CN110187393B - Aeromagnetic compensation method based on generalized regression neural network - Google Patents
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Abstract
The invention provides an aeromagnetic compensation method based on a generalized regression neural network, which comprises the following steps: determining input and output index factors of the generalized neural network according to a T-L equation mathematical model and an interference generation reason; calculating direction cosine and a derivative thereof after filtering the calibrated flight data, and normalizing the input and output samples to obtain normalized generalized regression neural network input and output vectors; and loading the preprocessed learning samples into GRNN, circularly verifying by adopting a ten-fold cross verification method, and selecting the optimal smooth factor, the optimal input sample and the output sample to determine a network structure to construct a compensation model. And taking the calibrated flight data as a sample to be compensated, loading the sample to be compensated into GRNN for compensation calculation, and performing inverse normalization processing on output data of a compensation network to obtain prediction of an airplane interference field. The method effectively avoids the ill-conditioned problem of the 16-term coefficient equation matrix, obtains a good compensation effect when the calibrated flight sample data is less, and realizes the aeromagnetic interference compensation of the unmanned aerial vehicle.
Description
Technical Field
The invention belongs to the field of aeromagnetic detection, and particularly relates to an aeromagnetic compensation method based on a generalized regression neural network.
Background
The magnetic force detection of aviation has become one of the mainstream methods for researching the distribution rules of geological structures and mineral resources or other detection objects, and has played an important role in the field of airborne geophysical exploration due to the unique advantages of high efficiency, high speed, small influence on the earth surface and the like. The aviation magnetic detection is to load a sensitive magnetometer at a proper position of an airplane, and collect magnetic data in air in a circulating flight mode, so that the magnetic anomaly of the earth surface is detected, and the purpose of detecting ore bodies is achieved. In recent years, along with the upgrading of hardware equipment and the rapid development of computer technology, the precision and the efficiency of aeromagnetic exploration equipment are greatly improved.
The aeromagnetic compensation is that because the airplane has ferromagnetic substances, when flying, the magnetic field generated by the magnetic object on the airplane and the magnetic field generated by the magnetic induction line of the metal-cutting geomagnetic field can also act on the sensor of the magnetometer together, so that the detection of magnetic anomaly is hindered, and the detection data must be compensated to obtain a good detection effect.
At present, the widely used magnetic interference compensation model is a 16-coefficient magnetic compensation method based on T-L equation proposed by Tolles and Lawson. While solving for the 16-term coefficients is the most difficult point for compensating the model. The solving of the coefficients is directly related to the precision of the compensation result, in the traditional solving method, due to other problems such as correlation possibly existing among the coefficients and the like, the equation has serious complex collinearity, and the solving by using a least square method (LS) and various improved methods can cause the solution of the equation to deviate from the original magnetic compensation coefficient seriously, thereby causing larger errors. The requirement of high-precision aeromagnetic compensation under the current large data volume is difficult to meet.
Disclosure of Invention
The invention aims to solve the technical problem of providing a aeromagnetic compensation method based on a generalized regression neural network, which solves the problem of difficulty in solving the compensation coefficient, and solves the equation by using a least square method and an improved algorithm thereof, wherein complex collinearity exists to a certain extent so that the solution of the equation is seriously deviated from the original magnetic compensation coefficient, and a larger error occurs under the condition of poor data quality, so that the compensation precision is not high.
The present invention is achieved in such a way that,
an aeromagnetic compensation method based on a generalized regression neural network comprises 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: and 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.
Further, step 1 specifically includes: 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:
Hp＝c1cosα+c2cosβ+c3cosγ
the induction field is represented as:
Hi＝|T|(c4cos2α+c5cosαcosβ+c6cosαcosγ+c7cos2β+c8cosβcosγ+c9cos2γ)
the eddy current field is represented as:
Hec＝|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:
Ht＝Hp+Hi+Hec
in the formula ciTo compensate for the coefficient, HtFor the total field of interference at the probe of the optical pumping magnetometer, | T | is the geomagnetismField mode value.
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 magnetometerx，Ty，TzFor expressing the directional cosine:
further, 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 the total interference value is used as an output index factor.
The constant magnetic field corresponds to input index factor 3:
Hp＝[u1u2u3](16)
the induction magnetic field corresponds to 5 items of input index factors:
the eddy magnetic field corresponds to input index factor 8:
Hec＝|T|·[u1u′1u2u′1u3u′1u1u′3
u2u′3u3u′3u1u′2u3u′2](18)
thereby determining the GRNN input index factor as 16X itemsn×16＝[HpHiHec]Output index factor Yn×1＝[Ht]，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.
Further, 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.
Compared with the prior art, the invention has the beneficial effects that:
the method determines index factors of 16 inputs and 1 output according to the 16 equations, and effectively avoids the ill-conditioned problem of a coefficient matrix when solving the 16 coefficient equations based on the generalized regression neural network method based on the probability density function, and can obviously improve the compensation precision compared with the traditional method.
After the unmanned aerial vehicle carries a certain load, the maneuvering performance is poor, the execution capacity for the calibrated flight is poor, the data is unstable, and the effect of processing the unstable data by the GRNN model established after 10-fold cross validation optimization is good, so that the GRNN has strong generalization capacity.
Drawings
FIG. 1 is a flow chart of the determination of the generalized neural network index factors based on the T-L equation;
FIG. 2 is a diagram of a generalized neural network architecture;
FIG. 3 is a flow chart of aeromagnetic compensation based on generalized neural network;
FIG. 4 is a flowchart illustrating the steps of implementing the generalized neural network-based aeromagnetic compensation method shown in FIG. 3;
FIG. 5 is a comparison graph of the unmanned aerial vehicle calibration flight magnetic interference compensation results obtained through experiments according to the embodiment of the invention;
fig. 6 is a diagram of the compensated error.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
The invention provides a aeromagnetic compensation method based on a generalized regression neural network, which comprises the following steps:
step S1: according to a T-L equation mathematical model and an interference generation reason, determining 16 items of input index factors of a generalized neural network and 1 item of output index factors;
step S2: filtering the calibrated flight data (data of an optical pump magnetometer and a three-axis fluxgate magnetometer), calculating input and output parameters (namely input index factors and output index factors), and normalizing the input and output samples to obtain normalized generalized regression neural network input and output samples serving as learning samples;
step S3: loading the learning sample preprocessed in 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, circularly verifying by adopting a ten-fold cross verification method, and selecting an optimal smoothing factor, an optimal input sample and an output sample to determine a network structure;
step S4: selecting the best scheme to establish GRNN, loading the calibrated flight data serving as a sample to be compensated into GRNN for compensation calculation, performing inverse normalization processing on output data of a compensation network to obtain prediction of an aircraft interference field, and subtracting the predicted value from data obtained by an optical pump magnetometer to obtain a compensated geomagnetic field value.
In order to solve the ill-conditioned nature of the compensation coefficient solving matrix, the invention provides a brand-new aeromagnetic compensation model solving method, which can be used for aeromagnetic compensation calculation and improves the compensation precision.
The generalized regression neural network needs to determine input and output index factors, fig. 1 is a flow chart for determining the index factors of the generalized neural network based on a T-L equation, fig. 2 is a structure chart of the generalized neural network, fig. 3 is a flow chart for aeromagnetic compensation based on the generalized neural network, fig. 4 is a flow chart of specific implementation steps of the aeromagnetic compensation based on the generalized neural network shown in fig. 3,
the aeromagnetic interference can be 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 can be expressed as follows according to a T-L model:
Hp＝c1cosa+c2cosβ+c3cosγ
the induction field can be expressed as:
Hi＝|T|(c4cos2α+c5cosαcosβ+c6cosαcosγ+c7cos2β+c8cosβcosγ
+c9cos2γ)
the eddy current field can be expressed as:
Hec＝|T|(c10cosαcos′α++c11cosβcos′α+c12cosγcos′α+c13cosαcos′Z
+c14cosβcos′γ+c15cosγcos′γ+c16cosαcos′β
+c17cosβcos′β+c18cosγcos′β)
the total interference can be expressed as:
Ht＝Hp+Hi+Hec
in the formula ciTo compensate for the coefficient, HtFor the interference total field at the probe of the optical pump magnetometer, | T | is the modulus of the geomagnetic field,. cos α, cos β, cos gamma is the direction cosine of the 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 magnetometerx，Ty，TzCan be used to represent the directional cosine:
determining network input and output index factors:
according to the 16-term coefficient equation of equation (16), the interference is classified into three categories according to the cause, including all factors of aeromagnetic interference. Therefore, GRNN input index factors are composed of constant field interference, induced field interference and eddy current field interference, and the total interference value is used as an output index factor.
The constant magnetic field corresponds to input index factor 3:
Hp＝[u1u2u3](16)
the induction magnetic field corresponds to 5 items of input index factors:
the eddy magnetic field corresponds to input index factor 8:
Hec＝|T|·[u1u′1u2u′1u3u′1u1u′3
u2u′3u3u′3u1u′2u3u′2](18)
thereby determining the GRNN input index factor as 16X itemsn×16＝[HpHiHec]Output index factor Yn×1＝[Ht]。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.
Before loading the data into the network, the calibration flight data is subjected to Butterworth bandpass filtering to obtain interference Yn×1＝[Ht]Calculating direction cosine and direction cosine derivative from the filtered triaxial data to obtain input index factor Xn×16；
GRNN uses radial basis functions as activation functions and is structurally composed of an input layer, a mode layer, a summation layer, and an output layer as shown in fig. 2;
the optimal parameters are led into a GRNN input layer, after training, the number of neurons in an output layer is equal to the dimension k of an output vector in a learning sample, each neuron divides the output of a summation layer, and the output of a neuron j corresponds to the jth element of an estimation result Y (X), namely:
the magnetic interference prediction value expression in GRNN is as follows:
Xi，Yiare respectively an input vector Xn×16And the output vector Yn×1N is the sample volume, σ is the smoothing factor;
data normalization calls a premmx function in MATLAB for processing; syntax format: [ Pn, min, maxp, Tn, mint, maxt ] ═ premmx (P, T);
loading the preprocessed learning sample into GRNN, setting the smoothing factor to be a value between 0.1 step length and 0.1 and 1, calling a cross Validation ('Kfold', x, k) function by adopting a ten-fold cross Validation (10-fold cross Validation) method, circularly validating, and selecting the optimal smoothing factor, the optimal input sample and the output sample to determine a network structure;
wherein the ten-fold cross validation: and (3) disordering the n samples, uniformly dividing the n samples into 10 parts, selecting 9 parts in turn as training samples for training, and taking the remaining 1 part as a verification sample, wherein the number of the samples is n/10. And obtaining 10 groups of training samples, wherein each group of training samples corresponds to different smoothing factors and verification samples for training and verification, and selecting the corresponding sample and smoothing factor when the MSE is minimum to establish a final compensation model.
Performing inverse normalization processing on the obtained predicted interference data, and calling a tramnmx function in MATLAB to realize; and (3) syntax realization: [ PN ] ═ tramnmx (P, min, maxp);
the obtained result is prediction of the airplane interference field;
and then, the predicted amount of the aircraft interference magnetic field is subtracted from the data measured by the calibrated flight optical pump magnetometer, so that the magnetic interference compensation is obtained.
According to the method, a calibration flight experiment is carried out to verify the feasibility of the method, and the experimental operation process is as follows: after the unmanned aerial vehicle calibrated flight is finished, magnetic data of the calibrated flight are obtained, the calibrated flight data are compensated by using the aeromagnetic interference compensation method based on the generalized regression neural network, and the results before and after compensation are compared, so that the feasibility of the method is verified.
In order to further verify the optimization effect of the 10-fold cross validation on the GRNN, two comparison models are set, wherein the model 1 is used for 10-fold cross validation in the GRNN model, and the GRNN model is trained by determining the optimal sigma through 10-fold cross validation cycle validation; model2, remove the 10-fold cross validation, input the optimal smoothing factor determined by model 1 into GRNN and train the network directly with the sample data.
FIG. 5 is a comparison graph of the unmanned aerial vehicle calibration flying magnetic disturbance compensation results obtained through experiments according to the embodiment of the invention, the results include the geomagnetic field intensity and the actually measured total field value compensated by the three methods, the compensation effect of model 1 is obviously better than that of model2, and the disturbance compensation effect of model2 on certain postures is poor. LS estimates the maximum deviation of the interference compensation generated by different attitudes of the airplane;
the compensated error is shown in fig. 6, and the compensated standard deviation (the value directly reflects the discrete degree of the compensated magnetic interference noise) and the improvement ratio (the ratio of the standard deviation of the uncompensated signal to the standard deviation of the residual interference after compensation) are calculated as shown in table 1; three methods are comprehensively compared to obtain: the standard deviation of model 1 determined by 10-fold cross validation is smaller, and the compensation precision is higher. After compensation is realized through the network, the interference magnetic field of the airplane can be well suppressed, the improvement ratio of aeromagnetic data is 80.2012, and the data quality is improved. The LS method cannot meet the current high-precision aeromagnetic compensation requirement.
TABLE 1
In summary, the following steps: the embodiment of the invention provides an aeromagnetic interference compensation method based on a generalized regression neural network, which is characterized in that 16 index factors are determined according to the interference reasons of an airplane to train the generalized regression neural network, optimal data are obtained through 10-fold cross validation to establish GRNN, the ability of processing unstable data is strong, the matrix ill-condition problem when the matrix is solved by 16 compensation methods is effectively avoided, and high aeromagnetic calibration flight compensation precision can be obtained.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention are intended to be included within the scope of the present invention.
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:
Hp＝c1cosα+c2cosβ+c3cosγ
the induction field is represented as:
Hi＝|T|(c4cos2α+c5cosαcosβ+c6cosαcosγ+c7cos2β+％cosβcosγ+c9cos2γ)
the eddy current field is represented as:
Hec＝|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:
Ht＝Hp+Hi+Hec
in the formula ciTo compensate for the coefficient, HtThe 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 magnetometerx，Ty，TzFor 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:
Hp＝[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 itemsn×16＝[HpHiHec]Output index factor Yn×1＝[Ht]，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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