Method and device for modeling disturbed motion of underwater vehicle based on hydrodynamic similarity guidance

Abstract

The application discloses a method and device for modeling disturbed motion of a submersible based on water dynamic similarity guidance, and belongs to the technical field of motion control of submersibles. The method comprises the following steps: determining a similarity parameter representing the degree of water dynamic essential similarity between a source submersible and a target submersible according to the distribution correlation of a source dimensionless feature set and a target dimensionless feature set in a dimensionless feature space; inputting the target dimensionless feature set into a teacher network with fixed parameters to obtain intermediate layer features and interference parameter representations output by the teacher network; inputting the intermediate layer features, the interference parameter representations and the similarity parameter into a similarity attention mechanism module to generate a knowledge distillation signal; and inputting the target dimensionless feature set into a student network comprising a lightweight adaptive layer to train the student network so as to deploy a disturbed motion prediction model of the target submersible. The method can improve the accuracy of motion prediction of the submersible in a disturbance environment such as a strong current and a turbulent flow.

Description

Technical Field

[0001] This application belongs to the field of motion control technology for submersibles, and particularly relates to a method and device for modeling disturbed motion of submersibles based on hydrodynamic similarity guidance. Background Technology

[0002] Autonomous Undersea Vehicles (AUVs) and Remotely Operated Vehicles (ROVs) are core equipment for performing tasks such as marine resource exploration, environmental monitoring, underwater search and rescue, and national defense. Their motion control accuracy and stability directly determine the success or failure of these missions. As marine development accelerates towards deeper waters and greater intelligence, submersibles need to achieve high-precision trajectory tracking and attitude stabilization in complex and disturbed environments such as strong currents, internal waves, and turbulence. This necessitates modeling the disturbed motion of submersibles to improve control accuracy.

[0003] Currently, mainstream models of submersible motion under disturbance rely on general deep learning models, which require the collection of massive amounts of motion test data for the target submersible to support model training. However, when dealing with small or new submersibles, the high cost of pool testing, the scarcity of sea trial windows, and the lack of historical data accumulation are all constraints. As a result, the high cost of testing and the scarcity of data make it difficult to establish a reliable prediction model, leading to inaccurate prediction of submersible motion in disturbed environments such as strong currents and turbulence. Summary of the Invention

[0004] This application aims to address at least one of the technical problems existing in the prior art. To this end, this application proposes a method and apparatus for modeling the disturbed motion of submersibles based on hydrodynamic similarity guidance, which can establish reliable prediction models for small or novel submersibles with lower experimental costs and less data, thereby improving the accuracy of motion prediction for submersibles in disturbed environments such as strong currents and turbulence.

[0005] In a first aspect, this application provides a method for modeling disturbed motion of a submersible based on hydrodynamic similarity guidance, the method comprising: The actual motion state data of the source submersible and the target submersible, as well as the motion test data under disturbed conditions, are obtained. Based on the hydrodynamic similarity criterion, dimensionless transformations are performed to obtain the corresponding source dimensionless feature set and target dimensionless feature set. The hydrodynamic similarity criterion is constructed based on Froude number and Reynolds number. Based on the distribution correlation of the source dimensionless feature set and the target dimensionless feature set in the dimensionless feature space, a similarity parameter characterizing the hydrodynamic essential similarity between the source submersible and the target submersible is determined. The teacher network is trained using the source dimensionless feature set and the corresponding actual motion state data of the source submersible, and the parameters of the trained teacher network are fixed. The target dimensionless feature set is input into the teacher network with fixed parameters to obtain the intermediate layer features and interference parameter representations output by the teacher network. The intermediate layer features, the interference parameter representation, and the similarity parameter are input into the similarity attention mechanism module to generate a knowledge distillation signal; The target dimensionless feature set is input into a student network containing a lightweight adaptation layer, and the student network is trained based on the knowledge distillation signal and the actual motion state data of the target submersible. The perturbed motion prediction model of the target submersible is deployed according to the trained student network. The lightweight adaptation layer is used to compensate for the residual deviation caused by the heterogeneity between the source submersible and the target submersible that is not characterized by the hydrodynamic similarity criterion.

[0006] According to one embodiment of this application, the dimensionless transformation based on the hydrodynamic similarity criterion includes: Based on the relative strength of the interaction between inertial force and gravity in the hydrodynamic similarity criterion, the source Froude number parameter is generated according to the characteristic velocity data and characteristic length parameter of the source submersible, and the target Froude number parameter is generated according to the characteristic velocity data and characteristic length parameter of the target submersible. Based on the relative strength of inertial and viscous forces in the hydrodynamic similarity criterion, the source Reynolds number parameter is determined according to the fluid density constant, the characteristic velocity data and characteristic length parameter of the source submersible, and the target Reynolds number parameter is generated according to the fluid density constant, the characteristic velocity data and characteristic length parameter of the target submersible. Based on the source Froude number parameter, the target Froude number parameter, the source Reynolds number parameter, and the target Reynolds number parameter, a scaling transformation is performed on each dimension feature of the motion test data to generate the source dimensionless feature set and the target dimensionless feature set; The decoupling consistency between the source dimensionless feature set and the target dimensionless feature set in the feature space is verified.

[0007] According to one embodiment of this application, determining the similarity parameter characterizing the hydrodynamic essential similarity between the source submersible and the target submersible based on the distribution correlation of the source dimensionless feature set and the target dimensionless feature set in the dimensionless feature space includes: Gaussian kernel density estimation is performed on all feature points of the source dimensionless feature set and the target dimensionless feature set respectively. The feature distribution is fitted by smoothing kernel function and bandwidth parameter to generate corresponding source feature distribution model and target feature distribution model. Based on the difference measure between the source feature distribution model and the target feature distribution model, the relative entropy of the distribution is determined to generate a distribution difference representation; The distribution difference representation is input into a linear mapping function based on historical hydrodynamic similarity to convert the distribution difference representation into the similarity parameter.

[0008] According to one embodiment of this application, the teacher network includes a first input layer, a first feature encoding module and a motion prediction module connected to the first input layer, wherein inputting the target dimensionless feature set into the teacher network with fixed parameters to obtain the intermediate layer features and interference parameter representations output by the teacher network includes: The target dimensionless feature set is transmitted to the first feature encoding module and the motion prediction module respectively through the first input layer; The first feature encoding module performs feature extraction and dimensionality reduction on the target dimensionless feature set to generate the intermediate layer features. The motion prediction module performs interference response modeling on the target dimensionless feature set to generate the interference parameter representation. By adjusting the number of channels, the intermediate layer features and the interference parameter representations are dimensionally aligned and output.

[0009] According to one embodiment of this application, the first feature encoding module includes a three-layer convolutional layer structure with the number of channels increasing sequentially, used to extract high-order features of hydrodynamic disturbance response; The motion prediction module includes a first fully connected layer and a second fully connected layer connected in sequence. The process of training a teacher network using the source dimensionless feature set and the corresponding actual motion state data of the source submersible to generate knowledge distillation signals includes: The first feature encoding module extracts and reduces the dimensionality of the source dimensionless feature set to generate teacher feature encoding output. The first fully connected layer performs dimensionality reduction mapping on the teacher feature encoding output to generate a dimensionally compressed feature representation. The second fully connected layer maps the dimensionally compressed feature representation to the interference parameter space to generate the interference parameter representation. The mean square error loss value is determined based on the teacher feature encoding output, the interference parameter representation, and the actual motion state data of the source submersible. Based on the mean squared error loss value, the teacher network parameters are optimized by stochastic gradient descent, and the parameters of the trained teacher network are fixed.

[0010] According to one embodiment of this application, the similarity attention mechanism module includes an attention weight generation unit, a feature weighted fusion unit, and a distillation signal output unit; The step of inputting the intermediate layer features, the interference parameter representation, and the similarity parameter into the similarity attention mechanism module to generate a knowledge distillation signal includes: The attention weight generation unit expands the similarity parameter into a weight vector that matches the feature dimension. The weighted feature fusion unit performs a dot product between the weight vector and the intermediate layer features and the interference parameter representation to generate a weighted feature. The distillation signal output unit performs feature aggregation on the weighted features to generate a knowledge distillation signal.

[0011] According to one embodiment of this application, the student network includes a second input layer, a second feature encoding module, and the lightweight adaptation layer connected in sequence; The second feature encoding module has the same structure as the first feature encoding module of the teacher network, and the lightweight adaptation layer includes a residual bias compensation unit; The step of inputting the target dimensionless feature set into a student network containing a lightweight adaptation layer, and training the student network based on the knowledge distillation signal and the actual motion state data of the target submersible, includes: The target dimensionless feature set is transmitted to the second feature encoding module through the second input layer; The second feature encoding module extracts and reduces the dimensionlessness of the target feature set to generate student feature encoding output. The lightweight adaptation layer is used to perform a full connection on the student feature encoding output to generate a residual mapping; Based on the residual mapping, bias compensation features are generated through feature addition operations; The bias compensation features are concatenated with the knowledge distillation signal to generate a training target. Based on the training objective and the actual motion state data of the target submersible, the parameters of the student network are optimized using gradient descent.

[0012] According to one embodiment of this application, the lightweight adaptation layer includes a single hidden layer fully connected structure and an activation function, wherein the number of hidden layer nodes in the single hidden layer fully connected structure is one-quarter of the input dimension; The step of performing a fully connected operation on the student feature encoding output through the lightweight adaptation layer to generate a residual mapping includes: The activation function is used to perform a non-linear transformation on the student feature encoding output to generate intermediate features. The residual mapping is generated based on the intermediate features through the single hidden layer fully connected structure. The step of generating bias compensation features based on the residual mapping through feature addition operations includes: Based on the vector dimension of the intermediate features, the residual mapping is linearly upgraded, and the upgraded residual mapping is added to the student feature encoding output to generate the deviation compensation feature.

[0013] According to one embodiment of this application, the disturbance motion prediction model for the student network-deployed target submersible, based on the trained model, includes: The trained student network is subjected to channel pruning to obtain the disturbed motion prediction model. The network structure and quantization weights of the disturbed motion prediction model are loaded into the embedded system of the target submersible and deployed through the model loading interface; The real-time data stream provided by the sensor system of the target submersible is converted into dimensionless features and added to the target dimensionless feature set; The target dimensionless feature set is input into the disturbed motion prediction model, and the disturbed motion prediction value is generated through forward propagation.

[0014] Secondly, this application provides a device for modeling disturbed motion of a submersible based on hydrodynamic similarity guidance, the device comprising: The acquisition module is used to acquire the actual motion state data of the source submersible and the target submersible, as well as the motion test data under disturbed conditions, and to perform dimensionless transformation based on the hydrodynamic similarity criterion to obtain the corresponding source dimensionless feature set and target dimensionless feature set. The hydrodynamic similarity criterion is constructed based on the Froude number and the Reynolds number. The first processing module is used to determine a similarity parameter that characterizes the hydrodynamic essential similarity between the source submersible and the target submersible based on the distribution correlation of the source dimensionless feature set and the target dimensionless feature set in the dimensionless feature space. The second processing module is used to train the teacher network using the source dimensionless feature set and the corresponding actual motion state data of the source submersible, and to fix the parameters of the trained teacher network. The third processing module is used to input the target dimensionless feature set into the teacher network with fixed parameters to obtain the intermediate layer features and interference parameter representations output by the teacher network. The fourth processing module is used to input the intermediate layer features, the interference parameter representation, and the similarity parameter into the similarity attention mechanism module to generate a knowledge distillation signal; The fifth processing module is used to input the target dimensionless feature set into a student network containing a lightweight adaptation layer, train the student network based on the knowledge distillation signal and the actual motion state data of the target submersible, and deploy a disturbed motion prediction model of the target submersible according to the trained student network. The lightweight adaptation layer is used to compensate for residual deviations caused by the heterogeneity between the source submersible and the target submersible that are not characterized by hydrodynamic similarity criteria.

[0015] Additional aspects and advantages of this application will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of this application.

[0016] This application provides a method and apparatus for modeling disturbed motion of a submersible based on hydrodynamic similarity, which has the following advantages over the prior art: (1) By mapping the motion data of heterogeneous submersibles to a physically consistent dimensionless feature space through the hydrodynamic similarity criterion, the hydrodynamic essential similarity is accurately quantified based on the feature distribution correlation, and the similarity attention mechanism is driven to generate knowledge distillation signals adapted to the target platform, so that the student network can efficiently transfer the hydrodynamic knowledge of the source platform; the lightweight adaptation layer accurately compensates for the residual bias not represented by the Froude number and Reynolds number through the single hidden layer structure and dimension upscaling operation; the amount of motion test data required for modeling the target submersible is reduced, effectively solving the dilemma of building a reliable prediction model for small or new submersibles due to high test costs and scarce historical data. The submersible can achieve high-precision trajectory tracking and intelligent anti-disturbance control in complex ocean disturbance environments, and can establish a reliable prediction model for small or new submersibles with lower test costs and less data, thereby improving the accuracy of motion prediction of submersibles in disturbance environments such as strong currents and turbulence.

[0017] (2) The dimensionless transformation driven by the Froude number and Reynolds number dual criteria maps the original motion data of the heterogeneous submersible to a feature space with consistent physical connotation, so that the hydrodynamic response characteristics of platforms of different scales have a comparable basis. In the decoupling consistency verification stage, it is ensured that the dimensionless features retain only the essential hydrodynamic information, effectively eliminating the interference of geometric parameters and the absolute dimensions of the flow field, while avoiding feature distribution shift caused by scale effect, and improving the physical rationality of cross-platform knowledge transfer and model generalization ability. Attached Figure Description

[0018] The above and / or additional aspects and advantages of this application will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which: Figure 1 This is a flowchart illustrating the method for modeling disturbed motion of a submersible based on hydrodynamic similarity guidance provided in this application embodiment; Figure 2 This is a schematic diagram of the structure of the submersible disturbed motion modeling device based on hydrodynamic similarity guidance provided in the embodiments of this application. Detailed Implementation

[0019] The technical solutions of the embodiments of this application will be clearly described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application are within the scope of protection of this application.

[0020] The terms "first," "second," etc., used in the specification and claims of this application are used to distinguish similar objects and not to describe a specific order or sequence. It should be understood that such use of data can be interchanged where appropriate so that embodiments of this application can be implemented in orders other than those illustrated or described herein, and the objects distinguished by "first," "second," etc., are generally of the same class and the number of objects is not limited; for example, a first object can be one or more. Furthermore, in the specification and claims, "and / or" indicates at least one of the connected objects, and the character " / " generally indicates that the preceding and following objects are in an "or" relationship.

[0021] The following, in conjunction with the accompanying drawings, provides a detailed description of the method and apparatus for modeling disturbed motion of a submersible based on hydrodynamic similarity guidance, through specific embodiments and application scenarios.

[0022] Among them, the submersible disturbed motion modeling method based on hydrodynamic similarity can be applied to the terminal, specifically executed by the hardware or software in the terminal.

[0023] The terminal includes, but is not limited to, portable communication devices such as mobile phones or tablets with touch-sensitive surfaces (e.g., touchscreen displays and / or touchpads). It should also be understood that, in some embodiments, the terminal may not be a portable communication device, but rather a desktop computer with touch-sensitive surfaces (e.g., touchscreen displays and / or touchpads).

[0024] The following embodiments describe a terminal including a display and a touch-sensitive surface. However, it should be understood that the terminal may include one or more other physical user interface devices such as a physical keyboard, mouse, and joystick.

[0025] The method for modeling disturbed motion of a submersible based on hydrodynamic similarity provided in this application embodiment can be executed by an electronic device or a functional module or entity within an electronic device that can implement the method. The electronic devices mentioned in this application embodiment include, but are not limited to, mobile phones, tablets, computers, cameras, and wearable devices. The following description uses an electronic device as an example to illustrate the method for modeling disturbed motion of a submersible based on hydrodynamic similarity provided in this application embodiment.

[0026] like Figure 1 As shown, the method for modeling disturbed motion of a submersible based on hydrodynamic similarity includes: Step 110: Obtain the actual motion state data of the source submersible and the target submersible, as well as the motion test data under disturbed conditions, and perform dimensionless transformation based on the hydrodynamic similarity criterion to obtain the corresponding source dimensionless feature set and target dimensionless feature set. The hydrodynamic similarity criterion is constructed based on Froude number and Reynolds number. It is understandable that the source submersible is a known configuration submersible that has completed system hydrodynamic tests and has a complete motion database, and that it differs significantly from the target submersible in terms of physical configuration, geometric dimensions, mass distribution, and inertial parameters.

[0027] The target submersible is a small or novel submersible to be modeled and predicted; Actual motion state data refers to dynamic parameters such as position, velocity, acceleration, attitude angle, and angular velocity collected by the submersible in a real or simulated marine environment. The motion test data is the sequence of disturbance response recorded by the submersible in a controlled pool or sea trial under set disturbance conditions such as fixed-velocity ocean currents and periodic eddies. The hydrodynamic similarity criterion is a physical criterion constructed based on the similarity theory of fluid mechanics. It establishes a cross-scale hydrodynamic behavior mapping relationship through the Froude number and Reynolds number, so that the generated dimensionless features are physically decoupled from the geometric scale of the submersible and the absolute parameters of the flow field.

[0028] Dimensionless transformation is a normalization process that scales the original motion data according to the Froude number and Reynolds number to eliminate the influence of scale and absolute velocity. The source dimensionless feature set is a set of features that characterize the hydrodynamic response mode of a source submersible after it has been dimensionlessized. The dimensionless feature set of a target is a set of comparable features formed by transforming a target submersible using the same criteria. The Froude number is the ratio of characteristic velocity to gravitational wave velocity, which dominates the characteristics of free surface flow; the Reynolds number is the ratio of inertial force to viscous force, which dominates the boundary layer and turbulence characteristics.

[0029] In step 110, the characteristic length, characteristic velocity, fluid density, and dynamic viscosity of the source and target submersibles are extracted respectively. For example, the characteristic length is taken as the maximum diameter of the hull, the characteristic velocity is taken as the experimentally set flow rate, and in a seawater environment, the fluid density is taken as the standard seawater density of 1025 kg / m³, and the dynamic viscosity is taken as... Pa·second.

[0030] For each original motion data sample, calculate its corresponding Froude number and Reynolds number; divide the original linear velocity value by the square root of the product of gravitational acceleration and characteristic length to make the linear velocity component dimensionless; multiply the original angular velocity value by the characteristic length and then divide it by the characteristic velocity to make the angular velocity component dimensionless; multiply the original acceleration value by the characteristic length and then divide it by the square of the characteristic velocity to make the acceleration component dimensionless; keep the original values ​​of dimensionless quantities such as attitude angles.

[0031] The transformed 12-dimensional feature vectors are organized according to time series to form a source dimensionless feature set and a target dimensionless feature set. Each feature vector carries a corresponding timestamp and disturbance condition label.

[0032] The 12-dimensional dimensionless eigenvectors include 3-dimensional linear velocity, 3-dimensional angular velocity, 3-dimensional acceleration, and 3-dimensional attitude angle, with the attitude angle itself being dimensionless.

[0033] Step 120: Based on the distribution correlation of the source dimensionless feature set and the target dimensionless feature set in the dimensionless feature space, determine the similarity parameter characterizing the hydrodynamic essential similarity between the source submersible and the target submersible. It is understandable that the dimensionless feature space is a Euclidean space composed of 12 dimensionless motion features. After eliminating the influence of geometric scale and absolute value of flow velocity, the feature distribution of heterogeneous platforms becomes physically comparable. Distribution correlation is the degree of statistical overlap between the probability density distributions of the source feature set and the target feature set in the dimensionless feature space; The hydrodynamic similarity between the source submersible and the target submersible is the level of inherent consistency between them in terms of the physical mechanism of disturbance response after removing differences in external dimensions. The similarity parameter is a scalar value that quantifies the degree of similarity in hydrodynamic nature. The value ranges from 0 to 1. The closer the value is to 1, the more similar the hydrodynamic nature. It is used to characterize the physical similarity of hydrodynamic disturbance response.

[0034] In step 120, firstly, Gaussian kernel density estimation is performed on all samples of the source dimensionless feature set in 12-dimensional space. The kernel function is a radial basis function, and the bandwidth parameter is calculated using the Silverman empirical rule to generate a probability density function model of the source feature distribution. Simultaneously, the same operation is performed on the target dimensionless feature set to generate a probability density function model of the target feature distribution. Secondly, the KL divergence (relative entropy) between the two probability density functions is calculated using numerical integration. Specifically, 10,000 Monte Carlo sampling points are generated in the feature space. For each sampling point, the ratio of the source distribution density value to the target distribution density value is calculated, the natural logarithm is taken, and then multiplied by the source distribution density value. The results of all sampling points are summed and divided by the total number of samples to obtain the distribution difference characterization value. Finally, the difference representation value is input into a preset linear mapping function: in, is the similarity parameter; D is the distribution difference characterization value; 0.5 is the historical calibration threshold, which is determined by experimental data from 10 sets of historical submersible pairs. Submersible pairs with hydrodynamic similarity >0.8 verified by high-precision CFD simulation are selected, and the mean value of their distribution difference characterization D is calculated as the historical calibration threshold. If the calculation result is less than 0, it is set to 0; if it is greater than 1, it is set to 1. The final similarity parameter is then output.

[0035] Step 130: Train the teacher network using the source dimensionless feature set and the corresponding actual motion state data of the source submersible, and fix the parameters of the trained teacher network. It is understandable that the teacher network is a deep neural network consisting of an input layer, a first feature encoding module composed of three convolutional layers with increasing channel count, and a motion prediction module composed of two fully connected layers. The parameters of the teacher network are the set of all convolutional kernel weights, fully connected layer weights, and bias terms in the network; In step 130, the source dimensionless feature set is divided into a training set, a validation set, and a test set in an 8:1:1 ratio. The source dimensionless feature vector is used as the input to the teacher network, and the corresponding actual motion state data of the source submersible, which has undergone the same dimensionless processing, is used as the supervision label. Mean squared error is used as the loss function, and the stochastic gradient descent method with momentum is selected as the optimizer. The initial learning rate is set to 0.001, and the batch size is set to 64. During the training process, the loss value is evaluated on the validation set in each round. If the validation loss does not decrease for 5 consecutive rounds, the training is terminated. After the training is completed, the parameter weights and bias values ​​of all layers of the teacher network are fixed and stored, and the network is set to inference mode, prohibiting parameter updates in subsequent training processes.

[0036] Step 140: Input the target dimensionless feature set into the teacher network with fixed parameters to obtain the intermediate layer features and interference parameter representations output by the teacher network; It is understandable that the intermediate layer features are high-dimensional feature maps output by the last convolutional layer of the first feature encoding module of the teacher network, which are then transformed into 256-dimensional vectors after global average pooling, containing deep abstract patterns of hydrodynamic disturbance response. The interference parameter is represented by a 32-dimensional vector output from the second fully connected layer of the motion prediction module of the teacher network, which characterizes key hydrodynamic interference physical quantities such as the added mass coefficient and the fluid damping coefficient. In step 140, each sample of the target dimensionless feature set is sequentially input into a teacher network with fixed parameters. After the data is processed by the first feature encoding module, the output of the last convolutional layer is extracted and global average pooling is performed to generate a 256-dimensional intermediate layer feature vector. Simultaneously, the vector is processed by the motion prediction module, reduced to 128 dimensions by the first fully connected layer, and then mapped to 32 dimensions by the second fully connected layer (32 neurons, linear activation) to generate a 32-dimensional interference parameter representation vector. When the dimensions of the two vectors are inconsistent, for example, 256 dimensions and 32 dimensions, linear projection is performed on the 32-dimensional interference parameter representation vector. The vector is transformed by a learnable 32×256 weight matrix to expand the output dimension to 256 dimensions, thereby aligning it with the dimensions of the intermediate layer features. The aligned vectors are then stored separately for later use.

[0037] Step 150: Input the intermediate layer features, the interference parameter representation, and the similarity parameter into the similarity attention mechanism module to generate a knowledge distillation signal; It is understandable that the similarity attention mechanism module is composed of a cascaded attention weight generation unit, a feature weight fusion unit, and a distillation signal output unit. In the similarity attention mechanism module, the parameters of the fully connected layer that expand the similarity parameters into weight vectors are determined and fixed during the teacher network training phase and remain unchanged during the student network training phase. They are used only as feature modulators, and their outputs change dynamically with the input similarity parameters. They are used only as dynamic feature modulators to generate guiding signals. The knowledge distillation signal is a guiding vector that integrates hydrodynamic similarity information, carries hydrodynamic knowledge of the source submersible, and is adapted to the characteristics of the target platform. Its dimension is consistent with the intermediate layer features. In step 150, firstly, the scalar similarity parameter is expanded into a 256-dimensional weight vector through a single-layer fully connected network containing 256 output neurons with the sigmoid activation function to ensure that the weight values ​​are in the range of 0 to 1. Secondly, in the feature weighted fusion unit, the weight vector is multiplied element-wise with the dimension-aligned intermediate layer feature vector and the interference parameter representation vector to obtain two weighted feature vectors, which are then fused element-wise. Finally, in the distillation signal output unit, the fused feature vector is subjected to layer normalization to eliminate scale differences and output a 256-dimensional knowledge distillation signal. This signal retains the hydrodynamic knowledge of the source platform and is dynamically modulated by the similarity parameter to adapt to the characteristics of the target platform.

[0038] Step 160: Input the target dimensionless feature set into a student network containing a lightweight adaptation layer, and train the student network based on the knowledge distillation signal and the actual motion state data of the target submersible. Deploy the disturbed motion prediction model of the target submersible according to the trained student network. The lightweight adaptation layer is used to compensate for the residual deviation caused by the heterogeneity between the source submersible and the target submersible that is not characterized by the hydrodynamic similarity criterion.

[0039] It is understandable that the lightweight adaptation layer is composed of a ReLU activation function and a single hidden layer fully connected structure, with the number of hidden layer nodes set to one-quarter of the input dimension (input 256 → hidden layer 64 → output 64). The student network is a simplified neural network consisting of an input layer, a second feature encoding module with the same structure as the first feature encoding module of the teacher network, a lightweight adaptation layer, and an output layer. The disturbed motion prediction model is a student network optimized by channel pruning and weight quantization, specifically designed for deployment in embedded systems of target submersibles.

[0040] In step 160, the target dimensionless feature set is input into the student network, and a 256-dimensional feature encoding output is generated by the second feature encoding module. This output is then fed into a lightweight adaptation layer: first, it undergoes a nonlinear transformation using the ReLU activation function to generate intermediate features, and then a single hidden layer fully connected structure (256-dimensional input, 64-dimensional hidden layer, 64-dimensional output) is used to generate a residual mapping. A linear dimensionality increase operation is performed on the 64-dimensional residual mapping (through a 64×256 weight matrix mapping), converting it into a 256-dimensional vector, which is then added element-wise with the original feature encoding output to generate bias compensation features. The difference-compensated features and knowledge distillation signals are concatenated along the feature dimension to form a 512-dimensional training objective. A joint loss function is constructed using this training objective and a small amount of actual motion state data from the target submersible (no fewer than 2000 samples), which is a weighted sum of the knowledge distillation loss and regression loss. The Adam optimizer is used to fine-tune the student network parameters. After training, channel pruning is performed on the network's convolutional layers: the L1 norm of each channel weight is calculated, and the 30% of channels with the smallest norm are removed to reconstruct the network structure. The pruned network weights are then quantized using 8-bit integer quantization. The optimized model is deployed to the target submersible's embedded computing unit via the ROS 2 model loading interface. For example, on the target submersible's embedded system (such as NVIDIA Jetson Xavier NX), the NVIDIA TensorRT inference engine is used to serialize the quantized model, generating an engine file (.engine). A ROS 2 functional node is developed, embedding the TensorRT runtime library. Upon node startup, the engine file is loaded, the inference context is initialized, real-time data is acquired by subscribing to sensor topics, and the prediction results are published to the control topic after inference.

[0041] According to the hydrodynamic similarity-guided submersible motion modeling method provided in this application, the motion data of heterogeneous submersibles are mapped to a physically consistent dimensionless feature space through hydrodynamic similarity criteria. Based on the correlation of feature distribution, the essential similarity of hydrodynamics is accurately quantified, and a similarity attention mechanism is driven to generate knowledge distillation signals adapted to the target platform, enabling the student network to efficiently transfer hydrodynamic knowledge from the source platform. The lightweight adaptation layer accurately compensates for residual biases not represented by Froude number and Reynolds number through a single hidden layer structure and dimensionality increase operation. The amount of motion test data required for target submersible modeling is reduced, effectively solving the dilemma of building reliable prediction models for small or new submersibles due to high test costs and scarce historical data. The submersible can achieve high-precision trajectory tracking and intelligent anti-disturbance control in complex ocean disturbance environments. It can establish reliable prediction models for small or new submersibles with lower test costs and less data, improving the accuracy of motion prediction for submersibles in disturbance environments such as strong currents and turbulence.

[0042] In some embodiments, the dimensionless transformation based on the hydrodynamic similarity criterion includes: Based on the relative strength of the interaction between inertial force and gravity in the hydrodynamic similarity criterion, the source Froude number parameter is generated according to the characteristic velocity data and characteristic length parameter of the source submersible, and the target Froude number parameter is generated according to the characteristic velocity data and characteristic length parameter of the target submersible. Based on the relative strength of inertial and viscous forces in the hydrodynamic similarity criterion, the source Reynolds number parameter is determined according to the fluid density constant, the characteristic velocity data and characteristic length parameter of the source submersible, and the target Reynolds number parameter is generated according to the fluid density constant, the characteristic velocity data and characteristic length parameter of the target submersible. Based on the source Froude number parameter, the target Froude number parameter, the source Reynolds number parameter, and the target Reynolds number parameter, a scaling transformation is performed on each dimension feature of the motion test data to generate the source dimensionless feature set and the target dimensionless feature set; The decoupling consistency between the source dimensionless feature set and the target dimensionless feature set in the feature space is verified.

[0043] It is understandable that the relative strength of the interaction between inertial force and gravity is the ratio of inertial effect to gravitational effect in fluid motion, which dominates the influence mechanism of free surface disturbance (such as wave generation) on the motion of submersible. Characteristic velocity data are representative velocity reference values ​​in the motion test data of a submersible under disturbed operating conditions, taken as the set flow velocity or cruising speed. Characteristic length parameters are typical dimensions used to characterize the scale in the geometry of a submersible, and are taken as the maximum diameter or length of the hull. The source Froude number parameter is a dimensionless number calculated based on the source submersible's characteristic velocity, characteristic length, and gravitational acceleration, quantifying the relative strength of the interaction between inertial force and gravity during its motion; The target Froude number parameter is a dimensionless number calculated based on the corresponding parameters of the target submersible, used to characterize the similar physical relationships of the target platform; The relative strength of inertial force and viscous force is the ratio of inertial effect to viscous dissipation effect in fluid motion, which dominates the characteristics of boundary layer flow and turbulence development. The fluid density constant is a known physical property of the fluid in the test environment (standard seawater), and is taken as 1025 kg per cubic meter. The source Reynolds number parameter is a dimensionless number calculated by combining the fluid density constant, the characteristic velocity and characteristic length of the source submersible, and the fluid dynamic viscosity. It characterizes the relative strength of the interaction between inertial forces and viscous forces in the flow. The target Reynolds number parameter is a dimensionless number calculated by combining the same fluid parameters and the characteristic parameters of the target submersible. The feature space is a multidimensional vector space composed of dimensionless physical quantities such as linear velocity, angular velocity, and acceleration, with each dimension having a clear hydrodynamic physical meaning. Decoupling consistency is a verification attribute that reflects the essential characteristics of hydrodynamic response and is independent of the individual attributes of the original submersible, such as its geometric scale and absolute flow field parameters, after the feature set has been dimensionlessly distributed in the feature space.

[0044] In actual execution, the characteristic velocity and characteristic length values ​​set by the source submersible and the target submersible during the motion test are extracted respectively, and substituted into the Froude number formula to calculate the source Froude number parameters and the target Froude number parameters. For example, the characteristic velocity value of the source submersible is taken as 1.5 m / s, the characteristic velocity value of the target submersible is taken as 0.8 m / s, the characteristic length value of the source submersible is taken as the maximum diameter of the hull as 1.2 m, and the characteristic length value of the target submersible is taken as 0.3 m. Combining the fluid density constant, fluid dynamic viscosity (1.08 × 10⁻³ Pa·s) and the aforementioned characteristic parameters, the source Reynolds number parameters and the target Reynolds number parameters are calculated respectively by substituting them into the Reynolds number formula; Targeted scaling is performed on each physical dimension of the motion test data. The linear velocity component is divided by the square root of the product of gravitational acceleration and characteristic length, the angular velocity component is multiplied by the characteristic length and then divided by the characteristic velocity, the acceleration component is multiplied by the characteristic length and then divided by the square of the characteristic velocity, and dimensionless quantities such as attitude angles are kept in their original values. Source dimensionless feature sets and target dimensionless feature sets are generated respectively, so that the features are decoupled from the geometric scale of the submersible and the absolute parameters of the flow field in a physical sense. The two feature sets are projected onto a unified feature space, and the two-sample Kolmogorov-Smirnov (KS) test method is used to perform univariate KS tests on 12 dimensions. If the p-value of all dimensions is greater than 0.05, the decoupling consistency verification is deemed to have passed, confirming that dimensionless transformation effectively removes the interference of geometric scale and flow field parameters.

[0045] In this embodiment, a dimensionless transformation driven by both Froude number and Reynolds number criteria is used to map the original motion data of heterogeneous submersibles to a feature space with consistent physical meaning, making the hydrodynamic response characteristics of platforms at different scales comparable. The decoupling consistency verification process ensures that the dimensionless features retain only the essential hydrodynamic information, effectively eliminating the interference of geometric parameters and the absolute dimensions of the flow field, while avoiding feature distribution shifts caused by scale effects, thus improving the physical rationality of cross-platform knowledge transfer and the model's generalization ability.

[0046] In some embodiments, determining the similarity parameter characterizing the hydrodynamic essential similarity between the source submersible and the target submersible based on the distribution correlation of the source dimensionless feature set and the target dimensionless feature set in the dimensionless feature space includes: Gaussian kernel density estimation is performed on all feature points of the source dimensionless feature set and the target dimensionless feature set respectively. The feature distribution is fitted by smoothing kernel function and bandwidth parameter to generate corresponding source feature distribution model and target feature distribution model. Based on the difference measure between the source feature distribution model and the target feature distribution model, the relative entropy of the distribution is determined to generate a distribution difference representation; The distribution difference representation is input into a linear mapping function based on historical hydrodynamic similarity to convert the distribution difference representation into the similarity parameter.

[0047] It is understandable that Gaussian kernel density estimation is a nonparametric probability density estimation method that generates a continuous and smooth probability density surface by applying a Gaussian kernel function to each feature point and superimposing the integrals. It is used to characterize the overall distribution of feature points in the dimensionless feature space. The smoothing kernel function is a kernel function in the form of a standard Gaussian function. Its output value decreases exponentially with increasing distance from the center point, ensuring the continuity and physical rationality of the density estimation. The bandwidth parameter is a key scalar that controls the smoothness of the Gaussian kernel. Too small a bandwidth will cause false peaks in the density estimation, while too large a bandwidth will mask the details of the true distribution. The bandwidth parameter is adaptively calculated based on the Silverman rule of thumb, combined with the feature dimension and sample size. The feature distribution is a statistical representation of the joint probability of each dimension of a dimensionless feature set in the feature space, reflecting the inherent laws of the hydrodynamic response of a submersible. The source feature distribution model is a probability density function model generated by Gaussian kernel density estimation of the source dimensionless feature set, which fully describes the statistical characteristics of the hydrodynamic response of the source submersible. The target feature distribution model is a probability density function model generated from the dimensionless feature set of the target through the same process; Difference measures are mathematical tools used to quantify the degree of deviation between two probability distributions; The relative entropy of the distribution is the physical expression of the Kullback-Leibler divergence. It is defined as the expected value of the logarithm of the ratio of the source distribution probability density function to the target distribution probability density function under the source distribution. It is used to measure the amount of information loss when approximating the source distribution with the target distribution. The distribution difference characterization is a non-negative scalar value calculated from relative entropy, and its magnitude directly reflects the degree of deviation between the source and target feature distributions; The linear mapping function based on historical hydrodynamic similarity is a monotonically decreasing linear function calibrated by multiple submersibles with known hydrodynamic similarity relationships on experimental data. Its input is a distribution difference representation, and the output is truncated and limited to the interval between 0 and 1 to ensure that the similarity parameter has a clear physical meaning and interpretability.

[0048] In practice, firstly, Gaussian kernel density estimation is performed on all sample points of the source dimensionless feature set in a 12-dimensional dimensionless feature space. A Gaussian kernel is constructed centered on each sample point, and the bandwidth parameter is calculated according to the Silverman rule. Where h is the Gaussian kernel bandwidth, used to control the smoothness of the kernel function. d is the sample standard deviation, which is the median of the standard deviations of each dimension of the 12-dimensional feature; d is the feature dimension, d=12; n is the number of samples participating in the kernel density estimation.

[0049] All Gaussian kernels are superimposed and normalized to generate a continuous source feature distribution probability density function model; simultaneously, the same kernel density estimation process is performed on the target dimensionless feature set to generate the target feature distribution probability density function model; secondly, the relative entropy between the two distribution models is calculated: 10,000 uniformly distributed Monte Carlo sampling points are generated in the feature space. , Let M be the total number of Monte Carlo sampling points, and let M be the j-th sampling point. Calculate the probability density values ​​of the source and target distributions for each sampling point, and substitute them into the discrete approximation formula for q: in, It is a Monte Carlo estimate of the KL divergence (relative entropy), used to quantify the degree of difference between the source distribution P and the target distribution Q, where P is the source feature distribution and Q is the target feature distribution; Is the source distribution density function in The estimated value at that location; Is the target distribution density function in The estimated value at that location; , is a numerical stability constant used to avoid logarithmic divergence caused by a density value of zero, where xi is the sampling point.

[0050] The summation yields the distribution difference characterization value; finally, the distribution difference characterization value is input into a pre-calibrated linear mapping function: Where k is a proportionality coefficient calibrated using historical hydrodynamic test data. T is the calibration threshold, ensuring that when When the distributions are completely uniform, λ=1; ,For exampleT =0.5, when the difference is extremely large, λ=0, boundary truncation ensures After boundary truncation, the final similarity parameter λ is output.

[0051] In this embodiment, a probability distribution model of the source and target submersibles in the dimensionless feature space is objectively constructed by Gaussian kernel density estimation, avoiding subjective assumptions about the distribution pattern. Relative entropy is used as a difference measure to accurately characterize the intrinsic deviation between the two distributions from an information theory perspective. Its asymmetric characteristics fit the physical logic of hydrodynamic knowledge transfer from the source to the target. Combined with the linear mapping function calibrated by historical hydrodynamic experiments, the abstract distribution differences are transformed into similarity parameters with clear physical meaning, which can truly reflect the essential similarity between the source and target submersibles at the level of hydrodynamic response mechanism. This enables the knowledge distillation process to dynamically adjust the intensity of knowledge transfer based on the hydrodynamic similarity between platforms, enhancing the learning relevance of the student network to the disturbed motion characteristics of the target submersible.

[0052] In some embodiments, the teacher network includes a first input layer, a first feature encoding module and a motion prediction module connected to the first input layer, wherein inputting the target dimensionless feature set into the teacher network with fixed parameters to obtain the intermediate layer features and interference parameter representations output by the teacher network includes: The target dimensionless feature set is transmitted to the first feature encoding module and the motion prediction module respectively through the first input layer; The first feature encoding module performs feature extraction and dimensionality reduction on the target dimensionless feature set to generate the intermediate layer features. The motion prediction module performs interference response modeling on the target dimensionless feature set to generate the interference parameter representation. By adjusting the number of channels, the intermediate layer features and the interference parameter representations are dimensionally aligned and output.

[0053] Understandably, the first input layer is the initial data distribution unit of the teacher network. After receiving the target dimensionless feature set, it generates two identical feature streams, which are fed to the first feature encoding module and the motion prediction module, respectively. The first feature encoding module is a hierarchical feature extraction subnetwork consisting of multiple one-dimensional convolutional layers, batch normalization layers, and nonlinear activation functions. It captures the spatiotemporal correlation patterns of hydrodynamic disturbance response through convolutional kernel sliding and achieves high-dimensional feature compression through global pooling. The motion prediction module is a parametric regression subnetwork composed of cascaded fully connected layers, which focuses on mapping input features to the parameter space composed of key physical quantities of hydrodynamic disturbances. The intermediate layer features are high-dimensional feature vectors output by the first feature encoding module, which encapsulate a deep abstract representation of hydrodynamic disturbances during the disturbed motion of the target submersible. The disturbance parameter representation is a low-dimensional vector output by the motion prediction module, which explicitly encodes core hydrodynamic parameters directly related to the disturbance response, such as the additional mass coefficient and fluid damping coefficient, and is used to characterize the key physical quantities of the submersible's hydrodynamic disturbance response under disturbed conditions. Channel number adjustment is an operation that maps the feature dimensions through a learnable linear projection layer (fully connected layer); dimension alignment is to make the intermediate layer features and the interference parameter representations have the exact same vector dimensions to meet the structural constraints of subsequent feature fusion.

[0054] In actual implementation, firstly, each 12-dimensional sample vector from the target dimensionless feature set is input into the first input layer. This layer internally replicates the data to generate two identical feature streams. The first feature stream is then fed into the first feature encoding module, sequentially passing through the first convolutional layer (64 kernels, kernel size 3, stride 1), a batch normalization layer, and a ReLU activation layer to generate a 64-dimensional temporal feature map. Next, the feature extraction is deepened layer by layer through the second convolutional layer (128 kernels) and the third convolutional layer (256 kernels), with batch normalization and ReLU applied after each layer. Finally, a global average pooling layer is used to... Temporal features are compressed into 256-dimensional vectors and used as intermediate layer feature outputs. The second feature stream is simultaneously fed into the motion prediction module: first, it enters the first fully connected layer (128 neurons, ReLU activation), which maps the 12-dimensional input to a 128-dimensional intermediate representation; then, it passes through the second fully connected layer (32 neurons, linear activation) to output a 32-dimensional interference parameter representation; it is then projected to 256 dimensions through a dedicated fully connected layer (32×256 weight matrix). Finally, the 256-dimensional intermediate layer features and the 256-dimensional aligned interference parameter representation are used as parallel output results and transmitted to the subsequent similarity attention mechanism module.

[0055] In this embodiment, the teacher network adopts a dual-branch parallel architecture, enabling the intermediate layer features and interference parameter representations to collaboratively characterize the disturbed motion characteristics of the target submersible from two dimensions: implicit feature abstraction and explicit physical parameters, respectively. The two complement each other, fully preserving the representational information of hydrodynamic interference. The channel number adjustment operation achieves dimensional unification of heterogeneous features through learnable linear projection, avoiding redundant noise introduced by zero padding and information loss caused by direct truncation. This allows the teacher network with fixed parameters to generate intermediate representations with consistent dimensions and clear physical meaning for target submersibles with heterogeneous geometric scales and configurations. This enhances the accuracy and relevance of hydrodynamic physics knowledge transfer during knowledge distillation and effectively supports the student network in accurately learning the disturbed motion laws of the target platform.

[0056] In some embodiments, the first feature encoding module includes a three-layer convolutional layer structure with the number of channels increasing sequentially, used to extract high-order features of hydrodynamic disturbance response; The motion prediction module includes a first fully connected layer and a second fully connected layer connected in sequence. The process of training a teacher network using the source dimensionless feature set and the corresponding actual motion state data of the source submersible to generate knowledge distillation signals includes: The first feature encoding module extracts and reduces the dimensionality of the source dimensionless feature set to generate teacher feature encoding output. The first fully connected layer performs dimensionality reduction mapping on the teacher feature encoding output to generate a dimensionally compressed feature representation. The second fully connected layer maps the dimensionally compressed feature representation to the interference parameter space to generate the interference parameter representation. The mean square error loss value is determined based on the teacher feature encoding output, the interference parameter representation, and the actual motion state data of the source submersible. Based on the mean squared error loss value, the teacher network parameters are optimized by stochastic gradient descent, and the parameters of the trained teacher network are fixed.

[0057] It is understandable that the three-layer convolutional structure with the number of channels increasing sequentially is a hierarchical feature extraction unit composed of three consecutive one-dimensional convolutional layers. The number of convolutional kernels in each layer increases sequentially, for example, 64, 128, and 256. By expanding the receptive field and the number of feature channels layer by layer, the system captures hierarchical features from local instantaneous response to global temporal pattern in hydrodynamic disturbances. The higher-order characteristics of hydrodynamic disturbance response refer to the abstract representations that are implicit after nonlinear convolution transformation and are closely related to the physical mechanism of fluid disturbance, such as the frequency coupling characteristics of vortex-induced vibration and the unsteady added mass effect, which are deep modes that go beyond the original motion parameters. The first fully connected layer and the second fully connected layer, which are connected in sequence, constitute the parameter regression path of the motion prediction module. The first fully connected layer realizes the compression mapping from high-dimensional features to compact intermediate representation in order to focus on the key modes of hydrodynamic disturbance. The second fully connected layer completes the directional projection to the preset disturbance parameter space. The teacher feature encoding output is a fixed-dimensional feature vector generated by the first feature encoding module after global pooling, which condenses the deep abstract information of hydrodynamic disturbance in the disturbed motion of the source submersible; The dimension-compressed feature representation is the intermediate vector output by the first fully connected layer, which is used to capture the core physical features of the hydrodynamic disturbance response. Its dimension is significantly lower than that of the teacher feature encoding output, thus preserving the core discriminative information of the disturbance response. The disturbance parameter space is a low-dimensional vector space composed of parameters with clear hydrodynamic physical meaning, such as the added mass coefficient, fluid damping coefficient, and restoring force coefficient. The mean squared error loss value is the sample mean of the squared difference between the interference parameters, which are represented by the motion state prediction output after dimensional adaptation, and the corresponding dimension of the source submersible's actual motion state data. It is used to quantify the teacher network prediction bias. Stochastic gradient descent is an optimization algorithm that uses mini-batch samples to calculate the loss gradient and iteratively updates the network parameters along the negative gradient direction. It combines momentum terms and learning rate decay strategies to improve convergence stability and generalization ability. Fixed parameters of the teacher network after training is completed refer to setting the weights and biases of all layers of the network to an untrainable state after training convergence, so as to ensure that it serves as a stable and reliable source of knowledge in the subsequent distillation process.

[0058] In practice, firstly, the source dimensionless feature set and the corresponding source submersible motion state data, which have undergone the same dimensionless processing, are divided into training and validation sets in an 8:2 ratio. The teacher network is initialized, with the first feature encoding module sequentially configured with convolutional layers (64 channels, kernel size 3), (128 channels, kernel size 3), and (256 channels, kernel size 3), followed by batch normalization and ReLU activation, and ending with a global average pooling layer. The motion prediction module is configured with a first fully connected layer (128 neurons, ReLU activation) and a second fully connected layer (32-dimensional neurons, linear activation), outputting a 32-dimensional representation of hydrodynamic parameters (i.e., interference parameters). Simultaneously, an independent motion prediction branch is added at the end of the teacher network, consisting of a first fully connected layer (128 neurons) and a second fully connected layer (12 neurons, linear activation), outputting a 12-dimensional motion state prediction value.

[0059] The training set samples are input into the network in batches of 64. The first feature encoding module generates a 256-dimensional teacher feature encoding output, which is then fed into the motion prediction module to generate a 64-dimensional compressed feature representation. This 64-dimensional feature representation is then passed through the second fully connected layer to output a 32-dimensional motion state prediction value for calculating the loss. The 32-dimensional interference parameter representation output from the second fully connected layer is mapped to 12 dimensions through a linear projection layer and used as the teacher network's prediction output for the motion state. The sum of squares of the differences between the prediction output and the corresponding actual motion state data for each dimension is calculated, and then averaged over all samples in the batch to obtain the mean squared error loss value. A stochastic gradient descent optimizer with a driving force of (0.9) is used, with an initial learning rate of 0.001. Every 5 training epochs, if the loss does not decrease significantly (e.g., if the relative change is less than 0.1%), the learning rate is reduced to 0.9 times. Training continues until the loss shows no improvement for 10 consecutive epochs. After training terminates, all parameter weights and biases of the teacher network are saved, and all layers of the network are set to a frozen state to ensure that the teacher network output strictly maintains the stable state after training convergence during subsequent knowledge distillation.

[0060] In this embodiment, the high-order hydrodynamic feature extraction and motion state regression tasks are organically integrated through the dual-path collaborative design of feature encoding and motion prediction in the teacher network: the increasing channel number structure of the convolutional layer ensures the full capture of multi-level physical patterns of the disturbance response, and the fully connected regression path accurately maps abstract features to a parameter space with clear hydrodynamic significance; the mean squared error loss function directly constrains the consistency between the predicted output and the physical measured data, driving the network to deeply learn the intrinsic laws of the hydrodynamic response of the source submersible; after training, the parameter solidification operation makes the teacher network a stable and reliable knowledge carrier, and its output teacher feature encoding output and disturbance parameter representation completely characterize the essence of hydrodynamic disturbance from two dimensions: implicit feature abstraction and explicit physical parameters, respectively, which can support the student network to accurately learn and generalize the disturbed motion characteristics of the target platform.

[0061] In some embodiments, the similarity attention mechanism module includes an attention weight generation unit, a feature weighted fusion unit, and a distillation signal output unit; The step of inputting the intermediate layer features, the interference parameter representation, and the similarity parameter into the similarity attention mechanism module to generate a knowledge distillation signal includes: The attention weight generation unit expands the similarity parameter into a weight vector that matches the feature dimension. The weighted feature fusion unit performs a dot product between the weight vector and the intermediate layer features and the interference parameter representation to generate a weighted feature. The distillation signal output unit performs feature aggregation on the weighted features to generate a knowledge distillation signal.

[0062] Understandably, the similarity attention mechanism module is a dynamic feature modulation unit that integrates hydrodynamic physical similarity information, and its output directly determines the strength and direction of knowledge transfer. The attention weight generation unit is a scalar expander consisting of a single-layer fully connected network and a sigmoid activation function, which maps the scalar similarity parameter into a continuous weight vector that is strictly matched with the feature dimension. The weight vector is a vector whose dimension is completely consistent with the intermediate layer features and interference parameters. The value of each element is limited to the range of 0 to 1, representing the contribution weight of the corresponding feature channel in knowledge transfer. The feature weighted fusion unit is a feature modulator that performs element-wise multiplication and addition operations. It performs differential scaling and fusion of two types of features through weight vectors. The weighted feature is a fused feature vector obtained by adding the intermediate layer features and the interference parameter representation after being modulated by the weight vector respectively, while retaining implicit hydrodynamic mode and explicit physical parameter information. The distillation signal output unit is a feature stabilizer containing a layer normalization layer, used to eliminate scale fluctuations in weighted features and enhance distribution stability; the knowledge distillation signal is a guiding vector generated after aggregation processing, with the same dimension as the original features, which carries both the hydrodynamic knowledge of the source submersible and is dynamically adapted to the characteristics of the target platform through similarity parameters.

[0063] In actual execution, firstly, in the attention weight generation unit, the scalar similarity parameter is input into a fully connected layer (without bias term) containing 256 output neurons. After processing by the Sigmoid activation function, a 256-dimensional weight vector is generated, ensuring that each element value is strictly within the range of 0 to 1. Secondly, in the feature weighting and fusion unit, the weight vector is multiplied element-wise with the 256-dimensional intermediate layer features to generate the first weighted feature. Simultaneously, the same weight vector is multiplied element-wise with the 256-dimensional interference parameter representation to generate the second weighted feature. The first weighted feature and the second weighted feature are added element-wise to form the 256-dimensional weighted feature. Finally, in the distillation signal output unit, layer normalization is performed on the weighted features: the mean and standard deviation of the vector are calculated, zero-mean unit variance standardization is performed, and affine transformation is performed through learnable scaling and offset parameters to output the final 256-dimensional knowledge distillation signal.

[0064] In this embodiment, the similarity attention mechanism module transforms the hydrodynamic similarity parameters into channel-level dynamic weights, enabling the knowledge distillation process to have physically interpretable adaptive adjustment capabilities: when the hydrodynamic similarity between the source and target submersibles is high, the weight vector as a whole approaches 1, fully preserving the hydrodynamic knowledge of the source platform; when the similarity is low, the weight vector automatically decays the corresponding channel contribution, effectively suppressing the risk of negative migration caused by platform heterogeneity; the weighted fusion of intermediate layer features and interference parameter representations enables the distillation signal to simultaneously fuse implicit feature abstraction and explicit physical parameter information, enhancing the integrity and physical consistency of knowledge representation; the layer normalization aggregation operation further improves the stability of signal distribution and avoids scale imbalance during gradient propagation.

[0065] In some embodiments, the student network includes a second input layer, a second feature encoding module, and the lightweight adaptation layer connected in sequence; The second feature encoding module has the same structure as the first feature encoding module of the teacher network, and the lightweight adaptation layer includes a residual bias compensation unit; The step of inputting the target dimensionless feature set into a student network containing a lightweight adaptation layer, and training the student network based on the knowledge distillation signal and the actual motion state data of the target submersible, includes: The target dimensionless feature set is transmitted to the second feature encoding module through the second input layer; The second feature encoding module extracts and reduces the dimensionlessness of the target feature set to generate student feature encoding output. The lightweight adaptation layer is used to perform a full connection on the student feature encoding output to generate a residual mapping; Based on the residual mapping, bias compensation features are generated through feature addition operations; The bias compensation features are concatenated with the knowledge distillation signal to generate a training target. Based on the training objective and the actual motion state data of the target submersible, the parameters of the student network are optimized using gradient descent.

[0066] Understandably, the student network is a lightweight neural network designed specifically for target submersibles. Its overall structure includes a second input layer, a second feature encoding module, a lightweight adaptation layer, and an implicit regression prediction layer, with a significantly lower number of parameters than the teacher network. The second input layer is the data entry unit of the student network, responsible for losslessly transmitting the target dimensionless feature set to the second feature encoding module. The second feature encoding module adopts a three-layer convolutional architecture that is completely consistent with the first feature encoding module of the teacher network, with the number of channels being 64, 128, and 256 respectively. It is used to extract the hierarchical spatiotemporal features of the disturbed motion of the target submersible, but its parameters are independently initialized and participate in the entire training process. The lightweight adaptation layer is a residual compensation unit composed of an activation function and a single hidden layer fully connected structure, which is dedicated to generating corrections for the heterogeneity of the source-target submersible. The residual bias compensation unit is the core functional module of the lightweight adaptation layer. By learning the residual mapping and superimposing it on the student feature encoding output, it achieves explicit compensation for residual physical biases that are not represented by Froude number and Reynolds number. The student feature encoding output is a fixed-dimensional feature vector generated by the second feature encoding module after global average pooling, which represents the preliminary abstract features of the disturbed motion of the target submersible; The residual mapping is a low-dimensional vector output by the lightweight adaptation layer, which is linearly up-dimensional and used to correct systematic biases in the student feature encoding output. The deviation compensation feature is a fusion feature obtained by adding the student feature encoding output and the residual mapping after dimensionality increase element by element. It simultaneously retains the original feature information and the compensation amount, and is used to compensate for the residual deviation caused by the heterogeneity between the source submersible and the target submersible. The training objective is to use the intermediate feature vector formed by concatenating the bias compensation features and the knowledge distillation signal in the feature dimension as the input to the student network regression prediction layer, organically integrating the target platform's own compensation features and the source platform's hydrodynamic knowledge. Gradient descent optimization is the process of calculating the joint loss function and updating all trainable parameters of the student network through backpropagation based on the difference between the predicted motion state output of the student network's regression prediction layer and the actual motion state data of the target submersible.

[0067] In actual implementation, firstly, each sample of the target dimensionless feature set is input into the second input layer. The data flows through the second feature encoding module: sequentially through three one-dimensional convolutional layers (64 / 128 / 256 channels, kernel size 3, stride 1), a batch normalization layer, and a ReLU activation layer, finally generating a 256-dimensional student feature code output through global average pooling. Secondly, the student feature code output is fed into a lightweight adaptation layer: first, it undergoes a non-linear transformation using the ReLU activation function, and then is input into a single hidden fully connected layer (256-dimensional input, 64-dimensional hidden layer, 64-dimensional output) to generate a 64-dimensional residual mapping. The 64-dimensional residual mapping is then expanded into a 256-dimensional vector through a linearly upgraded fully connected layer (weight matrix 64×256, no activation function), and combined with the original 256-dimensional student feature code. The code outputs are added element-wise to generate a 256-dimensional bias compensation feature. The 256-dimensional bias compensation feature is then concatenated with the 256-dimensional knowledge distillation signal along the feature dimension to form a 512-dimensional training target. The training target is input into the regression prediction layer implicit in the student network (consisting of two fully connected layers: 512-dimensional → 128-dimensional → 12-dimensional, with the last layer being linear activation), generating a 12-dimensional motion state prediction output. The mean squared error loss between this prediction output and the actual motion state data corresponding to the target submersible (after the same dimensionless processing) is calculated. Using the Adam optimizer (learning rate 0.001, batch size 32), all trainable parameters of the second feature encoding module, the lightweight adaptation layer, and the regression prediction layer are iteratively updated using the backpropagation algorithm based on this loss until the validation set loss converges.

[0068] In this embodiment, the lightweight adaptation layer explicitly models and compensates for residual physical deviations caused by the heterogeneity of the source and target submersibles, which are not covered by hydrodynamic similarity criteria, through residual mapping and feature addition operations. This makes the student network feature representation more accurately match the actual hydrodynamic characteristics of the target platform. The feature concatenation of deviation compensation features and knowledge distillation signals enables the student network to simultaneously integrate the target platform's own compensation information and the source platform's hydrodynamic knowledge during training, forming a dual guidance mechanism. The regression prediction layer generates motion state predictions based on the fused features and optimizes the network parameters to converge towards fitting the actual motion law of the target submersible through gradient descent. This design enables the student network to construct a disturbed motion model with a clear physical mechanism and high predictive reliability, relying only on a small amount of target submersible experimental data, effectively solving the modeling dilemma caused by data scarcity for small or new submersibles.

[0069] In some embodiments, the lightweight adaptation layer includes a single hidden layer fully connected structure and an activation function, wherein the number of hidden layer nodes in the single hidden layer fully connected structure is one-quarter of the input dimension; The step of performing a fully connected operation on the student feature encoding output through the lightweight adaptation layer to generate a residual mapping includes: The activation function is used to perform a non-linear transformation on the student feature encoding output to generate intermediate features. The residual mapping is generated based on the intermediate features through the single hidden layer fully connected structure. The step of generating bias compensation features based on the residual mapping through feature addition operations includes: Based on the vector dimension of the intermediate features, the residual mapping is linearly upgraded, and the upgraded residual mapping is added to the student feature encoding output to generate the deviation compensation feature.

[0070] It is understandable that a single hidden layer fully connected structure is a linear mapping unit consisting of an input layer, a single hidden layer, and an output layer. The number of neurons in the hidden layer is strictly set to one-quarter of the dimension of the input features in order to achieve significant compression of the number of parameters. The activation function is a mathematical operation unit that introduces non-linear expressive power. It adopts the modified linear unit (ReLU) function, and its output is the maximum value of the input value and zero. The number of hidden layer nodes being one-quarter of the input dimension means that the number of hidden layer neurons and the dimension of the input feature vector are in a 1:4 ratio. For example, when the input is 256-dimensional, the hidden layer is set to 64 neurons. Nonlinear transformation is achieved by performing element-wise operations on the input features using activation functions, thereby breaking linear constraints and enhancing the model's ability to fit complex deviation patterns. Intermediate features are feature vectors with the same dimensions as the input, generated after the activation function processes the student feature encoding output. The residual mapping is a low-dimensional vector output by a single hidden layer fully connected structure, with a dimension one-quarter of the dimension of the intermediate feature. Its numerical distribution represents the amount of residual physical bias that needs to be compensated. Linear dimensionality upscaling is an operation that projects low-dimensional residual maps to a high-dimensional space through a fully connected layer without activation functions, with the target dimension of the upscaling strictly aligned with the intermediate feature dimensions. The feature addition operation is a vector operation that adds the element-wise residual mapping after dimensionality increase to the student feature encoding output; The deviation compensation feature is a fusion vector generated by feature addition operations. It simultaneously retains the original feature information and the targeted compensation amount, and is specifically used to correct heterogeneous deviations that are not covered by hydrodynamic similarity criteria.

[0071] In actual execution, firstly, the 256-dimensional student feature encoding output is input into a lightweight adaptation layer, and then subjected to an element-wise nonlinear transformation using the ReLU activation function, with negative values ​​set to zero and positive values ​​retained, generating a 256-dimensional intermediate feature. Secondly, the intermediate feature is fed into a single hidden layer fully connected structure containing 64 hidden neurons (256 ÷ 4) with a weight matrix dimension of 256 × 64. After linear transformation and ReLU activation, it outputs a 64-dimensional residual mapping. Subsequently, linear dimensionality increase is performed: the 64-dimensional residual mapping is input into a fully connected layer without bias and activation function (weight matrix dimension 64 × 256), and expanded into a 256-dimensional increased residual vector through matrix multiplication. Finally, feature addition is performed: the 256-dimensional increased residual vector is added element-wise to the original 256-dimensional student feature encoding output to generate a 256-dimensional bias compensation feature. This feature retains the target submersible's own motion characteristics and explicitly superimposes compensation for source-target heterogeneity.

[0072] In this embodiment, the strict proportional constraint on the number of hidden layer nodes ensures compensation capability while suppressing model complexity, effectively avoiding the risk of overfitting under small sample training. Linear dimensionality increase and feature addition operations ensure that the compensation amount and the original features are strictly aligned in terms of physical dimensions and spatial scale, giving the deviation compensation process a clear physical meaning of vector superposition. This design enables the student network to explicitly separate and correct heterogeneous deviations that the hydrodynamic similarity criterion fails to represent, such as differences in local flow field disturbances and small configuration deviations caused by manufacturing tolerances, thereby enhancing the model's adaptation accuracy to the actual hydrodynamic characteristics of the target submersible while maintaining the network's lightweight characteristics.

[0073] In some embodiments, the disturbance motion prediction model for deploying the target submersible based on the trained student network includes: The trained student network is subjected to channel pruning to obtain the disturbed motion prediction model. The network structure and quantization weights of the disturbed motion prediction model are loaded into the embedded system of the target submersible and deployed through the model loading interface; The real-time data stream provided by the sensor system of the target submersible is converted into dimensionless features and added to the target dimensionless feature set; The target dimensionless feature set is input into the disturbed motion prediction model, and the disturbed motion prediction value is generated through forward propagation.

[0074] It is understandable that channel pruning is a structural optimization process that removes redundant channels and reconstructs network connections based on the importance of the channel weights in the convolutional layer, in order to reduce the computational load without significantly impairing the model's expressive power. The disturbed motion prediction model is a lightweight student network that has undergone channel pruning and weight quantization, and is designed specifically for embedded resource-constrained environments. Embedded systems are dedicated computing platforms carried by target submersibles, with limited computing resources, storage space, and power consumption budgets; The model loading interface is a standardized software interface pre-built in the embedded operating system, used to parse the model structure definition file and weight parameter file and initialize the inference engine; The sensor system consists of an inertial measurement unit, a Doppler log, a depth sensor, etc., and continuously outputs a stream of raw motion state data at a fixed sampling frequency; The conversion of real-time data streams into dimensionless features refers to performing a dimensionless transformation process on each frame of raw sensor data, based on hydrodynamic similarity criteria using Froude number and Reynolds number, which is completely consistent with the training phase. Single-sample target dimensionless feature input specifically refers to a dimensionless feature vector generated from a single sensor sampling, whose dimension is strictly aligned with the training features, and serves as the input unit for real-time inference of the model; Forward propagation is the reasoning process by which a disturbed motion prediction model, based on input features, sequentially executes calculations in each network layer and outputs prediction results.

[0075] In actual implementation, firstly, channel pruning is performed on the trained student network: for each convolutional layer of the second feature encoding module, the L1 norm of the weights of each output channel is calculated and sorted, the 30% of channels with the smallest norm are removed, and the input channel connections of subsequent layers are adjusted simultaneously to reconstruct a simplified network structure; then, all floating-point weights of the pruned network are quantized to 8 bits, mapping the weights to the integer range of 0-255, and generating a structure definition file and a quantization weight file; secondly, in the target submersible embedded system (such as ARM-based...)... During the startup phase of the Cortex-A78 computing unit, the aforementioned files are loaded through a pre-configured model loading interface, such as the TensorRT serialization engine or a custom C++ inference library. The inference engine is initialized and runtime memory is allocated. During runtime, the sensor system outputs raw motion data streams at a frequency of 100 Hz. The embedded preprocessing module calculates in real time according to the dimensionless formula based on parameters such as the characteristic length and characteristic velocity of the target submersible, generating a 12-dimensional single-sample dimensionless feature vector. This vector is directly input into the loaded disturbed motion prediction model. The model performs forward propagation operations such as convolution, activation, and full connection, and outputs a 12-dimensional dimensionless motion prediction value. The prediction value is de-dimensionalized, multiplied by the corresponding physical reference quantity, and then sent to the motion control module for real-time trajectory correction and attitude stabilization.

[0076] In this embodiment, channel pruning and weight quantization are optimized together to reduce the computational complexity and storage footprint of the model, ensuring that the prediction model is strictly adapted to the resource constraints and power consumption requirements of the embedded system. The hydrodynamic similarity criteria and dimensionless process established in the training phase are reused throughout the deployment phase to ensure that the input feature distribution is strictly consistent with the model training distribution, fundamentally guaranteeing the physical reliability and cross-condition stability of the prediction results. The single-sample real-time processing mechanism avoids data accumulation delays and realizes an end-to-end low-latency inference closed loop from sensor acquisition to motion prediction. This deployment scheme enables the disturbed motion prediction model to run stably for a long time on the resource-constrained submersible embedded platform, effectively enhancing the submersible's operational safety, trajectory tracking accuracy, and mission execution robustness in harsh sea conditions such as strong currents and turbulence.

[0077] The method for modeling disturbed motion of a submersible based on hydrodynamic similarity guidance provided in this application can be executed by a device for modeling disturbed motion of a submersible based on hydrodynamic similarity guidance. This application uses the example of a device for modeling disturbed motion of a submersible based on hydrodynamic similarity guidance executing the method for modeling disturbed motion of a submersible based on hydrodynamic similarity guidance to illustrate the device for modeling disturbed motion of a submersible based on hydrodynamic similarity guidance provided in this application.

[0078] This application also provides a device for modeling disturbed motion of a submersible based on hydrodynamic similarity.

[0079] like Figure 2 As shown, the submersible disturbed motion modeling device based on hydrodynamic similarity guidance includes: The acquisition module 210 is used to acquire the actual motion state data of the source submersible and the target submersible, as well as the motion test data under disturbed conditions, and to perform dimensionless transformation based on the hydrodynamic similarity criterion to obtain the corresponding source dimensionless feature set and target dimensionless feature set. The hydrodynamic similarity criterion is constructed based on the Froude number and the Reynolds number. The first processing module 220 is used to determine a similarity parameter that characterizes the hydrodynamic essential similarity between the source submersible and the target submersible based on the distribution correlation of the source dimensionless feature set and the target dimensionless feature set in the dimensionless feature space. The second processing module 230 is used to train the teacher network using the source dimensionless feature set and the corresponding actual motion state data of the source submersible, and to fix the parameters of the trained teacher network. The third processing module 240 is used to input the target dimensionless feature set into the teacher network with fixed parameters to obtain the intermediate layer features and interference parameter representations output by the teacher network. The fourth processing module 250 is used to input the intermediate layer features, the interference parameter representation and the similarity parameter into the similarity attention mechanism module to generate a knowledge distillation signal; The fifth processing module 260 is used to input the target dimensionless feature set into a student network containing a lightweight adaptation layer, train the student network based on the knowledge distillation signal and the actual motion state data of the target submersible, and deploy a disturbed motion prediction model of the target submersible according to the trained student network. The lightweight adaptation layer is used to compensate for residual deviations caused by the heterogeneity between the source submersible and the target submersible that are not characterized by hydrodynamic similarity criteria.

[0080] The submersible motion modeling device based on hydrodynamic similarity provided in this application maps heterogeneous submersible motion data to a physically consistent dimensionless feature space through hydrodynamic similarity criteria. It accurately quantifies the essential similarity of hydrodynamics based on feature distribution correlation and drives a similarity attention mechanism to generate knowledge distillation signals adapted to the target platform, enabling the student network to efficiently transfer hydrodynamic knowledge from the source platform. The lightweight adaptation layer accurately compensates for residual biases not represented by Froude and Reynolds numbers through a single hidden layer structure and dimensionality increase operations. This reduces the amount of motion test data required for target submersible modeling, effectively overcoming the dilemma of building reliable prediction models for small or new submersibles due to high test costs and scarce historical data. The submersible can achieve high-precision trajectory tracking and intelligent anti-disturbance control in complex ocean disturbance environments, enabling the establishment of reliable prediction models for small or new submersibles with lower test costs and less data, thus improving the accuracy of motion prediction in disturbance environments such as strong currents and turbulence.

[0081] The device for modeling disturbed motion of a submersible based on hydrodynamic similarity guided by this application embodiment can realize the various processes implemented in the above embodiments of the method for modeling disturbed motion of a submersible based on hydrodynamic similarity guided by hydrodynamic similarity. To avoid repetition, it will not be described again here.

[0082] The embodiments of this application have been described above with reference to the accompanying drawings. However, this application is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of this application without departing from the spirit and scope of the claims, and all of these forms are within the protection scope of this application.

[0083] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "illustrative embodiment," "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.

[0084] 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.

Claims

1. A method for modeling disturbed motion of a submersible based on hydrodynamic similarity guidance, characterized in that, include: The actual motion state data of the source submersible and the target submersible, as well as the motion test data under disturbed conditions, are obtained. Based on the hydrodynamic similarity criterion, dimensionless transformations are performed to obtain the corresponding source dimensionless feature set and target dimensionless feature set. The hydrodynamic similarity criterion is constructed based on Froude number and Reynolds number. Based on the distribution correlation of the source dimensionless feature set and the target dimensionless feature set in the dimensionless feature space, a similarity parameter characterizing the hydrodynamic essential similarity between the source submersible and the target submersible is determined. The teacher network is trained using the source dimensionless feature set and the corresponding actual motion state data of the source submersible, and the parameters of the trained teacher network are fixed. The target dimensionless feature set is input into the teacher network with fixed parameters to obtain the intermediate layer features and interference parameter representations output by the teacher network. The intermediate layer features, the interference parameter representation, and the similarity parameter are input into the similarity attention mechanism module to generate a knowledge distillation signal; The target dimensionless feature set is input into a student network containing a lightweight adaptation layer, and the student network is trained based on the knowledge distillation signal and the actual motion state data of the target submersible. The perturbed motion prediction model of the target submersible is deployed according to the trained student network. The lightweight adaptation layer is used to compensate for the residual deviation caused by the heterogeneity between the source submersible and the target submersible that is not characterized by the hydrodynamic similarity criterion.

2. The method for modeling disturbed motion of a submersible based on hydrodynamic similarity guidance according to claim 1, characterized in that, The dimensionless transformation based on the hydrodynamic similarity criterion includes: Based on the relative strength of the interaction between inertial force and gravity in the hydrodynamic similarity criterion, the source Froude number parameter is generated according to the characteristic velocity data and characteristic length parameter of the source submersible, and the target Froude number parameter is generated according to the characteristic velocity data and characteristic length parameter of the target submersible. Based on the relative strength of inertial and viscous forces in the hydrodynamic similarity criterion, the source Reynolds number parameter is determined according to the fluid density constant, the characteristic velocity data and characteristic length parameter of the source submersible, and the target Reynolds number parameter is generated according to the fluid density constant, the characteristic velocity data and characteristic length parameter of the target submersible. Based on the source Froude number parameter, the target Froude number parameter, the source Reynolds number parameter, and the target Reynolds number parameter, a scaling transformation is performed on each dimension feature of the motion test data to generate the source dimensionless feature set and the target dimensionless feature set; The decoupling consistency between the source dimensionless feature set and the target dimensionless feature set in the feature space is verified.

3. The method for modeling disturbed motion of a submersible based on hydrodynamic similarity guidance according to claim 2, characterized in that, The step of determining similarity parameters characterizing the hydrodynamic similarity between the source submersible and the target submersible based on the distribution correlation of the source dimensionless feature set and the target dimensionless feature set in the dimensionless feature space includes: Gaussian kernel density estimation is performed on all feature points of the source dimensionless feature set and the target dimensionless feature set respectively. The feature distribution is fitted by smoothing kernel function and bandwidth parameter to generate corresponding source feature distribution model and target feature distribution model. Based on the difference measure between the source feature distribution model and the target feature distribution model, the relative entropy of the distribution is determined to generate a distribution difference representation; The distribution difference representation is input into a linear mapping function based on historical hydrodynamic similarity to convert the distribution difference representation into the similarity parameter.

4. The method for modeling disturbed motion of a submersible based on hydrodynamic similarity guidance according to claim 1, characterized in that, The teacher network includes a first input layer, a first feature encoding module and a motion prediction module connected to the first input layer. The step of inputting the target dimensionless feature set into the teacher network with fixed parameters to obtain the intermediate layer features and interference parameter representations output by the teacher network includes: The target dimensionless feature set is transmitted to the first feature encoding module and the motion prediction module respectively through the first input layer; The first feature encoding module performs feature extraction and dimensionality reduction on the target dimensionless feature set to generate the intermediate layer features. The motion prediction module performs interference response modeling on the target dimensionless feature set to generate the interference parameter representation. By adjusting the number of channels, the intermediate layer features and the interference parameter representations are dimensionally aligned and output.

5. The method for modeling disturbed motion of a submersible based on hydrodynamic similarity guidance according to claim 4, characterized in that, The first feature encoding module includes a three-layer convolutional layer structure with the number of channels increasing sequentially, used to extract high-order features of hydrodynamic disturbance response; The motion prediction module includes a first fully connected layer and a second fully connected layer connected in sequence. The process of training a teacher network using the source dimensionless feature set and the corresponding actual motion state data of the source submersible to generate knowledge distillation signals includes: The first feature encoding module extracts and reduces the dimensionality of the source dimensionless feature set to generate teacher feature encoding output. The first fully connected layer performs dimensionality reduction mapping on the teacher feature encoding output to generate a dimensionally compressed feature representation. The second fully connected layer maps the dimensionally compressed feature representation to the interference parameter space to generate the interference parameter representation. The mean square error loss value is determined based on the teacher feature encoding output, the interference parameter representation, and the actual motion state data of the source submersible. Based on the mean squared error loss value, the teacher network parameters are optimized by stochastic gradient descent, and the parameters of the trained teacher network are fixed.

6. The method for modeling disturbed motion of a submersible based on hydrodynamic similarity guidance according to claim 1, characterized in that, The similarity attention mechanism module includes an attention weight generation unit, a feature weighted fusion unit, and a distillation signal output unit; The step of inputting the intermediate layer features, the interference parameter representation, and the similarity parameter into the similarity attention mechanism module to generate a knowledge distillation signal includes: The attention weight generation unit expands the similarity parameter into a weight vector that matches the feature dimension. The weighted feature fusion unit performs a dot product between the weight vector and the intermediate layer features and the interference parameter representation to generate a weighted feature. The distillation signal output unit performs feature aggregation on the weighted features to generate a knowledge distillation signal.

7. The method for modeling disturbed motion of a submersible based on hydrodynamic similarity guidance according to claim 1, characterized in that, The student network includes a second input layer, a second feature encoding module, and the lightweight adaptation layer connected in sequence. The second feature encoding module has the same structure as the first feature encoding module of the teacher network, and the lightweight adaptation layer includes a residual bias compensation unit; The step of inputting the target dimensionless feature set into a student network containing a lightweight adaptation layer, and training the student network based on the knowledge distillation signal and the actual motion state data of the target submersible, includes: The target dimensionless feature set is transmitted to the second feature encoding module through the second input layer; The second feature encoding module extracts and reduces the dimensionlessness of the target feature set to generate student feature encoding output. The lightweight adaptation layer is used to perform a full connection on the student feature encoding output to generate a residual mapping; Based on the residual mapping, bias compensation features are generated through feature addition operations; The bias compensation features are concatenated with the knowledge distillation signal to generate a training target. Based on the training objective and the actual motion state data of the target submersible, the parameters of the student network are optimized using gradient descent.

8. The method for modeling disturbed motion of a submersible based on hydrodynamic similarity guidance according to claim 7, characterized in that, The lightweight adaptation layer includes a single hidden layer fully connected structure and an activation function, wherein the number of hidden layer nodes in the single hidden layer fully connected structure is one-quarter of the input dimension. The step of performing a fully connected operation on the student feature encoding output through the lightweight adaptation layer to generate a residual mapping includes: The activation function is used to perform a non-linear transformation on the student feature encoding output to generate intermediate features. The residual mapping is generated based on the intermediate features through the single hidden layer fully connected structure. The step of generating bias compensation features based on the residual mapping through feature addition operations includes: Based on the vector dimension of the intermediate features, the residual mapping is linearly upgraded, and the upgraded residual mapping is added to the student feature encoding output to generate the deviation compensation feature.

9. The method for modeling disturbed motion of a submersible based on hydrodynamic similarity guidance according to claim 1, characterized in that, The disturbed motion prediction model for the student network-deployed target submersible, based on the trained model, includes: The trained student network is subjected to channel pruning to obtain the disturbed motion prediction model. The network structure and quantization weights of the disturbed motion prediction model are loaded into the embedded system of the target submersible and deployed through the model loading interface; The real-time data stream provided by the sensor system of the target submersible is converted into dimensionless features and added to the target dimensionless feature set; The target dimensionless feature set is input into the disturbed motion prediction model, and the disturbed motion prediction value is generated through forward propagation.

10. A device for modeling disturbed motion of a submersible based on hydrodynamic similarity guidance, characterized in that, include: The acquisition module is used to acquire the actual motion state data of the source submersible and the target submersible, as well as the motion test data under disturbed conditions, and to perform dimensionless transformation based on the hydrodynamic similarity criterion to obtain the corresponding source dimensionless feature set and target dimensionless feature set. The hydrodynamic similarity criterion is constructed based on the Froude number and the Reynolds number. The first processing module is used to determine a similarity parameter that characterizes the hydrodynamic essential similarity between the source submersible and the target submersible based on the distribution correlation of the source dimensionless feature set and the target dimensionless feature set in the dimensionless feature space. The second processing module is used to train the teacher network using the source dimensionless feature set and the corresponding actual motion state data of the source submersible, and to fix the parameters of the trained teacher network. The third processing module is used to input the target dimensionless feature set into the teacher network with fixed parameters to obtain the intermediate layer features and interference parameter representations output by the teacher network. The fourth processing module is used to input the intermediate layer features, the interference parameter representation, and the similarity parameter into the similarity attention mechanism module to generate a knowledge distillation signal; The fifth processing module is used to input the target dimensionless feature set into a student network containing a lightweight adaptation layer, train the student network based on the knowledge distillation signal and the actual motion state data of the target submersible, and deploy a disturbed motion prediction model of the target submersible according to the trained student network. The lightweight adaptation layer is used to compensate for residual deviations caused by the heterogeneity between the source submersible and the target submersible that are not characterized by hydrodynamic similarity criteria.

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