Maritime evaporation duct path loss adaptive prediction method based on small sample transfer learning

Abstract

The application discloses a sea evaporation duct path loss adaptive prediction method based on small sample transfer learning, and belongs to the technical field of sea wireless communication. In view of the problem that the prediction accuracy of a pure simulation data driven model is reduced due to the difference between a simulation scene and a measured scene in actual sea area application, a transfer learning framework of'source domain pre-training-target domain fine-tuning' is constructed. First, a Transformer model optimized by a tree structure Parzen estimator is pre-trained by using large-scale simulation data, so as to extract general physical features of evaporation duct propagation; second, for sparse single-point measured data, the encoder parameters are frozen and the decoder is fine-tuned, and a point constraint loss function is introduced, so as to calibrate the full path prediction curve by using the measured path loss value of a link specific distance point. The application can reduce the demand for measured data, improve the path loss prediction accuracy and time sequence stability, and is suitable for sea over-the-horizon communication link modeling and performance evaluation.

Description

Technical Field

[0001] This invention belongs to the field of maritime beyond-line-of-sight communication channel modeling, and in particular relates to a path loss calibration and prediction technology for maritime evaporating waveguide environments that integrates sparse measured data point constraints and physical feature migration. Background Technology

[0002] In maritime communication systems, the evaporation waveguide phenomenon enables electromagnetic waves to propagate beyond line of sight, significantly altering the path loss distribution. Accurate prediction of path loss in this environment is crucial for link planning and system performance evaluation.

[0003] Currently, path loss prediction mainly relies on two types of methods: traditional physical models, represented by parabolic equation models. These models have clear physical mechanisms and high computational accuracy, but involve numerical solutions to complex partial differential equations, resulting in large computational loads and long processing times, making them unsuitable for real-time dynamic prediction. Furthermore, they have strict requirements for environmental input data; in actual sea areas, factors such as sea surface roughness and Earth curvature errors often lead to significant deviations between simulation results and measured data. Deep learning models, on the other hand, learn the path loss distribution patterns through neural networks. However, most existing models rely on large-scale simulation datasets for training. Due to the difference between the simulation and measured domains, their prediction accuracy drops significantly when directly applied to specific actual operating frequencies. In addition, acquiring marine measured data is costly and highly sparse and discrete (usually only single-point data from the receiver). Existing models struggle to effectively calibrate the entire path loss curve in the absence of continuous measured samples.

[0004] Therefore, how to integrate the physical prior knowledge of simulation models with sparse measured constraint information to achieve accurate transfer from the "simulation domain" to the "real scenario" while taking into account the needs of real-time prediction and visualization remains a technical challenge in the current field of maritime communication. Summary of the Invention

[0005] In view of this, the purpose of this invention is to provide an adaptive prediction method for path loss of marine evaporating waveguides based on few-shot transfer learning. This addresses the problems of significantly reduced prediction accuracy, weak domain generalization ability, and extremely sparse marine measured data that are difficult to support complex model training in real-world marine environments (such as specific frequencies, sea surface roughness, and systematic errors) when using purely simulation-driven models. This invention discloses an adaptive prediction method for path loss of marine evaporating waveguides based on few-shot transfer learning, relating to the field of marine wireless communication technology. The method first obtains a TPE-Transformer model with general physical feature extraction capabilities through pre-training; then, it constructs a target domain dataset containing sparse single-point measured data for the target environment, and adopts a hierarchical fine-tuning strategy. While keeping the model encoder parameters unchanged, it fine-tunes the model decoder using a point-constrained loss function, and corrects the overall deviation of the full path loss prediction curve using single-point measured loss values ​​at specific locations in the link. This invention eliminates the domain differences between the simulation model and the measured scenario by reusing the physical prior knowledge of the source domain model and combining it with the point constraint mechanism of measured data, achieving accurate calibration of cross-frequency band marine path loss.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] An adaptive prediction method for path loss of marine evaporating waveguides based on small-sample transfer learning is characterized by the following steps:

[0008] 1. An adaptive prediction method for path loss of marine evaporating waveguides based on small-sample transfer learning, characterized by the following steps:

[0009] S101: Pre-training phase: Obtain a marine electromagnetic propagation simulation dataset covering multiple frequency bands and multiple evaporation waveguide heights, generated by a two-dimensional parabolic equation model, as the source domain;

[0010] S102: Physical Feature Extraction Pre-training: Construct a TPE-Transformer model based on the Transformer architecture and perform pre-training to obtain a pre-trained encoder with the ability to extract physical features of general electromagnetic propagation.

[0011] S103: Target domain construction stage: Obtain a sparse measured dataset of links in a specific sea area at the actual operating frequency as the target domain; the measured dataset contains single-point measured path loss reference values ​​at specific distances of the link.

[0012] S104: Model transfer configuration stage: Build the transfer learning framework, load the pre-trained encoder and freeze all its network parameters, and initialize the decoder module to be fine-tuned.

[0013] S105: Point Constraint Fine-tuning Stage: Input the target domain data into the model, introduce the point constraint loss function, use the measured path loss value of the single point as the constraint anchor point, calculate the residual between the predicted output value of the model at the same distance and the measured value, and iteratively optimize the parameters of the decoder only accordingly.

[0014] S106: Full Path Prediction Stage: Utilize the fine-tuned model to output a full-distance dimension path loss prediction sequence, thereby achieving amplitude calibration and overall deviation correction of the full path prediction curve.

[0015] S107: Software Integration and Visualization Stage: Integrate the methods described in steps S101 to S106 into the sea-skimming wireless channel characteristic analysis software. Receive system and environmental parameters input by the user through a graphical user interface, call the NPS diagnostic model to output the evaporation waveguide height, render and output the path loss curve as a function of distance or height in real time, and provide data saving functionality.

[0016] Based on the above technical solution, in step S101, the source domain dataset construction method is as follows:

[0017] The source domain data is a simulation dataset composed of environmental meteorological parameters retrieved from the WRF numerical weather prediction model, EDH forecasts from the NPS model, and PL sequences generated from two-dimensional PE simulations. The specific operation is as follows:

[0018] (1) Inversion and acquisition of mesoscale meteorological parameters

[0019] Using the WRF mesoscale numerical meteorological model, appropriate horizontal and vertical stratifications were selected to obtain large-area high-resolution environmental information. The optimal microphysical scheme was selected and the time span and time resolution were set to retrieve the environmental meteorological parameters of the tropospheric beyond-line-of-sight link region.

[0020] (2) Extraction of meteorological parameters and construction of data subsets for the link

[0021] In post-processing, each set time point is traversed, and the variable extraction function in wrrf-python is used to extract all meteorological parameters retrieved from all grid points. Based on the positions of the latitude and longitude coordinates of the two ends of the required link in the grid, the start and end points of the link are set. The fitting function is used to generate line pixel coordinates and remove duplicates. The interpolation position of each point on the link is calculated, and the average meteorological parameter values ​​at each point are used as the meteorological parameters of the link at the current time step, thus constructing a subset of meteorological parameter data for the tropospheric beyond-line-of-sight link channel environment.

[0022] (3) Evaporation waveguide height prediction based on NPS model

[0023] Predicting the characteristic parameters of evaporation waveguide height requires calculation using the atmospheric corrected refractive index. The atmospheric refractive index N is determined by atmospheric pressure p (in hPa), atmospheric temperature T (in K), and water vapor partial pressure e (in hPa), and the empirical relationship is as follows:

[0024]

[0025] The formula for calculating the partial pressure e of water vapor is:

[0026]

[0027]

[0028] In the formula, R h To better study the influence of atmospheric refractive index on electromagnetic wave propagation, the Earth's surface is approximated as a plane, and the atmospheric corrected refractive index M (unit M) is redefined. Its relationship with the atmospheric refractive index is as follows:

[0029]

[0030] z represents altitude (in meters), r e Assuming the average curvature of the Earth is 6371 km, substituting this value into the formula yields...

[0031]

[0032] In the NPS model, the vertical profiles of near-surface temperature T and specific humidity q are represented as follows:

[0033]

[0034]

[0035] Where T0 and q0 are the sea surface temperature and specific humidity, respectively, and T(z) and q(z) are the atmospheric temperature and specific humidity at altitude z, respectively, and θ * q * These are the characteristic scales for potential temperature θ and specific humidity q, respectively. Let Γ be a universal temperature function, κ be the Karman constant, and Γ be a universal temperature function. d The dry adiabatic lapse rate is approximately 0.00976 K / m, z 0t Let L be the roughness height of atmospheric temperature and L be the similarity length. A subset of meteorological parameter data is input into the NPS model to obtain high-resolution, long-term evaporation duct height forecasts for a large area.

[0036] (4) Path loss simulation based on two-dimensional parabolic equation

[0037] The corresponding recursive formula for the two-dimensional parabolic equation method is:

[0038]

[0039] in and These are the Fourier transform and the inverse transform, respectively. The refractive index term reflects the influence of the space medium on electromagnetic waves. The diffraction term reflects the diffraction effect of obstacles on electromagnetic waves along the propagation path, where... Let θ be the angle between the electromagnetic wave and the horizontal direction, given the initial field distribution. Then, the field distribution for the next step can be obtained. This allows for iterative solutions to the field across the entire computational space. For the current tropospheric beyond-line-of-sight link environment, a specific microwave scattering...

[0040] The system parameters of the communication equipment, including frequency, transmit antenna height, and receive antenna height, are combined with meteorological parameters and the predicted evaporation waveguide height. The path loss on this link is predicted using the two-dimensional bidirectional stepwise parabolic equation method.

[0041] (5) Construction and storage of path loss sequence dataset

[0042] The dataset required for training the path loss sequence model is constructed. The feature dimension of the dataset is (number of samples, time steps, feature dimension), where the number of samples represents the total number of combinations of meteorological parameters and communication equipment system parameters, and the time steps represent the total number of time steps under the current time span and time resolution. The dataset is grouped into set X and set Y. The features of dataset X are air temperature (AT), sea surface temperature (SST), atmospheric pressure (AP), relative humidity (RH), wind speed (WS), evaporation duct height (EDH), communication frequency (f), transmit antenna height (ht), and receive antenna height (hr). Each combination of communication equipment system parameters (f, ht, hr) constitutes a sample. It is strictly guaranteed that a sample contains all time step information. For example, if the time span is 72 hours and the time resolution is 1 hour, then the total number of time steps is 72. The dimension of a sample in dataset X is (72, 9), and the dimension of dataset X is (number of samples, 72, 9). The Y dataset is characterized by a path loss (PL) sequence. Each row of PL corresponds to a combination of meteorological and system parameters in a sample, ensuring the continuity of time steps. The dataset is then saved after the sequence is arranged.

[0043] Based on the above technical solution, in step S102, a TPE-Transformer model based on the Transformer architecture is constructed and pre-trained to obtain a pre-trained encoding network with the ability to extract general electromagnetic propagation physical features.

[0044] The overall model framework comprises four main modules: an input layer, a feature embedding and location encoding layer, a Transformer encoder-decoder layer, and an output layer, as well as a TPE hyperparameter optimization module. The input layer receives the temporal dataset (dimensions of [number of samples, time step, feature dimension]) constructed in step S101, covering nine core features. The feature embedding and location encoding layer maps discrete features into high-dimensional vectors and injects temporal information. The Transformer encoder-decoder layer captures global temporal correlations and local feature interactions through a multi-head self-attention mechanism and a feedforward network. The output layer outputs the path loss prediction value for the corresponding time step. The TPE hyperparameter optimization module adaptively optimizes the key hyperparameters of the Transformer network to improve the model's generalization ability.

[0045] The core advantages of this design are: first, it retains the native parallel computing capabilities and global dependency modeling advantages of the Transformer network, adapting to the needs of long-term path loss prediction; second, it solves the problem of blindness in manual hyperparameter tuning through the TPE algorithm, achieving accurate matching between model parameters and prediction tasks; and third, it preserves the spatiotemporal correlation of environmental features and waveguide parameters throughout the process, making up for the defect of static models that sever temporal correlations, and achieving an upgrade from "static point prediction" to "dynamic sequence prediction".

[0046] Based on the above technical solution, in step S103, a sparse measured dataset of a specific sea area link at the actual operating frequency is obtained as the target domain; the measured dataset contains measured path loss reference values ​​at specific distance points. The target domain data is the measured data of the marine scattering experimental link. The two ends of the link are Chaotanbi in Wenchang City, Hainan Province, and Fenghuojiaozui in Taishan City, Guangdong Province, respectively. The C-band data uses the measured data from the vehicle-mounted C-scattering communication equipment at Wenchang Station and the vehicle-mounted C-scattering communication equipment at Taishan Station, and the Ku-band data uses the measured data from the box-type Ku-scattering communication equipment at Wenchang Station and the box-type Ku-scattering communication equipment at Taishan Station. The test time is from 0:00 on December 15, 2024 to 24:00 on December 17, 2024, and the time interval is consistent with the retrieved meteorological parameters and EDH prediction, which is 1 hour. The measured data file is preprocessed to extract the received level and received rate, unify the units, remove outliers, and then calculate the path loss. :

[0047]

[0048] In the formula, For transmission power, The measured received power is in dBm. and These are the transmit and receive antenna gains, respectively, in dBi.

[0049] Based on the above technical solution, in the model transfer configuration stage of step S104, a transfer learning framework is constructed, the pre-trained encoder is loaded and its network parameters are frozen, and the decoder module to be fine-tuned is initialized. The encoder is mainly responsible for extracting meteorological environmental features and establishing a deep correlation between meteorological parameters and refractive index profiles and electromagnetic wave propagation modes. Therefore, the meteorological feature extraction capability learned by the source domain model can be seamlessly transferred to the target domain. In the fine-tuning stage, the present invention freezes the parameters of the encoder and its embedding layer to maintain the physical perception capability obtained in the pre-training stage, preventing overfitting caused by the sparsity of data in the target domain. The decoder is responsible for mapping the physical features extracted by the encoder to specific path loss values.

[0050] Based on the above technical solution, in the point constraint fine-tuning stage of step S105, considering the differences in data format and distribution between the source and target domains, this invention proposes a parameter update strategy of "freezing the encoder and fine-tuning the decoder" and designs a point constraint loss function. In one embodiment, the specific distance point of the link is the endpoint of the link where the receiver is located, for example, at 300 km, and the point constraint loss function is defined as L. point for:

[0051]

[0052] In the formula, This represents the model prediction value for the i-th sample. This represents the true value of the i-th sample. The loss function calculates the prediction error at a specific distance point on the link and updates the decoder parameters through backpropagation. Although only a single point is constrained, the shape of the entire curve output by the model is still controlled by the physical laws of the source domain because the encoder is frozen and the decoder is initialized using the conditions of the source domain, thus achieving the effect of "single-point calibration, full-line correction".

[0053] Based on the above technical solution, in step S106, the full-path prediction stage is addressed. Due to sea surface roughness, clutter interference, and systematic errors in the simulation model in the real environment, the main issues manifest as an overall shift in the amplitude or gain error of the predicted curve. Therefore, this invention sets the decoder parameters to a trainable state. By performing backpropagation on the target domain data, the model can learn a "calibration coefficient," adjusting the overall energy level of the output curve to adapt it to the loss characteristics of the real environment. On the measured dataset, MAE, RMSE, and other parameters were selected. The relative error (err) is used to quantitatively evaluate the model's accuracy. Its evaluation index expression is as follows:

[0054]

[0055]

[0056]

[0057]

[0058] This invention fully utilizes the theory of electromagnetic propagation at sea, endowing the model with initial physical prior knowledge through simulation data generated by a parabolic equation model. This allows the model to accurately characterize the electromagnetic wave propagation characteristics in complex environments such as evaporating waveguides without relying on cumbersome real-time physical modeling, thus enhancing its adaptability to dynamic sea surface environments. Compared to traditional empirical statistical models, this invention strictly guarantees the continuity of time steps and effectively exploits the nonlinear coupling and long-range temporal dependence between evaporating waveguide height and path loss using the Transformer's self-attention mechanism, achieving a technological leap from "static single-point prediction" to "dynamic sequence prediction."

[0059] The proposed transfer learning architecture effectively utilizes valuable sparse measured data from maritime links, achieving precise deviation correction of the entire path loss curve through a point constraint mechanism. This addresses the pain point of inconsistency between simulation data and actual measurement scenarios, providing high-resolution, long-term intelligent prediction support for the performance evaluation of maritime beyond-line-of-sight communication equipment. Experimental results show that the non-transfer model has a large prediction error (MAE 35.75dB) on measured data, making it difficult to meet engineering application requirements. All transfer learning schemes deliver orders of magnitude performance improvements, validating the necessity of transfer learning. Cross-band generalization experiments show that the transferred model maintains a low error of approximately 4dB across a wide frequency range from 4.4GHz to 15.2GHz. Particularly at the 14.65GHz and 15.2GHz high-frequency bands, the proposed method significantly reduces prediction errors compared to the non-transfer model, demonstrating that the model possesses cross-band general representation capabilities. Timeliness analysis further confirms that the prediction error of the transferred model remains stable and controllable within 72 hours, enabling it to stably track the dynamic evolution of meteorological parameters.

[0060] Based on the above technical solution, step S107, the software integration and visualization stage, integrates the proposed model, NPS model, and parabolic equation simulator into the "Sea-skimming Wireless Channel Characteristic Analysis Software," achieving user-friendly parameter input and result visualization, providing a practical tool for performance evaluation of maritime beyond-line-of-sight communication systems. The graphical user interface supports manual input or selection of system and environmental parameters from preset ranges, including communication frequency, transmitter altitude, receiver altitude, antenna elevation angle, beamwidth, maximum propagation distance, polarization, air temperature, sea surface temperature, atmospheric pressure, relative humidity, and wind speed. The visualization rendering module supports displaying the path loss curve after point constraint fine-tuning and provides a comparison view with the pure simulation prediction results. The software visualization module supports comparative display of path loss prediction results, pure simulation results, and calibrated results, and supports saving the prediction results as data files.

[0061] The present invention has the following beneficial effects:

[0062] (1) Effectively overcomes the domain difference between the simulation domain and the measured domain. This invention constructs a two-stage transfer learning framework of "source domain pre-training - target domain fine-tuning". While maintaining the physical feature extraction capability of the pre-trained encoder, it only performs target domain adaptation updates on the decoder, thereby reducing the prediction bias of the pure simulation data-driven model at the actual operating frequency.

[0063] (2) Reduced the requirement for measured data in the target domain. This invention only uses the measured path loss value at a single point at a specific distance on the link as a constraint anchor point to complete model fine-tuning and path loss curve calibration, without the need to obtain continuous measured data for the entire path, thus reducing the cost and difficulty of data acquisition in marine field tests.

[0064] (3) The overall calibration of the full path loss prediction curve is realized. This invention calculates the residual between the predicted value and the measured value at a specific distance point through the point constraint loss function, and updates the decoder parameters through backpropagation, so that the calibrated model can output a full-distance dimension path loss prediction sequence that conforms to the target domain scene, realizing "single-point calibration and full-line correction".

[0065] (4) Improved the adaptability of cross-frequency band path loss prediction. This invention utilizes the prior knowledge of electromagnetic propagation physics obtained from the source domain pre-trained model and combines it with the single-point measured constraint information of the target domain to realize the migration prediction from the simulated operating frequency to the actual operating frequency, thereby improving the model's adaptability and prediction stability under different frequency band conditions.

[0066] (5) It has engineering application value. This invention can be integrated with the NPS evaporating waveguide diagnostic model, parabolic equation simulation model and visualization software module to realize integrated processing of environmental parameter input, evaporating waveguide height calculation, path loss prediction, result display and data storage, thereby improving the efficiency of analysis and performance evaluation of maritime over-the-horizon communication links. Attached Figure Description

[0067] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein:

[0068] Figure 1 A flowchart illustrating the steps of a transfer learning method for predicting marine path loss by integrating measured data.

[0069] Figure 2 This is the core structure of the TPE-Transformer network;

[0070] Figure 3 A transfer learning framework constrained by fusion points. Detailed Implementation

[0071] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed 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 representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0072] The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. It is understood that some well-known structures and their descriptions may be omitted in the drawings for those skilled in the art.

[0073] like Figure 1 As shown, the adaptive prediction method for path loss of marine evaporating waveguides based on small-sample transfer learning is characterized by the following steps:

[0074] S101: Pre-training phase: Obtain a marine electromagnetic propagation simulation dataset covering multiple frequency bands and multiple evaporation waveguide heights, generated by a two-dimensional parabolic equation model, as the source domain;

[0075] S102: Physical Feature Extraction Pre-training: Construct a TPE-Transformer model based on the Transformer architecture and perform pre-training to obtain a pre-trained encoder with the ability to extract physical features of general electromagnetic propagation.

[0076] S103: Target domain construction stage: Obtain a sparse measured dataset of links in a specific sea area at the actual operating frequency as the target domain; the measured dataset contains single-point measured path loss reference values ​​at specific distances of the link.

[0077] S104: Model transfer configuration stage: Build the transfer learning framework, load the pre-trained encoder and freeze all its network parameters, and initialize the decoder module to be fine-tuned.

[0078] S105: Point Constraint Fine-tuning Stage: Input the target domain data into the model, introduce the point constraint loss function, use the measured path loss value of the single point as the constraint anchor point, calculate the residual between the predicted output value of the model at the same distance and the measured value, and iteratively optimize the parameters of the decoder only accordingly.

[0079] S106: Full Path Prediction Stage: Utilize the fine-tuned model to output a full-distance dimension path loss prediction sequence, thereby achieving amplitude calibration and overall deviation correction of the full path prediction curve.

[0080] S107: Software Integration and Visualization Stage: Integrate the methods described in steps S101 to S106 into the sea-skimming wireless channel characteristic analysis software. Receive system and environmental parameters input by the user through a graphical user interface, call the NPS diagnostic model to output the evaporation waveguide height, render and output the path loss curve as a function of distance or height in real time, and provide data saving functionality.

[0081] Based on the above technical solution, in step S101, the source domain dataset construction method is as follows:

[0082] The source domain data is a simulation dataset composed of environmental meteorological parameters retrieved from the WRF numerical weather prediction model, EDH forecasts from the NPS model, and PL sequences generated from two-dimensional PE simulations. The specific operation is as follows:

[0083] (1) Inversion and acquisition of mesoscale meteorological parameters

[0084] Using the WRF mesoscale numerical meteorological model, appropriate horizontal and vertical stratifications were selected to obtain large-area high-resolution environmental information. The optimal microphysical scheme was selected and the time span and time resolution were set to retrieve the environmental meteorological parameters of the tropospheric beyond-line-of-sight link region.

[0085] (2) Extraction of meteorological parameters and construction of data subsets for the link

[0086] In post-processing, each set time point is traversed, and the variable extraction function in wrrf-python is used to extract all meteorological parameters retrieved from all grid points. Based on the positions of the latitude and longitude coordinates of the two ends of the required link in the grid, the start and end points of the link are set. The fitting function is used to generate line pixel coordinates and remove duplicates. The interpolation position of each point on the link is calculated, and the average meteorological parameter values ​​at each point are used as the meteorological parameters of the link at the current time step, thus constructing a subset of meteorological parameter data for the tropospheric beyond-line-of-sight link channel environment.

[0087] (3) Evaporation waveguide height prediction based on NPS model

[0088] Predicting the characteristic parameters of evaporation waveguide height requires calculation using the atmospheric corrected refractive index. The atmospheric refractive index N is determined by atmospheric pressure p (in hPa), atmospheric temperature T (in K), and water vapor partial pressure e (in hPa), and the empirical relationship is as follows:

[0089]

[0090] The formula for calculating the partial pressure e of water vapor is:

[0091]

[0092]

[0093] In the formula, R h To better study the influence of atmospheric refractive index on electromagnetic wave propagation, the Earth's surface is approximated as a plane, and the atmospheric corrected refractive index M (unit M) is redefined. Its relationship with the atmospheric refractive index is as follows:

[0094]

[0095] z represents altitude (in meters), r e Assuming the average curvature of the Earth is 6371 km, substituting this value into the formula yields...

[0096]

[0097] In the NPS model, the vertical profiles of near-surface temperature T and specific humidity q are represented as follows:

[0098]

[0099]

[0100] Where T0 and q0 are the sea surface temperature and specific humidity, respectively, and T(z) and q(z) are the atmospheric temperature and specific humidity at altitude z, respectively, and θ * q *These are the characteristic scales for potential temperature θ and specific humidity q, respectively. Let Γ be a universal temperature function, κ be the Karman constant, and Γ be a universal temperature function. d The dry adiabatic lapse rate is approximately 0.00976 K / m, z 0t Let L be the roughness height of atmospheric temperature and L be the similarity length. A subset of meteorological parameter data is input into the NPS model to obtain high-resolution, long-term evaporation duct height forecasts for a large area.

[0101] (4) Path loss simulation based on two-dimensional parabolic equation

[0102] The corresponding recursive formula for the two-dimensional parabolic equation method is:

[0103]

[0104] in and These are the Fourier transform and the inverse transform, respectively. The refractive index term reflects the influence of the space medium on electromagnetic waves. The diffraction term reflects the diffraction effect of obstacles on electromagnetic waves along the propagation path, where... Let θ be the angle between the electromagnetic wave and the horizontal direction, given the initial field distribution. Then, the field distribution for the next step can be obtained. This allows for iterative solutions to the field across the entire computational space. For the current tropospheric beyond-line-of-sight link environment, a specific microwave scattering...

[0105] The system parameters of the communication equipment, including frequency, transmit antenna height, and receive antenna height, are combined with meteorological parameters and the predicted evaporation waveguide height. The path loss on this link is predicted using the two-dimensional bidirectional stepwise parabolic equation method.

[0106] (5) Construction and storage of path loss sequence dataset

[0107] The dataset required for training the path loss sequence model is constructed. The feature dimension of the dataset is (number of samples, time steps, feature dimension), where the number of samples represents the total number of combinations of meteorological parameters and communication equipment system parameters, and the time steps represent the total number of time steps under the current time span and time resolution. The dataset is grouped into set X and set Y. The features of dataset X are air temperature (AT), sea surface temperature (SST), atmospheric pressure (AP), relative humidity (RH), wind speed (WS), evaporation duct height (EDH), communication frequency (f), transmit antenna height (ht), and receive antenna height (hr). Each combination of communication equipment system parameters (f, ht, hr) constitutes a sample. It is strictly guaranteed that a sample contains all time step information. For example, if the time span is 72 hours and the time resolution is 1 hour, then the total number of time steps is 72. The dimension of a sample in dataset X is (72, 9), and the dimension of dataset X is (number of samples, 72, 9). The Y dataset is characterized by a path loss (PL) sequence. Each row of PL corresponds to a combination of meteorological and system parameters in a sample, ensuring the continuity of time steps. The dataset is then saved after the sequence is arranged.

[0108] Figure 2 This is the core structure of the TPE-Transformer network;

[0109] Based on the above technical solution, in step S102, a TPE-Transformer model based on the Transformer architecture is constructed and pre-trained to obtain a pre-trained encoding network with the ability to extract general electromagnetic propagation physical features.

[0110] The overall model framework comprises four main modules: an input layer, a feature embedding and location encoding layer, a Transformer encoder-decoder layer, and an output layer, as well as a TPE hyperparameter optimization module. The input layer receives the temporal dataset (dimensions of [number of samples, time step, feature dimension]) constructed in step S101, covering nine core features. The feature embedding and location encoding layer maps discrete features into high-dimensional vectors and injects temporal information. The Transformer encoder-decoder layer captures global temporal correlations and local feature interactions through a multi-head self-attention mechanism and a feedforward network. The output layer outputs the path loss prediction value for the corresponding time step. The TPE hyperparameter optimization module adaptively optimizes the key hyperparameters of the Transformer network to improve the model's generalization ability.

[0111] The core advantages of this design are: first, it retains the native parallel computing capabilities and global dependency modeling advantages of the Transformer network, adapting to the needs of long-term path loss prediction; second, it solves the problem of blindness in manual hyperparameter tuning through the TPE algorithm, achieving accurate matching between model parameters and prediction tasks; and third, it preserves the spatiotemporal correlation of environmental features and waveguide parameters throughout the process, making up for the defect of static models that sever temporal correlations, and achieving an upgrade from "static point prediction" to "dynamic sequence prediction".

[0112] Based on the above technical solution, in step S103, a sparse measured dataset of a specific sea area link at the actual operating frequency is obtained as the target domain; the measured dataset contains measured path loss reference values ​​at specific distance points. The target domain data is the measured data of the marine scattering experimental link. The two ends of the link are Chaotanbi in Wenchang City, Hainan Province, and Fenghuojiaozui in Taishan City, Guangdong Province, respectively. The C-band data uses the measured data from the vehicle-mounted C-scattering communication equipment at Wenchang Station and the vehicle-mounted C-scattering communication equipment at Taishan Station, and the Ku-band data uses the measured data from the box-type Ku-scattering communication equipment at Wenchang Station and the box-type Ku-scattering communication equipment at Taishan Station. The test time is from 0:00 on December 15, 2024 to 24:00 on December 17, 2024, and the time interval is consistent with the retrieved meteorological parameters and EDH prediction, which is 1 hour. The measured data file is preprocessed to extract the received level and received rate, unify the units, remove outliers, and then calculate the path loss. :

[0113]

[0114] In the formula, For transmission power, The measured received power is in dBm. and These are the transmit and receive antenna gains, respectively, in dBi.

[0115] Figure 3 A transfer learning framework constrained by fusion points;

[0116] Based on the above technical solution, in the model transfer configuration stage of step S104, a transfer learning framework is constructed, the pre-trained encoder is loaded and its network parameters are frozen, and the decoder module to be fine-tuned is initialized. The encoder is mainly responsible for extracting meteorological environmental features and establishing a deep correlation between meteorological parameters and refractive index profiles and electromagnetic wave propagation modes. Therefore, the meteorological feature extraction capability learned by the source domain model can be seamlessly transferred to the target domain. In the fine-tuning stage, the present invention freezes the parameters of the encoder and its embedding layer to maintain the physical perception capability obtained in the pre-training stage, preventing overfitting caused by the sparsity of data in the target domain. The decoder is responsible for mapping the physical features extracted by the encoder to specific path loss values.

[0117] Based on the above technical solution, in the point constraint fine-tuning stage of step S105, considering the differences in data format and distribution between the source and target domains, this invention proposes a parameter update strategy of "freezing the encoder and fine-tuning the decoder" and designs a point constraint loss function. In one embodiment, the specific distance point of the link is the endpoint of the link where the receiver is located, for example, at 300 km, and the point constraint loss function is defined as L. point for:

[0118]

[0119] In the formula, This represents the model prediction value for the i-th sample. This represents the true value of the i-th sample. The loss function calculates the prediction error at a specific distance point on the link and updates the decoder parameters through backpropagation. Although only a single point is constrained, the shape of the entire curve output by the model is still controlled by the physical laws of the source domain because the encoder is frozen and the decoder is initialized using the conditions of the source domain, thus achieving the effect of "single-point calibration, full-line correction".

[0120] Based on the above technical solution, in step S106, the full-path prediction stage is addressed. Due to sea surface roughness, clutter interference, and systematic errors in the simulation model in the real environment, the main issues manifest as an overall shift in the amplitude or gain error of the predicted curve. Therefore, this invention sets the decoder parameters to a trainable state. By performing backpropagation on the target domain data, the model can learn a "calibration coefficient," adjusting the overall energy level of the output curve to adapt it to the loss characteristics of the real environment. On the measured dataset, MAE, RMSE, and other parameters were selected. The relative error (err) is used to quantitatively evaluate the model's accuracy. Its evaluation index expression is as follows:

[0121]

[0122]

[0123]

[0124]

[0125] The present invention has the following beneficial effects:

[0126] (1) Effectively overcomes the domain difference between the simulation domain and the measured domain. This invention constructs a two-stage transfer learning framework of "source domain pre-training - target domain fine-tuning". While maintaining the physical feature extraction capability of the pre-trained encoder, it only performs target domain adaptation updates on the decoder, thereby reducing the prediction bias of the pure simulation data-driven model at the actual operating frequency.

[0127] (2) Reduced the requirement for measured data in the target domain. This invention only uses the measured path loss value at a single point at a specific distance on the link as a constraint anchor point to complete model fine-tuning and path loss curve calibration, without the need to obtain continuous measured data for the entire path, thus reducing the cost and difficulty of data acquisition in marine field tests.

[0128] (3) The overall calibration of the full path loss prediction curve is realized. This invention calculates the residual between the predicted value and the measured value at a specific distance point through the point constraint loss function, and updates the decoder parameters through backpropagation, so that the calibrated model can output a full-distance dimension path loss prediction sequence that conforms to the target domain scene, realizing "single-point calibration and full-line correction".

[0129] (4) Improved the adaptability of cross-frequency band path loss prediction. This invention utilizes the prior knowledge of electromagnetic propagation physics obtained from the source domain pre-trained model and combines it with the single-point measured constraint information of the target domain to realize the migration prediction from the simulated operating frequency to the actual operating frequency, thereby improving the model's adaptability and prediction stability under different frequency band conditions.

[0130] (5) It has engineering application value. This invention can be integrated with the NPS evaporating waveguide diagnostic model, parabolic equation simulation model and visualization software module to realize integrated processing of environmental parameter input, evaporating waveguide height calculation, path loss prediction, result display and data storage, thereby improving the efficiency of analysis and performance evaluation of maritime over-the-horizon communication links.

Claims

1. An adaptive prediction method for path loss of marine evaporating waveguides based on small-sample transfer learning, characterized in that, Includes the following steps: S101: Pre-training phase: Obtain a marine electromagnetic propagation simulation dataset covering multiple frequency bands and multiple evaporation waveguide heights, generated by a two-dimensional parabolic equation model, as the source domain; S102: Physical Feature Extraction Pre-training: Construct a TPE-Transformer model based on the Transformer architecture and perform pre-training to obtain a pre-trained encoder with the ability to extract physical features of general electromagnetic propagation. S103: Target domain construction stage: Obtain a sparse measured dataset of links in a specific sea area at the actual operating frequency as the target domain; the measured dataset contains single-point measured path loss reference values ​​at specific distances of the link. S104: Model transfer configuration stage: Build the transfer learning framework, load the pre-trained encoder and freeze all its network parameters, and initialize the decoder module to be fine-tuned. S105: Point Constraint Fine-tuning Stage: Input the target domain data into the model, introduce the point constraint loss function, use the measured path loss value of the single point as the constraint anchor point, calculate the residual between the predicted output value of the model at the same distance and the measured value, and iteratively optimize the parameters of the decoder only accordingly. S106: Full Path Prediction Stage: Utilize the fine-tuned model to output a full-distance dimension path loss prediction sequence, thereby achieving amplitude calibration and overall deviation correction of the full path prediction curve. S107: Software Integration and Visualization Stage: Integrate the methods described in steps S101 to S106 into the sea-skimming wireless channel characteristic analysis software. Receive system and environmental parameters input by the user through a graphical user interface, call the NPS diagnostic model to output the evaporation waveguide height, render and output the path loss curve as a function of distance or height in real time, and provide data saving functionality.

2. The method for predicting path loss of marine evaporating waveguides using fusion point-constrained transfer learning according to claim 1, characterized in that: The source domain simulation dataset construction process in step S101 includes: Based on a two-dimensional parabolic equation model, combined with the sea surface roughness effect and atmospheric environmental parameters of the evaporating waveguide, a path loss simulation matrix covering different frequency bands, antenna heights, and evaporating waveguide heights is generated.

3. The method for predicting path loss of marine evaporating waveguides using fusion point-constrained transfer learning according to claim 1, characterized in that: The TPE-Transformer model in step S102 has a multi-dimensional core feature set composed of meteorological environmental parameters, evaporation waveguide feature parameters, and communication system parameters as input features; the tree-structured Parzen estimator algorithm is used to optimize the hidden layer dimension, number of attention heads, and learning rate of the Transformer network.

4. The maritime path loss prediction transfer learning method according to claim 1, characterized in that: In step S103, real-time engineering parameters of the transmitter and receiver at both ends of the marine scattering experimental link are collected. The parameters include transmit power, receive power and antenna gain. The received power is converted into a path loss reference value at the corresponding distance point through a preset path loss calculation model. In the formula, For transmission power, The measured received power is in dBm. and These are the transmit and receive antenna gains, respectively, in dBi.

5. The maritime path loss prediction transfer learning method according to claim 1, characterized in that: In step S104, the parameter freezing logic is as follows: freeze the parameters of the pre-trained coding network and its feature embedding layer to maintain its physical perception capability; only update the weights of the fully connected layer and the linear mapping layer in the decoder module, thereby mapping the general physical features into the path loss values ​​of the target sea area.

6. The maritime path loss prediction transfer learning method according to claim 1, characterized in that: The point constraint loss function L in step S105 point By calculating the residual between the model prediction output value at a specific distance point on the link and the actual measured loss value corresponding to that point, a global magnitude correction of the entire path prediction curve is achieved. The point constraint loss function L point The calculation formula is as follows: In the formula, This represents the model prediction value for the i-th sample. This represents the true value of the i-th sample. The loss function calculates the prediction error at a specific distance point on the link and updates the decoder parameters through backpropagation. Although only a single point is constrained, the shape of the entire curve output by the model is still controlled by the physical laws of the source domain because the encoder is frozen and the decoder utilizes the conditions of the source domain for initialization, thus achieving the effect of "single-point calibration, full-line correction".

7. The method for predicting path loss of marine evaporating waveguides using fusion point-constrained transfer learning according to claim 1, characterized in that: In step S106, the target domain meteorological environment parameters, evaporation waveguide height parameters, and communication system parameters are input into the model after point constraint fine-tuning. The propagation environment features are extracted through the frozen encoder, and the path loss prediction sequence with full distance dimension is output by the decoder optimized by point constraints. This realizes the migration of path loss prediction from the source domain simulation scenario to the actual working frequency scenario of the target domain and the overall amplitude calibration of the full path prediction curve.

8. The method for predicting path loss of marine evaporating waveguides using fusion point-constrained transfer learning according to claim 1, characterized in that: In step S107, the software integration and visualization stage, the proposed model, along with the NPS model and parabolic equation simulator, is integrated into the "Sea-skimming Wireless Channel Characteristic Analysis Software," enabling user-friendly parameter input and result visualization. The graphical user interface supports manual input or selection of system and environmental parameters from preset ranges. These parameters include communication frequency, transmitter altitude, receiver altitude, antenna elevation angle, beamwidth, maximum propagation distance, polarization, air temperature, sea surface temperature, atmospheric pressure, relative humidity, and wind speed. The visualization rendering module supports displaying the path loss curve after point constraint fine-tuning and provides a comparison view with the pure simulation prediction results.

Images