CN113326817A - Chaotic small signal detection method and device - Google Patents

Chaotic small signal detection method and device Download PDF

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CN113326817A
CN113326817A CN202110873862.5A CN202110873862A CN113326817A CN 113326817 A CN113326817 A CN 113326817A CN 202110873862 A CN202110873862 A CN 202110873862A CN 113326817 A CN113326817 A CN 113326817A
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chaotic
support vector
sparrow
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聂晓鸿
尚强
李成
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Nanjing Tianlang Defense Technology Co ltd
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Abstract

The invention discloses a chaotic small signal detection method and a chaotic small signal detection device, wherein the detection method comprises the following steps: performing phase space reconstruction on the sea clutter signal to be detected by adopting a C-C method, and determining the embedding dimension and delay time of the phase space; learning sea clutter characteristics and predicting chaotic small signals by using a single-step prediction model of a support vector machine; optimizing a system parameter penalty coefficient and a kernel function parameter which influence the effect of the support vector machine by utilizing a sparrow search algorithm; analyzing the penalty coefficient and the kernel function parameter of the optimal parameter obtained by using a sparrow search algorithm, analyzing the effect of detecting the chaotic small signal by the support vector machine under the optimal parameter, and comparing the time-frequency characteristics of the original signal and the predicted signal of the support vector machine, thereby determining whether the chaotic small signal submerged in the sea clutter background is detected; the invention effectively detects the transient small signal from the chaotic background, and can detect the existence of the periodic small signal by using the frequency spectrum of the error.

Description

Chaotic small signal detection method and device
Technical Field
The invention relates to the field of radar signal processing, in particular to a chaotic small signal checking method and device.
Background
Sea clutter generally refers to the backscattered echo of the sea surface under radar illumination. The sea clutter has complex and changeable physical mechanism under the influence of various natural factors such as sea waves, tides and the like, and has the characteristics of non-Gaussian, non-linear and non-stable. The strong echoes caused by the wave spikes can severely interfere with the detection of the radar target. Therefore, the method for detecting the small targets under the chaotic sea clutter background has important application value for establishing a system for observing and monitoring the ocean safety and detecting the targets on the sea surface.
When the support vector machine is used for detecting small signals in the chaotic background, the influence of the penalty coefficient and the kernel function parameter on the detection precision is large, and the reasonable selection of the parameter has important significance for improving the performance of the support vector machine. The traditional optimization algorithm is easy to fall into local optimization and has low convergence speed, and the detection performance is seriously influenced.
Disclosure of Invention
In order to solve the above problems, the present invention provides a method and an apparatus for detecting a chaotic small signal with low detection threshold and high detection efficiency.
In order to achieve the above object, an aspect of the present invention provides a method for detecting a chaotic small signal, including the following steps:
step 1: performing phase space reconstruction on the sea clutter signal to be detected by adopting a C-C method, and determining the embedding dimension and delay time of the phase space;
step 2: learning sea clutter characteristics and predicting chaotic small signals by using a single-step prediction model of a support vector machine;
and step 3: optimizing a penalty coefficient and a kernel function parameter which affect the effect of the support vector machine by using a sparrow search algorithm, thereby determining the optimal penalty coefficient and kernel function parameter;
and 4, step 4: and analyzing the effect of the support vector machine for detecting the chaotic small signals under the optimal punishment coefficient and the kernel function parameter, and comparing the time-frequency characteristics of the original signals and the predicted signals of the support vector machine, thereby determining whether the chaotic small signals submerged in the sea clutter background are detected.
As a preferred technical solution, in step 1, the performing phase space reconstruction on the sea clutter signal to be detected by using a C-C method further includes:
step 1.1: for a time series
Figure 596403DEST_PATH_IMAGE001
To reconstruct the spatial sequence
Figure 846118DEST_PATH_IMAGE002
And the correlation dimension of the chaotic characteristic singular attractor can be solved by using the correlation integral:
Figure 34654DEST_PATH_IMAGE003
in the formula (I), the compound is shown in the specification,
Figure 813254DEST_PATH_IMAGE004
in order to correlate the functions of the integration,
Figure 618399DEST_PATH_IMAGE005
is the critical radius, and m is the embedding dimension of the phase space reconstruction; (ii) a
Step 1.2: for each sub-column
Figure 140648DEST_PATH_IMAGE006
Calculate its statistics
Figure 714848DEST_PATH_IMAGE007
Then, the average statistic of all sequences is found by using the statistical principle:
Figure 929929DEST_PATH_IMAGE008
in the formula (I), the compound is shown in the specification,
Figure 956791DEST_PATH_IMAGE009
to represent
Figure 282730DEST_PATH_IMAGE010
For critical radius
Figure 180279DEST_PATH_IMAGE005
Is measured in the mean value of the maximum deviation of,
Figure 566261DEST_PATH_IMAGE011
to represent
Figure 80419DEST_PATH_IMAGE012
The absolute value of the mean statistic of (a);
step 1.3: obtaining delay time according to minimum embedding obtained when correlation index is saturated and embedding delay window obtained by using statistical principle
Figure 944470DEST_PATH_IMAGE013
And width of embedded window
Figure 493263DEST_PATH_IMAGE014
。
As a preferred technical solution, the step 2 further comprises:
step 2.1: for the input training set data:
Figure 50146DEST_PATH_IMAGE015
wherein
Figure 786021DEST_PATH_IMAGE016
，
Figure 719342DEST_PATH_IMAGE017
，
Figure 857062DEST_PATH_IMAGE018
The regression estimation function is:
Figure 584847DEST_PATH_IMAGE019
in the formula (I), the compound is shown in the specification,
Figure 808018DEST_PATH_IMAGE020
is the hyperplane weight;
Figure 279450DEST_PATH_IMAGE021
is a function threshold;
Figure 271677DEST_PATH_IMAGE022
is a high-dimensional nonlinear function;
step 2.2: equation (3) is transformed into a convex optimization problem, namely:
Figure 435942DEST_PATH_IMAGE023
Figure 146409DEST_PATH_IMAGE024
in the formula (I), the compound is shown in the specification,
Figure 155953DEST_PATH_IMAGE004
a penalty factor for the support vector machine;
Figure 533845DEST_PATH_IMAGE025
、
Figure 337853DEST_PATH_IMAGE026
is a relaxation variable;
Figure 801195DEST_PATH_IMAGE027
representing a loss function;
Figure 348851DEST_PATH_IMAGE028
representing a total number of samples in the sample space;
step 2.3: when the Lagrange multiplier method is applied to the equations (4) and (5), the convex optimization problem is converted into an equivalent dual problem, and a spatial sample set
Figure 581250DEST_PATH_IMAGE029
Then, there are:
Figure 821738DEST_PATH_IMAGE030
in the formula (6), the reaction mixture is,
Figure 241218DEST_PATH_IMAGE031
；
Figure 858144DEST_PATH_IMAGE032
；
Figure 679470DEST_PATH_IMAGE033
、
Figure 356439DEST_PATH_IMAGE034
、
Figure 263215DEST_PATH_IMAGE035
、
Figure 418253DEST_PATH_IMAGE036
lagrange operator;
Figure 347945DEST_PATH_IMAGE037
for the kernel function, here, an RBF kernel function is selected,
Figure 195815DEST_PATH_IMAGE038
the regression equation of the chaotic time series can be expressed as follows by using a support vector regression machine:
Figure 855467DEST_PATH_IMAGE039
。
as a preferable technical solution, in the step (3):
the hypothetical sparrow population was represented using equation (8):
Figure 548616DEST_PATH_IMAGE040
in the formula (I), the compound is shown in the specification,
Figure 344534DEST_PATH_IMAGE041
representing the number of sparrows;
Figure 97726DEST_PATH_IMAGE042
the dimension representing the variable to be optimized;
the fitness value of a sparrow is represented using a vector (9):
Figure 244674DEST_PATH_IMAGE043
in the formula (I), the compound is shown in the specification,
Figure 741514DEST_PATH_IMAGE044
each row in
Figure 657518DEST_PATH_IMAGE045
The values of (a) represent fitness values for each individual;
the seeker's location update formula is as follows:
Figure 316032DEST_PATH_IMAGE046
in the formula (I), the compound is shown in the specification,
Figure 950276DEST_PATH_IMAGE047
representing the current iteration number;
Figure 985228DEST_PATH_IMAGE048
representing the maximum number of iterations;
Figure 21317DEST_PATH_IMAGE049
is shown as
Figure 116312DEST_PATH_IMAGE050
A sparrow is at the second place
Figure 972273DEST_PATH_IMAGE051
Position information of the dimension;
Figure 810916DEST_PATH_IMAGE052
is a random number and
Figure 170353DEST_PATH_IMAGE053
；
Figure 701828DEST_PATH_IMAGE054
the early-warning value is represented and,
Figure 779506DEST_PATH_IMAGE055
；
Figure 687419DEST_PATH_IMAGE056
a value indicative of a safety value is provided,
Figure 166942DEST_PATH_IMAGE057
；
Figure 869319DEST_PATH_IMAGE058
is a random number that follows a normal distribution;
Figure 434292DEST_PATH_IMAGE059
is that all elements are 1
Figure 880317DEST_PATH_IMAGE060
A matrix;
when in use
Figure 214346DEST_PATH_IMAGE061
When the situation is detected, the danger exists in the area, and the predators exist; otherwise, the area is safe and no predator exists;
the follower location update formula is as follows:
Figure 87624DEST_PATH_IMAGE062
in the formula (I), the compound is shown in the specification,
Figure 139894DEST_PATH_IMAGE063
representing a global worst location;
Figure 124031DEST_PATH_IMAGE064
represents the best location among the current discoverers;
Figure 843725DEST_PATH_IMAGE065
is an element having only 1 and-1
Figure 622325DEST_PATH_IMAGE066
Dimension matrix, and
Figure 427470DEST_PATH_IMAGE067
；
Figure 949718DEST_PATH_IMAGE041
representing the number of sparrows;
when in use
Figure 523919DEST_PATH_IMAGE068
When indicates the first
Figure 473421DEST_PATH_IMAGE050
The adaptability of the follower is low, food is not obtained, and the follower needs to fly to other directions to find food;
the location update formula for the alert is as follows:
Figure 500282DEST_PATH_IMAGE069
in the formula (I), the compound is shown in the specification,
Figure 826221DEST_PATH_IMAGE070
representing a current global optimal position;
Figure 989350DEST_PATH_IMAGE071
represents the step size and follows a normal distribution;
Figure 375332DEST_PATH_IMAGE072
is a random number that is a function of the number,
Figure 155069DEST_PATH_IMAGE073
；
Figure 19120DEST_PATH_IMAGE074
representing the fitness value of the current sparrow individual;
Figure 302333DEST_PATH_IMAGE075
representing a current global optimal fitness value;
Figure 859217DEST_PATH_IMAGE076
representing a current global worst fitness value;
Figure 860671DEST_PATH_IMAGE077
is a constant to avoid 0 appearing in the denominator;
when in use
Figure 528412DEST_PATH_IMAGE078
Time, it means that the peripheral sparrow found a predator; otherwise, it indicates that the sparrow has found the predator.
As a preferred technical solution, the step (3) further comprises:
step 3.1: setting the total number of sparrows owned by a sparrow population in a sparrow search algorithm, the maximum iteration times, the proportion of the discoverer and the followers in the total number of the sparrows, and setting the value range of parameters of a support vector machine;
step 3.2: calculating the fitness value of each sparrow and sequencing to determine the sparrow population;
step 3.3: updating the positions of the three types of sparrows according to a position updating formula;
step 3.4: calculating new fitness and comparing with the fitness before updating, and keeping better fitness for continuously updating;
step 3.5: judging whether the maximum iteration times is reached; if not, continuing from the step 3.2, otherwise, stopping running;
step 3.6: the finally obtained optimal fitness position is the penalty coefficient and the kernel function parameter of the SVM.
As a preferred technical solution, in the step (4):
predicting by using an SSA-SVM algorithm, analyzing the time-frequency characteristics of input and output signals under the optimal system parameters, and judging the existence of chaotic small signals;
and predicting by using an SSA-SVM model to obtain a prediction error, and performing spectrum analysis to judge the existence of the periodic small signal.
On the other hand, the present invention also provides a chaotic small signal detection device, comprising:
the phase space reconstruction unit is used for performing phase space reconstruction on the sea clutter signal to be detected by adopting a C-C method and determining the embedding dimension and delay time of the phase space;
the prediction unit is used for learning sea clutter characteristics and predicting the small chaotic signals by utilizing a single-step prediction model of a support vector machine;
the optimization unit is used for optimizing the system parameter penalty coefficient and the kernel function parameter which influence the effect of the support vector machine by utilizing a sparrow search algorithm;
and the determining unit is used for analyzing the penalty coefficient and the kernel function parameter of the optimal parameter searched by using the sparrow searching algorithm, analyzing the effect of the support vector machine for detecting the chaotic small signals under the optimal parameter, and comparing the time-frequency characteristics of the original signal and the predicted signal of the support vector machine, so as to determine whether the chaotic small signals submerged in the sea clutter background are detected.
Compared with the prior art, the invention has the beneficial effects that: according to the invention, the chaotic small signals are predicted through the single-step prediction model of the support vector machine, and the penalty coefficient of system parameters and kernel function parameters influencing the effect of the support vector machine are optimized by utilizing a sparrow search algorithm, so that transient small signals are effectively detected from a chaotic background, and the existence of periodic small signals can be detected by utilizing the frequency spectrum of errors; the SSA-SVM can effectively detect weak signals in the background of the chaotic noise, and compared with a conventional support vector machine and other neural network models, the detection threshold can be obviously reduced, and small targets can be detected under the condition of extremely low signal-to-noise ratio.
Drawings
Fig. 1 is a flowchart of a method for checking a chaotic small signal according to an embodiment of the present invention;
FIG. 2 illustrates predicted and actual values of a transient-containing small signal according to an embodiment of the present invention;
FIG. 3 illustrates a block diagram of a method for predicting an error including a transient small signal according to an embodiment of the present invention;
FIG. 4 illustrates the real and predicted values of a periodic signal provided in an embodiment of the present invention;
FIG. 5 illustrates an embodiment of the present invention including a periodic signal prediction error;
FIG. 6 shows a spectrum including a prediction error sequence of a periodic signal according to an embodiment of the present invention;
FIG. 7 illustrates the real and predicted values of the measured sea clutter without small targets according to an embodiment of the present invention;
FIG. 8 is a block diagram illustrating a method for predicting sea clutter without small targets according to an embodiment of the present invention;
FIG. 9 is a diagram of a target sea clutter prediction error spectrum according to an embodiment of the present invention;
fig. 10 is a structural diagram of a detection apparatus for chaotic small signals according to an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Referring to fig. 1, an embodiment of the present invention provides a chaotic small signal detection method, including the following steps:
step 1: performing phase space reconstruction on the sea clutter signal to be detected by adopting a C-C method, and determining the embedding dimension and delay time of the phase space;
specifically, the method for reconstructing the phase space of the sea clutter signal to be detected by using the C-C method further comprises the following steps:
step 1.1: for a time series
Figure 666133DEST_PATH_IMAGE079
To reconstruct the spatial sequence
Figure 393917DEST_PATH_IMAGE002
And the correlation dimension of the chaotic characteristic singular attractor can be solved by using the correlation integral:
Figure 882667DEST_PATH_IMAGE003
in the formula (I), the compound is shown in the specification,
Figure 354100DEST_PATH_IMAGE004
in order to correlate the functions of the integration,
Figure 346327DEST_PATH_IMAGE005
is the critical radius, and m is the embedding dimension of the phase space reconstruction; (ii) a
Step 1.2: for each sub-column
Figure 510592DEST_PATH_IMAGE006
Calculate its statistics
Figure 221059DEST_PATH_IMAGE080
Then, the average statistic of all sequences is found by using the statistical principle:
Figure 230603DEST_PATH_IMAGE008
in the formula (I), the compound is shown in the specification,
Figure 608495DEST_PATH_IMAGE009
to represent
Figure 615765DEST_PATH_IMAGE010
For critical radius
Figure 79108DEST_PATH_IMAGE005
Is measured in the mean value of the maximum deviation of,
Figure 892343DEST_PATH_IMAGE081
to represent
Figure 859162DEST_PATH_IMAGE012
The absolute value of the mean statistic of (a);
step 1.3: minimum embedding dimension and utilization system obtained according to saturation of correlation indexEmbedding delay window to obtain delay time
Figure 834071DEST_PATH_IMAGE013
And width of embedded window
Figure 784710DEST_PATH_IMAGE014
。
Step 2: learning sea clutter characteristics and predicting chaotic small signals by using a single-step prediction model of a support vector machine;
specifically, in this embodiment, for the input training set data:
Figure 136056DEST_PATH_IMAGE015
wherein
Figure 222961DEST_PATH_IMAGE082
，
Figure 634351DEST_PATH_IMAGE017
，
Figure 806706DEST_PATH_IMAGE018
The regression estimation function is:
Figure 696165DEST_PATH_IMAGE083
in the formula (I), the compound is shown in the specification,
Figure 903155DEST_PATH_IMAGE020
is the hyperplane weight;
Figure 485446DEST_PATH_IMAGE021
is a function threshold;
Figure 879519DEST_PATH_IMAGE022
is a high-dimensional nonlinear function;
step 2.2: equation (3) is transformed into a convex optimization problem, namely:
Figure 838247DEST_PATH_IMAGE023
Figure 634165DEST_PATH_IMAGE024
in the formula (I), the compound is shown in the specification,
Figure 652937DEST_PATH_IMAGE004
a penalty factor for the support vector machine;
Figure 799884DEST_PATH_IMAGE025
、
Figure 31145DEST_PATH_IMAGE026
is a relaxation variable;
Figure 947149DEST_PATH_IMAGE027
representing a loss function;
Figure 871242DEST_PATH_IMAGE028
representing a total number of samples in the sample space;
step 2.3: when the Lagrange multiplier method is applied to the equations (4) and (5), the convex optimization problem is converted into an equivalent dual problem, and a spatial sample set
Figure 505486DEST_PATH_IMAGE029
Then, there are:
Figure 806017DEST_PATH_IMAGE030
in the formula (6), the reaction mixture is,
Figure 310948DEST_PATH_IMAGE031
；
Figure 671522DEST_PATH_IMAGE032
；
Figure 527483DEST_PATH_IMAGE033
、
Figure 366126DEST_PATH_IMAGE034
、
Figure 256721DEST_PATH_IMAGE035
、
Figure 522618DEST_PATH_IMAGE036
lagrange operator;
Figure 865874DEST_PATH_IMAGE037
for the kernel function, here, an RBF kernel function is selected,
Figure 773787DEST_PATH_IMAGE038
the regression equation of the chaotic time series can be expressed as follows by using a support vector regression machine:
Figure 253310DEST_PATH_IMAGE084
the penalty coefficient can represent the generalization ability of the model, the kernel function parameter reflects the distribution characteristic of the training data, and the kernel function parameter is obtained by using a sparrow search algorithm
Figure 955687DEST_PATH_IMAGE085
And
Figure 532379DEST_PATH_IMAGE086
the optimum value of (2).
And step 3: utilizing a sparrow search algorithm to optimize a penalty coefficient and a kernel function parameter which affect the effect of the support vector machine, so that the detection signal effect of the support vector machine is optimal, and the optimal penalty coefficient and the kernel function parameter are determined;
specifically, in the present embodiment, the assumed sparrow population is represented using equation (8):
Figure 712825DEST_PATH_IMAGE040
in the formula (I), the compound is shown in the specification,
Figure 578013DEST_PATH_IMAGE041
representing the number of sparrows;
Figure 185712DEST_PATH_IMAGE042
the dimension representing the variable to be optimized;
the fitness value of a sparrow is represented using a vector (9):
Figure 503561DEST_PATH_IMAGE043
in the formula (I), the compound is shown in the specification,
Figure 222118DEST_PATH_IMAGE044
each row in
Figure 941812DEST_PATH_IMAGE045
The values of (b) represent fitness values for each individual.
In the searching process, the order of sparrows obtaining food is related to the adaptation level of the sparrows, and the sparrows preferentially obtaining food have higher adaptability. The leader of the sparrow population is called the seeker, who is responsible for searching for food and provides directions to other sparrows in the population to search for food, and therefore has the greatest range of food searched.
When the sparrow population is in an area without predators, the seeker search direction is arbitrary, and once predators appear around the population, the seeker will lead the follower to move away from the predators.
The seeker's location update formula is as follows:
Figure 985992DEST_PATH_IMAGE046
in the formula (I), the compound is shown in the specification,
Figure 525557DEST_PATH_IMAGE047
representing the current iteration number;
Figure 313385DEST_PATH_IMAGE048
representing the maximum number of iterations;
Figure 887586DEST_PATH_IMAGE049
is shown as
Figure 837087DEST_PATH_IMAGE050
A sparrow is at the second place
Figure 863949DEST_PATH_IMAGE051
Position information of the dimension;
Figure 189888DEST_PATH_IMAGE052
is a random number and
Figure 618595DEST_PATH_IMAGE053
；
Figure 4577DEST_PATH_IMAGE054
the early-warning value is represented and,
Figure 518735DEST_PATH_IMAGE055
；
Figure 382786DEST_PATH_IMAGE056
a value indicative of a safety value is provided,
Figure 666000DEST_PATH_IMAGE057
；
Figure 222883DEST_PATH_IMAGE058
is a random number that follows a normal distribution;
Figure 224337DEST_PATH_IMAGE059
is that all elements are 1
Figure 892079DEST_PATH_IMAGE060
A matrix;
when in use
Figure 29799DEST_PATH_IMAGE061
When the situation is detected, the danger exists in the area, and the predators exist; otherwise, it indicates that the area is safe and no predator is present.
In all sparrow populations, the ratio of seeker to follower is fixed, and if the follower can find a better food, it can become the seeker, and vice versa. Since only the seeker has a better foraging environment and a larger foraging range in the sparrow population, the followers can observe the conditions of the seeker all the time and compete for food in order to obtain better food, and if the followers compete successfully, the followers can obtain the food of the seeker instead of searching for food at a farther place. The follower location update formula is as follows:
Figure 23163DEST_PATH_IMAGE062
in the formula (I), the compound is shown in the specification,
Figure 246334DEST_PATH_IMAGE063
representing a global worst location;
Figure 717767DEST_PATH_IMAGE064
represents the best location among the current discoverers;
Figure 975573DEST_PATH_IMAGE065
is an element having only 1 and-1
Figure 874258DEST_PATH_IMAGE066
Dimension matrix, and
Figure 584725DEST_PATH_IMAGE067
；
Figure 859849DEST_PATH_IMAGE041
representing the number of sparrows;
when in use
Figure 972161DEST_PATH_IMAGE068
When indicates the first
Figure 41749DEST_PATH_IMAGE050
The follower has low fitness and does not acquire food, and needs to fly to other directions to find food.
The alertor is randomly generated, so that the positions of the alertor are random, the number of the alertor is generally set to be 10% -20% of the number of the whole sparrow population, and when the alertor finds that predators exist around, peripheral sparrows can quickly fly to a safe place to obtain a better search environment. The interior sparrows will move in safe zones to reduce the probability of being predated by the predator. The location update formula for the alert is as follows:
Figure 239512DEST_PATH_IMAGE069
in the formula (I), the compound is shown in the specification,
Figure 52747DEST_PATH_IMAGE070
representing a current global optimal position;
Figure 285145DEST_PATH_IMAGE071
represents the step size and follows a normal distribution;
Figure 525634DEST_PATH_IMAGE072
is a random number that is a function of the number,
Figure 210693DEST_PATH_IMAGE073
；
Figure 827619DEST_PATH_IMAGE074
representing the fitness value of the current sparrow individual;
Figure 648945DEST_PATH_IMAGE075
representing a current global optimal fitness value;
Figure 60334DEST_PATH_IMAGE076
representing a current global worst fitness value;
Figure 967110DEST_PATH_IMAGE077
is a constant to avoid 0 appearing in the denominator; when in use
Figure 387727DEST_PATH_IMAGE078
Time, it means that the peripheral sparrow found a predator; otherwise, it indicates that the sparrow has found the predator.
When a support vector machine is used for detecting small signals in a chaotic background, the penalty coefficient and the kernel function parameter play a role in determining the prediction precision and the detection capability.
The specific steps of optimizing the penalty coefficient and the kernel function of the support vector machine by the sparrow search algorithm are as follows:
step 3.1: setting the total number of sparrows owned by a sparrow population in a sparrow search algorithm, the maximum iteration times, the proportion of the discoverer and the followers in the total number of the sparrows, and setting the value range of parameters of a support vector machine;
step 3.2: calculating the fitness value of each sparrow and sequencing to determine the sparrow population;
step 3.3: updating the positions of the three types of sparrows according to a position updating formula;
step 3.4: calculating new fitness and comparing with the fitness before updating, and keeping better fitness for continuously updating;
step 3.5: judging whether the maximum iteration times is reached; if not, continuing from the step 3.2, otherwise, stopping running;
step 3.6: the finally obtained optimal fitness position is the penalty coefficient and the kernel function parameter of the SVM.
And 4, step 4: the best parameter to be found by the sparrow search algorithm
Figure 329139DEST_PATH_IMAGE087
And
Figure 911430DEST_PATH_IMAGE086
analyzing the effect of the support vector machine for detecting the small chaotic signals under the optimal parameters, comparing the time-frequency characteristics of the original signals and the predicted signals of the support vector machine, and judging whether submergence can be detected or notChaotic small signals in the background of sea clutter.
In this embodiment, in order to verify the feasibility of the proposed algorithm, a simulation experiment of transient small signal input is first performed. The background noise employs the Lorenz system. The Lorenz system is generated by the following iterative equation:
Figure 571081DEST_PATH_IMAGE088
in the formula (13), the reaction mixture is,
Figure 529810DEST_PATH_IMAGE089
the initial conditions x =8, y =5 and z =10 of C =8/3 are that the equation is solved by a Runge Kutta method with a step length of 0.01, the part of the system entering the chaotic state is taken to be subjected to phase space reconstruction by a C-C method (the embedding dimension is 5 and the time delay is 1), 2000 points are selected as a data set of a simulation experiment, and the method comprises the following steps of: the ratio of 2 divides the training set and the prediction set. The transient signal with the amplitude of 0.00004 is superposed at the 451-500 point of the prediction set to form an observation sequence with the signal-to-noise ratio (SNR) of-137.7073 dB. And predicting by using an SSA-SVM algorithm, analyzing the time-frequency characteristics of the input and output signals under the optimal system parameters, and judging the existence of the chaotic small signals.
In order to further verify the feasibility of the small signal detection method under the chaotic sea clutter background of the SSA-SVM, a periodic signal is adopted
Figure 325728DEST_PATH_IMAGE090
The frequency was set at 0.025, the signal-to-noise ratio was-90.6225 dB, and periodic small signal detection experiments were performed.
And predicting by using an SSA-SVM model to obtain a prediction error, and performing spectrum analysis to judge the existence of the periodic small signal.
And detecting the high-frequency small signals under the stochastic resonance system by using a variant differential evolution algorithm to obtain system parameters corresponding to the maximum signal-to-noise ratio of the output signals, and judging the existence of the high-frequency small signals by using a heterodyne stochastic resonance recovery principle.
In order to verify the practicability of the small signal detection method under the chaotic sea clutter background of the SSA-SVM, a chaotic small target detection experiment under the sea clutter background based on the SSA-SVM is carried out, and #54 sea clutter collected by an IPIX radar contains target signal data and a target data interval: primary target is 8, secondary target is 7: 10. and inputting the sea clutter data containing the target as actual measurement data, and analyzing the time-frequency characteristic of the prediction error 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. To verify the feasibility of the proposed algorithm, transient small target experiments were first performed. Phase space reconstruction is carried out on the part of the Lorenz system after the Lorenz system enters the chaotic state by adopting a C-C method (the embedding dimension is 5, the time delay is 1), 2000 points are selected as a data set of a simulation experiment, and the method comprises the following steps of (3): the ratio of 2 divides the training set and the prediction set. Transient signals with the amplitude of 0.00004 are superposed at 451-500 points of a prediction set to form an observation sequence with the signal-to-noise ratio (SNR) of-137.7073 dB, and after normalization and phase space reconstruction, single-step prediction is carried out by using an SSA-SVM. The prediction results are shown in FIG. 2, which has a Root Mean Square Error (RMSE) of 0.000434. The support vector machine parameters C =29.9765 optimized by the sparrow search algorithm,
Figure 344499DEST_PATH_IMAGE091
= 0.133. As can be seen from FIG. 3, the prediction result has a large error at 451-500 because the transient small signal with the amplitude of 0.00004 is superimposed at 451-500 in the prediction set, so that it can be concluded that there is a small target and the feasibility of the model is verified.
The detection capability of the model is reflected according to the signal-to-noise ratio of the observation sequence and the prediction error, and the detection capability of the SSA-SVM and other models is shown in Table 1.
TABLE 1 comparison of chaos time series prediction model performance
SSA-SVM GA-SVM dual constraint LS-SVM LS-SVM RBF neural network
SNR/dB -137.7073 -89.7704 -77.33 -62.82 -54.60 -30.20
RMSE 0.000434 0.00050 0.0080 0.022 0.049 0.058
From 1, the root mean square error of the SSA-SVM is 0.000434 when the signal-to-noise ratio is-133.7073 dB, compared with the GA-SVM, the detection threshold is greatly reduced, and compared with other algorithms, the performance is obviously improved. To further verify the feasibility of the algorithm, periodic signal experiments were performed. The experimental procedure is the same as the above experiment except that the superimposed transient signal is changed into a periodic signal
Figure 960288DEST_PATH_IMAGE092
Set the frequency to 0.025, signal to noise ratio to-90.6225 dB, use the optimized parameters of the sparrow search algorithm
Figure 722708DEST_PATH_IMAGE093
，
Figure 638711DEST_PATH_IMAGE094
The prediction result is shown in fig. 4, and the prediction error is shown in fig. 5. The result of fourier transforming the prediction error is shown in fig. 6, and it can be seen that a sharp peak appears at a frequency of 0.025, thus proving the existence of a periodic small signal. In order to further verify the effectiveness of the algorithm under the actual measurement of the sea clutter, a sea clutter actual measurement data experiment is carried out. The experiment adopts actually measured sea clutter data, which are acquired by a professor Haykin of the university of McMaster, canada in 1993 by using an IPIX (intellectual PIxelprocessing X-band) radar on the east coast of canada. The IPIX radar has a working frequency of 9.3GHz, a pulse repetition frequency of 1KHz and a resolution of 30 m. The target to be detected is a floating ball wrapped with aluminum wire, the diameter of which is 1 m. Firstly, 1800 points of data without small targets are selected as a training set, the first 1000 points are used as a training set, the rest part is used as a prediction sample, the model is used for prediction after phase space reconstruction, and parameters of the support vector machine are obtained through SSA optimization
Figure 562805DEST_PATH_IMAGE095
，
Figure 197049DEST_PATH_IMAGE096
The mean square error is 0.00119471, the prediction result is shown in figure 7,the prediction error is shown in fig. 8. The result of performing fourier transform on the prediction error is shown in fig. 9, and it can be seen that a sharp peak appears at a frequency of 0.01438, so that a periodic small signal exists in the chaotic sea clutter background.
Referring to fig. 10, in other embodiments, the present invention further provides a chaotic small signal detection apparatus, including:
the phase space reconstruction unit is used for performing phase space reconstruction on the sea clutter signal to be detected by adopting a C-C method and determining the key parameter embedding dimension and delay time of the phase space; it should be noted that, since the specific phase-space reconstruction method and process are already described in detail in step 1 of the above method for detecting a small chaotic signal, they are not described herein again.
The prediction unit is used for learning sea clutter characteristics and predicting the small chaotic signals by utilizing a single-step prediction model of a support vector machine; it should be noted that, since the specific prediction method and process are already described in detail in step 2 of the above method for detecting a small chaotic signal, they are not described herein again.
The optimization unit is used for optimizing the system parameter penalty coefficient and the kernel function parameter which influence the effect of the support vector machine by utilizing a sparrow search algorithm so as to ensure that the detection signal effect of the support vector machine is optimal; it should be noted that, since the detailed optimization method and process are already described in detail in step 3 of the above method for detecting a small chaotic signal, they are not described herein again.
The determining unit is used for analyzing the effect of the support vector machine for detecting the chaotic small signals under the optimal parameters by using the optimal parameter penalty coefficient and the kernel function parameter which are searched by using the sparrow searching algorithm, and comparing the time-frequency characteristics of the original signals and the predicted signals of the support vector machine, so as to determine whether the chaotic small signals submerged in the sea clutter background are detected; it should be noted that, since the specific determination method and process are already described in detail in step 4 of the above method for detecting a small chaotic signal, they are not described herein again.
In addition, an embodiment of the present invention further provides a computer-readable storage medium, where the computer-readable storage medium may store a program, and when the program is executed, the program includes some or all of the steps of any chaotic small signal detection method described in the above method embodiments.
In addition, functional units in the embodiments of the present invention may be integrated into one processing unit, or each unit may exist alone physically, or two or more units are integrated into one unit. The integrated unit can be realized in a form of hardware, and can also be realized in a form of a software functional unit.
The integrated unit, if implemented in the form of a software functional unit and sold or used as a stand-alone product, may be stored in a computer readable memory. Based on such understanding, the technical solution of the present invention may be embodied in the form of a software product, which is stored in a memory and includes several instructions for causing a computer device (which may be a personal computer, a server, a network device, or the like) to execute all or part of the steps of the method according to the embodiments of the present invention. And the aforementioned memory comprises: a U-disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a removable hard disk, a magnetic or optical disk, and other various media capable of storing program codes.
Those skilled in the art will appreciate that all or part of the steps in the methods of the above embodiments may be implemented by associated hardware instructed by a program, which may be stored in a computer-readable memory, which may include: flash Memory disks, Read-Only memories (ROMs), Random Access Memories (RAMs), magnetic or optical disks, and the like.
Exemplary flow charts for detection of real chaotic small signals according to embodiments of the present invention are described above with reference to the accompanying drawings. It should be noted that the numerous details included in the above description are merely exemplary of the invention and are not limiting of the invention. In other embodiments of the invention, the method may have more, fewer, or different steps, and the order, inclusion, function, etc. of the steps may be different from that described and illustrated.

Claims (8)

1. A method for detecting a chaotic small signal is characterized by comprising the following steps:
step 1: performing phase space reconstruction on the sea clutter signal to be detected by adopting a C-C method, and determining the embedding dimension and delay time of the phase space;
step 2: learning sea clutter characteristics and predicting chaotic small signals by using a single-step prediction model of a support vector machine;
and step 3: optimizing a penalty coefficient and a kernel function parameter which affect the effect of the support vector machine by using a sparrow search algorithm, thereby determining the optimal penalty coefficient and kernel function parameter;
and 4, step 4: and analyzing the effect of the support vector machine for detecting the chaotic small signals under the optimal punishment coefficient and the kernel function parameter, and comparing the time-frequency characteristics of the original signals and the predicted signals of the support vector machine, thereby determining whether the chaotic small signals submerged in the sea clutter background are detected.
2. The detection method according to claim 1, wherein in step 1, the performing phase-space reconstruction on the sea clutter signal to be detected by using the C-C method further comprises:
step 1.1: for a time series
Figure 767874DEST_PATH_IMAGE001
To reconstruct the spatial sequence
Figure 236902DEST_PATH_IMAGE002
And the correlation dimension of the chaotic characteristic singular attractor can be solved by using the correlation integral:
Figure 458DEST_PATH_IMAGE003
in the formula (I), the compound is shown in the specification,
Figure 506526DEST_PATH_IMAGE004
in order to correlate the functions of the integration,
Figure 988323DEST_PATH_IMAGE005
is the critical radius, and m is the embedding dimension of the phase space reconstruction;
step 1.2: for each sub-column
Figure 136407DEST_PATH_IMAGE006
Calculate its statistics
Figure 629837DEST_PATH_IMAGE007
Then, the average statistic of all sequences is found by using the statistical principle:
Figure 572385DEST_PATH_IMAGE008
in the formula (I), the compound is shown in the specification,
Figure 275899DEST_PATH_IMAGE009
to represent
Figure 962095DEST_PATH_IMAGE010
For critical radius
Figure 700244DEST_PATH_IMAGE005
Is measured in the mean value of the maximum deviation of,
Figure 548114DEST_PATH_IMAGE011
to represent
Figure 863558DEST_PATH_IMAGE012
The absolute value of the mean statistic of (a);
step 1.3: minimum embedding dimension obtained when correlation index is saturatedAnd using the embedded delay window obtained by the statistical principle to obtain the delay time
Figure 353445DEST_PATH_IMAGE013
And width of embedded window
Figure 680521DEST_PATH_IMAGE014
。
3. The detection method according to claim 1, wherein the step 2 further comprises:
step 2.1: for the input training set data:
Figure 230451DEST_PATH_IMAGE015
wherein
Figure 908557DEST_PATH_IMAGE016
，
Figure 811922DEST_PATH_IMAGE017
，
Figure 259084DEST_PATH_IMAGE018
The regression estimation function is:
Figure 979915DEST_PATH_IMAGE019
in the formula (I), the compound is shown in the specification,
Figure 879738DEST_PATH_IMAGE020
is the hyperplane weight;
Figure 711428DEST_PATH_IMAGE021
is a function threshold;
Figure 137730DEST_PATH_IMAGE022
is a high-dimensional nonlinear function;
step 2.2: equation (3) is transformed into a convex optimization problem, namely:
Figure 29463DEST_PATH_IMAGE023
Figure 416582DEST_PATH_IMAGE024
in the formula (I), the compound is shown in the specification,
Figure 786383DEST_PATH_IMAGE004
a penalty factor for the support vector machine;
Figure 208137DEST_PATH_IMAGE025
、
Figure 146138DEST_PATH_IMAGE026
is a relaxation variable;
Figure 754973DEST_PATH_IMAGE027
representing a loss function;
Figure 194045DEST_PATH_IMAGE028
representing a total number of samples in the sample space;
step 2.3: when the Lagrange multiplier method is applied to the equations (4) and (5), the convex optimization problem is converted into an equivalent dual problem, and a spatial sample set
Figure 470306DEST_PATH_IMAGE029
Then, there are:
Figure 703841DEST_PATH_IMAGE030
in the formula (6), the reaction mixture is,
Figure 799973DEST_PATH_IMAGE031
；
Figure 636211DEST_PATH_IMAGE032
；
Figure 32557DEST_PATH_IMAGE033
、
Figure 374677DEST_PATH_IMAGE034
、
Figure 958105DEST_PATH_IMAGE035
、
Figure 473400DEST_PATH_IMAGE036
lagrange operator;
Figure 848886DEST_PATH_IMAGE037
for the kernel function, here, an RBF kernel function is selected,
Figure 424224DEST_PATH_IMAGE038
the regression equation of the chaotic time series can be expressed as follows by using a support vector regression machine:
Figure 760527DEST_PATH_IMAGE039
。
4. the detection method according to claim 1, wherein in the step (3):
the hypothetical sparrow population was represented using equation (8):
Figure 813934DEST_PATH_IMAGE040
in the formula (I), the compound is shown in the specification,
Figure 919293DEST_PATH_IMAGE041
representing the number of sparrows;
Figure 540899DEST_PATH_IMAGE042
the dimension representing the variable to be optimized;
the fitness value of a sparrow is represented using a vector (9):
Figure 833340DEST_PATH_IMAGE043
in the formula (I), the compound is shown in the specification,
Figure 956017DEST_PATH_IMAGE044
each row in
Figure 915882DEST_PATH_IMAGE045
The values of (a) represent fitness values for each individual;
the seeker's location update formula is as follows:
Figure 833023DEST_PATH_IMAGE046
in the formula (I), the compound is shown in the specification,
Figure 268552DEST_PATH_IMAGE047
representing the current iteration number;
Figure 663761DEST_PATH_IMAGE048
representing the maximum number of iterations;
Figure 478134DEST_PATH_IMAGE049
is shown as
Figure 831755DEST_PATH_IMAGE050
A sparrow is at the second place
Figure 364367DEST_PATH_IMAGE051
Position information of the dimension;
Figure 438633DEST_PATH_IMAGE052
is a random number and
Figure 107512DEST_PATH_IMAGE053
；
Figure 632034DEST_PATH_IMAGE054
the early-warning value is represented and,
Figure 386364DEST_PATH_IMAGE055
；
Figure 654534DEST_PATH_IMAGE056
a value indicative of a safety value is provided,
Figure 177919DEST_PATH_IMAGE057
；
Figure 732397DEST_PATH_IMAGE058
is a random number that follows a normal distribution;
Figure 239602DEST_PATH_IMAGE059
is that all elements are 1
Figure 45884DEST_PATH_IMAGE060
A matrix;
when in use
Figure 423776DEST_PATH_IMAGE061
When the situation is detected, the danger exists in the area, and the predators exist; otherwise, the area is safe and no predator exists;
the follower location update formula is as follows:
Figure 290101DEST_PATH_IMAGE062
in the formula (I), the compound is shown in the specification,
Figure 894388DEST_PATH_IMAGE063
representing a global worst location;
Figure 504361DEST_PATH_IMAGE064
represents the best location among the current discoverers;
Figure 267918DEST_PATH_IMAGE065
is an element having only 1 and-1
Figure 773986DEST_PATH_IMAGE066
Dimension matrix, and
Figure 255783DEST_PATH_IMAGE067
；
Figure 528501DEST_PATH_IMAGE041
representing the number of sparrows;
when in use
Figure 880985DEST_PATH_IMAGE068
When indicates the first
Figure 823533DEST_PATH_IMAGE050
The adaptability of the follower is low, food is not obtained, and the follower needs to fly to other directions to find food;
the location update formula for the alert is as follows:
Figure 527047DEST_PATH_IMAGE069
in the formula (I), the compound is shown in the specification,
Figure 213243DEST_PATH_IMAGE070
indicating the current global maximumA preferred position;
Figure 685813DEST_PATH_IMAGE071
represents the step size and follows a normal distribution;
Figure 940208DEST_PATH_IMAGE072
is a random number that is a function of the number,
Figure 131018DEST_PATH_IMAGE073
；
Figure 620905DEST_PATH_IMAGE074
representing the fitness value of the current sparrow individual;
Figure 947981DEST_PATH_IMAGE075
representing a current global optimal fitness value;
Figure 497911DEST_PATH_IMAGE076
representing a current global worst fitness value;
Figure 46790DEST_PATH_IMAGE077
is a constant to avoid 0 appearing in the denominator;
when in use
Figure 340369DEST_PATH_IMAGE078
Time, it means that the peripheral sparrow found a predator; otherwise, it indicates that the sparrow has found the predator.
5. The detection method according to claim 4, wherein the step (3) further comprises:
step 3.1: setting the total number of sparrows owned by a sparrow population in a sparrow search algorithm, the maximum iteration times, the proportion of the discoverer and the followers in the total number of the sparrows, and setting the value range of parameters of a support vector machine;
step 3.2: calculating the fitness value of each sparrow and sequencing to determine the sparrow population;
step 3.3: updating the positions of the three types of sparrows according to a position updating formula;
step 3.4: calculating new fitness and comparing with the fitness before updating, and keeping better fitness for continuously updating;
step 3.5: judging whether the maximum iteration times is reached; if not, continuing from the step 3.2, otherwise, stopping running;
step 3.6: the finally obtained optimal fitness position is the penalty coefficient and the kernel function parameter of the SVM.
6. The detection method according to claim 1, wherein in step (4):
predicting by using an SSA-SVM algorithm, analyzing the time-frequency characteristics of input and output signals under the optimal system parameters, and judging the existence of chaotic small signals;
and predicting by using an SSA-SVM model to obtain a prediction error, and performing spectrum analysis to judge the existence of the periodic small signal.
7. A chaotic small signal detection device, comprising:
the phase space reconstruction unit is used for performing phase space reconstruction on the sea clutter signal to be detected by adopting a C-C method and determining the embedding dimension and delay time of the phase space;
the prediction unit is used for learning sea clutter characteristics and predicting the small chaotic signals by utilizing a single-step prediction model of a support vector machine;
the optimization unit is used for optimizing the system parameter penalty coefficient and the kernel function parameter which influence the effect of the support vector machine by utilizing a sparrow search algorithm;
and the determining unit is used for analyzing the penalty coefficient and the kernel function parameter of the optimal parameter searched by using the sparrow searching algorithm, analyzing the effect of the support vector machine for detecting the chaotic small signals under the optimal parameter, and comparing the time-frequency characteristics of the original signal and the predicted signal of the support vector machine, so as to determine whether the chaotic small signals submerged in the sea clutter background are detected.
8. A computer-readable storage medium, comprising: the computer-readable storage medium stores a computer program, wherein the computer program, when executed by a processor, implements the steps of a method of detecting chaotic small signals according to any one of claims 1 to 6.
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