BP neural network evaporation waveguide forecasting method based on GOA optimization

Abstract

The invention relates to a BP neural network evaporation waveguide forecasting method based on GOA optimization, and belongs to the field of radio wave propagation and deep learning. The method comprises the following steps: constructing a GOA-BP network architecture, introducing GOA to optimize initial parameters of a BP neural network, and remarkably enhancing the global search capability and convergence rate of a model; secondly, meteorological parameters such as regional environment sea surface temperature, atmospheric temperature, atmospheric pressure, relative humidity and wind speed are obtained by using a WRF mesoscale numerical mode; then, predicting the height of the evaporation waveguide in combination with an NPS model, and constructing a data set containing abundant environment information and a predicted value of the height of the evaporation waveguide; and finally, a GOA-BP model is obtained through training. According to the algorithm, the problem of local optimum is effectively avoided, the forecasting accuracy is remarkably improved, the convergence speed of the model is increased through the optimized initial parameters, and the calculation precision and stability of a traditional algorithm are further improved.

Description

Technical Field

[0001] The present invention belongs to the field of radio wave propagation and deep learning, and relates to a BP neural network evaporation waveguide prediction method based on GOA optimization. Background Art

[0002] As an important component of the integrated air-space-ground-sea network, maritime wireless communications increasingly emphasize high efficiency and high quality. The effective utilization of atmospheric ducts is a crucial means of enhancing beyond-horizon communication and radar detection capabilities in the tropospheric, complex electromagnetic space environment at sea. Atmospheric ducts are primarily due to differences in temperature and humidity gradients between the sea surface and the air, as well as the presence of inversion layers. These natural conditions combine to form a variety of ducting layer structures, including evaporation ducts, surface ducts, and lift ducts. The evaporation duct stratification has a particularly significant impact on the atmospheric refractive index, causing electromagnetic waves to experience trapped refraction within the specific spatial range of the ducting layer, enabling beyond-horizon propagation of electromagnetic waves and expanding the boundaries and capabilities of maritime communications and target detection. Currently, specific duct parameters in marine environments are primarily obtained by extracting relevant hydrological and meteorological data and inputting them into the evaporation duct prediction model. However, due to the development level and cost limitations of real-time meteorological measurement technology, obtaining evaporation duct parameters through direct measurement methods such as buoys, meteorological gradient towers, and sounding moored equipment has problems such as insufficient temporal and spatial resolution and poor data continuity; while obtaining evaporation duct parameters through calculation methods such as numerical simulation and remote sensing data inversion has limitations such as limited resolution, high data assimilation requirements, and large computing resource demands.

[0003] Therefore, the actual effects of the above methods still need to be improved, especially in establishing the evaporation duct prediction model, where there are problems such as poor prediction effect and low calculation efficiency.

[0004] Given the rapid development of artificial intelligence (AI), neural networks, as a key branch of AI methods, have been applied to atmospheric duct forecasting research due to their advantages in efficiently processing complex data and automating decision-making. However, the computational accuracy and stability of related algorithms still need to be further improved. Summary of the Invention

[0005] In view of this, the purpose of the present invention is to provide a BP neural network evaporation duct prediction method based on GOA optimization. First, an evaporation duct intelligent prediction model based on GOA-BP is constructed, which includes swarm intelligence algorithm optimization hyperparameters, input layer, two hidden layers, and output layer. Secondly, based on the characteristics of the sea area radio wave propagation environment, vertical and horizontal grid divisions are set, and appropriate microphysical schemes are selected. Based on the hydrological and meteorological adoption numbers of the WRF mesoscale numerical model forecast test environment, a meteorological parameter feature subset is constructed; the NPS model is used to predict the evaporation duct height in a large area with high resolution and long time effect, and a feature subset of the evaporation duct height forecast value is obtained, and then a joint data set is constructed with the meteorological parameter feature subset. Finally, model training is performed based on the data set to obtain the GOA-BP model. Its environmental characteristics of the evaporation duct height, which are affected by multiple factors and complexities, can effectively predict the distribution of the evaporation duct height in the area through given atmospheric temperature, sea surface temperature, atmospheric pressure, relative humidity, and wind speed on the tropospheric over-the-horizon communication link, with better prediction accuracy. It can provide a reference for the planning and application of ultra-short wave / microwave over-the-horizon radar and radio communication systems.

[0006] In order to achieve the above object, the present invention provides the following technical solutions:

[0007] A BP neural network evaporation waveguide prediction method based on GOA optimization, the method comprising the following steps:

[0008] S1. Obtain public high-resolution global analysis datasets and extract hydrological and meteorological parameters using the WRF model;

[0009] S2. Input the extracted hydrometeorological parameter data into the NPS evaporation duct prediction model to obtain evaporation duct related characteristic quantities, and combine the hydrometeorological parameter dataset and the evaporation duct height dataset;

[0010] S3, establish a BP neural network, and optimize the neural network weights using the Gannet Optimization Algorithm (GOA);

[0011] S4. Training the BP neural network model after weight optimization is performed, and saving the network parameters of the GOA-BP model after training is completed.

[0012] Furthermore, in step S1, the process of processing the obtained public dataset FNL using the WRF model specifically includes the following steps:

[0013] S11. Set nested region parameters in the WRF region setup wizard, including writing the shared parameter module &share, geographic grid parameter module &geogrid, meteorological data decoding module &ungrib, and meteorological field interpolation module &metgrid in the WPS parameter list script;

[0014] S12, obtaining public geographic field data and meteorological reanalysis data, and running the geographic grid generation program geogrid.exe execution file to obtain terrain data in a corresponding format; then running the meteorological data decoding program ungrib.exe execution file to read the meteorological file and generate corresponding reanalysis data;

[0015] S13, then running the meteorological field interpolation program metgrid.exe execution file to perform difference calculation on the terrain data and the meteorological reanalysis data;

[0016] S14, return to the WRF main mode, design the WRF input parameter list script namelist.input according to the scheme, and run the WRF initial field and boundary condition generation program real.exe executable file to obtain the initial field and boundary conditions;

[0017] S15. Use the WRF mesoscale numerical meteorological model, set horizontal and vertical layering parameters to obtain environmental information, select the one with the highest matching degree as the physical solution, set the corresponding time span and time resolution, and invert the environmental meteorological parameters of the tropospheric beyond-horizon link area;

[0018] S16. Link the obtained environmental meteorological parameter file to the running directory of the WRF model, and extract the corresponding hydrological and meteorological parameters through the variable extraction function.

[0019] Furthermore, in step S2, the specific process of constructing the data set is as follows:

[0020] First, the atmospheric correction refractive index M is obtained according to the atmospheric refractive index N, where the atmospheric refractive index N is expressed as:

[0021]

[0022] Where p represents atmospheric pressure, T represents atmospheric temperature, e represents water vapor partial pressure, and α and β represent empirical coefficients determined based on experience. The calculation formula for water vapor partial pressure e is:

[0023]

[0024] Where q is the specific humidity function related to the altitude z, ε is a constant, and p represents the atmospheric pressure;

[0025] If the earth's surface is approximated as a plane, the atmospheric correction refractive index M can be expressed as:

[0026]

[0027] Where z is the altitude, r e is the mean radius of the Earth;

[0028] Therefore, in the NPS evaporation duct prediction model, the vertical profile of temperature T and specific humidity q in the near-surface layer is expressed as:

[0029]

[0030] Where T0 and q0 are the sea surface temperature and specific humidity, T(z) and q(z) are the atmospheric temperature and specific humidity at the height z, respectively. * ,q * are the characteristic scales of potential temperature θ and specific humidity q, ψ h (·) is the temperature universal function, κ is the Karman constant, Γ d is the dry adiabatic lapse rate, z 0t is the roughness height of the atmospheric temperature, L is the similarity length;

[0031] A subset of meteorological parameter data, including atmospheric temperature, sea surface temperature, atmospheric pressure, relative humidity, and wind speed, is input into the NPS model to obtain a high-resolution, long-term evaporation duct height forecast for a large area.

[0032] The meteorological dataset and the evaporation duct height dataset were combined to construct a complete training dataset. The five meteorological parameters corresponding to each grid were combined with the evaporation duct height parameters calculated using the NPS model as a single set of data. The data from all these groups together constituted the joint dataset.

[0033] Furthermore, in step S3, the established back propagation neural network includes an input layer, two hidden layers and an output layer, wherein the input features of the input layer include atmospheric temperature, sea surface temperature, atmospheric pressure, relative humidity, and wind speed; the first hidden layer and the second hidden layer are set with different numbers of neurons, the output layer is set with one neuron, the activation function uses the Sigmoid function, and the MSE is used as the loss function.

[0034] Furthermore, the specific process of using the Gannet optimization algorithm to optimize the weights of the BP neural network is as follows:

[0035] Set the initialization parameters of the GOA optimization algorithm, including population size, maximum number of iterations, proportional factor β for balancing exploration and development, optimization problem dimension Dim, and variable upper and lower bound weight values ​​u b and l b ; Among them, the optimization problem dimension Dim and the variable upper and lower bound weight values ​​u b and l b Determined by the weight parameters corresponding to the network structure;

[0036] Initialize a population and adjust the position of individuals according to the fitness function in each iteration, and find the global optimal solution through local update rules and Levy flight mechanism, where

[0037] The local update rule is based on the U-shaped and V-shaped diving patterns in gannet hunting behavior. The mathematical model of the U-shaped diving is:

[0038] a=2×cos(2πr1)×t1

[0039] The mathematical model of V-type diving is:

[0040] b=2×V(2πr2)×t1

[0041] in, Where t is the current iteration number, I is the maximum iteration number, r1 and r2 are both random numbers between [0,1];

[0042] The mathematical model of Levy flight mechanism is:

[0043]

[0044] in, r3 is a random number between [0,1], β is a proportional factor used to balance exploration and development; Γ(·) represents the Gamma function,

[0045] Furthermore, in step S4, the training process for the BP neural network is as follows:

[0046] S41. Extract feature variables X and target variables Y from the data file. The features include sea surface temperature, atmospheric temperature, atmospheric pressure, relative humidity, and wind speed. The target variable is the evaporation duct height. Simultaneously, perform data cleaning and data normalization, and divide the data into a training set, a validation set, and a test set.

[0047] S42. Optimize the weights and biases from the input layer to the hidden layer, from the hidden layer to the hidden layer, and from the hidden layer to the output layer of the BP neural network according to the Gannet optimization algorithm, where Xb is the optimal individual obtained by the Gannet optimization algorithm. The optimal individual refers to the solution with the best fitness in all iterations.

[0048] S43. Define a function to perform training on a single training round number of epochs and return the training error; define a function to perform inference on the validation set and return the validation error; select the mean square error (MSE) as the loss function and determine whether the training is complete based on the loss function.

[0049] Furthermore, the mean square error loss function during training is defined as:

[0050]

[0051] Where n represents the total number of samples, y i is the target vector, is the prediction vector.

[0052] The beneficial effects of the present invention are:

[0053] The present invention uses historical data and third-party data for training, without relying on explicit physical modeling or assumptions. Instead, it learns the distribution of evaporation ducts in the marine environment through large-scale data, and can adapt to more complex dynamic sea surface environments. GOA (Gannet Optimization Algorithm) is a new heuristic global optimization algorithm with powerful global search capabilities and easy implementation. GOA can effectively optimize the initial weights of the BP neural network, thereby reducing the hyperparameter tuning time, improving training efficiency, and accelerating model convergence. Traditional BP neural networks initialize weights randomly, but due to the complexity of the search space, they are prone to falling into local optimality. GOA finds the best initial weights through a global optimization method, avoids local optimality, and improves the convergence of training. Through the network weights optimized by GOA, the BP neural network exhibits stronger fitting ability when processing complex data, especially in nonlinear and complex pattern recognition tasks such as evaporation duct height prediction, further improving the prediction accuracy.

[0054] Other advantages, objects, and features of the present invention will be described in part in the following description and, in part, will be apparent to those skilled in the art upon examination of the following description or may be learned from practice of the present invention. The objects and other advantages of the present invention may be realized and obtained through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention will be described in detail below with reference to the accompanying drawings, in which:

[0056] Figure 1 This is an overall flow chart of the evaporation duct prediction method based on GOA optimization using a BP neural network in an embodiment of the present invention;

[0057] Figure 2 Schematic diagram of the structure of the GOA-BP model according to an embodiment of the present invention;

[0058] Figure 3 This is a partial display of regional environmental meteorological parameters under a layer of nested effect in an embodiment of the present invention; wherein, Figure 3 (a) is the sea surface temperature result under the nesting effect; Figure 3 (b) is the atmospheric temperature result under the nested effect; Figure 3 (c) is the atmospheric pressure result under the nested effect; Figure 3 (d) is the relative humidity result under one layer of nesting effect; Figure 3(e) is the wind speed result under one layer of nesting effect;

[0059] Figure 4 This is a partial display of the results of regional environmental meteorological parameters under the two-layer nesting effect of the embodiment of the present invention, where: Figure 4 (a) is the sea surface temperature result under the two-layer nesting effect; Figure 4 (b) is the atmospheric temperature result under the two-layer nesting effect; Figure 4 (c) is the atmospheric pressure result under the two-layer nesting effect; Figure 4 (d) is the relative humidity result under the two-layer nesting effect; Figure 4 (e) is the wind speed result under the two-layer nesting effect;

[0060] Figure 5 This is a partial display of regional environmental meteorological parameters under the three-layer nesting effect of the embodiment of the present invention, where: Figure 5 (a) is the sea surface temperature result under the three-layer nesting effect; Figure 5 (b) is the atmospheric temperature result under the three-layer nesting effect; Figure 5 (c) is the atmospheric pressure result under the three-layer nesting effect; Figure 5 (d) is the relative humidity result under the three-layer nesting effect; Figure 5 (e) is the wind speed result under the three-layer nesting effect;

[0061] Figure 6 A process diagram for constructing a data set according to an embodiment of the present invention;

[0062] Figure 7 This is a flowchart of the NPS model operation under an embodiment of the present invention;

[0063] Figure 8 Flowchart of the GOA-BP model operation under an embodiment of the present invention;

[0064] Figure 9 1 is a comparison chart of the evaporation duct height prediction performance of different methods under the embodiments of the present invention. DETAILED DESCRIPTION

[0065] The following describes the embodiments of the present invention by means of specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic illustrations of the basic concept of the present invention, and the following embodiments and features in the embodiments can be combined with each other without conflict.

[0066] Among them, the accompanying drawings are only for illustrative purposes and represent only schematic diagrams rather than actual pictures, and should not be understood as limiting the present invention. In order to better illustrate the embodiments of the present invention, some parts of the accompanying drawings may be omitted, enlarged or reduced, and do not represent the dimensions of actual products. For those skilled in the art, it is understandable that some well-known structures and their descriptions may be omitted in the accompanying drawings.

[0067] The same or similar numbers in the drawings of the embodiments of the present invention correspond to the same or similar parts; in the description of the present invention, it should be understood that if there are terms such as "upper", "lower", "left", "right", "front", "back", etc. indicating directions or positional relationships, they are based on the directions or positional relationships shown in the drawings. They are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific direction, be constructed and operate in a specific direction. Therefore, the terms describing the positional relationship in the drawings are only used for illustrative purposes and cannot be understood as limiting the present invention. For ordinary technicians in this field, the specific meanings of the above terms can be understood according to specific circumstances.

[0068] See also Figures 1 to 9 , which is a BP neural network evaporation waveguide prediction method based on GOA optimization.

[0069] This embodiment first introduces a BP neural network evaporation waveguide prediction method based on GOA optimization. Figure 1 As shown, the method includes the following steps:

[0070] Step 1: Determine the BP network structure, determine the GOA parameters for iterative optimization, map the optimal gannet individuals to the weights and biases of the BP neural network, and determine the network model structure;

[0071] Step 2: First, obtain the FNL (Final Operational Global Analysis) reanalysis data from the FTP server of the National Centers for Environmental Prediction (NECP) of the United States. The data format is GRIB2, with a global temporal and spatial coverage, a temporal resolution of 6 hours, and a horizontal resolution of 0.25° × 0.25°. Then, use the WRF mesoscale numerical model to extract the hydrological and meteorological parameters required for forecasting.

[0072] Step 3: Input the WRF model output data into the NPS evaporation duct prediction model to further calculate the evaporation duct related characteristics (such as EDH). Finally, a complete training dataset is constructed by combining the five elements (sea surface temperature, atmospheric temperature, atmospheric pressure, relative humidity, and wind speed);

[0073] Step 4: The GOA-BP model is trained based on the dataset. The experimental data are input into the GOA-BP model to predict the evaporation duct height and evaluate the model prediction performance: the feasibility and effectiveness of the proposed method for offshore evaporation duct prediction are verified by comparing it with existing BP, GA-BP and other models in terms of mean square error, mean absolute error, root mean square error, and coefficient of determination.

[0074] In this embodiment, if Figure 2 As shown, step 1 specifically includes the following detailed steps:

[0075] Step 11: Use GOA (Gannet Optimization Algorithm) to optimize the neural network weights. The specific process is as follows:

[0076] Set the initialization parameters of the GOA optimization algorithm, including the population size, the maximum number of iterations, the proportional factor β for balancing exploration and exploitation, the optimization problem dimension Dim, and the upper and lower bound weights ub and lb of the variables; among them, the optimization problem dimension Dim and the upper and lower bound weights ub and lb of the variables are determined by the weight parameters corresponding to the network structure. Then, initialize a population, adjust the positions of individuals according to the fitness function in each round of iteration, and find the global optimal solution through local update rules and Levy flight mechanism.

[0077] The local update rule is based on the U-shaped and V-shaped diving patterns in gannet hunting behavior. The mathematical model of the U-shaped diving is:

[0078] a=2×cos(2πr1)×t1

[0079] The mathematical model of V-type diving is:

[0080] b=2×V(2πr2)×t1

[0081] in, Where t is the current iteration number, I is the maximum iteration number, and r1 and r2 are both random numbers between [0,1].

[0082] The mathematical model of Levy flight mechanism is:

[0083]

[0084] in, r3 is a random number between [0,1], β is a proportional factor used to balance exploration and development, generally a number in the range of [1,2]; Γ(·) represents the Gamma function,

[0085] Step 12: Use PyTorch to define a two-hidden-layer back-propagation neural network (BP neural network). The network structure consists of an input layer, two hidden layers, and an output layer. The input layer has five input features (air temperature, sea surface temperature, atmospheric pressure, relative humidity, and wind speed). The first hidden layer has 13 neurons, the second hidden layer has 10 neurons, and the output layer has one neuron, representing the predicted evaporation duct height. Use the sigmoid activation function and the mean square error (MSE) loss function.

[0086] In this embodiment, step 2 specifically includes the following detailed steps:

[0087] Step 21: Use tools such as WRF Domain Wizard to set the main parameters of the nested region and complete the writing of &share, &geogrid, &ungrib, and &metgrid in the namelist.wps script. This script controls the subsequent execution files geogrid.exe, ungrib.exe, and metgrid.exe.

[0088] Step 22: Obtain the required geographic field data and meteorological reanalysis data from the NCAR official website and run the geogrid.exe executable file to generate terrain data in .nc format that can be used by the model. Then run the ungrib.exe executable file to read the meteorological files and generate reanalysis data that can be used by the model.

[0089] Step 23: Then run the metgrid.exe file to perform interpolation operations on the previous result data;

[0090] Step 24: Then return to the WRF main model, design the namelist.input script according to the technical plan, execute the real.exe file, and generate the initial field and boundary conditions that can be used in the WRF model;

[0091] Step 25: Use the WRF mesoscale numerical meteorological model, select appropriate horizontal and vertical layers to obtain large-area, high-resolution environmental information, select the microphysics scheme that best matches the experiment, and set the time span and time resolution to invert the environmental meteorological parameters in the tropospheric beyond-horizon link area;

[0092] Step 26: Link the obtained results to the WRF mode run directory and submit the task. After the program is completed, the corresponding wrfout output file will be obtained;

[0093] Step 27: Use the variable extraction function in wrf-python to extract the required hydrological and meteorological parameters.

[0094] Figure 3-Figure 5This is a partial display of regional environmental meteorological parameter results. In each sub-graph, (a) shows the sea surface temperature, which refers to the temperature of the ocean's surface water layer; (b) shows the atmospheric temperature, which refers to the degree of hotness or coldness of the air, usually measured at an altitude of two meters near the ground; (c) shows the atmospheric pressure, which refers to the weight of the air column per unit area, that is, the pressure of the air on the ground; (d) shows the relative humidity, which is the ratio of the water vapor content in the air to its maximum water vapor capacity, expressed as a percentage. (e) Shown is the wind speed result, which refers to the speed of air movement and is usually related to the pressure gradient.

[0095] In this embodiment, if Figure 6 As shown, step 3 specifically includes the following processes:

[0096] Step 31: The prediction of the evaporation duct height characteristic parameters needs to be calculated through the atmospheric refractive index correction. The atmospheric refractive index N is determined by the atmospheric pressure p (unit: hPa), the atmospheric temperature T (unit: K), and the water vapor partial pressure e (unit: hPa). The empirical relationship is:

[0097]

[0098] Here, α and β represent empirical coefficients determined empirically. In this embodiment, α=77.6 and β=4810.

[0099] The calculation formula for water vapor partial pressure e is:

[0100]

[0101] Where q is the specific humidity function related to the altitude z, ε is a constant of 0.62197, and p represents the atmospheric pressure.

[0102] In order to better study the influence of atmospheric refractive index on electromagnetic wave propagation, the surface of the earth is approximately treated as a plane, and the atmospheric corrected refractive index M (unit M) is redefined. The relationship between it and the atmospheric refractive index is:

[0103]

[0104] z is the altitude (unit: m), r e is the average earth radius, which is 6371 km. In this embodiment, the atmospheric correction refractive index M is specifically: M=N+0.157z.

[0105] In the NPS model, the vertical profile of temperature T and specific humidity q in the near-surface layer is expressed as:

[0106]

[0107] Where T0 and q0 are the sea surface temperature and specific humidity, T(z) and q(z) are the atmospheric temperature and specific humidity at the height z, respectively. * ,q * are the characteristic scales of potential temperature θ and specific humidity q, ψ h (·) is the temperature universal function, κ is the Karman constant, Γ d is the dry adiabatic lapse rate, which is about 0.00976K / m, z 0t is the roughness height of the atmospheric temperature, and L is the similarity length.

[0108] The water vapor pressure profile, atmospheric temperature, and pressure are calculated from this, and then the atmospheric corrected refractive index profile is calculated using the corresponding formula. A subset of meteorological parameter data, including atmospheric temperature, sea surface temperature, atmospheric pressure, relative humidity, and wind speed, is input into the NPS model to obtain a high-resolution, long-term evaporation duct height forecast for a large area.

[0109] like Figure 7 As shown in the figure, the operation process of the NPS model is:

[0110] (1) Input meteorological data CSV file: Import meteorological data CSV file containing atmospheric temperature, sea surface temperature, atmospheric pressure, relative humidity, and wind speed.

[0111] (2) Calling functions to calculate turbulence parameters: Using the input meteorological data, calling related functions to calculate turbulence parameters, including friction velocity, turbulence temperature scale, turbulence humidity scale, friction coefficient, flux coefficient, etc.

[0112] (3) Calculate the modified refractive index profile M(z) using turbulence parameters: Based on the calculated turbulence parameters, calculate the modified refractive index profile M(z). Modify ψm for stable, neutral, and unstable conditions, and calculate the temperature θ, specific humidity q, and saturated water vapor pressure e.

[0113] (4) Determine the evaporation duct height based on the minimum point of M(z): Determine the evaporation duct height by analyzing the minimum point of the modified refractive index profile M(z).

[0114] (5) Save the result back to CSV file (ductHeight): Save the calculated evaporation duct height result back to CSV file and name the file ductHeight.

[0115] Step 32: Combine the meteorological dataset and the evaporation duct height dataset to construct a complete training dataset, wherein the five meteorological parameters corresponding to each grid are combined with the evaporation duct height parameters calculated by the NPS model as a group of data, and the data of all groups together constitute a joint dataset.

[0116] In this embodiment, if Figure 8 As shown, the specific process of step 4 is:

[0117] Step 41: In order to compare and evaluate the models, a back propagation neural network model (BP) and a back propagation neural network model optimized by a genetic algorithm (GA) were constructed for comparison;

[0118] Step 42: Data loading and preprocessing:

[0119] (1) Use the pandas.read_csv function to load the data file in CSV format and extract the feature variable X and target variable Y from the data. The features include sea surface temperature, atmospheric temperature, atmospheric pressure, relative humidity, and wind speed, and the target variable is the evaporation duct height.

[0120] (2) Perform data cleaning and data normalization.

[0121] (3) Use train_test_split to divide the data into training set, validation set and test set. Specifically, X_train, X_temp, y_train, y_temp are the training set and temporary data set after preliminary division, with a ratio of 70% and 30%. Then the temporary data set X_temp, y_temp is divided again into validation set (X_val, y_val) and test set (X_test, y_test), with a ratio of 50% and 50%.

[0122] (4) Convert all data (training set, validation set, and test set) into PyTorch Tensors and move them to the GPU (if available) to accelerate computation during training. The conversion operation uses the torch.tensor() function and moves the data to the GPU or CPU (depending on hardware support) via .to(device);

[0123] Step 43: The model uses a back-propagation neural network (BP neural network) with two hidden layers. The network architecture is defined using torch.nn.Module. A BPNeuralNetwork class is defined, inheriting from torch.nn.Module, which contains an input layer, two hidden layers, and an output layer. After defining the network structure, it is instantiated using the specified input, hidden, and output layer dimensions. The weights and biases between each layer are derived using GOA.

[0124] Step 44: Weight Bias Optimization:

[0125] In GOA, the optimal individual Xb refers to the solution with the best fitness across all iterations, that is, the optimal weight. After the GOA algorithm is run, Xb represents the weight of the optimal individual. The optimal solution (i.e., the optimal individual) obtained by the GOA algorithm can be accessed through optimizer.Xb. In the BP neural network, the weights and biases from the input layer to the hidden layer, from the hidden layer to the hidden layer, and from the hidden layer to the output layer must be extracted and assigned from Xb. When defining fitness_function, the parameters in the optimal individual Xb are used to update the weights of the BP neural network. Each piece of data in Xb needs to be mapped to the weights and biases of each layer of the neural network.

[0126] Step 45: Set up training and loss function:

[0127] (1) Define a function to train a single training round (epoch) and return the training error (mean square error MSE). The mean square error is defined as

[0128]

[0129] Where n represents the total number of samples, y i is the target vector, is the prediction vector.

[0130] (2) Define a function to perform inference on the validation set and return the validation error (mean square error MSE);

[0131] Step 46: Train and evaluate the model using the optimized parameters:

[0132] (1) Save the optimal hyperparameter values ​​and instantiate the final GOA-BP model.

[0133] (2) Set the training parameters, loss function and optimizer (Adam).

[0134] (3) Perform training in a defined training and validation cycle, and set up an early stopping mechanism.

[0135] (4) Calculate the mean square error (MSE), mean absolute error (MAE), root mean square error (RMSE) and coefficient of determination (R 2 ) and other evaluation indicators and record them. The evaluation indicator expressions are as follows:

[0136]

[0137] Figure 9The comparison chart of the evaporation duct height prediction performance of different methods shows that compared with the existing BP and GA-BP prediction models, the MAE is reduced by 55.11% and 40.15% respectively; the RMSE is reduced by 54.51% and 41.88% respectively; R 2 An increase of 12.45% and 6.11% respectively.

[0138] In terms of accelerating model convergence, the average execution time of the GA-BP and GOA-BP algorithms, calculated over 10 runs, showed that the average execution time from population initialization to optimal individual GA-BP was 138 seconds, with an average total execution time of 140 seconds. The GOA-BP algorithm based on our method took an average of 1.12 seconds from population initialization to optimal individual, with an average total execution time of 3.9 seconds. Comprehensive analysis shows that our method exhibits superior prediction accuracy and efficiency, providing a reference for the planning and application of ultrashortwave / microwave over-the-horizon radar and radio communication systems.

[0139] After training is completed, the current model is saved and applied to real-time evaporation duct height prediction.

[0140] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not limiting. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solutions, which should all be included in the scope of the claims of the present invention.

Claims

1. A BP neural network evaporation waveguide prediction method based on GOA optimization, characterized by: The method comprises the following steps: S1. Obtain public high-resolution global analysis datasets and extract hydrological and meteorological parameters using the WRF model; S2. Input the extracted hydrometeorological parameter data into the NPS evaporation duct prediction model to obtain evaporation duct related characteristic quantities, and combine the hydrometeorological parameter dataset and the evaporation duct height dataset; S3, establish a BP neural network, and optimize the neural network weights using the Gannet Optimization Algorithm (GOA); S4. Training the BP neural network model after weight optimization is performed, and saving the network parameters of the GOA-BP model after training is completed.

2. The evaporation duct prediction method based on the BP neural network optimized by GOA according to claim 1 is characterized in that: In step S1, the process of processing the obtained public dataset FNL using the WRF model specifically includes the following steps: S11. Set nested region parameters in the WRF region setup wizard, including writing the shared parameter module &share, geographic grid parameter module &geogrid, meteorological data decoding module &ungrib, and meteorological field interpolation module &metgrid in the WPS parameter list script; S12, obtaining public geographic field data and meteorological reanalysis data, and running the geographic grid generation program geogrid.exe execution file to obtain terrain data in a corresponding format; then running the meteorological data decoding program ungrib.exe execution file to read the meteorological file and generate corresponding reanalysis data; S13, then running the meteorological field interpolation program metgrid.exe execution file to perform difference calculation on the terrain data and the meteorological reanalysis data; S14, return to the WRF main mode, design the WRF input parameter list script namelist.input according to the scheme, and run the WRF initial field and boundary condition generation program real.exe executable file to obtain the initial field and boundary conditions; S15. Use the WRF mesoscale numerical meteorological model, set horizontal and vertical layering parameters to obtain environmental information, select the one with the highest matching degree as the physical solution, set the corresponding time span and time resolution, and invert the environmental meteorological parameters of the tropospheric beyond-horizon link area; S16. Link the obtained environmental meteorological parameter file to the running directory of the WRF model, and extract the corresponding hydrological and meteorological parameters through the variable extraction function.

3. The evaporation duct prediction method based on BP neural network optimized by GOA according to claim 1 is characterized in that: In step S2, the specific process of constructing the data set is as follows: First, the atmospheric correction refractive index M is obtained according to the atmospheric refractive index N, where the atmospheric refractive index N is expressed as: Where p represents atmospheric pressure, T represents atmospheric temperature, e represents water vapor partial pressure, and α and β represent empirical coefficients determined based on experience. The calculation formula for water vapor partial pressure e is: Where q is the specific humidity function related to the altitude z, and ε is a constant; If the earth's surface is approximated as a plane, the atmospheric correction refractive index M can be expressed as: Where z is the altitude, r e is the mean radius of the Earth; Therefore, in the NPS evaporation duct prediction model, the vertical profile of temperature T and specific humidity q in the near-surface layer is expressed as: Where T0 and q0 are the sea surface temperature and specific humidity, T(z) and q(z) are the atmospheric temperature and specific humidity at the height z, respectively. * ,q * are the characteristic scales of potential temperature θ and specific humidity q, ψ h (·) is the temperature universal function, κ is the Karman constant, Γ d is the dry adiabatic lapse rate, z 0t is the roughness height of the atmospheric temperature, L is the similarity length; A subset of meteorological parameter data, including atmospheric temperature, sea surface temperature, atmospheric pressure, relative humidity, and wind speed, is input into the NPS model to obtain a high-resolution, long-term evaporation duct height forecast for a large area. The meteorological dataset and the evaporation duct height dataset were combined to construct a complete training dataset. The five meteorological parameters corresponding to each grid were combined with the evaporation duct height parameters calculated using the NPS model as a single set of data. The data from all these groups together constituted the joint dataset.

4. The evaporation duct prediction method based on BP neural network optimized by GOA according to claim 1 is characterized in that: In step S3, the established back propagation neural network includes an input layer, two hidden layers and an output layer, wherein the input features of the input layer include atmospheric temperature, sea surface temperature, atmospheric pressure, relative humidity, and wind speed; the first hidden layer and the second hidden layer are set with different numbers of neurons, the output layer is set with one neuron, the activation function uses the Sigmoid function, and the MSE is used as the loss function.

5. The evaporation duct prediction method based on BP neural network optimized by GOA according to claim 4 is characterized in that: The specific process of using the Gannet optimization algorithm to optimize the weights of the BP neural network is as follows: Set the initialization parameters of the GOA optimization algorithm, including population size, maximum number of iterations, proportional factor β for balancing exploration and development, optimization problem dimension Dim, and variable upper and lower bound weight values ​​u b and l b ; Among them, the optimization problem dimension Dim and the variable upper and lower bound weight values ​​u b and l b Determined by the weight parameters corresponding to the network structure; Initialize a population and adjust the position of individuals according to the fitness function in each iteration, and find the global optimal solution through local update rules and Levy flight mechanism, where The local update rule is based on the U-shaped and V-shaped diving patterns in gannet hunting behavior. The mathematical model of the U-shaped diving is: a=2×cos(2πr1)×t1 The mathematical model of V-type diving is: b=2×V(2πr2)×t1 in, Where t is the current iteration number, I is the maximum iteration number, r1 and r2 are both random numbers between [0,1]; The mathematical model of Levy flight mechanism is: in, r3 is a random number between [0,1], β is a proportional factor used to balance exploration and development; Γ(·) represents the Gamma function, 6. The evaporation duct prediction method based on BP neural network optimized by GOA according to claim 1 is characterized in that: In step S4, the training process for the BP neural network is: S41. Extract feature variables X and target variables Y from the data file. The features include sea surface temperature, atmospheric temperature, atmospheric pressure, relative humidity, and wind speed. The target variable is the evaporation duct height. Simultaneously, perform data cleaning and data normalization, and divide the data into a training set, a validation set, and a test set. S42. Optimize the weights and biases from the input layer to the hidden layer, from the hidden layer to the hidden layer, and from the hidden layer to the output layer of the BP neural network according to the Gannet optimization algorithm, where Xb is the optimal individual obtained by the Gannet optimization algorithm. The optimal individual refers to the solution with the best fitness in all iterations. S43. Define a function to perform training on a single training round number of epochs and return the training error; define a function to perform inference on the validation set and return the validation error; select the mean square error (MSE) as the loss function and determine whether the training is complete based on the loss function.

7. The evaporation duct prediction method based on GOA optimization using a BP neural network according to claim 6 is characterized in that: The mean square error loss function during training is defined as: Where n represents the total number of samples, y i is the target vector, is the prediction vector.

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