A method and system for verifying a marine acoustic propagation model

Abstract

The application discloses a kind of verification method and system of ocean acoustic propagation model, it is related to data processing technical field, method includes: to multi-source heterogeneous data is filtered, denoised and synchronous calibration preprocessing, obtain preprocessed data;Wherein, multi-source heterogeneous data includes marine environment observation data and underwater acoustic signal data;Quantify the uncertainty distribution of multi-source heterogeneous data using Gaussian process regression method to the missing data in preprocessed data Probabilistic modeling;Based on preprocessed data, the verification of multiple dimensions is carried out to ocean acoustic propagation model, and the verification index of corresponding dimension is generated;The verification index of each dimension is weighted and fused and is synthesized according to uncertainty distribution, and the verification result of each dimension is output.The application can comprehensively and accurately verify ocean acoustic propagation model by the multidimensional consistency test of model physical hypothesis and real physical process of ocean.

Description

Technical Field

[0001] This application relates to the field of data processing technology, and in particular to a verification method and system for an ocean acoustic propagation model. Background Technology

[0002] Whether for underwater early warning and detection, submarine communication, deep-sea resource exploration, underwater oil and gas field development, marine environmental monitoring, or collaborative operations of unmanned underwater vehicles, all rely heavily on a precise understanding of the characteristics of underwater sound fields. Sound waves are currently the only known form of energy capable of transmitting information over long distances underwater; therefore, underwater acoustic technology is considered the "eyes and ears" of underwater perception. Against this backdrop, ocean acoustic propagation models, as mathematical and physical tools describing the laws governing sound wave propagation in the ocean, constitute the theoretical foundation for all underwater acoustic applications.

[0003] With the rapid development of marine observation technologies (such as high-precision CTD profilers, seabed observation networks, and underwater gliders) and underwater acoustic detection technologies (such as large-scale vertical / horizontal arrays and broadband sound sources), modern underwater acoustic engineering has placed unprecedented demands on the accuracy, computational efficiency, and environmental adaptability of sound propagation models. Traditionally, the development of sound propagation models has evolved from ray theory and normal wave theory to parabolic equations and the finite element method, resulting in a wide variety of models, each with its applicable frequency range, distance scale, and environmental conditions. However, any model is a mathematical abstraction and approximation of the complex marine environment, and its predictions inevitably contain errors. Therefore, systematic model validation is not only a necessary step in model development and improvement but also a "qualification certification" process that moves the model from theoretical research to engineering applications. A marine acoustic propagation model lacking sufficient validation cannot guarantee the detection performance, communication reliability, and positioning accuracy of underwater equipment in complex marine environments, potentially leading to significant system misjudgments and operational risks. Summary of the Invention

[0004] In view of this, embodiments of this application provide a method and system for verifying an ocean acoustic propagation model, so as to comprehensively and accurately verify the ocean acoustic propagation model.

[0005] One aspect of this application provides a method for verifying an ocean acoustic propagation model, the method comprising the following steps:

[0006] Multi-source heterogeneous data is preprocessed by filtering, denoising, and synchronous calibration to obtain preprocessed data; wherein, the multi-source heterogeneous data includes marine environmental observation data and underwater acoustic signal data;

[0007] Gaussian process regression is used to probabilistically model the missing data in the preprocessed data, thereby quantifying the uncertainty distribution of the multi-source heterogeneous data.

[0008] Based on the preprocessed data, the ocean acoustic propagation model is validated in multiple dimensions, and validation indicators for the corresponding dimensions are generated.

[0009] The verification metrics of each dimension are weighted and fused, and uncertainty is synthesized according to the uncertainty distribution to output the verification results of each dimension.

[0010] In some embodiments, the process of performing multi-dimensional validation on the ocean acoustic propagation model based on the preprocessed data and generating validation metrics for the corresponding dimensions includes the following steps:

[0011] The environmental parameter vector of the ocean acoustic propagation model and the error hyperparameter used to characterize the structural error scale of the ocean acoustic propagation model are used together as unknown parameters, and corresponding prior distributions are set respectively.

[0012] A likelihood function for a complex sound pressure field is constructed using measured sound pressure data containing amplitude and phase information; wherein the likelihood function includes the residual between the predicted sound pressure and the measured sound pressure of the ocean sound propagation model, and the covariance matrix of the likelihood function includes the error of the ocean sound propagation model and the observation noise.

[0013] The adaptive Metropolis-Hastings algorithm is used to perform Markov chain Monte Carlo sampling to obtain the posterior distribution of the unknown parameters, and the bridge sampling method is used to calculate the evidence value of the ocean acoustic propagation model as a self-consistency quantification index of the ocean acoustic propagation model.

[0014] In some embodiments, the process of performing multi-dimensional validation on the ocean acoustic propagation model based on the preprocessed data and generating validation metrics for the corresponding dimensions includes the following steps:

[0015] The seabed acoustic parameters are modeled as a spatial random field consisting of a mean field, a standard deviation field, and a random perturbation field; wherein the standard deviation field originates from the uncertainty distribution.

[0016] Multiple implementations are extracted from the spatial random field, and a sound propagation model is run for each implementation to calculate the set of sound pressure fields at the receiving location;

[0017] For each distance and depth grid point in the sound pressure field set, the quantiles of the sound pressure amplitude or propagation loss are counted to define the prediction interval of the ocean sound propagation model, and the percentage of points where the measured propagation loss falls within the prediction interval is counted and defined as the prediction interval coverage rate, which serves as a robustness verification indicator.

[0018] In some embodiments, the process of performing multi-dimensional validation on the ocean acoustic propagation model based on the preprocessed data and generating validation metrics for the corresponding dimensions includes the following steps:

[0019] An interactive interface is established between the ocean acoustic propagation model and the sound propagation model, so that the spatiotemporal four-dimensional sound velocity field output by the ocean acoustic propagation model is used as the dynamic input of the sound propagation model;

[0020] The ocean acoustic propagation model is initialized with multiple set members. At each assimilation time, the acoustic propagation model is run to calculate the predicted sound pressure value corresponding to each set member. The state of the ocean acoustic propagation model is updated using measured sound pressure data through the Kalman gain matrix, forming a two-way coupling closed loop between the ocean and acoustics.

[0021] The time accumulation of the normalized root mean square error of the sound pressure prediction value and the ratio of the set dispersion to the observation error during the assimilation process are calculated. The two are combined to generate the prediction capability index of the ocean sound propagation model in a time-varying environment.

[0022] In some embodiments, the process of performing multi-dimensional validation on the ocean acoustic propagation model based on the preprocessed data and generating validation metrics for the corresponding dimensions includes the following steps:

[0023] Broadband sound pressure data received by a vertical hydrophone array is used to solve a sparse optimization problem by compressed sensing mode extraction method. The amplitude of each mode is extracted as a function of frequency, and phase spectrum analysis is performed on the amplitude of the modes to calculate the group delay of each mode as the model mode group delay.

[0024] A mode matching cost matrix is ​​constructed with the absolute difference between the measured mode group delay and the model mode group delay as its elements, and the Hungarian algorithm is used to solve for the optimal matching to determine the correspondence between the measured modes and the model modes.

[0025] The deviation between the inner product of the measured modal function and the model modal function after matching and one is calculated as the modal orthogonality deviation, and the physical accuracy verification index of the ocean acoustic propagation model is generated based on the modal orthogonality deviation.

[0026] In some embodiments, the process of performing multi-dimensional validation on the ocean acoustic propagation model based on the preprocessed data and generating validation metrics for the corresponding dimensions includes the following steps:

[0027] Based on the sound pressure measurements at finite locations obtained from the sparse hydrophone array, an overcomplete dictionary matrix is ​​constructed, and the sparse coefficient vector is recovered by solving the sparse optimization problem, thereby reconstructing the full two-dimensional sound field interference fringes.

[0028] Feature parameters including the slope, fringe width, and interference period of the interference fringes are extracted from the full two-dimensional acoustic field interference fringes and the predicted fringes of the ocean acoustic propagation model, respectively, and the structural similarity index between the full two-dimensional acoustic field interference fringes and the predicted fringes is calculated.

[0029] The structural similarity index is weighted and combined with the feature matching degree calculated from the feature parameters to generate a sparse reconstruction verification index.

[0030] In some embodiments, the method further includes the following steps:

[0031] Based on the residual feature vectors obtained from the verification indicators of each dimension, the sources of error are identified by a preset decision tree classifier.

[0032] The corresponding correction strategy is executed according to the source of the error; wherein, if the source of the error is environmental parameter error, the posterior distribution of the parameters output during the verification process of the corresponding dimension of the verification index is called to update the preprocessed data; if the source of the error is algorithm error, the grid resolution or step size parameter of the ocean acoustic propagation model is adjusted; if the source of the error is missing physical process, the corresponding physical process correction term is added to the ocean acoustic propagation model.

[0033] The output includes a structured verification report containing a comprehensive verification score, verification results for each dimension, sources of error, applicability boundary conditions for the ocean acoustic propagation model, and suggested corrections.

[0034] Another aspect of this application embodiment provides a verification system for an ocean acoustic propagation model, the system comprising:

[0035] The data preprocessing unit is used to perform filtering, denoising, and synchronous calibration preprocessing on multi-source heterogeneous data to obtain preprocessed data; wherein, the multi-source heterogeneous data includes marine environmental observation data and underwater acoustic signal data;

[0036] The uncertainty quantification unit is used to perform probability modeling on the missing data in the preprocessed data using the Gaussian process regression method, and to quantify the uncertainty distribution of the multi-source heterogeneous data.

[0037] The indicator generation unit is used to perform multi-dimensional verification of the ocean acoustic propagation model based on the preprocessed data and generate corresponding verification indicators.

[0038] The model validation unit is used to weight and fuse the validation metrics of each dimension and perform uncertainty synthesis according to the uncertainty distribution, and output the validation results of each dimension.

[0039] Another aspect of this application embodiment provides an electronic device, including a processor and a memory;

[0040] The memory is used to store programs;

[0041] The processor executes the program to implement any of the methods described above.

[0042] Another aspect of this application provides a computer-readable storage medium storing a program that is executed by a processor to implement the method described in any of the above embodiments.

[0043] This application includes at least the following beneficial effects:

[0044] This application performs filtering, denoising, and synchronous calibration preprocessing on multi-source heterogeneous data to obtain preprocessed data. The multi-source heterogeneous data includes marine environmental observation data and underwater acoustic signal data. Gaussian process regression is used to probabilistically model missing data in the preprocessed data, quantifying the uncertainty distribution of the multi-source heterogeneous data. Based on the preprocessed data, a multi-dimensional validation of the marine acoustic propagation model is performed, generating corresponding validation indices. The validation indices of each dimension are weighted and fused, and uncertainty is synthesized according to the uncertainty distribution, outputting the validation results for each dimension. This application, through multi-dimensional consistency checks between the model's physical assumptions and real marine physical processes, can comprehensively and accurately validate the marine acoustic propagation model. The marine acoustic propagation model validated based on this application can ensure the detection performance, communication reliability, and positioning accuracy of underwater equipment in complex marine environments. Attached Figure Description

[0045] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0046] Figure 1 A flowchart illustrating a method for verifying a marine acoustic propagation model provided in an embodiment of this application;

[0047] Figure 2 This is a structural block diagram of a verification system for an ocean acoustic propagation model provided in an embodiment of this application. Detailed Implementation

[0048] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0049] Before providing a detailed description of the embodiments of this application, some related technologies involved in the embodiments of this application will be described first, as follows:

[0050] Although the validation of ocean acoustic propagation models has been underway for decades, a series of deep-rooted technical defects and bottlenecks still exist under current technological conditions, restricting the reliability of validation results, the degree of automation in the validation process, and the universality of validation conclusions. Specifically, existing technologies mainly face the following four problems that urgently need to be solved:

[0051] First, there are challenges of "coupling mismatch" and "non-uniqueness" in the verification of environmental parameters and acoustic models. Traditional verification methods typically employ an open-loop process of "measuring the environment first, running the model, and then comparing the sound field." However, marine environments (especially seabed acoustic parameters) are difficult to obtain on a large scale and with high precision through direct measurement in real-world scenarios. Key parameters such as sound velocity, density, layering structure, and attenuation coefficient of the seabed sediment often exhibit significant uncertainties. When model predictions do not match the measured sound field, existing technologies cannot effectively distinguish whether the error stems from defects in the model algorithm itself or from inaccurate input environmental parameters. This "multiple causes for one effect" non-uniqueness leads to ambiguous verification conclusions, often requiring extensive trial and error based on human experience, resulting in low verification efficiency and highly subjective conclusions.

[0052] Second, existing validation techniques struggle to address the time-varying and non-uniform nature of complex marine dynamic environments. The real ocean is not a static, stratified medium, but rather a complex dynamic process rife with internal waves, fronts, vortices, and turbulence. These processes cause dramatic fluctuations in the sound velocity field across time and space, resulting in non-stationary and nonlinear statistical characteristics of sound propagation. Most existing model validation methods are based on "quasi-static" assumptions, performing deterministic validation only for environmental inputs at a specific time point. They cannot assess the model's predictive ability in dynamic marine environments and lack validation methods for the statistical characteristics of the sound field (such as coherence attenuation and angle-of-arrival fluctuations). When models are applied to areas with active internal waves or complex nearshore hydrological environments, traditional validation methods often yield conclusions that deviate from reality, making it difficult to guarantee the model's engineering application effectiveness in real dynamic scenarios.

[0053] Third, traditional verification methods utilize sound field information in a single dimension, resulting in low information utilization. Currently widely used verification methods primarily rely on comparing propagation loss curves, focusing only on the energy attenuation characteristics of the acoustic signal while ignoring the rich phase information, modal structure information, and fine time delay structure of multipath arrivals contained within the sound field. This verification based on "low-dimensional" energy indicators has extremely weak constraint capability on the internal physical processes of the model (such as seabed reflection phase shift and modal coupling effects), easily leading to false verification results where "energy matches but physical processes are incorrect." Especially in shallow sea waveguide environments, different combinations of model parameters may yield similar propagation loss curves, but the corresponding sound field phase and modal distributions can be drastically different. Relying solely on energy verification will seriously mislead model selection and subsequent applications.

[0054] Fourth, existing verification systems lack intelligent and standardized closed-loop feedback mechanisms. Current verification work largely relies on researchers manually completing environmental data processing, model parameter configuration, simulation calculations, result comparisons, and error analysis. This process is fragmented, highly repetitive, and difficult to reproduce, lacking an integrated verification system platform. More importantly, existing technologies are mostly "one-way verification," meaning the verification conclusions are only used to evaluate the model's performance, failing to use the error information obtained during verification for automatic model correction or optimization of environmental parameters, thus failing to form a "verification-feedback-optimization" closed loop. With the exponential growth of underwater acoustic observation data and the development of artificial intelligence technology, traditional verification models relying on human experience, open-loop processing, and low-dimensionality can no longer meet the demands of modern marine acoustic engineering for high-efficiency, high-precision, and reproducible verification.

[0055] Disadvantages of existing technology:

[0056] Existing ocean acoustic propagation model verification technologies have several inherent defects in practical applications. These defects are mainly manifested in the miscoupling of environmental parameters and acoustic field verification, insufficient adaptability to dynamic ocean processes, single dimension of acoustic field information utilization, and lack of systematic closed-loop verification process.

[0057] First, existing technologies generally employ an open-loop verification model of "environmental parameter input—model simulation—sound field comparison," which heavily relies on the accuracy of pre-acquired marine environmental parameters (especially seabed acoustic parameters). However, in actual marine environments, key parameters such as sound velocity, density, layering structure, and attenuation coefficient of the seabed sediment are difficult to obtain accurately over a large area through direct measurement, leading to significant uncertainties in the environmental input. When the model prediction results deviate from the measured sound field data, existing verification methods cannot effectively distinguish whether the deviation stems from physical approximation errors in the model algorithm itself or from inaccuracies in the input environmental parameters. This non-uniqueness of "one result with multiple causes" makes the verification conclusions ambiguous, and the verification process often requires repeated trial and error based on human experience, making it difficult to form objective and quantitative verification results.

[0058] Second, existing verification techniques lack the ability to effectively handle complex ocean dynamic processes and their time-varying characteristics. Dynamic processes such as internal waves, fronts, vortices, and turbulence are widespread in the actual ocean. These processes cause dramatic fluctuations in the sound velocity profile across the spatial and temporal dimensions, resulting in non-stationary and nonlinear statistical characteristics of sound propagation. However, most existing verification methods are based on a "quasi-static" assumption, performing deterministic verification only for environmental parameters at a specific time point. They cannot assess the predictive ability of sound propagation models in dynamic ocean environments and lack verification methods for the statistical characteristics of the sound field (such as coherence attenuation, angle of arrival fluctuations, and modal energy fluctuations). In complex hydrological environments (such as shallow sea areas with active internal waves and nearshore frontal zones), the conclusions given by traditional static verification methods often deviate from reality, making it difficult to guarantee the reliability of the model in engineering applications in real dynamic scenarios.

[0059] Third, existing verification methods utilize sound field information in a relatively singular dimension, resulting in low information utilization. Current mainstream verification methods primarily rely on comparative analysis of propagation loss curves, focusing only on the energy attenuation characteristics of the acoustic signal while ignoring the rich information contained within the sound field, such as phase information, modal structure information, and fine time delay structures of multipath arrivals. This verification method based on low-dimensional energy indicators has extremely limited ability to constrain the internal physical processes of the model (such as seabed reflection phase shift, modal coupling effects, and waveguide invariants), easily leading to false verification results where "energy matches but the physical processes are incorrect." Especially in shallow sea waveguide environments, different combinations of model parameters or different model algorithms may calculate similar propagation loss curves, but their corresponding sound field phase distribution, modal energy allocation, and channel impulse response structures differ fundamentally. Relying solely on energy indicators for verification will seriously mislead model selection and subsequent applications.

[0060] Fourth, existing verification systems lack intelligent and standardized closed-loop feedback mechanisms. Currently, verification work largely relies on manual methods for environmental data processing, model parameter configuration, simulation calculations, result comparison, and error analysis. These steps are fragmented, involve a lot of repetitive work, and make it difficult to automate and reproducible the verification process. More importantly, existing technologies are mostly "one-way verification," meaning that verification conclusions are only used for qualitative evaluation of the model's merits. They fail to use the error information obtained during verification for automatic model correction, optimization of environmental parameters, or dynamic updates to the model's applicability boundaries, thus failing to form a closed-loop iterative mechanism of "verification-feedback-optimization." With the rapid increase in the volume of underwater acoustic observation data and the ever-increasing demands for model accuracy in application scenarios, this traditional verification model, which relies on manual experience, is open-loop, and inefficient, can no longer meet the demands of modern marine acoustic engineering for high efficiency, accuracy, and reproducibility in verification work.

[0061] Fifth, existing validation techniques lack a unified standard and quantitative indicator system for model validation. Different research institutions and application fields use different validation datasets, validation indicators, and decision criteria, leading to potentially significantly different conclusions for the same model under different validation conditions. This makes it difficult to compare model validation results horizontally and hinders the standardized promotion and engineering application of model technology. This lack of standardization further exacerbates the subjectivity and uncertainty of model validation work.

[0062] This application relates to underwater acoustics and marine engineering technology, aiming to quantitatively evaluate the prediction accuracy, applicable scenarios, and uncertainties of sound propagation models by comparing measured marine sound field data with theoretical model predictions. This application can be applied to underwater acoustic physics, marine environmental monitoring, signal processing, and computational mathematics.

[0063] Reference Figure 1 This application provides a method for verifying an ocean acoustic propagation model, specifically including the following steps S100~S130:

[0064] S100: Perform filtering, denoising, and synchronous calibration preprocessing on the multi-source heterogeneous data to obtain preprocessed data; wherein, the multi-source heterogeneous data includes marine environmental observation data and underwater acoustic signal data;

[0065] S110: Use the Gaussian process regression method to perform probability modeling on the missing data in the preprocessed data, and quantify the uncertainty distribution of the multi-source heterogeneous data;

[0066] S120: Based on the preprocessed data, perform multi-dimensional verification on the ocean acoustic propagation model and generate corresponding verification indicators;

[0067] S130: The verification indicators of each dimension are weighted and fused, and uncertainty is synthesized according to the uncertainty distribution to output the verification results of each dimension.

[0068] Optionally, the step of performing multi-dimensional validation on the ocean acoustic propagation model based on the preprocessed data and generating corresponding validation indicators includes the following steps:

[0069] The environmental parameter vector of the ocean acoustic propagation model and the error hyperparameter used to characterize the structural error scale of the ocean acoustic propagation model are used together as unknown parameters, and corresponding prior distributions are set respectively.

[0070] A likelihood function for a complex sound pressure field is constructed using measured sound pressure data containing amplitude and phase information; wherein the likelihood function includes the residual between the predicted sound pressure and the measured sound pressure of the ocean sound propagation model, and the covariance matrix of the likelihood function includes the error of the ocean sound propagation model and the observation noise.

[0071] The adaptive Metropolis-Hastings algorithm is used to perform Markov chain Monte Carlo sampling to obtain the posterior distribution of the unknown parameters, and the bridge sampling method is used to calculate the evidence value of the ocean acoustic propagation model as a self-consistency quantification index of the ocean acoustic propagation model.

[0072] Optionally, the step of performing multi-dimensional validation on the ocean acoustic propagation model based on the preprocessed data and generating corresponding validation indicators includes the following steps:

[0073] The seabed acoustic parameters are modeled as a spatial random field consisting of a mean field, a standard deviation field, and a random perturbation field; wherein the standard deviation field originates from the uncertainty distribution.

[0074] Multiple implementations are extracted from the spatial random field, and a sound propagation model is run for each implementation to calculate the set of sound pressure fields at the receiving location;

[0075] For each distance and depth grid point in the sound pressure field set, the quantiles of the sound pressure amplitude or propagation loss are counted to define the prediction interval of the ocean sound propagation model, and the percentage of points where the measured propagation loss falls within the prediction interval is counted and defined as the prediction interval coverage rate, which serves as a robustness verification indicator.

[0076] Optionally, the step of performing multi-dimensional validation on the ocean acoustic propagation model based on the preprocessed data and generating corresponding validation indicators includes the following steps:

[0077] An interactive interface is established between the ocean acoustic propagation model and the sound propagation model, so that the spatiotemporal four-dimensional sound velocity field output by the ocean acoustic propagation model is used as the dynamic input of the sound propagation model;

[0078] The ocean acoustic propagation model is initialized with multiple set members. At each assimilation time, the acoustic propagation model is run to calculate the predicted sound pressure value corresponding to each set member. The state of the ocean acoustic propagation model is updated using measured sound pressure data through the Kalman gain matrix, forming a two-way coupling closed loop between the ocean and acoustics.

[0079] The time accumulation of the normalized root mean square error of the sound pressure prediction value and the ratio of the set dispersion to the observation error during the assimilation process are calculated. The two are combined to generate the prediction capability index of the ocean sound propagation model in a time-varying environment.

[0080] Optionally, the step of performing multi-dimensional validation on the ocean acoustic propagation model based on the preprocessed data and generating corresponding validation indicators includes the following steps:

[0081] Broadband sound pressure data received by a vertical hydrophone array is used to solve a sparse optimization problem by compressed sensing mode extraction method. The amplitude of each mode is extracted as a function of frequency, and phase spectrum analysis is performed on the amplitude of the modes to calculate the group delay of each mode as the model mode group delay.

[0082] A mode matching cost matrix is ​​constructed with the absolute difference between the measured mode group delay and the model mode group delay as its elements, and the Hungarian algorithm is used to solve for the optimal matching to determine the correspondence between the measured modes and the model modes.

[0083] The deviation between the inner product of the measured modal function and the model modal function after matching and one is calculated as the modal orthogonality deviation, and the physical accuracy verification index of the ocean acoustic propagation model is generated based on the modal orthogonality deviation.

[0084] Optionally, the step of performing multi-dimensional validation on the ocean acoustic propagation model based on the preprocessed data and generating corresponding validation indicators includes the following steps:

[0085] Based on the sound pressure measurements at finite locations obtained from the sparse hydrophone array, an overcomplete dictionary matrix is ​​constructed, and the sparse coefficient vector is recovered by solving the sparse optimization problem, thereby reconstructing the full two-dimensional sound field interference fringes.

[0086] Feature parameters including the slope, fringe width, and interference period of the interference fringes are extracted from the full two-dimensional acoustic field interference fringes and the predicted fringes of the ocean acoustic propagation model, respectively, and the structural similarity index between the full two-dimensional acoustic field interference fringes and the predicted fringes is calculated.

[0087] The structural similarity index is weighted and combined with the feature matching degree calculated from the feature parameters to generate a sparse reconstruction verification index.

[0088] Optionally, the method further includes the following steps:

[0089] Based on the residual feature vectors obtained from the verification indicators of each dimension, the sources of error are identified by a preset decision tree classifier.

[0090] The corresponding correction strategy is executed according to the source of the error; wherein, if the source of the error is environmental parameter error, the posterior distribution of the parameters output during the verification process of the corresponding dimension of the verification index is called to update the preprocessed data; if the source of the error is algorithm error, the grid resolution or step size parameter of the ocean acoustic propagation model is adjusted; if the source of the error is missing physical process, the corresponding physical process correction term is added to the ocean acoustic propagation model.

[0091] The output includes a structured verification report containing a comprehensive verification score, verification results for each dimension, sources of error, applicability boundary conditions for the ocean acoustic propagation model, and suggested corrections.

[0092] The following section will provide a detailed introduction and explanation of the solutions in the embodiments of this application, using specific application examples.

[0093] The core innovation of this embodiment lies in the construction of a multimodal hierarchical verification framework. This framework introduces for the first time a "verification confidence transmission chain" and a "model error tracing and adaptive correction mechanism", realizing a leap from "single-dimensional comparison" to "multi-dimensional physical consistency verification" and from "static open-loop evaluation" to "dynamic closed-loop optimization".

[0094] I. Overall Technical Solution Framework.

[0095] This embodiment proposes a verification method and system for an ocean acoustic propagation model. The system adopts a four-layer progressive verification architecture, including a data layer, a core verification layer, a fusion decision layer, and a feedback optimization layer.

[0096] The data layer is responsible for the acquisition, preprocessing, and uncertainty quantification of multi-source heterogeneous data, providing standardized input for subsequent verification. The core verification layer consists of eight parallel or serially associated verification modules, which perform three-dimensional verification of the target acoustic propagation model from eight dimensions: environmental parameter self-consistency, statistical robustness, time-varying coupling, applicability to random media, modal structure consistency, sparse field reconstruction accuracy, physical information-driven consistency, and cross-oceanic generalization ability. The fusion decision layer introduces a verification confidence transmission chain mechanism, which performs weighted fusion and uncertainty synthesis of the output results of each module, outputting a multi-dimensional comprehensive verification report. The feedback optimization layer automatically identifies the source of model error and generates model correction suggestions or environmental parameter adjustment strategies based on the error residual characteristics in the verification results, forming a complete verification closed loop.

[0097] The overall innovation of this embodiment lies in upgrading the verification process from a simple comparison between model output and measured data to a multi-dimensional consistency test between the model's physical assumptions and the real physical processes of the ocean. It also builds for the first time an intelligent closed-loop verification system in which verification conclusions are traceable, error sources are locatable, and model parameters are correctable.

[0098] II. Composition and Functions of Each Module

[0099] (a) Data layer.

[0100] The data layer consists of a marine environmental observation submodule, an underwater acoustic signal acquisition submodule, and a data preprocessing and uncertainty quantification submodule. The marine environmental observation submodule integrates a temperature, salinity, and depth profiler, an acoustic Doppler current profiler, a seafloor seismometer, and a shallow seismic profiler to acquire water sound velocity profiles, ocean current fields, seafloor layering structures, and initial values ​​of ground acoustic parameters. The underwater acoustic signal acquisition submodule uses vertical or horizontal hydrophone arrays to receive broadband acoustic source transmission signals and simultaneously records the precise position and attitude of the transceiver system. The data preprocessing and uncertainty quantification submodule filters, denoises, and synchronizes the acquired data, and uses Gaussian process regression to probabilistically model missing environmental parameters, quantifying the uncertainty distribution of each input parameter and outputting it as a probability density function.

[0101] (ii) Core verification layer.

[0102] The core verification layer contains eight verification modules, each of which can run independently or in a pre-defined logical order.

[0103] First, the Bayesian sound field-environment dual-parameter synchronous verification module uses environmental parameters and model error terms together as unknown parameters to construct a Bayesian inversion framework. It obtains the posterior distribution of parameters through Markov chain Monte Carlo sampling and uses model evidence as a quantitative indicator of model self-consistency.

[0104] Second, the ground acoustic parameter uncertainty transfer verification module defines the ground acoustic parameters as a random field and calculates the probability distribution of the sound field output through Monte Carlo simulation, and defines the coverage rate of the model prediction interval as a robustness verification index.

[0105] Third, the ocean-acoustic two-way coupled time-varying verification module establishes an interactive interface between the ocean dynamics model and the sound propagation model. It uses ensemble Kalman filtering to assimilate measured sound pressure data into the coupled model and dynamically evaluates the model's predictive ability under time-varying environments.

[0106] Fourth, the random medium normal mode coherence decomposition verification module decomposes the sound field into coherent and incoherent components. By comparing the attenuation rate of the measured and model-predicted coherence coefficients with distance, the accuracy of the model's physical description of the random fluctuating medium is evaluated.

[0107] Fifth, the modal filtering and modal group delay matching verification module uses vertical array data to extract the amplitude and group delay of each normal mode through modal filtering, and uses the Hungarian algorithm for modal matching. The physical accuracy of the model is verified by modal orthogonality.

[0108] Sixth, the compressed sensing sparse sound field reconstruction verification module uses a sparse hydrophone array combined with compressed sensing theory to reconstruct two-dimensional sound field interference fringes. The model-predicted fringes and the reconstructed fringes are matched with image features, and the structural similarity index is calculated as a verification index.

[0109] Seventh, the physical information neural network hybrid driving verification module constructs a physical information neural network with the Helmholtz equation as the physical constraint, trains the network using measured data, and judges whether the model equation completely explains the experimental data by analyzing the convergence weight ratio of the physical loss term and the data loss term.

[0110] Eighth, the module for verifying the cross-oceanic generalization ability of transfer learning: a sound propagation proxy model is trained in the source sea area, and the model is adapted to the target sea area through transfer learning. The ratio of transfer error to de novo training error is calculated to quantify the physical generalization ability of the model.

[0111] (III) Integration of the judgment layer.

[0112] The fusion decision layer comprises a verification confidence propagation chain submodule, a multi-dimensional verification result fusion submodule, and a verification report generation submodule. The verification confidence propagation chain submodule defines the confidence index output by each verification module and constructs a directed acyclic graph of confidence propagation based on the logical dependencies between modules, realizing the propagation and synthesis of uncertainty in the verification conclusions. The multi-dimensional verification result fusion submodule uses DS evidence theory to fuse the outputs of the eight modules, handles potential conflicts between modules, and outputs a comprehensive verification score. The verification report generation submodule automatically generates a structured verification report containing verification results for each dimension, a comprehensive score, error source analysis, and model applicability boundary conditions.

[0113] (iv) Feedback optimization layer.

[0114] The feedback optimization layer comprises an error tracing submodule and a model adaptive correction submodule. The error tracing submodule, based on the residual feature vectors output by each validation module, identifies the main sources of error using a pre-defined decision tree classifier, categorizing them into three types: algorithm error, environmental parameter error, and missing physical processes. The model adaptive correction submodule automatically adjusts model parameters or suggests introducing correction terms based on the error tracing results, generating model optimization suggestions as output.

[0115] III. Specific implementation process of each module.

[0116] (I) Implementation process of Bayesian sound field-environment dual-parameter synchronous verification module.

[0117] This module first defines the parameter space, using the environmental parameter vector of the acoustic propagation model to be validated and the model error hyperparameters as unknown parameters. The environmental parameter vector includes key geosonic parameters such as seabed sound velocity, density, attenuation coefficient, and seabed layer thickness. The model error hyperparameters characterize the scale of the model's structural errors, including the magnitude of the systematic deviation between model predictions and actual physical processes. The prior distributions for both are set separately: the environmental parameter priors are derived from geological prior information or empirical statistical distributions, while the model error hyperparameters use uninformed priors to reflect a neutral attitude towards model structural errors.

[0118] Subsequently, a likelihood function is constructed using measured sound pressure data (including amplitude and phase information) to generate a likelihood function for the complex sound pressure field. This likelihood function is based on the residual between the model-predicted sound pressure and the measured sound pressure, and the covariance matrix simultaneously includes the joint contribution of model error and observation noise, enabling the likelihood function to comprehensively reflect both sources of uncertainty.

[0119] Next, posterior sampling is performed using the adaptive Metropolis-Hastings algorithm for Markov chain Monte Carlo sampling. This algorithm automatically adjusts the scale of the proposed distribution during sampling, improving sampling efficiency. The number of sampling iterations is set to 100,000, with the first 20% discarded as the burn-off period to ensure that the sampling results converge to a stationary distribution. The posterior distributions of environmental parameters and model error hyperparameters are obtained through sampling.

[0120] Finally, model evidence is calculated using the bridge sampling method. The magnitude of the model evidence value directly reflects the degree of self-consistency between the acoustic propagation model and the current marine environment under given observational data. This module outputs the model evidence value as the first-dimensional validation metric, and simultaneously outputs the posterior distribution of environmental parameters for uncertainty propagation in subsequent modules.

[0121] (II) Implementation process of the verification module for the uncertainty of ground acoustic parameters.

[0122] This module first performs random field modeling of seabed acoustic parameters. The seabed acoustic parameters (taking seabed sound velocity as an example) are modeled as a spatial random field, which consists of three parts: a mean field, a standard deviation field, and a random perturbation field. The mean field is derived from prior geological information, the standard deviation field is derived from the uncertainty distribution of the data layer output, and the random perturbation field uses a Gaussian covariance function, with its correlation length set according to geological statistics to reflect the continuous variation characteristics of the seabed parameters.

[0123] Monte Carlo propagation simulations were then performed. Five hundred instances were randomly selected from the constructed random field, and the sound propagation model was run on each instance to calculate the set of sound pressure fields at the receiving location. This process transfers the uncertainties of environmental parameters to the sound field prediction results through the sound propagation model.

[0124] Next, the prediction interval is calculated. For each distance and depth grid point, the 5th and 95th percentiles of the sound pressure amplitude or propagation loss are statistically analyzed to define the model prediction interval. This interval represents the reasonable range of fluctuation in the model prediction values ​​considering the uncertainties of environmental parameters.

[0125] Then, the coverage metric is calculated. The percentage of points where the measured propagation loss falls within the prediction interval is defined as the prediction interval coverage. The average width of the prediction interval is also calculated as a supplementary metric. The final robustness verification metric is a weighted combination of coverage and interval width, which comprehensively reflects the statistical reliability and accuracy of the model's predictions.

[0126] (III) Implementation process of marine-acoustic bidirectional coupling time-varying verification module.

[0127] This module first constructs a coupled model. An interactive interface is established between the regional ocean dynamics model and the sound propagation model. The ocean dynamics model outputs time series of temperature, salinity, and current fields, which are converted into a spatiotemporal four-dimensional sound velocity field using empirical formulas for sound velocity, serving as the dynamic input to the sound propagation model.

[0128] Ensemble Kalman filtering assimilation is then performed. One hundred ensemble members are set to initialize the ensemble state of the ocean model. At each assimilation time, the acoustic propagation model is run to calculate the predicted sound pressure levels for each ensemble member, and the ocean model state is updated using measured sound pressure data. The update process is implemented using a Kalman gain matrix, which balances the uncertainty of the model predictions with the uncertainty of the observational data. The assimilated ocean state then re-drives the acoustic propagation model, forming a closed loop of ocean-acoustic bidirectional coupling.

[0129] Next, the time-varying predictive capability is evaluated. The time-cumulative normalized root mean square error (RMSE) is defined, reflecting the overall agreement between model predictions and observed data over the entire observation window. Simultaneously, the ratio of ensemble dispersion to observation error during assimilation is calculated; a ratio close to one indicates that the model's quantification of uncertainty is reasonable. Combining these two metrics, a time-varying validation metric is output, used to evaluate the model's predictive capability in dynamic ocean environments.

[0130] (iv) Implementation process of the random medium normal wave coherence decomposition verification module.

[0131] This module first obtains a set of sound field statistics. In environments with random fluctuations (such as internal waves and turbulence), multiple implementations are obtained through repeated transmission and reception experiments or by dividing the time window to construct a set of sound pressure fields.

[0132] Coherence decomposition is then performed. For each receiving position, the coherent component is calculated as the mean field of all realizations, and the incoherent component is calculated as the difference between each realization and the mean field. The coherence coefficient is defined as the ratio of the energy of the coherent component to the total energy, and the decay rate of this coefficient with propagation distance reflects the degree of destruction of the sound field coherence by the random medium.

[0133] Next, the model-predicted coherence coefficient is calculated. Driven by a random medium model (such as an internal wave spectrum model), the acoustic propagation model is run to generate the attenuation curve of the model-predicted coherence coefficient with distance. The model needs to employ algorithms capable of handling random media, such as stochastic parabolic equations or normal mode random perturbation methods.

[0134] Finally, the attenuation rates are compared. The attenuation curves of the measured coherence coefficient with distance are fitted and compared with the model prediction curves to calculate the attenuation rate error. The output random medium suitability index is an exponential decay function of the attenuation rate error. The closer this index is to one, the more accurate the model's description of the statistical characteristics of the sound field in the random medium.

[0135] (V) Implementation process of the modal filtering and modal group delay matching verification module.

[0136] This module first performs modal filtering. Using broadband sound pressure data received by the vertical hydrophone array, a sparse optimization problem is solved by compressed sensing modal extraction method. While maintaining modal sparsity, the amplitude variation of each normal mode is extracted from finite array data.

[0137] The group delay is then extracted. Phase spectrum analysis is performed on the extracted modal amplitudes to calculate the group delay of each mode, which is the derivative of the phase with respect to the angular frequency. The group delay reflects the difference in propagation time of different frequency components in the same mode and is a key parameter characterizing the waveguide dispersion properties.

[0138] Next, the modal predictions of the model are calculated. The acoustic propagation model to be verified is run to calculate the modal amplitudes and group delays of each normal mode within the same frequency range.

[0139] Then, the Hungarian algorithm is used for matching. A modal matching cost matrix is ​​constructed, where each element represents the absolute difference between the measured mode group delay and the model mode group delay. The Hungarian algorithm is then used to find the optimal match. This algorithm can determine the best correspondence between the measured modes and the model modes in polynomial time, thus solving the problem of potentially inconsistent mode numbering.

[0140] Finally, a modal orthogonality test is performed. The orthogonality deviation between the measured modes and the model modes after matching is calculated, which is the deviation of the inner product of their modal functions from one. This deviation reflects the accuracy of the model in characterizing the modal functions (especially the modal shapes at the seabed boundary). The output modal matching verification index is an exponentially decaying function of the orthogonality deviation.

[0141] (vi) Implementation process of the compressed sensing sparse sound field reconstruction verification module.

[0142] This module first acquires sparse observation data. A sparsely deployed hydrophone array is used, with the element spacing much larger than the requirements of traditional Nyquist sampling, to obtain sound pressure measurements at a limited number of locations, while simultaneously recording the position coordinates of each element.

[0143] A complete dictionary was then constructed. The overcomplete dictionary matrix was constructed, with its column vectors representing the atomic representation of the sound field in the angle-range domain. The dictionary design employed waveguide invariant theory, and the dictionary elements were designed as basis functions with different interference fringe slopes, resulting in a sparse representation of the sound field interference fringes in the dictionary domain.

[0144] Next, compressed sensing reconstruction is performed. A sparse optimization problem is solved to find the sparsest coefficient representation while ensuring reconstruction accuracy meets residual constraints. By recovering the sparse coefficient vector, the full two-dimensional acoustic field interference fringes are reconstructed.

[0145] Then, image features are extracted. Three feature parameters—the slope, fringe width, and interference period—are extracted from the reconstructed fringes. The same feature parameters are extracted from the model-predicted sound field.

[0146] Finally, structural similarity is calculated. A structural similarity index is calculated between the reconstructed stripes and the model stripes, which comprehensively considers the brightness, contrast, and structural similarity of the two images. Simultaneously, the relative error of the features is calculated, which is the average of the relative errors of the three feature parameters. The output sparse reconstruction validation metric is a weighted combination of the structural similarity index and the feature matching degree.

[0147] (vii) Implementation process of physical information neural network hybrid driving verification module.

[0148] This module first constructs a physical information neural network. A deep neural network is built to approximate the sound pressure field; the network input is spatial coordinates, and the output is the real and imaginary parts of the complex sound pressure. The loss function consists of two parts: data loss forces the network output to approximate the measured sound pressure value, and physical loss forces the network output to satisfy the Helmholtz equation.

[0149] The network was then trained. An adaptive moment estimation optimizer was used to train the network, and the convergence curves of the data loss term and the physical loss term were recorded during the training process, including their initial values, decay rates, and final convergence values.

[0150] Next, a physical consistency analysis is performed. After training, the final ratio of physical loss to data loss is calculated. If this ratio is close to zero, it indicates that the model equations can explain the experimental data well; if the ratio is significantly greater than one, it indicates that there are physical processes in the experimental data that are not described by the model equations. Simultaneously, the difference in convergence speed between the two during training is analyzed. If the physical loss converges slowly while the data loss converges quickly, it also indicates a mismatch between the physical equations and the data.

[0151] Finally, the missing physical processes are identified. Further analysis of the spatial distribution characteristics of the physical loss residuals is conducted. Through spatial clustering and morphological analysis of residual hotspot areas, the types of missing physical processes are inferred. For example, residual concentration at the coastal bottom interface may indicate that seabed elastic effects have not been considered; a periodic spatial distribution of residuals may indicate the influence of internal waves; and a linear increase in residuals with distance may indicate three-dimensional refraction effects.

[0152] (viii) Implementation process of the transfer learning cross-sea area generalization capability verification module.

[0153] This module first trains a proxy model for the source ocean area. A deep neural network proxy model is trained in the source ocean area where environmental parameters are known and observational data is abundant. The network input consists of environmental parameters and transmit / receive geometric parameters, and the output is the propagation loss. A fully connected network structure is employed, and pre-training is performed using a large amount of simulation data generated from a high-precision acoustic model.

[0154] Transfer learning was then performed. The network weights trained in the source sea area were used as initialization and fine-tuned in the target sea area. The fine-tuning strategy was to freeze the parameters of the first few layers of the network and only fine-tune the last few layers. This preserved the general acoustic features learned from the source sea area while allowing the network to adapt to the specific environmental characteristics of the target sea area. Fine-tuning used a small amount of measured data and corresponding environmental parameters from the target sea area.

[0155] Next, a comparative verification was conducted. The prediction error of the transfer learning model in the target sea area and the prediction error of the de novo training model using only data from the target sea area were calculated. The de novo training model and the transfer learning model used the same network structure, differing only in their initialization methods.

[0156] Finally, the generalization ability is quantified. The generalization ability metric is defined as the ratio of the transfer model error to the error of the de novo training model. If this ratio is less than or equal to one, it indicates that transfer learning effectively improves prediction accuracy, and the model algorithm has good cross-oceanic generalization ability. If the ratio is greater than one, it indicates that knowledge from the source ocean area cannot be effectively transferred to the target ocean area, and the model's physical assumptions may not be applicable to the target ocean area's environmental type. Simultaneously, the transfer gain, i.e., the difference between the de novo training model error and the transfer model error, is calculated to quantify the benefits brought by transfer learning.

[0157] (ix) The collaborative implementation process of integrating the decision layer and the feedback optimization layer.

[0158] The fusion decision layer first constructs a confidence propagation chain. It defines the local confidence of each validation module, calculated based on the module's own data quality, algorithm convergence, and result stability. A directed acyclic graph of dependencies between modules is constructed; for example, the output confidence of the modality matching validation module depends on the convergence of the posterior distribution of the environmental parameters output by the Bayesian two-parameter validation module, as inaccurate environmental parameters can lead to modality calculation bias. Confidence is propagated along these dependencies, with each module's updated confidence equal to its local confidence multiplied by the product of the updated confidences of all its predecessor modules.

[0159] Subsequently, Dempster's evidence theory fusion was performed. The outputs of the eight modules were considered as eight pieces of evidence, and the identification framework was defined with four levels: excellent, good, average, and poor. A basic probability assignment function was constructed for each module to reflect the confidence level of each module for each verification level. All evidence was fused using Dempster's combination rule to obtain a comprehensive basic probability assignment. This fusion rule can effectively handle potentially conflicting information between modules, and when different modules give contradictory conclusions, a reasonable compromise is made through the conflict coefficient.

[0160] Next, the overall score is calculated. Based on the fused probability allocation, the overall verification score is calculated, which is the weighted sum of the probability allocation of each level and the corresponding score.

[0161] Then, error attribution is performed. A decision tree classifier is constructed, with the input feature vector being the output residuals of eight modules, and the output being the classification labels for the error sources, categorized into three types: algorithm error, environmental parameter error, and missing physical process data. The decision tree is trained based on a large amount of simulation experimental data, where the error sources are known. Splitting features and thresholds are selected based on the principle of maximizing information gain to form interpretable classification rules.

[0162] Finally, adaptive model correction is performed. Based on the error source tracing results, corresponding correction strategies are executed. If the error source is environmental parameter error, the posterior distribution of parameters output by the Bayesian module is used to update the model input parameters. If the error source is algorithm error, the model grid resolution and step size parameters are adjusted, or a more suitable model type is suggested based on the error characteristics. If the error source is missing physical processes, correction terms are added to the model, such as elastic seabed boundary conditions, internal wave disturbance terms, and three-dimensional refraction corrections, and specific model improvement suggestions are output.

[0163] The final structured validation report includes a comprehensive score, validation results for each dimension, error source analysis, model applicability boundary conditions, and correction suggestions, and is output in a standardized format for user use.

[0164] In summary, this embodiment includes the following key technical solutions:

[0165] This paper presents a closed-loop verification method for ocean acoustic propagation models based on a four-layer progressive architecture. The method constructs a four-layer progressive verification architecture consisting of a data layer, a core verification layer, a fusion decision layer, and a feedback optimization layer. The data layer is used for the acquisition and uncertainty quantification of multi-source heterogeneous data, outputting environmental parameters with probability distributions. The core verification layer contains multiple parallel verification modules, each independently outputting verification indicators and their local confidence scores. The fusion decision layer constructs a directed acyclic graph of confidence propagation based on the logical dependencies between modules, propagating along the dependencies and synthesizing confidence scores to generate a comprehensive verification score. The feedback optimization layer automatically identifies error sources and generates model correction strategies based on the comprehensive verification score and the residual characteristics of each module, forming a complete verification closed loop from data input to model optimization. This embodiment is the first to construct a verification system as a closed-loop architecture with self-iterative optimization capabilities, overcoming the shortcomings of open-loop and fragmented existing technologies.

[0166] This paper presents a Bayesian validation method based on joint sampling of model error hyperparameters and environmental parameters. This method synchronously incorporates the model error hyperparameters and environmental parameter vectors of the acoustic propagation model to be validated as unknown parameters into a Bayesian inversion framework. A likelihood function containing the model error covariance matrix is ​​constructed, which simultaneously characterizes the joint contribution of model structure error and observation noise. The posterior distributions of both are obtained through Markov chain Monte Carlo sampling. The model evidence value is calculated as a quantitative indicator of model self-consistency. When the model evidence value is lower than a preset threshold, the model structure is determined to be unsuitable for the current environment. This embodiment is the first to simultaneously sample model error hyperparameters and environmental parameters as unknowns, enabling the validation conclusions to clearly distinguish between two error sources: inaccurate environmental parameters and unsuitable model structure.

[0167] This paper presents a robustness verification method for sound propagation models based on predicted interval coverage. The method defines ground acoustic parameters as a spatial random field and models their spatial correlation using a Gaussian covariance function. Multiple instances are extracted from the random field for Monte Carlo propagation simulation to obtain the probability distribution of the sound field prediction results. For each distance-depth grid point, the quantile interval of the sound field amplitude is calculated and defined as the model prediction interval. The proportion of measured data falling within the prediction interval is defined as the predicted interval coverage. A robustness verification index is constructed as a weighted combination of the predicted interval coverage and the interval width, which simultaneously reflects the statistical reliability and accuracy of the model prediction. This embodiment is the first to use the predicted interval coverage as the core verification index, solving the misjudgment problem caused by inaccurate single-point estimation of environmental parameters in traditional verification.

[0168] This paper presents a time-varying model validation method based on ocean-acoustic bidirectional data assimilation. This method establishes a coupling interface between an ocean dynamics model and an acoustic propagation model, and achieves bidirectional data assimilation through an ensemble Kalman filter framework. Multiple ensemble members are set to initialize the ensemble state of the ocean model. At each assimilation time, the acoustic propagation model is run to calculate the predicted sound pressure level for each ensemble member. The ocean model state is updated using measured sound pressure data, and the assimilated ocean state re-drives the acoustic propagation model. The ratio of ensemble dispersion to observation error during the assimilation process is calculated as a time-varying validation index. This ratio is close to the one-time determination of the model's reasonable quantification of uncertainty. This embodiment is the first to achieve reverse correction of the ocean environmental field using acoustic observation data, enabling the validation process to dynamically evaluate the model's predictive ability in real time-varying environments.

[0169] This paper presents a method for verifying the applicability of a stochastic medium model based on coherence coefficient attenuation rate matching. The method obtains a sound pressure field set through multiple transmission and reception experiments in a stochastic environment; decomposes the sound field into coherent and incoherent components, and calculates the attenuation curve of the coherence coefficient with propagation distance; runs the sound propagation model under the drive of the stochastic medium model to generate the model-predicted coherence coefficient attenuation curve; calculates the relative error between the measured attenuation rate and the model-predicted attenuation rate, and constructs a stochastic medium applicability index; when this index is lower than a preset threshold, the model is deemed insufficient in describing the statistical characteristics of the sound field in the stochastic medium. This embodiment is the first to use the coherence coefficient attenuation rate as a verification index to directly test the model's ability to describe the statistical characteristics of the sound field in the stochastic medium.

[0170] This paper presents a modal domain verification method based on Hungarian algorithm modal matching and orthogonality deviation. The method utilizes broadband acoustic pressure data received by a vertical hydrophone array, and obtains the amplitude and group delay of each normal mode through compressed sensing mode extraction. It then runs the model to be verified to obtain the predicted modal amplitude and group delay. A modal matching cost matrix is ​​constructed, with elements representing the absolute difference between the measured modal group delay and the model modal group delay. The optimal match between the measured and model modes is solved using the Hungarian algorithm. The orthogonality deviation between the matched measured and model modes is calculated as a verification index, reflecting the accuracy of the model's characterization of modal functions at the seabed boundary. This embodiment introduces the Hungarian algorithm for the first time to achieve automatic optimal modal matching and uses orthogonality deviation to quantitatively evaluate the model's accuracy in characterizing modal structures.

[0171] This paper presents a verification method based on compressed sensing sparse reconstruction and interference fringe image feature matching. The method uses a sparse hydrophone array with an element spacing greater than half a wavelength to acquire sound pressure measurements at finite locations. An overcomplete dictionary guided by waveguide invariant theory is constructed, with dictionary elements designed as basis functions with different interference fringe slopes. Full-dimensional sound field interference fringes are reconstructed using compressed sensing. Three image feature parameters—fringe slope, fringe width, and interference period—are extracted from the reconstructed fringes and the model-predicted fringes, respectively. A weighted combination of the structural similarity index and the relative error of the features is calculated as the sparse reconstruction verification index. This embodiment is the first to apply compressed sensing theory to model verification, achieving high-dimensional sound field interference structure verification under sparse array conditions, significantly reducing the hardware deployment cost of the verification system.

[0172] This paper presents a model integrity verification method based on the ratio analysis of physical loss and data loss in a physical information neural network. The method constructs a physical information neural network with Helmholtz equations as physical constraints. The network loss function includes data loss and physical loss terms. The network is trained using measured sound pressure data, and the convergence curves of the physical and data loss terms are recorded during training. After training, the final ratio of physical loss to data loss is calculated. When this ratio is significantly greater than a preset threshold, it is determined that there are physical processes in the experimental data that are not described by the model equations. Further analysis of the spatial distribution characteristics of the physical loss residuals is conducted, and the type of missing physical process is automatically inferred through the spatial clustering pattern of residual hotspot regions. This embodiment is the first to quantify the integrity of the model equations using the ratio of physical loss to data loss and to achieve automatic identification of missing physical processes.

[0173] This paper presents a method for verifying the generalization ability of a cross-oceanic model based on the error ratio of transfer learning. The method trains a deep neural network surrogate model in a source ocean area with known environmental parameters and abundant observational data. The network weights trained in the source ocean area are used as initialization, and transfer learning is performed in the target ocean area for fine-tuning. The parameters of the first few layers of the network are frozen, and only the last few layers are fine-tuned. The prediction error of the transfer model in the target ocean area is calculated separately from the prediction error of the model trained from scratch. A generalization ability index is constructed as the ratio of the transfer model error to the recursive training model error. When this ratio is greater than one, the physical assumptions of the model are determined to be inapplicable to the environmental type of the target ocean area. This embodiment proposes for the first time a quantitative index of cross-oceanic generalization ability based on transfer learning, providing a feasible basis for the application of the model in data-scarce ocean areas.

[0174] This paper presents a multi-dimensional verification result fusion and error source tracing method based on a confidence propagation chain. The method defines the local confidence of each verification module and constructs a directed acyclic graph (DAG) for confidence propagation based on the logical dependencies between modules. Confidence is propagated along the dependencies, and the updated confidence of each module is equal to its local confidence multiplied by the product of the updated confidence of all its predecessor modules. The outputs of eight verification modules are fused using Dempster's evidence theory, and conflict information between modules is processed through Dempster's combination rule to output a comprehensive basic probability allocation. A decision tree classifier is constructed, with the input being the residual feature vectors of each module's output and the output being a classification label for the error source, categorized into three types: algorithm error, environmental parameter error, and missing physical process. This embodiment is the first to achieve the quantitative propagation and synthesis of confidence between modules and realize the automatic classification and source tracing of error sources.

[0175] This paper presents a model adaptive correction method based on error source tracing. When the error source tracing result indicates an environmental parameter error, the method updates the model input parameters by calling the posterior distribution of the environmental parameters output by the Bayesian validation module. When the error source tracing result indicates an algorithm error, the method automatically adjusts the model's grid resolution and step size parameters and outputs model type switching suggestions based on error characteristics. When the error source tracing result indicates a missing physical process, the method adds correction terms to the model, including elastic seabed boundary conditions, internal wave disturbance terms, or three-dimensional refraction corrections, and outputs specific model improvement suggestions. This embodiment achieves, for the first time, a closed-loop feedback from validation conclusions to model optimization, enabling the validation system to automatically execute correction strategies based on error type.

[0176] This paper presents a model applicability grading method based on dual threshold judgment of model evidence and comprehensive verification score. The method obtains the model evidence value output by the Bayesian simultaneous verification module and the comprehensive verification score output by the fusion decision layer. A two-dimensional judgment space is constructed with the model evidence value as the x-axis and the comprehensive verification score as the y-axis. A first threshold curve and a second threshold curve are preset in the judgment space, dividing the space into three regions: fully applicable, conditionally applicable, and inapplicable. When the verification result falls into the conditionally applicable region, further model usage constraints and parameter adjustment suggestions are output based on the error source tracing results. This embodiment is the first to construct a model applicability grading judgment mechanism based on dual indicators, providing a clear basis for model selection in engineering applications.

[0177] Reference Figure 2 This application provides a verification system for an ocean acoustic propagation model, comprising:

[0178] The data preprocessing unit is used to perform filtering, denoising, and synchronous calibration preprocessing on multi-source heterogeneous data to obtain preprocessed data; wherein, the multi-source heterogeneous data includes marine environmental observation data and underwater acoustic signal data;

[0179] The uncertainty quantification unit is used to perform probability modeling on the missing data in the preprocessed data using the Gaussian process regression method, and to quantify the uncertainty distribution of the multi-source heterogeneous data.

[0180] The indicator generation unit is used to perform multi-dimensional verification of the ocean acoustic propagation model based on the preprocessed data and generate corresponding verification indicators.

[0181] The model validation unit is used to weight and fuse the validation metrics of each dimension and perform uncertainty synthesis according to the uncertainty distribution, and output the validation results of each dimension.

[0182] It is understood that the content of the above method embodiments is applicable to this system embodiment. The specific functions implemented in this system embodiment are the same as those in the above method embodiments, and the beneficial effects achieved are also the same as those achieved in the above method embodiments.

[0183] In some alternative embodiments, the functions / operations mentioned in the block diagrams may not occur in the order shown in the operation diagrams. For example, depending on the functions / operations involved, two consecutively shown blocks may actually be executed substantially simultaneously, or the blocks may sometimes be executed in reverse order. Furthermore, the embodiments presented and described in the flowcharts of this application are provided by way of example to provide a more comprehensive understanding of the technology. The disclosed methods are not limited to the operations and logic flows presented herein. Alternative embodiments are contemplated in which the order of various operations is changed and sub-operations described as part of a larger operation are executed independently.

[0184] Furthermore, although this application is described in the context of functional modules, it should be understood that, unless otherwise stated, one or more of the functions and / or features may be integrated into a single physical device and / or software module, or one or more functions and / or features may be implemented in a separate physical device or software module. It is also understood that a detailed discussion of the actual implementation of each module is unnecessary for understanding this application. Rather, given the properties, functions, and internal relationships of the various functional modules in the apparatus disclosed herein, the actual implementation of the module will be understood within the scope of conventional technology for an engineer. Therefore, those skilled in the art can implement the application set forth in the claims using ordinary techniques without excessive experimentation. It is also understood that the specific concepts disclosed are merely illustrative and not intended to limit the scope of this application, which is determined by the full scope of the appended claims and their equivalents.

[0185] If a function is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0186] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a processor-including system, or other system that can fetch and execute instructions from, an instruction execution system, apparatus, or device). For the purposes of this specification, "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transmit programs for use by, or in conjunction with, an instruction execution system, apparatus, or device.

[0187] More specific examples (a non-exhaustive list) of computer-readable media include: electrical connections (electronic devices) having one or more wires, portable computer disk drives (magnetic devices), random access memory (RAM), read-only memory (ROM), erasable and editable read-only memory (EPROM or flash memory), fiber optic devices, and portable optical disc read-only memory (CDROM). Furthermore, computer-readable media can even be paper or other suitable media on which programs can be printed, because programs can be obtained electronically, for example, by optically scanning the paper or other media, followed by editing, interpreting, or otherwise processing as necessary, and then stored in computer memory.

[0188] It should be understood that various parts of this application can be implemented using hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented using software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, it can be implemented using any one or a combination of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0189] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this application. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0190] Although embodiments of this application have been shown and described, those skilled in the art will understand that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of this application, the scope of which is defined by the claims and their equivalents.

[0191] The above is a detailed description of the preferred embodiments of this application, but this application is not limited to the embodiments. Those skilled in the art can make various equivalent modifications or substitutions without departing from the spirit of this application, and these equivalent modifications or substitutions are all included within the scope defined by the claims of this application.

Claims

1. A method for verifying an ocean acoustic propagation model, characterized in that, The method includes the following steps: Multi-source heterogeneous data is preprocessed by filtering, denoising, and synchronous calibration to obtain preprocessed data; wherein, the multi-source heterogeneous data includes marine environmental observation data and underwater acoustic signal data; Gaussian process regression is used to probabilistically model the missing data in the preprocessed data, thereby quantifying the uncertainty distribution of the multi-source heterogeneous data. Based on the preprocessed data, the ocean acoustic propagation model is validated in multiple dimensions, and validation indicators for the corresponding dimensions are generated. The verification metrics of each dimension are weighted and fused, and uncertainty is synthesized according to the uncertainty distribution to output the verification results of each dimension.

2. The verification method for a marine acoustic propagation model according to claim 1, characterized in that, The process of performing multi-dimensional validation on the ocean acoustic propagation model based on the preprocessed data and generating corresponding validation metrics includes the following steps: The environmental parameter vector of the ocean acoustic propagation model and the error hyperparameter used to characterize the structural error scale of the ocean acoustic propagation model are used together as unknown parameters, and corresponding prior distributions are set respectively. A likelihood function for a complex sound pressure field is constructed using measured sound pressure data containing amplitude and phase information; wherein the likelihood function includes the residual between the predicted sound pressure and the measured sound pressure of the ocean sound propagation model, and the covariance matrix of the likelihood function includes the error of the ocean sound propagation model and the observation noise. The adaptive Metropolis-Hastings algorithm is used to perform Markov chain Monte Carlo sampling to obtain the posterior distribution of the unknown parameters, and the bridge sampling method is used to calculate the evidence value of the ocean acoustic propagation model as a self-consistency quantification index of the ocean acoustic propagation model.

3. The verification method for a marine acoustic propagation model according to claim 1, characterized in that, The process of performing multi-dimensional validation on the ocean acoustic propagation model based on the preprocessed data and generating corresponding validation metrics includes the following steps: The seabed acoustic parameters are modeled as a spatial random field consisting of a mean field, a standard deviation field, and a random perturbation field; wherein the standard deviation field originates from the uncertainty distribution. Multiple implementations are extracted from the spatial random field, and a sound propagation model is run for each implementation to calculate the set of sound pressure fields at the receiving location; For each distance and depth grid point in the sound pressure field set, the quantiles of the sound pressure amplitude or propagation loss are counted to define the prediction interval of the ocean sound propagation model, and the percentage of points where the measured propagation loss falls within the prediction interval is counted and defined as the prediction interval coverage rate, which serves as a robustness verification indicator.

4. The verification method for a marine acoustic propagation model according to claim 1, characterized in that, The process of performing multi-dimensional validation on the ocean acoustic propagation model based on the preprocessed data and generating corresponding validation metrics includes the following steps: An interactive interface is established between the ocean acoustic propagation model and the sound propagation model, so that the spatiotemporal four-dimensional sound velocity field output by the ocean acoustic propagation model is used as the dynamic input of the sound propagation model; The ocean acoustic propagation model is initialized with multiple set members. At each assimilation time, the acoustic propagation model is run to calculate the predicted sound pressure value corresponding to each set member. The state of the ocean acoustic propagation model is updated using measured sound pressure data through the Kalman gain matrix, forming a two-way coupling closed loop between the ocean and acoustics. The time accumulation of the normalized root mean square error of the sound pressure prediction value and the ratio of the set dispersion to the observation error during the assimilation process are calculated. The two are combined to generate the prediction capability index of the ocean sound propagation model in a time-varying environment.

5. The verification method for a marine acoustic propagation model according to claim 1, characterized in that, The process of performing multi-dimensional validation on the ocean acoustic propagation model based on the preprocessed data and generating corresponding validation metrics includes the following steps: Broadband sound pressure data received by a vertical hydrophone array is used to solve a sparse optimization problem by compressed sensing mode extraction method. The amplitude of each mode is extracted as a function of frequency, and phase spectrum analysis is performed on the amplitude of the modes to calculate the group delay of each mode as the model mode group delay. A mode matching cost matrix is ​​constructed with the absolute difference between the measured mode group delay and the model mode group delay as its elements, and the Hungarian algorithm is used to solve for the optimal matching to determine the correspondence between the measured modes and the model modes. The deviation between the inner product of the measured modal function and the model modal function after matching and one is calculated as the modal orthogonality deviation, and the physical accuracy verification index of the ocean acoustic propagation model is generated based on the modal orthogonality deviation.

6. The verification method for a marine acoustic propagation model according to claim 1, characterized in that, The process of performing multi-dimensional validation on the ocean acoustic propagation model based on the preprocessed data and generating corresponding validation metrics includes the following steps: Based on the sound pressure measurements at finite locations obtained from the sparse hydrophone array, an overcomplete dictionary matrix is ​​constructed, and the sparse coefficient vector is recovered by solving the sparse optimization problem, thereby reconstructing the full two-dimensional sound field interference fringes. Feature parameters including the slope, fringe width, and interference period of the interference fringes are extracted from the full two-dimensional acoustic field interference fringes and the predicted fringes of the ocean acoustic propagation model, respectively, and the structural similarity index between the full two-dimensional acoustic field interference fringes and the predicted fringes is calculated. The structural similarity index is weighted and combined with the feature matching degree calculated from the feature parameters to generate a sparse reconstruction verification index.

7. A verification method for a marine acoustic propagation model according to any one of claims 1 to 6, characterized in that, The method further includes the following steps: Based on the residual feature vectors obtained from the verification indicators of each dimension, the sources of error are identified by a preset decision tree classifier. The corresponding correction strategy is executed according to the source of the error; wherein, if the source of the error is environmental parameter error, the posterior distribution of the parameters output during the verification process of the corresponding dimension of the verification index is called to update the preprocessed data; if the source of the error is algorithm error, the grid resolution or step size parameter of the ocean acoustic propagation model is adjusted; if the source of the error is missing physical process, the corresponding physical process correction term is added to the ocean acoustic propagation model. The output includes a structured verification report containing a comprehensive verification score, verification results for each dimension, sources of error, applicability boundary conditions for the ocean acoustic propagation model, and suggested corrections.

8. A verification system for an ocean acoustic propagation model, characterized in that, The system includes: The data preprocessing unit is used to perform filtering, denoising, and synchronous calibration preprocessing on multi-source heterogeneous data to obtain preprocessed data; wherein, the multi-source heterogeneous data includes marine environmental observation data and underwater acoustic signal data; The uncertainty quantification unit is used to perform probability modeling on the missing data in the preprocessed data using the Gaussian process regression method, and to quantify the uncertainty distribution of the multi-source heterogeneous data. The indicator generation unit is used to perform multi-dimensional verification of the ocean acoustic propagation model based on the preprocessed data and generate corresponding verification indicators. The model validation unit is used to weight and fuse the validation metrics of each dimension and perform uncertainty synthesis according to the uncertainty distribution, and output the validation results of each dimension.

9. An electronic device, characterized in that, The electronic device includes a processor and a memory; The memory is used to store programs; The processor executes the program to implement the method as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, The storage medium stores a program that is executed by a processor to implement the method as described in any one of claims 1 to 7.

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