Envelope Spectrum Research Articles

Stockwell transform spectral amplitude modulation method for rotating machinery fault diagnosis

Spectral amplitude modulation (SAM) method, as an automated and empirical nonlinear filtering approach, has shown great promise for rotating machinery fault diagnosis. However, due to the inherent shortcomings of Fourier transform in SAM, leading to significant errors in the edited amplitude, also it is easy to fail with selecting the optimal weight value manually under intense background noise. To solve the aforementioned drawbacks, the Stockwell transform spectral amplitude modulation (STSAM) method is proposed. The Stockwell transform (S-transform) is first utilized to obtain the phase and amplitude with time–frequency information. Then, the edited signals can be reconstructed by inverse S-transform with the above actual phase and the modified amplitudes under different weights. Hence, more comprehensive and accurate information about the amplitude can be computed. After that, their normalized square envelope spectra under each cyclic frequency are calculated to showcase the fault characteristics. Moreover, a novel indicator is proposed to automatically choose the optimal weight in STSAM, thus clearer characteristic frequencies can be represented by the optimal square envelope spectrum (OSES). Finally, the effectiveness and superiority of the STSAM and OSES methods are systematically demonstrated by the comparative studies with the SAM and time–frequency SAM approaches using simulated signals and real-world datasets.

Concept and Application of Envelope Spectrum Analysis in the Field of Vibration Signal Processing

Concept and Application of Envelope Spectrum Analysis in the Field of Vibration Signal Processing

A multi-scale feature extraction and fusion method for diagnosing bearing faults

Bearing fault diagnosis is vital to safeguard the heath of rotating machinery. It can help to avoid economic losses and safe accidents in time. Effective feature extraction is the premise of diagnosing bearing faults. However, effective features characterizing the health status of bearings are difficult to extract from the raw bearing vibration signals. Furthermore, inefficient feature extraction results in substantial time wastage, making it hard to apply in real time monitoring. A novel feature extraction method for diagnosing bearing faults using multi-scale improved envelope spectrum entropy (MIESE) is proposed in this work. First, bearing vibration signals are analyzed across multiple scales, and improved envelope spectrum entropy (IESE) is extracted from these signals at each scale to form an original feature set. Subsequently, joint approximate diagonalization eigen (JADE) is applied to fuse above feature set for effectively eliminating redundancy and generated a refined feature set. Finally, the newly generated feature set is input into support vector machines (SVM) to effectively diagnose bearing health status. Two cases studies are employed to demonstrate the reliability of the proposed method. The results illustrate the proposed method can improve the stability of extracted features and increase the computational efficiency. Conflict of Interest Statement The authors declare no conflicts of interest.

An adaptive feature mode decomposition-guided phase space feature extraction method for rolling bearing fault diagnosis

Abstract The extraction of fault features from rolling bearings is a challenging and highly important task. Since they have complex operating conditions and are usually under a strong noise background. In this study, a novel approach termed phase space feature extraction guided by an adaptive feature mode decomposition (AFMDPSFE) is proposed to detect subtle faults in rolling bearings. Initially, a new method using Kullback-Leiber divergence is introduced to automatically select the optimal mode number and filter length for the decomposition of vibration signals, facilitating the automatic extraction of optimal components and ensuring efficient screening. This eliminates the need for manual configuration of feature mode decomposition parameters. Furthermore, a criterion that could determine two crucial parameters to capture system dynamics characteristics in phase space reconstruction is embedded into AFMDPSFE algorithm. Subsequently, a series of high-dimensional independent components is derived. The envelope spectrum of the principal component exhibiting the highest kurtosis value is computed to achieve fault identification, consequently enhancing the separation of signal from noise. Both simulations and experimental results confirm the effectiveness of AFMDPSFE approach. A comparison analysis shows the excellent performance of AFMDPSFE in extracting fault features from significant noise interference.

Envelope Spectrum of the Subwavelength Grating Slot Waveguide Microring Resonator for High-Sensitivity and Wide-Range Refractive Index Sensing Applications

Envelope Spectrum of the Subwavelength Grating Slot Waveguide Microring Resonator for High-Sensitivity and Wide-Range Refractive Index Sensing Applications

Fault diagnosis of railway freight car rolling bearings based on ACMD and improved MCKD

To address the issue of accurately extracting fault characteristic information of railway freight car bearings under noisy conditions, this paper proposes a fault diagnosis method based on Adaptive Chirp Mode Decomposition (ACMD) and an optimized Maximum Correlation Kurtosis Deconvolution (MCKD) using a Sparrow Search Algorithm Combining Sine-Cosine and Cauchy Mutation (SCSSA). Firstly, ACMD is used to decompose and reconstruct the original fault signal to obtain several Intrinsic Mode Functions (IMFs). Then, the IMFs are filtered according to the Gini coefficient indicator, with the IMF having the largest Gini coefficient selected as the optimal component. Secondly, the SCSSA is employed to iteratively optimize the filter length L, fault signal period T, and displacement parameter M in the MCKD algorithm, determining the optimal parameter combination for MCKD. This avoids the limitations of manual settings and enhances the accuracy of fault diagnosis. The optimized MCKD is then applied to the optimal component, and deconvolution is performed using maximum correlation kurtosis as the criterion to extract fault characteristic information through its envelope spectrum. To verify the effectiveness and generalizability of the proposed method, simulations, experimental signals from the Case Western Reserve University Bearing Center, and actual measured signals from railway freight car bearing 353130B are used to analyze inner ring faults. The experimental results demonstrate that the method can accurately extract fault characteristic information of railway freight car bearings under noise interference and identify the fault type.

Cyclostationarity blind deconvolution via eigenvector screening and its applications to the condition monitoring of rotating machinery

Maximum second-order cyclostationarity blind deconvolution (CYCBD) is accomplished by maximizing the second-order cyclostationarity of signals through the indicator of second-order cyclostationarity (ICS2). It is a significant method for extracting weak periodic pulses related to bearing faults. However, since the interference spectral lines generated by the interference signals in squared envelope spectrum do not be considered by ICS2, the method can be invalid for certain applications. In addition, when the detected signal contains compound faults, only one fault can be enhanced, and misdiagnosis is easily caused. This article proposes cyclostationarity blind deconvolution via eigenvector screening, abbreviated as ESCYCBD, for fault feature enhancement and extraction of rotating machinery in order to solve these problems. Different from existing deconvolution methods which use the maximum value of the index as a criterion to select the filter coefficients, this method proposes the concept of eigenvector subspace, which contains the optimal eigenvector as filter coefficients that are ignored by CYCBD. Subsequently, the Fourier coefficients related to a series of cyclic frequencies are extended for compound fault signals. Besides, by using the harmonic characteristics of fault features in the envelope spectrum, fault feature recognition and optimal selection are carried out in eigenvector subspaces. At the same time, the concept of signals set is created, by which means different feature modes of different fault can be extracted at one time. The analysis results of simulation signals and experimental data show that the proposed ESCYCBD has robustness and accuracy in extracting fault feature modes, whether it is single fault diagnosis or compound fault diagnosis.

Adaptive cyclic content ratiogram: a new signal decomposition method for bearing concurrent fault diagnosis

Fast kurtogram (FK) has been proven to be an effective tool for resonance frequency band detection, which is widely used in bearing fault diagnosis. However, FK is not robust to impulsive noise, and its frequency band segmentation rule is fixed, which leads to over-decomposition or under-decomposition of the fault resonance frequency band in its signal decomposition results. Therefore, an adaptive cyclic content ratiogram is proposed in this paper. Firstly, based on the energy distribution of vibration signals on different frequency components, the frequency spectral segmentation is performed adaptively, and multiple sub-signals containing different frequency components are obtained. Secondly, the ratio of cyclic content (RCC), which cannot only more accurately characterize the cyclostationarity of bearing fault impacts but also be insensitive to impulsive noise, is applied to evaluate the fault feature information contained in each sub-signal separately. In the meanwhile, considering that fault characteristic frequency information is required in the process of RCC evaluation, the proposed method performs adaptive fault characteristic frequency detection for each sub-signal based on the envelope spectrum. The RCC maximization is used to locate the fault resonance frequency band. Also, combined with the estimated fault characteristic frequencies, the proposed method can achieve the extraction of concurrent fault features. Simulation and experimental data verify the effectiveness of the proposed method.

Separation and Extraction of Compound-Fault Signal Based on Multi-Constraint Non-Negative Matrix Factorization.

To solve the separation of multi-source signals and detect their features from a single channel, a signal separation method using multi-constraint non-negative matrix factorization (NMF) is proposed. In view of the existing NMF algorithm not performing well in the underdetermined blind source separation, the β-divergence constraints and determinant constraints are introduced in the NMF algorithm, which can enhance local feature information and reduce redundant components by constraining the objective function. In addition, the Sine-bell window function is selected as the processing method for short-time Fourier transform (STFT), and it can preserve the overall feature distribution of the original signal. The original vibration signal is first transformed into time-frequency domain with the STFT, which describes the local characteristic of the signal from the time-frequency distribution. Then, the multi-constraint NMF is applied to reduce the dimensionality of the data and separate feature components in the low dimensional space. Meanwhile, the parameter WK is constructed to filter the reconstructed signal that recombined with the feature component in the time domain. Ultimately, the separated signals will be subjected to envelope spectrum analysis to detect fault features. The simulated and experimental results indicate the effectiveness of the proposed approach, which can realize the separation of multi-source signals and their fault diagnosis of bearings. In addition, it is also confirmed that the proposed method, juxtaposed with the NMF algorithm of the traditional objective function, is more applicable for compound fault diagnosis of the rotating machinery.

Statistical and sensitivity analysis of ultrasound signals for effective condition monitoring of electro-motors using industrial approach

This paper researches the importance of ultrasound methodology for swiftly detecting faults in electric motors and rotating machines. The primary focus of this research is on the intricate signal processing of ultrasound signals from both faulty and fault-free electro-motors. The principal goal is to conduct a comprehensive statistical investigation into signal factors, examining the effects of defect progression on the factors associated with continuously operating faulty electro-motors. In addition to the statistical analysis, this study explores the envelope-frequency spectrum of the signal under both healthy and defective conditions, employing the envelope method alongside Hilbert transformation. The objective is to thoroughly scrutinize the dynamic changes in ultrasound waveform and envelope spectrum of defective states, considering diverse degrees of defect severity over an extended time span. Moreover, the paper meticulously tracks the trajectory of factor changes over a 40-day operational period of a defective electro-motor. Additionally, the study delves into the sensitivity of the ultrasound method to impulse-wise shocks, which are recurrently observed in ultrasound signals, leading to deviations in certain signal factors from their established healthy thresholds. In response to this challenge, this paper conducts a particular analysis of signal factor sensitivity to impulse-wise noises, identifying robust factors that serve as reliable tools for firm condition monitoring. These identified factors are then presented as invaluable contributors to ensuring the precision and reliability of condition monitoring, especially in the presence of disruptive impulse-wise noises.

Simulation of multivariate ergodic stochastic processes using adaptive spectral sampling and non-uniform fast Fourier transform

The simulation of multivariate ergodic stochastic processes is critical for structural dynamic analysis and reliability evaluation. Although the traditional spectral representation method (SRM) has a wide application in many areas, it is highly inefficient in simulating stochastic processes with many simulation points or long durations due to the significant computational cost associated with matrix factorizations concerning frequency. To address the encountered challenge, this paper presents an efficient approach for simulating ergodic stochastic processes with limited frequencies. Central to this approach is a fusion of the adaptive spectral sampling and the non-uniform fast Fourier transform (NUFFT) techniques. The adaptive spectral sampling of the envelope spectrum enables the determination of limited non-equispaced frequencies, which are randomly sampled according to a uniform distribution. Thus, the Cholesky decomposition is only required at limited specific frequencies, which dramatically reduces the computational cost of matrix factorizations. Since the randomly sampled frequencies are not equispaced, utilizing FFT to accelerate the summation of trigonometric functions becomes impractical. Then, the NUFFT that adapts the non-equispaced sampling points is employed instead to expedite this process with the non-uniform increment approximated through reduced interpolation. By taking the wind field simulation of a long-span suspension bridge as an example, a parametric analysis is conducted to investigate the effect of random frequencies on the simulation error of the developed approach and the convergence of spectra. Finally, the developed approach is further validated by focusing on the spectra and probabilistic density functions of the simulated wind samples, and the simulation performance is compared with that of the traditional approach. The analytical results demonstrate the efficiency and accuracy of the developed approach in simulating ergodic stochastic processes.

Vibration shock disturbance modeling in the rotating machinery fault diagnosis: A generalized mixture Gaussian model

In real-world industrial environments, complex background noises are composed of various components, deviating from a simple Gaussian distribution like shock noise. In this work, a robust noise modeling method based on the mixture of exponential power (MoEP) distributions is developed to address this issue. To proficiently extract the fault characteristics, the signal’s 2-D representation is attained via Fast-SC, both of the fault features’ low-rankness and the complex noise are combined in a signal model. Then, a penalized function of the noise model is combined to further improve the performance of the method. The model is designated as the PMoEP enhanced low-rank model (PMoEP-LR). The Generalized Expectation–Maximization (GEM) algorithm is utilized to estimate the low-rank spectral correlation matrix and deduce all parameters of the PMoEP-LR model. Finally, the enhanced envelope spectrum (EES) is used to detect the defect characteristic. The efficacy of the proposed method is showcased by analyzing both simulated and real data.

Self-multivariate spectral decomposition and mode-fused envelope spectrum for enhancing bearing fault feature

In practical diagnostic scenarios, multivariate vibration data (MVD) actually contain more comprehensive fault information. Variational mode extraction (VME) has recently become a promising tool for extracting a specific mode from vibration data. However, its performance of feature extraction is restricted by presetting initial parameters and the joint information within MVD is ignored to be analyzed by VME. To address these issues, a self-multivariate spectral decomposition (SMSD), which includes multivariate spectral feature detector and multivariate mode extraction, is presented to efficiently decouple the fault-related features from MVD. The proposed method can avoid the omitting of effective modes and inclusion of interferential modes. Furthermore, a mode-fused envelope spectrum (MFES) is built to suppress in-band noise of extracted modes. Three cases demonstrate that SMSD can identify multivariate fault-related modes effectively and MFES can exhibit the fault-related frequencies clearly. Moreover, its superior performance is verified by comparing with some well-known multivariate decomposition methods.

Linewidth Measurement of a Narrow-Linewidth Laser: Principles, Methods, and Systems.

Narrow-linewidth lasers mainly depend on the development of advanced laser linewidth measurement methods for related technological progress as key devices in satellite laser communications, precision measurements, ultra-high-speed optical communications, and other fields. This manuscript provides a theoretical analysis of linewidth characterization methods based on the beat frequency power spectrum and laser phase noise calculations, and elaborates on existing research of measurement technologies. In addition, to address the technical challenges of complex measurement systems that commonly rely on long optical fibers and significant phase noise jitter in the existing research, a short-delay self-heterodyne method based on coherent envelope spectrum demodulation was discussed in depth to reduce the phase jitter caused by 1/f noise. We assessed the performance parameters and testing conditions of different lasers, as well as the corresponding linewidth characterization methods, and analyzed the measurement accuracy and error sources of various methods.

Iterative feature mode decomposition: a novel adaptive denoising method for mechanical fault diagnosis

Remaining useful life prediction of rolling bearings highly relies on feature extraction of signals. The use of denoising algorithms helps to better eliminate noise and extract features, thereby constructing health indicators to predict remaining useful life. This paper proposes a novel adaptive denoising method based on iterative feature mode decomposition (IFMD) to accurately and efficiently extract fault features. The feature mode decomposition (FMD) employs correlation kurtosis (CK) as the objective function for iterative filter bank updates, enabling rapid identification of fault features. To achieve IFMD, the sparrow search algorithm combines sine-cosine algorithm and cauchy variation (SCSSA) to optimize two key parameters in FMD. During the continuous iteration process of the SCSSA algorithm, filter length and number of modes were determined. IFMD does not require empirical setting of initial parameters. During iterative process, the signal is accurately decomposed and the noise is eliminated. Compared with other optimization algorithms, SCSSA has obvious advantages in iterative rate and global optimization. The envelope spectrum feature energy ratio (ES-FER) is used to select decomposed modes, and the mode with the largest ES-FER is chosen as the optimal mode. Bearing fault diagnosis is realized by envelope spectrum analysis of the optimal mode. The numerical simulations and experimental verifications both validate the effectiveness and superiority of the proposed IFMD in mechanical fault diagnosis.

Fault diagnosis method of rolling bearing based on MSSA-VMD algorithm

Abstract Early fault signals of rolling bearings are affected by environmental noise, which makes it challenging to extract fault characteristics. In this paper, a bearing fault diagnosis method based on Sparrow Search Algorithm (SSA) and Variable Modal Decomposition (VMD) is proposed to achieve adaptive signal decomposition and feature extraction. First, the fusion shock index is constructed based on the envelope spectrum pulse factor and correlation coefficient to measure the shock fault components. Then, the VMD parameters are adaptively optimized by the improved sparrow search algorithm MSSA, and the fusion shock index is established as the optimal modal component selection method of the fitness function. Finally, the envelope spectrum of the signal after noise reduction is analyzed to extract the fault characteristic frequency. By analyzing the bearing outer ring fault signal and inner ring fault signal under strong noise, the results show that this method can adaptively determine the mode number and penalty factor of VMD, effectively extract the fault signal characteristics, and realize rolling bearing fault diagnosis.

Viscoelastic characterization of coating layers by ultrasonic interference and critical attenuation

This study proposes a characterization technique for a viscoelastic coating layer on a metal substrate immersed in water based on ultrasonic interference and critical attenuation phenomena. Theoretical analysis shows that the reflection spectrum for the normal incidence wave has local minima at the resonance frequencies of the coating layer, which provide its elastic property if the layer thickness is given a priori. Furthermore, it is revealed that the lower envelope of the reflection spectrum takes a minimum, whose frequency can be related to the critical attenuation condition. This feature implies a possibility that the viscous property of the coating material can be estimated by similarly measuring a characteristic frequency to the estimation of the elastic property. Two bonded specimens consisting of polycarbonate (PC) sheets and metal substrates were prepared to validate the proposed method. The reflection spectra measured for the normal wave incidence showed multiple local minima and critical attenuation, which are predicted to appear by theoretical predictions. The wave velocities and loss factors of PC estimated from the two specimens are in fair agreement with the properties shown in the previous paper. This result demonstrates that the ultrasonic interference and critical attenuation behavior can be applied to the characterization of the viscoelastic coating layers.

Explainable Graph Wavelet Denoising Network for Intelligent Fault Diagnosis.

Deep learning (DL)-based intelligent fault diagnosis methods have greatly promoted the development of the field of fault diagnosis due to their powerful feature extraction ability for handling massive monitoring data. However, most of them still suffer from the following three limitations. First, many existing DL-based intelligent diagnosis methods cannot extract proper discriminative features from signals with strong noise. Second, the interactions or relationships between signals are ignored, while they mainly focus on extracting temporal features from the signal. Third, owing to their black-box nature, the learned features lack interpretability, which hinders their application in the industry. To tackle these issues, an explainable graph wavelet denoising network (GWDN) is proposed to achieve intelligent fault diagnosis under noisy working conditions in this article. In GWDN, the collected signals are first transformed into graph-structured data to consider the interactions among signals. Then, the graph wavelet denoising convolution (GWDConv) is proposed based on the discrete graph wavelet frame, which allows GWDN to achieve multiscale feature extraction for graph-structured data and realize signal denoising. Extensive experiments are implemented to verify the efficacy of the proposed GWDN, and the experimental results show that GWDN can achieve state-of-the-art performance among the comparison methods. Besides, by using the square envelope spectrum to analyze the extracted features of GWDConv, we find that it can well retain the fault-related components of the signal and realize signal denoising, which further proves that GWDN is explainable.

A Deep Learning Method for Bearing Cross-Domain Fault Diagnostics Based on the Standard Envelope Spectrum.

Intelligent fault diagnostics based on deep learning provides a favorable guarantee for the reliable operation of equipment, but a trained deep learning model generally has low prediction accuracy in cross-domain diagnostics. To solve this problem, a deep learning fault diagnosis method based on the reconstructed envelope spectrum is proposed to improve the ability of rolling bearing cross-domain fault diagnostics in this paper. First, based on the envelope spectrum morphology of rolling bearing failures, a standard envelope spectrum is constructed that reveals the unique characteristics of different bearing health states and eliminates the differences between domains due to different bearing speeds and bearing models. Then, a fault diagnosis model was constructed using a convolutional neural network to learn features and complete fault classification. Finally, using two publicly available bearing data sets and one bearing data set obtained by self-experimentation, the proposed method is applied to the data of the fault diagnostics of rolling bearings under different rotational speeds and different bearing types. The experimental results show that, compared with some popular feature extraction methods, the proposed method can achieve high diagnostic accuracy with data at different rotational speeds and different bearing types, and it is an effective method for solving the problem with cross-domain fault diagnostics for rolling bearings.

Rotating machinery fault diagnosis based on parameter-optimized variational mode decomposition

Variational Mode Decomposition (VMD) has been widely applied in rotating machinery fault diagnosis. However, VMD needs to solve two key problems in its application: parameter optimization and the selection of high-quality Intrinsic Mode Functions (IMFs). To address these issues, firstly, the Sparrow Search Algorithm (SSA) is employed to optimize VMD parameters, incorporating fitness functions based on the Hoyer measure and the square envelope spectrum negative entropy. Subsequently, by minimizing the fitness function, optimal parameters for VMD are obtained. Secondly, a novel IMF selection method is proposed, evaluating IMF quality through sample entropy, energy ratio, and Spearman rank correlation coefficient to identify IMFs sensitive to fault features. Finally, the proposed method is validated using gear and bearing datasets containing noise of varying intensities, demonstrating its outstanding capability for extracting sensitive information in different noise environments.