cited by 9 | Viewed by 4084
Abstract
Vibration-based local damage detection in rotating machines (i.e., rolling element bearings) is typically a problem of detecting low-energy cyclic impulsive modulations in the measured signal. This can be challenging as both the amplitude of a single damage-related impulse and the distance between impulses [...] Read more.
Vibration-based local damage detection in rotating machines (i.e., rolling element bearings) is typically a problem of detecting low-energy cyclic impulsive modulations in the measured signal. This can be challenging as both the amplitude of a single damage-related impulse and the distance between impulses might be changing in time. From the signal processing point of view, this means time varying regarding the the signal-to-noise ratio, location of information in the frequency domain, and loss of periodicity (this remains cyclic but not periodic). One of the many attempted approaches to this problem is filtration using custom filters derived in a data-driven fashion. One of the methods to obtain such filters is a selector approach, where the value of a certain statistic is calculated for individual frequency bands of a signal that results in the magnitude response of a filter. In this approach, each chosen statistic will yield different results, and the obtained filter will be focused on different frequency bands focusing on different behaviors. One of the most popular and powerful selectors is spectral kurtosis as popularized by Antoni, which uses kurtosis as an operational statistic. Unfortunately, after closer inspection, it is easy to notice that, although selectors can significantly enhance the signal, they accumulate a great deal of noise and other background content of signals, which occupies the space (or rather time) in between the impulses. Another disadvantage is that such filters are time-invariant, because, in the principle of their construction, they are not adaptive, and even slight changes in the signal yield suboptimal results either by missing relevant data when the conditions in the signal change (i.e., informative impulses widen in bandwidth), or by accumulating unnecessary noise when the relevant information is not present (in between impulses or in frequency bands that impulses no longer occupy). To address this issue, I propose generalization of the selector approach using the example of spectral kurtosis. This assumes creating a time-varying selector that can be seen as a spatial filter in the time-frequency domain. The time-varying SK (TVSK) is estimated for segments of the signal, and, instead of a vector of SK-based filter coefficients, one obtains a TVSK-based matrix of coefficients that takes into account the time-varying properties of the signal. The obtained structure is then binarized and used as a filter. The presented method is tested using a simulated signal as well as two real-life signals measured on heavy-duty bearings in two different types of machine. Full article
(This article belongs to the Section Fault Diagnosis & Sensors)
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27 pages, 5691 KB  
Article
Research on a Novel Improved Adaptive Variational Mode Decomposition Method in Rotor Fault Diagnosis
by Xiaoan Yan, Ying Liu, Wan Zhang, Minping Jia and Xianbo Wang
Appl. Sci. 2020, 10(5), 1696; https://doi.org/10.3390/app10051696 - 2 Mar 2020
Cited by 59 | Viewed by 5936
Abstract
Variational mode decomposition (VMD) with a non-recursive and narrow-band filtering nature is a promising time-frequency analysis tool, which can deal effectively with a non-stationary and complicated compound signal. Nevertheless, the factitious parameter setting in VMD is closely related to its decomposability. Moreover, VMD [...] Read more.
Variational mode decomposition (VMD) with a non-recursive and narrow-band filtering nature is a promising time-frequency analysis tool, which can deal effectively with a non-stationary and complicated compound signal. Nevertheless, the factitious parameter setting in VMD is closely related to its decomposability. Moreover, VMD has a certain endpoint effect phenomenon. Hence, to overcome these drawbacks, this paper presents a novel time-frequency analysis algorithm termed as improved adaptive variational mode decomposition (IAVMD) for rotor fault diagnosis. First, a waveform matching extension is employed to preprocess the left and right boundaries of the raw compound signal instead of mirroring the extreme extension. Then, a grey wolf optimization (GWO) algorithm is employed to determine the inside parameters ( α ^ , K) of VMD, where the minimization of the mean of weighted sparseness kurtosis (WSK) is regarded as the optimized target. Meanwhile, VMD with the optimized parameters is used to decompose the preprocessed signal into several mono-component signals. Finally, a Teager energy operator (TEO) with a favorable demodulation performance is conducted to efficiently estimate the instantaneous characteristics of each mono-component signal, which is aimed at obtaining the ultimate time-frequency representation (TFR). The efficacy of the presented approach is verified by applying the simulated data and experimental rotor vibration data. The results indicate that our approach can provide a precise diagnosis result, and it exhibits the patterns of time-varying frequency more explicitly than some existing congeneric methods do (e.g., local mean decomposition (LMD), empirical mode decomposition (EMD) and wavelet transform (WT) ). Full article
(This article belongs to the Special Issue Vibration-Based Structural Health Monitoring)
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