A method for modeling ocean multi-source disturbance composite propagation loss for ground wave communication

Abstract

A sea multi-source disturbance composite propagation loss modeling method for ground wave communication is disclosed: including 1) establishing a disturbance data acquisition module, outputting a six-channel disturbance tensor; 2) establishing a medium parameter correction module, outputting the corrected surface conductivity σ (ω, t) and relative permittivity ε r (ω, t); 3) establishing a disturbance spectrum extraction module, outputting disturbance spectrum embedding features F fused ; 4) establishing a path loss modeling module, including taking frequency ω and propagation distance d as core variables, and fusing medium dynamic characteristic parameters σ (ω), ε r (ω) and disturbance spectrum embedding features F fused output by the preceding modules to construct a dynamic estimation function of ground wave propagation path loss; 5) establishing a residual learning integrated compensation module, including introducing an integrated learning residual regression strategy based on a sliding time window to obtain a corrected path loss

Description

Technical Field

[0001] This invention relates to the field of wireless communication technology, and more specifically to a method for modeling the composite propagation loss of multi-source disturbances in oceans for ground wave communication. Background Technology

[0002] Currently, in marine wireless communication systems, especially in ground wave communication scenarios (such as NAVDAT broadcasting and HF / VHF long-distance links), propagation loss of the communication path is mainly estimated using traditional empirical models, such as the ITU-R P.528 model, the Hata model, and the Okumura model. These models are primarily based on fixed propagation environments (terrain, frequency band, antenna elevation differences, etc.), treating surface medium parameters (such as conductivity and relative permittivity) as static constants or using regional average values.

[0003] Under complex sea conditions (such as wind, waves, tidal disturbances, and extreme weather), although these disturbances significantly affect the electrical properties of the propagation medium, thus causing path loss fluctuations, existing models do not incorporate disturbance data or frequency response mechanisms. Some studies have attempted to introduce artificial neural networks or time-series prediction models (such as LSTM) for field strength prediction, but these approaches typically only perform learning-based modeling of received power or field strength, failing to establish a dynamic propagation loss modeling structure based on physical mechanisms, and further neglecting mechanisms for "disturbance spectral characteristics" and "frequency-dependent medium correction." Therefore, all of these approaches have some shortcomings.

[0004] For example, propagation models are static and cannot respond to changes in ocean disturbances. Traditional propagation loss models set conductivity and dielectric constant as constants or average values, ignoring the time-varying nature of disturbance factors such as wave height, wind speed, and salinity in the actual ocean environment. This leads to a significant increase in error in loss calculations under dynamic sea conditions. For example, they lack the ability to identify disturbance spectrum, resulting in low modeling accuracy. Ocean disturbances exhibit multi-frequency characteristics, with different time scales affecting the propagation path differently. Existing models fail to identify the dominant frequency distribution of disturbances and do not perceive or hierarchically model frequency-sensitive features. For example, they lack adaptive correction mechanisms and cannot cope with extreme weather or abnormal changes. Faced with strong disturbance scenarios such as hurricanes and typhoons, existing models cannot dynamically adjust or compensate for propagation loss estimates, lacking fault tolerance and self-recovery capabilities, thus affecting the steady-state operation of the system.

[0005] Therefore, new modeling techniques are needed to at least partially overcome the problems existing in the current techniques. Summary of the Invention

[0006] This invention addresses the problems of "static assumptions, lack of spectrum awareness, delayed disturbance response, and large modeling residuals" in existing marine ground wave communication propagation path loss modeling. It proposes a composite modeling method with frequency correlation and disturbance adaptation capabilities. Through modular design and cross-dimensional feature fusion, this invention achieves substantial technical improvements in propagation loss estimation accuracy, disturbance sensitivity, system stability, and engineering deployment adaptability.

[0007] According to one aspect of the present invention, a method for modeling the composite propagation loss of multi-source disturbances in oceans for ground wave communication is provided, comprising:

[0008] 1) Establish a disturbance data acquisition module, including the acquisition of disturbance data such as seawater salinity S, soil moisture H, air temperature T, atmospheric pressure P, wind speed W, and wave height A. Preprocess the acquired data to obtain a six-channel disturbance tensor.

[0009] X t Let t be the perturbation state vector, t be the sampling time, and w be the length of the sliding time window;

[0010] 2) Establish a medium parameter correction module, including one based on the disturbance state vector X. t Real-time correction of key medium parameters in the ground wave propagation path, namely the surface conductivity σ and relative permittivity ε. r Output the corrected surface conductivity σ(ω,t) and relative permittivity ε r (ω,t);

[0011] 3) Establish a perturbation spectrum extraction module, including one based on the six-channel perturbation tensor X. t By utilizing multi-scale convolution, spectral energy sensing, and channel weight fusion, a perturbation spectrum extraction module is established to identify potential multi-timescale fluctuation features in perturbation parameters. This module constructs a perturbation spectrum embedding representation highly correlated with changes in the ground wave propagation path, providing frequency-aware perturbation prior features for subsequent propagation loss modeling. Finally, the perturbation spectrum embedding feature F is output. fused ;

[0012] 4) Establish a path loss modeling module, including frequency ω and propagation distance d as core variables, and integrate the medium dynamic characteristic parameters σ(ω) and ε output from the preceding module. r (ω) and perturbation spectrum embedding feature F fused Construct a dynamic estimation function for ground wave propagation path loss.

[0013] 5) Establish a residual learning ensemble compensation module, including introducing an ensemble learning residual regression strategy based on a sliding time window, constructing a collaborative structure of support vector regression, random forest, and feedforward neural network to achieve online learning and adaptive error compensation, used for estimating the output of the path loss modeling module. Perform dynamic error correction to obtain the corrected path loss.

[0014] According to an embodiment of the present invention, in step 1), the preprocessing includes synchronous calibration, extended Kalman filtering (EKF), and window embedding.

[0015] According to the embodiment of the present invention, step 1) further includes a dynamic sampling strategy based on quality indicators. When the system detects a sudden change trend in the disturbance variable or determines that the current area is at a high risk level, the system will automatically increase the sampling frequency to ensure the parameter update frequency in a highly dynamic environment and enhance the system's ability to respond quickly to propagating sudden changes.

[0016] According to an embodiment of the present invention, step 2) includes:

[0017] 2.1) Based on the disturbance state vector X obtained in step 1), t A multiple linear regression model was constructed by comparing the measured conductivity and dielectric constant data with historical data.

[0018]

[0019]

[0020] Among them, w σ ,w ε b represents the model weights. σ ,b ε For the bias terms, σ0(t), ε r,0 (t) represents the static estimate of the basic regression output;

[0021] 2.2) The perturbation state vector X t The input radial basis function (RBF kernel function) is used for nonlinear mapping, and then combined with support vector regression (SVR) for fitting. The output is the correction terms Δσ(t) and Δε for the residuals. r (t), which are defined as follows:

[0022] Where ε meas (t) and ε r，meas (t) represents the measured conductivity and relative permittivity, respectively;

[0023] 2.3) Based on the Cole–Cole model, frequency dependence correction is performed to obtain σ(ω,t), εr (ω,t), expressed as:

[0024] σ(ω,t)=σ o (t)+Δσ(t)+k σ ·ω β

[0025]

[0026] Where, k σ β is the frequency domain conductivity correction factor, and ε is... s ε∞ represents the static dielectric constant and the limiting dielectric constant, respectively, and τ and α represent the relaxation time and the fractional-order adjustment factor, respectively.

[0027] According to an embodiment of the present invention, step 2) further includes obtaining the final fuzzy compensation amount σ based on a fuzzy logic compensation mechanism under extreme weather conditions. fuzzy (t) and ε r,fuzzy (t), the final outputs of the medium parameter correction module are σ(ω,t) and ε. r The expressions for (ω,t) are as follows:

[0028] σ(ω,t)=σ o (t)+Δσ(t)+σ fuzzy (t)+k σ ·ω β ;

[0029]

[0030] According to an embodiment of the present invention, in step 3), the convolutional structure includes three sets of one-dimensional convolutional paths with kernel sizes k∈{3, 5, 7}, which are used to extract perturbation patterns under short-period, high-frequency fluctuation, medium-period perturbation and low-frequency trend, respectively.

[0031] The convolution operation is defined as:

[0032] Among them, X t+τ To represent the input vector of the perturbation state sequence at time t+τ, the convolution kernel h... (k)

[0033] For a time-domain filter, its corresponding frequency response is:

[0034]

[0035] Wherein, each convolutional feature F (k) For the perturbation tensor X t In the corresponding frequency response range Ω k Local response mapping;

[0036] Spectrum energy sensing and channel weight fusion include:

[0037] The power spectral density (PSD) of the time series of perturbed channel i is estimated using the Welch method:

[0038]

[0039] in Indicates Fourier transform, This represents the disturbance signal segment within the m-th window;

[0040] The frequency response interval for each convolution scale k is defined as Ω. k The spectral energy of all channels integrated within this interval is:

[0041] in α is the normalization factor. k This indicates the weighted proportion of energy that is most likely to affect electromagnetic propagation in the current disturbance environment;

[0042] Finally, the multi-scale convolutional features are fused according to the spectral sensing weights to form the perturbation spectral embedding features:

[0043]

[0044] According to an embodiment of the present invention, step 3) further includes embedding a propagation correlation adjustment layer at the convolutional back end, by calculating F fused The Pearson correlation coefficient ρ with the rate of change of medium parameters at the current frequency is used to enhance the screening of highly correlated propagation factors by the perturbation spectrum eigenvector, retaining only those related to σ(ω) and ε. r (ω) A highly coupled spectral dimension used to drive the frequency adjustment term in the subsequent path loss function, outputting a perturbation spectral feature tensor.

[0045] According to an embodiment of the present invention, the ground wave communication is selected from NAVDAT broadcast and HF / VHF long-distance link.

[0046] According to an embodiment of the present invention, step 4) includes:

[0047] 4.1) Establish the preliminary loss estimation expression: L0(d, ω)=L sp (d,ω)+L gr (d, ω; σ, ε) r Among them, L sp Indicates space wave loss; L gr The ground wave component loss is approximately calculated as follows:

[0048] L gr (d, ω)≈A(ω)·log10 (d)+B(ω), where A(ω) represents the attenuation slope related to the surface conductivity and propagation frequency; B(ω) represents the initial loss related to the initial field strength and electromagnetic reflection characteristics;

[0049] 4.2) Design the disturbance modulation function ΔL env (ω, t) is used to express the effect of the perturbation on the additional loss of the propagation path, which is expressed by the perturbation spectrum feature tensor F. fised (t) is input to the perturbation sensitivity mapping function Φ(·) to obtain:

[0050] ΔL env (ω,t)=Φ(F fused (t);ω)

[0051] Where Φ(·) is a lightweight residual network designed based on frequency band correlation. The training objective is to minimize the sum of squared residuals between the predicted and measured field strengths, while maintaining its response enhancement mechanism in the high-perturbation frequency band: Φ(F, ω)=W2·ReLU(W1·F+b1)+b2

[0052] Where W1 and W2 are learnable weight matrices, and the mapping incorporates a perturbation frequency ω. d The channel weighting control factor enables the model output to have the ability to respond to differences in propagation frequency bands;

[0053] The path loss estimation function is expressed as:

[0054] According to an embodiment of the present invention, step 5) includes:

[0055] 5.1) Define the loss residual as ∈(d, ω, t),

[0056] Where L measured This is the measured loss value;

[0057] 5.2) Using the perturbation characteristic tensor F fused (t), medium parameters σ(ω), ε r (ω) and predicted path loss Together they constitute the input feature vector:

[0058]

[0059] 5.3) Local modeling is performed using a fixed-length sliding time window. Specifically, for each time step t, the input residual pairs for the window [t-w+1,t] are extracted from the history to construct the dataset.

[0060]

[0061] 5.4) Within each time window, the following three machine learning models are used for independent modeling: SVR (Support Vector Regression): used to model the stable trend between perturbation features and residuals; RF (Random Forest): to enhance the nonlinear capture of variable interactions; ANN (Feedforward Neural Network): used to model the complex residual response in a high-dimensional perturbation space.

[0062] 5.5) Each model is trained independently within the current time window and outputs the prediction error RMSE on the validation set. m , denoted as: RMSE SVR RMSE RF RMSE ANN

[0063] 5.6) Dynamically adjust the fusion weights of the predicted values ​​of each model based on the validation error:

[0064]

[0065] The final residual prediction value is:

[0066] The final corrected path loss is:

[0067] The proposed method for modeling the propagation loss of marine multi-source disturbances in ground wave communication can achieve beneficial technical effects:

[0068] 1. Multi-scale perturbation spectrum extraction and frequency-aware weighted fusion mechanism: This invention designs multiple sets of one-dimensional convolutional structures to extract short-period, medium-period, and long-period components from the perturbation sequence. Combined with a frequency-band weighted fusion strategy based on power spectral density (PSD), it achieves the identification, hierarchical modeling, and dynamic fusion of the dominant frequency component of the perturbation. The weight of each convolutional path is determined based on the distribution of perturbation spectral energy in different response frequency bands, enhancing the perception of the most sensitive perturbation frequency band at the current propagation frequency. This realizes a leap from "time-mean response" to "spectral difference response" in perturbation modeling, significantly improving the frequency band matching capability and prediction stability of the propagation model under multi-frequency ground wave communication conditions.

[0069] 2. Frequency-dependent modeling and dynamic correction mechanism for ocean propagation medium parameters: This invention obtains initial estimates of dynamic medium parameters by constructing a multiple regression model between perturbation variables and medium parameters, and a residual kernel function fitting module. Then, it combines the Cole–Cole model to express the frequency dependence, forming σ(ω) and ε. rThe expression for the medium parameter response at frequencies such as (ω) is presented. A fuzzy logic compensation mechanism is used to handle abrupt responses under extreme disturbances (such as typhoons and storm surges). This improves the timeliness and physical relevance of medium parameter modeling, enabling continuous correction of the propagation loss model under different frequency bands and complex disturbance conditions. It effectively solves the problem of prediction drift caused by parameter distortion in static modeling, making path loss estimation closer to actual propagation conditions.

[0070] 3. Residual Learning Integrated Compensation Mechanism for Propagation Error Self-Correction: This invention constructs a data update strategy based on a sliding time window. Within each time window, three residual prediction models—SVR (Support Vector Regression), RF (Random Forest), and ANN (Artificial Neural Network)—are trained respectively. Weighting coefficients are dynamically allocated based on the validation set RMSE, achieving integrated adaptive compensation output for propagation loss errors. This forms a closed-loop structure of "disturbance-driven—model estimation—residual correction," enabling the system to have online self-correction capabilities. It effectively improves the system's fault tolerance to non-stationary disturbances and abnormal fluctuations, maintaining low errors even under strong disturbance conditions, effectively ensuring communication link continuity and control stability.

[0071] 4. A method for constructing a dynamic path loss expression function based on perturbation: This invention constructs a function based on propagation distance d, frequency ω, and perturbation feature F. fused The path loss expression is the input. The perturbation modulation term is fitted nonlinearly through a lightweight residual network to capture the complex interaction between perturbation intensity and frequency, and is output to the final propagation estimation function. This results in a loss estimation structure with perturbation adaptability, frequency difference perception capability, and error feedback correction capability. Compared with the traditional static formula structure, it is more consistent with actual propagation behavior and exhibits stronger universality and prediction accuracy in multi-band, dynamic environments, and multi-node communication scenarios.

[0072] 5. Optimized Design of Disturbance Data Sensing and Structured Input Mechanism: This invention acquires disturbance parameters through distributed sensing devices and uses link delay modeling and time-label regression for unified time synchronization; it introduces extended Kalman filtering to perform state estimation and anomaly suppression of disturbance variables; and it employs a sliding window mechanism to structure the disturbance tensor, outputting a unified six-channel tensor input for spectrum identification. This ensures the synchronization and stability of disturbance data in the spatiotemporal dimensions, reduces sources of model input error, improves the robustness and convergence of the overall system's prediction link, and lays a high-quality data foundation for propagation loss modeling. Attached Figure Description

[0073] Figure 1 A flowchart illustrating a method for modeling the composite propagation loss of multi-source disturbances in oceanic communications according to an embodiment of the present invention; and

[0074] Figures 2a-2fThe simulation results of loss error based on probability distribution and path loss time series and error are shown in the figure below, which are simulation results of the method for determining the composite propagation loss of marine multi-source disturbances for ground wave communication according to the embodiment of the present invention, under different link distances. Detailed Implementation

[0075] The present invention can be better understood from the accompanying drawings and the following embodiments. However, those skilled in the art will readily understand that the descriptions in the embodiments are for illustrative purposes only and should not, and will not, limit the scope of the invention.

[0076] Figure 1 This is a flowchart illustrating the ocean multi-source disturbance composite propagation loss modeling method for ground wave communication according to an embodiment of the present invention. As shown in the figure, the ocean multi-source disturbance composite propagation loss modeling method for ground wave communication according to the embodiment is as follows:

[0077] 1. Establish a disturbance data acquisition module:

[0078] The disturbance data acquisition module, serving as the input front-end of the system, is responsible for collecting and standardizing multi-source marine environmental parameters that affect electromagnetic propagation loss, providing a continuous and structured time-series data foundation for subsequent medium parameter correction and path loss modeling. This module addresses the high sensitivity of ground wave communication to propagation paths under dynamic sea conditions by designing a highly reliable disturbance information acquisition mechanism that integrates multi-link collaboration, spatiotemporal alignment, and parallel state estimation.

[0079] The disturbance parameters collected by this module include six key physical variables: seawater salinity (S), soil moisture (H), air temperature (T), atmospheric pressure (P), wind speed (W), and wave height (A). These parameters can be acquired through nodes such as shore-based meteorological stations, ocean buoys, unmanned surface vessels, and satellite remote sensing, and uploaded via NB-IoT, LoRaWAN, C-band, or Starlink links. At sampling time t, each parameter is organized into a multi-dimensional disturbance vector: E(t) = [S(t), H(t), T(t), P(t), W(t), A(t)].

[0080] To ensure temporal consistency of multi-source data, the system collects unified UTC timestamps based on the built-in GPS modules of the nodes and establishes a link transmission delay fitting model. The system establishes a delay estimation model for the communication link corresponding to each collection node and performs time-backward correction on each component of the original disturbance sequence E(t). Suppose a disturbance component (e.g., wave height) is collected by node i, uploaded via link i, and received by the central system at time t. The theoretical transmission delay of the link is modeled as follows:

[0081] Where a0, a1, a2, and a3 are link delay fitting coefficients, obtained through multinomial regression based on historical measurement data. By estimating the delay of each link, the actual sampling time of the data can be deduced: t true =t-τ i (t).

[0082] The data from each disturbance channel is then back-aligned on the time axis. Since multiple disturbance variables may originate from different links, the system performs this correction operation on all disturbance channels, ultimately reconstructing the disturbance observation vector at a unified global time t: E * (t):

[0083] However, E * (t) represents only sensor observations and is susceptible to measurement errors, communication disturbances, and other factors. Considering that ocean disturbance variables are typically driven by nonlinear systems and exhibit significant time-varying and local abrupt change characteristics, this module further introduces an extended Kalman filter (EKF) mechanism to smooth and estimate the disturbance state. Let the state vector be x. t The observed value is z t =E * If (t), then the system model is as follows:

[0084] • State transition model: x t+1 =f(x) t )+w t

[0085] • Observation model: z t =h(x t )+v t

[0086] Among them, w t With v t The system noise and observation noise are respectively represented, both following a Gaussian distribution. Through EKF prediction and iterative updates, the denoised and estimated corrected perturbation state can be obtained. This refers to the smoothed perturbation state at the current moment, which improves the continuity and stability of the input data.

[0087] Furthermore, the perturbation sequence needs to be windowed and normalized before entering the downstream modeling module. This invention sets a sliding window length w for each perturbation variable E. i (t) Constructing local time vectors:

[0088]

[0089] After standardizing all variables to zero mean and unit variance within each window, they are concatenated into a six-channel perturbation tensor. This tensor structure serves as the input for the subsequent perturbation spectrum extraction module. It simultaneously preserves the short-term trends of the perturbation parameters and the synergistic relationships among multiple variables, providing a sound modeling foundation for multi-scale convolutional structures.

[0090] This module also features a dynamic sampling strategy based on quality indicators. When the system detects a sudden change in the trend of disturbance variables (such as a sharp increase in wind speed or an abnormal increase in wave height), or determines that the current area is at a high-risk level (such as a typhoon warning area), the system will automatically increase the sampling frequency from, for example, the default 1-10 minutes / time to 30 seconds / time, to ensure the frequency of parameter updates in a highly dynamic environment and enhance the system's ability to respond quickly to propagation changes.

[0091] The disturbance data acquisition module not only completes comprehensive sensing and preprocessing of ocean disturbance parameters, but also constructs a high-resolution, robust, and low-latency data input channel through time calibration, state filtering, window normalization, and frequency adaptive control. This module lays a solid environmental sensing foundation for the frequency-dependent propagation medium modeling and path loss correction mechanism proposed in this invention.

[0092] 2. Establish a media parameter correction module:

[0093] The medium parameter correction module is used to adjust the dynamic disturbance state estimate x output by the disturbance data acquisition module. t The core medium parameters upon which the ground wave propagation path depends are constructed in real time, including the surface conductivity σ(ω,t) and the relative permittivity ε. r (ω,t). This module achieves dynamic correction and frequency-related expression of medium parameters through a three-stage compensation mechanism of perturbation-driven regression modeling, residual learning, and fuzzy rule inference, thereby enhancing the adaptability of propagation modeling to multi-source perturbations and extreme scenarios.

[0094] First, based on the obtained perturbation state vector X t A multiple linear regression model was constructed by comparing the historical measured conductivity σ and relative permittivity data;

[0095]

[0096]

[0097] Among them, w σ ,w ε b represents the model weights (regression coefficient vector). σ ,b ε For the bias terms, σ0(t), ε r,0 (t) represents the static estimate of the basic regression output. Model training is based on a large-scale historical perturbation-medium measurement dataset, and preliminary estimates of the medium parameters (σ, ε) are obtained using least squares fitting. r, 0), forming a basic prediction model.

[0098] Secondly, to overcome the problem that linear models cannot accurately respond to complex dynamic disturbances, this module introduces a support vector regression model based on radial basis function (RBF) kernels to compensate for the offset trend of medium parameters.

[0099] The residual between the preliminary prediction and the measured value: Δσ = σ meas -σ0,Δε r =ε r，meas -ε r，0

[0100] The perturbation state vector X t The input radial basis function (RBF kernel function) is used for nonlinear mapping, and then combined with support vector regression (SVR) for fitting. The output is the residual correction terms Δσ(t) and Δε between the predicted and measured values. r (t), which are defined as follows:

[0101] Δσ(t)=σ meas (t)-σ o (t),

[0102] Δε r (t)=ε r,meas (t)-ε r，o (t),

[0103] Where σ meas (t) and ε r，meas (t) represents the measured conductivity and relative permittivity, respectively.

[0104] This compensation term can dynamically track the systematic shift of the model caused by disturbances and continuously update it over time. It has the ability to capture local change trends under complex disturbances, thereby improving the sensitivity and generalization ability of modeling.

[0105] Under extreme weather conditions (such as tropical storms, wave breaking, and high humidity and salinity environments), the properties of the medium may change abruptly, making it difficult for traditional fitting models to adapt quickly. To address this, this module introduces a fuzzy logic compensation mechanism, which models the impact of disturbance intensity on medium fluctuations through predefined membership functions and rule bases.

[0106] For example, if the wind speed W is "high" and the wave height A is "intense", then the conductivity should be increased; if the salinity S is "extremely high" and the humidity H is relatively high, then the dielectric constant should be decreased.

[0107] Let the rule number be k, and its corresponding output be (δσ). k ,δε r，k The final compensation is obtained by weighted summation of multiple rules:

[0108] Where μ k The membership strength of each rule is ∈ [0,1], calculated from the actual perturbation value using a fuzzy mapping function. This mechanism has the advantages of strong rule interpretability and sensitivity to sudden changes, ensuring the availability of the system under catastrophic perturbation conditions.

[0109] The two types of compensation mechanisms mentioned above—SVR prediction residuals (Δσ and Δε) r ) and fuzzy rule compensation term (σ) fuzzy ,ε r,fuzzy These two methods are applicable to scenarios with different perturbation complexities. The former is used for residual fitting and tracking under normal perturbation conditions, while the latter is used for fault tolerance adjustment under extreme or anomalous perturbations. The two methods complement each other in modeling. Through dual correction fusion, the final medium parameters possess dynamism, interpretability, and robustness, and the model's adaptability to non-stationary perturbations is enhanced.

[0110] Finally, to further demonstrate the sensitivity of the medium parameters to the propagation frequency, the module performs frequency-dependent corrections based on the Cole–Cole model. The conductivity σ(ω,t) and dielectric constant ε are related. r (ω,t) exhibits complex diffusion behavior as frequency ω and time t change, which can be expressed as:

[0111] σ(ω,t)=σ o (t)+Δσ(t)+σ fuzzy (t)+k σ ·ω β ;

[0112]

[0113] Where, k σ β are frequency domain conductivity correction coefficients, εs and ε∞ are the static dielectric constant and limiting dielectric constant, respectively, τ and α are the relaxation time and fractional-order adjustment factors, respectively; j is the imaginary unit.

[0114] All of the above parameters can be calibrated or predicted by dynamic regression using environmental disturbance variables, forming frequency-sensitive medium parameters that can be used for multi-band propagation modeling.

[0115] This module enhances the medium modeling's responsiveness to disturbances, frequency adaptability, and extreme event handling capabilities through a multi-stage combination mechanism: "disturbance-driven multivariate regression initial calibration + residual kernel function correction + fuzzy logic compensation + dynamic spectrum expansion." The final output σ(ω,t) and ε... r (ω,t) will be used as the core input variable of the path loss model, effectively enhancing the system's modeling accuracy for actual propagation changes.

[0116] 3. Establish a disturbance spectrum extraction module:

[0117] The disturbance spectrum extraction module is used to identify potential multi-timescale fluctuation characteristics in disturbance parameters and construct a disturbance spectrum embedding representation highly correlated with changes in the ground wave propagation path, thereby providing frequency-aware disturbance prior features for subsequent propagation loss modeling. Considering that disturbance variables such as wind speed, wave height, and air pressure exhibit typical multi-band energy distributions in the dynamic marine environment, this module designs a joint modeling structure based on multi-scale convolution, spectrum energy sensing, and channel weight fusion. It innovatively introduces disturbance spectral density estimation into the feature weight allocation process to achieve dynamic enhancement of propagation-sensitive frequency bands.

[0118] The input to this module is the six-channel perturbation tensor preprocessed by the perturbation data acquisition module. Where w represents the sliding time window length. The convolutional structure includes three sets of one-dimensional convolutional paths with kernel sizes k∈{3, 5, 7}, used to extract perturbation patterns under short-period, high-frequency fluctuations (such as wind surges), medium-period perturbations (such as temperature difference tides), and low-frequency trends (such as tides), respectively. The convolution operation is defined as:

[0119]

[0120] Among them, X t+τ To represent the input vector of the perturbation state sequence at time t+τ, the convolution kernel h... (k)

[0121] For a time-domain filter, its corresponding frequency response is:

[0122]

[0123] This structure enables each convolutional feature F to... (k) For the perturbation tensor X t In the corresponding frequency response range Ω k Local response mapping,

[0124] To avoid the problem of ignoring the spectral structure of perturbation signals in traditional weighted fusion, this invention designs a channel energy weighting mechanism based on power spectral density (PSD) estimation to construct a direct mapping of "spectrum-propagation contribution".

[0125] First, the PSD of the time series of the perturbation channel i is estimated using the Welch method:

[0126]

[0127] in Indicates Fourier transform, This represents the disturbance signal segment within the m-th window;

[0128] Subsequently, the frequency response interval for each convolution scale k is defined as Ω.k The spectral energy of all channels integrated within this interval is:

[0129] in, α is the normalization factor. k This indicates the weighted proportion of energy that is most likely to affect electromagnetic propagation in the current disturbed environment.

[0130] Finally, the multi-scale convolutional features are fused according to the spectral sensing weights to form the perturbation spectral embedding features:

[0131]

[0132] This spectrum fusion method differs from conventional attention-based or fixed-weighted strategies. Its core advantage lies in the fact that the fusion weights are directly derived from the physical measure of the actual spectrum energy density of the perturbation, enabling the convolutional structure to adaptively focus on the most sensitive frequency bands of the propagation path, effectively enhancing the interpretability and adaptability of frequency-related propagation modeling.

[0133] To further enhance the feature propagation perception capability, this module embeds an optional propagation correlation adjustment layer at the convolutional backend. This is achieved by calculating F... fused The Pearson correlation coefficient ρ with the rate of change of medium parameters at the current frequency is used to enhance the screening of highly correlated propagation factors by the perturbation spectrum eigenvector, retaining only those related to σ(ω) and ε. r (ω) A highly coupled spectral dimension used to drive the frequency adjustment term in the subsequent path loss function.

[0134] The final output perturbation spectrum feature tensor (Where C is the channel dimension and L is the time dimension), will be used as the input of the path loss modeling module to provide multi-band, dynamically sensed disturbance structure priors for the propagation loss function.

[0135] This module overcomes the bottleneck of traditional feature fusion, which cannot reflect the effect of disturbance propagation modulation, by introducing Fourier frequency response modeling, power spectral density estimation, and disturbance spectrum energy weighting mechanism. It is the first to realize a spectrum embedding modeling mechanism under the coupling of disturbance spectrum and propagation sensitive frequency, which enhances the system's adaptability to non-stationary disturbance scenarios and provides a solid frequency domain physical foundation for the dynamic modeling of path loss.

[0136] 4. Establish a path loss modeling module:

[0137] The path loss modeling module, as the core decision-making layer of the system of this invention, constructs a dynamic estimation function for the path loss of ground wave propagation based on the propagation medium parameters and disturbance spectrum characteristics reflected by the current disturbance environment. This module uses frequency ω and propagation distance d as core variables, and integrates the medium dynamic characteristic parameters σ(ω), ε output from the preceding modules. r(ω) and perturbation spectrum embedding feature F fused This enables a high-precision path loss modeling mechanism with spectrum sensing, disturbance response, and adaptive compensation capabilities.

[0138] First, a preliminary loss estimation expression is established. For example, based on the ITU-R P.528 model, we obtain L0(d,ω)=L sp (d,ω)+L gr (d,ω;σ,ε r )

[0139] Among them, L sp This represents space wave loss, typically calculated using the free space path loss formula; L gr This represents the ground wave component loss, which is strongly correlated with the surface conductivity σ(ω) and dielectric constant εr(ω). The calculation can be approximated using the following expression: L gr (d,ω)≈A(ω)·log 10 (d)+B(ω), where A(ω) represents the attenuation slope related to the surface conductivity and propagation frequency; B(ω) represents the initial loss related to the initial field strength and electromagnetic reflection characteristics.

[0140] Based on this, a perturbation modulation function ΔL is designed. env (ω,t) is used to express the effect of the perturbation on the additional loss of the propagation path, which is expressed by the perturbation spectrum feature tensor F. fused (t) is input to the perturbation sensitivity mapping function Φ(·) to obtain:

[0141] ΔL env (ω,t)=Φ(F fused (t);ω)

[0142] Where Φ(·) is a lightweight residual network designed based on frequency band correlation, which is a nonlinear mapping function representing the sensitivity adjustment of the disturbance to the loss change, that is, Φ(f,ω)=W2·ReLU(W1·F+b1)+b2. The training objective is to minimize the sum of squared residuals between the predicted field strength and the measured field strength, and to maintain its response enhancement mechanism in the high disturbance frequency band.

[0143] Where W1 and W2 are learnable weight matrices, and the mapping incorporates a perturbation frequency ω. d The channel weighting control factor enables the model output to have the ability to respond to differences in propagation frequency bands.

[0144] The path loss estimation function is expressed as:

[0145] The module fully integrates the perturbation spectral structure, propagation medium frequency response, and propagation path scale characteristics during loss modeling, constructing a dynamic, adaptive, and frequency-sensitive path loss expression mechanism that differs from traditional static models. Compared to existing models, this invention no longer models propagation loss with the simplified logic that "propagation loss is only related to terrain, conductivity, and distance." Instead, it introduces multi-scale perturbation influence factors and endows them with differential modulation capabilities across the propagation frequency band, effectively capturing the transient impact of perturbations such as typhoon waves, storms, and sudden drops in air pressure on HF / VHF link performance.

[0146] 5. Establish a residual learning integration compensation module

[0147] The residual learning ensemble compensation module is used to estimate the output of the path loss modeling module. Dynamic error correction is implemented. Considering the nonlinearity, suddenness, and multi-source interference (such as sea fog and ionospheric fluctuations) of disturbances in the actual marine propagation environment, even with thorough modeling of the medium and disturbance spectrum, systematic biases may still exist that cannot be completely absorbed through analytical modeling. Therefore, this module introduces an ensemble learning residual regression strategy based on a sliding time window, constructing a three-model collaborative structure to achieve online learning and adaptive error compensation.

[0148] First, define the loss residual as:

[0149] Where L measured This is the measured loss value;

[0150] Then, using the perturbation feature tensor F fused (t), medium parameters σ(ω), ε r (ω) and predicted path loss Together they constitute the input feature vector:

[0151]

[0152] To characterize the variation patterns across different disturbance periods, this module employs a fixed-length sliding time window (e.g., the last hour) for local modeling. Specifically, for each time step t, input-residual pairs for the window [t-w+1,t] are extracted from the historical data to construct the dataset.

[0153]

[0154] Then, within each time window, the following three machine learning models are used for independent modeling: SVR (Support Vector Regression): used to model the stable trend between perturbation features and residuals; RF (Random Forest): to enhance the nonlinear capture of variable interactions; ANN (Feedforward Neural Network): used to model the complex residual response in a high-dimensional perturbation space.

[0155] Each model is trained independently within the current time window and outputs the prediction error RMSE on the validation set. m , denoted as: RMSE SVR RMSE RF RMSE ANN

[0156] The fusion weights of the predicted values ​​from each model are dynamically adjusted based on the validation error.

[0157]

[0158] The final residual prediction value is:

[0159] The final corrected path loss is:

[0160] The output is the final propagation loss estimate of the system, which has the following characteristics: online learning capability: the sliding window mechanism enables the model to adapt to changes in disturbances; robust fusion mechanism: the integration strategy improves the response capability to local anomalies and short-term non-stationary disturbances; multi-model collaboration enhances generalization: it maintains prediction accuracy in scenarios such as strong sudden changes in wind and waves and drastic fluctuations in conductivity; residual feedback closed-loop characteristic: it can be linked with the acquisition module to trigger sampling frequency encryption or prediction path switching strategies.

[0161] This module is not merely a simple error fitting tool, but a key support point for the system at the "modeling uncertainty response" level. Its design reflects the extension of this invention from a "deterministic propagation loss model" to a "generalized robust modeling structure," and is one of the supporting mechanisms for achieving industrial-grade deployment and coping with extremely complex and disturbed sea conditions.

[0162] Final output It can serve as a direct basis for communication system transmit power planning, beamforming strategies, or channel switching mechanisms, providing traceable, controllable, and interpretable propagation state estimation results for the entire system.

[0163] Figure 2a , 2b Figures 2c, 2d, 2e, and 2f represent simulation results of loss error based on probability distribution and path loss time series and error, respectively, for the method for determining the composite propagation loss of multi-source disturbances in marine ground wave communication according to the embodiment of the present invention, under different link distances. The results show that the method for modeling and determining the composite propagation loss of multi-source disturbances in marine ground wave communication according to the embodiment of the present invention has good disturbance adaptability, frequency difference sensing capability, and error feedback correction capability, and the path loss estimation is closer to the actual propagation conditions.

[0164] The embodiments of the present invention have been described above by way of example, but the present invention is not limited to the embodiments described above. The basic idea of ​​the present invention lies in the above basic scheme. For those skilled in the art, designing various modified models, formulas, and parameters based on the teachings of the present invention does not require creative effort. Changes, modifications, substitutions, and variations made to the embodiments without departing from the principles and spirit of the present invention still fall within the protection scope of the present invention.

Claims

1. A method for modeling the propagation loss of multi-source disturbances in oceans for ground wave communication, characterized in that, include: 1) Establish a disturbance data acquisition module, including the acquisition of disturbance data such as seawater salinity S, soil moisture H, air temperature T, atmospheric pressure P, wind speed W, and wave height A. The acquired data is then preprocessed to obtain the disturbance state vector. , in, Let be the perturbation state vector, and t be the sampling time. Indicates the length of the sliding time window; 2) Establish a medium parameter correction module, including the disturbance state vector obtained in step 1). Real-time correction of key medium parameters in the ground wave propagation path, namely the surface conductivity σ and the relative permittivity. Output the corrected surface conductivity σ(ω,t) and relative permittivity ε r (ω,t); 3) Establish a disturbance spectrum extraction module, including the disturbance state vector from step 1). By utilizing multi-scale convolution, spectral energy sensing, and channel weight fusion, a perturbation spectrum extraction module is established to identify potential multi-timescale fluctuation features in perturbation parameters. This module constructs a perturbation spectrum embedding representation highly correlated with changes in the ground wave propagation path, providing frequency-aware perturbation prior features for subsequent propagation loss modeling. Finally, the perturbation spectrum embedding features are output. ; 4) Establish a path loss modeling module, including frequency ω and propagation distance d as core variables, and integrate the medium dynamic characteristic parameters σ(ω) and ε output from the previous module. r (ω) and perturbation spectrum embedding feature F fused Construct a dynamic estimation function for ground wave propagation path loss. ; 5) Establish a residual learning ensemble compensation module, including introducing an ensemble learning residual regression strategy based on a sliding time window, constructing a collaborative structure of support vector regression, random forest, and feedforward neural network to achieve online learning and adaptive error compensation. This module is used to dynamically correct the errors in the estimated values ​​output by the path loss modeling module, obtaining the corrected path loss. ; Step 2) includes: 2.1) Based on the disturbance state vector obtained in step 1), A multiple linear regression model was constructed by comparing the measured conductivity and dielectric constant data with historical data. Among them, w σ w ε b represents the model weights. σ b ε For the bias terms, σ0(t), ε r,0 (t) represents the static estimate of the basic regression output; 2.2) The perturbation state vector The input radial basis function is used for nonlinear mapping, and then combined with support vector regression for fitting. The output is the correction terms Δσ(t) and Δε for the residuals. r (t), which are defined as follows: in and These are the measured conductivity and relative permittivity, respectively. 2.3) Based on the Cole–Cole model, frequency dependence correction is performed to obtain σ(ω,t) and ε. r (ω,t), expressed as: σ(ω,t)=σ o (t) + Δσ (t) + k σ ⋅ω β e r (ω,t)= ε r,o (t) + De r (t) + Where, k σ β is the frequency domain conductivity correction factor, and ε is... s , τ and α are the static dielectric constant and the limiting dielectric constant, respectively; τ and α are the relaxation time and fractional-order adjustment factor, respectively; and j is the imaginary unit.

2. The method for modeling the composite propagation loss of multi-source disturbances in marine communication according to claim 1, characterized in that, In step 1), the preprocessing includes synchronous calibration, extended Kalman filtering, and window embedding.

3. The method for modeling the composite propagation loss of multi-source disturbances in oceans for ground wave communication according to claim 1, characterized in that, Step 1) also includes a dynamic sampling strategy based on quality indicators. When the system detects a sudden change in the disturbance variable or determines that the current area is at a high risk level, the system will automatically increase the sampling frequency to ensure the frequency of parameter updates in a highly dynamic environment and enhance the system's ability to respond quickly to propagation changes.

4. The method for modeling the composite propagation loss of multi-source disturbances in marine communication according to claim 1, characterized in that, Step 2) also includes obtaining the final fuzzy compensation quantity σ based on the fuzzy logic compensation mechanism under extreme weather conditions. fuzzy (t) and ε r,fuzzy (t), thus for σ(ω,t) and ε r After further modification of (ω,t), the final output expressions are as follows: and .

5. The method for modeling the composite propagation loss of multi-source disturbances in oceans for ground wave communication according to claim 1, characterized in that, In step 3), the convolutional structure includes three sets of one-dimensional convolutional paths, with kernel sizes of [missing information]. It is used to extract disturbance patterns under short-period, high-frequency fluctuations, medium-period disturbances, and low-frequency trends, respectively. The convolution operation is defined as: in, To represent the input vector of the perturbation state sequence at time t+τ, the convolution kernel... For a time-domain filter, its corresponding frequency response is: Each convolutional feature The perturbation state vector In the corresponding frequency response range Local response mapping; Spectrum energy sensing and channel weight fusion include: The power spectral density (PSD) of the time series of perturbed channel i is estimated using the Welch method: in Indicates Fourier transform, For the first Disturbance signal segments within a window; The frequency response interval for each convolutional scale k is defined as follows: The spectral energy of all channels integrated within this interval is: in Normalization factor; The weighted proportion of energy that most likely affects electromagnetic propagation in the current disturbance environment; Finally, the multi-scale convolutional features are fused according to the spectral sensing weights to form the perturbation spectral embedding features: 。 6. The method for modeling the composite propagation loss of multi-source disturbances in oceans for ground wave communication according to claim 5, characterized in that, Step 3) also includes embedding a propagation correlation adjustment layer at the convolutional backend, by calculating... The Pearson correlation coefficient ρ with the rate of change of medium parameters at the current frequency is used to enhance the screening of highly correlated propagation factors by the perturbation spectrum eigenvector, retaining only those with... A highly coupled spectral dimension is used to drive the frequency adjustment term in the subsequent path loss function, resulting in an output perturbation spectral feature tensor. .

7. The method for modeling the composite propagation loss of multi-source disturbances in oceans for ground wave communication according to claim 1, characterized in that, The ground wave communication is selected from NAVDAT broadcast and HF / VHF long-distance link.

8. The method for modeling the composite propagation loss of multi-source disturbances in marine communication according to claim 1, characterized in that, Step 4) includes: 4.1) Establish the preliminary loss estimation expression: Among them, L sp Indicates space wave loss; L gr The ground wave component loss is approximately calculated as follows: Where A(ω) represents the attenuation slope related to the surface conductivity and propagation frequency; B(ω) represents the initial loss related to the initial field strength and electromagnetic reflection characteristics. 4.2) Design the disturbance modulation function This is used to express the effect of perturbation on the additional loss of the propagation path, and it is composed of the perturbation spectrum feature tensor. Input to perturbation sensitivity mapping function get: The disturbance sensitivity mapping function This is a lightweight residual network designed based on frequency band correlation. The function is a nonlinear mapping function representing the sensitivity adjustment to changes in loss caused by perturbations. The training objective is to minimize the sum of squared residuals between the predicted and measured field strengths, while maintaining a response enhancement mechanism in the high-perturbation frequency band. Where W1 and W2 are learnable weight matrices, and the mapping incorporates a perturbation frequency ω. d The channel weighting control factor enables the model output to have the ability to respond to differences in propagation frequency bands; The dynamic estimation function is expressed as: .

9. The method for modeling the composite propagation loss of multi-source disturbances in oceans for ground wave communication according to claim 8, characterized in that, Step 5) includes: 5.1) Define the loss residual as , L measured This is the measured loss value; 5.2) Using the perturbation characteristic tensor F fused (t), medium parameters σ(ω), ε r (ω) and predicted path loss Together they constitute the input feature vector: 5.3) Local modeling is performed using a fixed-length sliding time window. Specifically, for each time step corresponding to sampling time t, the input residual pairs of the window [t-w+1,t] are extracted from the history to construct the dataset. ; 5.4) Within each time window, the following three machine learning models are used independently for modeling: Support Vector Regression (SVR): used to model the stable trend between perturbation features and residuals; Random Forest (RF): enhances the nonlinear capture of variable interactions; Feedforward Neural Network (ANN): used to model the complex residual response in a high-dimensional perturbation space. 5.5) Each model is trained independently within the current time window and outputs the prediction error on the validation set. , denoted as: 5.6) Dynamically adjust the fusion weights of the predicted values ​​of each model based on the validation error: ； The final residual prediction value is: , The final corrected path loss is: .

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