Envelope Demodulation Research Articles

Weak Compound Fault Identification of Gearboxes Based on Improved Symplectic Geometric Mode Decomposition and Optimized Cyclic Kurtosis Deconvolution

Abstract Given the complex and harsh operating conditions of gear transmission systems, gearboxes are prone to compound faults. These faults, involving multiple types, often couple together, causing the weak fault pulse characteristics to be entirely masked by strong environmental noise. This significantly complicates the extraction of relevant fault information from the gearbox. To address these issues, this paper proposes a method for extracting compound fault features based on improved symplectic geometric mode decomposition (SGMD) and optimized cyclic bispectrum deconvolution (CYCBD). Firstly, considering the periodic impact characteristics of different fault types, morphological envelope cyclic bispectrum is proposed to cluster the initial components obtained from SGMD decomposition, thereby adaptively separating different fault features contained in the compound fault signals. An adaptive filter length search strategy is subsequently introduced to optimize the CYCBD by deconvolving each initial fault component, thereby eliminating the interference caused by complex transmission paths and substantial environmental noise, which, in turn, enhances weak periodic fault pulses. Following this, the enhanced signals are subjected to envelope demodulation to extract fault characteristic frequencies, enabling the identification of various types of faults. The effectiveness and feasibility of the proposed method are demonstrated through both simulation signals and actual experimental data related to gearbox compound faults. Compared with existing methods, the proposed method demonstrates superior performance in identifying weak compound faults under strong environmental noise.

Method for enhancing fault feature signals of rolling bearings in gas turbine engines

Aiming at the problem that the weak fault signal of rolling bearings in gas turbine engines (GTEs) is affected by environmental noise, which leads to the difficulty of effective information extraction and easy to ignore, the characterization method for cyclic extraction of main bearing fault feature components in GTEs is proposed. The proposed method begins by subjecting raw vibration signals to wavelet packet decomposition and correlating correlation coefficient and kurtosis values for each node component. These values are then normalized and amalgamated into a comprehensive parameter denoted as P. Subsequently, a confidence interval is established to categorize node components into three groups: high signal-to-noise ratio signals, low signal-to-noise ratio signals, and high-noise signals. Then, the high signal-to-noise ratio signals are continuously filtered according to the feature component cyclic extraction criterion until the termination condition is reached. Finally, all high signal-to-noise ratio signals are reconstructed, followed by envelope demodulation to extract subtle bearing fault characteristics. The findings underscore the efficacy of this approach in extracting fault features within the intricate transmission path of rolling bearings, offering a robust solution for the intricate signal processing and diagnosis of complex rolling bearing faults in GTEs.

STAKgram: a method for optimal demodulation band selection in bearing fault diagnosis under complex interference

Abstract Within rotating machinery, bearings constitute critical and vulnerable components. When they operate in a compromised state, they generate periodic shock pulses. While spectral kurtosis (SK) has been demonstrated as an effective tool for pulse detection, in complex operating environments, the vibration signals of damaged bearings acquired through sensors often contain a variety of interfering pulses, such as ambient background noise, episodic single pulses, which cause SK to produce poor computational results. In this paper, an innovative bearing fault diagnostic method named subband trimmed average kurtogram (STAKgram) is proposed, aiming to minimize the effect of interfering signals on signal processing results, thus ensuring reliable diagnostic results even in complex interference environments. Firstly, the signal is segmented into N sub-signals by employing a sliding window method. Following, the subband kurtosis is calculated for every sub-signal. Ultimately, the trimmed average kurtosis of the respective sub-band is computed to construct the STAKgram, indicating the optimal demodulation frequency band. It is used for squared envelope demodulation analysis. By simulation analysis and the application of test signals obtained under conditions closely resembling authentic bearing operating conditions, the STAKgram method is proven to provide more accurate results for diagnosing bearing faults in complex interference.

A novel optimal resonance band selection method for wheelset-bearing fault diagnosis based on tunable-Q wavelet transform

The detection of faults in the wheelset-bearing system is crucial for guaranteeing the safety of train operations. The core is to extract the optimal resonance band (ORB) and repetitive transient impact signals from the collected axle box acceleration signals. Accordingly, a novel automatic fault detection method called the bidirectional iterative merging multi-Q tunable-Q wavelet transform (BIMMQTQWT) is proposed to address the issue that existing methods are vulnerable to background noise and irrelevant components. First, a series of band-pass filters with almost constant bandwidth are constructed by the improved multi-Q tunable-Q wavelet transform (IMQTQWT) derived from the fault characteristics. Second, the fault information contained in each sub-band coefficient is preliminarily estimated using the correlative envelope comprehensive indicator (CECI). Third, the ORBs are automatically selected using the maximum CECI based on a strategy called bidirectionally merging adjacent frequency bands (BIMFBs). Finally, Envelope demodulation based on the ORB is executed followed by identifying bearing faults. The effectiveness in detecting multiple wheelset-bearing faults of the proposed method is validated through simulation and bench experiment signals. And the superior performance of the proposed method is exhibited compared with the existing average infogram and resonance sparse decomposition.

A Method of Ship Target Modulation Feature Enhancement Based on Phase Information

Abstract Ship modulation features are commonly used in underwater acoustic target recognition, which contains propeller parameter information of the target. The basis processing of modulation spectrum is demodulation. Traditional envelope demodulation methods only consider amplitude information and make little use of phase information, which can fully characterize the dynamic characteristics of radiated noise. In this paper, a modulation feature enhancement method based on phase information is proposed, which takes full account of the phase information of the target signal. It uses the modified group delay function to demodulate the target signal, and utilizes the phase stability characteristics of the modulated line spectrum to enhance the modulation features of the ship target by weighted phase features. Simulation and sea trial data verification show that the proposed method can effectively enhance the energy of the line spectrum, suppress the background noise, and improve the signal-to-noise ratio of the modulation line spectrum, which lays a good foundation for further using the modulation line spectrum to carry out the estimation of modulation parameters, and has a good application prospect in the field of underwater acoustic target recognition.

Adaptive spectrum amplitude modulation method for rolling bearing fault frequency determination

Abstract Signal preprocessing and feature extraction are decisive factors in determining the frequency of bearing faults. The presence of noise interference in the status signal of rolling bearings often hampers accurate fault detection. Although there are various methods for preprocessing vibration signals in rolling bearings, they need further improvement in terms of enhancing fault feature expression and localizing fault frequency bands. This limitation significantly hinders the accuracy of fault frequency determination. In order to enhance the representation of fault information on the frequency spectrum, this study proposes a combined approach that incorporates sparse stacked autoencoder (SSAE), wavelet packet decomposition (WPD), and adaptive spectrum amplitude modulation (ASAM). The resulting method is referred to as SSAE-WPD-ASAM. Firstly, the bearing vibration signal is decomposed by wavelet packet according to the scale and frequency band of the signal. On this basis, the signal reconstruction is realized based on the wavelet packet coefficient and energy distribution in different frequency bands. Secondly, for the whole life cycle signal, the reconstructed signal is self-encoded by sparse stacked autoencoder to achieve dimensionality reduction of the reconstructed signal. Then, the spare reconstructed signal is subjected to ASAM. Finally, through envelope demodulation, peak detection of fault frequency and empirical fault frequency comparison, the specific fault types of rolling bearings are determined. The proposed method is verified by theoretical simulation and three groups of practical experiments. The results show that the proposed method has a significant improvement in diagnostic efficiency and accuracy compared with traditional diagnostic methods.

Research on a Fault Feature Extraction Method for an Electric Multiple Unit Axle-Box Bearing Based on a Resonance-Based Sparse Signal Decomposition and Variational Mode Decomposition Method Based on the Sparrow Search Algorithm.

In light of the issue that the vibration signal from an axle-box bearing collected during the operation of an electric multiple unit (EMU) is seriously polluted by background noise, which leads to difficulty in identifying fault characteristic frequency, this paper proposes a resonance-based sparse signal decomposition (RSSD) and variational mode decomposition (VMD) method based on sparrow search algorithm (SSA) optimization to extract the fault characteristic frequency of the bearing. Firstly, the RSSD method is utilized to decompose the signal based on the obtained optimal combination of quality factors, resulting in the optimal low-resonance component with periodic fault information. Then, the VMD method is performed on this low-resonance component. The parameter combinations for both methods are optimized utilizing the SSA method. Subsequently, envelope demodulation is applied to the intrinsic mode function (IMF) with maximum kurtosis, and fault diagnosis is achieved by comparing it with the theoretical fault characteristic frequency. Finally, experimental validation and comparison are conducted by utilizing simulated signals and example signals. The results demonstrate that the proposed method extracts more obvious periodic fault impact components. It effectively filters out the interference of complex noise and reduces the blindness of setting weights on parameters due to human experience, indicating excellent adaptability and robustness.

Transient Feature Extraction of Encoder Signal Based on Envelope Demodulation for Fault Diagnosis of RV Reducer

Transient Feature Extraction of Encoder Signal Based on Envelope Demodulation for Fault Diagnosis of RV Reducer

Turbine bearing fault diagnosis based on embedded system

Abstract Failure of the main components of the transmission mechanism of large machinery and equipment usually uses sensors to collect real-time vibration or audio information, followed by data processing on the computer to analyze whether the equipment is operating normally. In this paper, a multi-core embedded fault diagnosis platform based on ARM and DSP is designed. It is small in size. It can independently set the signal types, ranges, and filter parameters of multiple acquisition channels, and synchronously set high-precision acquisition and storage of voltage signals output from various sensors. The DSP adopts the fast Fourier algorithm to analyze the multi-channel sampling data in real time and extracts the fault characteristics through the analysis of envelope demodulation. The operation results show that the system can meet the routine online fault diagnosis of mechanical equipment transmission mechanism, and the fault analysis and diagnosis can reach 95% accuracy within one minute, with high real-time accuracy.

Research on Feature Extraction and Fault Diagnosis Method for Rolling Bearing Vibration Signals Based on Improved FDM-SVD and CYCBD

In mechanical equipment, rolling bearing components are constantly exposed to intricate and diverse environmental conditions, rendering them vulnerable to wear, performance degradation, and potential malfunctions. To precisely extract and discern rolling bearing vibration signals amidst intricate noise interference, this paper introduces a fault feature extraction and diagnosis methodology that seamlessly integrates an improved Fourier decomposition method (FDM), singular value decomposition (SVD), and maximum second-order cyclostationary blind convolution (CYCBD). Initially, the FDM is employed to meticulously decompose the bearing fault signals into numerous signal components. Subsequently, a comprehensive weighted screening criterion is formulated, aiming to strike a balance between multiple indicators, thereby enabling the selective screening and reconstruction of pertinent signal components. Furthermore, SVD and CYCBD techniques are introduced to carry out intricate processing and envelope demodulation analysis of the reconstructed signals. Through rigorous simulation experiments and practical rolling bearing fault diagnosis tests, the method’s noteworthy effectiveness in suppressing noise interference, enhancing fault feature information, and efficiently extracting fault features is unequivocally demonstrated. Furthermore, compared to traditional time–frequency analysis methods such as EMD, EEMD, ITD, and VMD, as well as traditional deconvolution methods like MED, OMEDA, and MCKD, this method exhibits significant advantages, providing an effective solution for diagnosing rolling bearing faults in environments with strong background noise.

An adaptive threshold-selected symplectic geometry mode decomposition for application to multi-modulation complex fault signals

The signals obtained from complex mechanical systems are characterized by multilevel modulation and strong noise, which can lead to difficulties in fault feature extraction. Symplectic geometry mode decomposition (SGMD) proves to be a valid approach for decomposing signals. However, inaccurate threshold selection in the iterative decomposition process can compromise the quality of fault diagnosis results. To address the shortcomings of SGMD, this paper proposes adaptive SGMD with adaptive threshold selection for fault diagnosis. Based on minimum dispersion entropy indicators, correlation coefficient and stopping thresholds are adaptively chosen using the proposed enhanced dung beetle optimizer algorithm. Then the optimal symplectic geometry component (SGC) is filtered based on the value of the integrated indicators after decomposition. Finally, the optimal SGC is analyzed by envelope demodulation to extract gear fault information. Through simulation and experimental analysis, this method surpasses SGMD and other signal decomposition methods in the aspect of fault feature extraction and noise robustness. Additionally, the results indicate an increase in feature energy ratio by 2.14%–9.85% compared to SGMD. The paper demonstrates that the proposed method extracts the fault feature frequencies of gears more effectively in complex mechanical systems.

Fault diagnosis of tooth surface spalling based on variational mode decomposition and maximum correlation kurtosis method

As the early fault features of tooth surface spalling are very weak and difficult to extract because of random noise and other types of signal interference, a method that combines maximum correlation kurtosis uncoiling and variational mode decomposition is proposed herein. First, a series of modes are obtained by variational mode decomposition, and the kurtosis criterion is applied to select the modes containing rich fault information for reconstruction and noise reduction. Second, the maximum correlation kurtosis deconvolution method is used to enhance the selected signals. Finally, the fault features are extracted by envelope demodulation of the reconstructed signal. The effectiveness of the proposed method is verified by analysis, and the different frequency components of the vibration signals of tooth surface spalling faults are shown to be separated accurately.

Narrow laser linewidth measurement with the optimal demodulated Lorentzian spectrum.

A method called the optimal demodulated Lorentzian spectrum is employed to precisely quantify the narrowness of a laser's linewidth. This technique relies on the coherent envelope demodulation of a spectrum obtained through short delayed self-heterodyne interferometry. Specifically, we exploit the periodic features within the coherence envelope spectrum to ascertain the delay time of the optical fiber. Furthermore, the disparity in contrast within the coherence envelope spectrum serves as a basis for estimating the laser's linewidth. By creating a plot of the coefficient of determination for the demodulated Lorentzian spectrum fitting in relation to the estimated linewidth values, we identify the existence of an optimal Lorentzian spectrum. The corresponding laser linewidth found closest to the true value is deemed optimal. This method holds particular significance for accurately measuring the linewidth of lasers characterized as narrow or ultranarrow.

Approximation of the Hilbert transform in the Lebesgue spaces

The Hilbert transform plays an important role in the theory and practice of signal processing operations in continuous system theory because of its relevance to such problems as envelope detection and demodulation, as well as its use in relating the real and imaginary components, and the magnitude and phase components of spectra. The Hilbert transform is a multiplier operator and is widely used in the theory of Fourier transforms. The Hilbert transform is the main part of the singular integral equations on the real line. Therefore, approximations of the Hilbert transform are of great interest. Many papers have dealt with the numerical approximation of the singular integrals in the case of bounded intervals. On the other hand, the literature concerning the numerical integration on unbounded intervals is by far poorer than the one on bounded intervals. The case of the Hilbert Transform has been considered very little. This article is devoted to the approximation of the Hilbert transform in Lebesgue spaces by operators which introduced by V.R.Kress and E.Mortensen to approximate the Hilbert transform of analytic functions in a strip. In this paper, we prove that the approximating operators are bounded maps in Lebesgue spaces and strongly converges to the Hilbert transform in these spaces.

Hybrid Vernier effect: sensitivity amplification and two-parameter measurement in cascaded Fabry-Perot interferometer fiber sensor

Vernier effect enhances the sensitivity for interferometric fiber sensor, but indiscriminately amplifies cross-sensitivity to environmental parameters. Here, hybrid Vernier effect, a new theory based on the cascaded FPI, is proposed and demonstrated for cross-sensitivity elimination under the premise of sensitivity amplification. It combines traditional and high-order harmonic Vernier effects to measure two parameters simultaneously. The proposed sensor achieves strain sensitivity of 960.1 pm/µɛ, and temperature sensitivity of 1260.86 pm/°C. Stability experiments demonstrate excellent stability of envelope demodulation method, with minimum temperature resolution of 0.44 °C and minimum strain resolution of 0.58 µɛ. The proposed the hybrid Vernier effect can be achieved widely in common cascaded fiber FPI fiber sensor structure, making it good candidate for practical applications.

Fault Feature Extraction Method for Rolling Bearings Based on Complete Ensemble Empirical Mode Decomposition with Adaptive Noise and Variational Mode Decomposition

Due to the difficulty in dealing with non-stationary and nonlinear vibration signals using the single decomposition method, it is difficult to extract weak fault features from complex noise; therefore, this paper proposes a fault feature extraction method for rolling bearings based on complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and variational mode decomposition (VMD) methods. CEEMDAN was used to decompose the signal, and the signal was then screened and reconstructed according to the component envelope kurtosis. Based on the kurtosis of the maximum envelope spectrum as the fitness function, the sparrow search algorithm (SSA) was used to perform adaptive parameter optimization for VMD, which decomposed the reconstructed signal into several IMF components. According to the kurtosis value of the envelope spectrum, the optimal component was selected for an envelope demodulation analysis to realize fault feature extraction for rolling bearings. Finally, by using open data sets and experimental data, the accuracy of envelope kurtosis and envelope spectrum kurtosis as a component selection index was verified, and the superiority of the proposed feature extraction method for rolling bearings was confirmed by comparing it with other methods.

Bearing fault diagnosis under non-stationary conditions based on a speed signal resonance component demodulation algorithm

This paper proposes a novel bearing fault diagnosis indicator, the resonance component, for motor speed signals. The speed signal was modulated into a higher-frequency band using a double-inertia system, and the bearing fault information was carried and reserved in this high-frequency resonance component. Variational mode decomposition was then used to separate the components unrelated to the resonance based on the parameters optimized using the artificial bee colony algorithm. After envelope demodulation and angular resampling, the multipoint optimal minimum entropy deconvolution adjusted algorithm was utilized to enhance the amplitude of the order spectrum at the corresponding faulty order. Additionally, experiments were successfully conducted on both the outer and inner raceway bearing faults under time-varying conditions using the proposed method. The results indicate that the ordinary diagnosis method using the basic bearing fault characteristic frequency as an indicator is less effective.

Multispectral Balanced Automatic Fault Diagnosis for Rolling Bearings under Variable Speed Conditions

As a key component of machine, most rolling bearings operate under variable speed conditions. Therefore, it is critical to complete automatic fault diagnosis for rolling bearings under variable speed conditions. Although there have been many research studies on fault diagnosis in recent years, the following two problems still exist in fault diagnosis of variable speed bearing: (1) due to the large range of energy distribution for signals under variable speed conditions, the existed signal processing methods lead to the loss of fault information; (2) when directional filtering is carried out according to four different types of faults, the difference in amplitudes of the obtained spectrums is large. This means that the filtering result with the maximum amplitude will be determined as the fault type by mistake. In order to integrate the information scattered across different frequency spectrums and use reasonable filtering to complete automatic diagnosis, Multispectral Balanced Automatic Fault Diagnosis is proposed for rolling bearings under variable speed conditions. On the one hand, signals are preprocessed by the Multispectral Lossless Preprocessing Module, which can eliminate the influence of variable rotating speeds and avoid the loss of fault information. On the other hand, the Balanced Envelope Demodulation Module is designed to realize automatic fault diagnosis by Protrugram and Balancing Envelope Spectrum. The effectiveness of the proposed method is verified by simulated signals and experimental data. Results indicate that the method can complete automatic fault diagnosis of rolling bearings under variable speed conditions with an accuracy of 76%, which outperforms state-of-the-art methods.

Composite fault feature extraction of rolling bearing using adaptive circulant singular spectrum analysis

Aiming to extract the weak composite fault characteristics of a rolling bearing under harsh operation conditions, a novel composite fault diagnosis method for bearings based on adaptive circulant singular spectrum analysis (ACiSSA) is proposed. The proposed method is able to adaptively obtain the eigenvalue of a non-stationary vibration signal in any dimension, and effectively reassemble the same frequency components and improve the signal-to-noise ratio (SNR). Specifically, circulant singular spectrum analysis is utilized to decompose the raw signal, and the optimal parameters, i.e. the embedding dimension and threshold value of cumulative contribution, are selected to maximum kurtosis through the grey wolf optimization method. The signal is reconstructed with high SNR according to the effective singular spectrum components. Envelope demodulation analysis is then implemented to extract the characteristic defect frequency in the reconstructed signal. Finally, feature extraction performance is quantitatively evaluated, and experimental results show that the proposed ACiSSA method is able to extract more sensitive features under more noisy conditions compared with other common methods, with higher computational efficiency.

Application of Demodulation Frequency Band Optimization in Compound Fault Detection of Rolling Element Bearing Based on Fast Spectrum Correlation

The key to demodulation analysis is determining the appropriate demodulation frequency band. However, the coupling of compound faults significantly increases the difficulty. How to determine the fault-related demodulation frequency band is a challenge for the application of demodulation analysis in compound fault detection. To address this issue, a demodulation frequency band optimization method based on fast spectral correlation (Fast-SC) is proposed to detect compound faults of rolling element bearing in this paper. Firstly, the bi-variable map of vibration signal is obtained by Fast-SC. Secondly, the bi-variable map is sliced according to the theoretical fault-related frequency along the carrier frequency axis, obtaining a curve of correlation value versus carrier frequency, which is regarded as the target spectrum correlation curves (T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">scc</sub> ). Thirdly, the carrier frequency corresponding to the maximum value of the T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">scc</sub> obtained from each component is used to determine the initial demodulation frequency band. Fourthly, the crest of envelope spectrum (EC) is used to optimize the demodulation frequency band. Finally, the characteristic frequencies are exposed by utilizing the envelope demodulation on the frequency bands of each component. Simulation and experiment show that the proposed method is effective for the detection of rolling element bearing compound faults. Compared with maximum correlated kurtosis deconvolution(MCKD) and variational mode decomposition(VMD), the calculation cost of the proposed method is significantly reduced to about 6.6% of the above two methods.