A method for extrapolating and predicting characteristics of an air bag vibration isolation system adapted to variable depth conditions

Abstract

The application belongs to the technical field of intelligent testing of marine equipment vibration reduction, and discloses a method for extrapolating and predicting the characteristics of an airbag vibration isolation system suitable for variable depth conditions. Based on the onshore staged constant pressure test data, the method realizes reliable prediction and quantification of the prediction confidence interval of the deep sea extreme working condition vibration isolation characteristics through three-stage progressive training. First, the staged sampling is carried out along the water depth gradient, the excitation and dynamic response data are collected to construct a data set, a deep learning extrapolation model embedded with multi-degree-of-freedom dynamic equations is constructed, three-stage isolation training including shallow water pre-training, physical pre-adaptation and step-by-step extrapolation fine-tuning is adopted to suppress the divergence of long-distance extrapolation errors, the prediction value and confidence interval of the state parameters of the target large diving depth working condition are inferred and output, and the reliability of the variable depth progressive extrapolation verification and evaluation method is evaluated. The application overcomes the defects of pure data model deep sea prediction against physical laws and traditional extrapolation error explosion, can output engineering quantitative indicators, has strong universality in technical route, and is suitable for performance prediction of various nonlinear boundary equipment.

Description

Technical Field

[0001] This invention belongs to the field of intelligent testing technology for vibration reduction of marine equipment, and specifically relates to an extrapolation prediction method for the characteristics of an airbag vibration isolation system that adapts to varying depth conditions. Background Technology

[0002] In underwater vehicles and other devices, airbag vibration isolation systems are widely used for vibration isolation and attitude control of power equipment due to their adjustable airbag pressure and excellent vibration reduction and noise reduction performance.

[0003] As marine equipment develops towards greater diving depths, the boundary conditions faced by airbag vibration isolation systems have changed significantly, creating an urgent need for performance prediction and control of these systems under extreme operating conditions. In deep-sea environments, the submersible hull is subjected to hydrostatic pressures of tens of megapascals (MPa). The hull structure undergoes compressive deformation under this high pressure, the most direct impact of which is the displacement of the airbag mounting base. The airbag not only bears vertical compressive loads but also shear deformation introduced by the base displacement, thereby disrupting the alignment of the power equipment relative to the hull. These multiple coupling effects cause key parameters such as the stiffness, vibration transmission characteristics, and airbag load-bearing state of the vibration isolation system to exhibit strong nonlinear changes along the water depth, significantly increasing the difficulty of predicting performance under deep-sea conditions.

[0004] In the field of vibration isolation at great depths, existing research mainly focuses on the structural optimization of vibration isolation devices (CN117432746A, 2024.01.23) and the structural optimization of propulsion devices (CN113859493A, 2021.12.31). Regarding vibration isolation devices, improvements to the airbag configuration reduce system stiffness, and the integration of additional air chambers achieves variable stiffness adjustment. Regarding propulsion devices, a low-vibration direct-drive scheme is proposed for deep-sea propulsion motors, suppressing vibration transmission through shaft sealing and structural vibration isolation. The performance evaluation and verification methods used in these studies all rely on land-based pressure tests and numerical simulations at finite depths, without extrapolating predictions from accessible operating conditions to inaccessible deep-sea operating conditions.

[0005] At the methodological level of extrapolation models, the materials science field has proposed a modified hyperbolic extrapolation model. In predicting internal stress during stress relaxation, a correction factor is introduced to modify the hyperbolic extrapolation model, ensuring effective agreement between predicted and experimentally measured values ​​under different pre-strain conditions. In the nuclear fusion field, a rapid analysis model and extrapolation method using a spectral diagnostic neural network have been proposed. In ion temperature diagnostics, a convolutional neural network is trained using only experimental data in the low-energy region (below 2 keV). By adding approximately 5% of high-energy synthetic spectral data to the training set as physical guidance, the extrapolation error in the inaccessible high-energy region (3–4 keV) is reduced by about 60%. Both of these methods rely on physical priors to achieve limited data extrapolation and are geared towards materials mechanics and plasma diagnostic scenarios, respectively. They cannot adapt to the strongly nonlinear mechanical evolution of underwater airbag vibration isolation systems with varying water depths, making it difficult to support the formulation of control strategies for deep-sea vibration isolation systems. Therefore, there is an urgent need for a data-driven method guided by physical constraints, which can use limited accessible operating condition data and physical prior knowledge to achieve reliable extrapolation to unreachable extreme operating conditions and provide a method for predicting the state parameters of vibration isolation systems to provide confidence reference for subsequent optimization control. Summary of the Invention

[0006] The purpose of this invention is to provide an extrapolation prediction method for the characteristics of an airbag vibration isolation system that adapts to varying depth conditions. Relying only on limited accessible test data from land-based operating conditions, this method enables reliable prediction of key characteristics of the vibration isolation system under extreme deep-sea operating conditions and outputs a quantitative confidence interval.

[0007] To achieve the above objectives, the present invention provides a method for extrapolating and predicting the characteristics of an airbag vibration isolation system adaptable to varying depth conditions, comprising the following steps: S1. Under the experimental conditions accessible on land, conduct a graded constant pressure systematic experiment on the airbag vibration isolation system along the direction of increasing simulated water depth; apply excitation to the airbag vibration isolation system under working condition labels that include at least environmental pressure, and simultaneously collect the original excitation data and the dynamic response data of the airbag vibration isolation system. After preprocessing, the original data forms a standardized dataset containing labels of key characteristic parameters of the vibration isolation system. S2. Construct a data-driven deep learning extrapolation model. During the model training process, the physical equations obeyed by the airbag vibration isolation system are embedded as physical constraint terms into the model's total loss function. S3. The deep learning extrapolation model is trained using a three-stage progressive training strategy that adapts to increasing depth. The three-stage progressive training strategy includes the following steps: Shallow water interpolation pre-training: Supervised learning is carried out using only data from the first few pressure subdomains of the shallow water area; Physically guided pre-adaptation: Training is conducted using all available terrestrial datasets, with physical equation constraints applied simultaneously and deep-sea virtual sampling points introduced as auxiliary constraints; Progressive extrapolation and fine-tuning for increasing depth: The systematic experimental data of graded constant pressure system is divided into several independent subdomains in ascending order of pressure, and the following steps are performed in a loop: the union of the first k subdomains is selected as the training set to train the model; the working condition parameters of the (k+1)th subdomain that did not participate in the previous training are predicted; the model is fine-tuned with a small number of rounds using the measured data of the (k+1)th subdomain, and the process is gradually advanced to the extreme working conditions of deep diving. S4. Utilize the trained deep learning extrapolation model to perform forward inference and output the predicted values ​​of the state parameters of the airbag vibration isolation system under extreme deep-sea conditions and the prediction confidence interval calibrated by shallow-water measured error. S5. Conduct progressive extrapolation verification at varying depths. Perform multi-level cross-subdomain extrapolation tests within the accessible depth range on land, fit the curve of extrapolation error as water depth increases, and evaluate the reference value and prediction accuracy of the method for extrapolating to the target extreme working conditions. If the extrapolation error does not show accelerated growth or abrupt change along the water depth direction, it is determined that the method has the feasibility of extrapolating to the target deep diving depth. At the same time, adjust the relevant training parameters based on the verification error feedback to guide the iterative optimization of the model.

[0008] Furthermore, the graded pressure system experiment described in step S1 is preferably carried out using a land-based pressurization test platform; the land-based pressurization test platform includes a pressure-resistant shell and an airbag vibration isolation system assembled inside the pressure-resistant shell, and uses a water tank pressurization device to apply pressure to simulate a water depth pressure environment.

[0009] Furthermore, the sampling distribution of the graded constant pressure system experiment described in step S1 satisfies the rule of large sampling intervals in shallow water sections and denser sampling intervals in sections with the maximum simulated water depth accessible from land.

[0010] Furthermore, the environmental pressure mentioned in step S1 is the environmental hydrostatic pressure; the operating condition label also includes the environmental temperature.

[0011] Furthermore, the key characteristic parameters of the vibration isolation system described in step S1 include at least one of the following: vibration transfer function, steady-state pressure change of the airbag, and displacement response of the base mounting point.

[0012] Furthermore, the physical equations obeyed by the airbag vibration isolation system in step S2 include at least the multi-degree-of-freedom dynamic equations of the airbag vibration isolation system, which are used to constrain the mechanical relationship between the excitation force, system stiffness, and structural response.

[0013] Furthermore, the deep learning extrapolation model described in step S2 includes a feature extraction module for extracting dynamic response features, a fusion module for fusing features and operating condition information, and a prediction module for outputting predicted values ​​of characteristic parameters.

[0014] Furthermore, the deep learning extrapolation model also includes an uncertainty estimation module, which is used to output the uncertainty of the prediction results.

[0015] Furthermore, the uncertainty estimate corresponding to the predicted state parameter value in step S4 is determined after shallow water trend calibration; the shallow water trend calibration is to establish a systematic deviation relationship between the model uncertainty estimate and the actual prediction error by using the model prediction value and the measured true value that exist simultaneously in the shallow water subdomain, and then transfer this calibration relationship to the uncertainty estimate of the target deep diving condition to correct the systematic deviation introduced by the water depth change.

[0016] Furthermore, the relevant training parameters mentioned in step S5 include at least the network structure, learning rate, number of training iterations, and weights of the physical equation constraint terms.

[0017] Compared with the prior art, the present invention has the following beneficial effects: 1. Establish a graded progressive extrapolation training paradigm adapted to varying working conditions: Based on graded constant pressure tests, the working condition subdomains are naturally divided. A progressive extrapolation training mode is adopted, and a strict data isolation mechanism is implemented to ensure the authenticity and reliability of the extrapolation verification process. Compared with traditional one-time large-span single-step extrapolation and simple interpolation prediction methods, it can effectively suppress the problem of rapid error divergence during long-distance extrapolation.

[0018] 2. Construct a predictive framework that integrates physical constraints and progressive training at varying depths. Qualitative mechanical boundary constraints for unknown deep-sea conditions are formed using the dynamic equations of airbag vibration isolation. A predictive path is built by progressively training at varying depths, gradually approximating known conditions to extreme deep-sea conditions. These two approaches complement each other, overcoming the shortcomings of purely data-driven models that produce predictions that violate physical laws under extreme conditions without available samples.

[0019] 3. Output multi-dimensional characteristic parameters with direct engineering application value. Key indicators such as vibration transfer function, airbag steady-state pressure change, and base installation displacement can be obtained simultaneously, corresponding to the vibration isolation effectiveness of the airbag isolation system, the airbag pressure bearing safety margin, equipment alignment, and shell structure safety status, respectively. The parameter set can be flexibly adjusted according to actual engineering needs, which facilitates the evaluation of vibration isolation schemes for submarines.

[0020] 4. Quantify the uncertainty of extrapolation prediction results. For inaccessible deep-sea operating conditions, the prediction confidence interval is calibrated with the measured error of the onshore operating conditions. The width of the interval intuitively represents the reliability of the prediction, providing a quantitative basis for the formulation of vibration isolation control strategies and safety margin design of deep-sea dynamic systems.

[0021] 5. The entire method possesses good versatility and transferability. The complete technical route formed by this invention, namely "graded test data acquisition - physical law constraints - progressive extrapolation prediction - confidence quantification evaluation," can be extended to all types of engineering equipment systems with continuous nonlinear progressive changes in boundary conditions. Attached Figure Description

[0022] Figure 1 This is a schematic diagram of the structure of the land-based pressurization test platform constructed according to the present invention.

[0023] Figure 2 This is the overall flowchart of the extrapolation prediction method for the characteristics of the airbag vibration isolation system of the present invention.

[0024] Figure 3 This is a schematic diagram of the graded constant pressure sampling distribution of the present invention.

[0025] Figure 4 This is a flowchart of the three-stage progressive training strategy of the present invention. Detailed Implementation

[0026] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and embodiments. These embodiments are only used to explain the present invention and do not limit the scope of protection of the present invention.

[0027] This embodiment uses a prototype of the airbag vibration isolation system for the power equipment of a certain type of unmanned underwater vehicle as the test object.

[0028] Set up Figure 1 The land-based pressurization test platform shown includes a pressure-resistant shell 10 and a prototype airbag vibration isolation system assembled inside the pressure-resistant shell 10. The prototype airbag vibration isolation system includes a base 21, several airbag vibration isolators 22, a raft 23, and an exciter 24. The base 21 is fixed to the bottom of the pressure-resistant shell 10. The airbag vibration isolators 22 are installed above the base 21. The raft 23 is erected on top of the airbag vibration isolators 22 and is elastically supported by the airbag vibration isolators 22. The exciter 24 is rigidly fixed to the center of the top surface of the raft 23 and is used to apply sweep frequency excitation to the raft 23. The airbag vibration isolators 22 have built-in pressure sensors for real-time acquisition of the air pressure inside the airbag. The base 21 has displacement sensors 25 installed on its sidewalls for acquisition of the pressure offset of the base and the deformation of the airbag. Acceleration sensors 26 are arranged at the lower end of the raft 23 and on the upper and lower end faces of the airbag vibration isolators 22 for acquisition of the system's vibration acceleration response. During the test, the land-based pressurization test platform was placed in a test water tank, and the water tank was pressurized using a water tank pressurization device to simulate a deep water pressure environment. When hydrostatic pressure was applied, the pressure-resistant shell 10 contracted and deformed inward under the confining pressure, causing the base 21 to shift, so that the airbag vibration isolator 22 simultaneously bore vertical compressive load and lateral shear load, thus reproducing the actual stress state under varying depth conditions.

[0029] The method for extrapolating and predicting the characteristics of an airbag vibration isolation system adapted to varying depth conditions according to the present invention is as follows: Figure 2 As shown, the data and model foundation are provided by two main modules: land-based graded experiments and physical model construction. After three stages of progressive extrapolation training, extrapolation verification is completed, ultimately achieving reliable predictions from accessible land-based data to extreme deep-sea conditions. The specific steps include: S1. Systematic Experiment and Data Acquisition of Land-based Staged Pressure Stabilization System Under accessible land-based experimental conditions, a graded, constant-pressure systematic experiment was conducted on the target model's airbag vibration isolation system along the simulated water depth increasing direction using a land-based pressurized test platform. Due to limitations in the test pool's pressure-bearing capacity and the performance of the pressurization device, the hydrostatic pressure could not be continuously and arbitrarily adjusted; therefore, the sampling distribution followed… Figure 3 The rules are as follows: In shallow water (0 to H1), the experimental cost is low and the nonlinear effect of the state characteristics is weak, so a larger sampling interval is set; in medium-deep water (H1 to H2), the nonlinear effect gradually appears, so the sampling interval is moderate; in deep water (H2 to H3), the nonlinear characteristics grow rapidly, so the sampling points are densified.

[0030] The experiment constructed a working condition label C=[P,T] containing the ambient hydrostatic pressure P and ambient temperature T. Under each working condition label, a full-band frequency sweep excitation was applied to the airbag vibration isolation system, and the raw excitation data, acceleration response at each measuring point, air pressure inside each airbag, and displacement response at the mounting point were collected simultaneously. The raw signals were preprocessed (filtered and de-trended), the frequency response function corresponding to each vibration transmission path was calculated, and the steady-state pressure change of the airbag and the displacement response of the base mounting point were extracted to form a standardized dataset containing labels of key characteristic parameters of the vibration isolation system. .

[0031] The dataset input characteristic vector Xi contains excitation force and working condition label Ci; the output state vector Yi contains the following three types of key parameters: The vibration transfer function of each path directly characterizes the vibration isolation efficiency of the airbag vibration isolation system and is the core evaluation index of vibration isolation performance. The steady-state pressure change of each airbag is directly related to the airbag stiffness and bearing limit, and is a key parameter for judging whether the vibration isolation device exceeds the safety boundary; The displacement response of the installation site reflects the offset caused by shell deformation and changes in airbag height, which directly affects the structural safety of the vibration isolation device.

[0032] S2, Data-driven Deep Learning Extrapolation Model Construction The deep learning extrapolation model includes a feature extraction module for extracting dynamic response features, a fusion module for fusing features and operating condition information, a prediction module for outputting predicted values ​​of characteristic parameters, and an uncertainty estimation module for outputting prediction uncertainty.

[0033] During model training, the physical equations obeyed by the airbag vibration isolation system are embedded as physical constraint terms into the model's total loss function. In this embodiment, the physical equations used are the multi-degree-of-freedom dynamic equations of the airbag vibration isolation system, with physical constraint loss residuals. As a physical constraint, the mechanical relationship exists between the constraint excitation force, system stiffness, and structural response. Here, M, C, and K represent the equivalent mass, damping, and stiffness matrices of the airbag vibration isolation system, respectively; x is the displacement at the installation point; and F(t) is the excitation force.

[0034] It should be noted that the physical information neural network infrastructure is a well-known technology in this field. The innovation of this invention lies not in the network infrastructure construction method, but in the overall strategy that combines physical guidance constraints with variable depth progressive extrapolation training. This embodiment uses a fully connected network to complete feature extraction and parameter prediction, but other network structures and other forms of dynamic equations can also be used.

[0035] S3, Three-Stage Increasingly Deeper Progressive Extrapolation Training Utilizing the inherent structure of the stress grading experiment in step S1, a three-stage progressive training strategy with adaptive depth is employed to train the deep learning extrapolation model, such as... Figure 4 As shown, strict data isolation is implemented throughout the extrapolation training process to ensure the effectiveness of the extrapolation verification; the three-stage progressive training strategy includes the following steps: Phase 1: Shallow Water Interpolation Pre-training The model is trained using supervised learning by using only data from the first few pressure subdomains in the shallow water area, enabling it to perform interpolation predictions within known operating conditions. The subdomain data used in this stage are only used as the learned area for subsequent extrapolation and are not used for the verification of the operating conditions to be predicted.

[0036] Phase Two: Physically Guided Pre-adaptation Training was conducted using all available land-based datasets, with physical equations constraining the loss simultaneously. Virtual sampling points were randomly generated within the parameter space of extreme deep-sea target conditions, and the prediction results of these virtual points were constrained to satisfy the dynamic equations. This ensured that the parameter space was pre-incorporated with the physical laws of deep-sea conditions even without access to actual deep-sea diving data, thus adapting the model for step-by-step extrapolation.

[0037] Phase 3: Gradual Extrapolation and Fine-tuning Using the natural pressure subdomain structure formed by the graded isobaric experiments in step S1, the graded isobaric experiment dataset is divided into several independent subdomains according to the ascending pressure order. Each fine-tuning step uses only the union of the first k subdomains as training data, excluding data from the (k+1)th subdomain and higher-level subdomains. The process is iterative: the union of the first k subdomains is used as the training set to train the model; the state parameters of the (k+1)th subdomain, which has not participated in any previous training, are predicted; the model is fine-tuned using measured data from the (k+1)th subdomain in a few rounds, progressively advancing towards deeper subdomains. Since the (k+1)th subdomain has not participated in any previous training stages, it ensures that the (k+1)th subdomain is completely unknown to the model when it is first predicted, thus recreating the real deep-sea extrapolation scenario.

[0038] S4, Target Deep Diving Condition Extrapolation Prediction The trained deep learning extrapolation model performs forward inference, outputting three types of predicted state parameters for the airbag vibration isolation system under extreme deep-sea conditions: the vibration isolation transfer function for each path, the predicted pressure change of each airbag, and the displacement response of the installation site. The uncertainty estimates corresponding to the predicted state parameters are determined through shallow water trend calibration. The shallow water trend calibration method is as follows: using the model predictions and measured true values ​​that exist simultaneously in the shallow water subdomain, a systematic deviation relationship between the model uncertainty estimate and the actual prediction error is established. This calibration relationship is then transferred to the uncertainty estimate of the target deep-sea conditions to correct the systematic deviation caused by water depth changes, and finally, the results with prediction confidence intervals are output.

[0039] S5. Variable-depth progressive extrapolation verification and model iterative optimization Based on the pressure range accessible from land-based experiments, progressive extrapolation verification is performed using tiered subdomains. Data from the shallow water subdomain is used to train the model, predict deeper subdomains, calculate the extrapolation error, and plot the extrapolation error as a function of water depth to assess its trend. The verification results can be used to further adjust the relevant training parameters in step three through error feedback, guiding model fine-tuning. If the extrapolation error does not show accelerated growth or abrupt changes along the water depth direction, it proves that the above method has reference value for extrapolating to target deep diving depths and can be used for predicting conditions inaccessible deep diving depths. Based on the verification error feedback, model parameters can be adjusted, including network structure, learning rate, training epochs, and physical constraint loss weights, iteratively optimizing the model's prediction accuracy.

[0040] It should be noted that the "accessible working conditions" mentioned in this invention refer to the water depth and pressure range that the land-based pressurization test platform can stably cover; the "inaccessible deep-diving working conditions" are not completely unreproducible, but rather refer to the fact that due to the limitations of equipment pressure-bearing capacity and safety costs, the cost of obtaining batch measured data in the deep-diving section is too high, and it is not feasible in engineering.

[0041] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit them; those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions will not cause the essence of the corresponding technical solutions to deviate from the protection scope of the present invention.

Claims

1. A method for extrapolating and predicting the characteristics of an airbag vibration isolation system adaptable to varying depth conditions, characterized in that, Includes the following steps: S1. Under the experimental conditions accessible on land, conduct a graded constant pressure systematic experiment on the airbag vibration isolation system along the direction of increasing simulated water depth; apply excitation to the airbag vibration isolation system under working condition labels that include at least environmental pressure, and simultaneously collect the original excitation data and the dynamic response data of the airbag vibration isolation system, and form a standardized dataset containing labels of key characteristic parameters of the vibration isolation system after preprocessing. S2. Construct a data-driven deep learning extrapolation model. During the model training process, the physical equations obeyed by the airbag vibration isolation system are embedded as physical constraint terms into the model's total loss function. S3. The deep learning extrapolation model is trained using a three-stage progressive training strategy that adapts to increasing depth. The three-stage progressive training strategy includes the following steps: Shallow water interpolation pre-training: Supervised learning is carried out using only data from the first few pressure subdomains of the shallow water area; Physically guided pre-adaptation: Training is conducted using all available terrestrial datasets, with physical equation constraints applied simultaneously and auxiliary constraints introduced from deep-sea virtual sampling points; Progressive extrapolation and fine-tuning for increasing depth: The systematic experimental data of graded constant pressure system is divided into several independent subdomains in ascending order of pressure, and the following steps are performed in a loop: the union of the first k subdomains is selected as the training set to train the model; the working condition parameters of the (k+1)th subdomain that did not participate in the previous training are predicted; the model is fine-tuned with a small number of rounds using the measured data of the (k+1)th subdomain, and the process is gradually advanced to the extreme working conditions of deep diving. S4. Utilize the trained deep learning extrapolation model to perform forward inference and output the predicted values ​​of the state parameters of the airbag vibration isolation system under extreme deep-sea conditions and the prediction confidence interval calibrated by shallow-water measured error. S5. Conduct progressive extrapolation verification at varying depths. Perform multi-level cross-subdomain extrapolation tests within the accessible depth range on land, fit the curve of extrapolation error as water depth increases, and evaluate the reference value and prediction accuracy of the method for extrapolating to the target extreme working conditions. If the extrapolation error does not show accelerated growth or abrupt change along the water depth direction, it is determined that the method has the feasibility of extrapolating to the target deep diving depth. At the same time, adjust the relevant training parameters based on the verification error feedback to guide the iterative optimization of the model.

2. The method for extrapolating and predicting the characteristics of an airbag vibration isolation system adaptable to varying depth conditions according to claim 1, characterized in that: The sampling distribution of the graded constant pressure system experiment in step S1 meets the rule of large sampling intervals in shallow water sections and denser sampling intervals in sections with the maximum simulated water depth accessible from land.

3. The method for extrapolating and predicting the characteristics of an airbag vibration isolation system adaptable to varying depth conditions according to claim 1, characterized in that: The environmental pressure mentioned in step S1 is the ambient hydrostatic pressure; the operating condition label also includes the ambient temperature.

4. The method for extrapolating and predicting the characteristics of an airbag vibration isolation system adaptable to varying depth conditions according to claim 1, characterized in that: The key characteristic parameters of the vibration isolation system described in step S1 include at least one of the following: vibration transfer function, steady-state pressure change of the airbag, and displacement response of the base mounting point.

5. The method for extrapolating and predicting the characteristics of an airbag vibration isolation system adaptable to varying depth conditions according to claim 1, characterized in that: The physical equations obeyed by the airbag vibration isolation system in step S2 include at least the multi-degree-of-freedom dynamic equations of the airbag vibration isolation system, which are used to constrain the mechanical relationship between the excitation force, system stiffness, and structural response.

6. The method for extrapolating and predicting the characteristics of an airbag vibration isolation system adaptable to varying depth conditions according to claim 1, characterized in that: The deep learning extrapolation model described in step S2 includes a feature extraction module for extracting dynamic response features, a fusion module for fusing features and operating condition information, and a prediction module for outputting predicted values ​​of characteristic parameters.

7. The method for extrapolating and predicting the characteristics of an airbag vibration isolation system adaptable to varying depth conditions according to claim 6, characterized in that: The deep learning extrapolation model also includes an uncertainty estimation module, which is used to output the uncertainty of the prediction results.

8. The method for extrapolating and predicting the characteristics of an airbag vibration isolation system adaptable to varying depth conditions according to claim 7, characterized in that: The uncertainty estimate corresponding to the predicted state parameter value in step S4 is determined after shallow water trend calibration. The shallow water trend calibration is to establish a systematic deviation relationship between the model uncertainty estimate and the actual prediction error by using the model prediction value and the measured true value that exist simultaneously in the shallow water subdomain, and then transfer this calibration relationship to the uncertainty estimate of the target deep diving condition to correct the systematic deviation introduced by the depth change.

9. The method for extrapolating and predicting the characteristics of an airbag vibration isolation system adaptable to varying depth conditions according to claim 1, characterized in that: The relevant training parameters mentioned in step S5 include at least the network structure, learning rate, number of training iterations, and weights of the physical equation constraint terms.

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