CN110187393B - An Aeromagnetic Compensation Method Based on Generalized Regression Neural Network - Google Patents

Abstract

The invention provides an aeromagnetic compensation method based on a generalized regression neural network. Direction cosine and its derivative, normalize the input and output samples, and obtain the normalized generalized regression neural network input and output vectors; load the preprocessed learning samples into GRNN, and use the ten-fold cross-validation method. , select the best smooth factor, the best input sample and output sample to determine the network structure to build the compensation model. The calibration flight data is loaded into the GRNN as the sample to be compensated for compensation calculation, and the output data of the compensation network is de-normalized to obtain the prediction of the aircraft interference field. The invention effectively avoids the ill-conditioned problem of the 16-term coefficient equation matrix, and when the calibration flight sample data is small, a better compensation effect is obtained, and the aeromagnetic interference compensation of the unmanned aerial vehicle is realized.

Description

An Aeromagnetic Compensation Method Based on Generalized Regression Neural Network

technical field

The invention belongs to the field of aeromagnetic detection, in particular to an aeromagnetic compensation method based on a generalized regression neural network.

Background technique

Aeromagnetic detection has become one of the mainstream methods for studying the distribution of geological structures and mineral resources or other detection objects. Due to its unique advantages such as high efficiency, fast speed, and little impact on the earth's surface, it has played a very important role in the field of airborne geophysical exploration. effect. Aerial magnetic detection is to load a sensitive magnetometer on the appropriate position of the aircraft, and fly in the air to collect magnetic data, which is used to detect magnetic anomalies on the surface and achieve the purpose of detecting ore bodies. In recent years, with the upgrading of hardware equipment and the rapid development of computer technology, the accuracy and efficiency of aeromagnetic exploration equipment have been greatly improved.

Aeromagnetic compensation is due to the existence of ferromagnetic substances in the aircraft itself. During flight, the magnetic field generated by the magnetic objects on the aircraft and the magnetic field generated by the metal cutting geomagnetic field lines will also act on the sensor of the magnetometer together, hindering the detection of magnetic anomalies. In order to obtain a better detection effect, the detection data must be compensated.

At present, the widely used magnetic interference compensation model is a 16-coefficient magnetic compensation method based on the T-L equation proposed by Tolles and Lawson. And solving the 16-term coefficient is the most difficult point of the compensation model. The solution of the coefficients is directly related to the accuracy of the compensation results. In the traditional solution method, due to the possible correlation between the coefficients and other problems, the equation has serious complex collinearity. The solution of the equation may seriously deviate from the original magnetic compensation coefficient, resulting in a large error. It is difficult to meet the needs of high-precision aeromagnetic compensation under the current large amount of data.

SUMMARY OF THE INVENTION

The technical problem to be solved by the present invention is to provide an aeromagnetic compensation method based on a generalized regression neural network, which solves the difficulty in solving the compensation coefficient, and there is a certain degree of complex collinearity when solving the equation using the least square method and its improved algorithm, which makes the equation The solution of is seriously deviated from the original magnetic compensation coefficient, and in the case of poor data quality, there will be larger errors, resulting in low compensation accuracy.

The present invention is realized in this way,

An aeromagnetic compensation method based on generalized regression neural network, the method includes:

Step S1: Determine the input index factor and the output index factor of the generalized neural network according to the mathematical model of the T-L equation and the cause of the interference;

Step S2: After filtering the calibration flight data, calculate the direction cosine and its derivative to obtain the input index factor and the output index factor, normalize the input index factor and the output index factor, and obtain the normalized generalized regression neural network input index factors and output index factors as learning samples;

Step S3: Load the learning sample of step S2 into GRNN, set the smoothing factor to a step size of 0.1, a value between 0.1 and 1, adopt the ten-fold cross-validation method, cyclically verify, and select the best smoothing factor and best input. Samples and output samples determine the network structure to establish a compensation model;

Step S4: Load the calibrated flight data into the established compensation model as the sample to be compensated for compensation calculation, and perform inverse normalization processing on the output data of the compensation model to obtain the prediction of the aircraft interference field, and then obtain it from the optical pump magnetometer The compensated geomagnetic field value can be obtained by subtracting the predicted value from the data of .

Further, step 1 specifically includes: the aeromagnetic interference is decomposed into a constant magnetic field, an induced magnetic field and an eddy current magnetic field according to the cause. According to the mathematical model of the T-L equation, the constant magnetic interference field generated by the aircraft is expressed as:

H _p =c ₁ cosα+c ₂ cosβ+c ₃ cosγ

The induction field is expressed as:

H _i =|T|(c ₄ cos ² α+c ₅ cosαcosβ+c ₆ cosαcosγ+c ₇ cos ² β+c ₈ cosβcosγ+c ₉ cos ² γ)

The eddy current field is expressed as:

H _ec =|T|(c ₁₀ cosαcos′α++c ₁₁ cosβcos′α+c ₁₂ cosγcos′α+c ₁₃ cosαcos′Z+c ₁₄ cosβcos′γ+c ₁₅ cosγcos′γ

+c ₁₆ cosαcos′β+c ₁₇ cosβcos′β+c ₁₈ cosγcos′β)

The total interference is expressed as:

H _t =H _p +H _i +H _ec

where c _i is the compensation coefficient, H _t is the total disturbance field at the probe of the optical pump magnetometer, and |T| is the modulus value of the geomagnetic field.

cosα, cosβ, cosγ are the directional cosines of the angle formed by the earth’s magnetic field and the plane’s axis;

where α, β, γ are the angles between the three axes in the aircraft coordinate system and the geomagnetic field vector respectively;

cos′α, cos′β, cos′γ are the derivatives of the direction cosine with respect to time t;

The three components of the magnetic field T _x , T _y , and T _z measured by the three-axis fluxgate magnetometer are used to express the direction cosine:

Further, determining the input index factor and output index factor of the generalized neural network includes:

The input index factors of GRNN are composed of constant field interference, induction field interference and eddy current field interference, and the total interference value is used as the output index factor.

The constant magnetic field corresponds to three input index factors:

H _p =[u ₁ u ₂ u ₃ ] (16)

The induced magnetic field corresponds to 5 input index factors:

The eddy current magnetic field corresponds to 8 input index factors:

H _ec =|T|·[u ₁ u′ ₁ u ₂ u′ ₁ u ₃ u′ ₁ u ₁ u′ ₃

u ₂ u′ ₃ u ₃ u′ ₃ u ₁ u′ ₂ u ₃ u′ ₂ ] (18)

Therefore, it is determined that the GRNN input index factors are 16 items X _n×16 =[H _p H _i H _ec ], and the output index factors Y _n×1 =[H _t ], u ₁ =cosα, u ₂ =cosβ, u ₃ =cosγ , u′ ₁ u′ ₂ u′ ₃ are the derivatives of the direction cosine cosα, cosβ, cosγ with respect to time t, respectively.

Further, the ten-fold cross-validation includes: scramble the n samples, evenly divide them into 10 samples, select 9 samples in turn as training samples for training, and the remaining 1 sample as a verification sample, and the number of samples is n/10. , 10 groups of training samples are obtained, each group of training samples corresponds to different smoothing factors and verification samples for training and verification, and the samples and smoothing factors corresponding to the minimum MSE are selected to establish the final network model.

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

The invention determines 16 input and 1 output index factors according to 16 equations, and based on the generalized regression neural network method based on the probability density function, so as to effectively avoid the ill-conditioned problem of the coefficient matrix when solving the 16 coefficient equation. Significantly improve compensation accuracy.

After carrying a certain load, the UAV has poor maneuvering performance, poor ability to perform calibration flight, and unstable data acquisition. The GRNN model established after 10-fold cross-validation optimization has a better effect on such unstable data, so that GRNN has Strong generalization ability.

Description of drawings

Figure 1 is the flow chart of the determination of the index factors of the generalized neural network based on the T-L equation;

Figure 2 is a generalized neural network structure diagram;

Fig. 3 is a flow chart of aeromagnetic compensation based on generalized neural network;

Fig. 4 is a flowchart showing the specific implementation steps of the aeromagnetic compensation based on the generalized neural network shown in Fig. 3;

FIG. 5 is a comparison diagram of magnetic interference compensation results for unmanned aerial vehicle calibration flight obtained by performing experiments according to an embodiment of the present invention;

Figure 6 is an error diagram after compensation.

Detailed ways

In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention, but not to limit the present invention.

The present invention provides an aeromagnetic compensation method based on generalized regression neural network, comprising:

Step S1: According to the mathematical model of the T-L equation and the causes of interference, determine 16 input index factors and 1 output index factor of the generalized neural network;

Step S2: After filtering the calibration flight data (optical pump magnetometer and three-axis fluxgate magnetometer data), calculate the input and output parameters, that is, the input index factor and the output index factor, and normalize the input and output samples, Obtain the normalized generalized regression neural network input and output samples as learning samples;

Step S3: Load the learning samples preprocessed in Step S2 into GRNN, set the smoothing factor to a step size of 0.1, a value between 0.1 and 1, adopt the ten-fold cross-validation method, cyclically verify, and select the best smoothing factor, The best input samples and output samples determine the network structure;

Step S4: Select the best scheme to build a GRNN, load the calibrated flight data as a sample to be compensated into the GRNN for compensation calculation, and de-normalize the output data of the compensation network to obtain the prediction of the aircraft interference field, and then use the optical The compensated geomagnetic field value is obtained by subtracting the predicted value from the data acquired by the pump magnetometer.

In order to solve the ill-conditioned nature of the compensation coefficient solution matrix, the present invention provides a brand-new aeromagnetic compensation model solution method, which can be used for aeromagnetic compensation calculation and improves the compensation accuracy.

The generalized regression neural network needs to determine the input and output index factors. Figure 1 is the flow chart of the determination of the index factors of the generalized neural network based on the T-L equation, Figure 2 is the structure diagram of the generalized neural network, and Figure 3 is the flow chart of the aeromagnetic compensation based on the generalized neural network. , Figure 4 is a flowchart of the specific implementation steps of the aeromagnetic compensation based on the generalized neural network shown in Figure 3,

Aeromagnetic interference can be decomposed into constant magnetic field, induced magnetic field and eddy current magnetic field according to the cause. According to the T-L model, the constant magnetic interference field generated by the aircraft can be expressed as:

H _p =c ₁ cosa+c ₂ cosβ+c ₃ cosγ

The induction field can be expressed as:

H _i =|T|(c ₄ cos ² α+c ₅ cosαcosβ+c ₆ cosαcosγ+c ₇ cos ² β+c ₈ cosβcosγ

+c ₉ cos ^{2 #} )

The eddy current field can be expressed as:

H _ec =|T|(c ₁₀ cosαcos′α++c ₁₁ cosβcos′α+c ₁₂ cosγcos′α+c ₁₃ cosαcos′Z

+c ₁₄ cosβcos′γ+c ₁₅ cosγcos′γ+c ₁₆ cosαcos′β

+c ₁₇ cosβcos′β+c ₁₈ cosγcos′β)

The total interference can be expressed as:

H _t =H _p +H _i +H _ec

where c _i is the compensation coefficient, H _t is the total disturbance field at the probe of the optical pump magnetometer, and |T| is the modulus value of the geomagnetic field. cosα, cosβ, cosγ are the directional cosines of the angle formed by the earth’s magnetic field and the plane’s axis;

where α, β, γ are the angles between the three axes in the aircraft coordinate system and the geomagnetic field vector respectively;

cos′α, cos′β, cos′γ are the derivatives of the direction cosine with respect to time t;

The three-component magnetic field T _x , T _y , T _z measured by a three-axis fluxgate magnetometer can be used to represent the direction cosine:

Determine the network input and output index factors:

According to the 16-term coefficient equation of equation (16), the interference is divided into three categories according to its causes, including all the factors of aeromagnetic interference. Therefore, the GRNN input index factor is composed of constant field disturbance, induced field disturbance and eddy current field disturbance, and the total disturbance value is used as the output index factor.

The constant magnetic field corresponds to three input index factors:

H _p =[u ₁ u ₂ u ₃ ] (16)

The induced magnetic field corresponds to 5 input index factors:

The eddy current magnetic field corresponds to 8 input index factors:

H _ec =|T|·[u ₁ u′ ₁ u ₂ u′ ₁ u ₃ u′ ₁ u ₁ u′ ₃

u ₂ u′ ₃ u ₃ u′ ₃ u ₁ u′ ₂ u ₃ u′ ₂ ] (18)

Therefore, it is determined that the GRNN input index factor is 16 items X _n×16 =[H _p H _{i Hec} ], and the output index factor Y _n×1 =[H _t ]. u ₁ =cosα, u ₂ =cosβ, u ₃ =cosγ, u′ ₁ u′ ₂ u′ ₃ are the derivatives of direction cosine cosα, cosβ, cosγ with respect to time t, respectively.

Before loading the data into the network, perform Butterworth band-pass filtering on the calibration flight data to obtain the interference Y _n×1 = [H _t ], and obtain the direction cosine and direction cosine derivative from the filtered three-axis data to obtain Input index factor X _n×16 ;

GRNN uses radial basis function as activation function, which is composed of input layer, mode layer, summation layer and output layer in structure, as shown in Figure 2;

The optimal parameters are imported into the GRNN input layer. After training, the number of neurons in the output layer is equal to the dimension k of the output vector in the learning sample. Each neuron divides the output of the summation layer, and the output of neuron j corresponds to the estimation The jth element of the result Y(X), i.e.:

The expression of the predicted value of magnetic interference in GRNN is as follows:

X _i , Y _i are the values of the input vector X _n×16 and the output vector Y _n×1 respectively, n is the sample size, and σ is the smoothing factor;

Data normalization is processed by calling the premnmx function in MATLAB; syntax format: [Pn,minp,maxp,Tn,mint,maxt]=premnmx(P,T);

Load the preprocessed learning samples into GRNN, set the smoothing factor with a step size of 0.1 and a value between 0.1 and 1, and use the 10-fold cross validation (10-fold cross Validation) method to call crossvalind('Kfold', x, k) function, loop verification, select the best smooth factor, the best input sample and output sample to determine the network structure;

Ten-fold cross-validation: scramble the n samples and divide them into 10 evenly, select 9 of them in turn as training samples for training, and the remaining 1 as a verification sample, and the number of samples is n/10. In this way, 10 groups of training samples are obtained, each group of training samples corresponds to different smoothing factors and verification samples for training and verification, and the samples and smoothing factors corresponding to the minimum MSE are selected to establish the final compensation model.

De-normalize the obtained predicted interference data, and call the tramnmx function in MATLAB to realize; implementation syntax: [PN]=tramnmx(P,minp,maxp);

The result obtained is the prediction of the aircraft interference field;

Then the magnetic interference compensation is obtained by subtracting the predicted amount of the aircraft interference magnetic field from the data measured by the calibrated flying optical pump magnetometer.

According to the method of the present invention, a calibration flight experiment was carried out to verify the feasibility of the present invention. The experimental operation process is as follows: after the UAV calibration flight is completed, the magnetic data of the calibration flight is obtained, and the above-mentioned generalized regression neural network-based navigation system is used. The magnetic interference compensation method is used to compensate the calibration flight data, and the results before and after the compensation are compared to verify the feasibility of the method.

In order to further verify the optimization effect of 10-fold cross-validation on GRNN, two comparison models are set: model 1, there is 10-fold cross-validation in the GRNN model, and the 10-fold cross-validation cycle validation is used to determine the optimal σ to train the GRNN model; model2, Remove the 10-fold cross-validation, input the best smoothing factor determined by model 1 into GRNN, and directly train the network with sample data.

Model 1 processes the flight data (X _13860×16 , Y _13860×1 ) to determine the smoothing factor as 0.2. At this time, the training data for the sixth cross-validation is the best, and the best input training sample is X _{12474 ×16} , the output training sample is Y _{12474 × 1} , and the optimal GRNN model is used to compensate the calibration flight data. In order to verify the method, the traditional aeromagnetic compensation method based on the least squares method is used to compensate the test calibration flight data.

5 is a comparison diagram of the magnetic interference compensation results of UAV calibration flight obtained by conducting experiments according to an embodiment of the present invention, including the geomagnetic field strength and the measured total field value after compensation by three methods, and the compensation effect of model 1 is obviously better than that of model 2. Model 2 is less effective in compensating for disturbances generated by certain poses. The LS estimation has the largest error compensation for the interference caused by the different attitudes of the aircraft;

The error after compensation is shown in Figure 6, and the standard deviation after compensation (the value of which directly reflects the dispersion degree of magnetic interference noise after compensation) and the improvement ratio (the standard deviation of the uncompensated signal and the standard of residual interference after compensation) are calculated. The ratio of difference) is shown in Table 1; the three methods are comprehensively compared and obtained: the standard deviation of model 1 determined by 10-fold cross-validation is smaller, and its compensation accuracy is higher. After the compensation is realized through the network, the interference magnetic field of the aircraft can be better suppressed. The improvement ratio of the aeromagnetic data is 80.2012, and the data quality has been greatly improved. The LS method cannot adapt to the current demand for high-precision aeromagnetic compensation.

Table 1

To sum up: the embodiment of the present invention provides an aeromagnetic interference compensation method based on a generalized regression neural network. The generalized regression neural network is trained by determining 16 index factors based on the cause of aircraft interference, and obtained by 10-fold cross-validation. The GRNN is established with the best data, which has a strong ability to deal with unstable data, effectively avoids the ill-posed problem of the matrix when solving the matrix by the 16-term compensation method, and can obtain higher aeromagnetic calibration flight compensation accuracy.

The above descriptions are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements and improvements made within the spirit and principles of the present invention shall be included in the protection of the present invention. within the range.

Claims (2)

1. An aeromagnetic compensation method based on a generalized regression neural network is characterized by comprising the following steps:

step S1: determining input index factors and output index factors of the generalized neural network according to a T-L equation mathematical model and an interference generation reason;

step S2: after filtering processing is carried out on the calibrated flight data, calculating direction cosine and a derivative thereof to obtain an input index factor and an output index factor, and carrying out normalization processing on the input index factor and the output index factor to obtain a normalized generalized regression neural network input index factor and an output index factor which are used as learning samples;

step S3: loading the learning sample of the step S2 into GRNN, setting the smoothing factor to be a value between 0.1 and 1 in a step length of 0.1, adopting a ten-fold cross validation method, circularly validating, selecting an optimal smoothing factor, an optimal input sample and an output sample to determine a network structure to establish a compensation model;

step S4: loading the calibrated flight data serving as a sample to be compensated into the well-established compensation model for compensation calculation, performing inverse normalization processing on output data of the compensation model to obtain prediction of an aircraft interference field, and subtracting a predicted value from data obtained by the optical pump magnetometer to obtain a compensated geomagnetic field value;

the step 1 specifically comprises the following steps: the aeromagnetic interference is decomposed into a constant magnetic field, an induction magnetic field and an eddy magnetic field according to the generated reason, and the constant magnetic interference field generated by the airplane is expressed as follows according to a T-L equation mathematical model:

H_p＝c₁cosα+c₂cosβ+c₃cosγ

the induction field is represented as:

H_i＝|T|(c₄cos²α+c₅cosαcosβ+c₆cosαcosγ+c₇cos²β+％cosβcosγ+c₉cos²γ)

the eddy current field is represented as:

H_ec＝|T|(c₁₀cosαcos′α++c1₁cosβcos′α+c₁₂cosγcos′α+c₁₃cosαcos′Z+c₁₄cosβcos′γ+c₁₅cosγcos′γ+c₁₆cosαcos′β+c₁₇cosβcos′β+c₁₈cosγcos′β)

the total interference is expressed as:

H_t＝H_p+H_i+H_ec

in the formula c_iTo compensate for the coefficient, H_tThe total interference field at the probe of the optical pump magnetometer is, | T | is the earth magnetic field modulus;

cos alpha, cos beta and cos gamma are direction cosines of an included angle formed by the geomagnetic field and the axial direction of the airplane;

wherein alpha, beta and gamma are included angles between three axes of the airplane coordinate system and the geomagnetic field vector respectively;

cos ' α, cos ' β, cos ' γ is the derivative of the directional cosine with respect to time t;

magnetic field three-component T measured by triaxial fluxgate magnetometer_x，T_y，T_zFor expressing the directional cosine:

determining the input index factors and the output index factors of the generalized neural network includes:

GRNN input index factors are formed by constant field interference, induction field interference and eddy current field interference, and a total interference value is used as an output index factor;

the constant magnetic field corresponds to input index factor 3:

H_p＝[u₁u₂u₃](16)

the induction magnetic field corresponds to 5 items of input index factors:

the eddy magnetic field corresponds to input index factor 8:

thereby determining the GRNN input index factor as 16X items_n×16＝[H_pH_iH_ec]Output index factor Y_n×1＝[H_t]，u₁＝cosα，u₂＝cosβ，u₃＝cosγ，u′₁u′₂u′₃The derivatives of the direction cosines cos α, cos β, cos γ, respectively, with respect to time t.

2. The method of claim 1, wherein the ten-fold cross-validation comprises: the n samples are disorganized and evenly divided into 10 parts, 9 parts of the samples are selected as training samples in turn to be trained, the remaining 1 part of the samples is used as verification samples, the number of the samples is n/10, 10 groups of training samples are obtained, each group of training samples corresponds to different smooth factors and verification samples to be trained and verified, and the corresponding sample and the smooth factor when the MSE is minimum are selected to establish a final network model.

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