CN113313102B - Random resonance chaotic small signal detection method based on variant differential evolution algorithm - Google Patents

Random resonance chaotic small signal detection method based on variant differential evolution algorithm Download PDF

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CN113313102B
CN113313102B CN202110878986.2A CN202110878986A CN113313102B CN 113313102 B CN113313102 B CN 113313102B CN 202110878986 A CN202110878986 A CN 202110878986A CN 113313102 B CN113313102 B CN 113313102B
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熊晨
王启凡
孙根
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Nanjing Tianlang Defense Technology Co ltd
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Abstract

The invention discloses a random resonance chaotic small signal detection method based on a variant differential evolution algorithm. In order to verify the feasibility of the algorithm, low-frequency and high-frequency small signal input simulation experiments are respectively carried out, and in the low-frequency small signal detection experiment, the output signal-to-noise ratio chaos variable-step-size firefly algorithm is averagely improved by 1.98 dB; in a high-frequency small signal detection experiment, small signals at a low-frequency section corresponding to the high-frequency small signals can be accurately recovered, and the existence of the high-frequency small signals is further deduced; simulation experiments are carried out on the actually measured sea clutter data, and the experimental results show that the method can effectively detect the small chaotic signals submerged in the sea clutter background.

Description

Random resonance chaotic small signal detection method based on variant differential evolution algorithm
Technical Field
The invention belongs to the field of chaotic small signal detection, and particularly relates to a random resonance chaotic small signal detection method based on a variant differential evolution algorithm.
Background
The research direction of the weak signal detection method can not only start from the small signal itself and search the difference between the small signal and background noise to verify the existence of the small signal, but also start from the background noise and realize the enhancement of the small signal by utilizing a stochastic resonance means to obtain the small signal, and the detection method can also be researched by combining the stochastic resonance theory for chaotic small signals under the background of strong sea clutter.
Theory of stochastic resonance is represented by Benzi]A mathematical analysis method is proposed by people in the research of climate problem of periodic change in the age of glaciers, and is used for qualitatively describing solar revolution eccentricityThe alternating phenomenon of the cold and hot climatic periods of the earth caused by the periodic variation of the rate. Afterwards, the stochastic resonance theory is widely varied and applied to various fields such as physics, chemistry, signal processing and the like, and researchers at home and abroad obtain abundant research results in the field of weak signal detection. In 1998, when Frank researches weak electric field and magnetic field signals, Frank utilizes a stochastic resonance theory to improve the signal-to-noise ratio by increasing the chaotic power spectral density of the weak signals so as to realize the detection of the weak signals; aditya in 2003 proposed a quantized stochastic resonance detector suitable for detecting weak sinusoidal signals in noise with detection performance superior to that of matched filters; in 2001, Wang Li ya et al put forward a basic method for detecting weak signals by stochastic resonance, and have a prospect on the application prospect in the field of mechanical fault diagnosis; the Wenxison et al put forward a mechanical fault early detection method based on stochastic resonance in 2009, and have profound influence on fault diagnosis and prediction theory development; in 2018, when a rehong tablet and the like are used for researching a weak signal detection method under a sea clutter background, a self-adaptive stochastic resonance weak signal detection method is provided, the multi-parameter optimization of a Duffing oscillator stochastic resonance system is realized, and the detection performance is improved. How to find the optimization algorithm of the multi-parameter synchronous tuning of the Duffing oscillator stochastic resonance system becomes a breakthrough of the stochastic resonance chaotic small signal detection method under the background of sea clutter.
Disclosure of Invention
The purpose of the invention is as follows: aiming at the defect that the traditional stochastic resonance small signal detection method cannot synchronously adjust and optimize multiple parameters, the stochastic resonance chaotic small signal detection method based on the variant differential evolution algorithm is provided, and stochastic resonance is realized to obtain high-frequency and low-frequency small signals submerged in strong noise.
The invention adopts the following technical scheme: the random resonance chaotic small signal detection method based on the variant differential evolution algorithm comprises the following steps:
firstly, performing phase space reconstruction on a sea clutter signal x (n) to be detected by adopting a C-C method, and determining the delay time of a phase space;
step two, establishing chaotic small signals and noise signalsObtaining the core parameters of the system based on the delay time by using the Duffing oscillator stochastic resonance equation under the combined action
Figure 964765DEST_PATH_IMAGE001
、
Figure 74803DEST_PATH_IMAGE002
、
Figure 921186DEST_PATH_IMAGE003
；
Thirdly, utilizing a variant differential evolution algorithm to carry out pair on core parameters influencing the effect of the stochastic resonance detection
Figure 65860DEST_PATH_IMAGE001
、
Figure 444888DEST_PATH_IMAGE004
、
Figure 291491DEST_PATH_IMAGE005
Optimizing according to the obtained core parameters of the system
Figure 187902DEST_PATH_IMAGE001
、
Figure 311716DEST_PATH_IMAGE006
、
Figure 18903DEST_PATH_IMAGE003
And (3) carrying out stochastic resonance output on the input signal, and analyzing the spectral characteristics of the output signal to obtain the chaotic small signal.
Further, in the step one, the C-C phase space reconstructing step includes:
step 1.1, dividing the sea clutter signals x (N), N =1,2,.. and N to be detected into t disjoint time rows with the length of N/t, and calculating the statistic S (m, N, r, tau) of each subsequence
Figure 103534DEST_PATH_IMAGE007
(1)
In the formula,
Figure 787325DEST_PATH_IMAGE008
is the first
Figure 500066DEST_PATH_IMAGE009
The correlation integral of the sub-sequences is,
Figure 627422DEST_PATH_IMAGE010
is the length of the data set and,
Figure 58404DEST_PATH_IMAGE011
is the search radius in the reconstruction space; m is the embedding dimension, τ is the time delay;
step 1.2, local maximum separation
Figure 310000DEST_PATH_IMAGE012
Zero point or for all radii
Figure 18193DEST_PATH_IMAGE013
The points in time at which the difference from each other is minimal. Selecting two radii with maximum and minimum corresponding values
Figure 565718DEST_PATH_IMAGE013
The difference is defined as
Figure 624941DEST_PATH_IMAGE014
(2)
According to the principle of statistics,
Figure 525901DEST_PATH_IMAGE013
is taken from
Figure 839333DEST_PATH_IMAGE015
In a ratio of (A) to (B),
Figure 308491DEST_PATH_IMAGE015
is the mean square of a time seriesThe difference, the equation is as follows:
Figure 714065DEST_PATH_IMAGE016
(3)
in the formula,
Figure 543349DEST_PATH_IMAGE017
is the mean of the statistics of all sub-sequences, and,
Figure 226134DEST_PATH_IMAGE018
、
Figure 725249DEST_PATH_IMAGE019
is a statistic defined according to the Brock-Decchert-Scheinkman BDS statistics,
Figure 235428DEST_PATH_IMAGE020
is the delta of the statistic of the sub-sequence,
Figure 353557DEST_PATH_IMAGE021
for a new indicator of determining the width of the embedding window,
Figure 15482DEST_PATH_IMAGE022
the corresponding point of the global minimum value is the width of the embedding window.
Further, the second step includes:
step 2.1, the Duffing oscillator stochastic resonance equation system under the combined action of a chaotic small signal and a noise signal is as follows:
Figure 810132DEST_PATH_IMAGE023
(4)
wherein,
Figure 331243DEST_PATH_IMAGE024
in order to output the signal for the system,
Figure 112117DEST_PATH_IMAGE025
in order to achieve a damping ratio,
Figure 520227DEST_PATH_IMAGE026
in order to be a function of the potential,
Figure 361144DEST_PATH_IMAGE027
in order to input the signals to the system,
Figure 103972DEST_PATH_IMAGE028
is an average value of 0 and a noise intensity of
Figure 813171DEST_PATH_IMAGE029
The white gaussian noise of (a) is,
Figure 449689DEST_PATH_IMAGE030
representing the shock function;
step 2.2, solving a formula according to a quadratic equation of unity to calculate a potential function
Figure 336873DEST_PATH_IMAGE031
Comprises three extreme points of
Figure 49221DEST_PATH_IMAGE032
The system critical value at this time is calculated as
Figure 703056DEST_PATH_IMAGE033
；
Step 2.3, if and only if the input signal amplitude
Figure 803868DEST_PATH_IMAGE034
When the signal, the noise and the system reach a matching cooperative relationship, partial energy of the noise signal is transferred to the signal, the signal enhancement is realized, namely, the signal enters a stochastic resonance state, and at the moment, the formula (4) is simplified as follows:
Figure 376800DEST_PATH_IMAGE035
(5)
equation (5) is the stochastic resonance system of a typical second-order Duffing vibrator, and the parameters
Figure 218854DEST_PATH_IMAGE036
、
Figure 286167DEST_PATH_IMAGE037
、
Figure 992217DEST_PATH_IMAGE038
To determine the core parameters of the Duffing vibrator stochastic resonance system.
Further, the detection method further comprises:
step four, utilizing a variant differential evolution algorithm to carry out pair on core parameters influencing the effect of the stochastic resonance detection
Figure 876997DEST_PATH_IMAGE036
、
Figure 550555DEST_PATH_IMAGE037
、
Figure 405247DEST_PATH_IMAGE039
Optimization is carried out, so that the bistable stochastic resonance system of the Duffing vibrator has the best signal detection effect.
Further, the third step includes:
step 3.1, initializing parameters, setting the initial population quantity asNPThe maximum number of iterations isGSecond, the dimension of the space variable isDCreating an initial population
Figure 605284DEST_PATH_IMAGE040
Randomly generating 0 th generationiThe individual isjDimension dereferencing:
Figure 536331DEST_PATH_IMAGE041
(6)
wherein,
Figure 556240DEST_PATH_IMAGE042
represents the firstiThe upper and lower limits of the value of the individual,
Figure 984597DEST_PATH_IMAGE043
is represented by (A)D,NP) Random numbers uniformly distributed in the interval;
step 3.2, calculating an objective function, wherein for a second-order Duffing oscillator stochastic resonance system, the signal-to-noise ratio of an output signal changes along with the change of system parameters, the signal-to-noise ratio can reflect the enhancement level of the system to chaotic small signals, and the objective function is as follows:
Figure 180086DEST_PATH_IMAGE044
(7)
in the formula (7), the reaction mixture is,
Figure 875510DEST_PATH_IMAGE045
in order to output a signal for the stochastic resonance system,
Figure 38507DEST_PATH_IMAGE046
signal-to-noise ratio of the output signal for the system;
and 3.3, performing mutation operation, namely performing mutation operation on the individuals by adopting a differential strategy, randomly selecting two parent individuals different from the individuals to be mutated, performing differential scaling on the two parent individuals, and synthesizing the two parent individuals with the individuals to obtain:
Figure 985734DEST_PATH_IMAGE047
(8)
Figure 160363DEST_PATH_IMAGE048
(9)
wherein,Frepresents an adaptive mutation operator and is characterized in that,
Figure 918366DEST_PATH_IMAGE049
representing iterationsgThe next generationiThe number of the individuals is small,
Figure 53812DEST_PATH_IMAGE050
is the value of the objective function that the optimal individual is,
Figure 194944DEST_PATH_IMAGE051
the value of the objective function of the current individual,
Figure 348713DEST_PATH_IMAGE052
is the value of the maximum objective function,
Figure 385939DEST_PATH_IMAGE053
is the minimum objective function value. The values of all individuals of the population are required to meet boundary conditions in the whole variation process, namely
Figure 274261DEST_PATH_IMAGE054
(10)
Step 3.4, crossover operation, pair iterationgLast individual
Figure 576673DEST_PATH_IMAGE055
And variant individuals
Figure 460315DEST_PATH_IMAGE056
And (3) performing cross calculation:
Figure 543809DEST_PATH_IMAGE057
(11)
in the formula (11), the reaction mixture is,crin order to be a cross-over factor,
Figure 903115DEST_PATH_IMAGE058
is composed of
Figure 386049DEST_PATH_IMAGE059
The intersection of the differential evolution algorithm is different from the intersection of each individual in the genetic algorithm;
step 3.5, selection operation, differential evolution algorithm utilizes greedy algorithm to carry out selection operation
Figure 265143DEST_PATH_IMAGE060
(12)
Step 3.6, updating the objective function value, calculating the signal-to-noise ratio of the output signal of the system according to the system parameter optimized by the current iteration times, comparing the signal-to-noise ratio output by the last iteration, and if the signal-to-noise ratio is smaller, performing a round of iteration optimization again; otherwise, outputting the optimizing parameter
Figure 801429DEST_PATH_IMAGE036
、
Figure 257818DEST_PATH_IMAGE061
、
Figure 154230DEST_PATH_IMAGE062
；
Step 3.7, outputting the optimal stochastic resonance, and when the iteration times reach the highest iteration timesGOutputting the stochastic resonance system parameters of the second-order Duffing oscillator corresponding to the maximum objective function value
Figure 402678DEST_PATH_IMAGE063
、
Figure 218187DEST_PATH_IMAGE037
、
Figure 37238DEST_PATH_IMAGE064
And carrying out stochastic resonance output on the input signal according to the obtained optimal parameter value, and analyzing the spectral characteristics of the output signal.
As a preferred embodiment of the present application, the detection method further comprises: step four, obtaining the optimal system parameters by using a variant differential evolution algorithm
Figure 237143DEST_PATH_IMAGE065
、
Figure 215463DEST_PATH_IMAGE037
、
Figure 77240DEST_PATH_IMAGE064
And analyzing the detection effect of the stochastic resonance chaotic small signals under the optimal parameters, comparing the time-frequency characteristics of the input and output signals of the stochastic resonance system of the Duffing oscillator, and judging whether the chaotic small signals submerged in the sea clutter background can be detected.
Has the advantages that: the method adopts a variant differential evolution algorithm optimization algorithm, and can ensure the occurrence probability of the variation at the initial stage of iteration, maintain the diversity of the population and prevent premature convergence by adding the self-adaptive variation operator; the optimal solution can be protected in the later iteration stage, the global search capability is improved, the system optimal parameter of the stochastic resonance system is found by utilizing the variant differential evolution algorithm, the speed is high, the accuracy is high, and the requirement of high-precision matching of the system parameter can be met. In order to verify the feasibility of the algorithm, high-frequency and low-frequency small signal detection is carried out, the found optimal parameters are substituted into a two-dimensional Duffing oscillator stochastic resonance system to realize stochastic resonance, the high-frequency and low-frequency small signals under the non-Gaussian noise background are detected, the output signal-to-noise ratio is improved, and the detection precision of the high-frequency and low-frequency small signals is enhanced.
In order to verify the practicability of the algorithm, a chaos small target detection experiment based on the random resonance theory under the sea clutter background is carried out, wherein #54 sea clutter collected by an IPIX radar contains target signal data, and a target data interval is as follows: the primary target is 8 and the secondary target is 7: 10. The sea clutter data containing the target replaces the input signal of the stochastic resonance system of the Duffing oscillator, and the system optimized by the variant differential evolution algorithm outputs the system parameter corresponding to the maximum signal-to-noise ratio
Figure 898434DEST_PATH_IMAGE065
、
Figure 995703DEST_PATH_IMAGE066
、
Figure 703896DEST_PATH_IMAGE039
The existence of the chaotic small signal can be judged in the output signal spectrogram.
Drawings
In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art that other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a flow chart of a stochastic resonance chaotic small signal detection method based on a variant differential evolution algorithm according to the present invention;
FIG. 2 is a schematic diagram of the convergence of random system parameters optimized by a variant differential evolution algorithm;
FIG. 3 is a diagram of the parameter analysis results of a stochastic resonance system of a low-frequency small-signal variant differential evolution algorithm;
(a) inputting a signal diagram; (b) inputting a signal spectrogram; (c) outputting a signal diagram; (d) outputting a signal spectrogram;
FIG. 4 is a diagram of the parameter analysis results of the stochastic resonance system of the high-frequency small-signal variant differential evolution algorithm;
(a) inputting a signal diagram; (b) inputting a signal spectrogram; (c) outputting a signal diagram; (d) outputting a signal spectrogram;
FIG. 5 is a diagram of the detection effect of a stochastic resonance chaotic small signal under a sea clutter background;
(a) inputting a signal diagram; (b) inputting a signal spectrogram; (c) outputting a signal diagram; (d) and outputting a signal spectrogram.
Detailed Description
The technical scheme of the invention is further explained by combining the attached drawings and implementation.
The method applies the variant differential evolution algorithm to the parameter synchronous optimization of the stochastic resonance system, and by adding the self-adaptive mutation operator, the probability of occurrence of mutation can be ensured at the initial stage of iteration, the population diversity is maintained, and premature convergence is prevented; the optimal solution can be protected in the later iteration stage, and the global search capability is improved. Bistable stochastic resonance system parameters of variant pair Duffing vibrator
Figure 861208DEST_PATH_IMAGE063
、
Figure 405584DEST_PATH_IMAGE067
、
Figure 447490DEST_PATH_IMAGE064
Optimizing, setting the signal-to-noise ratio of the system output signal as an objective function,
in order to verify the effectiveness of the detection method, low-frequency and high-frequency small signal simulation experiments are respectively carried out; in order to ensure the practicability of the detection method, an experiment is carried out by utilizing the actually measured sea clutter signal.
The technical scheme is as follows:
(1) performing phase space reconstruction on the sea clutter signals x (n) to be detected by adopting a C-C method, and determining the core parameter embedding dimension and delay time of the phase space;
(2) the detection of the chaotic small signal is realized by utilizing the capability that the bistable stochastic resonance system of the Duffing vibrator can match with the small signal in the collaborative chaotic state, background noise and the system;
(3) using a variant differential evolution algorithm to influence system parameters of a stochastic resonance detection effect
Figure 525036DEST_PATH_IMAGE036
、
Figure 853249DEST_PATH_IMAGE061
、
Figure 868609DEST_PATH_IMAGE062
Optimizing to ensure that the bistable stochastic resonance system of the Duffing vibrator has the best signal detection effect;
(4) optimal system parameters obtained by using variant differential evolution algorithm
Figure 573260DEST_PATH_IMAGE036
、
Figure 3848DEST_PATH_IMAGE037
、
Figure 378329DEST_PATH_IMAGE062
And analyzing the detection effect of the stochastic resonance chaotic small signals under the optimal parameters, comparing the time-frequency characteristics of the input and output signals of the stochastic resonance system of the Duffing oscillator, and judging whether the chaotic small signals submerged in the sea clutter background can be detected.
As shown in FIG. 1, the invention provides a random resonance chaotic small signal detection method based on a variant differential evolution algorithm, which comprises the following steps:
(1) performing phase space reconstruction on the sea clutter signals x (n) to be detected by adopting a C-C method, and determining the core parameter embedding dimension and delay time of the phase space;
(1.1) dividing the sea clutter signals x (N), N =1, 2.. and N to be detected into t disjoint time columns, rounding the time columns with the length of N/t, and calculating the statistic S (m, N, r, tau) of each subsequence
Figure 271199DEST_PATH_IMAGE068
(1)
In the formula,
Figure 638595DEST_PATH_IMAGE069
is the first
Figure 441466DEST_PATH_IMAGE070
The correlation integral of the sub-sequences is,
Figure 111482DEST_PATH_IMAGE071
is the length of the data set and,
Figure 852167DEST_PATH_IMAGE072
for the search radius in reconstruction space, m is the embedding dimension, τ is the time delay;
(1.2) local maximum separation can be removed
Figure 39566DEST_PATH_IMAGE073
Zero point of (2) or for all search radii
Figure 821577DEST_PATH_IMAGE072
The points in time at which the difference from each other is minimal. Selecting two radii with maximum and minimum corresponding values
Figure 787128DEST_PATH_IMAGE074
The difference is defined as
Figure 264376DEST_PATH_IMAGE075
(2)
Wherein,u,vthe sequence representing the parameter represents any unknown in the range and, according to statistical principles,mthe value is between 2 and 5 and,
Figure 848942DEST_PATH_IMAGE074
is taken from the value of
Figure 114488DEST_PATH_IMAGE076
And
Figure 267251DEST_PATH_IMAGE077
in the above-mentioned manner,
Figure 356430DEST_PATH_IMAGE078
is the mean square error of the time series, the equation is as follows:
Figure 869320DEST_PATH_IMAGE016
(3)
in the formula,
Figure 501290DEST_PATH_IMAGE079
is the mean of the statistics of all sub-sequences, and,
Figure 684009DEST_PATH_IMAGE018
、
Figure 886583DEST_PATH_IMAGE080
is a statistic defined according to the Brock-Decchert-Scheinkman BDS statistics,
Figure 812950DEST_PATH_IMAGE081
is the delta of the statistic of the sub-sequence,
Figure 299426DEST_PATH_IMAGE021
for a new indicator of determining the width of the embedding window,
Figure 777681DEST_PATH_IMAGE022
the corresponding point of the global minimum value is the width of the embedding window.
(2) The detection of the chaotic small signal is realized by utilizing the capability that the bistable stochastic resonance system of the Duffing vibrator can match with the small signal in the collaborative chaotic state, background noise and the system;
(2.1) the Duffing oscillator stochastic resonance equation system under the combined action of a chaotic small signal and a noise signal is as follows:
Figure 841452DEST_PATH_IMAGE082
(4)
wherein,
Figure 446877DEST_PATH_IMAGE083
in order to output the signal for the system,
Figure 535662DEST_PATH_IMAGE064
in order to achieve a damping ratio,
Figure 325764DEST_PATH_IMAGE084
in order to be a function of the potential,
Figure 752197DEST_PATH_IMAGE085
in order to input the signals to the system,
Figure 410580DEST_PATH_IMAGE086
is white gaussian noise with an average value of 0 and a noise intensity of 0,
Figure 730703DEST_PATH_IMAGE087
representing the shock function.
(2.2) solving according to a quadratic equation of one elementSolving the formula can calculate a potential function
Figure 301493DEST_PATH_IMAGE088
Comprises three extreme points of
Figure 965955DEST_PATH_IMAGE089
Defining the barrier height of the potential function as
Figure 37816DEST_PATH_IMAGE090
. If the pole of the potential function is equal to the inflection point, the system critical value is calculated as
Figure 87812DEST_PATH_IMAGE091
，
Figure 609929DEST_PATH_IMAGE092
、
Figure 604430DEST_PATH_IMAGE093
Are parameters.
(2.3) if and only if the input signal amplitude
Figure 620927DEST_PATH_IMAGE034
When the signal, the noise and the system reach a matching cooperative relationship, partial energy of the noise signal is transferred to the signal, the signal enhancement is realized, namely the signal enters a stochastic resonance state, and at the moment, the formula (4) can be simplified into the following steps:
Figure 384484DEST_PATH_IMAGE035
(5)
formula (5) is a stochastic resonance system of a typical second-order Duffing vibrator, and parameters are obtained by analyzing the formula
Figure 570178DEST_PATH_IMAGE036
、
Figure 192920DEST_PATH_IMAGE066
、
Figure 996797DEST_PATH_IMAGE039
In order to determine the core parameters of the Duffing vibrator stochastic resonance system, the following optimization algorithm is laid.
(3) Using a variant differential evolution algorithm to influence system parameters of a stochastic resonance detection effect
Figure 146019DEST_PATH_IMAGE036
、
Figure 760671DEST_PATH_IMAGE061
、
Figure 355862DEST_PATH_IMAGE062
Optimizing to ensure that the bistable stochastic resonance system of the Duffing vibrator has the best signal detection effect;
(3.1) initializing parameters, setting the number of initial population toNPThe maximum number of iterations isGSecond, the dimension of the space variable isDCreating an initial population
Figure 838796DEST_PATH_IMAGE094
Randomly generating 0 th generationiThe individual isjDimension dereferencing:
Figure 452311DEST_PATH_IMAGE041
(6)
wherein,
Figure 487132DEST_PATH_IMAGE095
represents the firstiThe upper and lower limits of the value of the individual,
Figure 943522DEST_PATH_IMAGE043
is represented by (A)D,NP) Random numbers are uniformly distributed in the interval.
(3.2) calculating an objective function, wherein for a second-order Duffing oscillator stochastic resonance system, the signal-to-noise ratio of an output signal changes along with the change of system parameters, the signal-to-noise ratio can reflect the enhancement level of the system to chaotic small signals, and the objective function is as follows:
Figure 839933DEST_PATH_IMAGE096
(7)
in the formula (7), the reaction mixture is,
Figure 698168DEST_PATH_IMAGE045
in order to output a signal for the stochastic resonance system,
Figure 136846DEST_PATH_IMAGE097
the signal-to-noise ratio of the system output signal.
And (3.3) mutation operation, which is one of the marks distinguished from genetic algorithm, of individuals by adopting a difference strategy. Randomly selecting two parent individuals different from the parent individuals to be mutated, carrying out differential scaling, and synthesizing with the individuals to obtain:
Figure 221477DEST_PATH_IMAGE098
(8)
Figure 780634DEST_PATH_IMAGE099
(9)
wherein,Frepresents an adaptive mutation operator and is characterized in that,
Figure 618009DEST_PATH_IMAGE100
representing iterationsgThe next generationiThe number of the individuals is small,
Figure 745365DEST_PATH_IMAGE050
is the value of the objective function that the optimal individual is,
Figure 176346DEST_PATH_IMAGE101
the value of the objective function of the current individual,
Figure 899714DEST_PATH_IMAGE052
is the value of the maximum objective function,
Figure 873486DEST_PATH_IMAGE102
is the minimum objective function value. Species in the whole mutation processThe values of all individuals in the group are required to satisfy boundary conditions, i.e.
Figure 30798DEST_PATH_IMAGE103
(10)
(3.4) crossover operation, pair iterationgLast individual
Figure 73709DEST_PATH_IMAGE055
And variant individuals
Figure 974669DEST_PATH_IMAGE104
And (3) performing cross calculation:
Figure 802948DEST_PATH_IMAGE105
(11)
in the formula (11), the reaction mixture is,crin order to be a cross-over factor,
Figure 760189DEST_PATH_IMAGE106
is composed of
Figure 165763DEST_PATH_IMAGE107
The cross of the differential evolution algorithm is different from the cross of each individual in the genetic algorithm, and only the individuals with the same dimension are crossed.
(3.5) selection operation, the differential evolution algorithm uses greedy algorithm to perform the selection operation
Figure 480201DEST_PATH_IMAGE108
(12)
(3.6) updating the objective function value, calculating the signal-to-noise ratio of the output signal of the system according to the system parameter optimized by the current iteration number, comparing the signal-to-noise ratio output by the last iteration, and if the signal-to-noise ratio is smaller, performing a round of iteration optimization again; otherwise, outputting the optimizing parameter
Figure 412254DEST_PATH_IMAGE036
、
Figure 176947DEST_PATH_IMAGE067
、
Figure 679604DEST_PATH_IMAGE038
；
(3.7) outputting the optimal random resonance, and when the iteration times reach the maximum iteration timesGOutputting the stochastic resonance system parameters of the second-order Duffing oscillator corresponding to the maximum objective function value
Figure 814044DEST_PATH_IMAGE063
、
Figure 210391DEST_PATH_IMAGE037
、
Figure 21352DEST_PATH_IMAGE025
And carrying out stochastic resonance output on the input signal according to the obtained optimal parameter value, and analyzing the spectral characteristics of the output signal.
(4) Optimal system parameters obtained by using variant differential evolution algorithm
Figure 526151DEST_PATH_IMAGE036
、
Figure 572605DEST_PATH_IMAGE037
、
Figure 698824DEST_PATH_IMAGE062
Analyzing the detection effect of the stochastic resonance chaotic small signals under the optimal parameters, comparing the time-frequency characteristics of the input and output signals of the stochastic resonance system of the Duffing oscillator, and judging whether the chaotic small signals submerged in the sea clutter background can be detected;
(4.1) to verify the feasibility of the proposed algorithm, a simulation experiment of low frequency small signal input was first performed. Considering that the system parameter is smaller when the stochastic resonance occurs, the population number is setNPIs 50, variable dimensionD10, initial mutation operator
Figure 805320DEST_PATH_IMAGE109
0.4, cross causeSeed of Japanese apricotcr0.1, maximum number of iterationsGAt 200, the following low frequency small signals are input:
Figure 295951DEST_PATH_IMAGE110
(13)
wherein, the frequency of the small signal is 0.01Hz, the sampling frequency is 5 Hz, and the number of sampling points is 800. Setting the amplitude A =0.1, 0.08, 0.06, 0.04, 0.02 of the low-frequency signal, corresponding to the noise intensity D =0.15, 0.3, 0.45, 0.6, 0.75, forming five groups of input signals 1,2, 3, 4, 5 with gradually decreasing signal-to-noise ratios, and setting the optimization range of the parameters of the optimized output system to be [0.001, 2]The parameter accuracy was 0.001. Taking the input signal amplitude A =0.1 and the noise intensity D =0.15 as an example for detailed description, and searching a system parameter corresponding to the maximum output signal-to-noise ratio of the Duffing oscillator stochastic resonance system under the current input signal characteristic by using a variant differential evolution algorithm
Figure 755882DEST_PATH_IMAGE065
、
Figure 392400DEST_PATH_IMAGE066
、
Figure 528852DEST_PATH_IMAGE039
. And analyzing the time-frequency characteristics of the input and output signals under the optimal system parameters to judge the existence of the chaotic small signals.
(4.2) to further verify the feasibility of the variant differential evolution algorithm to optimize the stochastic resonance small signal detection method, the input signal amplitude a =0.2, the noise intensity D =2.1, and the signal frequency
Figure 758976DEST_PATH_IMAGE111
High frequency small signal, sampling frequency
Figure 147232DEST_PATH_IMAGE112
The number of sampling points is 800, and the carrier frequency is set by combining the heterodyne stochastic resonance theory
Figure 998776DEST_PATH_IMAGE113
And the low-frequency signal component output after frequency mixing meets the adiabatic approximate theoretical requirement, and a high-frequency small signal detection experiment is carried out.
Detecting the high-frequency small signal under the stochastic resonance system by utilizing a variant differential evolution algorithm to obtain a system parameter corresponding to the maximum signal-to-noise ratio of the output signal
Figure 588020DEST_PATH_IMAGE065
、
Figure 164495DEST_PATH_IMAGE037
、
Figure 215496DEST_PATH_IMAGE064
And judging the existence of the high-frequency small signal by utilizing a heterodyne stochastic resonance recovery principle.
(4.3) in order to verify the practicability of the variant differential evolution algorithm, performing a chaotic small target detection experiment based on a random resonance theory under a sea clutter background, wherein #54 sea clutter collected by an IPIX radar contains target signal data, and a target data interval: the primary target is 8 and the secondary target is 7: 10. The sea clutter data containing the target replaces the input signal of the stochastic resonance system of the Duffing oscillator, and the system optimized by the variant differential evolution algorithm outputs the system parameter corresponding to the maximum signal-to-noise ratio
Figure 701972DEST_PATH_IMAGE065
、
Figure 55593DEST_PATH_IMAGE114
、
Figure 760111DEST_PATH_IMAGE039
And analyzing the time-frequency characteristics of the input and the output of the system to judge the existence of the small signal.
In order to illustrate the effectiveness of the method, the sea clutter data is subjected to chaotic phase space reconstruction to establish actual measurement data. In order to verify the feasibility of the algorithm, a low-frequency small signal detection experiment is firstly carried out, and low-frequency small signal mixed noise is used as Duffing vibrationAfter the input signal of the sub-stochastic resonance system is optimized by the system parameters through the variant difference algorithm, the output signal of the system is obtained and the time-frequency characteristic of the output signal is analyzed to verify the detection effect of the chaotic small signal, for example, the amplitude of the input signal A =0.1 and the noise intensity D =0.15, for example, in the figure 2, the variant difference evolution algorithm obtains the optimal parameters of the current input signal of the system through 33 times of iterative optimization, namely, the optimal parameters are respectively
Figure 631115DEST_PATH_IMAGE115
，
Figure 831153DEST_PATH_IMAGE116
，
Figure 745888DEST_PATH_IMAGE117
In this case, the signal-to-noise ratio of the output signal is 10.710dB at most, which is 29.391dB higher than the input signal-to-noise ratio (-18.681dB), the stochastic resonance diagram of the variant differential evolution algorithm of fig. 3 under the optimal parameters is shown, fig. 3 (a) is the input signal diagram, it can be seen that the chaotic small signal is buried in the noise, and as shown in fig. 3 (b), the spectral characteristics cannot be seen. However, by analyzing the output signal (c) in fig. 3, the outline of the signal can be briefly seen, and then analyzing the spectral characteristics (d) in fig. 3, the small signal can be obviously observed to be enhanced, and the small signal at 0.01Hz can be directly judged.
In order to further verify the feasibility of the small-signal detection method for optimizing stochastic resonance by using the variant differential evolution algorithm, it is considered that in the adiabatic approximation theory, the input signal is required to have low amplitude, low frequency and low noise intensity, but the input signal in practical engineering application may often be a high-frequency small signal with higher frequency, and for this problem, the heterodyne stochastic resonance can be used for solving.
Input signal amplitude a =0.2, noise intensity D =2.1, signal frequency
Figure 172321DEST_PATH_IMAGE118
High frequency small signal, sampling frequency
Figure 440491DEST_PATH_IMAGE119
The number of sampling points is 800, and the carrier frequency is set by combining the heterodyne stochastic resonance theory
Figure 386713DEST_PATH_IMAGE120
And the low-frequency signal component output after frequency mixing meets the adiabatic approximate theoretical requirement, and a high-frequency small signal detection experiment is carried out.
Detecting the high-frequency small signal under the stochastic resonance system by utilizing a variant differential evolution algorithm to obtain a system parameter corresponding to the maximum signal-to-noise ratio of the output signal
Figure 347716DEST_PATH_IMAGE065
、
Figure 261445DEST_PATH_IMAGE037
、
Figure 192361DEST_PATH_IMAGE064
Are respectively as
Figure 632569DEST_PATH_IMAGE121
，
Figure 374261DEST_PATH_IMAGE122
，
Figure 523089DEST_PATH_IMAGE123
And the maximum signal-to-noise ratio under the current condition is output, namely 3.54dB, which is improved by 26.76dB compared with the input signal-to-noise ratio (-23.22 dB). Fig. 4 is an optimized stochastic resonance chart in the case of inputting a high-frequency small signal, and from the analysis of (a) and (b) in fig. 4, no high-frequency small signal submerged in a strong noise background can be observed in the time-frequency characteristic chart of the input signal. However, the outline of the input signal can be clearly seen in the output signal diagram (c) in fig. 4, and the frequency analysis of the outline results in the output signal spectrogram (d) in fig. 4, so that the small signal is obviously enhanced, and the judgment is made
Figure 398641DEST_PATH_IMAGE124
The small signal is calculated according to the heterodyne stochastic resonance recovery principle
Figure 303143DEST_PATH_IMAGE125
And further deducing that the enhanced frequency represents that the input frequency is 20Hz, which shows that the Duffing oscillator stochastic resonance system optimized by the variant differential evolution algorithm can detect a high-frequency small signal.
In order to verify the practicability of the variant differential evolution algorithm, a chaos small target detection experiment based on the random resonance theory under the sea clutter background is carried out, wherein #54 sea clutter collected by an IPIX radar contains target signal data, and a target data interval is as follows: the primary target is 8 and the secondary target is 7: 10. The sea clutter data containing the target replaces the input signal of the stochastic resonance system of the Duffing oscillator, and the system optimized by the variant differential evolution algorithm outputs the system parameter corresponding to the maximum signal-to-noise ratio
Figure 605948DEST_PATH_IMAGE065
、
Figure 477958DEST_PATH_IMAGE061
、
Figure 32568DEST_PATH_IMAGE039
Are respectively as
Figure 916210DEST_PATH_IMAGE126
，
Figure 16015DEST_PATH_IMAGE127
，
Figure 126054DEST_PATH_IMAGE128
The output signal-to-noise ratio is 22.47dB, which is 83.50dB higher than the signal-to-noise ratio (-55.03dB) of the input signal, the detection effect of the chaotic small random resonance signal under the background of the sea clutter is shown in fig. 5, wherein (a) and (b) in fig. 5 are time-frequency characteristic diagrams of the input signal, which cannot analyze the existence of the chaotic small signal, after the optimized stochastic resonance system, the chaotic small signal profile submerged under the background of the sea clutter can be drawn out in a hidden way in (c) in fig. 5, and the spectral peak appearing at the position with the frequency of 0.01632 can be clearly identified in (d) in fig. 5, which represents the position where the spectral peak appearsChaotic small signals exist, and the effect of experimental research is achieved.
Those skilled in the art will recognize that in one or more of the examples described above, the functions described herein may be implemented in hardware, software, firmware, or any combination thereof. When implemented in software, the functions may be stored on or transmitted over as one or more instructions or code on a computer-readable medium. Computer-readable media includes both computer storage media and communication media including any medium that facilitates transfer of a computer program from one place to another. A storage media may be any available media that can be accessed by a general purpose or special purpose computer.
The above-mentioned embodiments, objects, technical solutions and advantages of the present application are further described in detail, it should be understood that the above-mentioned embodiments are only examples of the present application, and are not intended to limit the scope of the present application, and any modifications, equivalent substitutions, improvements and the like made on the basis of the technical solutions of the present application should be included in the scope of the present application.

Claims (4)

1. The random resonance chaotic small signal detection method based on the variant differential evolution algorithm is characterized by comprising the following steps of:
firstly, performing phase space reconstruction on a sea clutter signal x (n) to be detected by adopting a C-C method, and determining the delay time of a phase space;
establishing a Duffing oscillator stochastic resonance equation under the combined action of the chaotic small signal and the noise signal, and obtaining the core parameters of the system based on the delay time
Figure 803246DEST_PATH_IMAGE001
、
Figure 267289DEST_PATH_IMAGE002
、
Figure 789406DEST_PATH_IMAGE003
；
Thirdly, utilizing a variant differential evolution algorithm to carry out pair on core parameters influencing the effect of the stochastic resonance detection
Figure 456011DEST_PATH_IMAGE001
、
Figure 223241DEST_PATH_IMAGE004
、
Figure 658902DEST_PATH_IMAGE005
Optimizing according to the obtained core parameters of the system
Figure 617499DEST_PATH_IMAGE001
、
Figure 505821DEST_PATH_IMAGE002
、
Figure 604970DEST_PATH_IMAGE003
The value of (3) is to perform stochastic resonance output on an input signal, and analyze the spectral characteristics of the output signal to obtain a chaotic small signal;
the third step comprises:
step 3.1, initializing parameters, setting the initial population quantity asNPThe maximum number of iterations isGSecond, the dimension of the space variable isDCreating an initial population
Figure 550930DEST_PATH_IMAGE006
Randomly generating 0 th generationiThe individual isjDimension dereferencing:
Figure 696740DEST_PATH_IMAGE007
(6)
wherein,
Figure 823090DEST_PATH_IMAGE008
represents the firstiThe upper and lower limits of the value of the individual,
Figure 446970DEST_PATH_IMAGE009
is represented by (A)D,NP) Random numbers uniformly distributed in the interval;
step 3.2, calculating an objective function, wherein for a second-order Duffing oscillator stochastic resonance system, the signal-to-noise ratio of an output signal changes along with the change of system parameters, the signal-to-noise ratio can reflect the enhancement level of the system to chaotic small signals, and the objective function is as follows:
Figure 106490DEST_PATH_IMAGE010
(7)
in the formula (7), the reaction mixture is,
Figure 583389DEST_PATH_IMAGE011
in order to output a signal for the stochastic resonance system,
Figure 446302DEST_PATH_IMAGE012
signal-to-noise ratio of the output signal for the system;
and 3.3, performing mutation operation, namely performing mutation operation on the individuals by adopting a differential strategy, randomly selecting two parent individuals different from the individuals to be mutated, performing differential scaling on the two parent individuals, and synthesizing the two parent individuals with the individuals to obtain:
Figure 591982DEST_PATH_IMAGE013
(8)
Figure 591162DEST_PATH_IMAGE014
(9)
wherein,Frepresents an adaptive mutation operator and is characterized in that,
Figure 563928DEST_PATH_IMAGE015
representative stackSubstitute for Chinese traditional medicinegThe next generationiThe number of the individuals is small,
Figure 914138DEST_PATH_IMAGE016
is the value of the objective function that the optimal individual is,
Figure 129088DEST_PATH_IMAGE017
the value of the objective function of the current individual,
Figure 248353DEST_PATH_IMAGE018
is the value of the maximum objective function,
Figure 123512DEST_PATH_IMAGE019
is the minimum objective function value; the values of all individuals of the population are required to meet boundary conditions in the whole variation process, namely
Figure 147969DEST_PATH_IMAGE020
(10)
Step 3.4, crossover operation, pair iterationgLast individual
Figure 917342DEST_PATH_IMAGE021
And variant individuals
Figure 907426DEST_PATH_IMAGE022
And (3) performing cross calculation:
Figure 471262DEST_PATH_IMAGE023
(11)
in the formula (11), the reaction mixture is,crin order to be a cross-over factor,
Figure 45332DEST_PATH_IMAGE024
is composed of
Figure 352816DEST_PATH_IMAGE025
Is randomly adjustedThe crossing of the differential evolution algorithm is different from the crossing of each individual in the genetic algorithm;
step 3.5, selection operation, differential evolution algorithm utilizes greedy algorithm to carry out selection operation
Figure 618580DEST_PATH_IMAGE026
(12)
Step 3.6, updating the objective function value, calculating the signal-to-noise ratio of the output signal of the system according to the system parameter optimized by the current iteration times, comparing the signal-to-noise ratio output by the last iteration, and if the signal-to-noise ratio is smaller, performing a round of iteration optimization again; otherwise, outputting the optimizing parameter
Figure 602585DEST_PATH_IMAGE027
、
Figure 883525DEST_PATH_IMAGE002
、
Figure 853755DEST_PATH_IMAGE005
；
Step 3.7, outputting the optimal stochastic resonance, and when the iteration times reach the highest iteration timesGOutputting the stochastic resonance system parameters of the second-order Duffing oscillator corresponding to the maximum objective function value
Figure 287273DEST_PATH_IMAGE001
、
Figure 927333DEST_PATH_IMAGE002
、
Figure 944836DEST_PATH_IMAGE003
And carrying out stochastic resonance output on the input signal according to the obtained optimal parameter value, and analyzing the spectral characteristics of the output signal.
2. The stochastic resonance chaotic small signal detection method based on the variant differential evolution algorithm according to claim 1, wherein in the first step, the C-C phase space reconstruction step comprises:
step 1.1, dividing the sea clutter signals x (N), N =1,2,.. and N to be detected into t disjoint time rows with the length of N/t, and calculating the statistic S (m, N, r, tau) of each subsequence
Figure 187598DEST_PATH_IMAGE028
(1)
In the formula,
Figure 459311DEST_PATH_IMAGE029
is the first
Figure 394906DEST_PATH_IMAGE030
The correlation integral of the sub-sequences is,
Figure 132661DEST_PATH_IMAGE031
is the length of the data set and,
Figure 54481DEST_PATH_IMAGE032
is the search radius in the reconstruction space; m is the embedding dimension, τ is the time delay;
step 1.2, local maximum separation
Figure 570913DEST_PATH_IMAGE033
Zero point or for all radii
Figure 536464DEST_PATH_IMAGE032
Selecting the time point with the minimum difference, and selecting the radius with the maximum and minimum corresponding values
Figure 403926DEST_PATH_IMAGE032
The difference is defined as
Figure 863857DEST_PATH_IMAGE034
(2)
u,vAny unknown number within the sequence range representing the parameter is determined, according to statistical principles,
Figure 126473DEST_PATH_IMAGE035
is taken from
Figure 138292DEST_PATH_IMAGE036
In a ratio of (A) to (B),
Figure 837257DEST_PATH_IMAGE037
is the mean square error of the time series, the equation is as follows:
Figure 491093DEST_PATH_IMAGE038
(3)
in the formula,
Figure 106751DEST_PATH_IMAGE039
is the mean of the statistics of all sub-sequences, and,
Figure 164837DEST_PATH_IMAGE040
、
Figure 741311DEST_PATH_IMAGE041
is a statistic defined according to the Brock-Decchert-Scheinkman BDS statistics,
Figure 562287DEST_PATH_IMAGE042
is the delta of the statistic of the sub-sequence,
Figure 642238DEST_PATH_IMAGE043
for a new indicator of determining the width of the embedding window,
Figure 136804DEST_PATH_IMAGE044
the global minimum value point of (1) corresponds to the width of the embedding window。
3. The random resonance chaotic small signal detection method based on the variant differential evolution algorithm according to claim 1, wherein the second step comprises:
step 2.1, the Duffing oscillator stochastic resonance equation system under the combined action of a chaotic small signal and a noise signal is as follows:
Figure 325209DEST_PATH_IMAGE045
(4)
wherein,
Figure 55268DEST_PATH_IMAGE046
in order to output the signal for the system,
Figure 130671DEST_PATH_IMAGE047
in order to achieve a damping ratio,
Figure 812451DEST_PATH_IMAGE048
in order to be a function of the potential,
Figure 97938DEST_PATH_IMAGE049
in order to input the signals to the system,
Figure 241475DEST_PATH_IMAGE050
is an average value of 0 and a noise intensity of
Figure 561598DEST_PATH_IMAGE051
The white gaussian noise of (a) is,
Figure 912814DEST_PATH_IMAGE052
representing the shock function;
step 2.2, solving a formula according to a quadratic equation of unity to calculate a potential function
Figure 295384DEST_PATH_IMAGE053
Comprises three extreme points of
Figure 632825DEST_PATH_IMAGE054
The system critical value at this time is calculated as
Figure 430623DEST_PATH_IMAGE055
；
Step 2.3, if and only if the input signal amplitude
Figure 437894DEST_PATH_IMAGE056
When the signal, the noise and the system reach a matching cooperative relationship, partial energy of the noise signal is transferred to the signal, the signal enhancement is realized, namely, the signal enters a stochastic resonance state, and at the moment, the formula (4) is simplified as follows:
Figure 697974DEST_PATH_IMAGE057
(5)
equation (5) is the stochastic resonance system of a typical second-order Duffing vibrator, and the parameters
Figure 698159DEST_PATH_IMAGE058
、
Figure 868241DEST_PATH_IMAGE059
、
Figure 905467DEST_PATH_IMAGE060
To determine the core parameters of the Duffing vibrator stochastic resonance system.
4. The random resonance chaotic small signal detection method based on the variant differential evolution algorithm according to claim 1, characterized in that the detection method further comprises: step four, obtaining the optimal system parameters by using a variant differential evolution algorithm
Figure 544521DEST_PATH_IMAGE061
、
Figure 958185DEST_PATH_IMAGE062
、
Figure 982773DEST_PATH_IMAGE063
And analyzing the detection effect of the stochastic resonance chaotic small signals under the optimal parameters, comparing the time-frequency characteristics of the input and output signals of the stochastic resonance system of the Duffing oscillator, and judging whether the chaotic small signals submerged in the sea clutter background can be detected.
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