scholarly journals Using an Optimization Algorithm to Detect Hidden Waveforms of Signals

Sensors ◽  
2021 ◽  
Vol 21 (2) ◽  
pp. 588
Author(s):  
Yen-Ching Chang ◽  
Chin-Chen Chang
Keyword(s):  
White Noise ◽  
Optimization Algorithm ◽  
Signal Decomposition ◽  
Frequency Resolution ◽  
Intrinsic Mode Functions ◽  
Additional Information ◽  
Mode Decomposition ◽  
Main Components ◽  
Source Signals ◽  
Cosine Functions

Source signals often contain various hidden waveforms, which further provide precious information. Therefore, detecting and capturing these waveforms is very important. For signal decomposition (SD), discrete Fourier transform (DFT) and empirical mode decomposition (EMD) are two main tools. They both can easily decompose any source signal into different components. DFT is based on Cosine functions; EMD is based on a collection of intrinsic mode functions (IMFs). With the help of Cosine functions and IMFs respectively, DFT and EMD can extract additional information from sensed signals. However, due to a considerably finite frequency resolution, EMD easily causes frequency mixing. Although DFT has a larger frequency resolution than EMD, its resolution is also finite. To effectively detect and capture hidden waveforms, we use an optimization algorithm, differential evolution (DE), to decompose. The technique is called SD by DE (SDDE). In contrast, SDDE has an infinite frequency resolution, and hence it has the opportunity to exactly decompose. Our proposed SDDE approach is the first tool of directly applying an optimization algorithm to signal decomposition in which the main components of source signals can be determined. For source signals from four combinations of three periodic waves, our experimental results in the absence of noise show that the proposed SDDE approach can exactly or almost exactly determine their corresponding separate components. Even in the presence of white noise, our proposed SDDE approach is still able to determine the main components. However, DFT usually generates spurious main components; EMD cannot decompose well and is easily affected by white noise. According to the superior experimental performance, our proposed SDDE approach can be widely used in the future to explore various signals for more valuable information.

scholarly journals EMD OF GAUSSIAN WHITE NOISE: EFFECTS OF SIGNAL LENGTH AND SIFTING NUMBER ON THE STATISTICAL PROPERTIES OF INTRINSIC MODE FUNCTIONS

2009 ◽  
Vol 01 (04) ◽  
pp. 517-527 ◽  
Author(s):  
GASTÓN SCHLOTTHAUER ◽  
MARÍA EUGENIA TORRES ◽  
HUGO L. RUFINER ◽  
PATRICK FLANDRIN
Keyword(s):  
White Noise ◽  
Probability Density ◽  
Kernel Smoothing ◽  
Gaussian White Noise ◽  
Large Data ◽  
Intrinsic Mode Functions ◽  
Mode Decomposition ◽  
Non Gaussian ◽  
Data Length ◽  
Number Of Iterations

This work presents a discussion on the probability density function of Intrinsic Mode Functions (IMFs) provided by the Empirical Mode Decomposition of Gaussian white noise, based on experimental simulations. The influence on the probability density functions of the data length and of the maximum allowed number of iterations is analyzed by means of kernel smoothing density estimations. The obtained results are confirmed by statistical normality tests indicating that the IMFs have non-Gaussian distributions. Our study also indicates that large data length and high number of iterations produce multimodal distributions in all modes.

scholarly journals Analysis in the frequency domain of multicomponent oscillatory modes of the human electroencephalogram extracted with multivariate empirical mode decomposition

2020 ◽  
Author(s):  
Eduardo Arrufat-Pié ◽  
Mario Estévez-Báez ◽  
José Mario Estévez-Carreras ◽  
Calixto Machado Curbelo ◽  
Gerry Leisman ◽  
...  
Keyword(s):  
Spectral Analysis ◽  
Empirical Mode Decomposition ◽  
A Priori ◽  
Quantitative Eeg ◽  
Frequency Resolution ◽  
Intrinsic Mode Functions ◽  
Multivariate Empirical Mode Decomposition ◽  
Healthy Humans ◽  
Mode Decomposition ◽  
Mixing Problem

AbstractConsidering the properties of the empirical mode decomposition to extract from a signal its natural oscillatory components known as intrinsic mode functions (IMFs), the spectral analysis of these IMFs could provide a novel alternative for the quantitative EEG analysis without a priori establish more or less arbitrary band limits. This approach has begun to be used in the last years for studies of EEG records of patients included in database repositories or including a low number of individuals or of limited EEG leads, but a detailed study in healthy humans has not yet been reported. Therefore, in this study the aims were to explore and describe the main spectral indices of the IMFs of the EEG in healthy humans using a method based on the FFT and another on the Hilbert-Huang transform (HHT). The EEG of 34 healthy volunteers was recorded and decomposed using a recently developed multivariate empirical mode decomposition algorithm. Extracted IMFs were submitted to spectral analysis with, and the results were compared with an ANOVA test. The first six decomposed IMFs from the EEG showed frequency values in the range of the classical bands of the EEG (1.5 to 56 Hz). Both methods showed in general similar results for mean weighted frequencies and estimations of power spectral density, although the HHT is recommended because of its better frequency resolution. It was shown the presence of the mode-mixing problem producing a slight overlapping of spectral frequencies mainly between the IMF3 and IMF4 modes.

scholarly journals MONO-COMPONENTS VS IMFs IN SIGNAL DECOMPOSITION

2008 ◽  
Vol 06 (03) ◽  
pp. 353-374 ◽  
Author(s):  
TAO QIAN ◽  
LIMING ZHANG ◽  
HONG LI
Keyword(s):  
Empirical Mode Decomposition ◽  
Instantaneous Frequency ◽  
Signal Decomposition ◽  
Intrinsic Mode Functions ◽  
Mode Decomposition ◽  
Adaptive Decomposition

The concepts of intrinsic mode functions and mono-components are investigated in relation to the empirical mode decomposition. Mono-components are defined to be the functions for which non-negative analytic instantaneous frequency is well defined. We show that a great variety of functions are mono-components based on which adaptive decomposition of signals are theoretically possible. We justify the role of empirical mode decomposition in signal decomposition in relation to mono-components.

scholarly journals The Measurement and Elimination of Mode Splitting: From the Perspective of the Partly Ensemble Empirical Mode Decomposition

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Bin Liu ◽  
Peng Zheng ◽  
Qilin Dai ◽  
Zhongli Zhou
Keyword(s):  
Spectral Analysis ◽  
White Noise ◽  
Empirical Mode Decomposition ◽  
Ensemble Empirical Mode Decomposition ◽  
Permutation Entropy ◽  
Intrinsic Mode Functions ◽  
Mode Splitting ◽  
Mode Decomposition ◽  
Microseismic Signal ◽  
Mode Mixing

The problems of mode mixing, mode splitting, and pseudocomponents caused by intermittence or white noise signals during empirical mode decomposition (EMD) are difficult to resolve. The partly ensemble EMD (PEEMD) method is introduced first. The PEEMD method can eliminate mode mixing via the permutation entropy (PE) of the intrinsic mode functions (IMFs). Then, bilateral permutation entropy (BPE) of the IMFs is proposed as a means to detect and eliminate mode splitting by means of the reconstructed signals in the PEEMD. Moreover, known ingredient component signals are comparatively designed to verify that the PEEMD method can effectively detect and progressively address the problem of mode splitting to some degree and generate IMFs with better performance. The microseismic signal is applied to prove, by means of spectral analysis, that this method is effective.

scholarly journals Multi-Fault Diagnosis of Gearbox Based on Improved Multipoint Optimal Minimum Entropy Deconvolution

Entropy ◽  
2018 ◽  
Vol 20 (8) ◽  
pp. 611 ◽  
Author(s):  
Fuhe Yang ◽  
Xingquan Shen ◽  
Zhijian Wang
Keyword(s):  
White Noise ◽  
Signal To Noise Ratio ◽  
Ensemble Empirical Mode Decomposition ◽  
Original Signal ◽  
Intrinsic Mode Functions ◽  
Minimum Entropy ◽  
Feature Extraction Method ◽  
Mode Decomposition ◽  
Fault Features ◽  
Selection Of

Under complicated conditions, the extraction of a multi-fault in gearboxes is difficult to achieve. Due to improper selection of methods, leakage diagnosis or misdiagnosis will usually occur. Ensemble Empirical Mode Decomposition (EEMD) often causes energy leakage due to improper selection of white noise during signal decomposition. Considering that only a single fault cycle can be extracted when MOMED (Multipoint Optimal Minimum Entropy Deconvolution) is used, it is necessary to perform the sub-band processing of the compound fault signal. This paper presents an adaptive gearbox multi-fault-feature extraction method based on Improved MOMED (IMOMED). Firstly, EEMD decomposes the signal adaptively and selects the intrinsic mode functions with strong correlation with the original signal to perform FFT (Fast Fourier transform); considering the mode-mixing phenomenon of EEMD, reconstruct the intrinsic mode functions with the same timescale, and obtain several intrinsic mode functions of the same scale to improve the entropy of fault features. There is a lot of white noise in the original signal, and EEMD can improve the signal-to-noise ratio of the original signal. Finally, through the setting of different noise-reduction intervals to extract fault features through MOMED. The proposed method is compared with EEMD and VMD (Variational Mode Decomposition) to verify its feasibility.

scholarly journals Spectral Analysis of Electricity Demand Using Hilbert–Huang Transform

Sensors ◽  
2020 ◽  
Vol 20 (10) ◽  
pp. 2912
Author(s):  
Joaquin Luque ◽  
Davide Anguita ◽  
Francisco Pérez ◽  
Robert Denda
Keyword(s):  
Spectral Analysis ◽  
Electricity Demand ◽  
Frequency Resolution ◽  
Electrical Networks ◽  
Intrinsic Mode Functions ◽  
Hilbert Huang Transform ◽  
Mode Decomposition ◽  
Sequence Representation ◽  
Electrical Demand ◽  
Computer Resources

The large amount of sensors in modern electrical networks poses a serious challenge in the data processing side. For many years, spectral analysis has been one of the most used approaches to extract physically meaningful information from a sea of data. Fourier Transform (FT) and Wavelet Transform (WT) are by far the most employed tools in this analysis. In this paper we explore the alternative use of Hilbert–Huang Transform (HHT) for electricity demand spectral representation. A sequence of hourly consumptions, spanning 40 months of electrical demand in Spain, has been used as dataset. First, by Empirical Mode Decomposition (EMD), the sequence has been time-represented as an ensemble of 13 Intrinsic Mode Functions (IMFs). Later on, by applying Hilbert Transform (HT) to every IMF, an HHT spectrum has been obtained. Results show smoother spectra with more defined shapes and an excellent frequency resolution. EMD also fosters a deeper analysis of abnormal electricity demand at different timescales. Additionally, EMD permits information compression, which becomes very significant for lossless sequence representation. A 35% reduction has been obtained for the electricity demand sequence. On the negative side, HHT demands more computer resources than conventional spectral analysis techniques.

scholarly journals Optimized ELM based on Whale Optimization Algorithm for gearbox diagnosis

2019 ◽  
Vol 255 ◽  
pp. 02003
Author(s):  
M. Firdaus Isham ◽  
M. Salman Leong ◽  
M. H. Lim ◽  
Z. A.B. Ahmad
Keyword(s):  
Optimization Algorithm ◽  
Learning Algorithm ◽  
Whale Optimization Algorithm ◽  
Intrinsic Mode Functions ◽  
Mode Decomposition ◽  
Whale Optimization ◽  
Gearbox Vibration ◽  
Learning Machine ◽  
Hidden Layer ◽  
New Diagnosis

Extreme learning machine (ELM) is a fast and quick learning algorithm with better generalization performance. However, the randomness of input weight and hidden layer bias may affect the overall performance of ELM. This paper proposed a new approach to determine the optimized values of input weight and hidden layer bias for ELM using whale optimization algorithm (WOA), which we call WOA-ELM. An online gearbox vibration signals is used in this study. Empirical mode decomposition (EMD) and complementary mode decomposition (CEEMD) are used to decompose the signals into sub-signals known as intrinsic mode functions (IMFs). Then, statistical features are extracted from selected IMFs. WOA-ELM is used for classification of healthy and faulty condition of gearbox. The result shows that WOA-ELM provide better classification result as compared with conventional ELM. Therefore, this study provide a new diagnosis approach for gearbox application.

A Method of False Component Discriminant of EMD Based on Kolmogorov-Smirnov Test

2013 ◽  
Vol 427-429 ◽  
pp. 2005-2008
Author(s):  
Wang Can Yang ◽  
Pei Lin Zhang ◽  
Ding Hai Wu ◽  
Zhou Xin
Keyword(s):  
Vibration Signal ◽  
Threshold Value ◽  
Signal Decomposition ◽  
Original Signal ◽  
Intrinsic Mode Functions ◽  
The Real ◽  
Similarity Threshold ◽  
Mode Decomposition ◽  
Kolmogorov Smirnov ◽  
Smirnov Test

In order to solve the problem that empirical mode decomposition (EMD) will cause false components in the process of signal decomposition, a method of false component discriminant of EMD based on Kolmogorov-Smirnov test was put forward. First, the original signal was decomposed into several intrinsic mode functions (IMFs) by EMD. Then the K-S test was used to calculate the similarity between each IMF and the original signal. The reasonable similarity threshold was selected for judging the authenticity of the IMFs. The IMFs of which the similarity values were less than the threshold value were determined to be the false components. The others of which the similarity values were greater than the threshold value were determined to be the real components. As a result, the false components were removed and the real components were remained. The vibration signal of bearing experiment indicated that the method of K-S test could discriminate the real components and the false components obviously. Then the false components were removed quickly and accurately and the real components of the original signal were obtained.

Transform Operator Pair Assisted Hilbert–Huang Transform for Signals With Instantaneous Frequency Intersections

2015 ◽  
Vol 137 (6) ◽  
Author(s):  
Yuxin Sun ◽  
Chungang Zhuang ◽  
Zhenhua Xiong
Keyword(s):  
A Priori ◽  
Low Frequency ◽  
Ensemble Empirical Mode Decomposition ◽  
Frequency Resolution ◽  
Intrinsic Mode Functions ◽  
Hilbert Huang Transform ◽  
Time Frequency ◽  
Mode Decomposition ◽  
Start Up ◽  
Instantaneous Frequencies

Due to low frequency resolution for closely spaced spectral components, i.e., the instantaneous frequencies (IFs) lie within an octave or even have intersections, the Hilbert–Huang transform (HHT) fails to separate such signals and consequently generates inaccurate time–frequency distribution (TFD). In this paper, a transform operator pair assisted HHT is proposed to improve the capability of the HHT to separate signals, especially those with IF intersections. The two operators of a pair are constructed to remove the chosen component that is clearly observed in the TFD of the signal, and then recover it from intrinsic mode functions (IMFs). With this approach, the components can be clearly separated and the intersections can also be identified in the TFD. Since a priori knowledge of the transform operator is usually not available in real applications, an iterative algorithm is presented to obtain a global transform operator. The effectiveness of the proposed algorithm is demonstrated by analysis of numerical signals and a real signal collected from a cracked rotor–bearing system during the start-up process. Moreover, the proposed approach is shown to be superior to the normalized Hilbert transform (NHT) as well as the ensemble empirical mode decomposition (EEMD).

scholarly journals Location Detection Method of Detector in Pipeline Using VMD Algorithm and Machine Learning Classifier

Electronics ◽  
2021 ◽  
Vol 10 (12) ◽  
pp. 1436
Author(s):  
Tuoru Li ◽  
Senxiang Lu ◽  
Enjie Xu
Keyword(s):  
Machine Learning ◽  
Magnetic Flux ◽  
Magnetic Flux Leakage ◽  
Intrinsic Mode Functions ◽  
Detection Range ◽  
Vibration Signals ◽  
Feature Vectors ◽  
Learning Classifier ◽  
Mode Decomposition ◽  
Flux Leakage

The internal detector in a pipeline needs to use the ground marker to record the elapsed time for accurate positioning. Most existing ground markers use the magnetic flux leakage testing principle to detect whether the internal detector passes. However, this paper uses the method of detecting vibration signals to track and locate the internal detector. The Variational Mode Decomposition (VMD) algorithm is used to extract features, which solves the defect of large noise and many disturbances of vibration signals. In this way, the detection range is expanded, and some non-magnetic flux leakage internal detectors can also be located. Firstly, the extracted vibration signals are denoised by the VMD algorithm, then kurtosis value and power value are extracted from the intrinsic mode functions (IMFs) to form feature vectors, and finally the feature vectors are input into random forest and Multilayer Perceptron (MLP) for classification. Experimental research shows that the method designed in this paper, which combines VMD with a machine learning classifier, can effectively use vibration signals to locate the internal detector and has the characteristics of high accuracy and good adaptability.

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