CN104155518A - Signal frequency detection method based on stochastic resonance - Google Patents

Abstract

The invention discloses a signal frequency detection method based on stochastic resonance. The method comprises the following steps: (1), selecting any one stochastic resonance system parameter set from the following five kinds of stochastic resonance system parameter sets: a and b, a and h, a and k, b and h, as well as h and k; (2), after the parameter set is selected, determining all parameters of a stochastic resonance system; (3), adjusting the main parameters so as to enable the stochastic resonance system to produce resonance, and finely adjusting the auxiliary parameters; (4), if the frequency fx of the output signal power spectrum peak value of the stochastic resonance system keeps unchanged when the auxiliary parameters are adjusted finely, obtaining the signal frequency f according to the mathematical expression: f=fx*h/a; (5), if the frequency fx of the output signal power spectrum peak value of the stochastic resonance system is not fixed when the auxiliary parameters are adjusted finely, returning to the step (3). The signal frequency detection method disclosed by the invention solves the problem of the limitation that a small parameter signal value is far less than 1, the number of adjusted parameter is reduced, the parameters can be rapidly and efficiently adjusted, the parameters are traversed rapidly, optimal stochastic resonance can be found out conveniently, and the generation probability of stochastic resonance is improved greatly.

Description

A kind of signal frequency detection method based on accidental resonance

Technical field

The present invention relates to Technique of Weak Signal Detection field, be specifically related to a kind of signal frequency detection method based on accidental resonance.

Background technology

Since the ancient meteorological glacier of the research problems such as BenZi in 1981 propose accidental resonance (Stochastic resonance, SR) concept, SR phenomenon has been subject to paying close attention to widely.Stochastic Resonance Phenomenon is a kind of non-linear phenomena, it under certain condition, partial noise energy is transferred on signal, can make to be submerged in weak signal in noise and obtain resonance and strengthen falling the low noise while, greatly improve the signal to noise ratio (S/N ratio) of output, thereby realize the object that detects feeble signal from intense noise is disturbed.

Traditional detection method based on accidental resonance is subject to the restriction of adiabatic approximation theory, is only applicable to small parameter signal (signal amplitude, signal frequency, noise intensity are all much smaller than 1), and this has greatly restricted the application of accidental resonance in engineering reality.Although, representative have double sampling accidental resonance method, normalization variable metric method and a shift frequency scale transformation stochastic resonance method etc., for detecting, large parameter signal provides possibility in theory, but be all the detection for certain particular frequencies, and adjust ginseng means indefinite, there is no in other words Core constraint.

Summary of the invention

The invention provides a kind of signal frequency detection method based on accidental resonance, the method has solved small parameter signal value must be far smaller than 1 condition restriction, and reduced the quantity of adjusting ginseng, can adjust fast and efficiently ginseng, can travel through fast parameter, be beneficial to and search out best accidental resonance, significantly improve the probability that produces accidental resonance.

A signal frequency detection method based on accidental resonance, described method comprises the steps:

(1) choose any in following five kinds of stochastic resonance system parameter combinations: a and b, a and h, a and k, b and h, h and k.

(2), after selected parameter combinations, each parameter of stochastic resonance system definite follows following principle:

When selected a, b parameter group merge, determine that a is principal parameter, b while being second parameter, make h=1, k=1, the initial value of b is a ²/ 4 σ ²; When selected a, b parameter group merge, determine that b is principal parameter, a while being second parameter, make h=1, k=1, the initial value of a is when selected a, k parameter group merge, determine that a is principal parameter, k while being second parameter, make h=1, b=1, the initial value of k is when selected a, k parameter group merge, determine that k is principal parameter, a while being second parameter, make h=1, b=1, the initial value of a is when selected a, h parameter group merge, determine that a is principal parameter, h while being second parameter, make b=1, k=1, the initial value of h is a ²/ 4 σ ²; When selected a, h parameter group merge, determine that h is principal parameter, a while being second parameter, make b=1, k=1, the initial value of a is when selected b, h parameter group merge, determine that h is principal parameter, b while being second parameter, make a=1, k=1, the initial value of b is 1/4 σ ²h; When selected b, h parameter group merge, determine that b is principal parameter, h while being second parameter, make a=1, k=1, the initial value of h is 1/4 σ ²b; When selected h, k parameter group merge, determine that h is principal parameter, k while being second parameter, make a=1, b=1, the initial value of k is when selected h, k parameter group merge, determine that k is principal parameter, h while being second parameter, make a=1, b=1, the initial value of h is 1/4 σ ²k ².

(3) regulate principal parameter, make stochastic resonance system produce resonance, the second parameter initial value fine setting second parameter definite according to step (2).

(4) if while finely tuning second parameter, the frequency f of stochastic resonance system output signal power spectrum peak _xcan remain unchanged, according to mathematical expression: f=f _x* h/a, obtains signal frequency f.

(5) if the frequency f of fine setting stochastic resonance system output signal power spectrum peak during second parameter _xcan not fix, return to step (3).

In above steps: a, b are stochastic resonance system model parameter; H is sampling step length; K is signal amplification factor.

Accompanying drawing explanation

Fig. 1 is technical solution of the present invention process flow diagram.

Fig. 2 has described the process that stochastic resonance system adjusts ginseng to experience.

Fig. 3 has described and has not added the time-domain signal waveform of making an uproar.

Fig. 4 has described the time-domain signal waveform adding after making an uproar.

Fig. 5 has described the time-domain signal waveform of stochastic resonance system after parameter predigesting.

Fig. 6 has described the power spectrum waveform obtaining after parameter predigesting.

Embodiment

Below by the description to drawings and Examples, will be conducive to the understanding of the present invention.

Fig. 2 be in sampling than being 40, carrier frequency is 1Hz, parameter b, h, k fix, to once experiment, parameter a increases progressively and obtains that data paint out from one to 10,000 equal proportion very much, the horse-saddle of certain higher gained of signal to noise ratio (S/N ratio) is standard more.As another, for my hypothesis of accidental resonance, there is ergodic theorem, so Fig. 2 has general significance.And between first minimal value to the second minimal value, output top, all in same position, correctly detects the feeble signal frequency in very noisy.

1. bi-stable stochastic resonance theory model

According to Stochastic Resonance Theory, the coefficient bistable system model of periodic signal and noise is:

dx/dt＝ax-bx ³+[s(t)+n(t)]k； (1)

In formula, a and b are the structural parameters of bistable system; S (t) is weak periodic signal; N (t) is white noise.

Above formula is a kind of Nonlinear Stochastic Differential Equation, can carry out numerical solution by quadravalence Runge-Kutta method.Specific algorithm is as follows:

$\left\{\begin{array}{c}{k}_1=h({\mathrm{ax}}_n-{\mathrm{bx}}_n^3+s_n)\\ k_2=h[a(x_n+\frac{k_1}{2})-b{(x_n+\frac{k_1}{2})}^3+s_n]\\ k_3=h[a(x_n+\frac{k_2}{2})-b{(x_n+\frac{k_2}{2})}^3+s_{n+1}]n=\mathrm{1,2},\·\·\·,\mathrm{Length}\left(s_n\right)-1;\\ k_4=h[a(x_n+k_3)-b{(x_n+k_3)}^3+s_{n+1}]\\ x_{n+1}=x_n+\frac{1}{6}(k_1+{2k}_2+{2k}_3+k_4)\end{array}\right.---\left(2\right)$

In formula, s _nand x _nrespectively n the sampled value of bistable system input S (t)=k (u (t)+n (t)) and output X (t), h=1/f _s(f _sfor sample frequency) be numerical evaluation step-length.

When measured signal meets the theoretical small parameter condition of adiabatic approximation, calculate step-length and directly get the inverse of sample frequency, by regulating bistable system structural parameters just can reach good resonance state.And when measured signal is large parameter signal, the method existing is at present mostly to regulate four parameters to reach to produce resonance, to break through adiabatic approximation theory, is only applicable to the restriction of small parameter, thereby is applied to the large parameter signal in engineering reality.

Be provided with the signals and associated noises of a large parameter, signal frequency is f, and sample frequency is f _sif this signal can produce accidental resonance, can select and regulate a and b, a and h, a and k, b and h, h and the arbitrary parameter combinations of k, detect the feeble signal frequency in very noisy.

2. select the embodiment of a and b parameter combinations:

(1) first produce sampling than being 400, carrier frequency is 1Hz, the cycle sine wave signal that signal amplitude A is 1, as shown in Figure 3.

(2) Fig. 3 waveform is added after white Gaussian noise, signal to noise ratio (S/N ratio) is-10dB.As shown in Figure 4.

(3) Selecting All Parameters is combined as a and b, and to get a be principal parameter, h=1, k=1.

(4) parameter a increases progressively since 1, until produce accidental resonance (produce accidental resonance decision method: peak value account for summed power spectrum whether in 0.2 left and right and peak value not at power spectrum initiating terminal), this example a=40.

(5) according to b=a ²/ 4 σ ²determine the initial value of parameter b, owing to being under low signal-to-noise ratio, so σ ²can directly be tried to achieve by noisy signal, substitution formula obtains b=140.

(6) regulate parameter b, find that spectrum peak position does not change, obtain f _s=40, f=f _s* h/a=1, as shown in Figure 5, Figure 6, wherein Fig. 5 is time domain waveform, Fig. 6 is power spectrum waveform, and has only shown 1/80th.

Other parameter combinations is the same, wherein for a, h parameter combinations a=1.5, h=26; For a, k parameter combinations a=40, k=12; For b, h parameter combinations b=0.002, h=40; For h, k combines h=40, k=0.045; Can obtain the result of Fig. 5, Fig. 6.

Claims (1)

1. the signal frequency detection method based on accidental resonance, described method comprises the steps:

(1) choose any in following five kinds of stochastic resonance system parameter combinations: a and b, a and h, a and k, b and h, h and k;

(2), after selected parameter combinations, each parameter of stochastic resonance system definite follows following principle:

When selected a, b parameter group merge, determine that a is principal parameter, b while being second parameter, make h=1, k=1, the initial value of b is a ²/ 4 σ ²;

When selected a, b parameter group merge, determine that b is principal parameter, a while being second parameter, make h=1, k=1, the initial value of a is

When selected a, k parameter group merge, determine that a is principal parameter, k while being second parameter, make h=1, b=1, the initial value of k is

When selected a, k parameter group merge, determine that k is principal parameter, a while being second parameter, make h=1, b=1, the initial value of a is

When selected a, h parameter group merge, determine that a is principal parameter, h while being second parameter, make b=1, k=1, the initial value of h is a ²/ 4 σ ²;

When selected a, h parameter group merge, determine that h is principal parameter, a while being second parameter, make b=1, k=1, the initial value of a is

When selected b, h parameter group merge, determine that h is principal parameter, b while being second parameter, make a=1, k=1, the initial value of b is 1/4 σ ²h;

When selected b, h parameter group merge, determine that b is principal parameter, h while being second parameter, make a=1, k=1, the initial value of h is 1/4 σ ²b;

When selected h, k parameter group merge, determine that h is principal parameter, k while being second parameter, make a=1, b=1, the initial value of k is

When selected h, k parameter group merge, determine that k is principal parameter, h while being second parameter, make a=1, b=1, the initial value of h is 1/4 σ ²k ²;

(3) regulate principal parameter, make stochastic resonance system produce resonance, the second parameter initial value fine setting second parameter definite according to step (2);

(4) if while finely tuning second parameter, the frequency f of stochastic resonance system output signal power spectrum peak _xcan remain unchanged, according to mathematical expression: f=f _x* h/a, obtains signal frequency f;

(5) if the frequency f of fine setting stochastic resonance system output signal power spectrum peak during second parameter _xcan not fix, return to step (3);

Wherein: a, b are stochastic resonance system model parameter; H is sampling step length; K is signal amplification factor.