Fault feature extraction of wind turbine gearbox under variable speed based on improved adaptive variational mode decomposition

In this paper, a fault feature extraction method based on the combination of computational order tracking (COT) and variational mode decomposition (VMD) is proposed to solve the problem of fault feature extraction in a gearbox under variable speed conditions. First, a speed estimation method based on a forward-backward greedy algorithm and Fourier fitting is proposed to solve the speed estimation problem under variable speed conditions. Then, a feature extraction method based on COT, VMD, and fast kurtometry is proposed. COT is used to calculate the order. After the signal is decomposed by VMD, a fast kurtogram is used to filter the modal components with obvious fault features so as to extract fault features. Finally, combined with the analysis of actual equipment examples, the experimental results show that steady-state filtering can effectively filter the background noise and improve the signal-to-noise ratio. The rotation speed estimated by the forward–backward greedy algorithm and Fourier fitting is very close to the actual speed, which verifies that the method proposed in this paper can effectively solve the problem of fault feature extraction of a gearbox under variable speed conditions.

A motor bearing system is a nonlinear dynamics system with nonlinear support stiffness. It is an asymmetry system, which plays an extremely important role in rotating machinery. In this paper, a center frequency method of double thresholds is proposed to improve the variational mode decomposition (VMD) method, then an adaptive VMD (called DTCFVMD) method is obtained to extract the fault feature. In the DTCFVMD method, a center frequency method of double thresholds is a symmetry method, which is used to determine the decomposed mode number of VMD according to the power spectrum of the signal. The proposed DTCFVMD method is used to decompose the nonlinear and non-stationary vibration signals of motor bearing in order to obtain a series of intrinsic mode functions (IMFs) under different scales. Then, the Hilbert transform is used to analyze the envelope of each mode component and calculate the power spectrum of each mode component. Finally, the power spectrum is used to extract the fault feature frequency for determining the fault type of the motor bearing. To test and verify the effectiveness of the DTCFVMD method, the actual fault vibration signal of the motor bearing is selected in here. The experimental results show that the center frequency method of double thresholds can effectively determine the mode number of the VMD method, and the proposed DTCFVMD method can accurately extract the clear time frequency characteristics of each mode component, and obtain the fault characteristics of characteristics; frequency, rotating frequency, and frequency doubling and so on.

Aiming at the problems of difficulty in extracting vibration signal features and low recognition accuracy of bearing fault, a new fault diagnosis method based on ISSA-VMD and IMSE was proposed. This method leverages an improved sparrow search algorithm (ISSA) to optimize the variational mode decomposition (VMD) method and employs an improved multiscale sample entropy (IMSE) for fault feature extraction. Initially, the ISSA algorithm optimizes two critical parameters of the VMD method: the number of modes K and the penalty factor α, to obtain the optimal parameter combination [K, α]. The optimized VMD method is then used to decompose the bearing vibration signals for signal reconstruction analysis. Subsequently, the IMSE entropy algorithm is applied to the reconstructed signals to extract fault features, resulting in the required fault feature vector set. Finally, this extracted fault feature vector set is input into a multi-kernel extreme learning machine model for fault classification and diagnosis. The results show that the identification accuracy of the fault diagnosis of reciprocating compressor plain bearings and automobile rolling bearings is significantly improved, and the method has better fault feature extraction effect.

Variational mode decomposition has been widely applied to machinery fault diagnosis during these years. However, it remains difficult to set proper hyperparameters for the variational mode decomposition, including number of decomposed modes, initial center frequencies, and balance parameter. Moreover, the low efficiency of the existing variational mode decomposition methods hinders their applications to practical diagnostic task. This article proposes an adaptive and efficient variational mode decomposition method after thoroughly investigating its convergence property characteristic. A convergent tendency phenomenon is discovered and is explained mathematically for the first time. Motivated by the convergent tendency phenomenon, the proposed method rapidly and adaptively determines the number and the optimal initial center frequencies of signal latent modes with the guidance of the convergent tendencies of the initial center frequencies changing from small to large. In the proposed method, the number of decomposed modes and initial center frequencies are not hyperparameters that require to be set in advance any more, but are parameters learned from the analyzed signals. The determined parameters enable efficient extraction of the main latent modes contained in the analyzed signals. Therefore, the proposed variational mode decomposition method represents a major improvement in parameter adaption and decomposition efficiency over the existing variational mode decomposition methods. In the application for bearing fault diagnosis, the faulty modes are selected adaptively and the corresponding balance parameters are further optimized efficiently. Two experimental cases validate the proposed method and its superiority over the existing variational mode decomposition methods and the classical fast spectral kurtosis in bearing fault diagnosis.

The working environment of rotating machines is complex, and their key components are prone to failure. The early fault diagnosis of rolling bearings is of great significance; however, extracting the single scale fault feature of the early weak fault of rolling bearings is not enough to fully characterize the fault feature information of a weak signal. Therefore, aiming at the problem that the early fault feature information of rolling bearings in a complex environment is weak and the important parameters of Variational Modal Decomposition (VMD) depend on engineering experience, a fault feature extraction method based on the combination of Adaptive Variational Modal Decomposition (AVMD) and optimized Multiscale Fuzzy Entropy (MFE) is proposed in this study. Firstly, the correlation coefficient is used to calculate the correlation between the modal components decomposed by VMD and the original signal, and the threshold of the correlation coefficient is set to optimize the selection of the modal number . Secondly, taking Skewness (Ske) as the objective function, the parameters of MFE embedding dimension M, scale factor S and time delay T are optimized by the Particle Swarm Optimization (PSO) algorithm. Using optimized MFE to calculate the modal components obtained by AVMD, the MFE feature vector of each frequency band is obtained, and the MFE feature set is constructed. Finally, the simulation signals are used to verify the effectiveness of the Adaptive Variational Modal Decomposition, and the Drivetrain Dynamics Simulator (DDS) are used to complete the comparison test between the proposed method and the traditional method. The experimental results show that this method can effectively extract the fault features of rolling bearings in multiple frequency bands, characterize more weak fault information, and has higher fault diagnosis accuracy.

The variational mode decomposition (VMD) method for signal decomposition is severely affected by the number of components of the VMD method. In order to determine the decomposition modal number, K, in the VMD method, a new center frequency method of the multi-threshold is proposed in this paper. Then, an improved VMD (MTCFVMD) algorithm based on the center frequency method of the multi-threshold is obtained to decompose the vibration signal into a series of intrinsic modal functions (IMFs). The Hilbert transformation is used to calculate the envelope signal of each IMF component, and the maximum frequency value of the power spectral density is obtained in order to effectively and accurately extract the fault characteristic frequency and realize the fault diagnosis. The rolling element vibration data of the motor bearing is used to test the effectiveness of proposed methods. The experiment results show that the center frequency method of the multi-threshold can effectively determine the number, K, of decomposed modes. The proposed fault diagnosis method based on MTCFVMD and Hilbert transformation can effectively and accurately extract the fault characteristic frequency, rotation frequency, and frequency doubling, and can obtain higher diagnostic accuracy.

This paper proposes a novel method to improve the variational mode decomposition (VMD) method and to automatically acquire the sensitive intrinsic mode function (IMF). First, since fault signals are impulsive and periodic, a weighted autocorrelative function maximum (AFM) indicator is constructed based on the Gini index and autocorrelation function to serve as the optimization objective function. The mode number K and the penalty parameter α of VMD are automatically obtained through an optimal parameter searching process underpinned by the improved particle swarm optimization (PSO) algorithm with a variety of inertia weights. This improvement solves one of the major drawbacks of the conventional VMD method, that is, the need to manually set parameters. Then, an optimal IMF automatic selecting process is performed for single-failure faults and compound faults, according to the principles of the maximum weighted AFM indicator and maximum spectrum peak ratio (SPR), respectively. The sensitive IMFs are then subjected to an envelope demodulation analysis to obtain the fault characteristic frequency. The results of simulations and experiments show that the proposed method can effectively identify fault characteristics early, especially compound faults, demonstrating great potential for real-world applications.

In weak fault feature extraction for Autonomous Underwater Vehicles (AUVs), traditional methods typically employ wavelet transforms for signal denoising and the Modified Bayesian (MB) for feature extraction. Recently, the Variational Mode Decomposition (VMD) method has garnered significant attention in the fault diagnosis of rotating types of machinery, demonstrating promising results. In this context, the authors applied the VMD+MB method to extract fault features from AUVs, yielding some improvements. However, the ratios of fault eigenvalues to noise eigenvalues remain low, which limits diagnostic accuracy. To address the aforementioned problem, the improved VMD+MB method segments signals using the smoothed pseudo-Wigner–Ville distribution method, then applies VMD to each segmented signal to improve the denoising effect. Additionally, stochastic resonance is introduced to enhance the fault features. The proposed methodology effectively improves the extraction of fault features, and the efficacy of the improved VMD+MB algorithm is validated through experimental prototype pool experiments.

The bearing fault diagnosis is of vital significance in maintaining the safety of rotation machine. Among various fault detection techniques, the diagnosis based on vibration signal is widely applied in monitoring the condition of rotation machine. Variational mode decomposition (VMD) is a novel signal analysis method, which can decompose a multi-component signal into a certain number of band-limited intrinsic mode functions (BLIMFs) nonrecursively. VMD could overcome some problems such as mode mixing, the inference of noise, the determination of wavelet base, which exist in empirical mode decomposition, ensemble empirical mode decomposition, wavelet transform, respectively. However, the empirical selection of the parameters for VMD would affect the result of the decomposition. This paper presents an adaptive VMD method with parameter optimization for detecting the localized faults of rolling bearing. Kurtosis, sensitive to transient impulsive components, is employed as optimization index to evaluate the performance of the VMD. Two parameters in the VMD, namely the number of decomposition modes and data-fidelity constraint, are optimized synchronously based on the kurtosis index through artificial fish swarm algorithm. Executing VMD with the acquired parameters, the optimal BLIMF is obtained. The spectrum analysis of the optimal BLIMF could identify the characteristic frequency caused by the localized crack effectually. The validity of the proposed method is proved by means of a cyclic transient impulse response signal and two experiments with practical vibration signals of rolling bearings. Compared to several existing methods, the proposed method demonstrates reinforced results.

Enhancement of adaptive mode decomposition via angular resampling for nonstationary signal analysis of rotating machinery: Principle and applications

According to the non-stationary characteristic of rotating machinery vibration signals of a rotor system with a loose pedestal fault, variational mode decomposition was applied in the pedestal looseness fault diagnosis for such a rotor system. Variational mode decomposition is used to decompose the rotor vibration signal into several stable components. This can achieve the separation of the pedestal looseness fault signal from the background signals, and extract the fault characteristic of a vibration signal from a rotor system with pedestal looseness. Experimental data from a rotor system with pedestal looseness were used to verify the proposed method. The results showed that the stable components of the rotor vibration signal obtained by variational mode decomposition have obvious amplitude modulation characteristics. The components which contain fault information were analyzed by envelope demodulation, which can extract the pedestal looseness fault features of a rotor vibration signal. Therefore, the variational mode decomposition method can be effectively applied to the pedestal looseness fault diagnosis of such a rotor system.

As the gear is one of the most critical components of the high-speed rotating machinery, the fault identification of the gear has attracted increasing attention recently. However, the nonlinear and non-stationary vibration signals with mode mixing phenomenon and heavy background noise make it difficult to excavate the hidden weak fault feature. Variational Mode Decomposition (VMD), which can decompose the non-linear and non-stationary signals into a couple of Intrinsic Mode Functions (IMF) adaptively and non-recursively, bring a feasible tool. While the heavy background noise seriously affects the setting of the model number, which may lead to information loss or over decomposition problem. In this paper, a new improved VMD method, namely, Generalized Variational Mode Decomposition (GVMD) method is proposed to extract the fault characteristic information buried in the vibration signals adaptively. For the gear fault quantitative diagnosis, the corresponding relationship between the characteristic parameters and the working conditions is established under a specific condition, and it is no longer applicable to other conditions. Based on the dynamic model of the gear transmission system, the characteristic parameters that are sensitive and correlative to the gear tooth crack level, but not sensitive to the working conditions, can be extracted from the dynamic responses. Then the Normalized Feature Vector (NFV) can be formed with the extracted parameters. Based on the methods mentioned above, a novel intelligent method that combines the GVMD with NFV extraction to realize the quantitative diagnosis of the gear fault under variable working conditions is proposed. The NFV can be extracted from the experimental vibration signals preprocessed by the GVMD, and establish the relationship between the NFV and the gear tooth crack level. Then the quantitative diagnosis of the gear fault can be realized by the Support Vector Machine (SVM). The results show that the intelligent quantitative diagnosis method proposed in this paper is a potential quantitative diagnosis tool for the gear fault.

Ferromagnetic materials are extensively utilized in industrial settings where the early detection and repair of defects is paramount for ensuring industrial safety. During the enhanced magnetic memory detection of micro-defects, many interference signals appear in the detection signal, which makes it difficult to accurately extract the characteristics of the micro-defect signals, significantly affecting detection effectiveness. When improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN) is employed independently for signal denoising, the noise and feature signals of the transition components are retained or removed. When variational mode decomposition (VMD) is employed independently for signal denoising, the denoising effect is restricted because of the difficulty in determining the penalty factor α and the number of decomposition layers m. To solve these problems, a denoising method for enhanced magnetic memory detection signals based on ICEEMDAN and VMD, called ICEEMDAN–VMD, is proposed in this paper. First, a comprehensive index (CI) combining information entropy (IE) and the correlation coefficient R is proposed, then the signal components obtained by performing decomposition with the ICEEMDAN method are divided into noise-dominant components, transition components, and useful signal components based on the CI. Subsequently, VMD is employed to perform secondary decomposition on the transition components obtained from the ICEEMDAN method and calculate the correlation coefficients. Ultimately, the optimal VMD components and useful signal components obtained by the ICEEMDAN method are selected for signal reconstruction to obtain a denoised signal. To validate the effectiveness of the proposed method, the denoising effects of the ICEEMDAN–VMD, ICEEMDAN, and VMD methods were compared based on the signal-to-noise ratio (SNR) and fuzzy entropy (FE). The comparison indicated that the ICEEMDAN–VMD denoising method significantly enhanced the denoising effect, and the SNRs of the components of the magnetic field signal could be increased by up to 69.426%. The SNR of each gradient component of the magnetic field signal could be improved by up to ten times, and the FEs of the signal components and their corresponding gradient components could be reduced by 24.198%–81.011%, respectively.

Amyotrophic lateral sclerosis (ALS), also known as motor neuron disease, is a neurological disease that occurs as a result of damage to the nerves in the brain and restriction of muscle movements. Electroencephalography (EEG) is the most common method used in brain imaging to study neurological disorders. Diagnosis of neurological disorders such as ALS, Parkinson's, attention deficit hyperactivity disorder is important in biomedical studies. In recent years, deep learning (DL) models have been started to be applied in the literature for the diagnosis of these diseases. In this study, event-related potentials (ERPs) were obtained from EEG signals obtained as a result of visual stimuli from ALS patients and healthy controls. As a new method, variational mode decomposition (VMD) is applied to the produced ERP signals and the signals are decomposed into subbands. In addition, empirical mode decomposition (EMD), one of the popular decomposition methods in the literature, was also analyzed, and ERP signals were divided into subbands and compared with the VMD method. Subband signals were classified in two stages with the one-dimensional convolutional neural network (1D CNN) model, which is one of the DL techniques proposed in the study. Accuracy, sensitivity, specificity, and F1-Score measurements were obtained using 5- and 10-fold cross-validation to evaluate classifier performance. In the first stage of classification, only VMD and EMD subband signals were used and 92.95% classification accuracy was obtained by the VMD method. In the second stage, VMD, EMD subband signals, and original ERP signals were all classified together with the VMD+ERP model achieving the maximum classification accuracy rate of 90.42%. It is thought that the results of the study will contribute to the diagnosis of similar neurological disorders such as ALS, attention studies based on visual stimuli, and the development of brain-computer interface (BCI) systems using the method applied to the proposed ERP signals.

Condition monitoring plays a very important role in equipment fault diagnosis technology. However, existing monitoring methods often collect equipment fault signals from a single dimension, resulting in a major lack of fault information. To improve the problem, we built a gearbox preset fault test bench and constructed a dual-sensor acquisition system to realize the multiple dimensions of vibration signal acquisition in the horizontal and vertical directions of the gearbox. At the same time, given the poor adaptability of most current signal preprocessing methods, the improved nonlinear adaptive inertial weight particle swarm optimization algorithm (NAPSO) and variational modal decomposition (VMD) are combined to optimize the key parameters in VMD with the maximum correlation kurtosis convolution (MCKD) as the fitness function. Further, after extracting fault features from the intrinsic mode functions (IMFS) decomposed by VMD, the single-layer sparse autoencoder network (SAE) and the double-layer stacked sparse autoencoder network (SSAE) with different structures are used to realize an effective fusion of multidimensional information and deep feature extraction. Finally, the hybrid fault diagnosis of gearboxes is realized by using the random forest algorithm (RF) as the classifier. The experimental results show that the accuracy of the method proposed in this paper can reach 96.0%, and the accuracy can be improved by 3.0% and 4.0%, respectively, when compared with a single horizontal or vertical sensor signal input.