CN105067025A - Method for utilizing monostable system stochastic resonance effect to detect weak signals - Google Patents
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Abstract
The invention provides a method for utilizing a monostable system stochastic resonance effect to detect weak signals. Based on a stochastic resonance theory, the method utilizes noise rather than suppresses noise, by adjusting a system parameter and intensity of noise injected to the system for multiple times, enables a system output signal-to-noise ratio to be optimal, and the system output signal-to-noise ratio can be maximally improved, thereby realizing optimal detection of weak signals. The method provided by the invention is particularly suitable for detection of low signal-to-noise ratio and low frequency weak signals in mechanical failure and electronic failure detection.
Description
Technical Field
The invention belongs to a method for detecting weak signals under the condition of low signal-to-noise ratio, and particularly relates to a method for detecting weak signals by using a monostable system stochastic resonance effect.
Background
The primary task of weak signal detection is to improve the signal-to-noise ratio in order to detect useful weak signals from strong noise. The detection of weak signals can improve the measurement sensitivity and the lower limit of the detection, so the method is widely applied to the technical fields of physics, chemistry, biology and many engineering. The commonly adopted weak signal detection method is to suppress noise to extract a weak signal, and the method is useless under the condition of very low frequency of a strong noise background and a signal.
When the nonlinearity of the system and the input signal and noise are matched, the output signal-to-noise ratio of the system is optimal, and the nonlinear phenomenon is stochastic resonance. The concept of stochastic resonance was proposed in 1981 by the italian physicist roberto benzi, the american physicist alfonsutra and the italian physicist angelo vulpoiani et al in the study of the problem of ancient weather glaciers. When the system with noise generates stochastic resonance, part of noise energy can be converted into energy of useful signals, so that the output signal-to-noise ratio of the system is greatly improved, namely, noise with certain intensity is added to a specific system, and the performance of signal detection can not be improved on the contrary.
At present, the stochastic resonance-based detection signal model is generally a bistable system or a piecewise linear system model. Wherein,
(1) the bistable model satisfies the equation
WhereinIn order to input the signal, the signal is,in order to be a noise, the noise is,,function of potential energy of
(2) The piecewise linear model satisfies the equation
When a bistable model is used for detecting signals, model parameters are related to system characteristics, and when the system parameters are changed, the system characteristics can be changed along with the change of the system parameters, and two parameters of a system and a system b need to be adjusted; the piecewise linear system needs to adjust three parameters of a, b and c, and the model is complex to construct and is not beneficial to engineering application.
Disclosure of Invention
In order to solve the above problems, the present invention provides a method for detecting weak signals by using a monostable system stochastic resonance effect, the method comprising the steps of:
the method comprises the following steps: initializing monostable systemsB in (1),(ii) a In the case of the system described above,in order to output the signal for the system,as a parameter of the structure of the system,is additive white Gaussian noise, s (t) is a periodic signal,,is multiplicative gaussian distributed white noise injected into the system.
Step two: selecting a fixed system parameter b or multiplicative Gaussian distribution white noiseOne, the other, until the signal-to-noise ratio of the system output signal reaches a maximum;
step three: fixing the last value of the adjusted object in the previous step, and adjusting the other value until the signal-to-noise ratio of the output signal of the system reaches the maximum.
Step four: and returning to execute the step three until the output signal-to-noise ratio of the system is not increased any more.
Further, the system outputs a signalThe signal-to-noise ratio is calculated after a fourier transform (FFT).
Further, system configuration parametersThe adjustment range is (0, 5).
Further, multiplicative Gaussian distribution white noiseThe adjustment range of the intensity D is (0, 1).
The invention has the beneficial effects that:
aiming at the defects that the existing bistable stochastic resonance and piecewise linear stochastic resonance detection weak signals need more adjustment parameters and are not beneficial to engineering application, the invention provides a weak periodic signal detection method based on monostable stochastic resonance. The invention is especially suitable for detecting low signal-to-noise ratio and low-frequency weak characteristic signals such as mechanical fault and electronic fault detection.
Drawings
FIG. 1 is a block diagram of a monostable system of the invention.
FIG. 2 is a flow chart of weak low frequency periodic signal detection according to the method of the present invention.
Fig. 3 is a diagram of a simulated signal time domain waveform.
Fig. 4 is a simulated signal amplitude spectrum.
FIG. 5 is a diagram of adjusting system configuration parametersAnd the post monostable system outputs a signal amplitude spectrogram.
FIG. 6 is a graph showing adjustment of the intensity of multiplicative white Gaussian noiseAnd the post monostable system outputs a signal amplitude spectrogram.
FIG. 7 shows multiple adjustment parametersAndand outputting a signal amplitude spectrogram when the signal-to-noise ratio is not increased any more by the system.
Detailed Description
Aiming at the defects that the existing bistable stochastic resonance and piecewise linear stochastic resonance detection weak signals need more adjustment parameters and are not suitable for engineering, the invention provides a weak periodic signal detection method based on monostable stochastic resonance. The details will be described below.
In order to realize the method of the invention, a monostable model system is firstly established as follows:a block diagram representation of the system is shown in fig. 1.
Function of potential energy thereofIn the monostable form, the meaning of the individual parameters is:in order to output the signal for the system,as a parameter of the structure of the system,is an additive white gaussian noise, and is,to be noisedThe period of the signal that is flooded is,is multiplicative white gaussian noise injected into the system with an average of 0 and an intensity of D.
According to the stochastic resonance theory and a plurality of experimental researches and parameters of the applicantThe adjustment range is (0, 5), and the multiplicative white Gaussian noiseThe adjustment range of the intensity D is (0, 1).
The method for detecting the weak signal by using the model comprises the following steps:
the method comprises the following steps: initializing monostable systemsB in (1),。
Step two: selecting a fixed system parameter b or multiplicative white Gaussian noiseOne, and the other, until the signal-to-noise ratio of the system output signal is maximized.
Step three: fixing the last value of the adjusted object in the previous step, and adjusting the other value until the signal-to-noise ratio of the output signal of the system reaches the maximum.
Step four: and repeating the third step until the output signal-to-noise ratio of the system is not increased any more.
By adopting the method, only one system parameter needs to be adjusted, the method of injecting multiplicative white Gaussian noise into the monostable system is adopted, and the detection of weak low-frequency periodic signals is realized by adjusting the system parameter and the noise intensity of the injection system.
The technical principle of the system is as follows: monostable systemHaving only one steady stateWhen multiplicative white Gaussian noise is injected into the monostable system, the system becomesIf the multiplicative noise intensity is D, the system has two working states, one is steady stateOne is unstable. When the system inputs a weak signal containing noise, the system parameters are adjustedThe number and the strength of the injected multiplicative noise enable the nonlinear system to generate a stochastic resonance phenomenon, and convert a part of noise energy into signal energy, thereby greatly improving the output signal-to-noise ratio of the system and detecting weak periodic signals.
It is emphasized that the b-adjustment is optionally fixed firstOr alternatively fix firstThe adjustment b is feasible and is selected according to actual use. The selectable design and the single adjustment mode of the monostable model enable the method to have stronger operability, improve the application range and reduce the design difficulty.
Preferably, the system outputs a signalThe signal-to-noise ratio is calculated after a fourier transform (FFT).
Specific applications of the method of the present invention are illustrated below with reference to fig. 2 to 6. Fig. 2 is a schematic diagram of a signal detection process. Taking input signalsWhereinIn order to be the amplitude of the signal,which represents the time of day,representing the frequency of the signal. Additive white Gaussian noise input into monostable system together with signalIs zero mean Gaussian distributed white noise, whichHas a strength of. In this example take，，=0.1 Hz. Fig. 3 is a time domain waveform diagram of a simulated signal after additive white gaussian noise is added to an input signal, and it can be seen that the input signal is completely submerged by the noise. FIG. 4 is a graph of simulated signal amplitude spectra of an input signal summed with additive white Gaussian noise from which the signal cannot be distinguishedSo that it cannot detect。
The specific implementation of the example comprises the following steps:
the method comprises the following steps: initializing monostable modelsIncluding system parametersAnd injected multiplicative white Gaussian noiseStrength of. Initialization value fetch in this example=0.2，=0.4。
Step two: simulation signal adding monostable system。
Based on the stochastic resonance theory, the output signal-to-noise ratio of the system is
Wherein,.
WhereinFor a characteristic transfer rate between two states of the system without signal input,the derivative of the characteristic transfer rate between two states of the system with respect to the signal.
Step three: fixed injected multiplicative white gaussian noise intensityAdjusting system parameters. When in useWhen =0.6, the monostable system sendsStochastic resonance occurs, the output signal-to-noise ratio is 7 at the maximum, and the output signal amplitude spectrum is shown in fig. 5, and the signal existing at 0.1Hz can be obviously distinguished.
Step four: the parameters of the fixed system are=0.6, adjusting the intensity of multiplicative white Gaussian noise. When in useWhen the signal amplitude is 0.35, the monostable system generates stochastic resonance, the output signal-to-noise ratio is 12 at most, and the amplitude spectrum of the output signal is shown in fig. 6, so that the signal at 0.1Hz can be more obviously distinguished from the graph.
Step five: multiplicative white Gaussian noise in fixed step fourStrength ofFinal value taking and system parameter regulatingMaximizing the output signal-to-noise ratio of the system; then fix the system parameters toAdjusting multiplicative white Gaussian noiseStrength of. This step is repeated until the output signal-to-noise ratio no longer increases.
In this example when=0.05，And when the signal to noise ratio is not increased by 0.75, the output signal to noise ratio of the system is not increased any more. At this time, the output signal-to-noise ratio of the system is 25, and the amplitude spectrum of the output signal is shown in FIG. 7.
Simulation results show that: by the monostable system, weak low-frequency periodic signals submerged in noise can be well extracted by adjusting system parameters and the intensity of injected multiplicative white Gaussian noise and utilizing the characteristic of stochastic resonance. The system has few adjusting parameters, can reduce the system cost and is easy to realize engineering. In the embodiment, the output signal also contains noise, and can be cascaded with the monostable system to improve the output signal-to-noise ratio, and can also be further processed by adopting measures such as filtering, smoothing and the like.
The above description is only an example embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that are made within the technical scope of the present invention belong to the scope of the present invention
The invention has the beneficial effects that:
aiming at the defects that the existing bistable stochastic resonance and piecewise linear stochastic resonance detection weak signals need more adjustment parameters and are not beneficial to engineering application, the invention provides a weak periodic signal detection method based on monostable stochastic resonance. The invention is especially suitable for detecting low signal-to-noise ratio and low-frequency weak characteristic signals such as mechanical fault and electronic fault detection.
Claims (4)
1. A method for detecting weak signals by using the stochastic resonance effect of a monostable system, the method comprising the steps of:
the method comprises the following steps: initializing monostable systemsB in (1),(ii) a In the case of the system described above,in order to output the signal for the system,as a parameter of the structure of the system,is an additive white gaussian noise, and is,in the form of a periodic signal, the signal,is multiplicative gaussian distributed white noise injected into the system.
Step two: selecting a fixed system structure parameter b or multiplicative Gaussian distribution white noiseOne, the other, until the signal-to-noise ratio of the system output signal reaches a maximum;
step three: fixing the last value of the adjusted object in the previous step, and adjusting the other value until the signal-to-noise ratio of the system output signal reaches the maximum;
step four: and returning to execute the step three until the output signal-to-noise ratio of the system is not increased any more.
2. The method of claim 1, wherein the system outputs signals for weak signal detection using stochastic resonance effect of monostable systemThe signal-to-noise ratio is calculated after a fourier transform (FFT).
3. The method of claim 1, wherein the system is capable of detecting weak signals by using stochastic resonance effect of monostable systemStructural parametersThe adjustment range is (0, 5).
4. The method according to any of claims 1 to 3, wherein the weak signal is detected by using stochastic resonance effect of monostable system, multiplicative Gaussian distribution white noiseThe adjustment range of the intensity D is (0, 1).
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| CN106055802A (en) * | 2016-06-06 | 2016-10-26 | 石家庄铁道大学 | Fourth-order monostable stochastic resonance circuit |
| CN106338395A (en) * | 2016-10-27 | 2017-01-18 | 石家庄铁道大学 | Gear case fault diagnosis method based on six-order monostable system |
| CN106357349A (en) * | 2016-09-14 | 2017-01-25 | 青岛大学 | Signal detection method based on high-frequency oscillation resonance principle |
| CN108960032A (en) * | 2018-04-02 | 2018-12-07 | 安徽大学 | Tristable logic stochastic resonance method |
| CN110376575A (en) * | 2019-08-19 | 2019-10-25 | 西北工业大学 | A kind of low frequency spectrum lines detection method based on damping parameter matching accidental resonance |
| CN111351645A (en) * | 2019-11-22 | 2020-06-30 | 南京财经大学 | Weak fault signal diagnosis method for grain mechanical equipment |
| CN111783023A (en) * | 2020-06-16 | 2020-10-16 | 重庆邮电大学 | Application of frequency domain information exchange in cascade asymmetrical segmented stochastic resonance system |
| CN112162235A (en) * | 2020-09-08 | 2021-01-01 | 西北工业大学 | Smooth segmented stochastic resonance enhanced acoustic vector signal orientation method |
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| CN110376575A (en) * | 2019-08-19 | 2019-10-25 | 西北工业大学 | A kind of low frequency spectrum lines detection method based on damping parameter matching accidental resonance |
| CN110376575B (en) * | 2019-08-19 | 2022-09-02 | 西北工业大学 | Low-frequency line spectrum detection method based on damping parameter matching stochastic resonance |
| CN111351645A (en) * | 2019-11-22 | 2020-06-30 | 南京财经大学 | Weak fault signal diagnosis method for grain mechanical equipment |
| CN111783023A (en) * | 2020-06-16 | 2020-10-16 | 重庆邮电大学 | Application of frequency domain information exchange in cascade asymmetrical segmented stochastic resonance system |
| CN112162235A (en) * | 2020-09-08 | 2021-01-01 | 西北工业大学 | Smooth segmented stochastic resonance enhanced acoustic vector signal orientation method |
| CN112162235B (en) * | 2020-09-08 | 2022-11-11 | 西北工业大学 | Smooth segmented stochastic resonance enhanced acoustic vector signal orientation method |
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