CN113688502A - Variable frequency signal denoising method based on stochastic resonance system - Google Patents

Variable frequency signal denoising method based on stochastic resonance system Download PDF

Info

Publication number
CN113688502A
CN113688502A CN202110822703.2A CN202110822703A CN113688502A CN 113688502 A CN113688502 A CN 113688502A CN 202110822703 A CN202110822703 A CN 202110822703A CN 113688502 A CN113688502 A CN 113688502A
Authority
CN
China
Prior art keywords
signal
frequency
stochastic resonance
resonance system
parameters
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
CN202110822703.2A
Other languages
Chinese (zh)
Inventor
张海滨
翟中平
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.)
Zhihuan Technology Changzhou Co ltd
Original Assignee
Zhihuan Technology Changzhou Co ltd
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 Zhihuan Technology Changzhou Co ltd filed Critical Zhihuan Technology Changzhou Co ltd
Priority to CN202110822703.2A priority Critical patent/CN113688502A/en
Publication of CN113688502A publication Critical patent/CN113688502A/en
Pending legal-status Critical Current

Links

Images

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
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
    • G06F2111/08—Probabilistic or stochastic CAD
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/10—Noise analysis or noise optimisation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces

Landscapes

  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Theoretical Computer Science (AREA)
  • Mathematical Physics (AREA)
  • Data Mining & Analysis (AREA)
  • Pure & Applied Mathematics (AREA)
  • General Engineering & Computer Science (AREA)
  • Computational Mathematics (AREA)
  • Mathematical Analysis (AREA)
  • Mathematical Optimization (AREA)
  • Geometry (AREA)
  • Operations Research (AREA)
  • Evolutionary Computation (AREA)
  • Algebra (AREA)
  • Computer Hardware Design (AREA)
  • Databases & Information Systems (AREA)
  • Software Systems (AREA)
  • Complex Calculations (AREA)

Abstract

The invention discloses a variable frequency signal denoising method based on a stochastic resonance system, which comprises the steps of inputting a noise-containing signal, estimating a signal variable frequency coefficient, optimizing stochastic resonance system parameters and outputting a denoising signal; the invention better solves the problem that the noise energy, frequency and potential well can not be effectively matched due to the frequency change of the driving signal when the current stochastic resonance system is used for denoising the frequency-conversion signal; the variable parameter stochastic resonance system for denoising the variable frequency signals is provided, and denoising and extraction of the variable frequency signals under strong background noise can be realized; the variable parameter frequency normalization method breaks through the limitation that the frequency of an original variable frequency signal is too large in the operation process of a stochastic resonance system, and realizes the time-varying normalization operation of the original high-frequency signal; the method provided by the invention has good adaptability to the original frequency conversion broadband signal, and has high efficiency and strong accuracy for searching frequency conversion parameters and higher robustness of a filtering algorithm on the premise of knowing a frequency conversion model.

Description

Variable frequency signal denoising method based on stochastic resonance system
Technical Field
The invention relates to a signal processing technology, in particular to a variable frequency signal denoising method based on a stochastic resonance system.
Background
When the vibration signal of the mechanical equipment is subjected to feature extraction and analysis, the original effective signal is often submerged due to noise interference, and the corresponding fault feature is weak and cannot be identified. In the field of signal processing, noise is often viewed as a unwanted component that interferes with the original signal. However, in recent years, theoretical and experimental researches on nonlinear systems find that in a special system, noise with a proper size can be helpful for improving the signal-to-noise ratio of effective components in an original signal, and the purpose of amplifying and extracting effective signals by using the noise can be achieved by the aid of the nonlinear system, which is called stochastic resonance, and the nonlinear system is a stochastic resonance system.
Common stochastic resonance systems are different in monostable state, bistable state and multistable state, and are different in under-damping, over-damping, negative feedback and the like from the damping and feedback angles. It can be derived from the stochastic resonance theory that when a weak periodic signal in strong background noise passes through a stochastic resonance system, a phenomenon of noise energy transfer to signal energy occurs under the synergistic effect of noise and signal, so that the output signal-to-noise ratio of a nonlinear system is enhanced compared with that of an input signal. And the signal-to-noise ratio of the output signal shows a trend of increasing and then decreasing with the increase of noise, wherein the output signal-to-noise ratio has a peak value under certain noise energy. With the special effect of the stochastic resonance system, in recent years, many experts and scholars at home and abroad apply the stochastic resonance system to the fields of weak signal detection, fault diagnosis, feature extraction, signal denoising and the like.
At present, a plurality of experts provide a signal denoising or feature extraction method based on stochastic resonance: for example, yangjianhua et al propose a method for extracting weak characteristic signals by using a periodic potential system (yangjianhua is based on a periodic potential system adaptive stochastic resonance weak characteristic information extraction method CN 105893690B), and construct a stochastic resonance model by using a periodic potential well function; the Rohong cell is from the angle of optimization algorithm of system parameter, the chaos variable step-length firefly optimization algorithm of the behavior of knocking into the tail is adopted to search the optimum structural parameter of the system (Rohong cell a weak signal detection method of stochastic resonance CN 108645505A), substitute the parameter into two-dimentional Duffing's system to realize the signal amplification and extraction of stochastic resonance; and starting from a feedback form of the system, a method of combining time delay negative feedback and an index monostable system is adopted, and a steady-state probability distribution function and a sum of functions are obtained by a small-time-delay approximation technology, so that actual resonance calculation and output signal denoising are further realized (Happy a time delay feedback index monostable stochastic resonance system CN 109408771A).
However, in most scenarios of stochastic resonance applications, the assumption that the characteristic signal to be extracted has a fixed period is based on the assumption that the input signal of the system is composed of periodic signals and noise. However, in practical applications, when the method is used for diagnosing mechanical faults, many devices are actually in a variable rotation speed condition, such as a start-stop stage, an intrinsic rotation speed fluctuation caused by load change, power supply frequency fluctuation, open-loop control and the like, and some non-periodic signals (such as a chirp signal, a doppler signal and the like) are also encountered in other fields, so that many existing models and processing strategies are no longer applicable, and the application of the stochastic resonance system in practical situations is limited.
To address this problem, a few implementations have also been proposed. The method is applied to detection of single-frequency signals, and does not solve the problem that stochastic resonance cannot be applied to variable-frequency signals (Hedy is based on a bistable optimal stochastic resonance single-frequency weak signal detection method CN 101848177B); the method adopts a target signal and a modulation signal to carry out mixing modulation, processes a normalized signal through a stochastic resonance system, and realizes the feature extraction of a weak signal, but the invention does not propose a non-periodic signal type, does not carry out special system optimization on the non-periodic signal compared with the traditional method, and does not mention a measurement index of non-periodic signal output (the former method for extracting the feature of the non-periodic signal based on the stochastic resonance and the system CN 109905090A).
In the above mentioned several stochastic resonance methods, optimization or algorithm improvement of the existing nonlinear system model is mostly adopted, and when processing time-varying non-periodic signals, one or more of the following defects and shortcomings exist:
1. in the traditional stochastic resonance method, an input signal is required to meet three basic conditions of small signal, periodicity and strong noise in the calculation process, so that most variable-frequency non-periodic signals cannot be denoised and amplified by the method in practical application occasions, and the model fails.
2. In a common stochastic resonance system, the signal-to-noise ratio of an output signal is basically used as a measurement index, and in an actual scene, the index needs to accurately know the target frequency value of a signal to be extracted, which is obviously no longer applicable in most occasions, and limits the application of stochastic resonance in engineering.
3. When processing variable frequency unsteady state signals, the input signals still need to satisfy the small parameter condition due to the constraint of adiabatic approximate condition, and the frequency of the original signals changes with time, which causes that the common method such as parameter normalization is difficult to realize effective equivalent frequency matching.
4. The existing method for processing the unsteady signals does not start from the essence of a filter model, and still adopts the traditional system structure, so that the adaptability of the traditional system structure to the bandwidth of the signals is limited, and the stability of the filter is difficult to ensure.
Disclosure of Invention
The invention aims to provide a variable frequency signal denoising method based on a stochastic resonance system, so as to solve the problems in the background technology.
In order to achieve the purpose, the invention provides the following technical scheme:
a variable frequency signal denoising method based on a stochastic resonance system comprises the steps of inputting a noisy signal, estimating a signal variable frequency coefficient, optimizing stochastic resonance system parameters and outputting a denoising signal.
Specifically, a noisy signal is input: to be provided with
Figure 15667DEST_PATH_IMAGE001
Which represents the original input signal, is,
Figure 136070DEST_PATH_IMAGE002
can be expressed as:
Figure 56753DEST_PATH_IMAGE003
wherein
Figure 655224DEST_PATH_IMAGE004
In order to be effective for the frequency-converted signal,
Figure 610542DEST_PATH_IMAGE005
representing noise.
Optimizing stochastic resonance system parameters: in the stochastic resonance system, the bistable system driven by weak periodic force and noise is essentially that a mass point is simultaneously acted by external force and noise, the mass point moves in a symmetrical bistable potential well, and the dynamic model is described by the langevin equation:
Figure 633337DEST_PATH_IMAGE006
wherein
Figure 41316DEST_PATH_IMAGE007
Representing potential well function
Figure 443478DEST_PATH_IMAGE008
To position
Figure 518881DEST_PATH_IMAGE009
The first derivative of (a).
Estimating the frequency conversion coefficient of the signal: with conventional polynomial bistable systems, the potential well function is typically expressed as:
Figure 449928DEST_PATH_IMAGE010
Figure 610782DEST_PATH_IMAGE011
and
Figure 485810DEST_PATH_IMAGE012
calculating the symmetric potential well position and the potential barrier height for the stochastic resonance system parameters,when the original signal is used as input to act on the potential well, if the parameters of the potential well are matched with the signal frequency and the noise energy, the effect similar to resonance can be formed, the particles are subjected to periodic transition in the two potential wells, and the noise energy is transferred to the signal by the wall of the potential well, so that the purposes of signal denoising and characteristic amplification are achieved.
The normalization transformation method is adopted to enable the system to realize stochastic resonance under the condition of large parameters, and when the parameters in the bistable system are stable
Figure 946878DEST_PATH_IMAGE011
And
Figure 783247DEST_PATH_IMAGE012
when the value is not 1, taking:
Figure 228135DEST_PATH_IMAGE013
Figure 644204DEST_PATH_IMAGE014
and
Figure 694200DEST_PATH_IMAGE015
substituting the stochastic resonance kinetic model for a new position and time dimension and simplifying to obtain:
Figure 229699DEST_PATH_IMAGE016
the transformed stochastic resonance system parameters are all 1, and the original time scale
Figure 99566DEST_PATH_IMAGE017
Through transformation into
Figure 584905DEST_PATH_IMAGE015
The corresponding frequency scale is original
Figure 20565DEST_PATH_IMAGE018
Thereby passing through the parameters
Figure 464316DEST_PATH_IMAGE011
The design of (2) can make the input signal meet the small parameter input condition required by the system.
When estimating the frequency conversion coefficient of the signal, when the input signal
Figure 352638DEST_PATH_IMAGE019
Signal frequency of
Figure 373159DEST_PATH_IMAGE020
When the time variation occurs, a variable parameter stochastic resonance system is adopted, iterative search is carried out by utilizing a signal time variation coefficient, and parameters are designed
Figure 928905DEST_PATH_IMAGE021
The time-varying characteristic which is the same as the frequency of the input signal is kept, after normalization calculation, the variable frequency signal is actually equivalent to a stable frequency for a stochastic resonance system, and the input condition of the stochastic resonance phenomenon is met on the premise, and the model at the moment can be expressed as follows:
Figure 12399DEST_PATH_IMAGE022
the equivalent frequency of the signal after the normalized transformation is
Figure 388017DEST_PATH_IMAGE023
On one hand, the method meets the condition of small parameters, on the other hand, the equivalent transformation of the input signal frequency in the calculation process is kept, the frequency is equivalent to the frequency of the system and is not transformed any more, meanwhile, the equilibrium position is kept unchanged in the model change process, and then the discretization solution is carried out on the model equation by using a 4-order Runge-Kutta method (the method comprises the steps of (1)
Figure 11896DEST_PATH_IMAGE024
To solve for step size):
Figure 890990DEST_PATH_IMAGE025
if the variation parameter of the original signal, the system initial parameter
Figure 145385DEST_PATH_IMAGE026
Are unknown, and fixed stochastic resonance system parameters are adopted to obtain decision coefficients
Figure 5369DEST_PATH_IMAGE027
：
Figure 636202DEST_PATH_IMAGE028
Wherein the content of the first and second substances,
Figure 104223DEST_PATH_IMAGE029
and
Figure 60678DEST_PATH_IMAGE030
respectively representing the system output signal and its average value,
Figure 410888DEST_PATH_IMAGE031
refers to the fitting result of the output signal.
Compared with the prior art, the invention has the beneficial effects that:
1. the invention better solves the problem that the noise energy, frequency and potential well can not be effectively matched due to the frequency change of the driving signal when the current stochastic resonance system is used for denoising the frequency-conversion signal;
2. the variable parameter stochastic resonance system for denoising the variable frequency signals is provided, and denoising and extraction of the variable frequency signals under strong background noise can be realized;
3. the variable parameter frequency normalization method breaks through the limitation that the frequency of an original variable frequency signal is too large in the operation process of a stochastic resonance system, and realizes the time-varying normalization operation of the original high-frequency signal;
4. the method adopts a new fitting decision coefficient as an index for evaluating the quality of an output signal, overcomes the defect that the signal-to-noise ratio of the output signal is taken as a measurement index in the prior art, and does not need to accurately know the target frequency value of the signal to be extracted;
5. the decision coefficient is used as an evaluation index, the output quality evaluation of the variable frequency signal is realized, the algorithm can complete the operation in the time domain, the calculation complexity is low, the realization in an embedded system is facilitated, and the possibility of the application of the stochastic resonance system in the engineering is increased.
The method provided by the invention has good adaptability to the original frequency conversion broadband signal, and has high efficiency and strong accuracy for searching frequency conversion parameters and higher robustness of a filtering algorithm on the premise of knowing a frequency conversion model.
Drawings
FIG. 1 is a flow chart of a method algorithm according to the present invention.
Figure 2 is a model of a potential well of a bistable stochastic resonance system.
Fig. 3 shows a chirp signal, noise and a mixed signal in the first embodiment.
Fig. 4 shows the system parameter optimization and the stochastic resonance denoising result of the first embodiment.
Fig. 5 shows a chirp signal, noise, and a mixed signal in the second embodiment.
Fig. 6 shows the system parameter optimization and stochastic resonance denoising results of the second embodiment.
Detailed Description
The technical scheme of the patent is further described in detail by combining the following specific embodiments:
referring to fig. 1, a frequency-variable signal denoising method based on a stochastic resonance system includes inputting a noisy signal, estimating a frequency-variable coefficient of the signal, optimizing parameters of the stochastic resonance system, and outputting a denoising signal.
Specifically, a noisy signal is input: to be provided with
Figure 579832DEST_PATH_IMAGE001
Which represents the original input signal, is,
Figure 165010DEST_PATH_IMAGE002
can be expressed as:
Figure 292366DEST_PATH_IMAGE003
wherein
Figure 598713DEST_PATH_IMAGE004
In order to be effective for the frequency-converted signal,
Figure 102507DEST_PATH_IMAGE005
representing noise.
Optimizing stochastic resonance system parameters: in a stochastic resonance system, a common bistable system driven by weak periodic force and noise essentially describes that a particle is simultaneously subjected to external force and noise, the particle moves in a symmetric bistable potential well, and the dynamic model is generally described by the langevin equation:
Figure 607438DEST_PATH_IMAGE006
wherein
Figure 108957DEST_PATH_IMAGE007
Representing potential well function
Figure 719847DEST_PATH_IMAGE008
To position
Figure 496173DEST_PATH_IMAGE009
The first derivative of (a).
Estimating the frequency conversion coefficient of the signal: with a conventional polynomial bistable system, the potential well function is typically expressed as:
Figure 527714DEST_PATH_IMAGE010
Figure 528031DEST_PATH_IMAGE011
and
Figure 277812DEST_PATH_IMAGE012
symmetric potential well positions and barrier heights were calculated for stochastic resonance system parameters, as shown in FIG. 2
Figure 654567DEST_PATH_IMAGE032
The symmetric potential well position of the potential well function distribution is
Figure 68843DEST_PATH_IMAGE033
Barrier height
Figure 177745DEST_PATH_IMAGE034
. When the original signal is used as input to act on the potential well, if the parameters of the potential well are matched with the signal frequency and the noise energy, the effect similar to resonance can be formed, the particles are subjected to periodic transition in the two potential wells, and the noise energy is transferred to the signal by the wall of the potential well, so that the purposes of signal denoising and characteristic amplification are achieved.
However, the stochastic resonance phenomenon occurs and needs to meet the small parameter limiting condition of the signal, in order to realize the denoising by utilizing the stochastic resonance phenomenon under the actual signal condition (the frequency is far more than 1 Hz) and amplify the weak signal therein, the invention adopts a normalization transformation method to ensure that the system realizes the stochastic resonance under the condition of large parameter, and when the parameter in the bistable system is in a state of being stable
Figure 477139DEST_PATH_IMAGE011
And
Figure 126426DEST_PATH_IMAGE012
when the value is not 1, taking:
Figure 132559DEST_PATH_IMAGE013
Figure 474679DEST_PATH_IMAGE014
and
Figure 199052DEST_PATH_IMAGE015
substituting the stochastic resonance kinetic model for a new position and time dimension and simplifying to obtain:
Figure 649101DEST_PATH_IMAGE016
the transformed stochastic resonance system parameters are all 1, and the original time scale
Figure 572057DEST_PATH_IMAGE017
Through transformation into
Figure 22761DEST_PATH_IMAGE015
The corresponding frequency scale is original
Figure 296748DEST_PATH_IMAGE018
Thereby passing through the parameters
Figure 756679DEST_PATH_IMAGE011
The design of (2) can make the input signal meet the small parameter input condition required by the system.
When estimating the frequency conversion coefficient of the signal, when the input signal
Figure 737405DEST_PATH_IMAGE019
Signal frequency of
Figure 152818DEST_PATH_IMAGE020
When the variable-parameter stochastic resonance system changes along with time, in order to ensure the occurrence of stochastic resonance phenomenon and the effective denoising and amplification of an original signal, the invention provides a variable-parameter stochastic resonance system aiming at a variable-frequency signal, and the iterative search is carried out by utilizing a time-varying coefficient of the signal to design parameters
Figure 648521DEST_PATH_IMAGE021
The time-varying characteristic which is the same as the frequency of the input signal is kept, after normalization calculation, the variable frequency signal is actually equivalent to a random resonance system with stable frequency, and the requirement on the condition is metThe stochastic resonance phenomenon occurs under the input conditions, and the model at this time can be expressed as:
Figure 646564DEST_PATH_IMAGE022
the equivalent frequency of the signal after the normalized transformation is
Figure 544113DEST_PATH_IMAGE023
On one hand, the method meets the condition of small parameters, on the other hand, the equivalent transformation of the input signal frequency in the calculation process is kept, the equivalent frequency does not transform for the system, and meanwhile, the balance position is kept unchanged in the model change process. Then, discretizing the model equation by using a 4-order Runge-Kutta method to solve (
Figure 336620DEST_PATH_IMAGE024
To solve for step size):
Figure 585199DEST_PATH_IMAGE035
among the above system parameters, for the convenience of calculation, the invention takes
Figure 121353DEST_PATH_IMAGE036
. Due to the variation parameter of the original signal and the initial parameter of the system
Figure 870479DEST_PATH_IMAGE026
Are unknown, and an optimal parameter combination needs to be selected to obtain an optimal output result. Therefore, the invention provides a new frequency conversion signal stochastic resonance output evaluation index, and fixed stochastic resonance system parameters are adopted to obtain a decision coefficient
Figure 365045DEST_PATH_IMAGE027
：
Figure 241866DEST_PATH_IMAGE028
In the above formula
Figure 316132DEST_PATH_IMAGE029
And
Figure 125956DEST_PATH_IMAGE030
respectively representing the system output signal and its average value,
Figure 788494DEST_PATH_IMAGE031
refers to the fitting result of the output signal. The value represents the denoising effect of the output result, the closer the value is to 1, the better the effect is, and the optimal combination of each parameter can be searched for by the index in the method.
The following describes the specific implementation method and algorithmic processes of the present invention in detail with reference to specific embodiments.
Example 1:
referring to fig. 3-4, the frequency-converted signal in this case is a Chirp signal (Chirp signal, signal frequency linearly changes with time).
1. Firstly, the theoretical model of linear frequency modulation is as follows:
Figure 480507DEST_PATH_IMAGE037
it can be seen that the signal frequency
Figure 624043DEST_PATH_IMAGE038
. In this case, the line is taken to adjust the frequency
Figure 350691DEST_PATH_IMAGE039
Initial frequency of
Figure 921481DEST_PATH_IMAGE040
Initial phase
Figure 100789DEST_PATH_IMAGE041
Amplitude of signal
Figure 576245DEST_PATH_IMAGE042
. Setting the sampling frequency to 12800Hz and the sampling time to 0.5s, the representation of the original noise-free signal of 6400 points is shown in fig. 3(a), white noise with the density of 2.5 is added as shown in fig. 3(b), and in the obtained mixed signal (fig. 3(c), black curve), the noise energy is higher than that of the original Chirp signal, so that the effective signal (yellow curve) is submerged and cannot be distinguished.
2. According to the signal type, the nonlinear system equation for obtaining the stochastic resonance is expressed as:
Figure 626241DEST_PATH_IMAGE043
in order to solve the above ordinary differential equation, the signal parameters thereof need to be determined
Figure 367932DEST_PATH_IMAGE044
、
Figure 503378DEST_PATH_IMAGE045
And system parameters
Figure 519876DEST_PATH_IMAGE026
. Firstly, selecting preset parameters
Figure 158799DEST_PATH_IMAGE046
To parameter
Figure 865199DEST_PATH_IMAGE044
、
Figure 222362DEST_PATH_IMAGE045
Global search is carried out, and the computing system is calculated in different ways by utilizing the fourth-order Runge-Kutta method
Figure 308130DEST_PATH_IMAGE044
、
Figure 801559DEST_PATH_IMAGE045
Output under combination, determining coefficient by evaluation between actual system output signal and fitting signalAs an index, obtain
Figure 681790DEST_PATH_IMAGE044
、
Figure 322987DEST_PATH_IMAGE045
Is 30 and 140, under which the original noisy signal is at
Figure 884550DEST_PATH_IMAGE046
Calculating the decision coefficient of the output signal under the condition
Figure 580890DEST_PATH_IMAGE047
。
3. After the signal parameter combination is obtained, the search interval of the system parameter is set to [50, 2000 ]]The search step is set to 1, and the difference is calculated by using the decision coefficient between the output signal and the fitting signal as an index
Figure 835285DEST_PATH_IMAGE026
And (5) obtaining the optimal system parameters and calculating output signals according to the output results, wherein the optimization process and the final output result are shown in fig. 4. The optimal system parameter is 940, and the output signal under the parameter shows that the noise of the original signal is suppressed to a great extent, and the effective linear frequency modulation signal is amplified and can be obviously distinguished from the time domain.
Example 2:
referring to fig. 5-6, the frequency-converted signal in this case is a periodic frequency-converted signal (i.e., a non-linear frequency-converted signal, the frequency of which varies with the time period).
1. The theoretical model of the periodic frequency conversion signal is as follows:
Figure 901461DEST_PATH_IMAGE048
from the model, the signal frequency
Figure 63452DEST_PATH_IMAGE049
At an initial frequency of
Figure 593790DEST_PATH_IMAGE050
Over time to
Figure 19086DEST_PATH_IMAGE044
The frequency varies periodically. In this case, the frequency of the periodic variation of the signal is taken
Figure 835208DEST_PATH_IMAGE051
Amplitude of variation
Figure 800890DEST_PATH_IMAGE052
Initial frequency of
Figure 123418DEST_PATH_IMAGE053
Initial phase
Figure 781933DEST_PATH_IMAGE041
Amplitude of signal
Figure 822701DEST_PATH_IMAGE042
. Setting the sampling frequency to 12800Hz, the sampling time to be 1.28s, and acquiring 16384-point digital signal without noise, as shown in FIG. 5(a), adding white noise with the density of 2 as shown in FIG. 5(b), and obtaining the mixed signal (FIG. 5(c), black curve), as well as the case, because the noise energy is much higher than the original periodic frequency-converted signal, the effective signal (yellow curve) is drowned by the noise and cannot be distinguished.
2. And obtaining a system equation expression according to the signal type and the stochastic resonance system ordinary differential equation:
Figure 326495DEST_PATH_IMAGE054
followed by estimating parameters of the original signal
Figure 565846DEST_PATH_IMAGE050
、
Figure 330015DEST_PATH_IMAGE044
、
Figure 920397DEST_PATH_IMAGE055
And system parameters
Figure 165564DEST_PATH_IMAGE026
. Selecting preset parameters
Figure 525001DEST_PATH_IMAGE046
To parameter
Figure 728581DEST_PATH_IMAGE050
、
Figure 478362DEST_PATH_IMAGE044
、
Figure 852187DEST_PATH_IMAGE055
Performing global search, calculating output signals of the system under different parameter combinations, calculating a decision coefficient between the output signals and a fitting signal, and obtaining the decision coefficient by taking the decision coefficient as an index
Figure 800552DEST_PATH_IMAGE050
、
Figure 909453DEST_PATH_IMAGE044
、
Figure 208847DEST_PATH_IMAGE055
Is 30, 3 and 0.4, under which the original noisy signal is at
Figure 795818DEST_PATH_IMAGE046
Calculating the decision coefficient of the output signal under the condition
Figure 129847DEST_PATH_IMAGE056
。
3. After obtaining the parameter combination of the signal, setting the system parameter
Figure 406720DEST_PATH_IMAGE026
Has a search interval of [200, 4300 ]]The search step is set to 1, and the difference is calculated by using the decision coefficient between the output signal and the fitting signal as an index
Figure 193410DEST_PATH_IMAGE026
The optimal system parameters are obtained and output signal calculation is performed according to the output results, and the optimization process and the final output results are shown in fig. 6. The optimal system parameter is 1840, the lower graph in fig. 6 is the comparison result of the signal after the stochastic resonance denoising (black curve) and the original signal without the early signal (fitting signal), and as can be seen from the output result, the original ideal signal is better recovered, compared with the noise-containing mixed signal in fig. 5(c), the noise in the original signal is well removed, and the effective periodic frequency modulation signal is amplified and highlighted.
It can be seen from the processing results of the above two cases that the original frequency-conversion effective signal is effectively amplified after the frequency-conversion signal submerged in the strong background noise is processed by the variable-parameter stochastic resonance system provided by the invention, and the noise energy is transferred to the effective signal, so that the frequency-conversion effective signal is successfully extracted. Furthermore, it should be noted that the language used in the specification has been principally selected for readability and instructional purposes, and may not have been selected to delineate or circumscribe the inventive subject matter. Accordingly, many modifications and variations will be apparent to practitioners skilled in this art. The present invention has been disclosed in an illustrative rather than a restrictive sense, and the scope of the present invention is defined by the appended claims.
It will be evident to those skilled in the art that the invention is not limited to the details of the foregoing illustrative embodiments, and that the present invention may be embodied in other specific forms without departing from the spirit or essential attributes thereof. The present embodiments are therefore to be considered in all respects as illustrative and not restrictive, the scope of the invention being indicated by the appended claims rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein. Any reference sign in a claim should not be construed as limiting the claim concerned.
Furthermore, it should be understood that although the present description refers to embodiments, not every embodiment may contain only a single embodiment, and such description is for clarity only, and those skilled in the art should integrate the description, and the embodiments may be combined as appropriate to form other embodiments understood by those skilled in the art.

Claims (4)

1. A frequency conversion signal denoising method based on a stochastic resonance system is characterized by comprising the steps of inputting a noise-containing signal, estimating a signal frequency conversion coefficient, optimizing stochastic resonance system parameters and outputting a denoising signal;
wherein, input noise-containing signal: to be provided with
Figure 838970DEST_PATH_IMAGE001
Which represents the original input signal, is,
Figure 103204DEST_PATH_IMAGE002
can be expressed as:
Figure 366958DEST_PATH_IMAGE003
wherein
Figure 451064DEST_PATH_IMAGE004
In order to be effective for the frequency-converted signal,
Figure 51941DEST_PATH_IMAGE005
representing noise;
optimizing stochastic resonance system parameters: in the stochastic resonance system, a bistable system driven by weak periodic force and noise is a mass point simultaneously subjected to the action of external force and noise, the mass point moves in a symmetrical bistable potential well, and the dynamic model is described by the Langewan equation:
Figure 108365DEST_PATH_IMAGE006
wherein
Figure 480703DEST_PATH_IMAGE007
Representing potential well function
Figure 130734DEST_PATH_IMAGE008
To position
Figure 797951DEST_PATH_IMAGE009
The first derivative of (a);
estimating the frequency conversion coefficient of the signal: with a conventional polynomial bistable system, the potential well function is expressed as:
Figure 164341DEST_PATH_IMAGE010
Figure 894531DEST_PATH_IMAGE011
and
Figure 284055DEST_PATH_IMAGE012
the method comprises the steps of calculating symmetrical potential well positions and potential barrier heights for stochastic resonance system parameters, and when an original signal acts on the potential well as an input, forming an effect similar to resonance if the parameters of the potential well are matched with signal frequency and noise energy, wherein particles are subjected to periodic transition in the two potential wells, and the noise energy is transferred to the signal by the wall of the potential well, so that the purposes of signal denoising and characteristic amplification are achieved.
2. The stochastic resonance system-based frequency-converted signal denoising method of claim 1, wherein normalization is adoptedThe transformation method is used for enabling the system to realize stochastic resonance under the condition of large parameters when the parameters in the bistable system
Figure 82859DEST_PATH_IMAGE011
And
Figure 38177DEST_PATH_IMAGE012
when the value is not 1, taking:
Figure 798323DEST_PATH_IMAGE013
Figure 206301DEST_PATH_IMAGE014
and
Figure 811726DEST_PATH_IMAGE015
substituting the stochastic resonance kinetic model for a new position and time dimension and simplifying to obtain:
Figure 986266DEST_PATH_IMAGE016
the transformed stochastic resonance system parameters are all 1, and the original time scale
Figure 199204DEST_PATH_IMAGE017
Through transformation into
Figure 842281DEST_PATH_IMAGE015
The corresponding frequency scale is original
Figure 999200DEST_PATH_IMAGE018
Thereby passing through the parameters
Figure 538897DEST_PATH_IMAGE011
Can be designed such that the input signal isAnd the small parameter input condition required by the system is met.
3. The stochastic resonance system based frequency-converted signal denoising method of claim 1, wherein when estimating the frequency conversion coefficient of the signal, when the input signal is input
Figure 998434DEST_PATH_IMAGE019
Signal frequency of
Figure 191125DEST_PATH_IMAGE020
When the time variation occurs, a variable parameter stochastic resonance system is adopted, iterative search is carried out by utilizing a signal time variation coefficient, and parameters are designed
Figure 607194DEST_PATH_IMAGE021
The time-varying characteristic which is the same as the frequency of the input signal is kept, after normalization calculation, the variable frequency signal is actually equivalent to a stable frequency for a stochastic resonance system, and the input condition of the stochastic resonance phenomenon is met on the premise, and the model at the moment can be expressed as follows:
Figure 860452DEST_PATH_IMAGE022
the equivalent frequency of the signal after the normalized transformation is
Figure 602143DEST_PATH_IMAGE023
On one hand, the method meets the condition of small parameters, on the other hand, the equivalent transformation of the input signal frequency in the calculation process is kept, the frequency is equivalent to the frequency of the system and is not transformed any more, meanwhile, the equilibrium position is kept unchanged in the model change process, and then the discretization solution is carried out on the model equation by using a 4-order Runge-Kutta method (the method comprises the steps of (1)
Figure 937922DEST_PATH_IMAGE024
To solve for step size):
Figure 360944DEST_PATH_IMAGE025
。
4. the stochastic resonance system-based frequency-converted signal denoising method of claim 3, wherein when estimating the frequency conversion coefficient of the signal, if the variation parameter of the original signal, the system initial parameter
Figure 468708DEST_PATH_IMAGE026
Are unknown, and fixed stochastic resonance system parameters are adopted to obtain decision coefficients
Figure 362059DEST_PATH_IMAGE027
：
Figure 719223DEST_PATH_IMAGE028
Wherein the content of the first and second substances,
Figure 8253DEST_PATH_IMAGE029
and
Figure 991031DEST_PATH_IMAGE030
respectively representing the system output signal and its average value,
Figure 605683DEST_PATH_IMAGE031
refers to the fitting result of the output signal.
CN202110822703.2A 2021-07-21 2021-07-21 Variable frequency signal denoising method based on stochastic resonance system Pending CN113688502A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202110822703.2A CN113688502A (en) 2021-07-21 2021-07-21 Variable frequency signal denoising method based on stochastic resonance system

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202110822703.2A CN113688502A (en) 2021-07-21 2021-07-21 Variable frequency signal denoising method based on stochastic resonance system

Publications (1)

Publication Number Publication Date
CN113688502A true CN113688502A (en) 2021-11-23

Family

ID=78577547

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202110822703.2A Pending CN113688502A (en) 2021-07-21 2021-07-21 Variable frequency signal denoising method based on stochastic resonance system

Country Status (1)

Country Link
CN (1) CN113688502A (en)

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114649001A (en) * 2022-03-17 2022-06-21 厦门大学 Method for extracting underwater acoustic signal features of commercial fan based on self-adaptive stochastic resonance
CN116222750A (en) * 2023-03-22 2023-06-06 哈尔滨工程大学 Stochastic resonance detector and method suitable for high-frequency narrow pulse width acoustic beacon signals

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114649001A (en) * 2022-03-17 2022-06-21 厦门大学 Method for extracting underwater acoustic signal features of commercial fan based on self-adaptive stochastic resonance
CN114649001B (en) * 2022-03-17 2024-06-04 厦门大学 Underwater acoustic signal feature extraction method for operation fan based on self-adaptive stochastic resonance
CN116222750A (en) * 2023-03-22 2023-06-06 哈尔滨工程大学 Stochastic resonance detector and method suitable for high-frequency narrow pulse width acoustic beacon signals

Similar Documents

Publication Publication Date Title
CN113688502A (en) Variable frequency signal denoising method based on stochastic resonance system
WO2022165737A1 (en) Method for diagnosing early weak fault signal features of marine machinery
CN103674001B (en) A kind of optical fibre gyro denoising method based on strengthening self-adaptation time-frequency method
CN112255492B (en) Single-phase grounding high-resistance fault identification method for power distribution network under strong noise background
CN110135291B (en) Parameter estimation method for low signal-to-noise ratio signal
CN108108672B (en) Random resonance current weak information identification method based on linear search strategy
CN110376575B (en) Low-frequency line spectrum detection method based on damping parameter matching stochastic resonance
CN107800659B (en) LFM signal modulation parameter estimation method under Alpha stable distribution noise
CN109682526A (en) A kind of dynamic decoupling method of multi-dimension force sensor
CN109359378A (en) A kind of Weak Signal Detection Method of piecewise nonlinear bistable system
CN106451498A (en) Low frequency oscillation modal identification method based on improved generalized morphological filtering
Zhang et al. Signal detection based on second-order underdamped tristable stochastic resonance and its application to weak fault diagnosis
CN114280366B (en) Sinusoidal signal frequency estimation method based on improved frequency interpolation algorithm
CN104122456A (en) Variable step size monostable stochastic resonance weak signal detection method
CN108090270A (en) A kind of transient oscillation parameter identification method based on morphologic filtering and blind source separating
Li et al. The research of weak fault signal detection based on the Duffing oscillator coupled synchronization
CN115935143A (en) Fault signal detection method for plasticity controllable slope stochastic resonance
CN102256201A (en) Automatic environmental identification method used for hearing aid
CN111351645A (en) Weak fault signal diagnosis method for grain mechanical equipment
CN113541729B (en) Time-frequency graph denoising method based on time-frequency matrix
CN112929053B (en) Frequency hopping signal feature extraction and parameter estimation method
Liu et al. Method for acoustic leak detection of fast reactor steam generator using maximum modulus based on wavelet transform
Wu Application of adaptive length morphological filtering in gearbox bearing fault recognition in quantum domain
Shen et al. TWT output signal denoising based on improved wavelet threshold
Wu et al. A time domain estimation algorithm for speech signal pitch period

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication