Deep-sea pressure-resistant shell critical buckling load prediction method and related device

Abstract

The invention belongs to the field of deep-sea engineering, and discloses a deep-sea pressure-resistant shell critical buckling load prediction method and a related device, and the method comprises the steps: obtaining the feature data of a target shell; the characteristic data of the target shell comprises geometric parameters, defect characteristic information, material characteristic data and service temperature condition data of the target shell; preprocessing the feature data of the target shell to obtain preprocessed feature data of the target shell; taking the preprocessed feature data of the target shell as the input of a pre-constructed shell critical buckling load prediction model, and outputting to obtain a critical buckling load prediction result of the target shell; geometric parameters, defect characteristic information, material characteristic data and service temperature condition data of a target shell are obtained, preprocessed and then input into a pre-constructed shell critical buckling load prediction model, the coupling effect of defects and temperature is considered, and under the condition of small sample data, the target shell critical buckling load prediction method can be used for predicting the target shell critical buckling load. And accurate prediction of the critical buckling load of the target shell is realized.

Description

Technical Field

[0001] This invention belongs to the field of deep-sea engineering technology, and relates to the field of performance prediction of deep-sea pressure hulls, and in particular to a method and related device for predicting the critical buckling load of deep-sea pressure hulls. Background Technology

[0002] With the continuous development of deep-sea engineering, deep-sea pressure hulls play an important role in deep-sea exploration, resource extraction, and scientific research. Due to the extreme complexity of the deep-sea environment, deep-sea pressure hulls are subjected to extreme temperatures and pressures during service, which can easily lead to defects, reduce their ultimate bearing capacity, and in severe cases, even cause hull failure. Among these factors, the critical buckling load is a key indicator for assessing its ultimate bearing capacity. When the external load on the deep-sea pressure hull reaches its critical buckling load, instability and failure will occur. Therefore, accurately assessing the critical buckling load is crucial for ensuring the structural safety of deep-sea pressure hulls.

[0003] Currently, the assessment of critical buckling load for deep-sea pressure hulls mainly employs physical testing and finite element simulation. Physical testing involves establishing shell models under different conditions and applying different pressures based on actual circumstances to determine the critical buckling load. Finite element simulation involves establishing a finite element model of the deep-sea pressure hull, simulating the stress conditions under different working conditions, and then assessing its critical buckling load.

[0004] However, the existing assessment methods mentioned above generally require significant time and cost, and are highly susceptible to affecting the accuracy of the assessment results. Physical testing methods, in particular, are limited by factors such as testing costs and data availability, and cannot comprehensively and accurately reflect shell behavior in actual deep-sea environments. Specifically, firstly, conducting tests under deep-sea environmental conditions requires expensive equipment and high-end technical support. Due to the extreme complexity of the deep-sea environment, tests often need to simulate real-world extreme conditions such as high pressure, low temperature, and corrosion, making each experiment extremely costly. Furthermore, tests typically require the establishment of multiple physical models to simulate different operating conditions and environmental conditions, increasing both costs and prolonging the testing cycle. To ensure the representativeness and accuracy of the data, researchers usually need to conduct numerous repeated tests, further increasing the overall cost of the tests. Moreover, due to the variability of the deep-sea environment, tests can only simulate limited operating conditions, and the environmental changes that may occur in actual applications often cannot be fully reproduced. These limitations mean that the data obtained through experiments may not comprehensively reflect shell behavior in actual deep-sea environments, thus affecting the accurate assessment of critical buckling loads.

[0005] Furthermore, the finite element method faces a trade-off between modeling complexity and computational resource consumption, making it difficult to complete the analysis within a reasonable timeframe while ensuring model accuracy. Specifically, firstly, the structure of deep-sea pressure hulls is complex and subject to various operating conditions. Therefore, finite element modeling requires consideration of different material properties, geometric features, and variable defect conditions, making the modeling process extremely complex. For example, considering factors such as temperature, corrosion, and cracks, the finite element model needs to make numerous assumptions and simplifications to complete the analysis within an acceptable computation time. However, these simplifications may lead to deviations between the model and the actual situation, affecting the accuracy of the analysis results. Secondly, to improve model accuracy, fine meshing is usually required, significantly increasing the computational load. For larger-scale or higher-precision simulations, the consumption of computational resources may exceed the actual available computing power, resulting in a very time-consuming analysis process, or even making it impossible to complete within a reasonable timeframe. Therefore, the finite element analysis method faces a trade-off between modeling complexity and computational resource consumption when assessing critical buckling loads in complex deep-sea environments.

[0006] In summary, there is an urgent need for a method that can effectively, accurately, and efficiently assess the critical buckling load of deep-sea pressure hulls. Summary of the Invention

[0007] In view of the technical problems existing in the prior art, the present invention provides a method and related device for predicting the critical buckling load of deep-sea pressure hulls, so as to solve the technical problem that the existing evaluation methods generally require a lot of time and cost and are very likely to affect the accuracy of the evaluation results.

[0008] To achieve the above objectives, the technical solution adopted by the present invention is as follows: This invention provides a method for predicting the critical buckling load of deep-sea pressure hulls, comprising: Acquire the characteristic data of the target shell; wherein, the characteristic data of the target shell includes the geometric parameters, defect feature information, material property data and service temperature condition data of the target shell; The feature data of the target shell are preprocessed to obtain the preprocessed feature data of the target shell. The preprocessed target shell feature data is used as input to the pre-constructed shell critical buckling load prediction model, and the output is the critical buckling load prediction result of the target shell. The construction process of the pre-constructed shell critical buckling load prediction model is as follows: Obtain sample data of the sample shell; wherein, the sample data of the sample shell includes the characteristic data of the sample shell and the calculation results of the critical buckling load of the sample shell under different working conditions; Using sample data from the sample shell, several predetermined basic regression models are trained to obtain several trained basic regression models. Ridge regression is used to weight and merge several trained basic regression models to obtain an integrated model, which is then used as a pre-constructed prediction model for critical buckling loads of the shell.

[0009] Furthermore, the geometric parameters of the target shell include the radius and thickness of the target shell; the defect feature information of the target shell includes the defect type and defect size of the target shell; and the service temperature condition data of the target shell includes the inner wall temperature condition and the outer wall temperature condition of the target shell.

[0010] Furthermore, the sample shell is a deep-sea pressure-resistant shell of the same type or with the same geometric parameters as the target shell; The characteristic data of the sample shell includes the geometric parameters of the sample shell, defect characteristic information, material property data and service temperature condition data; The geometric parameters of the sample shell include its radius and thickness; the defect feature information of the sample shell includes its defect type and size; and the service temperature condition data of the sample shell includes its inner wall temperature and outer wall temperature.

[0011] Furthermore, the calculation results of the critical buckling load of the sample shell under different working conditions were obtained through physical experimental methods or finite element simulation methods.

[0012] Furthermore, several predetermined basic regression models include tabular prior data fitting network models, random forest models, and support vector regression models.

[0013] Furthermore, using the sample data from the sample shell, several predetermined basic regression models are trained to obtain several trained basic regression models. In the process, a five-fold cross-validation method is introduced to validate the models.

[0014] This invention also provides a critical buckling load prediction system for deep-sea pressure hulls, comprising: The target shell feature data acquisition module is used to acquire the feature data of the target shell; wherein, the feature data of the target shell includes the geometric parameters, defect feature information, material property data and service temperature condition data of the target shell; The target shell feature data preprocessing module is used to preprocess the feature data of the target shell to obtain the preprocessed target shell feature data. The critical buckling load prediction module is used to take the preprocessed target shell feature data as input to the pre-built shell critical buckling load prediction model and output the critical buckling load prediction result of the target shell. The construction process of the pre-constructed shell critical buckling load prediction model is as follows: Obtain sample data of the sample shell; wherein, the sample data of the sample shell includes the characteristic data of the sample shell and the calculation results of the critical buckling load of the sample shell under different working conditions; Using sample data from the sample shell, several predetermined basic regression models are trained to obtain several trained basic regression models. Ridge regression is used to weight and merge several trained basic regression models to obtain an integrated model, which is then used as a pre-constructed prediction model for critical buckling loads of the shell.

[0015] The present invention also provides an electronic device, comprising: A processor is used to execute computer programs; A computer-readable storage medium storing a computer program, which, when executed by the processor, performs the method for predicting the critical buckling load of a deep-sea pressure hull.

[0016] The present invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the method for predicting the critical buckling load of deep-sea pressure hulls.

[0017] The present invention also provides a computer program product, which includes a computer program that, when executed by a processor, implements the method for predicting the critical buckling load of deep-sea pressure hulls.

[0018] Compared with the prior art, the beneficial effects of the present invention are as follows: The critical buckling load prediction method for deep-sea pressure hulls provided by this invention acquires the geometric parameters, defect feature information, material property data, and service temperature condition data of the target hull. After preprocessing, these data are input into a pre-constructed critical buckling load prediction model. By considering the coupling effect of defects and temperature, the method can accurately predict the critical buckling load of the target hull even with small sample data. The pre-constructed critical buckling load prediction model is formed by weighted merging of multiple trained basic regression models using ridge regression, significantly improving the accuracy and stability of predicting the critical buckling load of deep-sea pressure hulls. Specifically, the ridge regression-based weighted merging strategy integrates the advantages of multiple basic regression models, fully utilizing their strengths even with small sample data. This minimizes the potential bias of a single model, significantly improving the prediction capability for critical buckling loads under complex operating conditions. Therefore, it effectively enhances the accuracy and reliability of critical buckling load assessment, providing efficient and accurate technical support for ensuring the structural safety of deep-sea pressure hulls.

[0019] The deep-sea pressure hull critical buckling load prediction system, electronic device, computer-readable storage medium, and computer program product provided by this invention possess all the advantages of the aforementioned deep-sea pressure hull critical buckling load prediction method. Attached Figure Description

[0020] Figure 1 A flowchart of the method for predicting the critical buckling load of deep-sea pressure hulls provided by the present invention; Figure 2 A flowchart of the method for predicting the critical buckling load of a deep-sea pressure hull provided in Example 1; Figure 3 This is a schematic diagram of the physical model of a deep-sea capsule-shaped pressure-resistant shell in Example 1; Figure 4 This is a schematic diagram of the finite element simulation results of a deep-sea capsule-shaped pressure hull in Example 1; Figure 5 This is the dataset constructed based on the finite element simulation results of a deep-sea capsule-shaped pressure hull in Example 1; Figure 6 The results show the comparison of R² scores between each basic regression model and the ensemble model in Example 1; Figure 7 This is a comparison chart of the prediction results and finite element simulation results of different models in Example 1; Figure 8 The image shows the SHAP interpretability analysis results of the prediction results of the integrated model in Example 1. Figure 9 This is a structural block diagram of the critical buckling load prediction system for deep-sea pressure hulls provided in Example 2; Figure 10 This is a structural block diagram of the electronic device provided in Example 3. Detailed Implementation

[0021] To make the technical problems solved by the present invention, the technical solutions, and the beneficial effects clearer, the following specific embodiments provide a further detailed description of the present invention. It should be understood that the specific embodiments described herein are merely illustrative and are not intended to limit the scope of the invention.

[0022] As attached Figure 1 As shown, this invention provides a method for predicting the critical buckling load of deep-sea pressure hulls, comprising the following steps: Step 100: Obtain the feature data of the target shell; wherein, the feature data of the target shell includes the geometric parameters of the target shell, defect feature information, material property data and service temperature condition data.

[0023] Step 200: Preprocess the feature data of the target shell to obtain the preprocessed feature data of the target shell.

[0024] Step 300: Use the preprocessed target shell feature data as input to the pre-constructed shell critical buckling load prediction model, and output the critical buckling load prediction result of the target shell.

[0025] In this invention, the construction process of the pre-constructed shell critical buckling load prediction model is as follows: Obtain sample data of the sample shell; wherein, the sample data of the sample shell includes the characteristic data of the sample shell and the calculation results of the critical buckling load of the sample shell under different working conditions; using the sample data of the sample shell, train several pre-determined basic regression models to obtain several trained basic regression models; based on ridge regression, weight and merge several trained basic regression models to obtain an integrated model, which is used as a pre-constructed prediction model for the critical buckling load of the shell.

[0026] In the above embodiments, by acquiring the geometric parameters, defect feature information, material property data, and service temperature condition data of the target shell, and inputting them into a pre-constructed shell critical buckling load prediction model after preprocessing, the critical buckling load of the deep-sea pressure hull can be accurately predicted under small sample data conditions, fully considering the coupling effect of defects and temperature. This avoids the problems of large-scale calculations and complex experimental models required in traditional methods, significantly improving prediction efficiency and economy. The pre-constructed shell critical buckling load prediction model is formed by weighted merging of multiple trained basic regression models using ridge regression. The weighted merging strategy based on ridge regression can integrate the advantages of multiple basic regression models, fully utilizing the strengths of each model to achieve the best results. By minimizing the potential biases of a single model, the method significantly improves the predictive ability of critical buckling loads under complex working conditions, thereby effectively enhancing the accuracy and reliability of critical buckling load assessment. Compared to traditional physical testing methods, the method described in this invention significantly reduces testing costs and time consumption, while avoiding the limitations of physical testing in comprehensively simulating complex and variable deep-sea working conditions, thus improving the adaptability of assessment results to actual service environments. Compared to finite element simulation methods, by replacing complex detailed modeling and extensive mesh generation calculations with an integrated model, the method effectively solves the trade-off between modeling complexity and computational resource consumption, significantly improving analysis efficiency while ensuring prediction accuracy, and enabling rapid output of critical buckling load assessment results.

[0027] The following specific embodiments further explain the method for predicting the critical buckling load of deep-sea pressure hulls provided by the present invention: Example 1 As attached Figure 2As shown in Example 1, this method for predicting the critical buckling load of a deep-sea pressure hull includes the following steps: Step 1: Obtain sample data of the sample shell; wherein, the sample data of the sample shell includes the characteristic data of the sample shell and the calculation results of the critical buckling load of the sample shell under different working conditions.

[0028] Specifically, the process is as follows: Step 11: Based on the actual situation of the target shell, select a deep-sea pressure-resistant shell of the same type or with the same geometric parameters as the target shell as the sample shell.

[0029] Step 12: Using physical experiments or finite element simulation, obtain the critical buckling load calculation results of the sample shell under different working conditions, and statistically analyze the characteristic data of the sample shell to obtain the sample data of the sample shell. The characteristic data of the sample shell includes its geometric parameters, defect characteristic information, material property data, and service temperature condition data; the geometric parameters of the sample shell include its radius and thickness; the defect characteristic information includes the defect type and defect size; and the service temperature condition data includes the inner wall temperature and outer wall temperature conditions.

[0030] Specifically, in the process of obtaining the critical buckling load calculation results of the sample shell under different working conditions using physical experiment methods or finite element simulation methods, shell solid models or shell finite element simulation models with different defects and different temperature boundary conditions are established. The critical buckling load of the shell solid models or shell finite element simulation models under different working conditions is calculated through physical experiments or shell finite element simulation methods, thus obtaining the critical buckling load calculation results of the sample shell under different working conditions. Among them, each shell solid model or shell finite element simulation model corresponds to the critical buckling load under one working condition. The goal is to obtain as many critical buckling load calculation result data as possible under limited conditions.

[0031] It should be noted that after obtaining the characteristic data of the sample shell and the calculation results of the critical buckling load of the sample shell under different working conditions, the data is processed to organize the sample data of the sample shell into a preset table format and store it in a predetermined local folder to provide sample support for subsequent modeling. Each data file stored in the predetermined local folder contains a set of sample data of the sample shell. The characteristic data of the sample shell in each set of sample data is used as the input part for training each subsequent basic regression model. The calculation results of the critical buckling load of the sample shell under different working conditions in each set of sample data are saved in correspondence with the characteristic data of the sample shell and serve as the unique output part of each basic regression model.

[0032] Step 2: Using the sample data from the sample shell, train several predetermined basic regression models to obtain several trained basic regression models.

[0033] Specifically, the process is as follows: Step 21: Load the data files stored in the predetermined local path folder through the Pands library; each data file contains multiple feature columns and one target column; the feature columns are the feature data of the sample shell in the sample data of each group of sample shells, and the target column is the calculation result of the critical buckling load of the sample shell under different working conditions in the sample data of each group of sample shells.

[0034] Step 22: After loading the data file, perform a preliminary check to ensure there are no omissions or format errors. This preliminary check includes checking for and filling in missing values. If missing values ​​exist in the data file, use a mean imputation strategy to fill in the missing values ​​to avoid inaccurate training results due to missing data. After the preliminary check, separate the feature columns and target columns in the data file to prepare for model training and testing. Finally, use a standardization method to normalize all feature columns in the data file to obtain a normalized data file. By normalizing all feature columns, it is ensured that the values ​​of different features have a uniform scale, eliminating the negative impact of scale differences between features, thereby improving model training efficiency and prediction accuracy.

[0035] Step 23: Divide the normalized data file into a dataset with an 80%:20% ratio to obtain a training set and a test set. The training set is used for learning the various basic regression models, and the test set is used to evaluate the performance of the trained basic regression models on unknown data. After the dataset is divided, perform data standardization on the training and test sets to ensure that the features in the training and test sets have the same mean and variance, resulting in preprocessed training and test sets. The standardization process is an important step to improve model training efficiency and ensure that each feature contributes equally. By performing data standardization on the training and test sets, the scale differences between different features can be effectively eliminated, avoiding unbalanced effects on model training.

[0036] Step 24: Using the preprocessed training set, train several predetermined basic regression models to obtain several trained basic regression models; among them, the several predetermined basic regression models include a table prior data fitting network model, a random forest model, and a support vector regression model.

[0037] The Tabular Prior-Fitted Network (TabPFN) model is a neural network model designed for tabular data. It can automatically select the most suitable pre-trained model based on the number of samples and features in the data for efficient training. This model excels at handling complex nonlinear relationships and performs well in environments with small sample data. Through its powerful learning capabilities, the TabPFN model can extract deep-seated patterns from the training data, improving prediction accuracy.

[0038] Random Forest (RFR) is a regression algorithm based on ensemble learning. It reduces model bias by integrating multiple decision trees. Each decision tree is trained independently on the dataset. By introducing randomness, it prevents overfitting and can effectively handle large-scale datasets, especially when the data has strong nonlinear relationships, showing high robustness.

[0039] Support Vector Regression (SVR) is an application of Support Vector Machine (SVM) to regression problems. It finds an optimal hyperplane in a high-dimensional space to fit the data, minimizing the sum of errors of all data points to that hyperplane. It uses a kernel function method for nonlinear modeling, making it particularly suitable for situations with high feature space dimensionality and complex nonlinear relationships in the dataset. By finding the optimal hyperplane and maximizing the margin, SVR reduces model error and improves prediction accuracy.

[0040] It should be noted that after training the network model fitted to the tabular prior data using the preprocessed training set, it can have good predictive ability, and the trained tabular prior data fitted network model can be directly obtained after training. After training the random forest model or support vector regression model using the preprocessed training set, the model hyperparameters are also tuned using a preset optimization algorithm to improve the model's predictive ability, resulting in the trained random forest model or support vector regression model. Among them, the preset optimization algorithm adopts Bayesian optimization.

[0041] Bayesian optimization (BO) is an optimization method based on Bayesian inference, primarily used to optimize costly and computationally difficult objective functions. It establishes a surrogate model of the objective function, models the function using historical evaluation results, and selects the next evaluation point by collecting the probability of the function's optimal value, thus gradually approaching the global optimum. The core function of Bayesian optimization lies in its efficient exploration and utilization of the parameter space, making it particularly suitable for problems such as hyperparameter tuning. It can find the optimal hyperparameter configuration within limited computational resources and time, avoiding the high computational costs of traditional grid search and random search. It accelerates the optimization process by balancing exploration (exploring under-evaluated regions) and utilization (deepening the search of known optimal regions).

[0042] Optionally, using sample data from the sample shell, several predetermined basic regression models are trained to obtain several trained basic regression models. During this process, a five-fold cross-validation method is introduced for model validation. Specifically, the five-fold cross-validation method is used to cross-validate several predetermined basic regression models to improve the model's generalization ability and prevent overfitting. In the cross-validation process, the training set is randomly divided into five subsets. Four subsets are used for training each time, and the remaining subset is used for validation. By validating different subsets in turn, the model's performance on different datasets is evaluated, ensuring that the model does not overfit to any particular dataset, thereby improving the model's reliability and prediction accuracy.

[0043] Step 3: Based on ridge regression, several trained basic regression models are weighted and merged to obtain an integrated model, which is used as a pre-constructed prediction model for critical buckling load of the shell.

[0044] Specifically, after several basic regression models have been trained, ridge regression is used as the meta-learner of the ensemble model. The prediction results of the basic regression models are weighted and merged to obtain the ensemble model, which is then used as a pre-built prediction model for the critical buckling load of the shell. Each basic regression model independently learns from the training set and generates prediction results. The prediction results of the basic regression models are used as new features and input into the ridge regression model to form a feature matrix containing the prediction results of multiple basic regression models, which is then used for ridge regression training.

[0045] Specifically, the Ridge Regression model effectively avoids overfitting by adding an L2 regularization term to the loss function. The L2 regularization term penalizes larger weights in the model, thus preventing the model from relying too much on certain features and reducing variance during training. In addition, Ridge Regression can effectively handle multicollinearity, that is, when there is a high correlation between features, the model can still stably estimate the contribution of each feature, thereby improving the robustness and generalization ability of the model.

[0046] After obtaining the pre-constructed shell critical buckling load prediction model, it is tested using a test set. Specifically, based on the test set, the TabPFN model, BO-RF model, and BO-SVR model in the pre-constructed shell critical buckling load prediction model are used to generate their respective prediction results. Then, the prediction results generated by the TabPFN model, BO-RF model, and BO-SVR model are used as inputs, and a ridge regression model is used for the final combined prediction. Afterward, the performance of the model is evaluated by calculating the mean squared error (MSE) and R² score. The mean squared error (MSE) measures the difference between the model's prediction results and the actual values, while the R² score reflects the model's explanatory power and good fit. The mean squared error (MSE) and R² score provide a direct understanding of the model's prediction performance on unknown data.

[0047] Step 4: Obtain the characteristic data of the target shell; the characteristic data of the target shell includes the geometric parameters, defect feature information, material property data, and service temperature condition data of the target shell. Specifically, the geometric parameters of the target shell include the radius and thickness of the target shell; the defect feature information of the target shell includes the defect type and defect size of the target shell; the service temperature condition data of the target shell includes the inner wall temperature condition and the outer wall temperature condition of the target shell.

[0048] Step 5: Preprocess the feature data of the target shell to obtain preprocessed target shell feature data. Specifically, first, check the feature data of the target shell for missing values; if there are missing items in the feature data of the target shell, the mean imputation strategy is used to impute the missing items in the feature data of the target shell, to obtain feature data with missing values ​​imputed; then, the feature data with missing values ​​imputed is normalized using standard methods to obtain preprocessed target shell feature data.

[0049] Step 6: Use the preprocessed target shell feature data as input to the pre-built shell critical buckling load prediction model, and output the critical buckling load prediction result of the target shell. Specifically, the preprocessed target shell feature data is input into the pre-built shell critical buckling load prediction model, and the TabPFN model, BO-RF model, and BO-SVR model in the pre-built shell critical buckling load prediction model are used to generate their respective prediction results; then, the prediction results generated by the TabPFN model, BO-RF model, and BO-SVR model are used as input to the ridge regression model, and the ridge regression model is used for weighted merging to output the critical buckling load prediction result of the target shell.

[0050] Optionally, interpretability analysis is used to perform importance analysis on the model output results. By assessing the characteristic importance of each influencing factor of the shell, a ranking of key factors affecting the change of the critical buckling load of the shell is established. Among them, SHAP interpretability analysis reveals the importance of different features in model prediction and analyzes the specific contribution of each influencing factor to the final prediction result. Specifically, SHAP can quantify its impact on the model output, thereby helping to identify which features have a greater role in influencing the prediction of the critical buckling load of the shell. In addition, SHAP analysis can also show the interaction between different features and reveal the hidden relationships in complex models.

[0051] It's important to note that SHAP (SHapley Additive exPlanations) is a game theory-based method for model interpretability. It helps interpret the predictions of machine learning models by assigning a "contribution value" to each input feature. The core idea of ​​SHAP is to calculate the marginal contribution of each feature to the model's output across all possible feature combinations, thus providing a fair contribution metric for each feature. This reveals the interactions between features and their specific impact on the model's decisions. SHAP analysis improves the transparency of machine learning models, helping to understand how the model makes predictions based on different input features, thereby providing crucial support for model optimization, result validation, and enhancing model credibility.

[0052] Step 7: Result Saving and Visualization. The predicted critical buckling load of the target shell is compared with the actual value of the critical buckling load, and visualized using various pre-defined charts. For example, a scatter plot shows the relationship between the actual value and the predicted result, intuitively reflecting the model's prediction accuracy; a prediction comparison chart shows the prediction effects of multiple basic regression models and ensemble models, helping to analyze the advantages and disadvantages of different models; and a residual plot analyzes the error distribution in the model prediction, helping to identify potential areas for model improvement.

[0053] Example explanation: Using the critical buckling load prediction method for deep-sea pressure hulls described in Example 1, the critical buckling load of a certain deep-sea capsule-shaped pressure hull is predicted; the physical model of the deep-sea pressure hull is attached. Figure 3 The attached diagram shows a schematic diagram of the finite element simulation results for a deep-sea capsule-shaped pressure hull. Figure 4 As shown in the attached figure; the dataset constructed based on the finite element simulation results of a deep-sea capsule-shaped pressure hull. Figure 5 As shown; it should be noted that the dataset constructed based on the finite element simulation results of a certain deep-sea capsule-shaped pressure hull is used for training and testing each basic regression model and ensemble model in the deep-sea pressure hull critical buckling load prediction method described in Example 1.

[0054] The prediction results and analysis are attached. Figure 6-8 As shown; among them, attached Figure 6 The table provides a comparison of the R² scores of each base regression model and the ensemble model, with appendices. Figure 7 The document presents a comparison chart of the prediction results from different models and the finite element simulation results, with appendices. Figure 8 As shown, attached Figure 8 The figure shows the SHAP interpretability analysis results of the prediction results of the ensemble model.

[0055] From the appendix Figure 6 As can be seen from this, the R values ​​of the TabPFN model, BO-RF model, BO-SVR model, and ensemble model are... 2 The values ​​were 0.9758, 0.8893, 0.9634, and 0.9787, respectively. The results show that, in the basic regression model, the TabPFN model maintained the best predictive performance without hyperparameter tuning, with R0... 2 The R-value is as high as 0.9758, indicating its excellent fitting ability and strong generalization ability; this shows that the TabPFN model can effectively model data without relying on complex tuning, and is suitable for many scenarios requiring high-precision prediction; after model ensemble, the R-value of the ensemble model is... 2 The value further increased to 0.9787, indicating that the integrated model's comprehensive prediction ability was significantly enhanced after fusing the three sub-models: TabPFN, BO-RF, and BO-SVR. By combining the advantages of multiple sub-models, the integrated model effectively compensated for the shortcomings of a single basic regression model, making the buckling load prediction results more robust and further improving the accuracy and generalization ability of the integrated model.

[0056] From the appendix Figure 7As can be seen, among the basic regression models, the BO-RF model exhibits extremely unstable prediction results with a large error range, and some predicted values ​​deviate from the actual values ​​by more than 2 MPa, demonstrating poor predictive performance. In contrast, the TabPFN model shows strong stability; although some predicted values ​​deviate from the actual values ​​by as much as 1.5 MPa, overall, the prediction error for most samples remains within 1 MPa, indicating that the TabPFN model is robust and accurate in the prediction task. When the three basic regression models—TabPFN, BO-RF, and BO-SVR—are integrated, the error range between the predicted and actual values ​​is significantly reduced, generally remaining around 0.5 MPa. This shows that integrating the prediction results of multiple basic regression models can effectively reduce the bias and volatility of a single model, thereby significantly improving the model's predictive performance and stability. Compared with a single basic regression model, the integrated model shows more uniform errors across all test samples, improving the model's accuracy and robustness.

[0057] From the appendix Figure 8 As can be seen from the data, in the ranking of the importance of factors affecting the critical buckling load of the shell, the shell inner wall temperature, crack length and corrosion depth are far more important than other factors, and are the most important factors affecting the change of the critical buckling load of the shell. This result provides a basis for the inspection and maintenance of the shell during its service.

[0058] The critical buckling load prediction method for deep-sea pressure hulls provided in Embodiment 1 uses ridge regression as the meta-learner of the ensemble model. Through ensemble learning technology, it effectively solves the problem of high time and cost required for ultimate bearing capacity analysis in traditional methods. In Embodiment 1, firstly, limited critical buckling load data and characteristic data of the sample hull under different working conditions are obtained through experiments or finite element simulations. The data is then preprocessed and standardized to ensure it meets the requirements for model training. Subsequently, multiple basic regression models are used for training, with each model independently learning data features and generating prediction results. To further… To further improve the accuracy and stability of predictions, ridge regression is used to weight and combine the prediction results of multiple basic regression models to form an ensemble model. Cross-validation is used to evaluate the model's generalization ability, and performance is assessed on a test set. The method described in this embodiment can accurately predict the critical buckling load of deep-sea pressure hulls under small sample data conditions, avoiding the problems of large-scale calculations and complex experimental models required in traditional methods, significantly improving prediction efficiency and economy. It not only has high accuracy but also good adaptability and promotional value, providing strong technical support for engineering design and safety assessment in related fields.

[0059] Example 2 As attached Figure 9 As shown in the figure, this embodiment 2 provides a critical buckling load prediction system for deep-sea pressure hulls, including a target hull feature data acquisition module, a target hull feature data preprocessing module, and a critical buckling load prediction module.

[0060] The target shell feature data acquisition module is used to acquire the feature data of the target shell; the feature data of the target shell includes the geometric parameters, defect feature information, material property data and service temperature condition data of the target shell.

[0061] The target shell feature data preprocessing module is used to preprocess the feature data of the target shell to obtain preprocessed target shell feature data.

[0062] The critical buckling load prediction module is used to take the preprocessed target shell feature data as a pre-built shell critical buckling load prediction model and output the critical buckling load prediction result of the target shell.

[0063] Optionally, the deep-sea pressure hull critical buckling load prediction system described in Embodiment 2 further includes... The sample shell sample data acquisition module is used to acquire sample data of the sample shell; the sample data of the sample shell includes the characteristic data of the sample shell and the calculation results of the critical buckling load of the sample shell under different working conditions.

[0064] The model training module is used to train several predetermined basic regression models using sample data from the sample shell, thereby obtaining several trained basic regression models.

[0065] The model ensemble module is used to weight and merge several trained basic regression models based on ridge regression to obtain an ensemble model, which serves as a pre-built prediction model for the critical buckling load of the shell.

[0066] Example 3 As attached Figure 10 As shown, this embodiment 3 provides an electronic device, including: a memory for storing a computer program; a processor for executing the computer program to implement the steps of the method for predicting the critical buckling load of a deep-sea pressure hull; or, the processor for executing the computer program to implement the functions of each module in the above-mentioned system for predicting the critical buckling load of a deep-sea pressure hull.

[0067] For example, the computer program may be divided into one or more modules / units, which are stored in the memory and executed by the processor to complete the present invention. The one or more modules / units may be a series of computer program instruction segments capable of performing a preset function, the instruction segments describing the execution process of the computer program in the electronic device.

[0068] The electronic device may be a desktop computer, laptop, handheld computer, or cloud server, etc. The electronic device may include, but is not limited to, a processor and memory. Those skilled in the art will understand that the above are examples of electronic devices and do not constitute a limitation on the electronic device. It may include more components than described above, or combine certain components, or different components. For example, the electronic device may also include input / output devices, network access devices, buses, etc.

[0069] The processor can be a central processing unit, or other general-purpose processors, digital signal processors, application-specific integrated circuits, off-the-shelf programmable gate arrays or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor can be a microprocessor, or any conventional processor, etc. The processor is the control center of the electronic device, connecting various parts of the entire electronic device through various interfaces and lines.

[0070] The memory can be used to store the computer program and / or module. The processor implements various functions of the electronic device by running or executing the computer program and / or module stored in the memory and by calling the data stored in the memory.

[0071] The memory may primarily include a program storage area and a data storage area. The program storage area may store the operating system and at least one application program required for a given function (such as sound playback, image playback, etc.). The data storage area may store data created based on the use of the mobile phone (such as audio data, phonebook, etc.). Furthermore, the memory may include high-speed random access memory and non-volatile memory, such as hard disks, RAM, plug-in hard disks, smart memory cards, secure digital cards, flash memory cards, at least one disk storage device, flash memory device, or other volatile solid-state storage devices.

[0072] Example 4 This embodiment 4 also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the steps of the method for predicting the critical buckling load of a deep-sea pressure hull.

[0073] If the modules / units integrated in the deep-sea pressure hull critical buckling load prediction system are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium.

[0074] Based on this understanding, the present invention can implement all or part of the process in the above-mentioned method for predicting the critical buckling load of deep-sea pressure hulls, or it can be accomplished by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the above-mentioned method for predicting the critical buckling load of deep-sea pressure hulls. The computer program includes computer program code, which can be in the form of source code, object code, executable file, or a preset intermediate form, etc.

[0075] The computer-readable storage medium may include any entity or device capable of carrying the computer program code, recording media, USB flash drive, portable hard drive, magnetic disk, optical disk, computer memory, read-only memory, random access memory, electrical carrier signal, telecommunication signal, and software distribution medium, etc.

[0076] Example 5 This embodiment 5 provides a computer product, which includes a computer program stored in a computer-readable storage medium. The processor of the electronic device reads the computer program from the computer-readable storage medium and executes the computer program, so that the electronic device can execute the deep-sea pressure hull critical buckling load prediction method described in embodiment 1, which will not be repeated here.

[0077] It should be noted that those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The program can be stored in a computer-readable storage medium, and when the program is executed, it can include the processes of the embodiments of the above methods.

[0078] The critical buckling load prediction method for deep-sea pressure hulls described in this invention acquires feature data including hull geometric parameters, defect characteristics, material properties, and temperature conditions. After imputing missing values ​​and standardizing the data, the data is input into a pre-constructed critical buckling load prediction model, and the predicted critical buckling load of the target hull is output. During the training process of the pre-constructed critical buckling load prediction model, TabPFN, random forest, and support vector regression models are used to capture nonlinear relationships in the data. Among them, Bayesian optimization is used to fine-tune the hyperparameters of the random forest and support vector regression models. Secondly, ridge regression is used to weightedly combine the prediction results of different basic regression models to improve the overall prediction accuracy and obtain the pre-constructed critical buckling load prediction model. This invention can achieve efficient prediction of the critical buckling load of deep-sea pressure hulls and exhibits high accuracy and stability under small sample data conditions. At the same time, the use of ensemble learning and cross-validation techniques significantly improves the generalization ability and robustness of the model, reduces experimental costs, and enhances the practicality and application value of the system.

[0079] Compared to existing technologies, the critical buckling load prediction method for deep-sea pressure hulls described in this invention uses ridge regression as the meta-learner. By combining the prediction results of multiple basic regression models, it employs ensemble learning technology to weightedly combine the model prediction results, thereby effectively improving the accuracy and stability of predicting the critical buckling load of deep-sea pressure hulls. This method, under conditions of small sample data, leverages the advantages of each basic regression model to minimize the bias that a single model might introduce, significantly improving the prediction capability for critical buckling loads under complex working conditions. Through ensemble learning, the pre-constructed critical buckling load prediction model for the hull outperforms traditional single models on the test set, more accurately reflecting the actual behavior of deep-sea pressure hulls under different defects and temperature conditions, thus improving the reliability of the prediction results. It effectively reduces the reliance on finite element simulation and experiments when assessing the ultimate bearing capacity of deep-sea hulls, greatly reducing the time and cost required for traditional methods in ultimate bearing capacity analysis. Specifically, the integration of the TabPFN model with other basic regression models effectively improves the prediction accuracy of the ultimate bearing capacity of deep-sea pressure hulls. Furthermore, by combining machine learning methods, it achieves efficient prediction of the ultimate bearing capacity of the hull under small sample data.

[0080] The above embodiments are merely one of the implementation methods for achieving the technical solution of the present invention. The scope of protection claimed by the present invention is not limited to this embodiment, but also includes any variations, substitutions and other implementation methods that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention.

Claims

1. A method for predicting the critical buckling load of a deep-sea pressure hull, characterized in that, include: Acquire the characteristic data of the target shell; wherein, the characteristic data of the target shell includes the geometric parameters, defect feature information, material property data and service temperature condition data of the target shell; The feature data of the target shell are preprocessed to obtain the preprocessed feature data of the target shell. The preprocessed target shell feature data is used as input to the pre-constructed shell critical buckling load prediction model, and the output is the critical buckling load prediction result of the target shell. The construction process of the pre-constructed shell critical buckling load prediction model is as follows: Obtain sample data of the sample shell; wherein, the sample data of the sample shell includes the characteristic data of the sample shell and the calculation results of the critical buckling load of the sample shell under different working conditions; Using sample data from the sample shell, several predetermined basic regression models are trained to obtain several trained basic regression models. Ridge regression is used to weight and merge several trained basic regression models to obtain an integrated model, which is then used as a pre-constructed prediction model for critical buckling loads of the shell.

2. The method for predicting the critical buckling load of a deep-sea pressure hull according to claim 1, characterized in that, The geometric parameters of the target shell include its radius and thickness; the defect feature information of the target shell includes its defect type and size; and the service temperature condition data of the target shell includes its inner wall temperature and outer wall temperature.

3. The method for predicting the critical buckling load of a deep-sea pressure hull according to claim 1, characterized in that, The sample shell is a deep-sea pressure hull of the same type or with the same geometric parameters as the target shell; the characteristic data of the sample shell includes the geometric parameters, defect characteristic information, material property data and service temperature condition data of the sample shell; The geometric parameters of the sample shell include its radius and thickness; the defect feature information of the sample shell includes its defect type and size; and the service temperature condition data of the sample shell includes its inner wall temperature and outer wall temperature.

4. The method for predicting the critical buckling load of a deep-sea pressure hull according to claim 1, characterized in that, The critical buckling load calculation results of the sample shell under different working conditions were obtained by physical experiment method or finite element simulation method.

5. The method for predicting the critical buckling load of a deep-sea pressure hull according to claim 1, characterized in that, Several predetermined basic regression models include tabular prior data fitting network models, random forest models, and support vector regression models.

6. The method for predicting the critical buckling load of a deep-sea pressure hull according to claim 1, characterized in that, Using sample data from the sample shell, several predetermined basic regression models are trained to obtain several trained basic regression models. In the process, a five-fold cross-validation method is introduced to validate the models.

7. A critical buckling load prediction system for deep-sea pressure hulls, characterized in that, include: The target shell feature data acquisition module is used to acquire the feature data of the target shell; wherein, the feature data of the target shell includes the geometric parameters, defect feature information, material property data and service temperature condition data of the target shell; The target shell feature data preprocessing module is used to preprocess the feature data of the target shell to obtain the preprocessed target shell feature data. The critical buckling load prediction module is used to take the preprocessed target shell feature data as input to the pre-built shell critical buckling load prediction model and output the critical buckling load prediction result of the target shell. The construction process of the pre-constructed shell critical buckling load prediction model is as follows: Obtain sample data of the sample shell; wherein, the sample data of the sample shell includes the characteristic data of the sample shell and the calculation results of the critical buckling load of the sample shell under different working conditions; Using sample data from the sample shell, several predetermined basic regression models are trained to obtain several trained basic regression models. Ridge regression is used to weight and merge several trained basic regression models to obtain an integrated model, which is then used as a pre-constructed prediction model for critical buckling loads of the shell.

8. An electronic device, characterized in that, include: A processor is used to execute computer programs; A computer-readable storage medium storing a computer program, which, when executed by the processor, performs the critical buckling load prediction method for deep-sea pressure hulls as described in any one of claims 1-6.

9. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the method for predicting the critical buckling load of deep-sea pressure hulls as described in any one of claims 1-6.

10. A computer program product, characterized in that, The computer program product includes a computer program that, when executed by a processor, implements the method for predicting the critical buckling load of deep-sea pressure hulls as described in any one of claims 1-6.

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