Multivariate Signal Denoising Based on Generic Multivariate Detrended Fluctuation Analysis

We propose a generic multivariate extension of detrended fluctuation analysis (DFA) that incorporates interchannel dependencies within input multichannel data to perform its long-range correlation analysis. We next demonstrate the utility of the proposed method within multivariate signal denoising problem. Particularly, our denosing approach first obtains data driven multiscale signal representation via multivariate variational mode decomposition (MVMD) method. Then, proposed multivariate extension of DFA (MDFA) is used to reject the predominantly noisy modes based on their randomness scores. The denoised signal is reconstructed using the remaining multichannel modes albeit after removal of the noise traces using the principal component analysis (PCA). The utility of our denoising method is demonstrated on a wide range of synthetic and real life signals

Denoising and Artifacts Removal in ECG Signals

ECG signal is a non-stationary biological signal and plays a pivotal role in the diagnosis of cardiac-related abnormalities. Reduction of noise in electrocardiography signals is a crucial and important problem because the artifacts corrupting the signal possesses similar frequency characteristics as that of the signal itself. Conventional techniques viz. filtering were proved to be uncap able of eliminating these interferences. Therefore the electrocardiography signals require a novel and efficient denoising strategy with a view to facilitate satisfactory noise-removal performance. A new yet adaptive and data-driven method for denoising of ECG signals using EMD and DFA algorithms has been investigated...The proposed algorithm has been tested with ECG signals (MIT-BIH Database) with added noise such as baseline wander and muscle contraction noise. Parameter are calculated to determine the effectiveness of the algorithm on a variety of signal types. The obtained results show that the proposed denoising algorithm is easy to implement and suitable to be applied with electrocardiography signals

Enhanced partial discharge signal denoising using dispersion entropy optimized variational mode decomposition

This paper presents a new approach for denoising Partial Discharge (PD) signals using a hybrid algorithm combining the adaptive decomposition technique with Entropy measures and Group-Sparse Total Variation (GSTV). Initially, the Empirical Mode Decomposition (EMD) technique is applied to decompose a noisy sensor data into the Intrinsic Mode Functions (IMFs), Mutual Information (MI) analysis between IMFs is carried out to set the mode length K. Then, the Variational Mode Decomposition (VMD) technique decomposes a noisy sensor data into K number of Band Limited IMFs (BLIMFs). The BLIMFs are separated as noise, noise-dominant, and signal-dominant BLIMFs by calculating the MI between BLIMFs. Eventually, the noise BLIMFs are discarded from further processing, noise-dominant BLIMFs are denoised using GSTV, and the signal BLIMFs are added to reconstruct the output signal. The regularization parameter [Formula: see text] for GSTV is automatically selected based on the values of Dispersion Entropy of the noise-dominant BLIMFs. The effectiveness of the proposed denoising method is evaluated in terms of performance metrics such as Signal-to-Noise Ratio, Root Mean Square Error, and Correlation Coefficient, which are are compared to EMD variants, and the results demonstrated that the proposed approach is able to effectively denoise the synthetic Blocks, Bumps, Doppler, Heavy Sine, PD pulses and real PD signals

Nonlinear trend removal should be carefully performed in heart rate variability analysis

$\bullet$ Background : In Heart rate variability analysis, the rate-rate time series suffer often from aperiodic non-stationarity, presence of ectopic beats etc. It would be hard to extract helpful information from the original signals. 10 $\bullet$ Problem : Trend removal methods are commonly practiced to reduce the influence of the low frequency and aperiodic non-stationary in RR data. This can unfortunately affect the signal and make the analysis on detrended data less appropriate. $\bullet$ Objective : Investigate the detrending effect (linear \& nonlinear) in temporal / nonliear analysis of heart rate variability of long-term RR data (in normal sinus rhythm, atrial fibrillation, 15 congestive heart failure and ventricular premature arrhythmia conditions). $\bullet$ Methods : Temporal method : standard measure SDNN; Nonlinear methods : multi-scale Fractal Dimension (FD), Detrended Fluctuation Analysis (DFA) \& Sample Entropy (Sam-pEn) analysis. $\bullet$ Results : The linear detrending affects little the global characteristics of the RR data, either 20 in temporal analysis or in nonlinear complexity analysis. After linear detrending, the SDNNs are just slightly shifted and all distributions are well preserved. The cross-scale complexity remained almost the same as the ones for original RR data or correlated. Nonlinear detrending changed not only the SDNNs distribution, but also the order among different types of RR data. After this processing, the SDNN became indistinguishable be-25 tween SDNN for normal sinus rhythm and ventricular premature beats. Different RR data has different complexity signature. Nonlinear detrending made the all RR data to be similar , in terms of complexity. It is thus impossible to distinguish them. The FD showed that nonlinearly detrended RR data has a dimension close to 2, the exponent from DFA is close to zero and SampEn is larger than 1.5 -- these complexity values are very close to those for 30 random signal. $\bullet$ Conclusions : Pre-processing by linear detrending can be performed on RR data, which has little influence on the corresponding analysis. Nonlinear detrending could be harmful and it is not advisable to use this type of pre-processing. Exceptions do exist, but only combined with other appropriate techniques to avoid complete change of the signal's intrinsic dynamics. 35 Keywords $\bullet$ heart rate variability $\bullet$ linear / nonlinear detrending $\bullet$ complexity analysis $\bullet$ mul-tiscale analysis $\bullet$ detrended fluctuation analysis $\bullet$ fractal dimension $\bullet$ sample entropy

Novel complete ensemble EMD with adaptive noise-based hybrid filtering for rolling bearing fault diagnosis

A feature extraction of fault bearing has attracted considerable attention in recent years. However, weak fault feature is difficult to extract under heavy background noise. To solve this problem, a novel multi-layer filtering method is proposed to filter out noise and extract weak fault feature. The first layer introduces a metric based on de-trended fluctuation analysis (DFA) to identify intrinsic mode function (IMF) that reflect period impulsive information for vibration signal adaptively. The second layer uses non-local mean (NLM) method as a pre-filter of the third layer to realize extraction of singular value decomposition (SVD) which reflect the most information of IMFs. The last layer introduces a relative energy difference criterion of a singular value to extract important feature of Hankel matrix of IMFs. The filtered signal is obtained by re-constructed signal from identified singular value of SVD. Experiment results on simulation and real vibration signals indicate that the hybrid filtering method removes heavy noise successfully and extract weak fault feature of rolling bearing effectively

Bearing fault diagnosis and degradation analysis based on improved empirical mode decomposition and maximum correlated kurtosis deconvolution

Detecting periodic impulse signal (PIS) is the core of bearing fault diagnosis. Earlier fault detected, earlier maintenance actions can be implemented. On the other hand, remaining useful life (RUL) prediction provides important information when the maintenance should be conducted. However, good degradation features are the prerequisite for effective RUL prediction. Therefore, this paper mainly concerns earlier fault detection and degradation feature extraction for bearing. Maximum correlated kurtosis deconvolution (MCKD) can enhance PIS produced by bearing fault. Whereas, it only achieve good effect when bearing has severe fault. On the contrary, PIS produced by bearing weak fault is always masked by heavy noise and cannot be enhanced by MCKD. In order to resolve this problem, a revised empirical mode decomposition (EMD) algorithm is used to denoise bearing fault signal before MCKD processing. In revised EMD algorithm, a new recovering algorithm is used to resolve mode mixing problem existed in traditional EMD and it is superior to ensemble EMD. For degradation analysis, correlated kurtosis (CK) value is used as degradation indicator to reflect health condition of bearing. Except of theory analysis, simulated bearing fault data, injected bearing fault data, real bearing fault data and bearing degradation data are used to verify the proposed method. Simulated bearing fault data is used to explain the existed problems. Then, injected bearing fault data and real bearing fault data are used to demonstrate the effectiveness of proposed method for fault diagnosis. Finally, bearing degradation data is used to verify the degradation feature CK extracted based on proposed method. All these case studies show the effectiveness of proposed fault diagnosis and degradation tracking method

Trend Filtering via Empirical Mode Decompositions

The present work is concerned with the problem of extracting low-frequency trend from a given time series. To solve this problem, the authors develop a nonparametric technique called empirical mode decomposition (EMD) trend filtering. A key assumption is that the trend is representable as the sum of intrinsic mode functions produced by the EMD. Based on an empirical analysis of the EMD, the authors propose an automatic procedure for selecting the requisite intrinsic mode functions. To illustrate the effectiveness of the technique, the authors apply it to simulated time series containing different types of trend, as well as real-world data collected from an environmental study (atmospheric carbon dioxide levels at Mauna Loa Observatory) and from a large-scale bicycle rental service (rental numbers of Grand Lyon Vélo'v