Optimal Demodulation Research Articles

An optimal demodulation frequency band selection method based on spectral coherence fault energy factor for rolling bearing fault diagnosis

Identifying a frequency band with abundant fault information from the original vibration signal under the condition of complex background noise and the interference of other rotating parts is still problematic for envelope spectrum-based bearing diagnosis. To address this issue, a new indicator called spectral coherence fault energy factor (SCFE) to is proposed to select the optimal demodulation frequency band (ODFB) under complex noise interference for bearing fault diagnosis. Firstly, the fast spectral correlation (Fast-SC) is used to analyze the raw vibration signal and generate the Spectral Coherence (SCoh) image. Then, SCFE is employed to locate the initial center frequency from the whole carrier frequency, and the threshold function is used to optimize the center frequency and bandwidth adaptively to obtain ODFB. Finally, the envelope spectrum (ES) is used to identify bearing faults. The effectiveness of the developed method in identifying the fault related frequency band and bearing fault diagnosis is validated and compared using simulated signals with different interference noises. The results of experimental signals demonstrate that the developed indicator can efficiently evaluate bearing failure information, and the presented approach can accurately discriminate the failure-related frequency band and detect different bearing faults compared with the traditional methods.

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.

Optimal demodulation domain for microwave SQUID multiplexers in presence of readout system noise

The Microwave SQUID Multiplexer (μMUX) is the device of choice for the readout of a large number of low-temperature detectors in a wide variety of experiments within the fields of astronomy and particle physics. While it offers large multiplexing factors, the system noise performance is highly dependent on the cold- and warm-readout electronic systems used to read it out, as well as the demodulation domain and parameters chosen. In order to understand the impact of the readout systems in the overall detection system noise performance, first, we extended the available μMUX simulation frameworks, including additive and multiplicative noise sources in the probing tones (i.e., phase and amplitude noise), along with the capability of demodulating the scientific data, either in the resonator’s phase or the scattering amplitude. Then, considering the additive noise as a dominant noise source, the optimum readout parameters to achieve minimum system noise were found for both open-loop and flux-ramp demodulation schemes in the aforementioned domains. Later, we evaluated the system noise sensitivity to multiplicative noise sources under the optimum readout parameters. Finally, as a case study, we evaluated the optimal demodulation domain and the expected system noise level for a typical software-defined radio readout system. This work leads to an improved system performance prediction and noise engineering based on the available readout electronics and the selected demodulation domain.

A High-Speed Train Axle Box Bearing Fault Diagnosis Method Based on Dimension Reduction Fusion and the Optimal Bandpass Filtering Demodulation Spectrum of Multi-Dimensional Signals

The operating state of axle box bearings is crucial to the safety of high-speed trains, and the vibration acceleration signal is a commonly used bearing-health-state monitoring signal. In order to extract hidden characteristic frequency information from the vibration acceleration signal of axle box bearings for fault diagnosis, a method for extracting the fault characteristic frequency based on principal component analysis (PCA) fusion and the optimal bandpass filtered denoising signal analytic energy operator (AEO) demodulation spectrum is proposed in this paper. PCA is used to measure the dimension reduction and fusion of three-direction vibration acceleration, reducing the interference of irrelevant noise components. A new type of multi-channel bandpass filter bank is constructed to obtain filtering signals in different frequency intervals. A new, improved average kurtosis index is used to select the optimal filtering signals for different channel filters in a bandpass filter bank. A dimensionless characteristic index characteristic frequency energy concentration coefficient (CFECC) is proposed for the first time to describe the energy prominence ability of characteristic frequency in the spectrum and can be used to determine the bearing fault type. The effectiveness and applicability of the proposed method are verified using the simulation signals and experimental signals of four fault bearing test cases. The results demonstrate the effectiveness of the proposed method for fault diagnosis and its advantages over other methods.

An improved envelope spectrum via Hoyer index-gram for bearing fault extraction

Resonance demodulation is one of the most commonly used methods in rolling bearing fault diagnosis, yet determining the optimal demodulation band has been a significant challenge. The vibration signal from a faulty bearing may include not only periodic fault impulses but also discrete harmonic interferences, random impulses, Gaussian white noise, among others. To enhance fault information and attenuate the impact of interference signals, this paper proposes an improved envelope spectrum via Hoyer index-gram (IESHoyergram). By utilizing the Hoyer index of the spectrum-related enhanced envelope spectrum as the frequency band filtering criterion, the proposed method extracts periodic impulses while suppressing interference from random impulses and other sources. Moreover, owing to the multilevel segmentation based on the different trend components in the spectral correlation spectrogram, IESHoyergram avoids the shortcomings of traditional segmentation methods. The proposed method is validated through both simulated and experimentally acquired data, demonstrating its capability not only to enhance the characteristics of a single fault but also to separate multiple component faults.

Ensefgram: An optimal demodulation band selection method for the early fault diagnosis of high-speed train bearings

Early fault diagnosis of high-speed train bearings under road spectrum shocks is challenging. As a conventional narrowband demodulation method, the Fast Kurtogram (FK) class of algorithms have some drawbacks: the fixed-band segmentation strategy makes it difficult for the method to find the optimal demodulation frequency band (ODFB); other major limitations are the poor robustness of the statistical index of the blind algorithm and the poor adaptiveness of the target algorithm given the need to the know the bearing operating state in advance. To address these issues, this paper proposes Ensefgram, an early fault detection method for high-speed train bearings with the acoustic emission signal as an example. First, a filter bank is designed by combining the spectral trend with the median dichotomy strategy, which adaptively segments the frequency band and retains the integrity of the sub-band fault components to the maximum extent. In addition, a novel statistical index, termed the maximum weighted spectral energy frequency factor, is proposed, and it is combined with the envelope spectrum negentropy (ES-negentropy) to form a composite index ENSEF, which can select the ODFB blindly. Finally, the proposed method was validated by simulation and applying test signals close to the real working conditions of a high-speed train. Compared with FK, Infogram, and other methods, Ensefgram provides more accurate detection results for the early fault diagnosis of bearings.

SEACKgram: a targeted method of optimal demodulation-band selection for compound faults diagnosis of rolling bearing

Rolling bearing plays an important role in carrying and transmitting power in rotating machinery, and the bearing fault is easy to lead to mechanical accidents, resulting in huge losses and casualties. Therefore, the condition monitoring and diagnosis of rolling bearings are very important to improve the safety of equipment. Compound fault is a common fault evolved from the initial defect, which is characterized by randomness, coupling, concealment, and secondary. The existence of these characteristics brings great challenges to the accurate diagnosis of compound faults. In the diagnosis of compound faults, the traditional methods that select the single optimal demodulation frequency band for analysis and identification sometimes cannot completely extract multiple fault components, which are prone to miss diagnosis and misdiagnosis. In order to solve this problem, the SEACKgram method is proposed by constructing a Square Envelope Unbiased Autocorrelation Correlation Kurtosis (SEACK) index. The frequency band of the original signal is divided by the Maximal Overlap Discrete Wavelet Packet Transform, and the SEACK index is used to quantitatively describe the fault signals of different frequency bands. According to the different fault periods, the resonant frequency bands of the maximum SEACK value are selected, then the resonance band signal is analyzed by square envelope spectrum, and the fault type is identified according to the fault characteristic frequency. The simulated and experimental vibration signals of rolling bearings with compound faults are used to verify the feasibility of the proposed method. The results show that the proposed SEACKgram can improve the accuracy of compound faults identification and would be applied in engineering practice to a certain extent.

The LFIgram: A Targeted Method of Optimal Demodulation Band Selection for Compound Faults Diagnosis of Rolling Bearing

The LFIgram: A Targeted Method of Optimal Demodulation Band Selection for Compound Faults Diagnosis of Rolling Bearing

High quality phase demodulation method for direct detection Φ-OTDR.

This article discovers that the excessive correlation between the selected temporal sensing sequences will lead to phase demodulation failure in the demodulation process of direct detection Φ-OTDR in certain duration, which reduces the quality of demodulated phase. Besides, we also first discover a phase polarity flipping phenomenon in the demodulation process, which will introduce additional errors and further degrade the quality of demodulated phase. In order to obtain the real phase change caused by external intrusion, a high-quality phase demodulation strategy with multi-position compensation based on leveraging the information redundancy between each Rayleigh back-scattered temporal sequence is proposed. The optimal demodulation position is selected by calculating the cross-correlation between temporal sensing sequences. The phase demodulation failure is then compensated by phase demodulation results from multiple positions. At the same time, the phase polarity change is also determined and corrected. The experimental results show that this strategy can effectively suppress the waveform distortion and improve the signal-to-noise ratio of the demodulated phase. This scheme can effectively improve the demodulation effect and detection performance of direct detection Φ-OTDR and may promote its application.

DTMSgram: a novel optimal demodulation frequency band selection method for wheelset bearings fault diagnosis under wheel-rail excitation

Due to the influence of the wheel-rail excitation and complex transmission path, the fault signature of wheelset bearings is often obscured by complex background noise, which brings great challenges to the adaptive determination of the informative frequency band (IFB) in envelope analysis. In this paper, the vibration response characteristics of the axle box under wheel–rail excitation are revealed through full-scale bench tests. The experimental results show that tread damage will provoke periodic transient impacts and it has an obvious sparsity in the frequency domain. Inspired by this feature, a DTMSgram method is proposed to enhance the fault feature components of vibration signals through time-domain and frequency-domain noise reduction technology, and improve the accuracy of demodulation frequency band selection. Firstly, the amplitude spectrum of different weight coefficients is used to preprocess the vibration signal and adjust the full band component of the vibration signal. Then, the autocorrelation process is performed on each layer’s narrowband filtered signal envelope in kurtogram to further reduce noise interference from a time-domain perspective. Moreover, a two-dimensional color map is constructed showing the normalized squared envelope spectrum of the IFBs determined simultaneously from the modified signal. Finally, the effectiveness of the proposed method is verified by simulated signal and experimental data of three sets of full-size wheelset bearing systems. The analysis results indicate this proposed method can effectively overcome the influence of complex wheel–rail excitation interference and can diagnose multi-source faults simultaneously.

Improved PGC demodulation algorithm for fiber optic interferometric sensors.

An improved phase generated carrier arctangent demodulation algorithm based on harmonic mixing and phase quadrature technology (PGC-Arctan-HP) is proposed in this paper, which can eliminate the effects of modulation depth shift, carrier phase delay, and light intensity disturbance (LID) on the demodulation results. The simulation results are consistent with theoretical analysis, and indicate that the PGC-Arctan-HP algorithm can achieve optimal demodulation compared with other demodulation algorithms. The results of interferometric experiments show that the demodulated waveforms of the improved algorithm are relatively stable with an amplitude error of 0.0294%. The total-harmonic-distortion (THD) and the signal-to-noise-and-distortion (SINAD) can reach -60.0286 dB and 59.5388 dB.

The LESGIRgram: A New Method to Select the Optimal Demodulation Frequency Band for Rolling Bearing Faults

Resonance demodulation of vibration signals is a common method for extracting fault information from rolling bearings. Nonetheless, demodulation quality is dependent on frequency band location. Established methods such as the Fast Kurtogram, Autogram, SKRgram, etc. have achieved satisfactory results in some cases, but the results are not good in the presence of strong white Gaussian noise and random impulses. To solve these issues, an algorithm that selects the optimal demodulation frequency band (ODFB) based on the ratio of the logarithmic envelope spectrum Gini coefficient (LESGIRgram) is proposed. The core idea of this paper is to capture the difference between the LESGIgrams of health and fault signals and accordingly locate the frequency bands that contain the most fault information. Initially, the baseline is constructed by calculating the logarithmic envelope spectrum Gini coefficient matrix of the health bearing (LESGIbaseline). Next, the LESGI matrix of the fault bearing (LESGImeasured) is computed. The ratio of LESGImeasured to LESGIbaseline is calculated, and the ODFB can be selected with the maximum LESGIR. The fault signal is then filtered using this derived ODFB, and envelope analysis is performed to extract fault features. The proposed algorithm for detecting rolling bearing faults has been verified for accuracy and effectiveness through simulation and experimental data.

Acceleration of the frequency-shift demodulation in phase-sensitive OTDR

Abstract The frequency-shift demodulation is a primary demodulation method in phase-sensitive optical time domain reflectometry (Φ-OTDR) with intrinsic resistance to interference fading. So far, the least mean squares (LMS) estimation method has the optimal demodulation accuracy and robustness. However, it takes much processing time due to the step-by-step sliding operation. In this work, we propose a fast LMS estimation method based on cross-correlation calculation to accelerate the demodulation while maintaining accuracy. Experiments are performed along a 9 km sensing fiber with a 4 m spatial resolution. The performance of the fast LMS, LMS, and cross-correlation methods are compared by using the same parameters. Compared with the LMS method, the fast LMS achieves a 12-time improvement in processing speed while remaining the same demodulation accuracy. Although the proposed fast LMS method takes slightly more time than the cross-correlation method (1.6 times), it improves the demodulation accuracy ∼6 dB for the vibration signal and ∼2.1 dB for the overall demodulation accuracy.

Study on Fault Feature Extraction of Rolling Bearing Based on Improved WOA-FMD Algorithm

The vibration signal of rolling bearing fault is nonlinear and nonstationary under the interference of background noise, and it is difficult to extract fault features from it. When feature mode decomposition is used to analyze signals, prior parameter settings can easily affect the decomposition results. Therefore, a fault feature extraction method based on improved whale optimization algorithm is proposed to optimize feature modal decomposition parameters. The improved WOA integrates Lévy flight and adaptive weight, and envelope entropy is used as fitness function to optimize feature modal decomposition parameters. The feature mode decomposition of the original signal is performed using the optimal combination of parameters to obtain multiple IMF components. The optimal IMF component envelope demodulation analysis is selected according to the kurtosis value, and the fault feature is extracted through the envelope spectrum. Comparing the LMWOA method with PSO and WOA methods by simulated and experimental signals, the results show that the optimization speed of LMWOA is faster than that of other methods. Compared with CEEMD, VMD, and FMD methods, the improved WOA-FMD method has higher fault feature ratio and can accurately extract fault features under noise interference. This method can effectively solve the parameter adaptive ability and improve the accuracy of fault diagnosis, which has practical significance.

Fault Diagnosis and Verification of Rolling Bearings Based on Optimal Resonance Demodulation with Deconvolution MRSVD

As one of the important aviation equipment components, rolling bearings will bring hidden dangers to the safety of aviation equipment once they fail. In aviation equipment, the sensor is far away from the bearing, and the collected signal of the rolling bearing is relatively weak. In this paper, the deconvolution algorithm is used to compensate the transfer function, and the optimal resonance demodulation algorithm based on the improved multi-resolution singular value decomposition (MRSVD) is constructed to determine the resonance frequency band, and then the bearing fault state is determined by the normalized squared envelope spectrum. The analysis results of the rolling bearing seed fault experiment show that this algorithm can adaptively extract the periodic fault pulse components under strong noise; compared with the normal spectral analysis and fast spectral kurtosis methods, this algorithm can completely extract the bearing fault characteristic frequency components, and effectively improve the bearing fault diagnosis accuracy.

Optimal Demodulation Band Extraction Method for Bearing Faults Diagnosis Based on Weighted Geometric Cyclic Relative Entropy

Optimal demodulation band extraction is a significant step in rolling bearing fault analysis. However, existing methods, primarily based on global indexes and neglecting negative local outliers, cannot identify compound faults in intense noise environments. To address this problem, a novel demodulation band extraction method based on weighted geometric cyclic relative entropy (WGCRE) is proposed. WGCRE is defined on the cyclic sub-bands model of the logarithmic envelope spectrum (LES) to fully consider the bearing characteristic frequency of pseudo-cyclostationarity. In detail, local and global thresholds are separately set by the white noise parameter and harmonic-to-noise ratio to exclude the exogenous noise outliers. On this basis, the WGCRE is defined as a geometrically weighted index of several different fault types to avoid harmonic interference and improve the identification of composite faults. WGCRE–gram, similar to fast kurtogram (FK), is then constructed by replacing kurtosis with WGCRE to extract the optimal demodulation band. Compared with FK and another LES-based method, logarithmic-cycligram, the proposed method is more robust for accurately identifying single and compound faults under external noise. The effectiveness of this method is verified through simulations and actual tests. Simulation experiments of different kinds and intensities of exogenous noise interference preliminarily determine the superior robustness of WGCRE in the face of solid noise. The inner ring, outer ring, and composite fault experiments further confirmed the robust adaptability of WGCRE in the face of complex working conditions.

CFFsgram: A candidate fault frequencies-based optimal demodulation band selection method for axle-box bearing fault diagnosis

How demodulate the vibration signal is an essential strategy for revealing the weak fault symptomatic of axle-box bearings. This paper proposed a candidate fault frequencies (CFFs)-based method, abbreviated as CFFsgram, for the optimal demodulation frequency band (DFB) identification of the axle-box bearing. The 1/3-binary tree filter bank constructed by empirical wavelet transform is adopted to divide the vibration signal into different narrowband with the same length. The local features of the squared envelope spectra of the narrowband signals are fully mined to identify the CFFs-a collection of frequencies most likely to be associated with bearing fault. An indicator calculated on the SESs of the narrowband signals is designed to guide the selection of the DFB. The superiority of the CFFsgram in resisting strong noise and random impulses is verified and confirmed by using four different challenging experimental datasets.

A dual-axis high-order harmonic and single-axis phase-insensitive demodulation atomic magnetometer for in situ NMR detection of Xe

Based on the parametric oscillation process, we demonstrate the dual-axis phase-sensitive demodulation (PSD) and single-axis phase-insensitive demodulation (PISD) for the atomic magnetometer in an in situ nuclear magnetic resonance (NMR) detection system, which can separate the precession signals of NMR from the oscillating magnetic fields. The two orthogonal magnetic fields can be detected simultaneously and independently by selecting the optimal demodulation phases with the traditional PSD method. The response signals of the parametric modulation magnetometer demodulated with high order harmonic signals are evaluated, which is a new exploration. The first order harmonic demodulation can present the best sensitivity about 250 fT/Hz1/2. The high order harmonic demodulation technology supplies a twofold 3 dB bandwidth. With the PISD method, a single-axis demodulation technique is proposed. The transverse nuclear spin precession magnetic fields can be extracted effectively with the demodulation R signal outputs by setting a specific longitudinal modulation magnetic field amplitude, which is a new demodulation strategy compared with the traditional demodulation method for the NMR system.

Scaling demodulation-based mode decomposition for analyzing nonstationary signal with close-spaced and intersecting frequency trajectories

Mode decomposition is an important tool for processing vibration signals in engineering fields. However, classic methods cannot work for decomposing a signal with close-spaced and intersecting frequency trajectories. For addressing the aforementioned problem, a novel technique, termed scaling demodulation-based mode decomposition (SDMD), is proposed in this paper. The main novelties of this paper are summarized as follows: (a) a scaling demodulation transform (SDT) is developed to estimate instantaneous frequency (IF) curves by selecting optimal demodulation parameters from a series of parameter sets with a criterion for searching maximal spectrum peaks of demodulated signals; and (b) a time–frequency representation (TFR) with high energy concentration is constructed using the Dirac delta function, estimated IFs and instantaneous amplitudes (IAs). The performance of the SDMD is evaluated through simulated and measured signals. Furthermore, comparison results with classic methods show that the developed technique has a much better ability to decompose and characterize nonstationary signals with close-spaced and intersecting frequency trajectories.

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