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Recently, the stochastic resonance effect has been widely used by the method of discovering and extracting weak periodic signals from strong noise through the stochastic resonance effect. The detection of the single-frequency weak signals by using stochastic resonance effect is widely used. However, the detection methods of the multifrequency weak signals need to be researched. According to the different frequency input signals of a given system, this paper puts forward a detection method of multifrequency signal by using adaptive stochastic resonance, which analyzed the frequency characteristics and the parallel number of the input signals, adjusted system parameters automatically to the low frequency signals in the fixed step size, and then measured the stochastic resonance phenomenon based on the frequency of the periodic signals to select the most appropriate indicators in the middle or high frequency. Finally, the optimized system parameters are founded and the frequency of the given signals is extracted in the frequency domain of the stochastic resonance output signals. Compared with the traditional detection methods, the method in this paper not only improves the work efficiency but also makes it more accurate by using the color noise, the frequency is more accurate being extracted from the measured signal. The consistency between the simulation results and analysis shows that this method is effective and feasible.

Now, we need to find and extract useful signal through the signal detection in engineering technology and scientific research. The traditional method to detect signal usually uses linear filtering, wavelet analysis [

With the development of the theory of stochastic resonance, the method of finding and extracting weak periodic signals from strong noise by stochastic resonance effect has been widely used in various fields of science such as nerve physiology, intelligence theory, nonlinear optics, signal processing, communication engineering, and sociology [

It is mainly used to realize stochastic resonance through adjusting system parameters manually or increasing the strength of noise so that we can find and extract the unknown multiple frequency signal. Due to the manual, adjusting has low work efficiency, and cannot achieve continuous search which will omit part of the signal, and it is difficult to find and search the optimal system parameters which will certainly omit part of the signal. This paper combines the theory of stochastic resonance and adaptive algorithm to put forward a kind of adaptive stochastic resonance detection method for multiple-frequency signal, respectively, of the low frequency and high frequency input signals. Based on the traditional single-frequency weak signal detection, selected the SNR to be a measurement index of the generation of stochastic resonance and reducing the range of parameter values by the threshold analysis, this method can find the optimal system parameters effectively and can detect a multiple weak periodic signals. A large number of simulation results show that the output signal of stochastic resonance system will be interfered by some noise which will lead to distortion of waveform slightly. Therefore, this paper makes processing the output signal of stochastic resonance by using the autocorrelation method which only changes the amplitude and phase, without changing the frequency. It can reduce the impact of noise, make the waveform more similar to measured signal, highlight the frequency of the signal cycle component, and enhance the SNR.

The methods to detect the high-frequency signals are sub-sampled, frequency-shifted and rescaling, wavelet analysis [

This paper uses the bistable system model: Langevin equation. It is actually an overdamped bistable system model driven by cycle, and its mathematical expression is [

As shown in Figure

When

Adaptive stochastic resonance signal detection involves two important factors: measurement index and iterative algorithm.

This paper uses the fourth-order Runge-Kutta method to solve the nonlinear systems. Set the sample step

Firstly, to set the system parameters, to input the signal to be measured with noise, to fix the step size, and to select the appropriate value range of parameter, increase the step size during this interval gradually to adjust the system parameters

Secondly, to use the Runge-Kutta algorithm to take numerical simulation to the corresponding system of each parameter, every parameter

Then, to calculate the SNR according to (

Finally, to reset nonlinear bistable system based on the optimal parameters to drive the signal to be measured with noise, generate stochastic resonance in this system. The output signal can show the signal to be measured to the greatest extent. The frequency corresponding to the spectrum peak in the spectrum diagram of the output signal is the frequency of the signal to be measured.

Let the input signal to be tested is

(a) The input signal to be measured. (b) The input signal to be measured contains white Gaussian noise. (c) The stochastic resonance output signal. (d) The spectrum figure of the stochastic resonance output signal.

Let the input signal be a constant

The variation curve of SNR while adjusting the system parameter

However, the frequency of low-frequency signal is prominent by the processing of the stochastic resonance system and is easy to be extracted. Although, as the Figure

Define the autocorrelation function of the signal

The output signal by autocorrelation processing can be abbreviated as

Compared to the original noise signal to be measured, the amplitude and phase of the two signals have changed, but the frequency is not changed. It improves the SNR to a certain extent. Therefore, this paper takes advantage of this feature to postprocess the output signal of stochastic resonance (see Figure

(a) The time-domain diagram of stochastic resonance output signal after correlation processing and (b) the spectrum diagram of stochastic resonance output signal after correlation processing.

When the input signal to be measured is the multi-frequency weak signal and parallel input, the multi-frequency input signal to be tested is

(a) The multi-frequency input signal to be measured. (b) The multi-frequency input signal to be measured contains white Gaussian noise. (c) The stochastic resonance output signal. (d) The spectrum figure of the stochastic resonance output signal.

The variation curve of SNR while adjusting the system parameter

(a) The time-domain diagram of stochastic resonance output signal after correlation processing. (b) The spectrum diagram of stochastic resonance output signal after correlation processing.

According to (

Stochastic resonance of the output signal spectrum is caused by the input signal and noise, as

In the measurement of the actual engineering, such as mechanical failure diagnosis, most of the signal to be measured is the high-frequency signal, and the noise is often colored noise, rather than idealized Gaussian white noise.

In the field of classical stochastic resonance, most theoretical studies only discuss the linear response of single frequency weak signal, and it can be observed clearly that the output signal of stochastic resonance system has some distortion. Compared to the original sinusoidal signal, the output signal is more similar to a rectangular wave. Depending on the nature of the rectangular wave, the Fourier expansion is

Let the input signal be measured as

It constantly approachs the frequency of the signal being measured

The steps of adaptive stochastic resonance in the high-frequency signal detection are as follows.

Set the system parameters, select the appropriate value interval, and fix the step size

Make numerical simulation of each

Sharp peaks will appear in the curve which is drawn above, and each frequency corresponding to the peak is the frequency of the signal to be measured

The flow chart is shown in Figure

Let the system parameters

The change curve about the reciprocal of the stochastic resonance output signal spectrum peak with the adjustment of

Let the input signal be detected with multiple high frequency as follows:

The change curve about the reciprocal of the stochastic resonance output signal spectrum peak with the adjustment of

The flow chart.

In order to meet the needs of practical engineering, this paper combined the adaptive algorithm with stochastic resonance theory. According to the frequency characteristics of the input signal to be tested, it proposed a feasible and effective adaptive stochastic resonance signal detection. Considering the actual situation, it improves work efficiency to a certain extent and has great value and development prospects in the measurement of the actual engineering. This paper chooses the SNR and the power spectrum of the autocorrelation function estimates as the index. The characteristics of the signal to be measured contain a lot of complexity in practical applications. In the actual engineering, we can choose a more precise measurement of indicators to measure the generation of stochastic resonance effect. Among the system parameters, noise intensity and the frequency of the signal being measured, which have a close relationship. We can analyze the degree of association by genetic algorithm to further expand the system of stochastic resonance signal detection.

This work was supported by National Natural Science Foundation of China (nos. 61104062 and 61174077), Jiangsu Qing Lan Project, and PAPD.