CN113627074B - Ground wave propagation delay prediction method based on transfer learning - Google Patents
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Abstract
The invention discloses a ground wave propagation delay prediction method based on transfer learning, which specifically comprises the following steps: step 1, establishing a theoretical database of ground wave propagation delay based on spatial variation; step 2, dividing the area within the working range of the transmitting station; step 3, respectively establishing BP neural network models for each area divided in the step 2 by using BP neural networks; step 4, training the BP neural network model of the corresponding area by using the long wave propagation delay theoretical value in the corresponding area generated in the step 1; and 5, obtaining measured data, and correcting the ground wave propagation delay theoretical value prediction model in the corresponding region trained in the step 4 by using transfer learning according to the measured data to obtain a final delay prediction neural network model. The ground wave propagation delay prediction method based on transfer learning realizes high-precision propagation delay prediction.
Description
Technical Field
The invention belongs to the technical field of land-based long-wave navigation/time service methods, and relates to a ground wave propagation delay prediction method based on transfer learning.
Background
Time delay in the process of ground wave propagation is the most important factor influencing the positioning accuracy of the system, and the propagation delay can be changed according to the propagation distance and the topographical features on the propagation path, so that the complex spatial variation characteristic is shown.
In the prior art, a great deal of theoretical research on a theoretical calculation method of the propagation delay of the ground wave has been carried out. However, because the propagation delay is affected by the change of the space factor on the propagation path, in areas with complex terrain and large terrain change amplitude, the difference between the propagation delay obtained by the theoretical calculation method and the data obtained by actual measurement is obvious.
In recent years, an artificial neural network is used as a popular field, and fitting can be completed on any mathematical model due to the deep layer and multi-node architecture of the artificial neural network. The transfer learning is used as a relatively new concept in the machine learning, and can train the existing network model in a small amount and quickly through a small amount of data, so that the learned knowledge and skills in the existing field/task can be applied and realized in the new field/task. Therefore, if the propagation delay obtained by theoretical calculation can be modeled by using the artificial neural network model, and transfer learning is performed by a small amount of measured data, high-precision prediction of the propagation delay space change characteristic is realized, a new propagation delay correction method is provided, and the method has important significance for further improving the positioning precision of a land-based long-wave navigation system.
Disclosure of Invention
The invention aims to provide a ground wave propagation delay prediction method based on transfer learning, which realizes high-precision propagation delay prediction.
The technical scheme adopted by the invention is that the ground wave propagation delay prediction method based on transfer learning is implemented according to the following steps:
step 1, establishing a theoretical database of ground wave propagation delay based on spatial variation by using an integral equation method;
Step 2, dividing the area in the working range of the transmitting station according to the spatial characteristics;
step 3, respectively establishing BP neural network models for each area divided in the step 2 by using BP neural networks;
Step 4, training the BP neural network model of the corresponding area by using the long wave propagation delay theoretical value in the corresponding area generated in the step 1 according to the established BP neural network model to obtain a prediction model of the ground wave propagation delay theoretical value in the corresponding area;
And 5, obtaining measured data, correcting the ground wave propagation delay theoretical value prediction model in the corresponding region trained in the step 4 by using transfer learning according to the measured data to obtain a final delay prediction neural network model, and performing ground wave propagation delay prediction by adopting the delay prediction neural network model.
The present invention is also characterized in that,
The step 1 specifically comprises the following steps:
and calculating the theoretical value of the propagation delay of each point in the working area of the radius NKm by using an integral equation method and taking the transmitting station as the center of a circle according to the mode that the transmission angle between paths is deflected by 0.1 DEG according to the step length of 100m on each path.
The step 2 is specifically as follows: dividing the working area of the radius NKm into the following parts by taking the working area as the circle center of the transmitting table: dividing the circular range with the radius of 0-N 1 Km into a plurality of sector areas, wherein the sector included angle of each sector area is A 1 degrees; in the annular range of N 1-N2 Km, N 1<N2 is divided according to the sector included angle A 2 degrees by taking the transmitting table as the center of a circle; in the annular range of N 2–N3 Km, N 2<N3 is divided according to the sector included angle A 3 degrees by taking the transmitting table as the center of a circle, and so on, in the annular range of N n-1 -N, N n-1 < N is divided according to the sector included angle A n degrees by taking the transmitting table as the center of a circle; a 1>A2>A3>…>An, N is the number of layers divided by the working area with radius N Km.
The step 3 is specifically as follows:
Modeling each region divided in the step 2 by using a BP neural network, wherein the BP neural network model of each region comprises an input layer, a multi-layer hidden layer and an output layer which are sequentially connected, and the working region is divided into multiple layers by dividing the circle center of a transmitting station, namely: the radius is 0-N 1 Km、N1-N2 Km、N2-N3 Km, the number of network layers of the BP neural network model of a plurality of areas in each layer is the same, the number of hidden layers of the corresponding area is designed according to the distance between each divided area and the transmitting station, the closer the distance is, the number of layers is more, the number of hidden layer nodes of the neural network model can be different between different areas in the same layer according to the difference of the terrain complex range of each area, and the larger the terrain variation range is, the more nodes are.
The transfer function of the output layer selects the Identity function, the hidden layer adopts a structure of a plurality of full connection layers, the transfer function is set as PReLU functions, and the cost function selects the MSE function.
In the step 4, the specific training process of the BP neural network model of the corresponding area is as follows:
Step 4.1, taking each point obtained in the step 1 as a training sample, taking the longitude value, the latitude value and the elevation information of each point as input characteristics of the training sample, and taking the corresponding propagation delay value as an output label of the training sample;
Step 4.2, subtracting the longitude, latitude and elevation information of the transmitting station from the longitude, latitude and elevation information of the training samples in the corresponding area, wherein X 1、x2、x3 is the longitude, latitude and elevation information of the training samples respectively, obtaining relative position information X '= [ X' 1,x'2,x'3 ], calculating the mean value mu and standard deviation of the X ', and then bringing the position information X' of each sample into a standardized formula Obtaining a standardized result;
Step 4.3, taking the standardized result as the input of the BP neural network model, and carrying out weighted summation and nonlinear activation conversion through each hidden layer to obtain a final output result;
step 4.4, setting a cost function, determining the difference between the final output result and the actual value in the step 4.3, and carrying out back propagation operation according to the result calculated by the cost function to calculate a gradient value corresponding to each layer of network;
step 4.5, updating parameters of the weight value in each layer of network according to the calculated gradient value;
And 4.6, traversing all training samples in the corresponding region, repeating the steps 4.2-4.5, stopping training when the predicted result is lower than a set threshold value or reaches a set cycle number, obtaining a final training result, and extracting and storing the BP neural network model after training is completed as a ground wave propagation delay theoretical value prediction model in the corresponding region.
The step 5 is specifically as follows:
Step 5.1, acquiring the actual value of the propagation delay number of a small number of uniformly distributed real measurement points in each divided area;
And 5.2, taking the obtained measured data as a training sample, adding a full-connection layer between the hidden layer and the output layer of the neural network model trained in the step 4 as a target network model, copying the input layer weight parameters and the hidden layer weight parameters of the last layer removed from the neural network model trained in the step 4 to the target network model, randomly initializing the output layer and the weight parameters of the last two layers of the hidden layer of the target network model, and training the target network model by using the measured training sample to obtain the neural network model with better fitting effect of the actual value of the ground wave propagation delay of the target area and more accurate prediction result.
The beneficial effects of the invention are as follows:
(1) By constructing a neural network model for predicting the propagation delay of the ground wave, researching the relation between the propagation delay and the spatial characteristics, and inputting longitude and latitude coordinates and elevation information of a target point, the predicted value of the propagation delay of any point can be obtained.
(2) The working coverage of each signal transmitting station is divided, neural network modeling is carried out on each divided area, and different areas adopt different network models, so that the accuracy of the propagation delay predicted value in the area is greatly improved.
(3) The method for performing migration learning on the neural network model by using the measured data is provided, and the error between the theoretical propagation delay prediction model and the actual propagation delay is reduced. Compared with a theoretical prediction method, the method combining the theory with the measured data has higher prediction precision; compared with a completely practical method, the method saves a great amount of manpower and material resources and time cost.
Drawings
FIG. 1 is a flow chart of a ground wave propagation delay prediction method based on transfer learning;
FIG. 2 is a schematic diagram of a method for dividing the working area of a transmitting station in a ground wave propagation delay prediction method based on transfer learning;
FIG. 3 is a neural network training flowchart in a ground wave propagation delay prediction method based on transfer learning;
fig. 4 is a graph showing comparison of migration learning effects in a ground wave propagation delay prediction method based on migration learning.
Detailed Description
The invention will be described in detail below with reference to the drawings and the detailed description.
The invention discloses a ground wave propagation delay prediction method based on transfer learning, which is implemented by the following steps, wherein the flow of the ground wave propagation delay prediction method is shown in a figure 1:
Step 1, establishing a theoretical database of ground wave propagation delay based on spatial variation by using an integral equation method; the method comprises the following steps:
Calculating the theoretical value of the propagation delay of each point in the working area of the radius NKm by using an integral equation method and taking the transmitting station as the center of a circle according to the mode that the transmitting angle between paths deflects by 0.1 DEG according to the step length of 100m on each path;
Step 2, dividing the area in the working range of the transmitting station according to the spatial characteristics; the method comprises the following steps: dividing the working area of the radius NKm into the following parts by taking the working area as the circle center of the transmitting table: dividing the circular range with the radius of 0-N 1 Km into a plurality of sector areas, wherein the sector included angle of each sector area is A 1 degrees; in the annular range of N 1-N2 Km, N 1<N2 is divided according to the sector included angle A 2 degrees by taking the transmitting table as the center of a circle; in the annular range of N 2–N3 Km, N 2<N3 is divided according to the sector included angle A 3 degrees by taking the transmitting table as the center of a circle, and so on, in the annular range of N n-1 -N, N n-1 < N is divided according to the sector included angle A n degrees by taking the transmitting table as the center of a circle; a 1>A2>A3>…>An, N is the number of layers divided by the working area with radius N Km.
Step 3, respectively establishing BP neural network models for each area divided in the step 2 by using BP neural networks; the method comprises the following steps:
Modeling each region divided in the step 2 by using a BP neural network, wherein the BP neural network model of each region comprises an input layer, a multi-layer hidden layer and an output layer which are sequentially connected, and the working region is divided into multiple layers by dividing the circle center of a transmitting station, namely: the radius is 0-N 1 Km、N1-N2 Km、N2-N3 Km, the number of network layers of the BP neural network model of a plurality of areas in each layer is the same, the number of layers of the hidden layer of the corresponding area is designed according to the distance between each divided area and the transmitting station, the closer the distance is, the number of layers is more, the number of nodes of the hidden layer of the neural network model is different among different areas in the same layer according to the difference of the terrain complex range of each area, the larger the terrain variation amplitude is, the more nodes are, wherein the transmission function of the output layer selects an Identity function, the hidden layer adopts the structure of a plurality of fully connected layers, the transmission function is set to be PReLU function, and the cost function selects an MSE function;
Step 4, training the BP neural network model of the corresponding area by using the long wave propagation delay theoretical value in the corresponding area generated in the step 1 according to the established BP neural network model to obtain a prediction model of the ground wave propagation delay theoretical value in the corresponding area; the specific training process for the BP neural network model of the corresponding area comprises the following steps:
Step 4.1, taking each point obtained in the step 1 as a training sample, taking the longitude value, the latitude value and the elevation information of each point as input characteristics of the training sample, and taking the corresponding propagation delay value as an output label of the training sample;
Step 4.2, subtracting the longitude, latitude and elevation information of the transmitting station from the longitude, latitude and elevation information of the training samples in the corresponding area, wherein X 1、x2、x3 is the longitude, latitude and elevation information of the training samples respectively, obtaining relative position information X '= [ X 1',x'2,x3', calculating the mean value mu and standard deviation of X ', and then bringing the position information X' of each sample into a standardized formula Obtaining a standardized result;
Step 4.3, taking the standardized result as the input of the BP neural network model, and carrying out weighted summation and nonlinear activation conversion through each hidden layer to obtain a final output result;
step 4.4, setting a cost function, determining the difference between the final output result and the actual value in the step 4.3, and carrying out back propagation operation according to the result calculated by the cost function to calculate a gradient value corresponding to each layer of network;
step 4.5, updating parameters of the weight value in each layer of network according to the calculated gradient value;
And 4.6, traversing all training samples in the corresponding region, repeating the steps 4.2-4.5, stopping training when the predicted result is lower than a set threshold value or reaches a set cycle number, obtaining a final training result, and extracting and storing the BP neural network model after training is completed as a ground wave propagation delay theoretical value prediction model in the corresponding region.
Step 5, obtaining measured data, correcting the ground wave propagation delay theoretical value prediction model in the corresponding area trained in the step 4 by using transfer learning according to the measured data to obtain a final delay prediction neural network model, and performing ground wave propagation delay prediction by adopting the delay prediction neural network model, wherein the method specifically comprises the following steps:
Step 5.1, acquiring the actual value of the propagation delay number of a small number of uniformly distributed real measurement points in each divided area;
And 5.2, taking the obtained measured data as a training sample, adding a full-connection layer between the hidden layer and the output layer of the neural network model trained in the step 4 as a target network model, copying the input layer weight parameters and the hidden layer weight parameters of the last layer removed from the neural network model trained in the step 4 to the target network model, randomly initializing the output layer and the weight parameters of the last two layers of the hidden layer of the target network model, and training the target network model by using the measured training sample to obtain the neural network model with better fitting effect of the actual value of the ground wave propagation delay of the target area and more accurate prediction result.
Examples
The ground wave propagation delay prediction method based on transfer learning has a flow shown in figure 1, and is implemented according to the following steps:
Step 1, establishing a theoretical database of ground wave propagation delay based on spatial variation by using an integral equation method; the method comprises the following steps:
calculating the theoretical value of the propagation delay of each point by using an integral equation method and taking a navigation table as a circle center and a working area with the radius of 1000Km according to the mode that the transmission angle between paths deflects by 0.1 DEG according to the step length of 100m on each path;
Step 2, dividing the area in the working range of the transmitting station according to the spatial characteristics; the method comprises the following steps: the specific mode of dividing the areas is shown in figure 2 by taking the circle center of the transmitting table, wherein the deflection angle of each area is 45 degrees within the range of 0-200 Km; in the range of 200-600Km, the deflection angle of each region is 15 degrees; in the range of 600-1000Km, the deflection angle of each zone is 10 degrees. The division mode can treat any point in the area far away from the transmitting station as the same propagation path with the transmitting station; the influence of different propagation paths on propagation delay is reduced. .
Step 3, respectively establishing BP neural network models for each area divided in the step 2 by using BP neural networks; the method comprises the following steps:
Modeling each region divided in the step 2 by using a BP neural network, wherein the BP neural network model of each region comprises an input layer, a multi-layer hidden layer and an output layer which are sequentially connected, and the working region is divided into multiple layers by dividing the circle center of a transmitting station, namely: the radius is 0-N 1 Km、N1-N2 Km、N2-N3 Km, the number of network layers of the BP neural network model of a plurality of areas in each layer is the same, the number of hidden layers of the corresponding area is designed according to the distance between each divided area and a transmitting station, the closer the distance is, the number of layers is more, the number of hidden layer nodes of the neural network model can be different among different areas in the same layer according to the difference of terrain complex courses of each area, the larger the number of nodes is, wherein the number of nodes is the larger the area with larger terrain variation amplitude, and the output layer transfer function selects the Identity function, namely f (x) =x because the numerical prediction of propagation delay belongs to regression problem. The hidden layer adopts a structure of a plurality of fully connected layers, and the transfer function is set as PReLU functions, namely f (x) =max (ax, x), and a is an extremely small positive number. The cost function selects the MSE function, i.e
Such as: different areas in the same radius are subjected to frame design according to the complexity of the terrain, and the number of nodes is relatively small in areas with small relief, such as plain areas, hills areas and the like; and the nodes are relatively more in areas with larger change of topography, such as mountain areas, basins and the like. For example: the area with the deflection angle of 300-310 degrees is a mountain area with complex topography, the total number of the network is 4 layers, and the node number of each layer is 3,7,5,1; the distance from the transmitting station is 400-600 km, the total network is 5 layers, the deflection angle is 285-300 degrees, the node number of each layer is 3,7,5,3,1, the deflection angle is 300-315 degrees, and the node number of each layer is 3,6,4,3,1.
Step 4, training the BP neural network model of the corresponding area by using the long wave propagation delay theoretical value in the corresponding area generated in the step1 according to the established BP neural network model to obtain a prediction model of the ground wave propagation delay theoretical value in the corresponding area; the specific training process for the BP neural network model of the corresponding region is as shown in fig. 3:
Step 4.1, taking each point obtained in the step 1 as a training sample, taking the longitude value, the latitude value and the elevation information of each point as input characteristics of the training sample, and taking the corresponding propagation delay value as an output label of the training sample;
Step 4.2, subtracting the longitude, latitude and elevation information of the transmitting station from the longitude, latitude and elevation information of the training samples in the corresponding area, wherein X 1、x2、x3 is the longitude, latitude and elevation information of the training samples respectively, obtaining relative position information X '= [ X 1',x'2,x3', calculating the mean value mu and standard deviation of X ', and then bringing the position information X' of each sample into a standardized formula Obtaining a standardized result;
Step 4.3, taking the standardized result as the input of the BP neural network model, and carrying out weighted summation and nonlinear activation conversion through each hidden layer to obtain a final output result;
step 4.4, setting a cost function, determining the difference between the final output result and the actual value in the step 4.3, and carrying out back propagation operation according to the result calculated by the cost function to calculate a gradient value corresponding to each layer of network;
step 4.5, updating parameters of the weight value in each layer of network according to the calculated gradient value;
And 4.6, traversing all training samples in the corresponding region, repeating the steps 4.2-4.5, stopping training when the predicted result is lower than a set threshold value or reaches a set cycle number, obtaining a final training result, and extracting and storing the BP neural network model after training is completed as a ground wave propagation delay theoretical value prediction model in the corresponding region.
Step 5, obtaining measured data, correcting the ground wave propagation delay theoretical value prediction model in the corresponding area trained in the step 4 by using transfer learning according to the measured data to obtain a final delay prediction neural network model, and performing ground wave propagation delay prediction by adopting the delay prediction neural network model, wherein the method specifically comprises the following steps:
Step 5.1, acquiring the actual value of the propagation delay number of a small number of uniformly distributed real measurement points in each divided area;
And 5.2, taking the obtained measured data as a training sample, adding a full-connection layer between the hidden layer and the output layer of the neural network model trained in the step 4 as a target network model, copying the input layer weight parameters and the hidden layer weight parameters of the last layer removed from the neural network model trained in the step 4 to the target network model, randomly initializing the output layer and the weight parameters of the last two layers of the hidden layer of the target network model, and training the target network model by using the measured training sample to obtain the neural network model with better fitting effect of the actual value of the ground wave propagation delay of the target area and more accurate prediction result.
In order to test the accuracy and effectiveness of the method, a verification experiment is carried out, an actual measurement experiment is designed in a Songshan region, and a small amount of propagation delay actual measurement data is obtained. Firstly, training the BP neural network model established in the step 3.1 by using the theoretical database established in the step 1, extracting 1000 points to serve as test samples, wherein the mean value of the error of the prediction result of the trained network on the test samples is 0.008563 mu s and the mean square error is 0.000127 mu s. And the neural network model is used for directly predicting the propagation delay of the actual measurement point position, and the obtained result error average value is 1.68584 mu s and the mean square error is 14.622 mu s. And extracting 40 points to serve as training samples, and performing migration learning on the neural network model of the theoretical value through a layer migration and model fine tuning method. 95 actual measurement points are selected, the prediction effect of the model before and after transfer learning is compared with the data of the actual measurement points, as shown in fig. 4, the prediction of the model after the transfer learning on the long wave propagation delay is closer to the error mean value of 0.31728 mu s, the mean square error of 0.15156 mu s, the effect is obviously improved, and the effectiveness of the method is verified.
Claims (6)
1. The ground wave propagation delay prediction method based on transfer learning is characterized by comprising the following steps:
step 1, establishing a theoretical database of ground wave propagation delay based on spatial variation by using an integral equation method;
Step 2, dividing the area in the working range of the transmitting station according to the spatial characteristics;
step 3, respectively establishing BP neural network models for each area divided in the step 2 by using BP neural networks;
Step 4, training the BP neural network model of the corresponding area by using the long wave propagation delay theoretical value in the corresponding area generated in the step 1 according to the established BP neural network model to obtain a prediction model of the ground wave propagation delay theoretical value in the corresponding area;
step 5, obtaining measured data, correcting the ground wave propagation delay theoretical value prediction model in the corresponding area trained in the step 4 by using transfer learning according to the measured data to obtain a final delay prediction neural network model, and performing ground wave propagation delay prediction by adopting the delay prediction neural network model, wherein the method specifically comprises the following steps:
Step 5.1, acquiring the actual value of the propagation delay number of a small number of uniformly distributed real measurement points in each divided area;
And 5.2, taking the obtained measured data as a training sample, adding a full-connection layer between the hidden layer and the output layer of the neural network model trained in the step 4 as a target network model, copying the input layer weight parameters and the hidden layer weight parameters of the last layer removed from the neural network model trained in the step 4 to the target network model, randomly initializing the output layer and the weight parameters of the last two layers of the hidden layer of the target network model, and training the target network model by using the measured training sample to obtain the neural network model with better fitting effect of the actual value of the ground wave propagation delay of the target area and more accurate prediction result.
2. The method for predicting the propagation delay of a ground wave based on transfer learning according to claim 1, wherein the step 1 is specifically:
and calculating the theoretical value of the propagation delay of each point in the working area of the radius NKm by using an integral equation method and taking the transmitting station as the center of a circle according to the mode that the transmission angle between paths is deflected by 0.1 DEG according to the step length of 100m on each path.
3. The method for predicting the propagation delay of the ground wave based on the transfer learning according to claim 2, wherein the step 2 is specifically: dividing the working area of the radius NKm into the following parts by taking the working area as the circle center of the transmitting table: dividing the circular range with the radius of 0-N 1 Km into a plurality of sector areas, wherein the sector included angle of each sector area is A 1 degrees; in the annular range of N 1-N2 Km, N 1<N2 is divided according to the sector included angle A 2 degrees by taking the transmitting table as the center of a circle; in the annular range of N 2–N3 Km, N 2<N3 is divided according to the sector included angle A 3 degrees by taking the transmitting table as the center of a circle, and so on, in the annular range of N n-1 -N, N n-1 < N is divided according to the sector included angle A n degrees by taking the transmitting table as the center of a circle; a 1>A2>A3>…>An, N is the number of layers divided by the working area with radius N Km.
4. The method for predicting the propagation delay of a ground wave based on transfer learning according to claim 3, wherein the step3 is specifically:
Modeling each region divided in the step 2 by using a BP neural network, wherein the BP neural network model of each region comprises an input layer, a multi-layer hidden layer and an output layer which are sequentially connected, and the working region is divided into multiple layers by dividing the circle center of a transmitting station, namely: the radius is 0-N 1 Km、N1-N2 Km、N2-N3 Km, the number of network layers of the BP neural network model of a plurality of areas in each layer is the same, the number of layers of the hidden layer of the corresponding area is designed according to the distance between each divided area and the transmitting station, the closer the distance is, the more the layers are, the number of nodes of the hidden layer of the neural network model can be different according to the difference of the terrain complex range of each area between different areas in the same layer, and the more the nodes are in the area with larger terrain variation amplitude.
5. The method for predicting propagation delay of ground waves based on transfer learning as set forth in claim 4, wherein the output layer transfer function selects an Identity function, the hidden layer adopts a structure of a plurality of fully connected layers, the transfer function is set as PReLU functions, and the cost function selects an MSE function.
6. The method for predicting the propagation delay of ground waves based on transfer learning according to claim 5, wherein the training specific process of the BP neural network model of the corresponding region in step 4 is as follows:
Step 4.1, taking each point obtained in the step 1 as a training sample, taking the longitude value, the latitude value and the elevation information of each point as input characteristics of the training sample, and taking the corresponding propagation delay value as an output label of the training sample;
step 4.2, latitude, longitude and elevation information of all training samples in the corresponding area Wherein X 1、x2、x3 is the longitude, latitude and elevation information of the training sample, and subtracting the longitude, latitude and elevation information of the transmitting station from X to obtain a relative position information/>Calculation/>Mean/>And standard deviation, then position information/>, for each sampleBring into the normalized equation/>Obtaining a standardized result;
Step 4.3, taking the standardized result as the input of the BP neural network model, and carrying out weighted summation and nonlinear activation conversion through each hidden layer to obtain a final output result;
step 4.4, setting a cost function, determining the difference between the final output result and the actual value in the step 4.3, and carrying out back propagation operation according to the result calculated by the cost function to calculate a gradient value corresponding to each layer of network;
step 4.5, updating parameters of the weight value in each layer of network according to the calculated gradient value;
And 4.6, traversing all training samples in the corresponding region, repeating the steps 4.2-4.5, stopping training when the predicted result is lower than a set threshold value or reaches a set cycle number, obtaining a final training result, and extracting and storing the BP neural network model after training is completed as a ground wave propagation delay theoretical value prediction model in the corresponding region.
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