CN110188448A - A kind of improved Empirical Mode Decomposition Algorithm - Google Patents

A kind of improved Empirical Mode Decomposition Algorithm Download PDF

Info

Publication number
CN110188448A
CN110188448A CN201910444137.9A CN201910444137A CN110188448A CN 110188448 A CN110188448 A CN 110188448A CN 201910444137 A CN201910444137 A CN 201910444137A CN 110188448 A CN110188448 A CN 110188448A
Authority
CN
China
Prior art keywords
signal
emd
end effect
hemd
mpc
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Withdrawn
Application number
CN201910444137.9A
Other languages
Chinese (zh)
Inventor
张学军
霍延
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Nanjing Post and Telecommunication University
Original Assignee
Nanjing Post and Telecommunication University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Nanjing Post and Telecommunication University filed Critical Nanjing Post and Telecommunication University
Priority to CN201910444137.9A priority Critical patent/CN110188448A/en
Publication of CN110188448A publication Critical patent/CN110188448A/en
Withdrawn legal-status Critical Current

Links

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation

Landscapes

  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Theoretical Computer Science (AREA)
  • Computer Hardware Design (AREA)
  • Evolutionary Computation (AREA)
  • Geometry (AREA)
  • General Engineering & Computer Science (AREA)
  • General Physics & Mathematics (AREA)
  • Complex Calculations (AREA)
  • Compression, Expansion, Code Conversion, And Decoders (AREA)

Abstract

The invention discloses a kind of improved Empirical Mode Decomposition Algorithms, new signal is obtained to signal progress end effect first and solves the problems, such as end effect, then upper lower envelope is solved using subsection curve fitting algorithm to obtained signal and solves the problems, such as overshoot and owe punching, EMD is consistent finally obtains IMFs for step and tradition later.The present invention has done following improvement on the basis of traditional EMD: first carrying out end effect to pretreated signal and then replaces original cubic spline interpolation algorithm using subsection curve fitting method and obtain improved EMD (MPC-HEMD).Present invention improves end effect problem in decomposable process and overshoot owe punching problems.The IMFs analysis and assessment that MPC-HEMD and original EMD are handled, it was confirmed that the validity of this method.

Description

A kind of improved Empirical Mode Decomposition Algorithm
Technical field
The present invention relates to a kind of improvement Empirical Mode Decomposition Algorithms, belong to Intelligent Information Processing field.
Background technique
Common signal processing method has: in wave character description, autoregression AR model, energy spectrum, power spectrum, quick Fu Leaf transformation (Fast Fourier Transform, FFT), wavelet transformation etc..Wherein, fast Fourier decomposition algorithm is simply easy Row, but single frequency time feature can only be extracted, it is difficult to ensure that the matching rate of classification；It is needed during wavelet transform process Base is selected, does not have adaptivity.
In order to make up the defect of conventional decomposition signal, E Huang proposed a kind of new non-thread for handling in 1998 The method of the unstable signal of property, introduces the concept of modular function (Intrinsic Mode Function, IMF), proposes EMD The algorithm for being limited IMF by signal decomposition.The calculating of envelope signal influences the process of entire EMD in EMD, utilizes cubic spline Interpolation method, which seeks envelope in many cases, can obtain preferable as a result, still crossing envelope, owing envelope and fly at endpoint The wing is still inevitable, and be will cause the mean value of transfer signal and is inserted into the influences such as false frequency, so needing to carry out EMD Further research.
Summary of the invention
Goal of the invention: dividing the deficiency of decomposition algorithm for Conventional wisdom mode, proposes a kind of improved EMD (MPC- HEMD signal method) is handled.This method is based on following content: 1, the signal processing based on improved empirical mode decomposition；2 mirrors As continuation solves the problems, such as end effect；3 subsection curve fitting algorithms replace cubic spline interpolation algorithm improve overshoot with And owe punching problem.End effect (mirror extension) first is carried out to emulation signal in the present invention and then utilizes segmentation three Secondary Hermite interpolation method (Piecewise cubic Hermite interpolation) replaces original cubic spline interpolation Algorithm simultaneously obtains improved EMD (MPC-HEMD), and preferable effect may be implemented, obtain envelope after two interpolation algorithm processing Signal simultaneously compares and analyzes, and MPC-HEMD and original EMD handle to obtain IMFs, carries out spectrum analysis to it and utilization is square Root error, signal-to-noise ratio, related coefficient carry out Performance Evaluation, it was confirmed that the validity of this method.
Technical solution: to achieve the above object, the technical solution adopted by the present invention are as follows:
A kind of improved Empirical Mode Decomposition Algorithm, of the invention obtains new signal to signal progress end effect first It solves the problems, such as end effect, upper lower envelope then is solved using subsection curve fitting algorithm to obtained signal Solve the problems, such as overshoot and owe punching, EMD is consistent finally obtains IMFs for step and tradition later.The present invention is traditional EMD's On the basis of done following improvement: first to pretreated signal carry out end effect (mirror extension) then using point Section cubic Hamiltonian symmetrical systems method (Piecewise cubic Hermite interpolation) replaces original cubic spline Interpolation algorithm simultaneously obtains improved EMD (MPC-HEMD).Specifically includes the following steps:
A kind of improved Empirical Mode Decomposition Algorithm, comprising the following steps:
Step 1: the sinusoidal signal for choosing more than two different center frequencies is combined into emulation signal x (t)；
Step 2: MPC-HEMD decomposition is carried out to signal x (t)；The envelope diagram that decomposes for the first time is obtained to compare and one Serial intrinsic mode function IMFiAnd all intrinsic mode function energy spectrum diagrams are drawn, i is the order of intrinsic mode function；
Carrying out MPC-HEMD decomposition to emulation signal x (t), specific step is as follows:
(1) local extremum for judging each x (t) is held by the method for end effect (mirror extension) Point continuation, obtains new signal.
(2) subsection curve fitting method (Piecewise cubic Hermite interpolation) generation is utilized It carries out curve fitting for cubic spline interpolation, local maximum forms coenvelope hmax(t), local minimum forms lower envelope hmin(t)。
(3) mean value of lower envelope is sought are as follows:
(4) difference of input signal and mean value is calculated:
C (t)=x (t)-s (t)
Whether verifying c (t) meets the definition condition of IMF, if c (t) meets the condition of IMF, for an IMF, original letter Number transformation are as follows:
R (t)=x (t)-c (t)
Otherwise, by c (t) as new signal x (t) repetitive process (1)-(4).
(5) signal x (t) r (t) new as one obtains next intrinsic mode function by the above identical process. When r (t) is a monotonic function or one and only one extreme point, decomposable process terminates.Original signal x (t) is divided Solution is n intrinsic mode function and a residual components r (t), therefore available:
X (t) indicates emulation signal, ci(t) difference is indicated, r (t) indicates residual components.
The present invention compared with prior art, has the advantages that
1, improvement is made for Empirical Mode Decomposition Algorithm: end effect (mirror first being carried out to the signal after emulation Extension) obtaining new signal improves end effect problem.
2, the present invention replaces cubic spline interpolation algorithm to obtain new signal progress subsection curve fitting algorithm The envelope diagram up and down of signal, and the envelope handled with original cubic spline interpolation compares and analyzes advantage.
3, the present invention by MPC-HEMD decompose with original EMD decompose after multistage intrinsic mode function carry out spectrum analysis with And Performance Evaluation is carried out using root-mean-square error, signal-to-noise ratio, related coefficient.
Detailed description of the invention
Fig. 1 the method for the present invention flow chart-MPC-HEMD algorithm flow chart
Specific embodiment
In the following with reference to the drawings and specific embodiments, the present invention is furture elucidated, it should be understood that these examples are merely to illustrate this It invents rather than limits the scope of the invention, after the present invention has been read, those skilled in the art are to of the invention various The modification of equivalent form falls within the application range as defined in the appended claims.
A kind of improved Empirical Mode Decomposition Algorithm, as shown in Figure 1, comprising the following steps:
Step 1: choosing the sinusoidal signal that three centre frequencies are respectively 5Hz, 30Hz and 50Hz and be combined into emulation signal x (t)。
Method in step 1 is packaged, emulation signal synthesizing module is obtained and is obtained for the method in operating procedure 1 To the emulation signal x (t) being combined into.
Step 2: MPC-HEMD decomposition is carried out to emulation signal x (t)；Obtain the envelope diagram that decomposes for the first time compare with A series of and intrinsic mode function IMFi(order that i is intrinsic mode function) simultaneously draws all intrinsic mode function energy spectrum diagrams；
EEG signal emulation carries out (MPC-HEMD), and specific step is as follows for decomposition:
Step 21, the local extremum for judging each x (t), by the method for end effect (mirror extension) into Row end extending obtains new signal.The maximum point and minimum point for judging each x (t), pass through end effect (mirror Extension method) carries out end extending, obtains new signal.
Method in step 21 is packaged, end extending module is obtained, for the method in operating procedure 21, is obtained New signal.
Step 22, subsection curve fitting method (Piecewise cubic Hermite is utilized Interpolation) cubic spline interpolation is replaced to carry out curve fitting new signal, local maximum forms coenvelope Hmax (t), local minimum form lower envelope hmin (t).
Method in step 22 is packaged, subsection curve fitting method module is obtained, is used for operating procedure 22 In method, obtain coenvelope hmax (t) and lower envelope hmin (t).
The upper lower envelope comparative analysis formed with cubic spline interpolation processing, it can be seen that subsection curve fitting The envelope signal performance that method obtains is better than the envelope signal that cubic spline interpolation algorithm obtains.
Step 23, the mean value of lower envelope is sought are as follows:
Method in step 23 is packaged, lower envelope mean module is obtained, for the method in operating procedure 23, Obtain the mean value of lower envelope.
Step 24, the difference of input signal and mean value is calculated:
C (t)=x (t)-s (t)
Method in step 24 is packaged, the difference block of input signal and mean value is obtained, is used for operating procedure 24 In method, obtain the difference of input signal and mean value.
Step 25, whether verifying c (t) meets the definition condition of IMF, if c (t) meets two conditions of IMF: first is that whole In a signal time domain, the maximum number of signal amplitude is equal with the number of zero crossing, or at most difference one, second is that signal The average value for the envelope that the envelope and amplitude minimum that amplitude maximum is formed are formed is zero.It is then an IMF, original signal turns Become:
R (t)=x (t)-c (t)
Otherwise, by c (t) as new signal x (t) repetitive process (1)-(4).
Method in step 25 is packaged, module is verified, for the method in operating procedure 25, obtains residue Component r (t) and intrinsic mode function.
Step 26, signal x (t) r (t) new as one obtains next natural mode of vibration letter by the above identical process Number.When r (t) is a monotonic function or one and only one extreme point, decomposable process terminates.Original signal x (t) quilt It is decomposed into n intrinsic mode function and a residual components r (t), therefore available:
Method in step 26 is packaged, residual components decomposing module is obtained, for the method in operating procedure 26, It obtains original signal x (t) and is broken down into n intrinsic mode function and a residual components r (t).
A kind of improved empirical mode decomposition system, including emulation signal synthesizing module, end extending module, segmentation are three times Hermite interpolation method module, upper lower envelope mean module, input signal and mean value difference block, authentication module and residue Component decomposing module.
Performance Evaluation following steps:
Step 1: choosing the sinusoidal signal that three centre frequencies are respectively 5Hz, 30Hz and 50Hz and be combined as emulation letter Number x (t).
Step 2: emulation signal x (t) being handled by two methods of EMD and MPC-HEMD, is respectively obtained a series of IMFs, and obtained IMFs is reconstructed.
Step 3: two methods reconstruction signal and original emulation signal contrast respectively obtain related coefficient, root-mean-square error with And the superiority it can be concluded that this method is compared in signal-to-noise ratio, analysis.
Root-mean-square error, signal-to-noise ratio and formula of correlation coefficient difference are as follows:
SNR=20log10(SNRv)
Wherein, xnIt (t) is original signal, ynIt (t) is the signal after reconstruct, anIt (t) is the noise signal of removal, N is signal Sequence length.
For crossing envelope existing for empirical mode decomposition, owing envelope and end effect problem, the invention proposes one kind to change Into EMD method-MPC-HEMD, in order to solve to cross envelope and deficient Inclusion in EMD method, with segmentation hermite three times Interpolation algorithm replaces cubic spline interpolation algorithm；And end effect algorithm is added in decomposable process and reduces end effect.Fortune Envelope signal is obtained with this method and original EMD method processing compounded sine signal, comparative analysis this method has obtained preferably Envelope signal；And a series of intrinsic mode functions (Intrinsic Mode Functions, IMFs) is respectively obtained, it will weigh Signal after structure related coefficient, signal-to-noise ratio and root-mean-square error compared with original emulation signal is by analysis show that MPC-HEMD has There is preferable performance.
The above is only a preferred embodiment of the present invention, it should be pointed out that: for the ordinary skill people of the art For member, various improvements and modifications may be made without departing from the principle of the present invention, these improvements and modifications are also answered It is considered as protection scope of the present invention.

Claims (3)

1. a kind of improved Empirical Mode Decomposition Algorithm, which comprises the following steps:
Step 1: the sinusoidal signal for choosing more than two different center frequencies is combined into emulation signal x (t)；
Step 2: MPC-HEMD decomposition is carried out to signal x (t)；The envelope diagram that decomposes for the first time is obtained to compare and a series of Intrinsic mode function IMFiAnd all intrinsic mode function energy spectrum diagrams are drawn, i is the order of intrinsic mode function；
Carrying out MPC-HEMD decomposition to emulation signal x (t), specific step is as follows:
Step 21: judging the local extremum of each emulation signal x (t), end extending is carried out by the method for end effect, is obtained New signal；
Step 22: the new signal for replacing cubic spline interpolation to obtain step 21 using subsection curve fitting method It carries out curve fitting, local maximum forms coenvelope hmax(t), local minimum forms lower envelope hmin(t)；
Step 23: seeking the mean value s (t) of lower envelope are as follows:
Step 24: calculate the difference c (t) of input signal and mean value:
C (t)=x (t)-s (t)
Step 25: whether verifying difference c (t) meets the definition condition of IMF, if c (t) meets the condition of IMF, for an IMF, Emulate signal x (t) transformation are as follows:
R (t)=x (t)-c (t)
C (t) indicates residual components；
Otherwise, c (t) is repeated into step 21- step 25 as new signal x (t)；
Step 25: by residual components r (t) the emulation signal x (t) new as one, repetition step 21- step 25 obtains next Intrinsic mode function；When residual components r (t) is a monotonic function or one and only one extreme point, decomposable process Terminate；Original emulation signal x (t) is broken down into n intrinsic mode function and a residual components r (t), therefore can obtain It arrives:
X (t) indicates emulation signal, ci(t) difference is indicated, r (t) indicates residual components.
2. improved Empirical Mode Decomposition Algorithm according to claim 1, it is characterised in that: the number of different centre frequencies It is three.
3. improved Empirical Mode Decomposition Algorithm according to claim 2, it is characterised in that: three centre frequencies are respectively 5Hz, 30Hz and 50Hz.
CN201910444137.9A 2019-05-27 2019-05-27 A kind of improved Empirical Mode Decomposition Algorithm Withdrawn CN110188448A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201910444137.9A CN110188448A (en) 2019-05-27 2019-05-27 A kind of improved Empirical Mode Decomposition Algorithm

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201910444137.9A CN110188448A (en) 2019-05-27 2019-05-27 A kind of improved Empirical Mode Decomposition Algorithm

Publications (1)

Publication Number Publication Date
CN110188448A true CN110188448A (en) 2019-08-30

Family

ID=67717824

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201910444137.9A Withdrawn CN110188448A (en) 2019-05-27 2019-05-27 A kind of improved Empirical Mode Decomposition Algorithm

Country Status (1)

Country Link
CN (1) CN110188448A (en)

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112949237A (en) * 2021-02-25 2021-06-11 中国人民解放军海军航空大学 Mean value curve construction method based on local feature scale decomposition improved algorithm
CN114722334A (en) * 2022-04-11 2022-07-08 哈尔滨工程大学 STFT-based online identification method for gas injection time characteristics of high-pressure natural gas direct injection engine
CN115060496A (en) * 2022-06-08 2022-09-16 株洲中车时代电气股份有限公司 Fault diagnosis method for rolling bearing of walking part

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112949237A (en) * 2021-02-25 2021-06-11 中国人民解放军海军航空大学 Mean value curve construction method based on local feature scale decomposition improved algorithm
CN114722334A (en) * 2022-04-11 2022-07-08 哈尔滨工程大学 STFT-based online identification method for gas injection time characteristics of high-pressure natural gas direct injection engine
CN115060496A (en) * 2022-06-08 2022-09-16 株洲中车时代电气股份有限公司 Fault diagnosis method for rolling bearing of walking part
CN115060496B (en) * 2022-06-08 2024-01-19 株洲中车时代电气股份有限公司 Rolling bearing fault diagnosis method for running part

Similar Documents

Publication Publication Date Title
CN110188448A (en) A kind of improved Empirical Mode Decomposition Algorithm
CN107462785B (en) The more disturbing signal classifying identification methods of power quality based on GA-SVM
Gomez-Morante et al. A wavelet-based differential transformer protection
CN113094993B (en) Modulation signal denoising method based on self-coding neural network
CN107316653B (en) Improved empirical wavelet transform-based fundamental frequency detection method
Wang et al. Fractal complexity-based feature extraction algorithm of communication signals
CN110175560A (en) A kind of radar signal intra-pulse modulation recognition methods
CN104459398B (en) A kind of quality of power supply of use Two-dimensional morphology noise reduction is combined disturbance identification method
CN105760347A (en) HHT end effect restraining method based on data/extreme value joint symmetric prolongation
Yang et al. Ship recognition via its radiated sound: The fractal based approaches
CN109241849B (en) Feature decomposition selection and fault diagnosis method for main engine of intelligent power plant steam turbine
CN104635223A (en) Laser echo denoising method based on empirical mode decomposition and fractional Fourier transformation
Qin et al. Radar waveform recognition based on deep residual network
CN111680737A (en) Radar radiation source individual identification method under differential signal-to-noise ratio condition
CN108334872A (en) Based on the feature extracting method for improving HHT transformation
CN113239880A (en) Radar radiation source identification method based on improved random forest
CN113378652A (en) Disturbance classification method based on EWT-MPE-PSO-BP
CN107239739A (en) A kind of scale parameter controls adjustable signal envelope extracting method
CN117633656A (en) Radar signal identification method based on time-frequency analysis and improved convolutional neural network
Limin et al. Low probability of intercept radar signal recognition based on the improved AlexNet model
CN108169560A (en) A kind of segmentation Sine-Fitting decomposition method
CN109558857B (en) Chaotic signal noise reduction method
Huang et al. Modulation identification method based on time-frequency analysis and support vector machine
CN116842450A (en) Depth measurement learning-based radar radiation source individual identification method
CN116304559A (en) Microseismic signal noise reduction method and system based on convolution self-coding network

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
WW01 Invention patent application withdrawn after publication
WW01 Invention patent application withdrawn after publication

Application publication date: 20190830