Band-limited Intrinsic Mode Functions Research Articles

VMD-RiM: Rician Modeling of Temporal Feature Variation Extracted From Variational Mode Decomposed EEG Signal for Automatic Sleep Apnea Detection

Electroencephalogram (EEG) is getting special attention of late in the detection of sleep apnea as it is directly related to the neural activity. But apnea detection through visual monitoring of EEG signal by an expert is expensive, difficult, and susceptible to human error. To counter this problem, an automatic apnea detection scheme is proposed in this paper using a single lead EEG signal, which can differentiate apnea patients and healthy subjects and also classify apnea and non-apnea frames in the data of an apnea patient. Each sub-frame of a given frame of EEG data is first decomposed into band-limited intrinsic mode functions (BLIMFs) by using the variational mode decomposition (VMD). The advantage of using VMD is to obtain compact BLIMFs with adaptive center frequencies, which give an opportunity to capture the local information corresponding to varying neural activity. Furthermore, by extracting features from each BLIMF, a temporal within-frame feature variation pattern is obtained for each mode. We propose to fit the resulting pattern with the Rician model (RiM) and utilize the fitted model parameters as features. The use of such VMD-RiM features not only offers better feature quality but also ensures very low feature dimension. In order to evaluate the performance of the proposed method, K nearest neighbor classifier is used and various cross-validation schemes are carried out. Detailed experimentation is carried out on several apnea and healthy subjects of various apnea-hypopnea indices from three publicly available datasets and it is found that the proposed method achieves superior classification performances in comparison to those obtained by the existing methods, in terms of sensitivity, specificity, and accuracy.

A hybrid approach to fault diagnosis of roller bearings under variable speed conditions

Rolling element bearings are one of the main elements in rotating machines, whose failure may lead to a fatal breakdown and significant economic losses. Conventional vibration-based diagnostic methods are based on the stationary assumption, thus they are not applicable to the diagnosis of bearings working under varying speeds. This constraint limits the bearing diagnosis to the industrial application significantly. A hybrid approach to fault diagnosis of roller bearings under variable speed conditions is proposed in this work, based on computed order tracking (COT) and variational mode decomposition (VMD)-based time frequency representation (VTFR). COT is utilized to resample the non-stationary vibration signal in the angular domain, while VMD is used to decompose the resampled signal into a number of band-limited intrinsic mode functions (BLIMFs). A VTFR is then constructed based on the estimated instantaneous frequency and instantaneous amplitude of each BLIMF. Moreover, the Gini index and time-frequency kurtosis are both proposed to quantitatively measure the sparsity and concentration measurement of time-frequency representation, respectively. The effectiveness of the VTFR for extracting nonlinear components has been verified by a bat signal. Results of this numerical simulation also show the sparsity and concentration of the VTFR are better than those of short-time Fourier transform, continuous wavelet transform, Hilbert–Huang transform and Wigner–Ville distribution techniques. Several experimental results have further demonstrated that the proposed method can well detect bearing faults under variable speed conditions.

Depositional sequence characterization based on seismic variational mode decomposition

Subtle variations in otherwise similar seismic data can be highlighted in specific spectral components. Our goal is to highlight repetitive sequence boundaries to help define the depositional environment, which in turn provides an interpretation framework. Variational mode decomposition (VMD) is a novel data-driven signal decomposition method that provides several useful features compared with the commonly used time-frequency analysis. Rather than using predefined spectral bands, the VMD method adaptively decomposes a signal into an ensemble of band-limited intrinsic mode functions, each with its own center frequency. Because it is data adaptive, modes can vary rapidly between neighboring traces. We address this shortcoming of previous work by constructing a laterally consistent VMD method that preserves lateral continuity, facilitating the extraction of subtle depositional patterns. We validate the accuracy of our method using a synthetic depositional cycle example, and then we apply it to identify seismic sequence stratigraphy boundaries for a survey acquired in the Dutch sector, North Sea.

Bi-dimensional variational mode decomposition of laser speckle contrast imaging data: A clinical approach to critical limb ischemia?

The number of patients suffering from peripheral arterial occlusive disease (PAOD) is growing worldwide. PAOD corresponds to an impairment of perfusion in the distal portion of some arteries that can generate critical limb ischemia. For some patients, the pathology leads to the necessity of amputation. PAOD may be diagnosed and studied with transcutaneous oxygen (tcpO2) measurements. However, the tcpO2 technique is a contact technique: probes have to be positioned on the limb, which may be impossible in case of ulcers and can lead to infection risks. We therefore herein propose to study if the laser speckle contrast imaging (LSCI) technique, an optical contactless technique, could be of interest in studying limb ischemia. For this purpose, tcpO2 and LSCI data were recorded in 48 persons suffering or not from PAOD (different levels of criticality). The LSCI data were then processed with the recently introduced bi-dimensional variational mode decomposition (2D–VMD). 2D–VMD leads to band-limited intrinsic mode functions (LSCI 2D–BLIMFs in our case). From these LSCI 2D–BLIMFs, we propose a new index. Our results show that this index and the tcpO2 values have a Pearson's r correlation coefficient of −0.401. Moreover, the Bland-Altman graph shows that the LSCI 2D–BLIMFs-based index and the tcpO2 values are consistent. LSCI might therefore be of interest for a contactless study of limb ischemia.

Variational mode decomposition denoising combined with the Hausdorff distance.

Variational mode decomposition (VMD) is a recently introduced adaptive signal decomposition algorithm with a solid theoretical foundation and good noise robustness compared with empirical mode decomposition (EMD). However, there is still a problem with this algorithm associated with the selection of relevant modes. To solve this problem, this paper proposes a novel signal-filtering method that combines VMD with Hausdorff distance (HD) in the VMD-HD method. A noisy signal is first decomposed into a given number K of band-limited intrinsic mode functions by VMD. The probability density function is then estimated for each mode. The aim of this method is to reconstruct the signal using the relevant modes, which are selected on the basis of noticeable similarities between the probability density function of the input signal and that of each mode. Various similarity measures are investigated and compared, and the HD is shown to offer the best performance. The results of filtering of simulation signals illustrate the validity of the proposed method when compared with EMD-based methods under comprehensive quantitative evaluation criteria. As a specific example, the proposed method is successfully used for filtering the pipeline leakage signal as evaluated by the de-trended fluctuation analysis algorithm.

AR based quadratic feature extraction in the VMD domain for the automated seizure detection of EEG using random forest classifier

Abstract Visual inspection of epileptic electroencephalogram (EEG) by neurologists is time-consuming and tedious. To overcome the problems, numerous automated seizure detection techniques, combining signal processing and machine learning, have been developed. Although 100% accuracy has been achieved for classifying non-seizure and seizure EEG records in up-to-date articles, the result of distinguishing normal, interictal and ictal EEG is still not satisfying. In this paper, a fusion method of variational mode decomposition (VMD) and autoregression (AR) based quadratic feature extraction was proposed for feature extraction and the random forest classifier was employed to hand with three-classification task. The raw EEG was decomposed into a fixed number of band-limited intrinsic mode functions (BLIMFs) using VMD, then a logarithmic operation was imposed on each BLIMF. Subsequently, optimal AR based quadratic feature extraction was conducted on all the BLIMFs and the extracted feature vectors were fed into random forest classifier for classification. Experimental results on the Bonn epilepsy EEG dataset show that the best accuracy of the proposed scheme is 97.352% and it outperforms than the fixed-order AR based feature extraction technique. The developed technology is proven efficient for seizure detection. It can be further programmed into software and the software can be applied in hospitals to assist the neurologists for seizure detection.

A rolling bearing fault diagnosis method based on VMD – multiscale fractal dimension/energy and optimized support vector machine

To achieve the goal of automated rolling bearing fault diagnosis, a variational mode decomposition (VMD) based diagnosis scheme was proposed. VMD was firstly used to decompose the vibration signals into a series of band-limited intrinsic mode functions (BLIMFs). Subsequently, the multiscale fractal dimension (MSFD) and multiscale energy (MSEN) of each BLIMF were calculated and combined together as features of the original vibration signals. In an attempt to accelerate the classification speed, one-way analysis of variance (ANOVA) test was adopted to extract significant features from the redundant features. Finally, those significant features were fed into the optimized support vector machine (SVM), which was optimized by the genetic algorithm (GA), for classification. Experimental results on the international public Case Western Reserve University bearing data indicate the effectiveness of the proposed method with a classification accuracy of 99.75 % for seven classes. Moreover, our approach also shows good anti-noise performance in different signal-to-noise ratios (SNRs).

Adaptive variational mode decomposition based on artificial fish swarm algorithm for fault diagnosis of rolling bearings

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.

Underdetermined Blind Source Separation with Variational Mode Decomposition for Compound Roller Bearing Fault Signals

In the condition monitoring of roller bearings, the measured signals are often compounded due to the unknown multi-vibration sources and complex transfer paths. Moreover, the sensors are limited in particular locations and numbers. Thus, this is a problem of underdetermined blind source separation for the vibration sources estimation, which makes it difficult to extract fault features exactly by ordinary methods in running tests. To improve the effectiveness of compound fault diagnosis in roller bearings, the present paper proposes a new method to solve the underdetermined problem and to extract fault features based on variational mode decomposition. In order to surmount the shortcomings of inadequate signals collected through limited sensors, a vibration signal is firstly decomposed into a number of band-limited intrinsic mode functions by variational mode decomposition. Then, the demodulated signal with the Hilbert transform of these multi-channel functions is used as the input matrix for independent component analysis. Finally, the compound faults are separated effectively by carrying out independent component analysis, which enables the fault features to be extracted more easily and identified more clearly. Experimental results validate the effectiveness of the proposed method in compound fault separation, and a comparison experiment shows that the proposed method has higher adaptability and practicability in separating strong noise signals than the commonly-used ensemble empirical mode decomposition method.

Variational mode decomposition denoising combined the detrended fluctuation analysis

A novel signal denoising method that combines variational mode decomposition (VMD) and detrended fluctuation analysis (DFA), named DFA–VMD, is proposed in this paper. VMD is a recently introduced technique for adaptive signal decomposition, which is theoretically well founded and more robust to sampling and noise compared with empirical mode decomposition (EMD). The noisy signal is first broken down into a given number K band-limited intrinsic mode functions (BLIMFs) by VMD. Then a simple criterion based on DFA is designed to select the number K, aiming to avoid the impact of overbinning or underbinning on the VMD denoising. In addition, DFA is also developed to define the relevant modes to construct the filtered signal. After that, the computational complexity of DFA–VMD denoising is analyzed, and its time complexity is equivalent to the EMD. Experimental results, on simulated and real signals, show the superior performance of this proposed filtering over EMD-based denoisings and discrete wavelet threshold filtering.