Aeromagnetic compensation method based on clustering analysis, factor analysis and neural network

Abstract

The invention discloses an aeromagnetic compensation method based on clustering analysis, factor analysis and a neural network, and the method comprises the steps: obtaining flight data through compensation flight, and processing the flight data to obtain input and output data needed by a T-L model; performing standardization processing on the input data; clustering is carried out on the data after standardization processing; factor analysis is carried out on the small classes with the sample number larger than 1 after clustering; a principal component and other independent variables are selected from each subclass subjected to factor analysis to serve as new independent variables to calculate a compensation coefficient for primary compensation; constructing a neural network model for secondary compensation, taking residual magnetic interference after primary compensation as output, and taking new independent variable data and uncompensated total field data as input; dividing a training sample and a test sample, and loading the training sample to obtain a trained network; and loading a test set for secondary compensation. According to the method based on clustering and factor analysis, constant, eddy current and inductive interference is eliminated. Swing noise is eliminated through secondary compensation based on the neural network.

Description

Technical Field

[0001] The invention relates to the field of aeromagnetic compensation, and in particular to an aeromagnetic compensation method based on cluster analysis, factor analysis and neural network. Background Art

[0002] Aeromagnetic detection technology is a technology that uses instruments such as three-axis fluxgate magnetometers and optical pumps on drones to detect magnetic fields. It plays an important role in geophysical exploration. Aeromagnetic detection has the advantages of wide coverage, high accuracy, low cost, and high efficiency. It is widely used in many fields such as geological surveys, mineral resource exploration, and unexploded bomb detection. During aerial operations, the interference caused by the operation of the drone motor and the interference caused by the metal objects on the fuselage cutting the magnetic field lines will also act on the magnetometer, reducing the accuracy of the measurement results. Therefore, it is necessary to use aeromagnetic compensation methods to process aeromagnetic data and compensate for this part of the maneuvering interference.

[0003] The earliest compensation model was proposed by Tolles and Lawson in 1950. According to the mechanism of magnetic disturbance of the flight platform, they divided the maneuvering interference into three parts: constant field, induction field, and eddy current field, and established the TL model related to magnetic disturbance and UAV attitude. In 1961, Leliak established a general compensation equation and designed the Figure of Merit (FOM) flight method to solve the compensation coefficient of the model. In 1980, Leach applied the ridge regression method to the coefficient solution. Since the variables used to solve the compensation coefficient are calculated by three direction cosines, the variables are not independent and there is a certain linear relationship, namely multicollinearity, which leads to low accuracy of coefficient solution and low versatility, which ultimately affects the accuracy of aeromagnetic compensation.

[0004] Neural networks have strong function fitting capabilities and can theoretically approximate any function. They are also used to solve compensation coefficients. In 1993, Williams believed that the position, attitude and other information of the drone could be modeled as functions of roll, pitch, yaw and their time derivatives, and established a related neural network model, and proposed a coefficient solution algorithm using neural networks as a tool. Neural networks can establish nonlinear compensation models and perform secondary compensation for swing noise that is nonlinearly related to the compensation variable, but occasionally problems such as network overload and gradient explosion may occur, leading to compensation failure. Summary of the invention

[0005] The purpose of the present invention is to provide an aeromagnetic compensation method based on cluster analysis, factor analysis and neural network, to suppress the multicollinearity between the variables of the linear regression magnetic compensation algorithm based on the TL model, and to make the neural network focus on learning the noise and interference that cannot be fitted by the linear regression equation by using the neural network for quadratic compensation, thereby further improving the effect of aeromagnetic compensation.

[0006] The technical solution to achieve the purpose of the present invention is: an aeromagnetic compensation method based on cluster analysis, factor analysis and neural network, comprising the following steps:

[0007] S1: Acquire the total aeromagnetic field data and triaxial component data, process the collected total field data and triaxial component data, and obtain the input data and output data required by the TL model;

[0008] S2: Standardize the input independent variable data;

[0009] S3: Perform cluster analysis on the input independent variable data after S2 standardization;

[0010] S4: After clustering in S3, select each small class with a sample size greater than 1 for factor analysis;

[0011] S5: Select the principal component from each sub-category of factor analysis, perform multiple linear regression analysis with the remaining independent variables, obtain the compensation coefficient and perform a compensation;

[0012] S6: Construct a neural network model for quadratic compensation, using the residual data after linear regression compensation as the output of the neural network, and the independent variable data after factor analysis and the total magnetic interference field data as the input of the neural network;

[0013] S7: Divide the training samples and the test samples, load them into the neural network model for quadratic compensation established in S6, and obtain a trained network;

[0014] S8: Load the S7 test set samples into the neural network model for quadratic compensation to perform quadratic compensation.

[0015] Furthermore, in S1, to obtain the total aeromagnetic field data and the three-axis component data, the UAV needs to perform compensation flight, fly in a "mouth" shape clockwise or counterclockwise, hover in the middle of each heading, and complete the three maneuvers of pitch, roll and yaw to continue flying; the processing of the total field data includes removing the constant DC component of the geomagnetic field through spectrum analysis and filtering out high-frequency noise through low-pass filtering. The data processing of the three-axis component is to calculate the direction cosine and its derivative. The TL model is:

[0016] H t =H p +H i +H ec =Xβ

[0017] Among them, H t is the total magnetic field of the UAV interference, H p is a constant interference field, H i is the induced interference field, H ecis the eddy current interference field, β is a 16×1 vector, which is the 16 compensation coefficients required, and X is the matrix composed of the direction cosines cosα, cosβ, cosγ of the geomagnetic field in three directions and their derivatives cos'α, cos'β, cos'γ in the UAV coordinate system:

[0018] X=(u1,u2,u3,u1 2 ,u1u2,u1u3,u2 2 ,u2u3,u1u1',u2u1',u3μ1',u1u2',u2u2',u3u2',u1u3',u2u3')

[0019] Among them, u1=cosα, u2=cosβ, u3=cosγ.

[0020] Furthermore, in S2, the Z-Score standardization method is used to standardize the independent variable data, and the data is standardized row by row, and the data of different magnitudes are converted into Z-Score values ​​of uniform measurement for comparison. The calculation formula of the Z-Score standardization method is: Z-Score = (x-μ) / δ, where x is the observed value, μ is the population mean, and δ is the population standard deviation.

[0021] Furthermore, in S4, the purpose of each subclass with a sample size greater than 1 is to reduce the dimension to solve the multicollinearity problem in the variables, and the subclass with a sample size of 1 does not need to perform factor analysis.

[0022] Furthermore, in S6, the constructed neural network consists of an input layer, multiple hidden layers and a neural network output layer. The output layer is a regression output. The structure of the hidden layer is a triple convolution-normalization-activation-pooling layer, followed by a flattening-discarding-fully connected layer. The activation function of the activation layer is selected. The first two layers are Relu functions, and the third layer is LeakyreLu function. Therefore, the overall structure is:

[0023] Input→[Conv→Batchnorm→Relu→Maxpool]×2→[Conv→Batchnorm→Leakyrelu→Maxpool]→F1→Dropout→Fc→RegressionOutput

[0024] Among them, F1 is the flattening layer, Fc is the fully connected layer, and the Relu function is: R (x) = max(0, x), the LeakyreLu function is: f LR (x)=max(αx,x), where α is a positive constant less than 1.

[0025] Furthermore, in S7, the first 70% of the data is divided into training samples, and the last 30% is divided into test samples.

[0026] Compared with the prior art, the present invention has the following beneficial effects:

[0027] (1) The linear regression compensation method based on cluster analysis and factor analysis proposed in the present invention effectively suppresses the multicollinearity between the interference model variables, so that the coefficients obtained by solving have high versatility and are less affected by interference.

[0028] (2) The method of using a neural network for quadratic compensation proposed in the present invention can compensate for the interference and partial noise related to the nonlinearity of the variables in the linear regression compensation method based on the TL model. At the same time, since the compensated residual interference is compensated on the basis of the TL model compensation, the neural network can focus more on learning the noise and interference that cannot be compensated by the linear regression compensation method. At the same time, it can also ensure the basic compensation effect when the compensation fails occasionally due to network overload or gradient explosion.

[0029] The present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 This is the main flow chart of the aeromagnetic compensation method based on cluster analysis, factor analysis and neural network of the present invention.

[0031] Figure 2 This is the structural diagram of the neural network.

[0032] Figure 3 This is a comparison chart of the interference after compensation and the original interference in the neural network training set.

[0033] Figure 4 This is a comparison chart of the interference after compensation and the original interference of the neural network test set. DETAILED DESCRIPTION

[0034] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0035] like Figure 1 As shown, the aeromagnetic compensation method based on cluster analysis, factor analysis and neural network of the present invention comprises the following steps:

[0036] S1: Obtain the total aeromagnetic field data and three-axis component data, process the collected total field data and three-axis component data, and obtain the input data and output data required by the TL model; wherein the total field data is measured by the optical pump sensor, and the three-axis component data is measured by the fluxgate sensor;

[0037] S2: Standardize the input independent variable data;

[0038] S3: Perform cluster analysis on the input independent variable data after S2 standardization;

[0039] S4: After clustering in S3, select each small class with a sample size greater than 1 for factor analysis;

[0040] S5: Select the principal component (cumulative variance contribution rate greater than 99.5%) from each sub-category of factor analysis, perform multiple linear regression analysis with the remaining independent variables, obtain the compensation coefficient and perform a compensation;

[0041] S6: Construct a neural network model for quadratic compensation, using the residual data after linear regression compensation as the output of the neural network, and the independent variable data after factor analysis and the total magnetic interference field data as the input of the neural network;

[0042] S7: Divide the training samples and the test samples, load them into the neural network model for quadratic compensation established in S6, and obtain a trained network;

[0043] S8: Load the S7 test set samples into the neural network model for quadratic compensation to perform quadratic compensation.

[0044] In S1, the total aeromagnetic field data and three-axis component data are obtained. The UAV needs to perform compensation flight, fly in a clockwise or counterclockwise direction, hover in the middle of each heading, and complete the three maneuvers of pitch, roll and yaw to continue flying; the processing of the total field data includes removing the constant DC component of the geomagnetic field through spectrum analysis and filtering out high-frequency noise through low-pass filtering. The data processing of the three-axis component is to calculate the direction cosine and its derivative; the TL model is:

[0045] H t =H p +H i +H ec =Xβ

[0046] Among them, H t is the total magnetic field of the UAV interference, H p is a constant interference field, H i is the induced interference field, H ecis the eddy current interference field, β is a 16×1 vector, which is the 16 compensation coefficients required, and X is the matrix composed of the direction cosines cosα, cosβ, cosγ of the geomagnetic field in three directions and their derivatives cos'α, cos'β, cos'γ in the UAV coordinate system:

[0047] X=(u1,u2,u3,u1 2 ,u1u2,u1u3,u2 2 ,u2u3,u1u1',u2u1',u3u1',u1u2',u2u2',u3u2',u1u3',u2u3')

[0048] Among them, u1=cosα, u2=cosβ, u3=cosγ.

[0049] In S2, the Z-Score standardization method is used to standardize the independent variable data. The data is standardized row by row, and data of different magnitudes are converted into Z-Score values ​​of uniform measurement for comparison. The calculation formula of the Z-Score standardization method is: Z-Score = (x-μ) / δ, where x is the observed value, μ is the population mean, and δ is the population standard deviation.

[0050] In S4, the purpose of each small class with a sample size greater than 1 is to reduce the dimension to solve the multicollinearity problem in the variables, and the small class with a sample size of 1 does not need to perform factor analysis.

[0051] In S6, Figure 2 As shown in the figure, the constructed neural network consists of an input layer, multiple hidden layers and a neural network output layer. The output layer is the regression output. The structure of the hidden layer is a triple convolution-normalization-activation-pooling layer, followed by a flattening-discarding-fully connected layer. The activation function of the activation layer is selected. The first two layers are Relu functions, and the third layer is LeakyreLu function, so the overall structure is:

[0052] Input→[Conv→Batchnorm→Relu→Maxpool]×2→[Conv→Batchnorm→Leakyrelu→Maxpool]→F1→Dropout→Fc→RegressionOutput

[0053] F1 is the flattening layer, Fc is the fully connected layer, and the Relu function is: R (x) = max(0, x), the LeakyreLu function is: f LR (x)=max(αx,x), where α is a positive constant less than 1.

[0054] In S7, the first 70% of the data is divided into training samples, and the last 30% is divided into test samples; the compensation results of the training samples are as follows Figure 3 shown.

[0055] In S8, the compensation result of the test sample is as follows Figure 4 shown.

[0056] The present invention proposes a compensation method based on cluster analysis, factor analysis and neural network, wherein the primary compensation based on cluster analysis and factor analysis effectively suppresses the complex collinearity between the variables of the interference model, so that the coefficients obtained by the solution have high versatility and are less affected by interference. The method of using a neural network for secondary compensation can fit and compensate for the interference and partial noise related to the nonlinearity of the variables that cannot be fitted by the linear regression compensation method based on the TL model. At the same time, because the residual interference after the primary compensation is compensated on the basis of the primary compensation, the neural network can focus more on learning the noise and interference that cannot be compensated by the linear regression compensation method, and can also ensure the basic compensation effect when the compensation fails occasionally due to network overload or gradient explosion.

[0057] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. An aeromagnetic compensation method based on cluster analysis, factor analysis and neural network, characterized in that: The steps include: S1, obtain the total aeromagnetic field data and three-axis component data, process the collected total field data and three-axis component data, and obtain the input data and output data required by the TL model; S2, standardize the input independent variable data; S3, cluster analysis of the input independent variable data after standardization in S2; After clustering in S4 and S3, each small cluster with a sample size greater than 1 was selected for factor analysis; S5, select the principal component from each sub-category of factor analysis, conduct multiple linear regression analysis with the remaining independent variables, obtain the compensation coefficient and perform a compensation; S6, constructing a neural network model for quadratic compensation, using the residual data after linear regression compensation as the output of the neural network, and the independent variable data after factor analysis and the total magnetic interference field data as the input of the neural network; S7, dividing the training samples and the test samples, loading them into the neural network model for quadratic compensation established in S6, and obtaining a trained network; S8, loading the S7 test set samples into the neural network model for quadratic compensation to perform quadratic compensation.

2. The aeromagnetic compensation method based on cluster analysis, factor analysis and neural network according to claim 1 is characterized in that: In S1, to obtain the total aeromagnetic field data and three-axis component data, the UAV needs to perform compensatory flight, flying in a "mouth" shape clockwise or counterclockwise, hovering in the middle of each heading, and completing the three maneuvers of pitch, roll and yaw to continue flying.

3. The aeromagnetic compensation method based on cluster analysis, factor analysis and neural network according to claim 1 is characterized in that: In S1, the processing of the total field data includes removing the constant DC component of the geomagnetic field through spectrum analysis and filtering out high-frequency noise through low-pass filtering, and the data processing of the three-axis components is to calculate the direction cosines and their derivatives.

4. The aeromagnetic compensation method based on cluster analysis, factor analysis and neural network according to claim 1 is characterized in that: In S1, the TL model is: H t =H p +H i +H ec =Xβ Among them, H t is the total magnetic field interfered by the drone, H p is a constant interference field, H i is the induced interference field, H ec is the eddy current interference field, β is a 16×1 vector, which is the 16 compensation coefficients required, and X is the matrix composed of the direction cosines cosα, cosβ, cosγ of the geomagnetic field in three directions and their derivatives cos'α, cos'β, cos'γ in the UAV coordinate system: X = (u1, u2, u3, u1 2 ,u1u2,u1u3,u2 2 ,u2u3,u1u1',u2u1',u3u1',u1u2',u2u2',u3u2',u1u3',u2u3') Among them, u1=cosα, u2=cosβ, u3=cosγ.

5. The aeromagnetic compensation method based on cluster analysis, factor analysis and neural network according to claim 1 is characterized in that: In S2, the Z-Score standardization method is used to standardize the independent variable data. The data is standardized row by row, and the data of different magnitudes are converted into Z-Score values ​​of uniform measurement for comparison.

6. The aeromagnetic compensation method based on cluster analysis, factor analysis and neural network according to claim 5 is characterized in that: The calculation formula of the Z-Score standardization method is: Z-Score = (x-μ) / δ, where x is the observed value, μ is the population mean, and δ is the population standard deviation.

7. The aeromagnetic compensation method based on cluster analysis, factor analysis and neural network according to claim 1, characterized in that: In S6, the constructed neural network consists of an input layer, multiple hidden layers and a neural network output layer, and the output layer is a regression output.

8. The aeromagnetic compensation method based on cluster analysis, factor analysis and neural network according to claim 7 is characterized in that: The structure of the hidden layer is a triple convolution-normalization-activation-pooling layer, followed by a flattening-discarding-fully connected layer. The activation function of the activation layer is Relu function for the first two layers and LeakyreLu function for the third layer, so the overall structure is: Input→[Conv→Batchnorm→Relu→Maxpool]×2→[Conv→Batchnorm→Leakyrelu→Maxpool]→F1→Dropout→Fc→RegressionOutput Among them, F1 is the flattening layer and Fc is the fully connected layer.

9. The aeromagnetic compensation method based on cluster analysis, factor analysis and neural network according to claim 8, characterized in that: The Relu function is: R (x) = max(0, x), the LeakyreLu function is: f LR (x) = max(αx, x), where α is a positive constant less than 1.

10. The aeromagnetic compensation method based on cluster analysis, factor analysis and neural network according to claim 1, characterized in that: In S7, the first 70% of the data is selected as training samples, and the last 30% is selected as testing samples.

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