Machine-learning-enabled adaptive signal decomposition for a brain-computer interface using EEG

In recent years, order tracking methods based on time-frequency (TF) ridge detection have attracted considerable attention for bearing fault detection under varying speed conditions. Inevitably, these methods are subjected to the resolution of the time–frequency representation (TFR). Hence, to overcome the limitations of the current order tracking techniques, adaptive signal decomposition methods have drawn the growing interest, in which variational nonlinear chirp mode decomposition (VNCMD) is a recently introduced method for adaptive signal analysis. Unfortunately, the successful applicability of the VNCMD method considerably depends on the prior knowledge of initial parameters. To address this issue, a new decomposition strategy called the optimization tendency guiding VNCMD method is proposed for the instantaneous frequency (IF) estimation of bearings. In particular, the proposed method consists of two steps. First, a coarse TF spectrum is presented to roughly extract a dominant IF by the ridge extraction method. Second, the optimization tendency guiding VNCMD decomposition strategy is constructed to accurately extract the meaningful modes until meeting the stop criterion. The new method is especially suitable for bearing fault diagnosis under varying speed conditions, which is confirmed by an experimental case of bearing fault diagnosis.

Accurate extraction of time-varying instantaneous frequency (IF) is crucial for fault diagnosis in rotating machinery operating under time-varying speed conditions, as real-world signals often exhibit nonlinearity and complexity. Variational nonlinear chirp mode decomposition (VNCMD) demonstrates significant capability and adaptability in extracting time-varying IFs by converting broadband signals into narrowband signals through a demodulation technique. However, its accuracy is limited by the fact that it only enforces smoothness on the demodulated signals, and it does not consider the inherent proportional relationships among IFs in rotating machine vibration signals. These limitations hinder VNCMD from accurately extracting IFs and result in poor noise robustness, a strong dependence on the initial IFs, and difficulties in handling nonlinear chirp signals (NCSs) with closely spaced IFs. To overcome these limitations, this article proposes hybrid constraints embedding VNCMD (HCVNCMD), which places further constraints on demodulated signals and IFs. Specifically, a sparse constraint is first applied to the demodulated signals. This improves their estimation accuracy and reduces errors in the subsequent IF estimates. Second, a low-rank constraint is applied to the IFs, effectively capturing their proportional relationships and optimizing inaccurate initial IFs to achieve the true IFs. The hybrid constraints embedded in HCVNCMD significantly enhance noise robustness and improve IF estimation accuracy, enabling effective processing of NCSs with closely spaced IFs. Both simulation and experimental cases demonstrate that the HCVNCMD outperforms existing time–frequency analysis (TFAs) methods in accurately estimating the IFs of NCSs. Furthermore, it successfully identifies fault features in gear and bearing under time-varying speed conditions, confirming its effectiveness and practicability.

Signal analysis is a fundamental field in engineering and data science, focused on the study of signal representation, transformation, and manipulation. The accurate estimation of harmonic vibration components and their associated parameters in vibrating mechanical systems presents significant challenges in the presence of very similar frequencies and mode mixing. In this context, a hybrid strategy to estimate harmonic vibration modes in weakly damped, multi-degree-of-freedom vibrating mechanical systems by combining Empirical Mode Decomposition and Variational Mode Decomposition is described. In this way, this hybrid approach leverages the detection of mode mixing based on the analysis of intrinsic mode functions through Empirical Mode Decomposition to determine the number of components to be estimated and thus provide greater information for Variational Mode Decomposition. The computational time and dependency on a predefined number of modes are significantly reduced by providing crucial information about the approximate number of vibratory components, enabling a more precise estimation with Variational Mode Decomposition. This hybrid strategy is employed to compute unknown natural frequencies of vibrating systems using output measurement signals. The algorithm for this hybrid strategy is presented, along with a comparison to conventional techniques such as Empirical Mode Decomposition, Variational Mode Decomposition, and the Fast Fourier Transform. Through several case studies involving multi-degree-of-freedom vibrating systems, the superior and satisfactory performance of the hybrid method is demonstrated. Additionally, the advantages of the hybrid approach in terms of computational efficiency and accuracy in signal decomposition are highlighted.

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.

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.

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.

Emotion can be defined as a voluntary or involuntary reaction to external factors. People express their emotions through actions, such as words, sounds, facial expressions, and body language. However, emotions expressed in such actions are sometimes manipulated by people and real feelings cannot be conveyed clearly. Therefore, understanding and analyzing emotions is essential. Recently, emotion analysis studies based on EEG signals appear to be in the foreground, due to the more reliable data collected. In this study, emotion analysis based on EEG signals was performed and a deep learning model was proposed. The study consists of four stages. In the first stage, EEG data were obtained from the GAMEEMO dataset. In the second stage, EEG signals were transformed with both VMD (variation mode decomposition) and EMD (empirical mode decomposition), and a total of 14 (nine from EMD, five from VMD) IMFs were obtained from each signal. In the third stage, statistical features were obtained from IMFs and maximum value, minimum value, and average values were used for this. In the last stage, both binary-class and multi-class classifications were made. The proposed deep learning model is compared with kNN (k nearest neighbor), SVM (support vector machines), and RF (random forest). At the end of the study, an accuracy of 70.89% in binary-class classification and 90.33% in multi-class classification was obtained with the proposed deep learning method.

We have proposed a new denoising method for the simultaneous noise reduction and preservation of seismic signals based on variational mode decomposition (VMD). VMD is a recently developed adaptive signal decomposition method and an advance in non-stationary signal analysis. It solves the mode-mixing and non-optimal reconstruction performance problems of empirical mode decomposition that have existed for a long time. By using VMD, a multi-component signal can be non-recursively decomposed into a series of quasi-orthogonal intrinsic mode functions (IMFs), each of which has a relatively local frequency range. Meanwhile, the signal will focus on a smaller number of obtained IMFs after decomposition, and thus the denoised result is able to be obtained by reconstructing these signal-dominant IMFs. Synthetic examples are given to demonstrate the effectiveness of the proposed approach and comparison is made with the complete ensemble empirical mode decomposition, which demonstrates that the VMD algorithm has lower computational cost and better random noise elimination performance. The application of on field seismic data further illustrates the superior performance of our method in both random noise attenuation and the recovery of seismic events.

Soldiers rely heavily on their vision, which is crucial not only for daily activities but also for the effective operation of defense systems, weaponry, and other military applications. However, various eye disorders, such as those related to increased intra-ocular pressure, can lead to irreversible vision loss, severely impacting a soldier’s operational capabilities. While extensive research has been conducted on detecting such ocular conditions, there remains a critical need for more accurate diagnostic methods to ensure early detection and treatment. In this study, we propose a novel approach combining Empirical Mode Decomposition (EMD) and Variational Mode Decomposition (VMD) for enhanced detection of eye disorders from retinal fundus images. The proposed method includes a comprehensive preprocessing phase, followed by decomposition using EMD and VMD techniques. The decomposed images undergo feature extraction through feature combination, with subsequent normalization and selection using z-score and the Relief method, respectively. Classification is performed using Support Vector Machines (SVM) with various kernels, including cubic, Gaussian, linear, and quadratic. The results demonstrate that the proposed method achieves high accuracy, with SVM kernel functions yielding accuracies of 98.30 %, 96.59 %, 96.59 %, and 97.87 % for 10-fold cross-validation, respectively. Additionally, the evaluation metrics, including sensitivity and specificity, indicate superior performance compared to state-of-the-art methods for similar datasets. This advanced diagnostic approach offers significant improvements in detecting eye disorders, which could be crucial in defense applications. Early and accurate diagnosis by military ophthalmologists can lead to better decision-making and timely interventions, ultimately preserving the vision and effectiveness of soldiers in the war.

Variational mode decomposition (VMD), which is an alternative to empirical mode decomposition (EMD), has been widely used to extract the feature components of nonstationary signals. However, as a parameterized method, the performance of VMD is heavily influenced by its parameters. Meanwhile, it cannot efficiently extract weak feature components submerged in powerful ones. To address these problems, a novel method based on an optimized VMD is developed for precisely extracting the weak feature of viscoelastic sandwich cylindrical structures (VSCSs). In this method, a parameter optimization algorithm first is proposed to simultaneously select the crucial parameters in the VMD, and to reveal the characteristics of the influence of these parameters on the decomposition performance. Then, the weak feature components submerged in low-frequency strong ones are extracted twice by using the VMD with the optimized parameters. The effectiveness of the proposed method is verified by simulation signals and the experiment vibration signal collected from the VSCS. Its robustness to noise is also discussed. The results indicate that the parameter optimization algorithm can adaptively obtain optimal parameters, and compared with the optimized complementary ensemble EMD (CEEMD) and the original VMD, the proposed method can precisely extract the weak feature components submerged in strong ones.

Due to the complicated structure, vibration signal of rotating machinery is multicomponent with nonstationary and nonlinear features, so it is difficult to diagnose faults effectively. Therefore, effective extraction of vibration signal characteristics is the key to diagnose the faults of rotating machinery. Mode mixing and illusive components existed in some conventional methods, such as EMD and EEMD, which leads to misdiagnosis in extracting signals. Given these reasons, a new fault diagnosis method, namely, variation mode decomposition (VMD), was proposed in this paper. VMD is a newly developed technique for adaptive signal decomposition, which can decompose a multicomponent signal into a series of quasi-orthogonal intrinsic mode functions (IMFs) simultaneously, corresponding to the components of signal clearly. To further research on VMD method, the advantages and characteristics of VMD are investigated via numerical simulations. VMD is then applied to detect oil whirl and oil whip for rotor systems fault diagnosis via practical vibration signal. The experimental results demonstrate the effectiveness of VMD method.

Variational mode decomposition is a new signal decomposition method, which can process non-linear and non-stationary signals. It can overcome the problems of mode mixing and compensate for the shortcomings in empirical mode decomposition. Permutation entropy is a method which can detect the randomness and kinetic mutation behavior of a time series. It can be considered for use in fault diagnosis. The complexity of wind power generation systems means that the randomness and kinetic mutation behavior of their vibration signals are displayed at different scales. Multi-scale permutation entropy analysis is therefore needed for such vibration signals. This research investigated a method based on variational mode decomposition and permutation entropy for the fault diagnosis of a wind turbine roller bearing. Variational mode decomposition was adopted to decompose the bearing vibration signal into its constituent components. The components containing key fault information were selected for the extraction of their permutation entropy. This entropy was used as a bearing fault characteristic value. The nearest neighbor algorithm was employed as a classifier to identify faults in a roller bearing. The experimental data showed that the proposed method can be applied to wind turbine roller bearing fault diagnosis.

Devising a reliable method for implementing brain computer interface (BCI) systems using electroencephalogram (EEG) signals is proposed. Applicability of two modal decomposition methods, variational mode decomposition (VMD) and empirical wavelet transform (EWT) on EEG signals for identifying the four different motor imaginary movements by the investigation of event-related desynchronisation (ERD) activity in the Mu-beta rhythm of EEG signals is analysed and compared. The EEG signals from each electrode corresponding to the sensorimotor cortex area of the brain are decomposed using VMD and EWT methods. Each decomposed modes are modelled using auto regressive (AR) modeling and feature vector is formed using the AR model parameters. On classification, better accuracy is perceived for VMD method in comparison with EWT and common spatial pattern (CSP) methods developed on the same dataset.

An operating condition information-guided iterative variational mode decomposition method based on Mahalanobis distance criterion for surge characteristic frequency extraction of the centrifugal compressor

The decomposition number $K$ and penalty factor $\alpha $ in the variational mode decomposition (VMD) algorithm have a great influence on the decomposition effect and the accuracy of subsequent fault diagnosis. Therefore, a gear fault diagnosis method based on genetic mutation particle swarm optimization VMD and probabilistic neural network (GMPSO-VMD-PNN) algorithm is proposed in this paper. Firstly, the GMPSO algorithm is used to optimize the $[K,\alpha]$ parameter combination in the VMD algorithm, and the optimal $[K,\alpha]$ parameter combination of each gear fault vibration signal to be decomposed is selected. Then, the gear fault vibration signal is decomposed into several intrinsic mode functions (IMFs) by VMD, and the sample entropy value of each IMFs is extracted to form the feature vector of subsequent fault diagnosis. Finally, the characteristic vector of gear fault vibration signal is input into PNN model, and gear fault is accurately classified. By comparing with fixed parameter VMD algorithm, empirical mode decomposition (EMD) and complete ensemble empirical mode decomposition adaptive noise (CEEMDAN) algorithm, the superiority of this method in gear fault diagnosis is verified. Therefore, the GMPSO-VMD-PNN algorithm proposed in this paper has certain application value for gear fault diagnosis.