CN116295740A - Signal denoising reconstruction method based on adaptive variational modal decomposition - Google Patents

Signal denoising reconstruction method based on adaptive variational modal decomposition Download PDF

Info

Publication number
CN116295740A
CN116295740A CN202211609768.XA CN202211609768A CN116295740A CN 116295740 A CN116295740 A CN 116295740A CN 202211609768 A CN202211609768 A CN 202211609768A CN 116295740 A CN116295740 A CN 116295740A
Authority
CN
China
Prior art keywords
signal
modal
decomposition
components
frequency
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.)
Pending
Application number
CN202211609768.XA
Other languages
Chinese (zh)
Inventor
于宁
杨旭源
冯仁剑
吴银锋
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.)
Beihang University
Original Assignee
Beihang 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 Beihang University filed Critical Beihang University
Priority to CN202211609768.XA priority Critical patent/CN116295740A/en
Publication of CN116295740A publication Critical patent/CN116295740A/en
Pending legal-status Critical Current

Links

Images

Classifications

    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01G—WEIGHING
    • G01G3/00—Weighing apparatus characterised by the use of elastically-deformable members, e.g. spring balances
    • G01G3/12—Weighing apparatus characterised by the use of elastically-deformable members, e.g. spring balances wherein the weighing element is in the form of a solid body stressed by pressure or tension during weighing
    • G01G3/14—Weighing apparatus characterised by the use of elastically-deformable members, e.g. spring balances wherein the weighing element is in the form of a solid body stressed by pressure or tension during weighing measuring variations of electrical resistance
    • G01G3/1414—Arrangements for correcting or for compensating for unwanted effects
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01G—WEIGHING
    • G01G23/00—Auxiliary devices for weighing apparatus
    • G01G23/01—Testing or calibrating of weighing apparatus
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation

Landscapes

  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Measurement Of Mechanical Vibrations Or Ultrasonic Waves (AREA)

Abstract

The invention belongs to a dynamic signal denoising technology, and relates to a modal decomposition and reconstruction method of a dynamic measurement signal. The signal denoising method based on the adaptive variation modal decomposition comprises the steps of predetermining the number of signal decomposition layers, checking the correlation of modal components, determining a secondary penalty factor, performing variation modal decomposition and reconstructing the signal check. The measuring method utilizes the signal frequency band self-adaptive separation characteristic of variation modal decomposition to self-adaptively decompose an original measuring signal into a plurality of different inherent modal function components, performs detection of separation results through parameters such as sample entropy and the like, and reconstructs the extracted effective components into new observation signals so as to realize separation of environmental noise. The core thought of the measuring method is to separate and extract actual effective signals from original signals mixed with noise in different frequency bands, especially noise close to the environment vibration noise in the frequency band of the source signal, so that the signal processing purpose of reducing interference of the environment vibration noise close to the frequency band is achieved.

Description

Signal denoising reconstruction method based on adaptive variational modal decomposition
Technical Field
The invention belongs to a dynamic signal denoising technology, and relates to a modal decomposition and reconstruction method of a dynamic measurement signal.
Background
Under the promotion of the development of various subjects such as material technology, electronic technology and computer technology, the weighing technology has been developed from simple and rough mechanical weighing equipment to high-precision and automatic electronic weighing machines nowadays. In high-end manufacturing, the weighing research requirements are also upgraded from the initial static, intermittent weighing to the dynamic, continuous weighing requirements. For a strain weighing signal, the numerical accuracy of the weighing signal is critical to the manufacture of part of high-precision parts, and the strain resistance sensor is widely applied in the industrial production field.
The natural vibration characteristics of the measured member tend to affect the strain measurement results. In a strain weighing field, a strain resistance sensor often needs to work under severe environments such as vibration conditions, and the direct output measurement result is always influenced by environmental noise sources and is difficult to eliminate. Therefore, the subsequent denoising processing for the field signal data is of great importance.
In the field of dynamic strain measurement data processing, a traditional filtering noise reduction method cannot obtain an ideal noise reduction effect aiming at noise signals with close frequency bands from an environmental vibration source, and a signal extraction noise reduction technology with more excellent time-frequency performance and multi-resolution needs to be researched. The variational modal decomposition algorithm effectively solves the problems of modal aliasing and end-point effect, and has stronger robustness.
Aiming at the problem that the strain signal measured on the weighing site is influenced by the environmental noise with the frequency band close, the method for adaptively determining the variable-decomposition mode decomposition denoising reconstruction of the parameters is provided, and the high-precision utilization of the subsequent effective signal measured value is ensured.
Disclosure of Invention
The purpose of the invention is that: a signal denoising reconstruction method based on adaptive variation modal decomposition is provided.
The technical scheme of the invention is as follows: a dynamic signal denoising technique comprising the steps of:
step 1: predetermined number of decomposition layers K
The empirical mode decomposition method is capable of adaptively decomposing a signal into a plurality of modal components and a residual component by recursively. And taking the number of the modal components with the signal time domain energy ratio larger than a certain threshold value as the initial decomposition layer number input of the variation modal decomposition. When the obtained decomposition layer number K value is used for a variation modal decomposition algorithm, the incomplete modal decomposition phenomenon can be prevented theoretically. The calculation formula of the signal time domain energy ratio is as follows:
Figure BDA0003992759320000011
wherein x (T) is an original signal, T is total time, IMF is each modal component, and k is a modal component sequence number.
Step 2: correlation verification of modal components
The correlation coefficient calculated with the modal component as a sample is:
Figure BDA0003992759320000012
wherein n is the total data point number, S IMF Is the standard deviation of the modal component S x Standard deviation of the original signal. The pearson correlation coefficient (Pearson Correlation Coefficient, PCC) is used to determine the inter-variable correlation. Modes with PCC values greater than 0.1 are considered valid modes, and modes with PCC values less than 0.1 are considered ambient noise signals or residuals. The number of decomposition layers K is selected so that the decomposition is exactly complete, and the criterion of the exactly complete decomposition is: when K takes a certain value, the PCC of the highest strain mode is just smaller than 0.1, and when k=k+1, the PCC values of both the highest and second highest strain modes are smaller than 0.1.
Step 3: determining a secondary penalty factor
The number of the sampling data points is N, the time sequence formed by the sampling data points is X= [ X (N), n=1, 2, … N ], and the calculation formula of the sample entropy of the modal component is as follows:
Figure BDA0003992759320000021
wherein: m is the embedding dimension, typically taken as 1 or 2; r is a similar tolerance, and is selected to be (0.1-0.2) delta IMF ,δ IMF Is the standard deviation of the modal components; n (N)The number of the data points is generally 100-15000; b (B) m (r) is the probability that two signal sequences match an m-point with similar tolerance; b (B) m+1 (r) is the probability that two signal sequences match m+1 points.
The larger entropy means that the more frequency components are in the decomposed signal, and the smaller entropy means that the fewer frequency components are in the decomposed signal, i.e. the frequency band components are single, and the aliasing phenomenon is not serious. The value range of the secondary penalty factor is preset to be 100-2500, and an alpha value which enables the entropy value of the low-frequency modal component sample to be smaller is selected as the secondary penalty factor of the variation modal decomposition algorithm by taking the step length of 100 as a unit.
Step 4: variational modal decomposition
The original signal can be decomposed into K modal components at a preset scale using a variational modal decomposition (Variation Mode Decomposition, VMD). The expression of the modal function is:
u k (t)＝A k (t)cos[φ k (t)]
wherein: a is that k (t) is the instantaneous amplitude of the amplitude-frequency signal, φ k (t) is the phase. The constraint variation model of the VMD for continuous iterative update solution during calculation operation is expressed as:
Figure BDA0003992759320000022
Figure BDA0003992759320000023
wherein,,
Figure BDA0003992759320000024
representing a deviation derivative; omega k Is the modal center frequency; delta (t) is the dirac distribution; * Representing a convolution operation; k=1, 2, …, K; f (t) is the original signal.
The VMD algorithm converts the Lagrangian multiplier and the quadratic penalty term into an unconstrained variable state by adding the Lagrangian multiplier and the quadratic penalty term to solve the corresponding decomposition optimization problem, and the expression is as follows:
Figure BDA0003992759320000025
Figure BDA0003992759320000026
Figure BDA0003992759320000027
Figure BDA0003992759320000031
wherein u is k 、ω k Lambda refers to the modal component, center frequency and Lagrangian multiplier, respectively;
Figure BDA0003992759320000032
λ n+1 the result is obtained after each update.
The above equation is solved in the frequency domain of the strain signal using Parseval/Planchrel Fourier equidistant under the norm:
Figure BDA0003992759320000033
the constraint conditions of the iteration are:
Figure BDA0003992759320000034
wherein,,
Figure BDA0003992759320000035
representing strain modal component->
Figure BDA0003992759320000036
Corresponding Fourier transform, representing the current strainThe center of gravity of the modal power spectrum; />
Figure BDA0003992759320000037
Fourier transforming the original signal; />
Figure BDA0003992759320000038
Is the fourier transform of the lagrangian multiplier. Repeating the calculation, and ending the loop when the iteration stop requirement is met.
Step 5: signal verification reconstruction
The mode obtained by decomposition contains noise with low frequency band and close frequency band and high-frequency invalid residual components, so that reconstruction after denoising of signals mixed with low-frequency band environmental noise is realized.
The invention has the advantages that from the perspective of signal separation, the Variational Modal Decomposition (VMD) method is applied to the field of denoising reconstruction of dynamic signals, so that the effective modal separation of measurement signals is realized, the denoising result can more completely retain the characteristics of theoretical strain signals, the improvement of the follow-up processing precision is facilitated, and the feasibility and the superiority of the data processing method are proved.
Drawings
FIG. 1 is a flow chart of a signal denoising reconstruction method of adaptive variation modal decomposition according to the present invention;
FIG. 2 is a diagram of the strain measurement raw signal according to an embodiment of the present invention;
FIG. 3 is an empirical mode pre-decomposition strain signal according to an embodiment of the present invention;
fig. 4 shows the decomposition effect of the variation mode when k=4 according to the embodiment of the present invention;
fig. 5 shows the decomposition effect of the variation mode when k=3 according to the embodiment of the present invention;
FIG. 6 is a graph showing sample entropy as a function of penalty factor according to an embodiment of the present invention;
FIG. 7 is a schematic diagram of denoising reconstruction effect of a weighing field strain signal according to an embodiment of the present invention;
Detailed Description
The invention is further illustrated by the following examples in conjunction with the accompanying drawings:
as shown in FIG. 1, the method for decomposing and reconstructing the mode of the whole measurement signal mainly comprises five steps, including the steps of predetermining the number of layers of signal decomposition, checking the correlation of mode components, determining a secondary penalty factor, decomposing the variation mode and reconstructing the signal check. Fig. 2 is data of strain measurement signals from a weighing site, the sampling frequency being 4kHz, and for practical measurement situations the measurement source signal should be a periodic signal with a spectrum centered at a low frequency band and an amplitude close to zero.
It can be observed that the strain signal contains obvious high-frequency noise characteristics, and the high-frequency noise like Gaussian noise can be eliminated by means of traditional smoothing, median processing, low-pass filtering and the like, but the mixed high-energy low-frequency noise in the actual signal is difficult to play a role in the traditional denoising method.
Step 1: predetermining the number of decomposition layers
The empirical mode decomposition method is capable of adaptively decomposing a signal into a plurality of modal components and a residual component by recursively. And taking the number of the modal components with the signal time domain energy ratio larger than a certain threshold value as the initial decomposition layer number input of the variation modal decomposition. The calculation formula of the signal time domain energy ratio is as follows:
Figure BDA0003992759320000041
wherein x (T) is an original signal, T is total time, IMF is each modal component, and k is a modal component sequence number.
First, the strain signal actually measured on site is primarily decomposed by using an empirical mode decomposition algorithm, and the decomposition result is shown in fig. 3. The empirical mode decomposition algorithm decomposes the measured residual current signal into 10 IMFs and one residual component. The time domain energy ratios of IMF4, IMF5, IMF6 and IMF7 are 19.57%, 21.96%, 33.86% and 10.30%, respectively, so that the decomposition layer number parameter of the variation modal decomposition is initially set to be 4, and the field strain signal is initially decomposed, and the result is shown in fig. 4.
Step 2: correlation verification of modal components
The correlation coefficient calculated with the modal component as a sample is:
Figure BDA0003992759320000042
wherein n is the total data point number, S IMF Is the standard deviation of the modal component S x Standard deviation of the original signal. The pearson correlation coefficient (Pearson Correlation Coefficient, PCC) is used to determine the inter-variable correlation. Modes with PCC values greater than 0.1 are considered valid modes, and modes with PCC values less than 0.1 are considered ambient noise signals or residuals. The number of decomposition layers K is selected so that the decomposition is exactly complete, and the criterion of the exactly complete decomposition is: when K takes a certain value, the PCC of the highest strain mode is just smaller than 0.1, and when k=k+1, the PCC values of both the highest and second highest strain modes are smaller than 0.1.
And then, the pearson correlation coefficient PCC is utilized to test the modal components of the IMF1 and the IMF2, so that PCC values of the modal components are respectively 0.0304 and 0.0418, and the values are smaller than 0.1, so that the phenomenon of overdriving exists when K=4. And taking the decomposition layer number K as 3, and carrying out variation modal decomposition.
As can be seen from fig. 5, after the K value is reduced, high frequency noise represented by IMF1 and IMF2 at k=4 is integrated together, and at k=3, PCC coefficient values of the IMF components are respectively: 0.0322, 0.7710 and 0.8719, when k=3, high-frequency noise with no correlation is just decomposed, and each strain modal component can be used for noise reconstruction, that is, K takes 3 as the optimal decomposition layer number of the actual strain signal, and the corresponding IMF2 component should be regarded as the actual strain weighing measurement signal after reconstruction.
Step 3: determining a secondary penalty factor
The number of the sampling data points is N, the time sequence formed by the sampling data points is X= [ X (N), n=1, 2, … N ], and the calculation formula of the sample entropy of the modal component is as follows:
Figure BDA0003992759320000043
wherein: m is the embedding dimension, typically taken as 1 or 2; r is a similar tolerance, and is selected to be (0.1-0.2) delta IMF ,δ IMF Is the standard deviation of the modal components; n is the number of data points, and the general value range is 100-15000; b (B) m (r) is the probability that two signal sequences match an m-point with similar tolerance; b (B) m+1 (r) is the probability that two signal sequences match m+1 points.
The larger entropy means that the more frequency components are in the decomposed signal, and the smaller entropy means that the fewer frequency components are in the decomposed signal, i.e. the frequency band components are single, and the aliasing phenomenon is not serious. The value range of the secondary penalty factor is preset to be 100-2500, and an alpha value which enables the entropy value of the low-frequency modal component sample to be smaller is selected as the secondary penalty factor of the variation modal decomposition algorithm by taking the step length of 100 as a unit.
After determining the number of decomposition layers K, the quadratic penalty factor α is traversed to find the α value that minimizes the entropy of the low frequency component samples, making a change in α value from 100 to 2000 as shown in fig. 6. As can be seen from the figures: for the decomposition result of the strain signal, as the secondary penalty factor increases, the sample entropy of the IMF2 effective signal shows a change trend of decreasing first and then increasing second, and when the alpha value is larger than 1200, the sample entropy basically does not change obviously, so that a penalty factor value larger than 1200 can be selected.
Step 4: variational modal decomposition
The original signal can be decomposed into K modal components at a preset scale using a variational modal decomposition (Variation Mode Decomposition, VMD). The expression of the modal function is:
u k (t)＝A k (t)cos[φ k (t)]
wherein: a is that k (t) is the instantaneous amplitude of the amplitude-frequency signal, φ k (t) is the phase. The constraint variation model of the VMD for continuous iterative update solution during calculation operation is expressed as:
Figure BDA0003992759320000051
Figure BDA0003992759320000052
wherein,,
Figure BDA0003992759320000053
representing a deviation derivative; omega k Is the modal center frequency; delta (t) is the dirac distribution; * Representing a convolution operation; k=1, 2, …, K; f (t) is the original signal.
The VMD algorithm converts the Lagrangian multiplier and the quadratic penalty term into an unconstrained variable state by adding the Lagrangian multiplier and the quadratic penalty term to solve the corresponding decomposition optimization problem, and the expression is as follows:
Figure BDA0003992759320000054
Figure BDA0003992759320000055
Figure BDA0003992759320000056
Figure BDA0003992759320000057
wherein u is k 、ω k Lambda refers to the modal component, center frequency and Lagrangian multiplier, respectively;
Figure BDA0003992759320000058
λ n+1 for the corresponding result after each update.
The above equation is solved in the frequency domain of the strain signal using Parseval/Planchrel Fourier equidistant under the norm:
Figure BDA0003992759320000059
the constraint conditions of the iteration are:
Figure BDA0003992759320000061
wherein,,
Figure BDA0003992759320000062
representing strain modal component->
Figure BDA0003992759320000063
The corresponding fourier transform represents the center of gravity of the current strain modal power spectrum; />
Figure BDA0003992759320000064
Fourier transforming the original signal; />
Figure BDA0003992759320000065
Is the fourier transform of the lagrangian multiplier. Repeating the calculation, and ending the loop when the iteration stop requirement is met. The final decomposition results are shown in fig. 5.
Step 5: signal verification reconstruction
The mode obtained by decomposition contains noise with low frequency band and close frequency band and high-frequency invalid residual components, so that reconstruction after denoising of signals mixed with low-frequency band environmental noise is realized.
The adaptive VMD algorithm and the equivalent denoising method are adopted to decompose, denoise and reconstruct the acquired field strain signals, and the comparison of the effects before and after denoising by the algorithm is made, as shown in fig. 7.
From the figure, the strain modal signals after separation and reconstruction are concentrated near the zero value, and the characteristics of periodic variation are achieved, and the characteristics of the strain source signals accord with the measurement site theory are achieved. From the perspective of quantitative analysis, compared with a VMD algorithm under the default condition, the self-adaptive VMD denoising reconstruction method provided by the invention has the advantages that the signal-to-noise ratio is improved by 4.55dB, the root mean square error is smaller, the difference between a strain signal after denoising by the method and a theoretical signal is smaller, the signal-to-noise ratio of the denoising method such as wavelet packet thresholding and Empirical Mode Decomposition (EMD) is lower than that of the self-adaptive VMD algorithm, and the self-adaptive VMD denoising reconstruction method has more excellent performance in processing a weighing field strain measurement signal. After the self-adaptive VMD algorithm processing, most high-frequency noise in the signal is filtered, low-frequency high-energy environmental noise with the frequency band close to that of the on-site vibration source is eliminated, the waveform of the low-frequency high-energy environmental noise is basically consistent with that of the theoretical strain signal, the follow-up analysis processing process is facilitated, and the denoising effect is reliable.
Thus, the denoising reconstruction of the signal mixed with the low-frequency environmental noise is realized, and the flow chart of the whole algorithm is shown in fig. 1.

Claims (2)

1. A signal denoising reconstruction method based on variation modal decomposition is characterized by being self-adaptive, and comprises the following steps:
step 1: predetermining the number of decomposition layers
The empirical mode decomposition method is capable of adaptively decomposing a signal into a plurality of modal components and a residual component by recursively. And taking the number of the modal components with the signal time domain energy ratio larger than a certain threshold value as the initial decomposition layer number input of the variation modal decomposition. The calculation formula of the signal time domain energy ratio is as follows:
Figure FDA0003992759310000011
wherein x (T) is an original signal, T is total time, IMF is each modal component, and k is a modal component sequence number.
Step 2: correlation verification of modal components
The correlation coefficient r calculated by taking the modal component as a sample is:
Figure FDA0003992759310000012
wherein n is the total data point number, S IMF Is the standard deviation of the modal component S x Standard deviation of the original signal. The pearson correlation coefficient (Pearson Correlation Coefficient, PCC) is used to determine the inter-variable correlation. Modes with PCC values greater than 0.1 are considered valid modes, and modes with PCC values less than 0.1 are considered ambient noise signals or residuals. The number of decomposition layers K is selected so that the decomposition is exactly complete, and the criterion of the exactly complete decomposition is: when K takes a certain value, the PCC of the highest strain mode is just smaller than 0.1, and when k=k+1, the PCC values of both the highest and second highest strain modes are smaller than 0.1.
Step 3: determining a secondary penalty factor
The number of the sampling data points is N, the time sequence formed by the sampling data points is X= [ X (N), n=1, 2, … N ], and the calculation formula of the sample entropy of the modal component is as follows:
Figure FDA0003992759310000013
wherein: m is the embedding dimension, typically taken as 1 or 2; r is a similar tolerance, and is selected to be (0.1-0.2) delta IMF ,δ IMF Is the standard deviation of the modal components; n is the number of data points, and the general value range is 100-15000; b (B) m (r) is the probability that two signal sequences match an m-point with similar tolerance; b (B) m+1 (r) is the probability that two signal sequences match m+1 points.
The larger entropy means that the more frequency components are in the decomposed signal, and the smaller entropy means that the fewer frequency components are in the decomposed signal, i.e. the frequency band components are single, and the aliasing phenomenon is not serious. The value range of the secondary penalty factor is preset to be 100-2500, and an alpha value which enables the entropy value of the low-frequency modal component sample to be smaller is selected as the secondary penalty factor of the variation modal decomposition algorithm by taking the step length of 100 as a unit.
Step 4: variational modal decomposition
The original signal can be decomposed into K modal components at a preset scale using a variational modal decomposition (Variation Mode Decomposition, VMD). The expression of the modal function is:
u k (t)＝A k (t)cos[φ k (t)]
wherein: a is that k (t) is the instantaneous amplitude of the amplitude-frequency signal, φ k (t) is the phase. The constraint variation model of the VMD for continuous iterative update solution during calculation operation is expressed as:
Figure FDA0003992759310000021
Figure FDA0003992759310000022
wherein,,
Figure FDA0003992759310000023
representing a deviation derivative; omega k Is the modal center frequency; delta (t) is the dirac distribution; * Representing a convolution operation; k=1, 2, …, K; f (t) is the original signal.
Step 5: signal verification reconstruction
The mode obtained by decomposition contains noise with low frequency band and close frequency band and high-frequency invalid residual components, so that reconstruction after denoising of signals mixed with low-frequency band environmental noise is realized.
2. The constrained variation model of claim 1, step 4, solved in that it is transformed into an unconstrained variation case by adding lagrangian multipliers and quadratic penalty terms. The iterative update expression is:
Figure FDA0003992759310000024
Figure FDA0003992759310000025
Figure FDA0003992759310000026
Figure FDA0003992759310000027
wherein u is k 、ω k Lambda refers to the modal component, center frequency and Lagrangian multiplier, respectively;
Figure FDA0003992759310000028
λ n+1 for the corresponding result after each update.
CN202211609768.XA 2022-12-12 2022-12-12 Signal denoising reconstruction method based on adaptive variational modal decomposition Pending CN116295740A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202211609768.XA CN116295740A (en) 2022-12-12 2022-12-12 Signal denoising reconstruction method based on adaptive variational modal decomposition

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202211609768.XA CN116295740A (en) 2022-12-12 2022-12-12 Signal denoising reconstruction method based on adaptive variational modal decomposition

Publications (1)

Publication Number Publication Date
CN116295740A true CN116295740A (en) 2023-06-23

Family

ID=86782233

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202211609768.XA Pending CN116295740A (en) 2022-12-12 2022-12-12 Signal denoising reconstruction method based on adaptive variational modal decomposition

Country Status (1)

Country Link
CN (1) CN116295740A (en)

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117454095A (en) * 2023-12-22 2024-01-26 北京建筑大学 Bridge dynamic deflection data noise reduction method
CN117977636A (en) * 2024-03-28 2024-05-03 西安热工研究院有限公司 Sample entropy-based frequency modulation method and system for fused salt coupling thermal power generating unit

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117454095A (en) * 2023-12-22 2024-01-26 北京建筑大学 Bridge dynamic deflection data noise reduction method
CN117454095B (en) * 2023-12-22 2024-03-15 北京建筑大学 Bridge dynamic deflection data noise reduction method
CN117977636A (en) * 2024-03-28 2024-05-03 西安热工研究院有限公司 Sample entropy-based frequency modulation method and system for fused salt coupling thermal power generating unit
CN117977636B (en) * 2024-03-28 2024-06-11 西安热工研究院有限公司 Sample entropy-based frequency modulation method and system for fused salt coupling thermal power generating unit

Similar Documents

Publication Publication Date Title
CN116295740A (en) Signal denoising reconstruction method based on adaptive variational modal decomposition
CN113780055B (en) MOMEDA and compression sensing rolling bearing fault diagnosis method
CN111397868B (en) Breaker fault analysis method based on aggregation empirical mode decomposition algorithm
CN112945546B (en) Precise diagnosis method for complex faults of gearbox
CN109946518A (en) Electric harmonic signal analysis method and analytical equipment based on bayes method
CN112560699A (en) Gear vibration information source underdetermined blind source separation method based on density and compressed sensing
CN108828658A (en) A kind of ocean bottom seismic data reconstructing method
CN117713505B (en) High-side current detection method and system for switching power supply
Sun et al. Application of a novel improved adaptive CYCBD method in gearbox compound fault diagnosis
CN114970646A (en) Artificial source electromagnetic pseudorandom signal detrending and noise identification method
CN113702666B (en) Signal joint noise reduction method for optical fiber gyroscope inertia measurement unit
CN117093857B (en) Rapid processing method for intelligent ring test data
CN114813123A (en) Rolling bearing weak fault diagnosis method based on PSO-VMD-MCKD
CN110069744B (en) Method for estimating stable value of step response signal of pressure sensor
CN111323233B (en) Local mean decomposition method for low-speed rotating machine fault diagnosis
CN111582205B (en) Noise reduction method based on multi-resolution singular value decomposition model
Ding et al. Research on adaptive modulus maxima selection of wavelet modulus maxima denoising
CN113281047A (en) Bearing inner and outer ring fault quantitative trend diagnosis method based on variable-scale Lempel-Ziv
Liu et al. Sparse coefficient fast solution algorithm based on the circulant structure of a shift-invariant dictionary and its applications for machine fault diagnosis
CN113655534B (en) Nuclear magnetic resonance FID signal noise suppression method based on multi-linear singular value tensor decomposition
CN113376629B (en) In-well radar least square inversion method based on non-uniform input parameter grid
Yan et al. Time-frequency distribution decomposition with applications to recognize the looseness state of the viscoelastic sandwich structure
Mao et al. A gearbox fault feature extraction method based on wingsuit flying search algorithm-optimized orthogonal matching pursuit with a compound time-frequency atom dictionary
Lu et al. A Novel Weak Fault Diagnosis Method Based on Sparse Representation and Empirical Wavelet Transform for Rolling Bearing
Zhong et al. Bi-LSTM fault diagnosis method for rolling bearings based on segmented interception AR spectrum analysis and information fusion

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