A method and system for extending a marine sound speed profile

Abstract

The application discloses a method and system for extending a marine sound velocity profile, and relates to the technical field of data processing. The method comprises the following steps: performing space-time matching and normalization processing on real-time shallow sound velocity measurement data, sea surface remote sensing data and historical profile data of a target sea area, and then extracting a shallow sound velocity gradient and a thermocline characteristic parameter; generating a structured input vector according to the shallow sound velocity gradient and the thermocline characteristic parameter; inputting the structured input vector into a pre-constructed physical information neural network model, and outputting a preliminary sound velocity profile in a full sea depth range through the physical information neural network model; performing physical consistency constraint correction on the preliminary sound velocity profile, and obtaining a posterior distribution of a sound velocity prediction value of each depth point through uncertainty quantization processing; and generating a full sea depth sound velocity profile with a confidence interval identifier according to the posterior distribution. The application can efficiently and accurately obtain a full sea depth sound velocity profile with a confidence interval identifier.

Description

Technical Field

[0001] This application relates to the field of data processing technology, and in particular to a method and system for extending ocean sound velocity profiles. Background Technology

[0002] The sound velocity profile of seawater refers to the vertical distribution structure of sound velocity in the sea. It is a core parameter describing the sound propagation characteristics of seawater and directly reflects the vertical distribution characteristics of hydrological elements such as temperature and salinity in a local sea area. Accurate acquisition of the sound velocity profile has a fundamental and decisive impact on many marine technology fields, including underwater sound field modeling, sonar equipment performance evaluation, multibeam echo sounder system calibration, underwater communication and navigation, and marine environmental monitoring. Specifically, in multibeam measurement applications, due to the different propagation speeds of sound at different depths, refraction effects occur, and accurate sound velocity profile information is a prerequisite for sound velocity correction and obtaining accurate beam point coordinates. In the field of sound field prediction, understanding the spatiotemporal variation characteristics of sound velocity across the entire ocean depth is directly related to the accuracy of sound propagation loss calculation and sonar range estimation. Summary of the Invention

[0003] In view of this, embodiments of this application provide a method and system for extending ocean sound velocity profiles to efficiently and accurately obtain full-ocean-depth sound velocity profile information.

[0004] One aspect of this application provides a method for extending ocean sound velocity profiles, the method comprising the following steps:

[0005] The shallow sound velocity real-time measurement data, sea surface remote sensing data and historical profile data of the target sea area are spatiotemporally matched and normalized to extract the shallow sound velocity gradient and thermocline characteristic parameters.

[0006] A structured input vector is generated based on the shallow sound velocity gradient and the characteristic parameters of the thermocline.

[0007] The structured input vector is input into a pre-built physical information neural network model, and the physical information neural network model outputs a preliminary sound velocity profile covering the entire ocean depth range.

[0008] Physical consistency constraint corrections are applied to the preliminary sound velocity profile, and the posterior distribution of the sound velocity prediction values ​​at each depth point is obtained through uncertainty quantization.

[0009] A full-ocean-depth sound velocity profile with confidence interval identifiers is generated based on the posterior distribution.

[0010] In some embodiments, before inputting the structured input vector into a pre-built physical information neural network model, the method further includes the following steps:

[0011] In the offline phase, the historical profile dataset is adaptively decomposed using the variational mode decomposition algorithm to obtain a set of modal basis functions that characterize the time-varying features of the sound velocity profile in the target sea area. Then, cluster analysis is performed on the set of modal basis functions to identify multiple first profile mode types.

[0012] During the online extension phase, the vertical gradient distribution and depth features of the first derivative extreme points of shallow sound velocity are extracted from the structured input vector to form a modal feature vector, and the modal feature vector is input into a classifier to identify the second profile mode type to which the current profile belongs.

[0013] Based on the first profile mode type and the second profile mode type, a pre-trained nonlinear reconstruction network corresponding to the profile mode type is dynamically selected or weighted and fused through a gating mechanism. The deep sound velocity features are obtained by using the real-time shallow sound velocity measurement data as input, and the deep sound velocity features are fused with the structured input vector and used as input to the physical information neural network model.

[0014] In some embodiments, the physical information neural network model is trained through the following steps:

[0015] In the offline phase, based on historical sea surface height anomaly data, a clustering algorithm is used to divide the target sea area into multiple sub-regions with uniform dynamic characteristics. In each sub-region, a sound speed profile data matrix is ​​independently constructed and singular value decomposition is performed to retain the first few orders of singular vectors as the low-rank basis of the corresponding sub-region.

[0016] For sub-regions with scarce historical data, a meta-learner is used to transfer prior knowledge from similar sea areas to the target. The pre-trained meta-learner is then adaptively fine-tuned in the target sea area using measured profiles to obtain a small-sample extended model suitable for the sub-region.

[0017] During the online extension phase, the reconstruction results based on the local low-rank subspace and the reconstruction results based on few-shot transfer learning are calculated simultaneously. The weights of the two are dynamically adjusted and fused through an attention mechanism. The fused result is used as prior information to assist the physical information neural network model in collaborative reconstruction.

[0018] The physical information neural network model uses the seawater state equation and the sound propagation and refraction laws as physical constraints during training. The loss function consists of three parts: data fitting loss, physical constraint loss, and multi-physics field collaborative loss.

[0019] In some embodiments, performing physical consistency constraint correction on the preliminary sound velocity profile includes the following steps:

[0020] A hard constraint layer is constructed, and the preliminary sound velocity profile is checked layer by layer through projection operation. Numerical points that do not meet the layering stability conditions or the physical allowable range of the sound velocity gradient are corrected to the most recent valid values.

[0021] A soft constraint layer is constructed, the vertical gradient curve of the sound velocity profile is calculated and the continuity is constrained in the form of a penalty function, and the seasonal rationality of the thermocline location is evaluated and corrected.

[0022] A consistency verification layer is constructed, and a physical diagnostic model independent of the training data is used to perform post-hoc verification of the elongation results after being corrected by hard constraint layer and soft constraint layer, and to check the dynamic consistency with synchronous sea surface height anomaly data.

[0023] In some embodiments, obtaining the posterior distribution of the predicted sound velocity at each depth point through uncertainty quantization includes the following steps:

[0024] In the inference stage of the physical information neural network model, the Monte Carlo dropout method is used to apply random dropout to the key layers of the physical information neural network model and perform multiple forward propagations to obtain the predicted sound speed value at each depth point.

[0025] Based on the parameter uncertainties of the physical information neural network model obtained by the variational inference method, the total uncertainty of the predicted sound speed at each depth point is calculated.

[0026] The mean of the predicted sound speed values ​​is used as the final output sound speed value. The total uncertainty is converted into a confidence interval corresponding to the confidence level, and the confidence level is automatically labeled according to the interval width to obtain the posterior distribution.

[0027] In some embodiments, the method further includes the following steps:

[0028] The full-ocean-depth sound velocity profile with confidence interval markers is loaded by the edge computing processing unit and displayed in real time through the human-computer interaction unit.

[0029] The extension results generated locally by the edge computing processing unit are uploaded to the cloud platform through the communication and collaboration unit.

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

[0031] The structured input vector is input into a pre-built physical information neural network model, which outputs temperature and salinity profiles across the entire ocean depth range.

[0032] Another aspect of this application embodiment provides a system for extending ocean sound velocity profiles, the system comprising:

[0033] The data preprocessing module is used to perform spatiotemporal matching and normalization on real-time shallow sound velocity measurement data, sea surface remote sensing data and historical profile data of the target sea area, and then extract the shallow sound velocity gradient and thermocline characteristic parameters.

[0034] A vector generation module is used to generate a structured input vector based on the shallow sound velocity gradient and the characteristic parameters of the thermocline layer.

[0035] The sound velocity profile generation module is used to input the structured input vector into a pre-built physical information neural network model, and output a preliminary sound velocity profile covering the entire ocean depth range through the physical information neural network model.

[0036] The correction and posterior module is used to perform physical consistency constraint correction on the preliminary sound velocity profile and obtain the posterior distribution of the sound velocity prediction value at each depth point through uncertainty quantization processing.

[0037] A confidence identification module is used to generate a full-ocean-depth sound velocity profile with confidence interval identification based on the posterior distribution.

[0038] Another aspect of this application embodiment provides an electronic device, including a processor and a memory;

[0039] The memory is used to store programs;

[0040] The processor executes the program to implement any of the methods described above.

[0041] 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.

[0042] This application includes at least the following beneficial effects:

[0043] This application performs spatiotemporal matching and normalization on real-time shallow sound velocity measurement data, sea surface remote sensing data, and historical profile data of the target sea area to extract shallow sound velocity gradient and thermocline feature parameters. A structured input vector is generated based on the shallow sound velocity gradient and thermocline feature parameters. This structured input vector is then fed into a pre-constructed physical information neural network model, which outputs a preliminary sound velocity profile covering the entire ocean depth. Physical consistency constraints are applied to the preliminary sound velocity profile, and the posterior distribution of the predicted sound velocity values ​​at each depth point is obtained through uncertainty quantization. Finally, a full-ocean-depth sound velocity profile with confidence interval markers is generated based on the posterior distribution. This application, by outputting a preliminary sound velocity profile covering the entire ocean depth through a physical information neural network model and performing corrections and posterior measurements, can efficiently and accurately obtain a full-ocean-depth sound velocity profile with confidence interval markers. Attached Figure Description

[0044] 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.

[0045] Figure 1 A schematic flowchart illustrating a method for extending ocean sound velocity profiles according to an embodiment of this application;

[0046] Figure 2 This is a structural block diagram of an ocean sound velocity profile extension system provided in an embodiment of this application. Detailed Implementation

[0047] 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.

[0048] 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:

[0049] (1) Limitations of traditional methods for obtaining sound velocity profiles.

[0050] Currently, the most direct method for obtaining seawater sound velocity profiles is to conduct on-site point-by-point measurements using equipment such as sound velocity profilers or CTDs (Conductivity, Temperature, Depth) meters. While these methods can obtain high-precision sound velocity profile data, they have significant limitations: firstly, the measurement operations are time-consuming, labor-intensive, and costly, and can only obtain profile data that is discretely distributed in time and space, making it difficult to meet the needs of large-scale, continuous marine environmental monitoring; secondly, these devices can usually only measure data within a limited depth range, while practical applications often require sound velocity distribution information across the entire ocean depth.

[0051] (2) The problem of incomplete data caused by observation methods.

[0052] With the rapid development of marine observation technology, observation platforms such as marine remote sensing, underwater gliders, and unmanned underwater vehicles are now able to acquire marine environmental parameters over a wide range, providing new possibilities for overcoming the spatiotemporal limitations of traditional measurement methods. However, the data collected by these observation methods is often incomplete—it often only provides measurements at certain specific depth points or depth ranges, lacking continuous profile information across the entire ocean depth. This data incompleteness brings practical difficulties to subsequent acoustic field prediction and sonar applications, urgently requiring the development of technical methods that can "extend" shallow measured data to deeper layers and "complete" sparse measurements into a complete profile.

[0053] The core technical essence of the sound velocity profile extension problem is to extrapolate the sound velocity distribution characteristics of deeper seawater based on the vertical distribution information of shallow seawater measured in actual measurements, using various technical means. This technical problem is essentially a problem of inverting and estimating marine environmental parameters based on partial observational information. The difficulty lies in the complex spatiotemporal variation characteristics of the ocean sound velocity profile, which is influenced by multiple factors such as temperature, salinity, structure, and ocean dynamic processes. The key to achieving sound velocity profile extension is how to accurately reconstruct the sound velocity distribution across the entire ocean depth from limited observations, supported by historical data.

[0054] Extensive research has been conducted on the problem of sound velocity profile extension (or completion, reconstruction), resulting in a variety of technical approaches.

[0055] (1) The method based on empirical orthogonal function decomposition.

[0056] Empirical Orthogonal Function (EOF) decomposition is one of the most widely used techniques in sound velocity profile reconstruction. The basic principle is to perform EOF decomposition on historical sound velocity profile samples to obtain eigenvectors (EOF basis functions) representing the main modes of sound velocity variation. Then, any sound velocity profile can be represented as a superposition of the background profile (such as the historical average profile) and EOF basis functions of various orders multiplied by projection coefficients. By inverting the projection coefficients from shallow-sea measured data, the full-depth sound velocity profile can be reconstructed. This method can describe the main variation characteristics of the sound velocity profile with fewer degrees of freedom and has high compression efficiency for sound velocity profile data; studies have shown that compression rates exceeding 90% can be achieved. Its advantages lie in its clear physical meaning and high computational efficiency. However, the reconstruction accuracy is limited by the ability of historical data to characterize the sound velocity variation characteristics of the target sea area. For non-stationary or strongly nonlinear sound velocity profiles, a single linear EOF decomposition is difficult to accurately represent.

[0057] (2) The method of combining historical average data with measured data.

[0058] In the absence of sufficient historical measured profiles, a common technical approach is to reconstruct the sound velocity profile using publicly available marine climatological databases (such as WOA2018) as the background field, combined with in-situ measured data. This method typically begins by acquiring historical average data for the target sea area (such as the temperature, salinity, and climatological mean field from WOA2018), and then calculates the steady-state background profile using empirical sound velocity formulas (such as the Del Grosso formula). Finally, the background profile is corrected using measured data to obtain a sound velocity profile reflecting the in-situ characteristics. While this method is simple to operate, in complex marine environments, relying solely on climatological averages is insufficient to accurately reflect the characteristics of small- to medium-scale sound velocity disturbances.

[0059] (3) Machine learning-based methods.

[0060] In recent years, machine learning methods have been introduced into the field of sound velocity profile completion, providing new insights to address the limitations of traditional methods. For example, some studies have proposed using the EOF projection coefficients of historical profile data and measured data from Argo buoys as training samples. Unsupervised learning algorithms are used to train neurons representing different reference classification information (such as self-organizing map networks) to establish a nonlinear mapping relationship between measured shallow data and the complete profile. In field applications, the best-matching reference neuron is selected based on the correlation between the measured data and the neuron, and the full-depth sound velocity profile is reconstructed by combining it with historical average data. This type of method can better characterize the nonlinear perturbation features of the sound velocity profile and avoid unrealistic reconstruction results, but it requires sufficient historical data to support model training, and the model's generalization ability and interpretability still need improvement.

[0061] (4) The method based on low-rank matrix completion.

[0062] For application scenarios with relatively limited historical data, a sound velocity profile extension method based on low-rank matrix completion has been proposed. This method constructs a matrix to be completed by combining multiple historical complete profiles with shallow profile data to be extended. Utilizing the low-rank characteristic of sound velocity profile data in the spatiotemporal domain, the missing deep sound velocity data is solved using low-rank matrix completion algorithms (such as singular value thresholding and alternating direction multiplier methods). This method can achieve high-precision profile extension even with a limited number of historical samples. Its theoretical basis lies in the high correlation of ocean sound velocity profile data in the spatiotemporal dimensions, which can be approximated by a low-dimensional subspace. Experimental verification shows that this method can achieve relatively ideal extension results.

[0063] (5) Sound velocity correction method applied to multibeam measurement.

[0064] In the specific application scenario of multibeam bathymetry, the processing of sound velocity profile data has special technical requirements. Related research has proposed a sound velocity correction method based on layered refraction calculation: The sampling time is calculated based on the number of samples and the sampling frequency of the beam points. After obtaining the layered information of the sound velocity profile, the refraction angle is calculated layer by layer according to Snell's law, thus obtaining the propagation time and horizontal offset of each layer. Through iterative iteration to the seabed, the beam point coordinates are obtained, ultimately generating a seabed topographic point cloud. This type of method focuses on the engineering application of sound velocity profiles, emphasizing the real-time performance and accuracy of the calculations, and placing higher demands on the completeness and accuracy of the sound velocity profile data.

[0065] Based on the above technical background analysis, existing methods for extending sound velocity profiles still have the following main technical shortcomings:

[0066] First, it relies heavily on historical data. Both EOF decomposition and machine learning methods require relatively complete historical profile data as support. In sea areas where historical data is scarce or insufficiently representative, the effectiveness of these methods is significantly limited.

[0067] Second, traditional linear methods have limited ability to characterize complex disturbances. EOF-based linear decomposition methods struggle to accurately represent the nonlinear variations in sound velocity profiles and the structures of small- to medium-scale disturbances.

[0068] Third, the field measurement data is not fully utilized. Existing methods often only use shallow sound velocity information for projection coefficient inversion when processing field measurement data, failing to fully utilize the multi-dimensional marine environmental information contained in the measurement data.

[0069] Fourth, there is insufficient integration of physical mechanisms and data-driven approaches. Existing methods either focus on purely data-driven statistical fitting or on simplified physical models, lacking a technical framework that deeply integrates ocean dynamics mechanisms with data-driven methods.

[0070] In the existing ocean sound velocity profile extension technology system, although various methods based on empirical orthogonal function decomposition, machine learning, and low-rank matrix completion have been developed, these technical solutions still reveal many fundamental defects in practical applications, mainly in the following aspects:

[0071] First, existing methods are heavily reliant on historical data samples, severely limiting their effectiveness in data-scarce marine areas. Whether it's empirical orthogonal function decomposition, self-organizing map networks (SOMAs), or low-rank matrix completion methods, their core premise is the need to acquire a sufficient quantity of complete historical profile data representing the sound velocity variation characteristics of the target marine area as training samples or prior information. However, in real-world marine environments, large-scale, long-term, and high-precision historical sound velocity profile data are often extremely scarce, especially in the mid-deep sea, polar regions, and open ocean areas, where the spatiotemporal coverage of measured profiles is very low. When the number of historical samples is insufficient or fails to cover the typical sound velocity variation modes of the target marine area, the reconstructed model trained based on these samples will exhibit significant overfitting or underfitting, causing the extension results to deviate from the true profile structure. Even in areas with relatively abundant historical data, existing methods lack an effective mechanism for evaluating the spatiotemporal representativeness of historical data, making it difficult to determine whether historical samples are suitable for the current extension task. This "black box" dependence on historical data quality further exacerbates the uncertainty of the extension results.

[0072] Second, existing methods for utilizing shallow subsurface measurement information remain at the level of statistical fitting, failing to fully explore the multi-dimensional physical information contained in the measured data. Current mainstream techniques generally use shallow subsurface measured sound velocity profile data as "constraints," retrieving modal coefficients or model parameters by minimizing the error between measured and reconstructed values. This approach is essentially a mathematical fitting strategy, utilizing only the numerical magnitude of shallow subsurface sound velocity values, while failing to effectively explore and utilize the richer information contained in the measured data—such as the vertical gradient variation characteristics of sound velocity, the depth and intensity information of the thermocline, and the intrinsic relationship between shallow hydrological structures and deep ocean dynamic processes. The formation of ocean sound velocity profiles is controlled by various physical processes such as seawater temperature and salinity structure, water mass distribution, and internal wave activity. The vertical variation characteristics of shallow subsurface sound velocity often have a deterministic physical coupling relationship with deep structures. Existing methods lack effective means to incorporate this physical constraint into the reconstruction framework, leading to the possibility that the extended results physically violate fundamental oceanographic laws.

[0073] Third, linear methods based on empirical orthogonal function decomposition (EOF) struggle to accurately characterize the nonlinear and non-stationary changes in sound velocity profiles. EFOF, the most widely used method in sound velocity profile reconstruction, essentially represents the sound velocity profile as a linear superposition of several fixed modes. This linear decomposition framework assumes that the variation patterns of the sound velocity profile are stationary in both the time and spatial domains, and that the modes are mutually orthogonal. However, in actual oceans, sound velocity profiles are influenced by nonlinear processes such as thermo-salinity fine structure, frontal processes, and mesoscale eddies, often exhibiting significant non-stationarity and nonlinear characteristics. When modal transitions occur in the sound velocity profile (such as the formation and disappearance of seasonal thermoclines) or complex multi-scale perturbations exist, traditional linear EOF decomposition struggles to accurately reconstruct the fine structure of the profile using a finite number of modes, especially in depth ranges with drastic sound velocity gradient changes, such as near thermoclines. Linear reconstruction often produces smoothing biases, losing the inflection point characteristics of the true profile.

[0074] Fourth, low-rank matrix completion methods suffer from a mismatch between constraints and actual conditions when dealing with complex marine environments. The core assumption of low-rank matrix completion methods is that sound velocity profile data possesses a low-rank structure in the spatiotemporal domain, meaning multiple profiles can be approximated by low-dimensional subspaces. This assumption holds true in stable sea areas with limited spatial extent and short time scales. However, in regions with complex ocean dynamic processes—such as the Kuroshio Current extension, active internal waves in the South China Sea, and seasonal polar ice melt zones—the spatiotemporal variations of sound velocity profiles exhibit high-dimensional characteristics, and the actual rank of the data is far higher than the low-rank constraints pre-set by the method. In this case, forcibly imposing low-rank constraints will cause the extended results to lose important physical change modes. Furthermore, existing matrix completion algorithms typically rely on the selection of regularization parameters during the solution process. The determination of these parameters lacks objective physical basis and often relies on manual experience for adjustment in practical applications. This subjectivity further affects the stability and repeatability of the extended results.

[0075] Fifth, existing methods lack effective constraints and quality evaluation mechanisms for the physical rationality of the extended results. Currently, all sonic velocity profile extension methods use numerical fitting accuracy (such as root mean square error, correlation coefficient, etc.) as the main evaluation index, pursuing the minimum numerical deviation between the reconstructed profile and the true profile. However, a numerically well-fitted extension result may not be physically reasonable—problems such as non-physical reversal of sound velocity with depth, negative gradient absolute values ​​exceeding the stable stratification range, and thermocline locations inconsistent with oceanographic seasonal characteristics may occur. Existing methods generally lack mechanisms to embed oceanographic physical laws (such as water mass temperature and salinity characteristics, stratification stability, and seasonal evolution of sonic velocity profile morphology) as hard constraints into the reconstruction process, and have not established a technical process for verifying the physical consistency of the extended results. This "numerical-only" evaluation system may introduce unpredictable errors into subsequent engineering applications such as acoustic field prediction and multibeam measurement.

[0076] Sixth, existing technical solutions lack an adaptive weight allocation mechanism when fusing measured data with the background field. Some existing methods utilize marine climatological databases as the background field, correcting it with measured data. However, the background field reflects a long-term statistical average state, which may differ significantly from the real-time state in the field, and this difference exhibits different characteristics at different depths, seasons, and sea areas. Existing methods typically use fixed weight coefficients or simple linear interpolation to fuse measured data with the background field, failing to dynamically adjust the fusion weights based on the quality, depth, and consistency of the measured data with the background field. This leads to over-reliance on the background field even when the confidence level of the measured data is high, or excessive weighting when the measured data is sparse, thus affecting the reliability of the extension results.

[0077] Seventh, existing technologies are insufficient in addressing the balance between real-time performance and accuracy in sound velocity profile enhancement during engineering applications such as multibeam bathymetry. In applications with high real-time requirements, such as multibeam bathymetry, it is necessary to rapidly enhance the sound velocity profile and correct beam point coordinates within limited computational resources. Existing methods either prioritize accuracy at the expense of computational efficiency (e.g., matrix completion methods based on iterative optimization) or excessively simplify the computational process while neglecting enhancement accuracy (e.g., directly using empirical formulas to estimate deep sound velocities). The lack of a technical solution that can dynamically balance enhancement accuracy and computational efficiency based on actual measurement task requirements makes it difficult to meet the practical needs of high-precision, large-scale, real-time multibeam measurement operations.

[0078] In summary, existing ocean sound velocity profile extension technologies have significant technical shortcomings in terms of historical data dependence, physical mechanism integration, nonlinear feature characterization capability, adaptability to complex environments, result rationality constraints, and engineering application relevance. These shortcomings make it difficult to fully meet the urgent needs of current ocean observation and underwater acoustic applications for high-precision, high-reliability, and highly adaptable full-ocean-depth sound velocity profiles.

[0079] Reference Figure 1 This application provides a method for extending the ocean sound speed profile, specifically including the following steps S100~S140:

[0080] S100: Spatiotemporal matching and normalization are performed on real-time shallow sound velocity measurement data, sea surface remote sensing data and historical profile data of the target sea area to extract shallow sound velocity gradient and thermocline characteristic parameters.

[0081] S110: Generate a structured input vector based on the shallow sound velocity gradient and the characteristic parameters of the thermocline layer;

[0082] S120: Input the structured input vector into the pre-built physical information neural network model, and output a preliminary sound velocity profile for the entire ocean depth range through the physical information neural network model;

[0083] S130: Perform physical consistency constraint correction on the preliminary sound velocity profile, and obtain the posterior distribution of the sound velocity prediction value at each depth point through uncertainty quantization.

[0084] S140: Generate a full-ocean-depth sound velocity profile with confidence interval identifiers based on the posterior distribution.

[0085] Optionally, before inputting the structured input vector into a pre-built physical information neural network model, the method further includes the following steps:

[0086] In the offline phase, the historical profile dataset is adaptively decomposed using the variational mode decomposition algorithm to obtain a set of modal basis functions that characterize the time-varying features of the sound velocity profile in the target sea area. Then, cluster analysis is performed on the set of modal basis functions to identify multiple first profile mode types.

[0087] During the online extension phase, the vertical gradient distribution and depth features of the first derivative extreme points of shallow sound velocity are extracted from the structured input vector to form a modal feature vector, and the modal feature vector is input into a classifier to identify the second profile mode type to which the current profile belongs.

[0088] Based on the first profile mode type and the second profile mode type, a pre-trained nonlinear reconstruction network corresponding to the profile mode type is dynamically selected or weighted and fused through a gating mechanism. The deep sound velocity features are obtained by using the real-time shallow sound velocity measurement data as input, and the deep sound velocity features are fused with the structured input vector and used as input to the physical information neural network model.

[0089] Optionally, the physical information neural network model is trained through the following steps:

[0090] In the offline phase, based on historical sea surface height anomaly data, a clustering algorithm is used to divide the target sea area into multiple sub-regions with uniform dynamic characteristics. In each sub-region, a sound speed profile data matrix is ​​independently constructed and singular value decomposition is performed to retain the first few orders of singular vectors as the low-rank basis of the corresponding sub-region.

[0091] For sub-regions with scarce historical data, a meta-learner is used to transfer prior knowledge from similar sea areas to the target. The pre-trained meta-learner is then adaptively fine-tuned in the target sea area using measured profiles to obtain a small-sample extended model suitable for the sub-region.

[0092] During the online extension phase, the reconstruction results based on the local low-rank subspace and the reconstruction results based on few-shot transfer learning are calculated simultaneously. The weights of the two are dynamically adjusted and fused through an attention mechanism. The fused result is used as prior information to assist the physical information neural network model in collaborative reconstruction.

[0093] The physical information neural network model uses the seawater state equation and the sound propagation and refraction laws as physical constraints during training. The loss function consists of three parts: data fitting loss, physical constraint loss, and multi-physics field collaborative loss.

[0094] Optionally, performing physical consistency constraint correction on the preliminary sound velocity profile includes the following steps:

[0095] A hard constraint layer is constructed, and the preliminary sound velocity profile is checked layer by layer through projection operation. Numerical points that do not meet the layering stability conditions or the physical allowable range of the sound velocity gradient are corrected to the most recent valid values.

[0096] A soft constraint layer is constructed, the vertical gradient curve of the sound velocity profile is calculated and the continuity is constrained in the form of a penalty function, and the seasonal rationality of the thermocline location is evaluated and corrected.

[0097] A consistency verification layer is constructed, and a physical diagnostic model independent of the training data is used to perform post-hoc verification of the elongation results after being corrected by hard constraint layer and soft constraint layer, and to check the dynamic consistency with synchronous sea surface height anomaly data.

[0098] Optionally, obtaining the posterior distribution of the predicted sound velocity at each depth point through uncertainty quantization includes the following steps:

[0099] In the inference stage of the physical information neural network model, the Monte Carlo dropout method is used to apply random dropout to the key layers of the physical information neural network model and perform multiple forward propagations to obtain the predicted sound speed value at each depth point.

[0100] Based on the parameter uncertainties of the physical information neural network model obtained by the variational inference method, the total uncertainty of the predicted sound speed at each depth point is calculated.

[0101] The mean of the predicted sound speed values ​​is used as the final output sound speed value. The total uncertainty is converted into a confidence interval corresponding to the confidence level, and the confidence level is automatically labeled according to the interval width to obtain the posterior distribution.

[0102] Optionally, the method further includes the following steps:

[0103] The full-ocean-depth sound velocity profile with confidence interval markers is loaded by the edge computing processing unit and displayed in real time through the human-computer interaction unit.

[0104] The extension results generated locally by the edge computing processing unit are uploaded to the cloud platform through the communication and collaboration unit.

[0105] Optionally, the method further includes the following steps:

[0106] The structured input vector is input into a pre-built physical information neural network model, which outputs temperature and salinity profiles across the entire ocean depth range.

[0107] The following section will provide a detailed introduction and explanation of the solutions in the embodiments of this application, using specific application examples.

[0108] I. Overall Technical Solution Framework

[0109] This embodiment proposes a method and system for extending ocean acoustic profiles based on physical information deep learning. Its overall technical framework is organically integrated from seven core modules, forming a closed-loop system covering the entire chain from data acquisition, multi-source fusion, core processing, uncertainty quantification to engineering applications. This framework, with "physical mechanism embedding—multi-source data collaboration—adaptive mode decomposition—hierarchical low-rank reconstruction—physical consistency constraints—task-driven computation—hardware and software integration" as its main thread, constructs a novel technical path that differs from existing technologies.

[0110] The overall framework includes: a multi-source data collaborative acquisition and preprocessing module, a physical information deep extension core module, an adaptive time-varying mode decomposition and reconstruction module, a hierarchical low-rank and few-shot learning fusion module, a physical consistency constraint and uncertainty quantification integrated module, a task-driven adaptive real-time extension module, and an integrated sound velocity profile extension device. Among these, the physical information deep extension core module, as the central hub of the entire technical solution, receives input from the multi-source data collaborative acquisition module, calls the adaptive mode decomposition module and the hierarchical low-rank fusion module for collaborative computation, outputs the full-ocean-depth sound velocity profile and its uncertainty quantification results under the supervision of the physical consistency constraint module, and achieves dynamic adaptation with downstream engineering applications through the task-driven adaptive module. Finally, the integrated device completes real-time on-site processing and cloud-based collaborative iteration.

[0111] II. Composition and Functions of Each Module

[0112] (a) Multi-source data collaborative acquisition and preprocessing module.

[0113] This module consists of a real-time shallow sound velocity measurement unit, a sea surface remote sensing data receiving unit, a historical profile database unit, and a data fusion preprocessing unit. The real-time shallow sound velocity measurement unit acquires continuous vertical distribution data of sound velocity in the shallow layer (typically within the 0-200 meter depth range) of the target sea area. The sea surface remote sensing data receiving unit acquires synchronous remote sensing products such as sea surface temperature, sea surface height anomalies, and sea surface salinity via satellite communication links. The historical profile database unit stores long-term accumulated complete sound velocity and temperature-salinity profile data of the target sea area and its adjacent regions, and labels them according to water mass characteristics. The data fusion preprocessing unit performs spatiotemporal matching, quality control, and normalization on multi-source data, and extracts derived features such as shallow sound velocity gradients and thermocline characteristic parameters, providing standardized input data for subsequent core processing modules. The core innovation of this module lies in establishing a physical correlation feature extraction mechanism between shallow measured data and sea surface remote sensing parameters, enabling the subsequent extension process to fully utilize the inherent coupling relationship between multi-source information.

[0114] (ii) Core module for deep extension of physical information.

[0115] This module is the core innovation of this embodiment, consisting of a physically constrained neural network construction unit, a partial differential equation embedding unit, and a multi-physics collaborative inversion unit. The physically constrained neural network construction unit designs a novel network architecture that departs from the traditional pure data-driven approach. Instead, it embeds the seawater state equation, empirical formula for sound velocity, and physical laws governing the vertical distribution of temperature and salinity into the deep learning model as loss function terms and network structure constraints. Specifically, the network output layer simultaneously predicts three physical quantities: sound velocity profile, temperature profile, and salinity profile, and forces them to satisfy the state equation constraints through a physical consistency loss function. The partial differential equation embedding unit introduces the refraction law from the sound propagation equation as a soft constraint into the network training process, ensuring that the derived deep sound velocity distribution maintains physical consistency with shallow measured data in terms of sound ray bending characteristics. The multi-physics collaborative inversion unit utilizes the physical coupling relationship between sea surface remote sensing data and shallow measured data to simultaneously invert key oceanographic parameters such as thermocline depth, thermocline strength, and deep water mass type through a multi-task learning framework. These parameters are then used as auxiliary outputs to provide physical prior information for subsequent modules. The core innovation of this module lies in achieving deep coupling between physical laws and deep learning models, rather than simple superposition or post-processing correction, which makes the extended results interpretable in terms of physical mechanisms.

[0116] (III) Adaptive Time-Varying Mode Decomposition and Reconstruction Module.

[0117] This module consists of a data-adaptive mode decomposition unit, a mode feature recognition and classification unit, and a nonlinear reconstruction unit. The data-adaptive mode decomposition unit employs an improved variational mode decomposition algorithm to adaptively decompose historical profile datasets, obtaining a set of modal basis functions that characterize the time-varying features of the target sea area's sound velocity profile. This decomposition process does not require a pre-set number of modes; instead, it dynamically determines the optimal number of modes based on the spectral characteristics of the data itself. The mode feature recognition and classification unit utilizes gradient and curvature features extracted from shallow measured data to identify the mode type of the current profile (e.g., uniform, positive gradient, strong hopping, weak hopping, multi-hopping, etc.) using a lightweight classifier. The nonlinear reconstruction unit trains corresponding nonlinear mapping networks for different types. This network takes shallow sound velocity data as input and directly outputs the deep sound velocity profile. Its core innovation lies in introducing a gating mechanism, dynamically selecting or weighting and fusing the outputs of multiple sub-networks based on the mode recognition results to achieve accurate reconstruction of different mode profiles. This module solves the fundamental problem that traditional EOF linear decomposition cannot characterize nonlinear and nonstationary features.

[0118] (iv) The module that integrates hierarchical low-rank and few-sample learning.

[0119] This module consists of a dynamic partitioning and local low-rank modeling unit, a few-shot transfer learning unit, and a collaborative reconstruction unit. The dynamic partitioning and local low-rank modeling unit first divides the target sea area into several sub-regions with relatively uniform dynamic characteristics using a clustering algorithm based on historical sea surface height anomaly data and sea surface temperature gradient distribution. A low-rank subspace model is independently constructed within each sub-region, avoiding the failure of the global low-rank assumption in complex dynamic environments. The few-shot transfer learning unit targets sub-regions with scarce historical samples, employing meta-learning techniques to transfer prior knowledge from data-rich similar sea areas. Specifically, a meta-learner is pre-trained on a large amount of source domain data, enabling it to "quickly learn the profile features of a new sea area from a small number of samples," and then rapidly adaptively fine-tuned using a small number of measured profiles in the target sea area. The collaborative reconstruction unit fuses the local low-rank subspace reconstruction results with the few-shot transfer learning results, using an attention mechanism to dynamically adjust the weights of both in the final output. The weight coefficients are adaptively determined based on the historical data abundance of the current region and the degree of matching between the measured data and the low-rank subspace. The innovation of this module lies in combining the hierarchical processing of global low-rank structures with transfer learning, which can still achieve high-precision extension under the condition of sparse historical data.

[0120] (v) Integrated module for physical consistency constraints and uncertainty quantification.

[0121] This module consists of a multi-level physical constraint unit, a Bayesian uncertainty quantization unit, and an output confidence calibration unit. The multi-level physical constraint unit constructs a three-layer constraint system: the first layer is a hard constraint layer, which ensures that the output sound velocity profile strictly satisfies stratification stability conditions, temperature-salinity boundary constraints, and water mass characteristic range constraints through projection operations; the second layer is a soft constraint layer, which constrains the continuity of the vertical sound velocity gradient and the seasonal rationality of the thermocline location through a penalty function; the third layer is a consistency verification layer, which uses a physical diagnostic model independent of the training data to perform post-hoc verification of the extension results, such as checking the dynamic consistency between the sound velocity profile and synchronous sea surface height anomaly data. The Bayesian uncertainty quantization unit uses Monte Carlo dropout combined with variational inference techniques during deep network training to approximate the distribution of network parameters, thereby obtaining the posterior distribution of the sound velocity prediction value at each depth point during the inference phase. The output confidence calibration unit transforms the posterior distribution into an engineering-usable confidence interval and automatically adjusts the accuracy label of the output result according to the confidence level for downstream application decision-making. The innovation of this module lies in embedding physical laws into an uncertainty quantification framework in the form of multi-level constraints, thereby enabling the credibility of the extended results to be quantifiable and traceable.

[0122] (vi) Task-driven adaptive real-time extension system.

[0123] The system consists of a task parameter parsing unit, a dynamic computing resource scheduling unit, and a multi-mode extension engine. The task parameter parsing unit receives task instructions from downstream applications (such as multibeam echo sounding systems), extracts key parameters including the water depth range of the survey area, accuracy requirements, real-time constraints, and computing resource limitations, and transforms these parameters into the objective function for the extension strategy. The dynamic computing resource scheduling unit automatically decides whether the extension computation should be executed on the field device, at the edge node, or in the cloud, based on currently available computing resources (such as CPU / GPU load of field devices, cloud computing power availability, and communication bandwidth) and task constraints, and dynamically allocates computing resources. The multi-mode extension engine incorporates three computing modes: a fast mode uses a lightweight proxy model (such as a shallow network after knowledge distillation) to achieve millisecond-level response, suitable for scenarios with extremely high real-time requirements; a standard mode calls the aforementioned core modules for complete computation, suitable for routine operation scenarios; and a high-precision mode adds iterative optimization and physical consistency verification loops to the standard mode, suitable for scenarios with the highest accuracy requirements. Switching between the three modes is decided collaboratively by the task parameter parsing unit and the resource scheduling unit, achieving a dynamic balance between accuracy and efficiency. The innovation of this system lies in its deep integration of extended computing with engineering application tasks, enabling adaptive optimization of computing strategies.

[0124] (vii) Integrated sound velocity profile extension equipment.

[0125] This device, the physical embodiment of this example, is integrated and packaged from a real-time sound velocity profile acquisition unit, an edge computing processing unit, a communication and collaboration unit, and a human-machine interaction unit. The real-time sound velocity profile acquisition unit employs a combination design of a high-frequency sound velocity probe and a temperature, salinity, and depth sensor, enabling continuous acquisition of sound velocity, temperature, and salinity data, with an adaptively adjustable acquisition frequency. The edge computing processing unit adopts a heterogeneous computing architecture, integrating embedded CPU, GPU, or neural network processing units, and pre-configured lightweight deployment versions of the aforementioned core modules. It can perform real-time elevation calculations on-site, outputting a full-ocean-depth sound velocity profile and its confidence interval. The communication and collaboration unit supports multiple communication methods, including BeiDou short message service, 4G / 5G, and satellite communication. It is responsible for uploading the on-site elevation results to the cloud platform and simultaneously receiving updated model parameters and algorithm versions from the cloud, achieving "edge-cloud collaboration and continuous evolution." The human-machine interaction unit is equipped with a high-brightness touchscreen display, which displays key information such as the measurement trajectory, elevation profile curve, and confidence interval in real time, and provides one-click start, mode switching, and data export functions. The innovation of this device lies in its deep integration of complex extension algorithms with field measurement equipment, forming an integrated solution from data acquisition to product output, which solves the problem of poor timeliness caused by the separation of data acquisition and post-processing in the traditional operation mode.

[0126] III. Specific implementation process of each module.

[0127] (I) Implementation process of multi-source data collaborative acquisition and preprocessing module.

[0128] Before the operation begins, the system first loads the historical profile database of the target sea area, performs cluster analysis by season and region, and establishes a background knowledge base. After the operation begins, the real-time sound velocity profile acquisition unit collects shallow sound velocity data at a preset frequency (typically 2Hz). The data acquisition depth range is dynamically set by the task parameter analysis unit according to the water depth of the survey area, usually one-third of the water depth or a fixed upper limit of 200 meters. Simultaneously, the sea surface remote sensing data receiving unit requests sea surface temperature and sea surface height anomaly data for the current day and the previous seven days through a satellite communication link, and performs spatiotemporal interpolation matching to the measurement point location. The data fusion preprocessing unit performs the following steps: First, outlier removal and moving average filtering are applied to the raw sound velocity data; second, the vertical gradient sequence of shallow sound velocity is calculated to identify the upper boundary depth of the thermocline and the thermocline intensity; then, the influence depth range of mesoscale eddies is estimated using sea surface height anomaly data through geostrophic relationships; finally, all data are standardized into a unified temporal and spatial reference system and packaged into a structured input vector containing shallow sound velocity sequences, sound velocity gradient features, thermocline parameters, sea surface remote sensing features, geographical location, and measurement time, for use by subsequent modules.

[0129] (II) Implementation process of the core module for deep extension of physical information.

[0130] The core of this module is a physical information neural network model. The model input is a structured input vector output by the preprocessing module, and the output is a sound velocity profile, temperature profile, and salinity profile across the entire ocean depth (0 to a preset maximum depth, typically 2000 meters or the seabed depth). The network structure adopts a multi-branch encoder-decoder architecture: the encoder part uses a multilayer perceptron to extract a deep representation of the input features; the decoder part uses a depth-separable convolutional structure, taking depth as a continuous coordinate input, to generate a vertically continuous profile output. The loss function for model training consists of three parts: the first part is the data fitting loss, which calculates the mean square error between the output profile and the measured shallow data; the second part is the physical constraint loss, which includes three sub-terms: (1) the state equation constraint term, which forces the output temperature and salinity to be consistent with the sound speed calculated by the state equation and the sound speed directly output; (2) the ray refraction constraint term, which uses the sound speed gradient of the shallow output to calculate the ray bending angle through Snell's law to be consistent with the ray bending angle calculated based on the complete profile; (3) the gradient smoothing constraint term, which ensures that the continuity of the vertical gradient of the sound speed conforms to the characteristics of ocean stratification; the third part is the multi-physics field collaborative loss, which uses the dynamic correlation between sea surface height anomaly and deep temperature and salinity structure to construct a constraint term based on the conservation of potential vorticity. The model training adopts a two-stage strategy: the first stage uses historical complete profile data for pre-training, and the second stage uses a small amount of measured data collected on-site for fine-tuning. After training, the model can complete a single extension calculation in milliseconds.

[0131] (III) Implementation process of the adaptive time-varying mode decomposition and reconstruction module.

[0132] This module first performs offline modal basis construction. All complete sound velocity profiles for the target sea area are extracted from the historical profile database. Variational mode decomposition is performed on each profile to obtain a set of intrinsic mode functions. Cluster analysis is then performed on the decomposition results of all profiles to identify 4 to 8 typical modal morphologies, each corresponding to a set of modal basis functions and typical shallow feature patterns. During the online extension phase, the module executes the following process: First, it obtains the shallow sound velocity sequence from the preprocessing module and extracts features such as its vertical gradient distribution, the depth of the first derivative extremum points, and the zero-crossing points of the second derivative to form a modal feature vector. Second, it inputs the feature vector into a trained lightweight classifier (such as a support vector machine or a small neural network) to obtain the probability distribution of the modal type to which the current profile belongs. Third, based on the classification results, it calls the corresponding nonlinear reconstruction network—each modal type corresponds to an independent deep residual network, which takes the shallow sound velocity sequence as input and directly regresses the deep sound velocity profile. If the classification probabilities are not concentrated (i.e., the probabilities of multiple modal types are similar), a gated weighted fusion strategy is used to sum the outputs of multiple sub-networks according to their probabilities to obtain the final reconstruction result. The advantage of this module is that it can adaptively select the most suitable reconstruction model based on the morphological characteristics of the actual sound velocity profile, avoiding the problem of insufficient generalization ability of a single model across different types of profiles.

[0133] (iv) Implementation process of the fusion module of hierarchical low-rank and few-shot learning.

[0134] This module first performs offline dynamic zoning modeling. Historical sea surface height anomaly data of the target sea area and its surrounding regions are collected. A density-based spatial clustering algorithm is used to divide the area into dynamic zones. Within each zone, an independent sound velocity profile data matrix is ​​constructed, and singular value decomposition is performed. The first 3 to 5 singular vectors are retained as the low-rank basis for that zone. Meta-information such as water depth range and seasonal variation characteristics of each zone are also recorded. For zones with abundant historical data, low-rank subspaces are directly constructed using local data; for zones with scarce historical data, a few-shot transfer learning process is initiated. The few-shot transfer learning unit first loads a pre-trained meta-learning model from similar sea areas with abundant data (determined through water mass feature matching). This model is trained based on a model-independent meta-learning framework, enabling it to quickly adapt to new tasks. After collecting a small number (e.g., 3 to 5) complete or near-complete profiles in the field, these samples are used to perform several gradient updates on the meta-learning model to obtain an extended model suitable for the current sea area. During online inference, the collaborative reconstruction unit simultaneously calculates the reconstruction results based on the local low-rank subspace and the reconstruction results based on few-shot transfer learning, and calculates the fusion weight of the two through the attention module. The input of the attention module includes the fitting residual between the current measured shallow data and the low-rank subspace, the confidence estimate of the transfer learning model, and the historical data abundance index of the partition. The output is the weighted coefficient of the two reconstruction results, and finally outputs the fused sound velocity profile.

[0135] (v) Implementation process of the integrated module of physical consistency constraint and uncertainty quantification.

[0136] This module works collaboratively during the model inference and training phases. During inference, after the physical information depth extension core module outputs a preliminary sound velocity profile, this module first performs hard constraint correction: it checks the output sound velocity profile layer by layer; if density inversion or sound velocity gradients exceed physically permissible limits (e.g., absolute gradient value greater than 1.5 s⁻¹), it corrects them to the nearest valid value using a projection operator. Subsequently, it performs soft constraint checks, calculating the vertical gradient curve of the sound velocity profile and evaluating the seasonal plausibility of the thermocline location—for example, if it is currently summer and the thermocline depth exceeds 200 meters, a penalty correction is applied. The soft constraint correction employs an optimization method to minimize the degree of violation of physical laws while maintaining a good fit with shallow measured data. The uncertainty quantification unit uses the Monte Carlo dropout method: during inference, random dropouts are applied to key layers of the network, and multiple forward propagations are performed (typically 30 to 50 times) to obtain the sound velocity prediction distribution at each depth point; combined with the parameter uncertainties obtained from variational inference, the total uncertainty is calculated. The output confidence calibration unit uses the mean of the predicted values ​​as the final output, converts the standard deviation into a 95% confidence interval, and automatically labels the confidence level (high confidence, medium confidence, low confidence) based on the interval width. Information from low confidence regions is fed back to the task-driven module, prompting for additional measured sampling in that depth interval.

[0137] (vi) Implementation process of task-driven adaptive real-time extension system.

[0138] After system startup, the system first establishes communication with downstream applications through the task parameter parsing unit to obtain the task description file for this operation. The task description file contains the following key fields: latitude and longitude range of the survey area, expected maximum water depth, accuracy requirements (such as the maximum allowable sound velocity error), real-time requirements (such as the maximum allowable rise time), and computing resource budget (such as the number of available CPU cores, memory limit, etc.). The system transforms these constraints into an optimization problem: the cost function is defined as the weighted sum of rise time and computation time, with the weighting coefficients determined by the priority of accuracy and real-time requirements. The computing resource dynamic scheduling unit evaluates the current environment—if on-site equipment resources are sufficient and network conditions are good, cloud computing mode is prioritized to obtain higher accuracy; if the network is interrupted or real-time requirements are extremely high, edge computing mode is switched; if the on-site equipment is a low-power embedded platform, fast mode is forced to be used. The multi-mode extension engine activates corresponding modes based on scheduling decisions: The fast mode calls a lightweight network after knowledge distillation, compressing the model parameters to less than 10% of the original model and controlling inference time to within 10 milliseconds; the standard mode calls the complete physical information deep extension core module, with inference time approximately 100 to 500 milliseconds; the high-precision mode, based on the standard mode, adds an iterative optimization step—the extension result is input into the physical consistency constraint module for verification. If the constraint is violated, the input features are adjusted and recalculated, with a maximum of 3 iterations. Simultaneously, a hierarchical low-rank and few-shot learning fusion module is called for cross-validation. The entire system's decision-making process forms a closed loop, recording the actual error and time consumption after each extension calculation for dynamic adjustment of subsequent decision thresholds.

[0139] (vii) Implementation process of integrated sound velocity profile extension equipment.

[0140] The equipment features an integrated waterproof and sealed shell, with a portable size (length x width x height not exceeding 40cm x 30cm x 20cm) and a weight of less than 10kg. It supports both shipborne fixed installation and portable deployment. The operating procedure is as follows: The operator starts the equipment via the human-machine interface, and the equipment automatically performs self-checks and sensor calibration. After deployment or installation, the equipment automatically begins collecting shallow sound velocity data, with the collection depth monitored in real time by a built-in depth sensor. When the shallow data accumulates to a preset depth (e.g., 100 meters), the edge computing processing unit automatically activates, loads pre-set model parameters, performs standard mode extension calculations, generates a full-ocean-depth sound velocity profile, and displays the profile curve and confidence interval on the display screen in real time. The operator can switch modes at any time—for extremely high real-time requirements, a fast mode can be switched to, compressing the system response time to milliseconds; for extremely high accuracy requirements, a high-precision mode can be switched to, where the system automatically collects more shallow data and performs iterative optimization. The equipment also features data storage capabilities, storing all raw data and augmentation results locally and uploading them to a cloud platform via a communication and collaboration unit according to a preset strategy. The cloud platform aggregates data uploaded from multiple devices, continuously optimizes the global model, and periodically pushes model updates to each device. The equipment also supports an offline operation mode—in environments without network access, the equipment independently completes augmentation calculations using a locally pre-built model, automatically synchronizing data once the network is restored. This equipment achieves full automation from data acquisition and real-time processing to result output, significantly improving the efficiency of marine survey operations and the timeliness of data products.

[0141] The above technical solution, driven by deep learning of physical information, integrates multi-source data collaboration, adaptive mode decomposition, hierarchical low-rank reconstruction, physical consistency constraints, uncertainty quantification, task-driven computation, and integrated hardware and software design to construct a complete and highly innovative method, system, and equipment for ocean acoustic profile extension. The modules work together organically, ensuring both the physical rationality and numerical accuracy of the extension results, while also achieving dynamic adaptation to engineering application scenarios, overcoming fundamental shortcomings of existing technologies in many aspects.

[0142] In summary, the embodiments of this application include the following key technical solutions:

[0143] (1) Physical law encoding type deep network architecture.

[0144] This embodiment proposes a physical information deep network architecture that directly encodes the seawater state equation and the empirical formula for sound speed into the network structure layers, unlike existing technologies that use physical laws merely as soft constraints in the loss function. Specifically, the network is designed as a three-output parallel structure, simultaneously predicting temperature, salinity, and sound speed profiles. A physical transformation module is embedded in the middle layer of the network—this module incorporates the differential form of the Del Grosso sound speed calculation formula, forcing the intermediate features of temperature and salinity to be calculated through this module before generating the sound speed output. This structural design ensures that the sound speed prediction naturally satisfies the constraints of the physical equations, eliminating the need to introduce additional penalty terms into the loss function. This fundamentally guarantees the physical consistency of the output results and avoids the conflicting optimization problems between physical laws and data fitting objectives under soft constraints.

[0145] (2) A method for utilizing shallow measured data based on acoustic ray bending feature matching.

[0146] This embodiment proposes a technique for deep profile inversion using ray bending features from shallow sound velocity data, differing from existing techniques that only statistically fit the sound velocity values ​​themselves. This method extracts cumulative ray bending features from the shallow sound velocity sequence—including the rate of change of the Snell's refraction angle at each depth layer, the sequence of curvature radii of the sound ray trajectory, and the cumulative distribution of the horizontal offset of the sound ray—and uses these ray bending features as input features to a deep learning model, rather than directly inputting the original sound velocity values. Since the ray bending features contain physical coupling information between the vertical gradient of the sound velocity and the deep structure, this method can extract more information related to the deep structure from shallow data, significantly improving the accuracy of the inversion.

[0147] (3) Fusion mechanism of dynamic tracking and modal recognition of thermocline.

[0148] This embodiment proposes a mechanism for the coordinated operation of dynamic tracking of the thermocline and modal recognition of sound velocity profiles, which differs from the fixed modal decomposition or independent modal classification methods in existing technologies. This mechanism calculates three parameters in real time during shallow sound velocity data acquisition: the upper boundary depth of the thermocline, the thermocline thickness, and the thermocline strength. These parameters are then used as dynamic inputs to the modal recognition classifier, allowing the modal recognition results to update in real time following the spatiotemporal evolution of the thermocline. Simultaneously, the modal recognition results are used to correct the thermocline parameter tracking algorithm—adaptively increasing the sensitivity threshold for thermocline detection when a strong thermocline profile is identified, and decreasing the priority of thermocline detection when a uniform profile is identified. This bidirectional coupling mechanism achieves synergistic optimization of thermocline features and modal classification.

[0149] (4) Dynamic constraint method for inverting deep temperature and salinity structure from sea surface height anomaly.

[0150] This embodiment proposes a dynamic constraint method for inverting deep temperature and salinity structures and constraining the extension of sound velocity profiles using sea surface height anomaly data, which differs from existing technologies that only use remote sensing data as background field correction. This method is based on the principle of potential vorticity conservation, establishing a quantitative relationship between sea surface height anomalies and the undulation of deep isodense surfaces—the displacement of isodense surfaces below the thermocline is calculated from sea surface height anomalies, thereby estimating the perturbation field of deep temperature and salinity. This perturbation field serves as a physical prior constraint, injected into the physical information depth network as conditional input, enabling the network to generate reasonable extension results based on sea surface dynamic information even when deep-layer measured data is lacking.

[0151] (5) Adaptive method for determining the number of modes in variational mode decomposition.

[0152] This embodiment proposes an adaptive mode number determination method based on spectral energy distribution to improve the application of variational mode decomposition in sound velocity profile processing. Unlike existing methods that rely on experience to set the mode number, this method first performs spectral analysis on a set of historical sound velocity profiles, calculating the dominant bandwidth and energy attenuation characteristics of each profile's spectrum. The statistical median of the dominant bandwidth of all profiles is used as the initial mode number. Subsequently, the mode energy separation index is used to evaluate the decomposition effect. When the energy separation between adjacent modes falls below a threshold, the mode number is automatically increased until the separation converges. This adaptive mechanism can automatically determine the optimal mode number based on the complexity of the sound velocity profile in the target sea area, avoiding subjective biases caused by manual setting.

[0153] (6) Gated weighted fusion multimodal nonlinear reconstruction mechanism.

[0154] This embodiment proposes a gated weighted fusion multimodal nonlinear reconstruction mechanism, which differs from existing technologies that use a single model to process all types of profiles or simple model selection. The core of this mechanism is a gated network unit, whose inputs are shallow sound velocity features and thermocline parameters, and whose outputs are the fusion weights of each sub-network (corresponding to different profile modes). The gated network employs an attention mechanism design, enabling it to learn the nonlinear mapping relationship between the activation modes of the corresponding sub-networks for different profile types. During actual inference, the gated network dynamically calculates the weight vector, and the outputs of all sub-networks are weighted and summed according to this weight to obtain the final result, rather than simply selecting the single sub-network with the highest probability. This soft fusion mechanism enables smoother and more accurate reconstruction results for profiles in modal transition regions or when modal features are not obvious.

[0155] (7) A rapid marine adaptation method based on meta-learning.

[0156] This embodiment proposes a rapid marine area adaptation method based on meta-learning to address the problem of sound velocity profile extension in marine areas with scarce historical data. Unlike existing technologies that require large amounts of source domain data or simple fine-tuning for transfer learning, this method employs a model-independent meta-learning framework for pre-training in data-rich source marine areas. The training objective is not to achieve optimal accuracy in the source domain, but rather to enable the model to "rapidly adapt to new marine areas"—that is, to achieve high accuracy with only a small number of target marine area samples (3 to 5 profiles) and a small number of gradient update steps (less than 10 steps). During field operations, a small number of complete profiles of the target marine area are collected as a support set, and rapid adaptive fine-tuning under the meta-learning framework is performed to generate a customized extension model suitable for the current marine area.

[0157] (8) Physical correction mechanism of hierarchical hard constraints and iterative soft constraints.

[0158] This embodiment proposes a physical correction mechanism that combines hierarchical hard constraints and iterative soft constraints, differing from existing single-constraint methods or post-processing corrections. The hard constraint layer directly performs a projection operation at the model output, mapping output values ​​that violate physical laws to the feasible region boundary, ensuring that the output strictly satisfies the layered stability and water mass characteristic boundary conditions. The soft constraint layer employs an iterative optimization framework, using the hard-constrained corrected profile as the initial value to construct an objective function containing a data fitting term and a physical rationality penalty term. Iterative optimization is performed using gradient descent to minimize the degree of physical violation while maintaining consistency with measured data. The two constraint layers work together to form a feedback loop—the result of the hard constraints serves as the initial value for the soft constraints; if the optimization result of the soft constraints triggers the hard constraint boundary again, it re-enters the hard constraint correction process until convergence.

[0159] (9) Confidence-driven dynamic sampling depth optimization method.

[0160] This embodiment proposes a confidence-driven dynamic sampling depth optimization method to guide the acquisition depth strategy of measured data during field operations. Based on the confidence interval width versus depth curve output by the uncertainty quantification module, this method identifies depth intervals with confidence levels below a preset threshold. Once a low-confidence interval is identified, the system automatically generates sampling depth suggestions—prioritizing the addition of sampling points at the upper and lower boundaries of the low-confidence interval, as the sound velocity gradient changes most significantly at these boundaries, making it most effective for constraining deep structures. This method quantifies the uncertainty of the extension results into actionable sampling guidance, forming a closed loop of "extension—confidence assessment—sampling optimization—extension update," maximizing information acquisition efficiency with limited sampling resources.

[0161] (10) Task-oriented precision-efficiency dynamic optimization scheduling algorithm.

[0162] This embodiment proposes a task-oriented precision-efficiency dynamic optimization scheduling algorithm for task-driven adaptive real-time latency systems. The algorithm models task constraints (precision requirements, real-time requirements, and computational resources) as a multi-objective optimization problem and employs a reinforcement learning-based scheduling strategy—using task parameters and the current system state as the state space, mode selection and resource allocation as the action space, and a weighted negative value of latency error and computation delay as the reward function to train the scheduling strategy network. During actual operation, this network makes the optimal scheduling decision based on real-time task input and output, achieving a Pareto optimal balance between precision and efficiency. Unlike existing technologies that use fixed rules or simple threshold judgments, this algorithm can learn the optimal strategy from historical scheduling experience and continuously optimize as job data accumulates.

[0163] (11) The incremental update and version management mechanism of the edge-cloud collaboration model.

[0164] This embodiment proposes an edge-cloud collaborative model incremental update and version management mechanism for the continuous evolution of integrated sonic profiling extension devices. The cloud platform aggregates measured data and extension results uploaded by all devices and periodically performs incremental training—fine-tuning existing models using only new data, rather than retraining from scratch, significantly reducing cloud computing overhead. The cloud maintains model parameters for multiple historical versions and records the performance evaluation results for each version. Devices periodically request updates from the cloud, which pushes the optimal model version based on the water mass characteristics of the sea area where the device is located and the current version's performance, rather than simply pushing the latest version. The device supports model version rollback; if performance degradation is detected after an update, it can automatically switch to a previous stable version. This mechanism enables collaborative evolution and personalized adaptation of device groups.

[0165] (12) A real-time feedback correction method for multi-beam measurement of sound velocity profile extension results.

[0166] This embodiment proposes a real-time feedback correction method for multi-beam measurement of sound velocity profile extension results, achieving closed-loop optimization between the extension algorithm and downstream applications. During multi-beam measurement operations, the system collects echo time and angle data of beam points in real time and calculates beam point coordinates using the current extended sound velocity profile. The calculated underwater topographic point cloud is compared with a priori depth map or overlapping areas of adjacent survey lines to extract topographic stitching errors and topographic anomaly features. When the topographic error exceeds a threshold, the correction amount of the sound velocity profile in a specific depth range is calculated by inversion. This correction amount is used as an online learning sample to fine-tune the physical information depth extension core module in real time. This method enables the extension model to self-correct using actual measurement results from downstream applications, forming a positive feedback loop where measurement and extension mutually reinforce each other.

[0167] Reference Figure 2This application provides a system for extending ocean sound velocity profiles, comprising:

[0168] The data preprocessing module is used to perform spatiotemporal matching and normalization on real-time shallow sound velocity measurement data, sea surface remote sensing data and historical profile data of the target sea area, and then extract the shallow sound velocity gradient and thermocline characteristic parameters.

[0169] A vector generation module is used to generate a structured input vector based on the shallow sound velocity gradient and the characteristic parameters of the thermocline layer.

[0170] The sound velocity profile generation module is used to input the structured input vector into a pre-built physical information neural network model, and output a preliminary sound velocity profile covering the entire ocean depth range through the physical information neural network model.

[0171] The correction and posterior module is used to perform physical consistency constraint correction on the preliminary sound velocity profile and obtain the posterior distribution of the sound velocity prediction value at each depth point through uncertainty quantization processing.

[0172] A confidence identification module is used to generate a full-ocean-depth sound velocity profile with confidence interval identification based on the posterior distribution.

[0173] 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.

[0174] 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.

[0175] 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 described 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.

[0176] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they 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 portion 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 described in 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.

[0177] 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.

[0178] More specific examples of computer-readable media (a non-exhaustive list) 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 the program can be printed, because the program can be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, interpreting, or otherwise processing as necessary, and then stored in computer memory.

[0179] 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.

[0180] 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.

[0181] 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.

[0182] The above is a detailed description of the preferred embodiments of this application, but this application is not limited to the embodiments described. 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 extending ocean sound velocity profiles, characterized in that, The method includes the following steps: The shallow sound velocity real-time measurement data, sea surface remote sensing data and historical profile data of the target sea area are spatiotemporally matched and normalized to extract the shallow sound velocity gradient and thermocline characteristic parameters. A structured input vector is generated based on the shallow sound velocity gradient and the characteristic parameters of the thermocline. The structured input vector is input into a pre-built physical information neural network model, and the physical information neural network model outputs a preliminary sound velocity profile covering the entire ocean depth range. Physical consistency constraint corrections are applied to the preliminary sound velocity profile, and the posterior distribution of the sound velocity prediction values ​​at each depth point is obtained through uncertainty quantization. A full-ocean-depth sound velocity profile with confidence interval identifiers is generated based on the posterior distribution.

2. The method for extending the ocean sound velocity profile according to claim 1, characterized in that, Before inputting the structured input vector into the pre-built physical information neural network model, the method further includes the following steps: In the offline phase, the historical profile dataset is adaptively decomposed using the variational mode decomposition algorithm to obtain a set of modal basis functions that characterize the time-varying features of the sound velocity profile in the target sea area. Then, cluster analysis is performed on the set of modal basis functions to identify multiple first profile mode types. During the online extension phase, the vertical gradient distribution and depth features of the first derivative extreme points of shallow sound velocity are extracted from the structured input vector to form a modal feature vector, and the modal feature vector is input into a classifier to identify the second profile mode type to which the current profile belongs. Based on the first profile mode type and the second profile mode type, a pre-trained nonlinear reconstruction network corresponding to the profile mode type is dynamically selected or weighted and fused through a gating mechanism. The deep sound velocity features are obtained by using the real-time shallow sound velocity measurement data as input, and the deep sound velocity features are fused with the structured input vector and used as input to the physical information neural network model.

3. The method for extending the ocean sound velocity profile according to claim 1, characterized in that, The physical information neural network model is trained through the following steps: In the offline phase, based on historical sea surface height anomaly data, a clustering algorithm is used to divide the target sea area into multiple sub-regions with uniform dynamic characteristics. In each sub-region, a sound speed profile data matrix is ​​independently constructed and singular value decomposition is performed to retain the first few orders of singular vectors as the low-rank basis of the corresponding sub-region. For sub-regions with scarce historical data, a meta-learner is used to transfer prior knowledge from similar sea areas to the target. The pre-trained meta-learner is then adaptively fine-tuned in the target sea area using measured profiles to obtain a small-sample extended model suitable for the sub-region. During the online extension phase, the reconstruction results based on the local low-rank subspace and the reconstruction results based on few-shot transfer learning are calculated simultaneously. The weights of the two are dynamically adjusted and fused through an attention mechanism. The fused result is used as prior information to assist the physical information neural network model in collaborative reconstruction. The physical information neural network model uses the seawater state equation and the sound propagation and refraction laws as physical constraints during training. The loss function consists of three parts: data fitting loss, physical constraint loss, and multi-physics field collaborative loss.

4. The method for extending the ocean sound velocity profile according to claim 1, characterized in that, The physical consistency constraint correction of the preliminary sound velocity profile includes the following steps: A hard constraint layer is constructed, and the preliminary sound velocity profile is checked layer by layer through projection operation. Numerical points that do not meet the layering stability conditions or the physical allowable range of the sound velocity gradient are corrected to the most recent valid values. A soft constraint layer is constructed, the vertical gradient curve of the sound velocity profile is calculated and the continuity is constrained in the form of a penalty function, and the seasonal rationality of the thermocline location is evaluated and corrected. A consistency verification layer is constructed, and a physical diagnostic model independent of the training data is used to perform post-hoc verification of the elongation results after being corrected by hard constraint layer and soft constraint layer, and to check the dynamic consistency with synchronous sea surface height anomaly data.

5. The method for extending an ocean sound velocity profile according to claim 1, characterized in that, The process of obtaining the posterior distribution of the predicted sound velocity at each depth point through uncertainty quantization includes the following steps: In the inference stage of the physical information neural network model, the Monte Carlo dropout method is used to apply random dropout to the key layers of the physical information neural network model and perform multiple forward propagations to obtain the predicted sound speed value at each depth point. Based on the parameter uncertainties of the physical information neural network model obtained by the variational inference method, the total uncertainty of the predicted sound speed at each depth point is calculated. The mean of the predicted sound speed values ​​is used as the final output sound speed value. The total uncertainty is converted into a confidence interval corresponding to the confidence level, and the confidence level is automatically labeled according to the interval width to obtain the posterior distribution.

6. The method for extending an ocean sound velocity profile according to claim 1, characterized in that, The method further includes the following steps: The full-ocean-depth sound velocity profile with confidence interval markers is loaded by the edge computing processing unit and displayed in real time through the human-computer interaction unit. The extension results generated locally by the edge computing processing unit are uploaded to the cloud platform through the communication and collaboration unit.

7. A method for extending an ocean acoustic profile according to any one of claims 1 to 6, characterized in that, The method further includes the following steps: The structured input vector is input into a pre-built physical information neural network model, which outputs temperature and salinity profiles across the entire ocean depth range.

8. A system for extending ocean sound velocity profiles, characterized in that, The system includes: The data preprocessing module is used to perform spatiotemporal matching and normalization on real-time shallow sound velocity measurement data, sea surface remote sensing data and historical profile data of the target sea area, and then extract the shallow sound velocity gradient and thermocline characteristic parameters. A vector generation module is used to generate a structured input vector based on the shallow sound velocity gradient and the characteristic parameters of the thermocline layer. The sound velocity profile generation module is used to input the structured input vector into a pre-built physical information neural network model, and output a preliminary sound velocity profile covering the entire ocean depth range through the physical information neural network model. The correction and posterior module is used to perform physical consistency constraint correction on the preliminary sound velocity profile and obtain the posterior distribution of the sound velocity prediction value at each depth point through uncertainty quantization processing. A confidence identification module is used to generate a full-ocean-depth sound velocity profile with confidence interval identification based on the posterior distribution.

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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