A magnetic anomaly detection method based on orthogonal basis neural network
By performing bandpass filtering and decomposition of the magnetic signal, weak and strong classifiers of orthogonal basis neural networks are constructed, which solves the problems of low accuracy and slow training in magnetic anomaly detection in traditional neural networks, and realizes efficient magnetic anomaly detection.
Patent Information
- Application Number
- CN202211707599.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-12-29
- Publication Date
- 2025-08-12
- Estimated Expiration
- 2042-12-29
AI Technical Summary
In magnetic abnormality detection, traditional BP neural networks are prone to low detection accuracy due to low signal-to-noise ratio, and the convergence speed during training is slow, which is easy to fall into local extreme values.
Using a method based on orthogonal basis neural network, the signal is bandpass filtered preprocessing and orthogonal basis function decomposition, three weak classifier models are constructed, and the activation function is expanded by Fourier series to form a strong classifier for magnetic anomaly detection.
It improves the accuracy of magnetic anomaly detection, reduces training time, avoids local optimal problems, and improves the convergence speed of the model.
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Figure CN115879053B_ABST
Abstract
Description
Technical Field
[0001] The technology of the present invention relates to signal processing and neural network, and belongs to the field of magnetic anomaly detection. Background Art
[0002] Magnetic anomaly target detection is a method of detecting the presence of ferromagnetic objects by determining whether there are anomalies in the magnetic field. It has many advantages. It is a passive non-destructive test that is not easily detected by the target and has good concealment. It can complete the detection even if the light is blocked. It has a wide range of applications in underwater target detection, mineral exploration and other fields.
[0003] When applying neural networks to magnetic anomaly detection, using traditional BP neural networks can lead to low detection accuracy due to a low signal-to-noise ratio. When there are too many nodes, the neural network structure becomes complex, convergence is slow during training, and the network can sometimes get stuck in local extremes.
[0004] The present invention discloses a magnetic anomaly detection method based on an orthogonal basis neural network. The method first performs bandpass filtering preprocessing on the signal to filter out noise outside the frequency band of the magnetic anomaly signal. The denoised signal is then decomposed using an orthogonal basis function (OBF) to obtain three sets of decomposition coefficients. The three sets of decomposition coefficients are then used as inputs of three orthogonal basis neural networks, and three weakly classified orthogonal basis neural networks are trained. Finally, the outputs of the weak classifications are fused to obtain a strong classifier. The presence of a magnetic anomaly is determined based on the output of the strong classifier. In the neural network model, an orthogonal basis neural network is used, the activation function is Fourier series expanded, orthogonal trigonometric functions are used as the activation functions of each hidden layer node of the neural network, and a weighted sum is used as the nonlinear output of the network to form a Fourier orthogonal basis neural network model. Since the weights from the input layer to the hidden layer are all 1, only the weights from the hidden layer to the output layer need to be obtained during training, which can greatly reduce training time and improve convergence speed. This method can reduce the training time of the neural network model, avoid falling into local optimality, and improve detection accuracy. Summary of the Invention
[0005] The present invention discloses a magnetic anomaly detection method based on an orthogonal basis neural network. The method is implemented as follows:
[0006] Step 1: Generate a training sample dataset. First, based on the magnetic dipole theory model, ideal magnetic anomaly signals under different conditions are generated, including magnetic anomaly signals of ferromagnetic targets at different CPA distances and different movement speeds. Then, pure geomagnetic background signals are collected at different time periods at the detection location. The ideal magnetic anomaly signals are added to the pure geomagnetic background signals to obtain magnetic anomaly signals containing geomagnetic noise. Labels are then added to each set of data, with the data label of the noisy magnetic anomaly signal set to 1 and the data label of the pure geomagnetic background signal set to 0. A dataset for training an orthogonal basis neural network is constructed using the noisy magnetic anomaly signals and the pure geomagnetic background signals.
[0007] Step 2: Preprocess the signal and perform bandpass filtering using wavelet decomposition and reconstruction to remove the mean and trend terms. Then, perform orthogonal basis function (OBF) decomposition on the filtered signal to obtain the decomposition coefficients of each group of signals on the three orthogonal basis functions. The calculation formula of the decomposition coefficients is:
[0008]
[0009] Among them, m is the data point number of the signal, α j (m) is the decomposition coefficient of the signal on the jth basis function, W is the size of the window, f j (w i ) is the standard orthogonal basis function, S(w m+i ) is the magnetic signal, w is a dimensionless parameter of the magnetic target motion trajectory, w i represents the i-th value, Δw is the interval between two adjacent w values, and the calculation formula of w is:
[0010]
[0011] Where D is the trajectory of the magnetic target, R0 is the shortest distance from the magnetic detector to the trajectory of the magnetic target, that is, the CPA (Closest Proximity Approach) distance; the three orthogonal basis functions f j (w i ) are calculated as follows:
[0012]
[0013]
[0014]
[0015] Step 3: Process the data obtained in step 1 as described in step 2, and then group the decomposition coefficients corresponding to each orthogonal basis into one category to form a data set. The three orthogonal bases form three data sets, called alpha1, alpha2, and alpha3 respectively.
[0016] Step 4: Build Figure 2 The Fourier orthogonal basis neural network shown in FIG has a three-layer structure, namely, an input layer, a hidden layer and an output layer, wherein the hidden layer contains n nodes, and the activation function of each node is an orthogonal triangular basis function; the weights between the input layer and the hidden layer are all 1, and the weights between the hidden layer and the output layer are obtained through training. The value of the output layer after the activation function is used as the detection result, and the output 1 indicates the presence of magnetic anomaly, and the output 0 indicates the absence of magnetic anomaly; the data sets alpha1, alpha2 and alpha3 obtained in step 3 and their labels are respectively used as the input and output of the orthogonal basis neural network model for training, and the connection weights between the hidden layer and the output layer are modified by feedback of the expected result error value, thereby obtaining three weak classifier models h1, h2 and h3 corresponding to the three groups of decomposition coefficients; then the outputs of the three weak classifiers are fused to obtain a model such as Figure 3 The strong classifier H shown in FIG. 1 ; wherein, the activation function formula of the orthogonal basis neural network is:
[0017]
[0018] The activation function is expanded and approximated by Fourier series as the sum of a series of orthogonal trigonometric functions:
[0019] g(x)=a+a0 cos x+b0 sin x+a1 cos 2x+b1 sin 2x+…+a n cos nx+b n sin nx
[0020] in:
[0021]
[0022]
[0023] Where T is the period of the Fourier series expansion, x0 is an arbitrary point of the Fourier series expansion, and n is the order of the Fourier series expansion. The above formula is converted into the output form of the general feedforward as follows:
[0024]
[0025] in, is the orthogonal basis function of the hidden layer, that is, the orthogonal trigonometric function after the activation function is expanded by Fourier series, c i is the connection weight between the hidden layer and the output layer, R(X) is the error value; y is the output of the neural network.
[0026] Step 5: Perform the preprocessing described in step 2 on the data to be detected, and then use the three decomposition coefficients obtained after preprocessing as the input of the three weak classifier models respectively. Finally, determine whether there is a magnetic anomaly based on the output of the strong classifier H. When the output of H is greater than the threshold, it indicates that a magnetic anomaly signal exists; when it is less than the threshold, it indicates that no magnetic anomaly signal exists. The calculation formula of the output of the strong classifier H is:
[0027]
[0028] Among them, Y H is the output of the strong classifier H, y hi is the output of weak classifier h1, h2, h3. H When it is greater than the threshold, it indicates that there is a magnetic anomaly signal; when it is less than the threshold, it indicates that there is no magnetic anomaly signal. BRIEF DESCRIPTION OF THE DRAWINGS
[0029] Figure 1 This is a flow chart of the magnetic anomaly detection method based on orthogonal basis neural network.
[0030] Figure 2 Schematic diagram of the structure of the orthogonal basis neural network.
[0031] Figure 3 This is the structural block diagram of the orthogonal basis neural network strong classifier. DETAILED DESCRIPTION
[0032] The following describes in detail a method for detecting magnetic anomalies based on an orthogonal basis neural network, with reference to the accompanying drawings and specific embodiments. The method comprises the following steps:
[0033] Step 1: Construct a data set of magnetic signals at the detection point. According to the magnetic dipole theoretical model, ideal magnetic anomaly signals under different conditions are generated, including magnetic anomaly signals of magnetic targets at different CPA distances and different movement speeds. At the same time, the pure geomagnetic background signals of the detection point in different time periods are collected at a sampling frequency of 10 Hz. The ideal magnetic anomaly signal is then superimposed with different pure geomagnetic background signals to obtain multiple groups of magnetic anomaly signals containing geomagnetic noise. Labels are then added to each group of data, and the data label of the noisy magnetic anomaly signal is set to 1, and the data label of the pure geomagnetic background signal is set to 0. The noisy magnetic anomaly signal and the pure geomagnetic background signal are used to construct a data set for training an orthogonal basis neural network. The calculation formula of the magnetic dipole theoretical model is:
[0034]
[0035] Where B is the magnetic field strength of the ideal magnetic anomaly signal, is the magnetic moment vector of the magnetic target, is the direction vector of the line connecting any point to the center point of the magnetic target, and μ0 is the magnetic permeability of vacuum.
[0036] Step 2: Preprocess the signal and perform wavelet decomposition on it. Decompose it into 10 layers and set the detail coefficients D1 to D3 and the approximate coefficient A10 to zero, that is, only retain the detail coefficients D4 to D10. Then reconstruct it to obtain the bandpass filtered signal. At this time, the mean and trend terms in the signal have been removed. Then perform orthogonal basis function (OBF) decomposition on the filtered signal to obtain the decomposition coefficients of each group of signals on three orthogonal bases. The calculation formula of the OBF decomposition coefficients is:
[0037]
[0038] Among them, m is the data point number of the signal, α j (m) is the decomposition coefficient of the signal on the jth basis function, W is the size of the window, f j (w i ) is the standard orthogonal basis function, S(w m+i ) is the magnetic signal, w is a dimensionless parameter of the magnetic target motion trajectory, w i represents the i-th value, Δw is the interval between two adjacent w values, and the calculation formula of w is:
[0039]
[0040] Where D is the coordinate point of the magnetic target motion trajectory, R0 is the shortest distance from the magnetic detector to the magnetic target motion trajectory, also known as CPA distance; the three orthogonal basis functions f j (w i ) are calculated as follows:
[0041]
[0042]
[0043]
[0044] Step 3: Process the data obtained in step 1 as described in step 2, and then classify the decomposition coefficients corresponding to each orthogonal basis into one category to form a data set. The three orthogonal bases form three data sets, which are called alpha1, alpha2 and alpha3 respectively.
[0045] Step 4: Build Figure 2The Fourier orthogonal basis neural network shown in FIG has a three-layer structure, namely, an input layer, a hidden layer and an output layer, wherein the hidden layer contains n nodes, and the activation function of each node is an orthogonal triangular basis function; the weights between the input layer and the hidden layer are all 1, and the weights between the hidden layer and the output layer are obtained through training. The value of the output layer after the activation function is used as the detection result, and the output 1 indicates the presence of magnetic anomaly, and the output 0 indicates the absence of magnetic anomaly; the data sets alpha1, alpha2 and alpha3 obtained in step 3 and their labels are respectively used as the input and output of the orthogonal basis neural network model for training, and the connection weights between the hidden layer and the output layer are modified by feedback of the expected result error value, thereby obtaining three weak classifier models h1, h2 and h3 corresponding to the three groups of decomposition coefficients; then the outputs of the three weak classifiers are fused to obtain a model such as Figure 3 The strong classifier H shown in FIG. 1 ; wherein, the activation function formula of the orthogonal basis neural network is:
[0046]
[0047] The activation function is expanded and approximated by Fourier series as the sum of a series of orthogonal trigonometric functions:
[0048] g(x)=a+a0 cosx+b0 sinx+a1 cos2x+b1 sin2x+…+a n cosnx+b n sinnx
[0049] in:
[0050]
[0051]
[0052] Where T is the period of the Fourier series expansion, x0 is an arbitrary point of the Fourier series expansion, and n is the order of the Fourier series expansion. The above formula is converted into the output form of the general feedforward as follows:
[0053]
[0054] in, is the orthogonal basis function of the hidden layer, that is, the orthogonal trigonometric function after the activation function is expanded by Fourier series, c i is the connection weight between the hidden layer and the output layer, R(X) is the error value; y is the output of the neural network; the calculation formula of the strong classifier H output is:
[0055]
[0056] Among them, Y H is the output of the strong classifier H, yhi is the output of weak classifiers h1, h2, and h3.
[0057] Step 5: Perform the preprocessing described in step 2 on the data to be detected, and then use the three decomposition coefficients obtained after OBF decomposition as the input of the three weak classifier models respectively. Finally, judge whether there is magnetic anomaly based on the output of the strong classifier H. Assuming the threshold is 0.9, when Y H When it is greater than 0.9, it indicates the presence of a magnetic anomaly signal; when it is less than 0.9, it indicates the absence of a magnetic anomaly signal.
[0058] Obviously, the above embodiments of the present invention are merely examples for the purpose of clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. Those skilled in the art will appreciate that other variations or modifications can be made based on the above description. It is not necessary and impossible to enumerate all embodiments here. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention shall be included within the scope of protection of the claims of the present invention.
Claims
1. A magnetic anomaly detection method based on an orthogonal basis neural network, characterized in that: The implementation steps are as follows: Step 1: Generate a training sample dataset. First, based on the magnetic dipole theory model, ideal magnetic anomaly signals under different conditions are generated, including magnetic anomaly signals of ferromagnetic targets at different CPA distances and different movement speeds. Then, pure geomagnetic background signals are collected at different time periods at the detection location. The ideal magnetic anomaly signals are added to the pure geomagnetic background signals to obtain magnetic anomaly signals containing geomagnetic noise. Labels are then added to each set of data, with the data label of the noisy magnetic anomaly signal set to 1 and the data label of the pure geomagnetic background signal set to 0. The noisy magnetic anomaly signals and pure geomagnetic background signals are used to construct a dataset for training the orthogonal basis neural network. Step 2: Preprocess the signal by performing bandpass filtering using wavelet decomposition and reconstruction to remove the mean and trend terms. Then, perform orthogonal basis function (OBF) decomposition on the filtered signal to obtain the decomposition coefficients of each signal group on three orthogonal bases. Step 3: Process the data obtained in step 1 as described in step 2, and then group the decomposition coefficients corresponding to each orthogonal basis into one category to form a data set. The three orthogonal bases form three data sets, called alpha1, alpha2, and alpha3 respectively. Step 4: Construct a Fourier orthogonal basis neural network. The network has a three-layer structure, namely the input layer, the hidden layer, and the output layer. The hidden layer contains n nodes, and the activation function of each node is an orthogonal triangular basis function. The weight between the input layer and the hidden layer is 1, and the weight between the hidden layer and the output layer is obtained through training. The value of the output layer after the activation function is used as the detection result. The output 1 indicates the presence of magnetic anomaly, and the output 0 indicates the absence of magnetic anomaly. The datasets alpha1, alpha2, and alpha3 obtained in step 3 and their labels are used as the input and output of the orthogonal basis neural network model for training. The connection weights between the hidden layer and the output layer are modified by feedback of the expected result error value, thereby obtaining three weak classifier models h1, h2, and h3 corresponding to the three sets of decomposition coefficients; then the outputs of the three weak classifiers are fused to obtain a strong classifier H; Step 5: The magnetic signal data to be detected is first preprocessed as described in step 2, and then the corresponding three decomposition coefficients are used as the input of the three weak classifier models to obtain the outputs of the three weak classifiers. Finally, the output of the strong classifier H is used to determine whether there is a magnetic anomaly. When the output of H is greater than the threshold, it indicates that a magnetic anomaly signal exists; when it is less than the threshold, it indicates that no magnetic anomaly signal exists.
2. The method according to claim 1, characterized in that The calculation formula for the OBF decomposition coefficient in step 2 is: Among them, m is the data point number of the signal, α j (m) is the decomposition coefficient of the signal on the jth basis function, W is the size of the window, f j (w i ) is the standard orthogonal basis function, S(w m+i ) is the magnetic signal, w is a dimensionless parameter of the magnetic target motion trajectory, w i represents the i-th value, Δw is the interval between two adjacent w values, and the calculation formula of w is: Where D is the trajectory of the magnetic target, R0 is the shortest distance from the magnetic detector to the trajectory of the magnetic target, that is, the CPA (Closest Proximity Approach) distance; the three orthogonal basis functions f j (w i ) are calculated as follows: 。 3. The method according to claim 1, wherein The activation function formula of the orthogonal basis neural network described in step 4 is: The activation function is expanded and approximated by Fourier series as the sum of a series of orthogonal trigonometric functions: g(x)=a+a0 cosx+b0 sinx+a1 cos2x+b1 sin2x+…+a n cosnx+b n sinnx in, Where T is the period of the Fourier series expansion, x0 is an arbitrary point of the Fourier series expansion, and n is the order of the Fourier series expansion. The above formula is converted into the output form of the general feedforward as follows: in, is the orthogonal basis function of the hidden layer, that is, the orthogonal trigonometric function after the activation function is expanded by Fourier series, c i is the connection weight between the hidden layer and the output layer, R(X) is the error value; y is the output of the neural network.