CN112596004A - Self-adaptive Duffing oscillator magnetic anomaly signal detection method - Google Patents
Self-adaptive Duffing oscillator magnetic anomaly signal detection method Download PDFInfo
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Abstract
The invention discloses a self-adaptive Duffing oscillator magnetic anomaly signal detection method, which can solve the problem that a Duffing oscillator can only detect a weak magnetic anomaly signal with single frequency under a strong noise background, and selects a multi-resolution analysis algorithm to remove Gaussian white noise and non-Gaussian white noise in a target magnetic anomaly signal under a non-Gaussian strong noise background of an ocean, so as to obtain a de-noised target magnetic anomaly weak signal and improve the signal-to-noise ratio; carrying out scale transformation on the target after multi-resolution analysis, accurately detecting each frequency component contained in the target signal after multi-resolution analysis by using a self-adaptive Duffing oscillator multi-frequency weak signal detection model, and judging whether the target signal enters a large-period state or not according to a drawn phase plane trajectory diagram; judging whether the frequency of the target signal is greater than a set threshold value, if so, outputting the frequency of the target signal; otherwise, the frequency is updated in a self-adaptive manner, and the scale transformation is continued to realize the sufficient extraction of the frequency components contained in the weak target signal.
Description
Technical Field
The invention relates to the technical field of magnetic anomaly signal detection and identification, in particular to a self-adaptive Duffing oscillator magnetic anomaly signal detection method.
Background
Under the strong magnetic background noise of ocean diversity, a weak magnetic target signal is drowned by colored noise, white Gaussian noise and other noises, and cannot be effectively detected. The existing main solution is to adopt a detection algorithm based on an Orthonormal Basis Function (OBF) decomposition, and the noise background adapted by the algorithm is Gaussian white noise. For magnetic abnormal signals polluted by Gaussian white noise, a target detection algorithm based on standard orthogonal basis function decomposition has a lower false alarm rate on a target detection result, but under the magnetic background of non-Gaussian white noise or colored noise, the detection effect of the algorithm on weak magnetic targets is not ideal. Due to the complexity of the marine environment, in the actual detection process of the weak magnetic target, the actually measured data contains strong non-gaussian noise.
Therefore, there is a need for a method for detecting a target magnetic anomaly characteristic signal under the background of strong non-gaussian noise in the ocean, which overcomes the problem that a weak magnetic target signal is submerged by other noise and cannot be detected.
Disclosure of Invention
In view of the above, the present invention provides a method for detecting a magnetic anomaly signal of a self-adaptive Duffing oscillator, which can simultaneously detect a plurality of frequency signals included in the magnetic anomaly signal and sufficiently extract a frequency component of a target under a background of non-gaussian strong noise in an ocean.
In order to achieve the purpose, the technical scheme of the invention is as follows:
the invention provides a self-adaptive Duffing oscillator magnetic anomaly signal detection method, which comprises the following steps:
and S1, detecting the magnetic abnormal signal of the magnetic target in the marine environment by using the sensor.
And S2, selecting the magnetic anomaly signal by utilizing Hamming window function sliding.
S3, decomposing the magnetic abnormal signal by using a multi-resolution analysis algorithm, dividing the magnetic abnormal signal into a high-frequency part and a low-frequency part, reserving the coefficient of the low-frequency part for reconstruction, and obtaining a target signal Sn(t) the frequency of the target signal is wtargetSetting wtargetThe initial value of (c).
S4, converting the target signal Sn(t) carrying out scale transformation, wherein the scale transformation relation is as follows:
t′＝wtarget×t
wherein t is a time variable, and t' is a time variable after scale transformation.
And (3) carrying out scale transformation on the target signal according to a modeling formula:
wherein s isn(t') is a target signal by scaling; x (t') is a parameter to be solved of the model obtained according to the modeling formula;
the second derivative of x (t').
And solving and drawing the modeling formula by using a fourth-order Runge-Kutta algorithm to obtain a phase plane trajectory diagram of each equation solution, judging whether the phase plane trajectory diagram enters a large-period state, if so, continuing to execute S5, and if not, returning to S1 to continue executing.
S5, judgment wtarget＞wmaxIf yes, the algorithm iteration is ended, and w of the target signal is outputtarget(ii) a Otherwise adaptively update wtarget，wtargetThe increment of (a) is 0.1 xwtargetAnd update wtargetSolving by substituting tThe solution, i.e., return to S4 to continue execution.
Further, the number of sample points of the hamming window function in S2 is 512.
Further, w in S5targetThe initial value of (a) is 0.01, and Δ w is 0.001.
Further, the specific method for judging whether the phase plane trajectory diagram enters the large-period state comprises the following steps:
the phase plane trajectory diagram is an elliptical phase plane trajectory, and the inside of the elliptical phase plane trajectory is not in a chaotic state, so that the phase plane trajectory diagram is considered to enter a large-period state.
Further, f (t) in S3 is decomposed by the multi-resolution analysis algorithm according to the formula:
wherein, f (t) is a magnetic abnormal signal, t is a time variable, j is an expansion scale, and k is a fixed parameter; c. Cj，k、dj，kRespectively, f (t) expansion coefficients on the j scale: c. Cj，kIs a scale factor, dj，kIs a wavelet coefficient; phi (2)-jt-k) is a scale function, ψ (2)-jt-k) is a wavelet function; z is an integer set.
Further, c in S3j，kThe formula after the scale decomposition is as follows:
wherein h is0(t-2k) is a low-pass filter function, h1(t-2k) is a high pass filter function.
Has the advantages that: the invention provides a self-adaptive Duffing oscillator magnetic anomaly signal detection method, which can solve the problem that a Duffing oscillator can only detect a weak magnetic anomaly signal with single frequency under a strong noise background. The method can remove Gaussian white noise and non-Gaussian white noise in the target magnetic abnormal signal by using a multi-resolution analysis algorithm under the background of non-Gaussian strong noise of the ocean to obtain the de-noised target magnetic abnormal weak signal and improve the signal-to-noise ratio. The multi-resolution analysis denoising algorithm divides the original target magnetic anomaly signal into a high-frequency signal and a low-frequency signal. The main component of the high-frequency signal is noise, the target signal is a low-frequency weak signal, the frequency is low, and the amplitude is small. The target signal in a certain frequency band is obtained by multi-resolution analysis denoising, and the frequency of the target signal cannot be determined. The embodiment of the invention overcomes the defect, carries out scale transformation on the target after multi-resolution analysis, and can accurately detect each frequency component contained in the target signal after multi-resolution analysis by using the self-adaptive Duffing oscillator multi-frequency weak signal detection model, namely, detect the frequency component with the initial phase coverage range (-pi, pi) of the input signal. Therefore, the present invention can simultaneously detect a plurality of frequency signals included in an abnormal signal and sufficiently extract frequency components included in a weak target signal.
Drawings
FIG. 1 is a flow chart of a method for detecting a magnetic anomaly signal of a self-adaptive Duffing oscillator based on multi-resolution analysis.
FIG. 2 is a schematic diagram of the decomposition and reconstruction of the Mallat tower algorithm.
Fig. 3 (a) is an original signal diagram of a target magnetic anomaly x-axis magnetic field component, (b) is a de-noised signal diagram of the target magnetic anomaly x-axis magnetic field component, (c) is a phase-frequency trajectory diagram of a signal not detected by the detection system, and (d) is a phase-frequency trajectory diagram of a signal detected by the detection system.
Detailed Description
The invention is described in detail below by way of example with reference to the accompanying drawings.
As shown in fig. 1, the invention provides a method for detecting a magnetic anomaly signal of a self-adaptive Duffing oscillator, which comprises the following steps:
and S1, detecting the magnetic abnormal signal of the magnetic target in the marine environment by using the sensor to form an original target magnetic abnormal signal sample set.
And S2, selecting the magnetic anomaly signal by utilizing Hamming window function sliding. In the embodiment of the invention, the number of sample points of the Hamming window function is 512.
S3, LiDecomposing the magnetic anomaly signal by using a multi-resolution analysis algorithm to obtain a decomposed magnetic anomaly signal; decomposing the scale coefficient of the low-frequency part to realize the gradual decomposition of the magnetic anomaly signal; reconstructing the coefficient of the low-frequency part reserved after the magnetic abnormal signal is decomposed to obtain a target signal sn(t) the frequency of the target signal is wtarget. Setting wtargetSpecifically, the frequency range of the target signal may be estimated according to the class of the magnetic target to determine the initial value, for example, the initial value in the embodiment of the present invention is selected to be 0.01. The decomposition and reconstruction algorithm used is shown in fig. 2.
In the embodiment of the present invention, in S2, the formula of f (t) decomposed by using the multi-resolution analysis algorithm is:
wherein, the first part on the right side of the equation is a low-frequency part, and the second part is a high-frequency part; f (t) is a magnetic abnormal signal, t is a time variable, j is an expansion scale, and k is a fixed parameter; c. Cj，k、dj，kRespectively, f (t) expansion coefficients on the j scale: c. Cj，k＝<f(t)，ψj，k(t)>Is a scale factor, dj，k＝<f(t)，ψj，k(t)>Is a wavelet coefficient; phi (2)-jt-k) is a scale function, ψ (2)-jt-k) is a wavelet function and Z is an integer set.
Since the decomposition of a signal is the decomposition of its corresponding coefficients, the scaling coefficient c for the wavelet functionj，kThe dimension decomposition is carried out to obtain:
in the embodiment of the invention, c in S2 is pointed outj，kThe formula after the scale decomposition is as follows:
wherein h is0(t-2k)、h1(t-2k) are the expansion coefficients of the scale equation of the wavelet, respectively, from the filter point of view,h0(t-2k) corresponds to the low-pass filter function, h, in the wavelet analysis1(t-2k) is the high pass filter function in the corresponding wavelet analysis.
In the embodiment of the invention, a multi-resolution analysis algorithm is selected to remove Gaussian white noise and non-Gaussian white noise in the target magnetic anomaly signal to obtain a de-noised target magnetic anomaly weak signal, so that the signal-to-noise ratio is improved. The multi-resolution analysis denoising algorithm divides the original target magnetic anomaly signal into a high-frequency signal and a low-frequency signal. The main component of the high-frequency signal is noise, the target signal is a low-frequency weak signal, the frequency is low, and the amplitude is small. The multi-resolution analysis algorithm reconstructs the coefficient of the low-frequency part reserved after the target signal is decomposed to obtain the frequency range [ w ]min，wmax]Target signal sn(t)。
S4, converting the target signal Sn(t) carrying out scale transformation, wherein the scale transformation relation is as follows:
t′＝wtarget×t
wherein t' is a time variable after the scale transformation.
And (3) carrying out scale transformation on the target signal according to a modeling formula:
wherein s isn(t') is a target signal by scale transformation, t is a time variable; x (t') is a parameter to be solved of the model obtained according to the modeling formula;
the second derivative of x (t'). The model is a self-adaptive Duffing oscillator multi-frequency weak signal detection model, and the position of each point in a phase plane trajectory diagram is determined by solving parameters x (t ') and x (t') of the model
It is determined that all points constitute a phase plane trajectory.
And solving and drawing the modeling formula by using a fourth-order Runge-Kutta algorithm to obtain a phase plane trajectory diagram of each equation solution, judging whether the phase plane trajectory diagram enters a large-period state, if so, continuing to execute S5, and if not, returning to S1 to continue executing.
In the embodiment of the present invention, a specific method for determining whether the phase plane trajectory diagram enters a large period state is as follows: the phase plane trajectory diagram is an elliptical phase plane trajectory, and the inside of the elliptical phase plane trajectory does not present a chaotic state, which indicates that a large period state is entered. When the trace diagram of the phase plane shows a large period state, the magnetic anomaly signal to be detected contains wtargetFrequency component, if the phase plane trace is chaotic, it indicates that w is not detectedtargetSignal component of frequency.
In the embodiment of the invention, the frequency of the model is wmin≤wtarget≤wmaxThe detection range of the initial phase of the input signal can be the whole section of frequency (-pi, pi), and the limitation that the model can only detect a certain section of initial phase is overcome. The target signal in a certain frequency band is obtained by multi-resolution analysis denoising, and the frequency of the target signal cannot be determined. The embodiment of the invention overcomes the defect, carries out scale transformation on the target after multi-resolution analysis, and can accurately detect each frequency component contained in the target signal after multi-resolution analysis by using the self-adaptive Duffing oscillator multi-frequency weak signal detection model, namely, detect the frequency component with the initial phase coverage range (-pi, pi) of the input signal.
S5, judgment wtarget＞wmaxIf yes, the algorithm iteration is ended, and w of the target signal is outputtarget(ii) a Otherwise adaptively update wtarget，wtargetThe increment of (a) is 0.1 xwtargetAnd update wtargetSubstituting t' to solve, namely returning to S4 to continue execution. In the embodiment of the invention, w in S5targetThe initial value of (a) is 0.01, and Δ w is 0.001.
In another embodiment of the invention, the target original signal is magnetic field total field data, the size of a data sample is 4 ten thousand sampling points, the signal sampling frequency is 500Hz, and the target is a large-scale commercial ship running in an ocean background.
First, raw data is shown in fig. 3 (a), signals in the graph are decomposed and reconstructed by using a multi-resolution analysis algorithm, noise interference is removed, and a target signal to be measured at a low frequency band is obtained, as shown in fig. 3 (b). The frequency range of the target signal to be measured is more than 0 and less than wtarget＜1Hz。
Second, get the initial w0＝0.01，Δw＝0.001。
And thirdly, carrying out scale transformation on the magnetic abnormal signal of the target to be detected, namely t' is 0.01 multiplied by t. And substituting the target signal to be measured after the scale transformation into the following formula, solving and drawing a phase plane trajectory graph by using a four-order Runge-Kutta algorithm, and judging whether the phase plane trajectory graph enters a large-period state or not.
Fig. 3 (c) shows a signal component of the target signal to be detected, where the packet w is 0.022Hz, and the phase plane trajectory diagram enters a large period state. Fig. 3 (d) shows that when no contained frequency component is detected, the system is in a chaotic state.
Step four, updating w in a self-adaptive mannerk＝wk-1+0.01, k ∈ (2,3,... n), and returning to the third step for iterative solution.
The fifth step, judge wkAnd > 1, and the algorithm iteration is ended. And outputting a frequency result contained in the target signal.
In summary, the above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (6)
1. A self-adaptive Duffing oscillator magnetic anomaly signal detection method is characterized by comprising the following steps:
s1, detecting a magnetic abnormal signal of the magnetic target in the marine environment by using the sensor;
s2, selecting the magnetic anomaly signal by utilizing Hamming window function sliding;
s3, decomposing the magnetic abnormal signal by using a multi-resolution analysis algorithm, dividing the magnetic abnormal signal into a high-frequency part and a low-frequency part, reserving the coefficient of the low-frequency part for reconstruction, and obtaining a target signal Sn(t) the frequency of the target signal is wtargetSetting wtargetAn initial value of (d);
s4, converting the target signal Sn(t) carrying out scale transformation, wherein the scale transformation relation is as follows:
t′＝wtarget×t
wherein t is a time variable, and t' is a time variable after scale transformation;
and the target signal after the scale transformation is subjected to the following steps according to a modeling formula:
wherein s isn(t') is the target signal by scaling; x (t') is a parameter to be solved of the model obtained according to the modeling formula;
is the second derivative of x (t');
solving and drawing the modeling formula by using a fourth-order Runge-Kutta algorithm to obtain a phase plane trajectory diagram of each equation solution, judging whether the phase plane trajectory diagram enters a large-period state, if so, continuing to execute S5, otherwise, returning to S1 to continue executing;
s5, judgment wtarget＞wmaxIf yes, finishing the iteration of the algorithm and outputting w of the target signaltarget(ii) a Otherwise adaptively update wtarget，wtargetThe increment of (a) is 0.1 xwtargetAnd update wtargetSubstituting t' to solve, namely returning to S4 to continue execution.
2. The adaptive Duffing oscillator magnetic anomaly signal detection method as claimed in claim 1, wherein the number of sample points of the hamming window function in S2 is 512.
3. The adaptive Duffing oscillator magnetic anomaly signal detection method as claimed in claim 1, wherein w in S5targetThe initial value of (a) is 0.01, and Δ w is 0.001.
4. The method for detecting the adaptive Duffing oscillator magnetic anomaly signal according to claim 1, wherein the specific method for judging whether the phase plane trajectory diagram enters a large period state comprises the following steps:
the phase plane trajectory diagram is an elliptical phase plane trajectory, and the interior of the elliptical phase plane trajectory is not in a chaotic state, so that the phase plane trajectory diagram is considered to enter a large-cycle state.
5. The adaptive Duffing oscillator magnetic anomaly signal detection method according to claim 1, wherein f (t) in S3 is decomposed by a multi-resolution analysis algorithm according to the formula:
wherein, f (t) is a magnetic abnormal signal, t is a time variable, j is an expansion scale, and k is a fixed parameter; c. Cj，k、dj，kRespectively, f (t) expansion coefficients on the j scale: c. Cj，kIs a scale factor, dj，kIs a wavelet coefficient; phi (2)-jt-k) is a scale function, ψ (2)- jt-k) is a wavelet function; z is an integer set.
6. The adaptive Duffing oscillator magnetic anomaly signal detection method as claimed in claim 1, wherein c in S3j，kThe formula after the scale decomposition is as follows:
wherein h is0(t-2k) is a low-pass filter function, h1(t-2k) is a high pass filter function.
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Application publication date: 20210402 |