Noise-assisted Empirical Mode Decomposition Research Articles

NA-MEMD Is Actually What You Need for Computational Pulse Analysis

Time-frequency analysis is of necessity for wrist pulse signal due to its complexity, among which, empirical mode decomposition (EMD) algorithm and its improved noise-assisted versions (such as ensemble EMD, noise-assisted multivariate EMD (NA-MEMD) and very recently median EMD) are deemed to be the most representative ones. In this study, we provide an in-depth evaluation of these well-established noise-assisted EMD algorithms in computational pulse analysis for the first time. In particular, we compare the performance of the different algorithms systematically and quantitatively based on objective quantitative criteria: number and central frequency of intrinsic mode function (IMF) components, total orthogonality index and mode mixing. Rather than using synthetic signals with visual inspection in most existing literature, the wrist pulse signals used in the evaluation are real recorded samples acquired from both healthy and patient subjects. Through extensive experiments, we found that: 1) Advanced EMD algorithm that has the best performance in other areas may not be the most suitable method for pulse signal analysis, which indicates its high dependence on the type of signal to be analyzed; 2) Adding noise can significantly improve algorithm performance, but tends to produce physiologically not relevant components, which however are usually neglected throughout the intelligent pulse diagnosis literature. Therefore, excluding redundant components and then extracting features is expected to improve performance further. Together, currently NA-MEMD achieves a better performance consistently, potential to become a powerful tool for computational pulse analysis, which in itself have not been applied in wrist pulse analysis before. We believe our works can bring up a new perspective to application of EMD-like algorithms in computational pulse analysis/diagnosis with effective information and guidance. Additionally, considering the similarity between physiological signals, especially such as photoplethysmogram/electrocardiogram, our research can be extended to wearable health monitoring technologies, including smart watches and fitness trackers, and their potential future applications, such as in heart rate estimation and evaluate various cardiovascular-related diseases. The present study underscored the necessity of evaluation noise-assisted EMDs or other adaptive decomposition algorithms based on real recorded signals with more objective measures. Especially, caution the possible redundant components that are introduced.

Influence of Sampling Frequency Ratio on Mode Mixing Alleviation Performance: A Comparative Study of Four Noise-Assisted Empirical Mode Decomposition Algorithms

Four noise-assisted empirical mode decomposition (EMD) algorithms, i.e., ensemble EMD (EEMD), complementary ensemble EMD (CEEMD), complete ensemble EMD with adaptive noise (CEEMDAN), and improved complete ensemble EMD with adaptive noise (ICEEMDAN), are noticeable improvements to EMD, aimed at alleviating mode mixing. However, the sampling frequency ratio (SFR), i.e., the ratio between the sampling frequency and the maximum signal frequency, may significantly impact their mode mixing alleviation performance. Aimed at this issue, we investigated and compared the influence of the SFR on the mode mixing alleviation performance of these four noise-assisted EMD algorithms. The results show that for a given signal, (1) SFR has an aperiodic influence on the mode mixing alleviation performance of four noise-assisted EMD algorithms, (2) a careful selection of SFRs can significantly improve the mode mixing alleviation performance and avoid decomposition instability, and (3) ICEEMDAN has the best mode mixing alleviation performance at the optimal SFR among the four noise-assisted EMD algorithms. The applications include, for instance, tool wear monitoring in machining as well as fault diagnosis and prognosis of complex systems that rely on signal decomposition to extract the components corresponding to specific behaviors.

Fault diagnosis of rotating machines based on the EMD manifold

Abstract One challenge of the existing noise-assisted methods for solution of mode mixing problem of empirical mode decomposition (EMD) is that, the decomposed modes contain much residual noise derived from both added and self-contained noise. This paper proposes a new noise-assisted method, called EMD manifold (EMDM), for enhanced fault diagnosis of rotating machines. The major contribution is that the new method nonlinearly and adaptively fuses the fault-related modes containing different noise via a manifold learning algorithm, by which true fault-related transients are preserved, while fault-unrelated components including mode-mixing-induced components and the residual noise derived from both the added and self-contained noise are greatly suppressed. First, the sensitive mode is located among the modes obtained by the EMD method according to a newly proposed criterion. Then, a high-dimensional matrix is constructed of the sensitive modes obtained through a small number of EMD trials on the signals plus noise of different amplitudes. Finally, the manifold learning algorithm is performed on the high-dimensional matrix to extract intrinsic manifold of the fault-related transients. The high-dimensional matrix is repeatedly constructed with random noise added to adjust local data distribution of the matrix for adaptive EMDM feature learning. Experimental studies on gearbox and bearing faults are conducted to validate the proposed method and its enhanced performance over traditional noise-assisted EMD methods.

Application of SN-EMD in Mode Feature Extraction of Ship Radiated Noise

Due to the randomness of added noise, noise-assisted versions based on EMD (empirical mode decomposition) usually cause new “mode mixing” problem. In addition, these algorithms also have problems such as high time-consuming and large recovering error. For the reasons, a new method SN-EMD (Selective Noise-assisted EMD) is put forward in this paper. It determines whether to add noise as assistance by judging whether there is high frequency intermittent component contained in the signal or not. The new method was proved to have the optimal performance by comparing the performance parameters for evaluating the decomposition. In this paper, SN-EMD was used to decompose ship radiated noise. On account of the differences in the original information contained in each mode of radiated noise signals from different ship, we selected the first three modes for processing. Average instantaneous frequency, center frequency, energy density, and energy distribution ratio were extracted as mode feature of ship targets for classification and recognition. Spatial distribution of the feature quantities in three-dimensional space verified similarity of the same target and separability of different targets.

A new approach for denoising multichannel electrogastrographic signals

Abstract Electrogastrography (EGG) can be considered as a non-invasive method for the measurement of gastric myoelectrical activity. The multichannel signal is non-invasively captured by disposable electrodes placed on the surface of a stomach. The recorded signal can include not only EGG components, but also the interfering signals from other organs, for instance, the disturbances connected with respiratory movements and random noise. In order to correctly calculate the parameters of the EGG examination and improve the patient's diagnosis, the EGG signal requires effective methods for removing disturbances. The aim of this work was to investigate a new approach for denosing the multichannel electrogastrographic signals, performed by means of the Noise-Assisted Empirical Mode Decomposition (NA-MEMD) and adaptive filtering. The proposed method uses NA-MEMD for extracting the reference signal for adaptive filtering in the cosine domain. The suggested technique was validated by comparing the obtained results with the outcomes acquired by the reference method based on the classical bandpass filtering, Independent Component Analysis (ICA) and adaptive filtering. The effectiveness of the proposed algorithm was established by examining the influence of adaptive filtering on the basic diagnostic parameters, calculated from the EGG signal, such as the dominant frequency (DF), the normogastric rhythm index (NI), the frequency instability coefficient (FIC), and the power instability coefficient (PIC). In addition, the effectiveness of the noise attenuation by the proposed method was verified. The paper presents the results of research carried out for the five healthy subjects. Validation of the proposed method was performed using real human EGG signals and real EGG signals with added synthetic noise.

Uniform Phase Empirical Mode Decomposition: An Optimal Hybridization of Masking Signal and Ensemble Approaches.

The empirical mode decomposition (EMD) is an established method for the time-frequency analysis of nonlinear and nonstationary signals. However, one major drawback of the EMD is the mode mixing effect. Many modifications have been made to resolve the mode mixing effect. In particular, disturbance-assisted EMDs, such as the noise-assisted EMD and the masking EMD, have been proposed to resolve this problem. These disturbance-assisted approaches have led to a better performance of the EMD in the analysis of real-world data sets, but they may also have two side effects: the mode splitting and residual noise effects. To minimize or eliminate the mode mixing effect while avoiding the two side effects of traditional disturbance-assisted EMDs, we propose an EMD-based algorithm assisted by sinusoidal functions with a designed uniform phase distribution with a comprehensive theoretical explanation for the substantial reduction of the mode splitting and the residual noise effects simultaneously. We examine the performance of the new method and compare it to those of other disturbance-assisted EMDs using synthetic signals. Finally numerical experiments with real-world examples are conducted to verify the performance of the proposed method.

On the temporal variability of the surface solar radiation by means of spectral representations

Abstract. This work deals with the temporal variability of daily means of the global broadband surface solar irradiance (SSI) impinging on a horizontal plane by studying a decennial time-series of high-quality measurements recorded at a BSRN ground station. Since the data have a non-linear and non-stationary character, two time-frequency-energy representations of signal processing are compared in their ability to resolve the temporal variability of the pyranometric signal. First, the continuous wavelet transform is used to construct the wavelet power spectrum of the data. Second, the adaptive, noise-assisted empirical mode decomposition is employed to extract the intrinsic mode functions of the signal, followed by Hilbert spectral analysis. In both spectral representations, the temporal variability of the SSI is portrayed having clearly distinguishable features: a plateau between scales of two days and two-three months that has decreasing power with increasing scale, a large spectral peak corresponding to the annual variability cycle, and a low power regime in between the previous two. It is shown that the data-driven, noise-assisted method yields a somewhat more sparse representation and that it is a suitable tool for inspecting the temporal variability of SSI measurements.

EMD VIA MEMD: MULTIVARIATE NOISE-AIDED COMPUTATION OF STANDARD EMD

A noise-assisted approach in conjunction with multivariate empirical mode decomposition (MEMD) algorithm is proposed for the computation of empirical mode decomposition (EMD), in order to produce localized frequency estimates at the accuracy level of instantaneous frequency. Despite many advantages of EMD, such as its data driven nature, a compact decomposition, and its inherent ability to process nonstationary data, it only caters for signals with a sufficient number of local extrema. In addition, EMD is prone to mode-mixing and is designed for univariate data. We show that the noise-assisted MEMD (NA-MEMD) approach, which utilizes the dyadic filter bank property of MEMD, provides a solution to the above problems when used to calculate standard EMD. The method is also shown to alleviate the effects of noise interference in univariate noise-assisted EMD algorithms which directly add noise to the data. The efficacy of the proposed method, in terms of improved frequency localization and reduced mode-mixing, is demonstrated via simulations on electroencephalogram (EEG) data sets, over two paradigms in brain-computer interface (BCI).

Ensemble Noise-Reconstructed Empirical Mode Decomposition for Mechanical Fault Detection

Various faults inevitably occur in mechanical systems and may result in unexpected failures. Hence, fault detection is critical to reduce unscheduled downtime and costly breakdowns. Empirical mode decomposition (EMD) is an adaptive time-frequency domain signal processing method, potentially suitable for nonstationary and/or nonlinear processes. However, the EMD method suffers from several problems such as mode mixing, defined as intrinsic mode functions (IMFs) with incorrect scales. In this paper, an ensemble noise-reconstructed EMD method is proposed to ameliorate the mode mixing problem and denoise IMFs for enhancing fault signatures. The proposed method defines the IMF components as an ensemble mean of EMD trials, where each trial is obtained by sifting signals that have been reconstructed using the estimated noise present in the measured signal. Unlike traditional denoising methods, the noise inherent in the input data is reconstructed and used to reduce the background noise. Furthermore, the reconstructed noise helps to project different scales of the signal onto their corresponding IMFs, instrumental in alleviating the mode mixing problem. Two critical issues concerned in the method, i.e., the noise estimation strategy and the number of EMD trials required for denoising are discussed. Furthermore, a comprehensive noise-assisted EMD method is proposed, which includes the proposed method and ensemble EMD (EEMD). Numerical simulations and experimental case studies on accelerometer data collected from an industrial shaving process are used to demonstrate and validate the proposed method. Results show that the proposed method can both detect impending faults and isolate multiple faults. Hence, the proposed method can act as a promising tool for mechanical fault detection.

Effect of Adaptive Threshold Filtering on Ultrasonic Nakagami Parameter to Detect Variation in Scatterer Concentration

The Nakagami parameter is associated with the Nakagami distribution estimated from ultrasonic backscattered signals and closely reflects the scatterer concentrations in tissues. There is an interest in exploring the possibility of enhancing the ability of the Nakagami parameter to characterize tissues. In this paper, we explore the effect of adaptive thresholdfiltering based on the noise-assisted empirical mode decomposition of the ultrasonic backscattered signals on the Nakagami parameter as a function of scatterer concentration for improving the Nakagami parameter performance. We carried out phantom experiments using 5 MHz focused and nonfocused transducers. Before filtering, the dynamic ranges of the Nakagami parameter, estimated using focused and nonfocused transducers between the scatterer concentrations of 2 and 32 scatterers/mm3, were 0.44 and 0.1, respectively. After filtering, the dynamic ranges of the Nakagami parameter, using the focused and nonfocused transducers, were 0.71 and 0.79, respectively. The experimental results showed that the adaptive threshold filter makes the Nakagami parameter measured by a focused transducer more sensitive to the variation in the scatterer concentration. The proposed method also endows the Nakagami parameter measured by a nonfocused transducer with the ability to differentiate various scatterer concentrations. However, the Nakagami parameters estimated by focused and nonfocused transducers after adaptive threshold filtering have different physical meanings: the former represents the statistics of signals backscattered from unresolvable scatterers while the latter is associated with stronger resolvable scatterers or local inhomogeneity due to scatterer aggregation.

An adaptive threshold filter for ultrasound signal rejection

The threshold filter is a frequently used technique in ultrasound B-scan to reject the small echoes contributed from backscattering that blur the tissue interface and reduce the image contrast. Note that using the threshold based on one value would simultaneously destroy local waveform features of the reflection echoes with amplitudes larger than threshold value. To resolve this problem, we developed an adaptive threshold filter based on the noise-assisted empirical mode decomposition (EMD). Computer simulations at 7.5 MHz using a single-element transducer with a bandwidth of 60% and a pulselength of 0.5 μs were carried out to explore the feasibility of the algorithm. Image measurements on the carotid artery using a 7.5 MHz, 128 elements, 1D linear array transducer with the same characteristics as those in simulations were used to verify the performance of the algorithm in practice. Compared to the result from the conventional threshold technique, the adaptive threshold filter is able to successfully suppress the smaller backscattering signals without changing the local waveform features of the preserved significant echoes due to refection.