A Method and System for Detecting Axial Frequency Magnetic Field of Underwater Targets Based on Inductive Sensor Array

Abstract

This invention discloses an underwater target axial frequency magnetic field detection method based on an inductive sensor array, comprising: setting up a first sensor array and a second sensor array to capture a first signal and a second signal; preprocessing the first signal and the second signal and suppressing noise and interference line spectra to obtain a detection signal, a reference signal, and a target signal; inputting the target signal into an intermittent chaotic oscillator system to obtain the time-domain diagram output by the intermittent chaotic oscillator system, and determining the target line spectrum in the target signal based on the time-domain diagram and obtaining the internal driving frequency of the intermittent chaotic oscillator in this state; and using Hilbert envelope analysis to obtain its spectral information and analyzing the line spectrum information of the target signal. The technical solution of this invention can suppress interference in the detection signal; improve the signal-to-noise ratio of the target signal by more than 20 dB under extremely low signal-to-noise ratio conditions; and achieve long-distance axial frequency magnetic field signal detection with high accuracy and low false alarm rate.

Description

Technical Field

[0001] This invention relates to the field of weak signal amplification and underwater target detection technology, and in particular to a method and system for detecting the axial frequency magnetic field of underwater targets based on an inductive sensor array. Background Technology

[0002] Shaft-frequency magnetic fields are extremely low-frequency alternating magnetic fields generated by the periodic changes in contact resistance of the corrosion circuit in a ship's hull due to the rotation of an underwater target's propeller. This modulation of corrosion current and protective current results in the formation of these fields. The period of the shaft-frequency magnetic field is highly correlated with the propeller rotation frequency of the underwater target, containing rich ship characteristics in both the time and frequency domains. This provides a reliable basis for the detection, identification, and tracking of moving underwater targets. Furthermore, as an extremely low-frequency magnetic field, the attenuation effect of seawater during propagation is weak, enabling long-distance detection. However, the marine magnetic field environment is complex, especially in the complex magnetic field environment of nearshore areas where shaft-frequency signals are often submerged in noise, resulting in an extremely low signal-to-noise ratio.

[0003] Currently, shaft frequency magnetic field detection mainly relies on linear algorithms, including Fourier transform, bandpass filtering, Welch power spectrum analysis, and wavelet transform. However, these methods cannot achieve accurate detection under low signal-to-noise ratio (SNR) conditions. To address this issue, existing technologies have proposed methods such as sliding power spectrum estimation, lock-in amplification, and correlation detection. For example, wavelet modulus maxima are used to denoise the shaft velocity electric field, improving the performance of the detection algorithm. However, linear algorithms are not robust to non-Gaussian noise. To address this, decomposition methods such as empirical mode decomposition (EMD) are used to effectively screen intrinsic mode functions and suppress Gaussian noise with higher-order cumulants before extracting the shaft frequency electromagnetic field signal. However, the detection effect is limited in environments with an SNR below -5 dB. Furthermore, existing schemes propose methods such as stochastic resonance, adaptive filtering, and mode decomposition. However, existing nonlinear detection methods all suffer from problems such as mode aliasing, poor resolution, and ambiguous decision criteria.

[0004] Therefore, to address the shortcomings of the aforementioned known solutions and achieve high-precision detection of the underwater target axial frequency magnetic field, it is urgently necessary to find a method and system for underwater target axial frequency magnetic field detection based on an inductive sensor array to solve the above problems. This invention uses the raw signal collected after optimizing the node structure design and deployment position of the inductive sensor array as the target signal. Through target signal preprocessing, noise and interference spectrum suppression, intermittent chaotic oscillator system detection, and Hilbert envelope spectrum analysis, especially in the noise and interference spectrum suppression stage, multi-window spectral subtraction and whitening filtering are applied to signals from different nodes to suppress interference in the detected signal. Furthermore, the signal-to-noise ratio of the target signal is improved by more than 20 dB under low signal-to-noise ratio conditions. Finally, the success rate of axial frequency magnetic field signal detection is improved, and the number of false alarms is reduced. Summary of the Invention

[0005] To address the shortcomings and improvement needs of existing technologies, this invention provides a method for detecting the axial frequency magnetic field of underwater targets based on an inductive sensor array, characterized by comprising:

[0006] S1, A first sensor array and a second sensor array are set in the underwater target water area to capture the first signal and the second signal;

[0007] S2, after preprocessing the first signal and the second signal, the noise and interference line spectrum in the first signal and the second signal are suppressed to obtain the detection signal, reference signal, differential signal and target signal;

[0008] S3, input the target signal into the intermittent chaotic oscillator system to obtain the time-domain diagram of the output of the intermittent chaotic oscillator system, and determine the target line spectrum in the target signal based on the time-domain diagram and obtain the internal driving frequency of the intermittent chaotic oscillator in this state; and

[0009] S4. Use Hilbert envelope analysis to analyze the time domain diagram of the intermittent chaotic oscillator system output and obtain its spectrum information. Combine this with the internal driving frequency of the intermittent chaotic oscillator in this state to analyze the line spectrum information of the target signal.

[0010] Preferably, the first sensor array and the second sensor array constitute a first detection node and a second detection node, each including three inductive sensors. The inductive sensors form the X, Y, and Z axes of the Cartesian coordinate system of the detection node with the center of gravity of the detection node as the origin. The inductive sensors are fixed in a fixed bracket, and an inertial navigation device is installed on the fixed bracket.

[0011] Preferably, the preprocessing step for the first signal and the second signal includes:

[0012] S201, Remove outliers from the first signal and the second signal;

[0013] S202, Remove the DC quantity from the first signal and the second signal;

[0014] S203, convert the first signal and the second signal in the carrier coordinate system to signal expressions in the geographic coordinate system; and

[0015] S204, bandpass filtering is performed on the first signal and the second signal under the geographic coordinate system to complete the preprocessing.

[0016] Preferably, the method for removing outliers from the first and second signals in step S201 is as follows:

[0017] Calculate the first quartile Q1 and the third quartile Q3 in the signal;

[0018] Calculate the interquartile range (IQR) in the signal, and set the lower and upper limits for the threshold of outliers; and replace outliers with the previous non-outlier.

[0019] Preferably, step S203 specifically includes:

[0020] Read the yaw angle φ from the inertial navigation system output bn Pitch angle θ bn and roll angle ψ bn ;

[0021] Rotate φ about the Z-axis of the carrier coordinate system bn The angle is used to obtain the transition coordinate system ψ;

[0022] Rotate θ about the Y-axis of the transition coordinate system ψ bn The angle is used to obtain the transition coordinate system Θ; and

[0023] Rotate ψ about the X-axis of the transition coordinate system Θ bn The angle is used to obtain the geographic coordinate system, thereby obtaining the first signal and the second signal in the geographic coordinate system.

[0024] Preferably, the bandpass filtering step in step S204 is as follows:

[0025] The passband range of the bandpass filter is set to [0.130] Hz;

[0026] The bandpass filter is a second-order Butterworth bandpass filter, used to filter out power frequency electromagnetic field noise and geomagnetic field noise in the first signal and the second signal. The transfer function H(s) of the second-order Butterworth bandpass filter is expressed as follows:

[0027]

[0028] Where ω0 is the center circular frequency and Q is the quality factor.

[0029] Preferably, the step of suppressing noise and interference line spectra in the first signal and the second signal in step S2 includes:

[0030] S205, the first signal and the second signal are windowed using a Hamming window;

[0031] S206, For the windowed signal, perform Fourier transform on each window to extract the spectrum and phase spectrum of the first signal and the second signal;

[0032] S207, the spectra of the windowed signals of the first signal and the second signal are differentially divided, and the detection signal, reference signal, and differential signal are identified based on the differential result; and

[0033] S208, using the phase spectrum of each window of the detection signal and the spectrum of the differential signal to obtain the interference line spectrum suppression signal.

[0034] Preferably, the Hamming window segmentation formula in step S205 is as follows:

[0035]

[0036] Where w(n) is the Hamming window function, N is the number of windows, and a0 is the Hamming window coefficient.

[0037] Preferably, the discrete Fourier transform used to extract the spectrum and phase spectrum in step S206 is performed as follows:

[0038] The frequency domain sequence after the discrete Fourier transform is as follows:

[0039]

[0040] Where x(n) is the discrete time-domain sequence of the first signal or the second signal, X(k) is the frequency-domain sequence after its discrete Fourier transform, N is the length of the sequence, k represents the discrete frequency index, and n is the discrete time index.

[0041] The discrete-time Fourier transform is used to extract the phase spectrum as follows:

[0042]

[0043] Where Im represents the imaginary part of the complex number, and Re represents the real part of the complex number.

[0044] Preferably, in step S207, the spectra of the probe signal and the reference signal after windowing are differentially analyzed, as shown in the following expression:

[0045]

[0046] Where x k (n) represents the data of each window after windowing, w(n) is the Hamming window function, and x k1 (ω) represents the spectral data of each window of the probe signal, x k2 (ω) represents the spectral data of each window of the reference signal, Y k (ω) is the spectrum after subtraction of the k-th window, denoted as the k-th window differential signal in the differential signal.

[0047] Preferably, step S208 specifically includes the following steps:

[0048] The average of the spectral data from each window of the differential signal is calculated using the following formula:

[0049]

[0050] Where M is the number of windows;

[0051] The method for obtaining the interference line spectrum suppression signal based on the phase spectrum of each window of the detection signal and the spectrum of the differential signal is as follows:

[0052]

[0053] Where y(n) is the interference line spectrum suppression signal and N is the sequence length.

[0054] Preferably, step S2, which involves suppressing noise and interference line spectra in the first and second signals, further includes whitening filtering and variational mode decomposition, as follows:

[0055] S209, the interference line spectrum suppression signal is input to the whitening filter to obtain the whitening filtered signal, wherein the expression of the whitening filter is:

[0056]

[0057] Where P is the model order, a k The coefficients are those of the autoregressive model, and z is a complex variable in the Z-transform.

[0058] S210, Perform variational mode decomposition on the whitening filtered signal, and update the modes and frequencies of the decomposed whitening filtered signal, wherein the objective function expression is:

[0059]

[0060] Where K is the number of modes in the decomposition, u k It is the k-th mode, f k It is the frequency corresponding to the k-th mode.

[0061] α is the penalty factor, the number of modes K in the decomposition is set to 8, and the penalty factor α is set to 9500;

[0062] S211, after the objective function reaches the preset convergence condition, extract each modal component of the whitening filtered signal and the frequency corresponding to each modal component; and

[0063] S212, Select the modal component containing the target signal from each modality to obtain the denoised target signal.

[0064] Preferably, step S3 further includes:

[0065] S31, determine the driving force of the intermittent chaotic oscillator system, wherein the intermittent chaotic model is:

[0066] y″+ky′-ay+by 3 =γcos(ωt)+s(t)

[0067] Where k is the damping coefficient, -ax+bx 3 It is a nonlinear dynamic term, γ is the internal driving force, y is the output of intermittent chaos, s(t) is the target signal, and ω is the internal driving frequency; and

[0068] S32, change the solution step size of the intermittent chaotic oscillator system and the magnitude of the internal driving force, and detect the target signal. When the target signal contains a frequency difference of less than 0.08ω from the internal driving frequency, the system will exhibit intermittent chaos.

[0069] Preferably, step S4 specifically includes:

[0070] S41: Perform Hilbert envelope analysis on the time-domain output of the intermittent chaotic oscillator system, where the Hilbert transform expression is as follows:

[0071]

[0072] The Hilbert envelope expression is as follows:

[0073]

[0074] S42: Perform a Fourier transform on the Hilbert envelope;

[0075] S43: Based on the spectrum diagram, analyze the detection results of the target signal. When the spectrum of the Hilbert envelope shows a line spectrum within 0.08ω, calculate the energy ratio of the line spectrum relative to the line spectra of other frequencies. If the energy ratio exceeds 10dB, determine that the intermittent chaotic oscillator system has detected the target signal.

[0076] This invention also discloses an underwater target axial frequency magnetic field detection system based on an inductive sensor array, characterized in that it comprises:

[0077] The signal acquisition unit is used to acquire the axial frequency magnetic field signal of the underwater target, including the first signal and the second signal;

[0078] A signal processing unit is used to process the first signal and the second signal according to the method shown in step S2 above.

[0079] A signal detection unit is used to detect the target signal according to the method shown in step S3 above; and

[0080] The signal analysis unit is used to analyze the target signal according to the method shown in step S4 above.

[0081] In summary, the above-described technical solutions conceived in this invention can achieve the following beneficial effects:

[0082] (1) It can suppress interference present in the detection signal;

[0083] (2) Improve the signal-to-noise ratio of the target signal by more than 20dB under extremely low signal-to-noise ratio conditions;

[0084] (3) It can detect long-distance axial frequency magnetic field signals and has high accuracy and low false alarm rate. Attached Figure Description

[0085] Figure 1 The diagram shown is a flowchart of an underwater target axial frequency magnetic field detection method based on an inductive sensor array according to an embodiment of the present invention.

[0086] Figure 2 The diagram shows a flowchart of signal processing in an underwater target axial frequency magnetic field detection method based on an inductive sensor array according to an embodiment of the present invention.

[0087] Figure 3 The diagram shows a flowchart of signal detection in an underwater target axial frequency magnetic field detection method based on an inductive sensor array according to an embodiment of the present invention.

[0088] Figure 4 The diagram shows a flowchart of signal analysis in an underwater target axial frequency magnetic field detection method based on an inductive sensor array according to an embodiment of the present invention.

[0089] Figure 5 The diagram shown is a block diagram of an underwater target axial frequency magnetic field detection system based on an inductive sensor array according to an embodiment of the present invention.

[0090] Figure 6 The diagram shows the mounting bracket for the fixed inductive sensor array used in the experiment.

[0091] Figure 7 The figure shows the time-domain plot and spectrum of the target signal when the target signal contains the axis frequency signal in the experiment;

[0092] Figure 8 The figure shows the time-domain diagram and the spectrum of the target signal after signal processing in the embodiment of the present invention.

[0093] Figure 9The figure shows the time-domain plot of the intermittent chaotic system output after the target signal is input into the intermittent chaotic oscillator system and after Hilbert envelope analysis, as well as the linear amplitude spectrum of the Hilbert envelope.

[0094] Figure 10 The table shown is the detection error table from the experiment; and

[0095] Figure 11 The table shown is a statistical table of false alarm rates during the experiment; Detailed Implementation

[0096] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0097] In this invention, the terms "first," "second," etc. (if present) in the invention and the accompanying drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence.

[0098] Figure 1 The diagram shows a flowchart of an underwater target axial frequency magnetic field detection method based on an inductive sensor array according to an embodiment of the present invention. In axial frequency magnetic field detection, background noise mainly consists of environmental magnetic field noise such as geological noise from the Earth's magnetic field, diurnal variation noise, and power frequency electromagnetic field noise. Compared to environmental noise, the axial frequency magnetic field signal is often much weaker. Figure 1 As shown, the underwater target axis frequency magnetic field detection method disclosed in this invention includes the following steps:

[0099] Step S1: Set up a first sensor array and a second sensor array in the target underwater water area to capture the first and second signals. Specifically, set up two detection points in the water area where the axial frequency magnetic field to be captured. Each detection point is equipped with an inductive sensor array, one of which is the first sensor array and the other is the second sensor array. The axial frequency magnetic field signal captured by the first sensor array is called the first signal, and the axial frequency magnetic field signal captured by the second sensor array is called the second signal. Both the first and second signals are raw signals containing the target magnetic field signal and noise signal. Usually, the raw signal is denoted as x(t), the target magnetic field signal is denoted as s(t), and the noise signal is denoted as n(t), where t is the observation time, and x(t) = s(t) + n(t).

[0100] Furthermore, each of the sensor arrays at the aforementioned detection points includes three inductive sensors. The inductive sensors form the X, Y, and Z axes of the Cartesian coordinate system of the detection node with the centroid of the detection node as the origin. The inductive sensors are fixed in a fixed bracket, and an inertial navigation device is installed on the fixed bracket. The first sensor array and the second sensor array are also referred to as the first detection node and the second detection node.

[0101] Step S2: After preprocessing the first signal and the second signal, noise and interference line spectrum in the first signal and the second signal are suppressed to obtain the detection signal, reference signal, differential signal and target signal.

[0102] Figure 2 The diagram shows a flowchart of signal processing in the underwater target axial frequency magnetic field detection method based on an inductive sensor array according to an embodiment of the present invention, specifically a flowchart of signal processing in step S2.

[0103] Specifically, the preprocessing methods for the first and second signals are as follows:

[0104] S201, Remove outliers from the first and second signals; In one embodiment, firstly calculate the first quartile Q1 and the third quartile Q3 for each data point, then calculate the interquartile range (IQR), and simultaneously set a threshold for outliers, for example, using 1.5 times the IQR as the fluctuation value, where the lower limit of the threshold is Q1 - 1.5 × IQR and the upper limit of the threshold is Q3 + 1.5 × IQR. Values ​​below the lower limit or above the upper limit are considered outliers. Finally, replace the outlier with the previous non-outlier value, where the previous non-outlier value refers to the value in the original data that precedes the outlier value.

[0105] S202, Remove DC noise from the first and second signals; specifically, after completing step S201, remove DC noise from the first and second signals to filter out the influence of DC magnetic field noise in the environment.

[0106] S203, the first and second signals in the carrier coordinate system are transformed into signal expressions in the geographic coordinate system; further, the first and second signals after processing in step S202 are subjected to coordinate transformation processing. In the embodiments of the present invention, since the attitude and orientation of the two detection nodes cannot be kept completely consistent when the first and second detection nodes are deployed, in order to maintain the accuracy of the data, the first and second signals collected by the two detection nodes, namely the first detection node and the second detection node, are uniformly transformed into the geographic coordinate system. Specifically, the original coordinate system is called the carrier coordinate system, and the formula for transforming the carrier coordinate system to the geographic coordinate system is as follows:

[0107]

[0108] in, This refers to the data from three single-axis inductive sensors at the detection node, in the carrier coordinate system, specifically the coordinate values ​​along the x, y, and z axes. These are the coordinate values ​​of the x, v, and z axes in the transformed geographic coordinate system, where

[0109] Let φ be the rotation matrix from the carrier coordinate system to the geographic coordinate system. bn θ bn ψ bn These are the yaw angle, pitch angle, and roll angle output by the attitude sensors of the detection node, respectively. For example, the yaw angle φ is obtained by an inertial navigation device mounted on a fixed support for the fixed sensor array. bn Pitch angle θ bn and roll angle ψ bn Specifically, rotating φ around the Z-axis of the carrier coordinate system bn An angle is used to obtain the transition coordinate system ψ; rotation θ around the Y-axis of the transition coordinate system ψ bn The angle is used to obtain the transition coordinate system Θ; and the rotation ψ around the X-axis of the transition coordinate system Θ is also used. bn The angle is used to obtain the geographic coordinate system, thereby obtaining the expressions for the first and second signals in the geographic coordinate system.

[0110] S204, bandpass filtering is performed on the first and second signals in the geographic coordinate system to complete the preprocessing. In one embodiment, after converting the first and second signals in the carrier coordinate system to the geographic coordinate system, bandpass filtering is performed on the converted signals. Based on the distribution of typical underwater background magnetic field noise frequency bands, in this embodiment of the invention, the filter is a second-order Butterworth bandpass filter, and the passband range of the filter is set to [0.130] Hz. The transfer function H(s) of the second-order Butterworth bandpass filter is expressed as follows:

[0111]

[0112] Wherein, ω0 is the center circular frequency and Q is the quality factor. In one embodiment of the present invention, the center circular frequency ω0 is set to 94.561937Hz and the quality factor Q is set to 1.00668896. After the first signal and the second signal are input to the second-order Butterworth bandpass filter, the filter can filter out the environmental magnetic field noise of power frequency electromagnetic field and geomagnetic field.

[0113] S205, the first signal and the second signal are windowed using a Hamming window. Here, the first and second signals are the signals obtained after filtering in step S204. In this invention, the signals in each step are based on the results of previous processing; to avoid redundancy, subsequent steps will not emphasize that they are the processed first and second signals. The first and second signals are then windowed and framed. Specifically, a Hamming window is applied to the signals, and the windowing formula is as follows:

[0114]

[0115] w(n) is the Hamming window function, N is the number of windows, and a0 is the Hamming window coefficient.

[0116] S206, For the windowed signal, perform a Fourier transform on each window to extract the spectrum and phase spectrum of the first and second signals; the specific formula for obtaining the spectrum by performing a Fourier transform on the signal is as follows:

[0117]

[0118] Where x(n) is the discrete time-domain sequence of the input signal, specifically the discrete time-domain sequence of either the first or second signal, X(k) is its frequency-domain sequence after discrete Fourier transform, N is the length of the sequence, k represents the discrete frequency index, and n is the discrete time index. Furthermore, the formula for obtaining the phase spectrum by performing a Fourier transform on the signal is as follows:

[0119]

[0120] Where Im represents the imaginary part of the frequency domain sequence X(k), and Re represents the real part of the frequency domain sequence X(k).

[0121] S207, the spectra of the windowed signals of the first signal and the second signal are differentially analyzed, and the probe signal, reference signal, and differential signal are identified based on the differential result. In an embodiment of the present invention, after differentially analyzing the spectra of the windowed signals of the first signal and the second signal, if line spectrum information is displayed in the differential result, then the first signal is the probe signal and the second signal is the reference signal; otherwise, the first signal is the reference signal and the second signal is the probe signal. The differential signal is the spectrum of the probe signal minus the spectrum of the reference signal. The method for selecting the probe signal and reference signal from the first signal and the second signal is a conventional method in the art and will not be described in detail to avoid redundancy. Further, the formula for differentially analyzing the spectra of the probe signal and the reference signal after windowing is as follows:

[0122]

[0123] Where, x kw(n) represents the data of each window after windowing, w(n) is the Hamming window function, and x(n) is the input signal, such as a probe signal or a reference signal. k1 (ω) represents the spectral data of each window of the probe signal, x k2 (ω) represents the spectral data of each window of the reference signal, Y k (ω) is the spectrum of the subtraction of the k-th window, denoted as the k-th window differential signal in the differential signal.

[0124] S208, the interference line spectrum suppression signal is obtained using the phase spectrum of each window of the probe signal and the spectrum of the differential signal. Further, the average value of the spectrum of each window of the differential signal is obtained, denoted as the spectrum estimate with the smallest error, calculated using the following formula:

[0125]

[0126] Where M is the number of windows.

[0127] Furthermore, based on the phase spectrum and spectral estimation of each window of the detected signal... The interference line spectrum suppression signal is obtained using the following calculation formula:

[0128]

[0129] Where y(n) is the interference line spectrum suppression signal. For spectrum estimation, N is the number of windows.

[0130] S209, The interference line spectrum suppression signal is input to the whitening filter to obtain the whitening filtered signal, where the expression of the whitening filter is:

[0131]

[0132] Where P is the model order, a k Here are the coefficients of the autoregressive model, z is the complex variable in the Z-transform, and the interference line spectrum suppression signal y(n) is input into the AR whitening filter to obtain the output signal W(n) whose power spectral density is closer to that of white noise, which is denoted as the whitening filter signal.

[0133] S210, Perform variational mode decomposition on the whitening filtered signal W(n), and update the modes and frequencies of the decomposed whitening filtered signal, where the objective function expression is:

[0134]

[0135] Where K is the number of modes in the decomposition, u k It is the k-th mode, f kis the frequency corresponding to the k-th mode, α is the penalty factor, the number of decomposed modes K is set to 8, and the penalty factor α is set to 9500. Specifically, after determining the number of modes K and the penalty factor α of the variational mode decomposition, the whitening filter signal W(n) can be input into the objective function of the variational mode decomposition, and the Lagrange multiplier is introduced. The alternating direction multiplier method is used to iteratively solve the objective function to update the decomposed modes and frequencies.

[0136] S211. After the objective function reaches the preset convergence condition, extract each modal component of the whitening filter signal W(n) and the frequency corresponding to each modal component. Specifically, after the objective function reaches the set convergence condition during the cyclic iteration process, the iteration can be stopped, and each mode and its corresponding frequency can be extracted from the optimization result. Here, the convergence condition can be set according to experience.

[0137] S212. Select the modal components containing the target signal from each mode to obtain the denoised target signal. Specifically, when the iteration stops, select the modal components containing the target signal from each mode to complete the suppression of the background magnetic field noise and environmental interference line spectrum in the original detection signal, and obtain the denoised target signal. Here, the target signal refers to the detection signal after completing step S2, that is, the signal representing the position or information of the underwater target in the axial frequency magnetic field of the underwater target extracted from the detection signal. After obtaining the target signal through the method disclosed in step S2, further detect the target signal to check the quality of the target signal.

[0138] S3: Input the target signal into the intermittent chaotic oscillator system to obtain the time-domain diagram output by the intermittent chaotic oscillator system, and judge the target line spectrum in the target signal according to the time-domain diagram and obtain the internal driving frequency of the intermittent chaotic oscillator in this state. Step S3 is the detection of the target signal.

[0139] S4: Use Hilbert envelope analysis for the time-domain diagram output by the intermittent chaotic oscillator system to obtain its spectral information, and analyze the line spectrum information of the target signal in combination with the internal driving frequency of the intermittent chaotic oscillator in this state. Step S4 is the analysis of the target signal.

[0140] Figure 3 The figure shows the flowchart of signal detection in the underwater target axial frequency magnetic field detection method based on an inductive sensor array provided by an embodiment of the present invention. Figure 1 The detailed step diagram of step S3 in the figure. Figure 3 will be described in combination with Figure 1 The specific steps in step S3 are as follows:

[0141] S31. Determine the driving force of the intermittent chaotic oscillator system, where the intermittent chaotic oscillator model is:

[0142] y″+ky′ - ay+by3 =γcos(ωt)+s(t)

[0143] Where k is the damping coefficient, -ax+bx 3 It is a nonlinear dynamic term, γ is the internal driving force, y is the output of intermittent chaos, s(t) is the target signal, and ω is the internal driving frequency.

[0144] In one embodiment of the present invention, the method for determining the internal driving force γ is as follows: First, the threshold of the intermittent chaotic oscillator system is determined. In the absence of an input signal, the expression for the intermittent chaotic oscillator system is:

[0145] x″+kx′-ax+bx 3 =γcos(ωt)

[0146] Where k is the damping coefficient, -ax+bx 3 Here, γ is the nonlinear dynamic term, x is the output of the intermittent chaos, and ω is the internal driving frequency. Without input, the parameters are determined by calculating the multi-scale entropy of the output of the intermittent chaos with different parameters. The formula for calculating the multi-scale entropy is as follows:

[0147]

[0148] Where SampleEn is the sample entropy, m is the embedding dimension, r is the similarity tolerance, N is the data length, and τ is the time scale. The output state of the intermittent chaotic oscillator system is measured by multi-scale entropy to find the critical value between chaos and large-period state. The threshold at this time is used as the magnitude of the internal driving force γ. The internal driving force γ is substituted into the intermittent chaotic oscillator model to determine the intermittent chaotic oscillator model.

[0149] S32, the target signal is detected by changing the solution step size and the magnitude of the internal driving force of the intermittent chaotic oscillator system. Specifically, after the target signal is input into the intermittent chaotic oscillator system, the target signal is detected by continuously changing the solution step size and the magnitude of the internal driving force γ. If the input target signal contains a frequency with a frequency difference less than 0.08ω (ω is the magnitude of the internal driving frequency) from the internal driving frequency, the intermittent chaotic oscillator system will exhibit intermittent chaos. Furthermore, the flowchart of the underwater target axial frequency magnetic field detection method based on an inductive sensor array disclosed in this invention also includes:

[0150] Figure 4 The diagram shows a flowchart of signal analysis in an underwater target axial frequency magnetic field detection method based on an inductive sensor array according to an embodiment of the present invention. Figure 1 The detailed steps for analyzing the target signal in step S4 include:

[0151] S41: Perform Hilbert envelope analysis on the time-domain output of the intermittent chaotic oscillator system, where the Hilbert transform expression is as follows:

[0152]

[0153] The Hilbert envelope expression is as follows:

[0154]

[0155] S42: Perform Fourier transform on the Hilbert envelope;

[0156] S43: Based on the spectrum diagram, analyze the detection results of the target signal. When the spectrum of the Hilbert envelope shows a line spectrum within 0.08ω, calculate the energy ratio of the line spectrum relative to the line spectrum of other frequencies. If the energy ratio exceeds 10dB, it is determined that the intermittent chaotic oscillator system has detected the target signal.

[0157] In summary, the underwater target axial frequency magnetic field detection method based on an inductive sensor array disclosed in this invention suppresses background environmental magnetic field noise and false line spectra in underwater targets, and detects the axial frequency line spectrum signal of the underwater target. The detection method disclosed in this invention can suppress interference present in the detection signal, improve the signal-to-noise ratio of the target signal by more than 20 dB under extremely low signal-to-noise ratio conditions, and achieve long-distance axial frequency magnetic field signal detection with high accuracy and low false alarm rate.

[0158] Figure 5 An underwater target axial frequency magnetic field detection system based on an inductive sensor array, according to an embodiment of the present invention, Figure 5 Combining Figure 1 Describe it. For example... Figure 5 As shown, the underwater target axial frequency magnetic field detection system based on an inductive sensor array includes: a signal acquisition unit 501, a signal processing unit 502, a signal detection unit 503, and a signal analysis unit 504. The signal acquisition unit 501 includes... Figure 1 The first and second inductive sensor arrays disclosed herein are used to collect axial frequency magnetic field signals within an underwater target water area, respectively capturing a first signal and a second signal; the signal processing unit 502 is used to process the signals according to the above... Figure 1 The method disclosed in step S2 processes the first signal and the second signal. The signal detection unit 503 is used to process the first signal and the second signal according to the above... Figure 1 The method disclosed in step S3 is used to detect the target signal; the signal analysis unit 504 is used to detect the target signal according to the above. Figure 1 The method disclosed in step S4 is used to analyze the target signal.

[0159] The underwater target axial frequency magnetic field detection system based on an inductive sensor array disclosed in this invention designs and optimizes the structure and placement of the sensor array nodes, and acquires detection and reference signals through the optimized inductive magnetic sensor array. After preprocessing the detection and reference signals, background noise and environmental interference line spectra in the detection signals are suppressed through windowing subtraction, whitening filtering, and variational mode decomposition. The noise-reduced detection signals are detected by an intermittent chaotic oscillator system. After obtaining the output time-domain diagram of the intermittent chaotic oscillator system, a preliminary judgment can be made on the presence of target line spectra in the target signal. Subsequently, Hilbert envelope analysis is used to extract the line spectrum information in the target signal, and the results of the Hilbert envelope analysis are evaluated. Compared with existing technologies, the underwater target axial frequency magnetic field detection system based on an inductive sensor array proposed in this invention can effectively suppress background noise and interference line spectra in underwater target axial frequency magnetic field detection, effectively achieve background noise suppression and detection of weak axial frequency line spectrum signals at extremely low signal-to-noise ratios, and solve the technical problems of high background noise intensity and numerous false line spectrum interferences in existing underwater target axial frequency magnetic field detection, which lead to difficulties in line spectrum identification.

[0160] To demonstrate the superior performance of this invention in detecting axis frequency magnetic field signals, the performance of this method is shown and analyzed using field test data.

[0161] Figure 6 The figure shows the fixed support for the fixed inductive sensor array used in the experiment; as shown in the figure, the inductive sensor array in the fixed support is arranged in the form of a three-dimensional coordinate diagram.

[0162] The experiment used a coil to generate a periodic magnetic field signal to simulate the shaft frequency magnetic field signal. The period of the simulated magnetic field signal was set to 9.5 Hz, and the equivalent magnetic moment of the coil was approximately 50 Am². Following the aforementioned placement of the detection nodes, the two detection nodes were approximately 200 meters apart. The coil was placed approximately 320 meters from the nearest detection node, with a sampling rate of 250 Hz and a sampling time of 5 minutes. The five-minute signal was then analyzed.

[0163] Figure 7 The figure shows the time-domain plot and spectrum of the target signal when the target signal contains the axis frequency signal in the experiment; Figure 8 The figure shows the time-domain diagram and the spectrum of the target signal after signal processing in the embodiment of the present invention.

[0164] The test results clearly show that it exhibits excellent performance in all key performance indicators. Regarding the signal-to-noise ratio improvement, as indicated in the instruction manual appendix... Figure 7 and attached Figure 8 contrast, Figure 7 For the signal acquired from the nearest measuring point, from Figure 7 As can be seen, a 9.5Hz signal cannot be directly detected, either in the time domain or in the signal's spectrum analysis. Figure 8 It can be seen that the target signal after calculation and processing is clearly visible in the spectrum. Signal-to-noise ratio (SNR) calculations show that the SNR has improved by nearly 40 dB. This is mainly due to techniques for suppressing environmental background noise, magnetic field noise, and spurious line spectra. By performing multi-window spectral subtraction on two sets of detection nodes 200 meters apart, environmental background noise, magnetic field noise, and interfering spurious line spectra are suppressed. Simultaneously, whitening filtering is applied to the differential data, effectively suppressing 1 / f magnetic field noise in the environment. Finally, variational mode decomposition is used to remove significant noise, effectively improving the SNR of the target signal.

[0165] Figure 9 The figure shows the time-domain plot of the intermittent chaotic system output after the target signal is input into the intermittent chaotic oscillator system and after Hilbert envelope analysis, as well as the linear amplitude spectrum of the Hilbert envelope. Figure 10 The table shown is the detection error table from the experiment; and Figure 11 The table shown is a statistical table of false alarm rates during the experiment.

[0166] In terms of detection indicators, its unique design and technology enable precise detection of target signal frequencies. Regarding detection indicators, such as... Figure 9 As shown, the detection results yielded a detection frequency of 9.499372 Hz, with an error of only 0.0066% between the calculated result and the actual target signal frequency of 9.5 Hz. Among the 15 data samples detected, as shown in Appendix Table 10 of the specification, 14 detections were successful, achieving a success rate of 93.3%. This experiment also analyzed the false alarm rate of the detection signal. Thirty environmental magnetic field data samples without target signals were selected and processed using the method of this patent. The final processed data, as shown in Appendix Table 11 of the specification, showed only one false alarm, with a false alarm rate of only 3.3%, fully demonstrating the superiority and advancement of the underwater target axial frequency magnetic field detection method based on an inductive sensor array disclosed in this invention.

[0167] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for detecting the axial frequency magnetic field of an underwater target based on an inductive sensor array, characterized in that, include: S1, A first sensor array and a second sensor array are set in the target underwater water area to capture the first signal and the second signal; S2, after preprocessing the first signal and the second signal, the noise and interference line spectrum in the first signal and the second signal are suppressed to obtain the detection signal, reference signal, differential signal and target signal. Background noise and environmental interference line spectrum in the detection signal are suppressed by windowing spectrum subtraction, whitening filtering and variational mode decomposition. S3, input the target signal into the intermittent chaotic oscillator system to obtain the time domain diagram output by the intermittent chaotic oscillator system, and determine the target line spectrum in the target signal based on the time domain diagram and obtain the internal driving frequency of the intermittent chaotic oscillator in this state; as well as S4. Use Hilbert envelope analysis to analyze the time domain diagram of the intermittent chaotic oscillator system output and obtain its spectrum information. Combine this with the internal driving frequency of the intermittent chaotic oscillator in this state to analyze the line spectrum information of the target signal.

2. The underwater target axial frequency magnetic field detection method based on an inductive sensor array according to claim 1, characterized in that, The first sensor array and the second sensor array constitute a first detection node and a second detection node, each including three inductive sensors. The inductive sensors form the X, Y, and Z axes of the Cartesian coordinate system of the detection node with the centroid of the detection node as the origin. The inductive sensors are fixed in a fixed bracket, and an inertial navigation device is installed on the fixed bracket.

3. The underwater target axial frequency magnetic field detection method based on an inductive sensor array according to claim 1, characterized in that, The steps for preprocessing the first signal and the second signal include: S201, Remove outliers from the first signal and the second signal; S202, Remove the DC quantity from the first signal and the second signal; S203, convert the first signal and the second signal in the carrier coordinate system to signal expressions in the geographic coordinate system; and S204, bandpass filtering is performed on the first signal and the second signal under the geographic coordinate system to complete the preprocessing.

4. The underwater target axial frequency magnetic field detection method based on an inductive sensor array according to claim 3, characterized in that, The method for removing outliers from the first and second signals in step S201 is as follows: Calculate the first quartile Q1 and the third quartile Q3 in the signal; Calculate the interquartile range (IQR) in the signal and set the lower and upper limits for the threshold of outliers; as well as Replace the outlier with the previous non-outlier.

5. The underwater target axial frequency magnetic field detection method based on an inductive sensor array according to claim 3, characterized in that, Step S203 specifically includes: Read the yaw angle output by the inertial navigation system Pitch angle and roll angle ; Rotation about the Z-axis of the carrier coordinate system Angles obtain the transition coordinate system ; Around the transition coordinate system Y-axis rotation Angles obtain the transition coordinate system ;as well as Around the transition coordinate system X-axis rotation The angle is used to obtain the geographic coordinate system, thereby obtaining the first signal and the second signal in the geographic coordinate system.

6. The underwater target axial frequency magnetic field detection method based on an inductive sensor array according to claim 3, characterized in that, The bandpass filtering step in step S204 is as follows: The passband range of the bandpass filter is set to [0.1, 30] Hz; The bandpass filter is a second-order Butterworth bandpass filter, used to filter out power frequency electromagnetic field noise and geomagnetic field noise in the first signal and the second signal. The transfer function of the second-order Butterworth bandpass filter is... The expression is as follows: in, Let Q be the center circular frequency and Q be the quality factor.

7. The underwater target axial frequency magnetic field detection method based on an inductive sensor array according to claim 1, characterized in that, The suppression of noise and interference line spectra in the first signal and the second signal in step S2 includes: S205, the first signal and the second signal are windowed using a Hamming window; S206, For the windowed signal, perform Fourier transform on each window to extract the spectrum and phase spectrum of the first signal and the second signal; S207, the spectra of the windowed signals of the first signal and the second signal are differentially analyzed, and the detection signal, reference signal, and differential signal are identified based on the differential result; and S208, using the phase spectrum of each window of the detection signal and the spectrum of the differential signal to obtain the interference line spectrum suppression signal.

8. The underwater target axial frequency magnetic field detection method based on an inductive sensor array according to claim 7, characterized in that, The Hamming window division formula mentioned in step S205 is as follows: in Here, N is the Hamming window function, and N is the number of windows. This represents the Hamming window coefficient.

9. The underwater target axial frequency magnetic field detection method based on an inductive sensor array according to claim 7, characterized in that, The method for extracting the spectrum and phase spectrum using discrete Fourier transform in step S206 is as follows: The frequency domain sequence after the discrete Fourier transform is as follows: in It is a discrete time-domain sequence of either the first signal or the second signal. It is the frequency domain sequence after its discrete Fourier transform, where N is the length of the sequence, k represents the discrete frequency index, and n is the discrete time index. The discrete-time Fourier transform is used to extract the phase spectrum as follows: in Represents the imaginary part of a complex number. It represents the real part of a complex number.

10. The underwater target axial frequency magnetic field detection method based on an inductive sensor array according to claim 7, characterized in that, In step S207, the windowed spectra of the probe signal and the reference signal are differentially analyzed, as shown in the following expression: in For the data in each window after splitting, For Hamming window functions, For input signal, The spectrum data for each window of the probe signal. The spectral data for each window of the reference signal. The spectrum after subtraction of the k-th window is denoted as the k-th window differential signal in the differential signal.

11. The underwater target axial frequency magnetic field detection method based on an inductive sensor array according to claim 7, characterized in that, The specific steps of step S208 are as follows: The average of the spectral data from each window of the differential signal is calculated using the following formula: Where M is the number of windows; The method for obtaining the interference line spectrum suppression signal based on the phase spectrum of each window of the detection signal and the spectrum of the differential signal is as follows: in, The signal is the interference line spectrum suppression signal, and N is the sequence length.

12. The underwater target axial frequency magnetic field detection method based on an inductive sensor array according to claim 7, characterized in that, The step S2, which involves suppressing noise and interference line spectra in the first and second signals, further includes whitening filtering and variational mode decomposition, as follows: S209, the interference line spectrum suppression signal is input to the whitening filter to obtain the whitening filtered signal, wherein the expression of the whitening filter is: Where P is the model order, The coefficients are those of the autoregressive model, and z is a complex variable in the Z-transform. S210, Perform variational mode decomposition on the whitening filtered signal, and update the modes and frequencies of the decomposed whitening filtered signal, wherein the objective function expression is: in It is the number of modes in the decomposition. It is the first One modality, It is the first The frequency corresponding to each mode The number of modes in the decomposition is the penalty factor. Set to 8, penalty factor Set to 9500; S211, after the objective function reaches the preset convergence condition, extract each modal component of the whitening filter signal and the frequency corresponding to each modal component; as well as S212, Select the modal component containing the target signal from each modality to obtain the denoised target signal.

13. The underwater target axial frequency magnetic field detection method based on an inductive sensor array according to claim 1, characterized in that, Step S3 also includes: S31, determine the driving force of the intermittent chaotic oscillator system, wherein the intermittent chaotic model is: in, The damping coefficient is... It is a nonlinear dynamic term. It is an internal driving force. It is an intermittent chaotic output. For target signal, For internal driving frequency; and S32, change the solution step size of the intermittent chaotic oscillator system and the magnitude of the internal driving force, and detect the target signal. When the target signal contains a frequency difference of less than 0.08ω from the internal driving frequency, the system will exhibit intermittent chaos.

14. The underwater target axial frequency magnetic field detection method based on an inductive sensor array according to claim 1, characterized in that, Step S4 specifically includes: S41: Perform Hilbert envelope analysis on the time-domain output of the intermittent chaotic oscillator system, where the Hilbert transform expression is as follows: The Hilbert envelope expression is as follows: S42: Perform a Fourier transform on the Hilbert envelope; S43: Based on the spectrum diagram, analyze the detection results of the target signal. When the spectrum of the Hilbert envelope shows a line spectrum within 0.08ω, calculate the energy ratio of the line spectrum relative to the line spectra of other frequencies. If the energy ratio exceeds 10dB, determine that the intermittent chaotic oscillator system has detected the target signal.

15. An underwater target axial frequency magnetic field detection system based on an inductive sensor array, characterized in that, include: The signal acquisition unit is used to acquire the axial frequency magnetic field signal of the underwater target, including the first signal and the second signal; A signal processing unit is configured to process the first signal and the second signal according to the method described in claim 1; A signal detection unit is configured to detect a target signal according to the method described in claim 1; and A signal analysis unit is used to analyze a target signal according to the method described in claim 1.

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