A machine learning profile plunging into water slamming load prediction method fusing physical characteristics

Abstract

The application discloses a machine learning profile water entry slamming load prediction method fusing physical characteristics, and relates to the technical field of ship and ocean engineering structure hydrodynamic performance prediction, which obtains multi-working condition time history data of profile water entry slamming load, constructs a physical guide characteristic vector containing a geometric characteristic parameter, a water entry speed coupling term and a time square term according to a slamming mechanics physical principle, takes the characteristic vector as input, corresponding slamming load value as output, trains a random forest regression model to output a slamming load prediction result under a given working condition. Through testing, the determination coefficient of the test set reaches 0.92 to 0.99 under the wedge-shaped profile working condition, the single working condition prediction time is shortened to within seconds, the efficiency and accuracy of ship and ocean structure hydrodynamic performance analysis are significantly improved, and the core system of the method has the potential of extending application to various profile shapes.

Description

Technical Field

[0001] This invention relates to the field of hydrodynamic performance prediction technology for ships and marine engineering structures, and in particular to a method and system for predicting profile water impact loads by integrating machine learning with physical features. Background Technology

[0002] Slamming impact is a typical hydrodynamic phenomenon in shipbuilding and marine engineering, and accurate prediction of slamming loads is crucial for structural safety design. Traditional slamming load prediction methods mainly include the following categories: Empirical formula methods, such as Wagner theory and Von Karman theory, are based on simplified theoretical derivations. Although they are simple to calculate, their accuracy is limited and their applicability is narrow. For working conditions with strong nonlinearity, such as large-angle geometry and high-speed water entry, the prediction error can be large, reaching more than 50%.

[0003] Computational fluid dynamics (CFD) numerical simulation obtains flow field information by solving the Navier-Stokes equations. Although it has high accuracy, it is computationally expensive, requiring several hours to several days of computation time for a single working condition. The technical requirements for mesh generation and turbulence model selection are high, which cannot meet the needs of rapid iteration in engineering design.

[0004] The experimental method, which directly measures the impact load through physical model tests, is reliable but has a long cycle, high cost, and problems such as scale effect and measurement error, making it difficult to be widely used in engineering design.

[0005] With the development of machine learning technology, existing research has attempted to introduce data-driven methods into the field of hydrodynamic prediction. However, most methods suffer from problems such as insufficient feature engineering, failure to fully utilize domain knowledge, inappropriate model selection, limited generalization ability, lack of physical constraints, lack of physical interpretability of prediction results, and imperfect evaluation systems. Existing machine learning methods are mostly designed for specific fixed shapes and lack a general prediction framework that can flexibly adapt to different cross-sectional geometries and has clear physical interpretability. Summary of the Invention

[0006] To address the inherent contradiction between computational efficiency and accuracy in traditional methods for predicting water impact loads from water profiles, existing machine learning methods suffer from a lack of physical guidance in feature engineering, poor interpretability of prediction results, poor adaptability to complex conditions, inability to achieve rapid prediction, and limited engineering applicability. This invention proposes a method and system for predicting water impact loads from water profiles that integrates machine learning with physical features. Specifically, this invention provides a fast and accurate intelligent prediction solution for water impact loads generated during water entry of common water profile shapes in shipbuilding and marine engineering. It can be widely applied in ship design, marine engineering equipment development, and equipment splashdown analysis. This invention combines the high precision of theoretical model calculations / numerical simulations with the high efficiency of machine learning, providing an innovative technical approach for the engineering application of complex hydrodynamic problems. The intelligent prediction framework provided by this invention, based on a combination of physical-guided feature engineering and random forest algorithms, constructs a knowledge transfer bridge from multi-source data to machine learning models, significantly improving computational efficiency while ensuring prediction accuracy. Its core methodology has the potential to be extended to water impact problems with various water profile shapes. The technical solution of this invention is as follows: This application provides a machine learning-based method for predicting water entry slamming loads in a profile, which integrates physical features. The method first collects slamming load time-history data of the target profile's water entry process under various operating conditions. Each data point records the geometric feature parameters, water entry velocity, time point, and slamming load value for the corresponding operating condition combination. Then, based on the physical laws of slamming mechanics, the original operating condition parameters are transformed and combined. A coupling term reflecting the synergistic effect of geometric feature parameters and water entry velocity, and a time-squared term characterizing the nonlinear evolution of the slamming load over time, are constructed on top of the basic features, thus forming a feature vector with clear physical meaning. Based on this, the constructed feature vector is used as the model input, and the corresponding slamming load value is used as the model output to train a random forest regression model. After training, only the original operating condition parameters of the target profile need to be input; the model can automatically construct features and output the predicted water entry slamming load result for that operating condition combination.

[0007] Regarding data sources, multi-condition time-history data is acquired through at least one of several methods, including MLM slamming theory models, CFD numerical simulations, and physical model experiments. Regardless of the data source, a unified preprocessing and training process is employed. The preprocessing process includes: automatically identifying the condition data files in a pre-defined directory structure using an automated traversal algorithm; automatically extracting geometric parameters, water ingress velocity, and time point parameters; and uniformly converting the multi-source data into a standardized training set format. Based on the principle of physical consistency, data points with negative slamming load values ​​or those that do not conform to physical specifications are automatically filtered and cleaned to ensure the quality and reliability of the training data.

[0008] In terms of feature construction, this invention extracts the slope angle from the original time history data for wedge-shaped profiles. , water entry speed and time point These three fundamental physical quantities serve as basic operating condition characteristics; based on the physical principles of impact mechanics, angle-velocity coupling terms are further constructed through cross-combination of these characteristics. Sum of time squared terms As a nonlinear interaction feature, It can simulate the synergistic enhancement effect of geometric characteristic parameters and water entry velocity on slamming load, and its physical meaning corresponds to the slamming load and... Approximate relationship, This reflects the nonlinear law of the quadratic increase of the impact load over time, characterizing the acceleration effect of the impact process; based on mathematical and geometric principles, the fundamental characteristics are normalized and transformed, including... Convert from degrees to radians As a characteristic of geometric transformation, the conversion satisfies the requirements of trigonometric function operations and paves the way for the subsequent introduction of sin( ), cos( It lays the foundation for more complex geometric features, and also includes optional position normalization features, which construct normalized position coordinates when the data contains measurement point position information, eliminating the influence of position scale on the model; Using the above feature construction method, the original three-dimensional feature vector [ , , The system is systematically expanded into a high-dimensional feature vector composed of the above six features. This results in a complete mathematical representation of the spatiotemporal evolution of impact force, which not only enhances the physical meaning of the features and the interpretability of the model, but also significantly improves the machine learning model's ability to capture complex physical phenomena. For other profile shapes besides wedge-shaped profiles (semi-circular profiles, V-shaped profiles, or combinations thereof), based on the geometric feature parameters of the target profile shape and following the same physical principles, coupling terms and geometric transformation features of the geometric feature parameters and water entry velocity corresponding to the target profile shape are constructed, forming a high-dimensional physical guidance feature vector for that target profile shape.

[0009] In terms of model training, the random forest regression model extracts multiple sample subsets with replacement from the training set through Bootstrap resampling. On each sample subset, the corresponding decision tree is trained using the CART regression tree algorithm. During the node splitting process of each decision tree, a feature random selection strategy is adopted, and the optimal splitting feature and splitting threshold are determined by minimizing the square error criterion, thereby constructing multiple decision trees with differences. Finally, the prediction results of all decision trees are arithmetically averaged to obtain the output of the random forest regression model, which can effectively reduce the variance of the model, improve prediction stability and generalization ability.

[0010] Furthermore, during the splitting process at each node, after randomly selecting a subset of features from all input features, each feature in the subset and all its possible values ​​are traversed. The feature that minimizes the sum of the squared errors of the slam load values ​​of the samples in the two sub-regions after the split, and the specific value of that feature are selected as the optimal splitting feature and splitting threshold. After the split is completed, the predicted value of each leaf node is the arithmetic mean of the true values ​​of the slam load of all training samples in that node.

[0011] In terms of model optimization, this invention can also supplement training samples in weak working condition areas with large prediction errors based on residual analysis and feature importance analysis of the prediction results output by the random forest regression model, and / or adjust the composition of the physical guidance feature vector (such as removing features with low contribution and adding physical features that can capture residual patterns) to improve the prediction accuracy of the model in the region and optimize the feature vector. The random forest regression model is then retrained based on the updated data and features, thereby forming a closed-loop optimization mechanism.

[0012] This application also provides a profile entry slamming load prediction system that implements the above method. The system includes a data acquisition and preprocessing module, a physical-guided feature engineering module, a random forest model training module, and a prediction application module, all connected in series. The data acquisition and preprocessing module is responsible for acquiring and cleaning multi-condition time-history data of the target profile entry slamming load. The time-history data includes different geometric feature parameters of the target profile, entry velocity, time-point condition combinations, and corresponding slamming load values. The physical-guided feature engineering module is responsible for performing feature transformation and combination on the original condition parameters in the time-history data according to the physical principles of slamming mechanics, constructing a physical-guided feature vector containing a coupling term of geometric feature parameters and entry velocity, as well as a time squared term. The random forest model training module is responsible for training a random forest regression model using the physical-guided feature vector as input and the corresponding slamming load value as output. The prediction application module is responsible for receiving the actual original condition combination parameters of the target profile and outputting the profile entry slamming load prediction result under that condition combination based on the trained random forest regression model.

[0013] Furthermore, the physics-guided feature engineering module can be internally divided into a basic operating condition feature extraction unit, a nonlinear interactive feature construction unit, and a geometric transformation feature construction unit. These units are responsible for extracting basic physical quantities from the original time-history data, constructing angle-velocity coupling terms and time square terms, and performing angle unit conversions, respectively, ultimately outputting a six-dimensional feature vector. .

[0014] The system also features a visualization analysis module, providing prediction interfaces for sparse, medium, and dense time resolutions. It also allows users to customize the number of time points to generate slam load prediction results with varying time point densities, balancing prediction accuracy and computational efficiency. The visualization analysis module generates six types of visualization graphs, including a comparison graph of predicted and actual values ​​for a single load condition, a residual analysis graph, a comparison graph of predictions at different time densities, a comparison graph of different geometric feature parameters at a fixed velocity, a comparison graph of different velocities with fixed geometric feature parameters, and a feature importance analysis graph. Specifically, the comparison graph of predicted and actual values ​​for a single load condition displays both the time-history curve comparison and a scatter plot of predicted and actual values; the residual analysis graph includes a residual-predicted value relationship graph and a residual distribution histogram; the comparison graph of predictions at different time densities displays prediction curves for sparse, medium, and dense time resolutions under the same load condition; the comparison graph of different geometric parameters at a fixed velocity displays the differences and trends in the slam load time-history curves for different geometric feature parameters at the same velocity; and the comparison graph of different velocities with fixed geometric parameters displays the differences and trends in the slam load time-history curves for different velocities with the same geometric feature parameters. All visualizations support both PNG and PDF output formats to ensure image quality and compatibility. Prediction results are also saved in CSV and TXT formats. CSV format is easy for data processing and analysis software to read, while TXT format uses tab delimiters for easy reading by other programs, ensuring the portability and usability of the prediction results.

[0015] Furthermore, the system can also be configured with a feedback optimization module, which, based on the results of residual analysis and feature importance analysis, sends directional data augmentation instructions to the data acquisition and preprocessing module, and / or sends feature adjustment instructions to the physically guided feature engineering module, in order to drive iterative optimization of the system.

[0016] Compared with the prior art, the present invention has the following advantages: First, this invention integrates the physical principles of impact mechanics into feature engineering, constructing features with clear physical meanings such as angle-velocity coupling terms and time square terms. This enables the random forest model to learn the nonlinear relationship between impact load and various physical quantities. Tests have shown that, under given conditions in a wedge profile (incline angle 10° to 45°, entry velocity 0.1 to 1.0 m / s), the coefficient of determination on the test set... The predicted values ​​reached 0.92 to 0.99, and the results were in high agreement with the benchmark data provided by the MLM theoretical model, verifying the effectiveness and reliability of the prediction model in this application. Within the operating conditions covered by the training data, the model can accurately reproduce and predict the time-history curve of the impact force, demonstrating that the model has the potential to predict the impact force of water entry into more complex profiles.

[0017] Secondly, this invention, through a modeling process of one-time modeling in the training phase and a second-level response in the prediction phase, can complete the prediction of the complete time history of a single working condition within a few seconds to tens of seconds. Compared with traditional CFD numerical simulation methods, the computational efficiency is improved by 2 to 3 orders of magnitude (based on the same wedge profile working condition range), which can meet the needs of rapid evaluation in engineering design and parameter analysis.

[0018] Third, the physical-guided feature engineering framework constructed in this invention can systematically characterize the combined effects of different working conditions (geometric feature parameters, water entry velocity, and time), enabling the trained model to handle complex parameter combinations. Compared to some simplified theoretical formulas with limited applicability, this method, through data-driven learning, exhibits good generalization ability within the parameter space defined by the training data, which is beneficial for expanding adaptability to complex parameter combinations.

[0019] Fourth, each input feature of this invention (such as angle, velocity, time squared term, and angle-velocity coupling term) has a clear physical meaning. After the model is trained, feature importance analysis can be performed, which enhances the physical credibility of the prediction results and helps engineers understand and trust the model output.

[0020] Fifth, this invention achieves fully automated processing of the entire chain, from automatic loading of raw multi-source data, physical cleaning, feature engineering, model training to result prediction and visualization, which helps to reduce the cost of manual intervention and the threshold for technical application.

[0021] Sixth, the intelligent prediction framework combining physical guidance feature engineering and random forest algorithm proposed in this invention has methodological universality. For other profile shapes besides wedges (such as semicircles and V-shapes), those skilled in the art can follow the same physical modeling ideas, identify the key geometric feature parameters of the new shape, construct the corresponding physical guidance features, and retrain and predict using the same model architecture provided by this system. This provides a scalable and transferable intelligent prediction framework for solving a wider range of profile entry slamming problems. Attached Figure Description

[0022] Figure 1 This is a block diagram of the overall system architecture of the present invention, showing the connection relationships between the data acquisition and preprocessing module, the physical guided feature engineering module, the random forest model training module, the prediction application and visualization analysis module, and the feedback path.

[0023] Figure 2 This is a workflow diagram for the data acquisition and preprocessing module, showing the sequence of steps including directory traversal, multi-source data loading, operating condition parameter annotation, physical consistency cleaning, and dataset construction.

[0024] Figure 3 This is a schematic diagram of the feature construction of the physical-guided feature engineering module, showing the transformation process from the three-dimensional original feature space to the six-dimensional physical-guided feature space.

[0025] Figure 4 This is a schematic diagram of the algorithm for the training module of the random forest model, showing the hierarchical structure of Bootstrap resampling, decision tree construction, and ensemble prediction.

[0026] Figure 5 This is a schematic diagram of the interface for the predictive application and visualization analysis module, showing the input area for operating parameters, the display area for prediction results, and the multi-tab visualization display area.

[0027] Figure 6 The core verification results of the intelligent prediction model of this invention are shown in (1), which shows the comparison of the time history curves of the wedge profile water slamming load under typical working conditions, and (2) which shows the scatter plot of the predicted value and the actual (benchmark) value of the wedge profile water slamming load under the same working conditions. Detailed Implementation

[0028] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings.

[0029] This application provides a method and system for predicting water entry slamming loads from a profile using machine learning and physical features. Both are based on the same inventive concept, and the following detailed description focuses on the water entry slamming load prediction system. This embodiment uses a wedge-shaped profile as the preferred implementation. The system's hardware requirements include a CPU i5 or higher processor, 8GB or more of memory, and 10GB or more of hard disk space for storing training data and result files. The software requirements include Python 3.7 or higher, with necessary libraries installed, including scientific computing libraries NumPy 1.19+ and Pandas 1.2+, machine learning library Scikit-learn 0.24+, data visualization libraries Matplotlib 3.3+ and Seaborn 0.11+, and standard libraries for file operations.

[0030] The implementation of the system consists of four main modules, each with a clearly defined technical implementation and parameter settings. Figure 1The system architecture diagram of this invention is shown. The diagram clearly depicts the complete workflow of the system from data input to result output in flowchart form. The system's workflow begins with multi-source data input. This data first enters the data acquisition and preprocessing module, which automatically traverses the directory structure, extracts operating parameters, performs physical consistency cleaning, and constructs standardized training and test sets. The preprocessed data flows to the next core module: the physical-guided feature engineering module. This module transforms and combines the original features based on the principles of impact mechanics, constructing nonlinear interactive features and geometric transformation features with clear physical meaning, forming a high-dimensional feature space. Next, the featured data enters the random forest model training module. This module uses Bootstrap resampling and random feature selection strategies to train multiple decision trees and constructs the final prediction model through ensemble learning methods. Simultaneously, a test set is used to evaluate the model's performance. The trained model serves the prediction application and visualization analysis module. This module receives raw operating parameters input by the user, automatically converts them into high-dimensional physical guidance feature vectors, and generates slamming load predictions for multiple time points. It also outputs comprehensive visualization results, including time-history comparison charts, residual analysis charts, and multi-operating-condition comparison charts, ultimately generating a comprehensive performance report. The entire architecture combines linear serial processing with feedback loops, with modules connected through standardized data interfaces to form a complete, automated, and scalable intelligent prediction system.

[0031] One of the core advantages of this system lies in its scalability of data acquisition and compatibility with data sources. Regarding operational condition scalability, the system utilizes a dynamic directory traversal algorithm, without limiting fixed geometric feature parameters, velocity quantities, or values. Users can provide arbitrary combinations of operational condition data as needed, and the system can automatically identify and process them, greatly expanding the applicability of the method. In terms of multi-source data compatibility, to reduce data acquisition costs and improve the practicality of the method, the system supports data generated by the efficient semi-analytical method of MLM (Modified Logvinovich Model) impact theory. While maintaining a certain level of accuracy, the MLM model's computational speed far exceeds that of CFD, enabling the rapid generation of a large number of high-quality samples for machine learning training. Simultaneously, the system is also compatible with data generated from high-precision CFD numerical simulations and physical model experiments, achieving full-spectrum data fusion from high efficiency to high precision. Regarding a unified processing workflow, regardless of the data source, the system employs a unified preprocessing, feature engineering, and model training process to ensure the consistency and universality of the technical solution.

[0032] The following is a detailed explanation of each module. The steps in the profile water impact load prediction method can also be implemented by referring to the specific technical content of the corresponding module, which will not be repeated here.

[0033] (1) Data acquisition and preprocessing module This module is responsible for acquiring raw time history data from multi-source impact load data, and its design is highly scalable, capable of adapting to data acquisition needs of different profile shapes. Figure 2 The flowchart illustrates the workflow of the data acquisition and preprocessing module, detailing the entire process from raw data to a standardized training set. The workflow begins with a directory structure traversal step, where the module uses an automated traversal algorithm to identify working condition data files within a pre-defined directory structure. For example, it automatically scans the data storage directory according to a pre-defined "angle / velocity / data file" hierarchy, identifying all available working condition data files. Next, the module proceeds to a multi-source data loading step, reading time-impact force time-history data in CSV format. Regardless of whether the data originates from MLM or other impact theory models, CFD simulations, or physical experiments, a unified data parsing method is used. Following this is the automatic working condition parameter labeling step, where the module intelligently extracts key working condition parameters such as geometric feature parameters and entry velocity from the directory path and filenames, adding corresponding labels to each data point, including geometric feature parameters (for wedge profiles, this is the slope angle). ), water entry speed and time point In this embodiment, the module automatically traverses 48 working conditions, including 8 ramp angles (10°, 15°, 20°, 25°, 30°, 35°, 40°, 45°) and 6 water entry velocities (0.1, 0.2, 0.4, 0.6, 0.8, 1.0 m / s), ensuring the comprehensiveness and representativeness of the training data. Furthermore, for extremely large datasets, the sampling rate can be adjusted or an incremental learning strategy can be employed to balance memory usage and model performance.

[0034] The next step is physical consistency data cleaning. Based on physical consistency principles (such as the hydrodynamic principle of non-negative impact loads), this module automatically filters and cleans data points that do not conform to physical reality, such as those with negative impact load values, and records the cleaning log to ensure the quality and reliability of the training data. Finally, the dataset construction and standardization steps convert the cleaned data into a standardized training set format, providing standard input for subsequent feature engineering. The entire process connects each step with arrows, forming a clear data processing chain, and includes error handling and logging mechanisms to ensure the reliability and traceability of data processing.

[0035] (2) Physical guidance feature engineering module This module integrates the physical principles of impact mechanics into the machine learning feature engineering process. Through feature transformation and combination techniques, it transforms the original operating parameters into a high-dimensional feature space with clear physical meaning and mathematical completeness. Figure 3This diagram illustrates the feature construction of the Physically Guided Feature Engineering module. Through a visualization of feature space transformation, it clearly presents the construction process from raw features to physically guided features. The left side of the diagram shows the raw feature space, containing three basic features: slope angle... (Unit: degrees) Water entry velocity (Unit: m / s) and time (Unit: seconds), these features are represented in three-dimensional coordinates, with each set of data points corresponding to the slamming load value of a specific working condition at a specific time. The middle section illustrates the feature transformation and combination process, which achieves feature expansion through the following three core building blocks: The basic working condition feature extraction unit directly retains the original feature space, constituting the core elements of the model input. The nonlinear interactive feature construction unit constructs nonlinear interactive features based on the physical laws of impact mechanics, including angle-velocity coupling terms (…). ) and time squared term ( The diagram uses cross lines and square operators to visually represent the geometric transformation features. Geometric transformation feature construction units, based on mathematical and geometric principles, perform normalized transformations on fundamental features, including angle-radian conversions (…). This converts the angle unit from degrees to radians, satisfying the requirements of trigonometric function operations and laying the foundation for introducing more complex geometric features such as sin(β) and cos(β). When the data includes measurement point location information, normalized location coordinates can also be constructed to eliminate the influence of location scale on the model.

[0036] Among them, the angle-velocity coupling term simulates the synergistic enhancement effect of the lift angle and entry velocity on the slamming load, and its physical meaning corresponds to the slamming load and... The approximate relationship is explained in the following principle: Based on Wagner's slamming theory, the approximate expression for the slamming force of a wedge entering water is:

[0037] in, For fluid density, For the speed of entry into the water, The length of the wetted section. This is the angle of ascent. Under small angle conditions, (in radians), therefore the impact force can be approximated as:

[0038] This provides a basis for constructing angle-velocity coupling terms ( This provides the theoretical foundation for the physical theory. The time square term ( The introduction of ) is based on the nonlinear evolution law of the impact load exhibiting a quadratic increase over time in the initial stage, which characterizes the acceleration effect of the impact process.

[0039] The diagram on the right shows the expanded high-dimensional feature space. Using the aforementioned feature construction method, this module transforms the original three-dimensional feature space... , , Expanded into a six-dimensional feature vector , , , , , This forms a mathematical representation of the spatiotemporal evolution of impact loads. The figure shows this extension by adding coordinate dimensions, and uses different outer shapes to distinguish between original features and structural features.

[0040] In this embodiment, all constructed features are deterministic mathematical transformations based on the original three-dimensional features, and no additional experimental data or physical quantities are introduced during the construction process. The original three-dimensional features of a sample correspond one-to-one with the constructed six-dimensional feature vector in the time dimension, and the output impact load value of that sample corresponds to a specific moment. and specific working conditions ( , The true value of the impact load.

[0041] (3) Random Forest Model Training Module This module uses the random forest algorithm from the ensemble learning method as the core prediction model, and determines the optimal configuration through parameter optimization, including key parameters such as the number of decision trees, the maximum tree depth, the minimum number of samples required for internal node splits, and the minimum number of samples required for leaf nodes. Figure 4 This diagram illustrates the algorithmic principle of the random forest model training module. Through a multi-layered structured illustration, it details the core principles and workflow of the random forest ensemble learning algorithm. The upper part of the diagram shows the Bootstrap resampling process, which involves randomly sampling multiple subsets of samples with replacement from the original training set (three subsets in the example). An independent decision tree model is trained on each subset, ensuring the model's diversity and robustness. In this embodiment, the preferred value for the number of decision trees, B, is 200, with an adjustable range of 100 to 300. A higher value results in a more stable model but also increases computational cost.

[0042] The central part of the diagram illustrates the decision tree construction and training process. For each sample subset, the CART (Classification and Regression Tree) regression tree method is employed. During the node splitting process of each decision tree, a feature random selection strategy is used. This involves randomly selecting a feature subset from all six features, traversing all features within that subset, and searching for the optimal splitting threshold for all possible values ​​of each feature. This ensures that the impact load values ​​of the samples in the two sub-regions after splitting are most similar, i.e., the sum of squared errors is minimized. Specifically, during node splitting, for the feature set of the wedge profile... The algorithm needs to traverse all possible features. and all possible split thresholds Choose the feature that minimizes the sum of the following squared errors. and threshold :

[0043] in: The splitting feature, in this embodiment, can be the angle of ascent. , water entry speed ,time Time squared term Angle-velocity interaction item or angle in radians Any one of them. The splitting threshold is defined for a selected feature. A specific numerical value. For example, if the feature is selected as the slope angle. ,So It's an angle value (like 20°) used to divide the data into... ≤ 20° and Two regions >20°. Indicates based on features and threshold The first region to be divided (e.g., all) (Samples ≤ 20°). Indicates based on features and threshold The second region (e.g., all) Samples >20°). Indicates the area The average of the true values ​​of the slam load for all samples within the sample. Indicates the area The average of the true values ​​of the slam load for all samples. Indicates the first The true impact load value of each sample (unit: N). Indicates the first The feature vector of each sample contains the values ​​of the above 6 features.

[0044] The diagram illustrates a typical structure of a decision tree, including the root node (as shown in the example ""). ≤20°?”), internal nodes (such as “ in the example”) ≤10, ≤0.01s” and leaf nodes (such as “Predicted value: 120N” in the example), and labeled the splitting features at the nodes (such as ≤20° >0.6, etc.) and predicted values. By recursively applying this splitting criterion, the decision tree divides the feature space into multiple rectangular regions, each corresponding to a predicted value, which is the average of the true impact loads of the samples within that region. In this embodiment, the preferred maximum depth of the decision tree is 25, with an adjustable range of 20 to 30, used to control model complexity and overfitting risk; the preferred minimum number of samples required for internal node splitting is 5, and the preferred minimum number of samples required for leaf nodes is 2. Both can be adjusted according to the actual amount of data, and can be appropriately increased when the amount of data is large.

[0045] The lower part of the diagram illustrates the integrated prediction and output process. After all decision trees are constructed, the new input feature vector constructed by the physical-guided feature engineering module is... Each decision tree provides an independent slam load prediction. The final prediction result output by the random forest regression model is the arithmetic mean of the predictions from all decision trees, expressed as:

[0046] in, Indicates the first b Decision trees for input The predicted value is B, where B is the total number of decision trees (preferably B=200).

[0047] This module also sets a random seed (preferably random_state=42) to ensure experimental repeatability, enables multi-core parallel computing to fully utilize computing resources, and uses an 80%-20% training-test set split to evaluate the model's generalization performance. The right side of the figure also shows model performance evaluation metrics, including mean squared error (MSE) and coefficient of determination (COP). The calculation formula and numerical results of the model are used to quantitatively evaluate and compare model performance through these two indicators. The mean squared error (MSE) measures the predicted value. Compared with the true value The mean squared difference between them is expressed as:

[0048] Coefficient of determination ( The proportion of data variability explained by the model is expressed as:

[0049] in, The model predicts the first The slam load value of each sample. The average of the true slam loads for all samples. This represents the number of samples in the test set.

[0050] After the model is trained, the contribution of each feature to the prediction can be extracted using the feature importance attribute built into the random forest model, such as... Figure 3 The feature importance is shown in the bar chart. This contribution is calculated based on the reduction in mean squared error and can be used to verify the rationality of the physically guided feature construction.

[0051] (4) Predictive Application and Visualization Analysis Module This module provides complete predictive applications and results analysis capabilities. Figure 5 The diagram illustrates the interface of the predictive application and visualization analysis module. It presents the system's user interaction and result visualization functions in the form of a software interface layout. The upper left corner of the interface is the input area for operating parameters, providing drop-down menus and numerical input boxes for users to select or input parameters such as the ramp angle and inlet velocity, as well as time density options (sparse, medium, dense). This module receives low-dimensional raw operating parameters input by the user, namely the ramp angle. , water entry speed and the time point that users expect to predict Alternatively, after selecting the time density option, the system automatically calls a pre-trained random forest model for prediction. The six-dimensional feature vector is automatically constructed by the system in the background, transparent to the user. In this embodiment, the module provides three preset time resolution prediction interfaces: sparse (20 points), medium (50 points), and dense (100 points). It also supports custom time series with any number of points to adapt to different accuracy requirements. The prediction time range is adaptively determined based on the time span of the training set's time history data.

[0052] The upper right corner of the interface displays real-time prediction results, showing key indicators such as maximum slamming load and slamming impulse under the current parameters in the form of numbers and simple curves. The middle of the interface is a multi-tab visualization area, containing six tabs corresponding to different types of analysis graphs: The first page is a "Single-condition Time History Comparison Chart," which displays the time history curves of predicted values ​​and actual (benchmark) values ​​side by side, as well as a scatter plot of predicted values ​​versus actual values; the second page is a "Residual Analysis Chart," which shows the relationship between residuals and predicted values, as well as a residual distribution histogram; the third page is a "Comparison Chart of Different Time Densities," which plots prediction curves with sparse, medium, and dense time resolutions in the same coordinate system; the fourth page is a "Fixed-velocity Multi-angle Comparison Chart," which displays a cluster of slamming load time history curves at different ramp angles under the same velocity; the fifth page is a "Fixed-angle Multi-velocity Comparison Chart," which displays a cluster of slamming load time history curves at different entry velocities under the same ramp angle; and the sixth page is a "Special Analysis Report," which summarizes the model performance indicators and statistical analysis results. The bottom of the interface features a function operation area, providing buttons for prediction execution, result export (supporting CSV / TXT / PNG / PDF formats), report generation, and system status and log display bars. The entire interface design follows user experience principles, with a logical layout, clear functions, and support for interactive exploration and analysis.

[0053] (5) Feedback optimization module like Figure 1 As shown, this system contains two feedback paths, forming a closed-loop optimization mechanism. Feedback path A points to the data acquisition and preprocessing module: when visualization analysis reveals a systematic prediction bias in a specific operating condition area, this module generates targeted data augmentation tasks to supplement training samples in weak areas. For example, when the prediction error heatmap shows a significantly warm color and high error in the operating condition area at an angle of 15° and a speed of 0.8 m / s, the system generates supplementary data acquisition tasks for this area and its adjacent parameter ranges (12° to 18°, 0.6 to 1.0 m / s). Additional training samples can be quickly calculated using the MLM theoretical model, cleaned, and added to the training set. Feedback path B points to the physical-guided feature engineering module: when feature importance analysis shows a consistently low contribution of a certain feature, or residual analysis reveals residual patterns that the current feature fails to capture, this module assesses whether redundant features need to be removed or new physical-guided features added to optimize the feature space composition. For example, when the feature "time"... When the importance score is significantly lower than other features, the feature can be evaluated for removal (because its physical information has been...). More effective characterization), while adding an angle sine term sin( ) and the square term of velocity Features such as these are used to attempt to capture residual nonlinear patterns.

[0054] The two feedback paths work together to retrain the random forest model based on the simplified and enhanced feature space and the expanded training dataset, enabling the system to continuously evolve through iterative loops and continuously improve its prediction performance and generalization ability.

[0055] (6) Verification results Figure 6 The core verification results of the prediction model of this invention are shown. The figure systematically verifies the accuracy and reliability of the intelligent prediction system through two parallel sub-figures. Sub-figure (1) is a comparison of the time history curves under typical working conditions. Under the typical working conditions of wedge profile, 30° incline angle and 0.6m / s water entry velocity, the slamming load time history curve (blue solid line) calculated by MLM theory is used as the benchmark. The predicted value (red dots) of the model of this invention under this working condition is highly consistent with the benchmark curve, which intuitively proves the model's ability to accurately capture the evolution law of time history under a single working condition. Sub-figure (2) is a scatter plot of the prediction accuracy of the corresponding working condition under the test set. The horizontal axis is the benchmark value of the slamming force calculated by MLM theory (also known as the true value), and the vertical axis is the predicted value of the model. The scatter plots of the predicted value and the benchmark value are closely distributed on both sides of the diagonal of y=x, and the coefficient of determination is... The accuracy reached 0.92 to 0.99, which statistically validated the model's high-precision predictive ability across the entire test set.

[0056] In this embodiment, subgraph (1) can intuitively show the trend consistency of the entire curve, making it easy to observe whether the model accurately captures the overall pattern of the slamming force increasing, peaking, and decaying over time; subgraph (2) tends to extract the predicted value at each time point separately and compare it with the benchmark value one by one, making it easy to observe whether there is a systematic deviation (such as whether all points are evenly distributed on both sides of the diagonal of y=x, or whether there is an overall trend of being too high or too low). The combination of the two achieves a comprehensive verification of the model's predictive ability from both trend and numerical perspectives. The two verification graphs together prove that the prediction model of this invention can accurately reproduce the slamming force prediction results of the MLM theoretical model, verifying the effectiveness and reliability of the intelligent prediction system.

[0057] Notes on other visualization capabilities: Although Figure 6 Only two core verification graphs are shown, but the system of this invention also has the ability to generate other types of analysis graphs, including residual analysis graphs, comparison graphs of different time densities, multi-angle comparison graphs at a fixed speed, and multi-speed comparison graphs at a fixed angle. These visualization functions have been systematically described above and will not be repeated here.

[0058] (7) Application scenario description The applications of this invention are multifaceted. In ship design optimization, it can rapidly assess the slamming loads of different bow shapes at varying speeds during the design phase, optimizing hull design and improving design efficiency. In offshore platform safety assessment, it can predict the slamming force of offshore platform pillars under wave action, assess structural fatigue life, and provide a basis for safe design. In seaplane landing analysis, it can predict the slamming loads during seaplane landing, optimize landing attitude and speed, and improve landing safety. In academic research, it can serve as an auxiliary tool for slamming mechanics research, rapidly generating large amounts of slamming load data under various operating conditions, supporting mechanism research and theoretical verification.

[0059] (8) Extended application to other cross-sectional shapes The technical framework proposed in this application, which combines physical mechanism-guided feature construction with data-driven model training, is not limited to wedge-shaped sections and can be extended to other section shapes according to the same physical modeling ideas.

[0060] In terms of data foundation, it is necessary to obtain the impact load time history data of the new target profile shape under various working conditions. The data sources can also be MLM theoretical models, CFD numerical simulations or physical model tests.

[0061] In terms of adaptive adjustments to feature engineering, technicians need to analyze the impact physics mechanism of the new profile shape, identify its key geometric and mechanical parameters, and retention time. , water entry speed Time squared term By reconstructing shape-related features from general features independent of the cross-sectional shape, and constructing new physically guided interaction terms based on the geometric properties of the new shape, the construction principle is consistent with the physical idea of ​​the interaction terms in the wedge cross-section. Simultaneously, the new key geometric feature parameters undergo appropriate mathematical transformations to better facilitate model learning. For example, for a semi-circular cross-section, the key geometric feature parameter is the radius. A radius-velocity interaction term can be constructed. For a V-shaped profile, the key geometric feature parameter is the opening angle. An opening angle-velocity interaction term can be constructed. The constructed interaction terms all reflect the synergistic enhancement effect of geometric characteristic parameters and water ingress velocity on slamming load, and are related to the angle-velocity coupling terms in the wedge profile. The physical meaning is the same.

[0062] In terms of model training and optimization, the random forest model is retrained using the newly constructed feature set and data with the new profile shape, following the same process described in this invention. The core architecture of the model remains unchanged, but the hyperparameters (number of decision trees, maximum depth, minimum number of samples required for splits, minimum number of samples required for leaf nodes, etc.) need to be readjusted according to the size and complexity of the new dataset to achieve the best prediction performance for the new profile shape. In terms of validation and application, the model's prediction accuracy for the new profile shape is evaluated using an independent test set, and the results are validated through a visualization analysis module.

[0063] It should be noted that when applying this method to profile shapes other than wedges, the specific feature combinations and model hyperparameters given in the wedge profile examples may not be optimal. The optimal configuration needs to be re-determined based on the physical characteristics and data features of the target profile shape, following the overall framework and adjustment principles provided by this invention. Based on this general framework, a slamming load prediction model library for multiple typical profile shapes can be further developed, or an expert system that can automatically recommend feature construction schemes based on input profile geometric feature parameters can be constructed, thereby forming a more comprehensive intelligent hydrodynamic design platform for ships and marine engineering.

[0064] The above descriptions are merely preferred embodiments of this application, and the present invention is not limited to the above embodiments. It is understood that other improvements and variations directly derived or conceived by those skilled in the art without departing from the spirit and concept of the present invention should be considered to be included within the protection scope of the present invention.

Claims

1. A method for predicting water entry slamming loads by integrating machine learning with physical features, characterized in that, Includes the following steps: Acquire multi-condition time-history data of the target profile's water entry slamming load, the time-history data including different geometric feature parameters of the target profile, water entry velocity, time point combination of conditions and corresponding slamming load values; Based on the physical principles of impact mechanics, the original operating parameters in the time history data are transformed and combined to construct a physical guiding feature vector containing a coupling term of geometric feature parameters and water entry velocity, as well as a time square term. Using the physical guidance feature vector as input and the corresponding slamming load value as output, train a random forest regression model; The actual original working conditions of the target profile are input into the trained random forest regression model, and the predicted water inrush load of the profile under the working conditions is output.

2. The method for predicting water-entry slamming loads in profiles according to claim 1, characterized in that, When the target profile shape is a wedge-shaped profile, its geometric feature parameter is the slope angle, and the corresponding physical guidance feature vector is constructed as follows: Extract the slope angle from the original time history data. , water entry speed and time point As a basic operating condition characteristic; Based on the physical principles of impact mechanics, an angle-velocity coupling term is constructed through characteristic cross-combination. Sum of time squared terms As a nonlinear interaction feature, wherein The method is used to simulate the synergistic amplification effect of geometric characteristic parameters and water entry velocity on slamming loads. Used to characterize the nonlinear law of the quadratic growth of impact load over time; Based on mathematical and geometric principles, the above Convert from degrees to radians As a feature of geometric transformation, it enables normalization transformation; The six-dimensional feature vector is composed of the basic operating condition features, nonlinear interaction features, and geometric transformation features. .

3. The method for predicting water impact load in profiles according to claim 1, characterized in that, The trained random forest regression model includes: Bootstrap resampling is used to extract multiple subsets of samples with replacement from the training set constructed with the physical guide feature vector and the corresponding slam load value samples; The corresponding decision tree is trained using the CART regression tree algorithm on each sample subset. At the same time, a feature random selection strategy is adopted during the node splitting process of each decision tree, and the optimal splitting feature and splitting threshold are determined by minimizing the square error criterion. The arithmetic mean of the predictions from all decision trees is taken as the output of the random forest regression model.

4. The method for predicting water impact load in profiles according to claim 3, characterized in that, The method for determining the optimal splitting feature and splitting threshold includes: When splitting a node, a subset of features is randomly selected from all input features. Each feature in the subset and all possible values ​​of the feature are traversed. The feature that minimizes the sum of the squared errors of the sample impact load values ​​in the two sub-regions after splitting and the specific value of the feature are selected as the optimal splitting feature and splitting threshold. After splitting, the predicted value for each leaf node is the arithmetic mean of the true values ​​of the slam loads of all training samples within that node.

5. The method for predicting water-entry slamming loads in profiles according to claim 1, characterized in that, The method also includes a feedback optimization step: Based on the residual analysis and feature importance analysis of the prediction results output by the random forest regression model, training samples in weak working condition areas are supplemented in a targeted manner and / or the feature composition of the physical guidance feature vector is adjusted to improve the prediction accuracy of the model in that area and optimize the feature vector, and the random forest regression model is retrained.

6. The method for predicting water-entry slamming loads in a profile according to claim 1, characterized in that, The method for obtaining the multi-condition time history data includes: The multi-condition time history data is obtained based on at least one of the following methods: MLM slamming theory model, CFD numerical simulation and physical model test. Based on the principle of physical consistency, data points with negative impact load values ​​and those that do not conform to physical specifications in the time history data are filtered out and converted into a standardized training set format.

7. The method for predicting water impact load in profiles according to claim 2, characterized in that, The target profile shape includes, but is not limited to, a wedge-shaped profile, a semi-circular profile, a V-shaped profile, or a combination thereof; For other profile shapes that are not wedge-shaped, based on the geometric feature parameters of the target profile shape and following the same physical principles, a coupling term of the geometric feature parameters and the water ingress velocity corresponding to the target profile shape and a geometric transformation feature are constructed to form a physical guidance feature vector for the target profile shape.

8. A profile water entry slamming load prediction system that integrates machine learning and physical features, characterized in that, include: The data acquisition and preprocessing module is used to acquire multi-condition time-history data of the target profile's water entry slamming load. The time-history data includes different geometric feature parameters of the target profile, water entry velocity, time point combination of working conditions and corresponding slamming load values. The physical guidance feature engineering module is used to perform feature transformation and combination on the original working condition parameters in the time history data according to the physical principle of impact mechanics, and construct a physical guidance feature vector containing a coupling term of geometric feature parameters and water entry velocity as well as a time square term. The random forest model training module is used to train a random forest regression model with the physical guidance feature vector as input and the corresponding slamming load value as output. The prediction application module is used to input the actual original working conditions combination of the target profile into the trained random forest regression model and output the prediction result of the water ingress slamming load of the profile under the working condition combination.

9. The profile water ingress slamming load prediction system according to claim 8, characterized in that, When the target profile shape is a wedge-shaped profile, its geometric feature parameter is the slope angle, and the corresponding physical guidance feature engineering module includes: The basic working condition feature extraction unit is used to extract the slope angle from the raw time history data. , water entry speed and time point ; Nonlinear interactive feature construction units are used to construct angle-velocity coupling terms through feature cross-combination based on the physical principles of impact mechanics. Sum of time squared terms , wherein The method is used to simulate the synergistic amplification effect of geometric characteristic parameters and water entry velocity on slamming loads. Used to characterize the nonlinear law of the quadratic growth of impact load over time; Geometric transformation feature construction unit, used to perform geometric transformations on the aforementioned features based on mathematical and geometric principles. Convert from degrees to radians To achieve standardized transformation; The physical guidance feature engineering module outputs a six-dimensional feature vector. .

10. The profile water entry slamming load prediction system according to claim 8, characterized in that, It also includes a visualization analysis module, which provides prediction interfaces with three preset time resolutions: sparse, medium, and dense, or supports prediction with a custom number of time points to generate slam load prediction results with different time point densities. The visualization analysis module is also used to generate comparison charts of predicted and actual values, residual analysis charts, comparison charts of predictions at different time densities, comparison charts of different geometric feature parameters at a fixed speed, comparison charts of different speeds at fixed geometric feature parameters, and feature importance analysis charts.

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