A ship motion response prediction method based on radial basis function multi-dimensional interpolation

Abstract

This invention discloses a method for predicting ship motion response based on radial basis function multidimensional interpolation, belonging to the field of shipbuilding and ocean engineering technology. The method first collects model test, numerical simulation, and actual ship monitoring data to construct a multidimensional sample database. It then constructs an interpolation prediction model using scaled distance metrics and radial basis function interpolation, and introduces a physical baseline composed of empirical formulas or simplified potential flow models for hybrid modeling to improve generalization ability. In the prediction stage, for any new operating condition input parameters, the trained interpolation prediction model is used to quickly calculate the predicted motion response value, which can be accelerated by combining spatial indexing technology. The method also features an adaptive correction mechanism based on error assessment and a risk warning function. This invention achieves rapid prediction, significantly improves computational efficiency and cross-operating condition generalization ability, and provides effective support for ship design and real-time operational decision-making.

Description

Technical Field

[0001] This invention relates to the field of shipbuilding and marine engineering technology, and more specifically, to a method for predicting ship motion response based on radial basis function multidimensional interpolation. Background Technology

[0002] Predicting a ship's motion response in waves is a crucial research area in marine engineering and ship design. The accuracy of its calculations directly impacts a ship's seakeeping analysis, stability assessment, mooring safety, and operational feasibility evaluation. Currently, commonly used ship motion analysis methods in engineering practice mainly fall into three categories: empirical formula methods, potential flow theory methods, and viscous flow numerical methods.

[0003] Empirical formula method: This method is based on a large amount of historical ship type test data and actual ship observation statistics. It establishes an empirical relationship between motion response and key parameters (such as ship length, beam, and wave elements) through regression analysis. Its advantage is that the calculation speed is extremely fast and it can be used for preliminary estimation. However, its disadvantages are also very significant: the formula is based on specific ship types and sea states, and its applicability is narrow. The prediction accuracy drops sharply for new ship types, irregular waves, or complex sea states (such as oblique waves and large movements). It is difficult to capture nonlinear motion characteristics and has poor generalization ability.

[0004] Potential flow theory: This is currently the most widely used frequency domain or time domain analysis method in engineering design. This method assumes the fluid to be an ideal fluid that is inviscid, incompressible, and irrotational. By solving linear or weakly nonlinear potential flow boundary value problems, it obtains the six-degree-of-freedom motion response amplitude operator (RAO) of the ship. This method has high computational accuracy under regular wave or small-amplitude wave conditions. However, its limitations are: the calculation process heavily relies on fine three-dimensional hull surface mesh generation, the solution process is complex, and the computation time is long, making it difficult to meet the real-time requirements of rapid forecasting of actual ships or large-scale scheme comparison. Furthermore, its simulation capabilities for strongly nonlinear phenomena (such as deck waves and slamming) and complex fluid-structure interactions (such as those involving propellers, rudders, and mooring systems) are limited.

[0005] Numerical simulation of viscous flow (CFD): Based on computational fluid dynamics (CFD), the viscous flow method can accurately simulate the viscous effects, turbulence, and large nonlinear deformations of free surfaces of fluids by solving the Navier-Stokes equations. Theoretically, it has the strongest adaptability to various complex flows. However, this method consumes huge amounts of computational resources, and the preprocessing (modeling, mesh generation) and solution processes are extremely time-consuming. A single simulation usually takes several hours or even days, making it completely unsuitable for rapid evaluation and decision support in engineering fields. In addition, its computational accuracy is significantly affected by various parameters such as mesh quality, turbulence model, and time step, and its stability and universality still need to be improved. Summary of the Invention

[0006] The purpose of this invention is to provide a ship motion response prediction method based on radial basis function multidimensional interpolation, so as to solve the above-mentioned problems existing in the prior art.

[0007] The application is as follows: This invention provides a method for predicting ship motion response based on radial basis function multidimensional interpolation, comprising the following steps: S1. Data Acquisition and Construction of Training Sample Set: Collect data from model experiments, numerical simulations, and actual ship monitoring. Normalize, dimensionlessize, and remove outliers from the data to construct the training sample set D.

[0008] Where N is the total number of samples, The input vector contains ship type parameters, sea state parameters, and mooring state parameters. This corresponds to the motion response; S2. Definition of Scaled Distance Metric: Based on the input vector, define a scaled distance function. Used to measure the relationship between any input vector x and the sample input vector. Distance between: S3. Construction of Radial Basis Function Interpolation Prediction Model: Selection of Radial Basis Functions Construct an interpolation prediction model:

[0009] in, For the predicted motion response corresponding to the input vector x, These are the radial basis function weight coefficients corresponding to the j-th sample. These are polynomial terms used to ensure the stability of the model; S4. Solving for interpolation prediction model coefficients: Based on the training sample set, the weight coefficients are determined by solving the linear system. and the polynomial terms The coefficient; S5. Motion Response Prediction: Input vector of the target ship's operating condition parameters. The data is then input into the interpolation prediction model to calculate the predicted motion response of the ship. .

[0010] Furthermore, a hybrid modeling approach based on physical constraints is adopted, specifically including: Introducing a baseline prediction model based on physical mechanisms The baseline prediction model is calculated using empirical formulas or a simplified potential flow model; Calculate the residuals of each sample in the training sample set. This constitutes the residual training sample set. ; Using the residual training sample set As a new training sample set, repeat steps S2 to S4 to construct a radial basis function interpolation prediction model for predicting residuals. ; Therefore, the final interpolation prediction model used in step S5 is a hybrid prediction model, which takes the following form: .

[0011] Furthermore, in step S2, the scaled distance function Defined as:

[0012] in, Let be the scale factor matrix, and d be the dimension of the input vector. This is a preset scaling factor used to scale the difference in the input vector along the k-th dimension.

[0013] Furthermore, in step S3, the radial basis function ,in For shape parameters.

[0014] Furthermore, in step S3, the multiple items... With M basis functions It is composed of linear combinations of (k=1,…,M): , These are the coefficients of the polynomial terms.

[0015] Furthermore, in step S4, to satisfy the orthogonality constraint, the radial basis function weight coefficient vector is determined by solving the following regularized linear system. and the coefficient vector of the polynomial terms :

[0016] in, For a symmetric matrix, its elements I is The identity matrix; Let be a polynomial matrix, its elements ; Let be the sample motion response vector; and the matrix equation c=0 corresponds to the orthogonality constraint.

[0017] Furthermore, the motion response When the model is multidimensional, in step S3, when constructing the interpolation prediction model, any of the following methods may be used: a. Response to the motion For each dimension component, establish an interpolation prediction model as described in step S3; b. First, the motion response... Principal component analysis (PCA) is performed to reduce dimensionality. Then, an interpolation prediction model is established on the dimensionality-reduced principal components as described in step S3. Finally, the prediction results of the principal components are reconstructed into a complete motion response.

[0018] Furthermore, in step S5, when calculating the predicted value, spatial indexing technology is used to accelerate the search for the target input vector. The radial basis function interpolation prediction model is calculated based on the neighboring training samples and only on the neighboring samples.

[0019] Furthermore, it also includes step S6: evaluating the error of the predicted value; if the error exceeds a preset threshold, an adaptive correction is triggered, the correction including adding training samples in the neighborhood of the target parameter or adjusting the shape parameter σ of the radial basis function.

[0020] Furthermore, it also includes step S7: visualizing the predicted motion response and comparing it with a preset safety threshold; if the safety threshold is exceeded, an excessive motion risk warning message is generated.

[0021] Compared with the prior art, the embodiments of the present invention achieve the following beneficial effects: This invention establishes a radial basis function interpolation prediction model to learn and solidify the nonlinear relationship between complex ship motion response and multidimensional input parameters offline. In actual prediction, only simple interpolation calculations are required to obtain prediction results within seconds. This provides immediate and efficient technical support for real-time ship maneuvering, dynamic route optimization, and rapid assessment of offshore operation windows.

[0022] This invention effectively unifies the dimensions and numerical ranges of parameters for different ship types, sizes, and sea states through multidimensional distance scaling, sample data normalization, and dimensionless processing. Furthermore, by introducing a hybrid modeling strategy of "physical baseline model + data-driven residual correction," universal physical laws are used as the benchmark framework for prediction, while an interpolation prediction model is employed to learn local biases caused by specific ship types or complex nonlinearities. This fusion approach significantly enhances the model's extrapolation prediction capability and physical plausibility under new ship type parameters not covered by the training data or under extreme sea states.

[0023] The method of this invention can utilize existing (or selectively supplemented) model test, numerical simulation, and shipboard monitoring data as training samples. Once the model training is complete, the high-cost CFD simulations or detailed potential flow calculations can be completely avoided in subsequent large-scale design condition screening, parameter sensitivity analysis, or operational sea state assessment. This significantly reduces the overall computational resource consumption and time cost in the ship design optimization, safety assessment, and operational decision-making processes. Attached Figure Description

[0024] Figure 1 This is a flowchart illustrating a ship motion response prediction method based on radial basis function multidimensional interpolation provided in an embodiment of the present invention. Detailed Implementation

[0025] The specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. It should be understood that the specific embodiments given herein are for illustration and explanation only and are not intended to limit the present invention.

[0026] It should be noted that many specific details are set forth in the following description in order to provide a full understanding of the present invention. However, the present invention may have other embodiments, and therefore, the scope of protection of the present invention is not limited to the specific embodiments disclosed below.

[0027] See attached document Figure 1 As shown in the figure, this embodiment provides a method for predicting ship motion response based on radial basis function multidimensional interpolation, the specific steps of which include: S1 Data Acquisition and Construction of Training Sample Set: Establish a multi-dimensional training sample set covering the design parameter space.

[0028] For the target ship type, collect data in three aspects: Numerical simulation data: The six-degree-of-freedom motion response amplitude operator of the ship under different sea states (wave height H, wave direction θ, encounter frequency ω) and different ship speeds V was calculated using potential flow theory or computational fluid dynamics methods; Model test data: The seakeeping test of this ship type was carried out in the towing tank to obtain motion response data under key operating conditions; Actual ship monitoring data: The motion and sea state data of the actual ship during operation are recorded by shipboard sensors (inertial measurement unit (IMU), wave radar, anemometer, current meter and other sensors installed on the hull). All data are preprocessed: input parameters are normalized to eliminate the influence of dimensions, thereby eliminating differences between ship types and sea states at different scales; moving average or low-pass filtering is used to remove data noise, and statistical methods are used to identify and remove outlier samples. For sparse sample areas, numerical simulation data is used to supplement the data, thus forming a multi-dimensional training sample set D covering various wave parameters, ship type parameters, and mooring states.

[0029] Where N is the total number of samples, The input vector contains ship type parameters, sea state parameters, and mooring state parameters. This represents the corresponding motion response, such as the six-degree-of-freedom RAO amplitude at each discrete frequency point.

[0030] S2 Scaled Distance Metric Definition: To accurately measure the distance between points in a multidimensional parameter space, a scaled distance function is defined. for:

[0031] in, Let be the scale factor matrix, and d be the dimension of the input vector. The preset scaling factor is used to scale the difference of the input vector in the k-th dimension. It can be determined by methods such as standard deviation based on parameters, sensitivity analysis, or cross-validation learning.

[0032] S3 Radial Basis Function Interpolation Prediction Model Construction: Selection of Radial Basis Functions In this embodiment, it is defined as:

[0033] in For shape parameters.

[0034] The interpolation prediction model with polynomial terms is constructed as follows:

[0035] in, For the predicted motion response corresponding to the input vector x, These are the radial basis function weight coefficients corresponding to the j-th sample. These are polynomial terms used to ensure the stability of the model.

[0036] The aforementioned matters With M basis functions It is composed of linear combinations of (k=1,…,M): , These are the coefficients of the polynomial terms.

[0037] Model building strategy for multidimensional motion response: Due to the ship's motion response Typically, these are multi-dimensional vectors (such as six-degree-of-freedom RAOs). This embodiment provides two equivalent modeling strategies: Strategy A (component-independent modeling): for motion response For each dimension component (such as pitch, roll, etc.), a separate interpolation prediction model is established. Each model is trained independently and has its own coefficients. and .

[0038] Strategy B (Modeling after Dimensionality Reduction): First, analyze the multidimensional motion responses of all training samples. Principal component analysis (PCA) is performed to extract the first L principal components (L is less than the original dimension). Then, an interpolation prediction model is built for each principal component. During prediction, the values ​​of each principal component are predicted first, and then the complete multidimensional motion response is reconstructed through inverse PCA. This method can effectively reduce model complexity, and is especially suitable for situations where there is a strong correlation between responses in different dimensions.

[0039] Solving for the coefficients of the S4 interpolation prediction model: Solving a regularized linear system to determine all the unknown coefficients of the interpolation prediction model. and .

[0040] For all training samples ( , The model output must satisfy the smooth interpolation condition. ≈yi. Meanwhile, to eliminate the degrees of freedom introduced by the polynomial terms and ensure the uniqueness of the solution, orthogonality constraints are added:

[0041] To improve numerical stability and prevent overfitting to noisy data, a regularization parameter λ (λ≥0) is introduced to relax the interpolation conditions into smoothing conditions, which are then integrated with orthogonality constraints, resulting in the following regularized linear system:

[0042] in, For a symmetric matrix, its elements I is The identity matrix; Let be a polynomial matrix, its elements ; The sample motion response vector; Radial basis function weight coefficient vector This is the coefficient vector of the lower-order polynomial terms.

[0043] Solving this regularized linear system yields the coefficient vector c and This means that the interpolation prediction model has been determined.

[0044] As a preferred embodiment of the present invention, a hybrid modeling approach with physical constraints can be adopted to improve the predictive rationality and generalization ability of the model in sparse data regions.

[0045] By employing simplified empirical formulas or a fast calculation procedure based on linear potential flow theory, a baseline prediction model with extremely low computational cost is constructed. .

[0046] Calculate the residuals between the high-precision data in the training samples and the baseline model predictions. This constitutes the residual training sample set. Using the aforementioned residual training sample set As a new training sample set, repeat steps S2 to S4 to construct a radial basis function interpolation prediction model for predicting residuals. ; Therefore, the final interpolation prediction model used in step S5 is a hybrid prediction model, which takes the following form:

[0047] S5 motion response prediction: When a new target working condition is required... When making predictions, Input a pre-trained (hybrid) interpolation prediction model to directly calculate the predicted motion response. According to application requirements, the predicted motion response should... It can be manifested in one of the following two forms: Frequency domain response form: The model output is directly the amplitude and phase of the frequency domain response amplitude operator (RAO) at each discrete frequency point. This form can be directly used for nonwave performance spectrum analysis.

[0048] Time-domain response format: The model output is a time-domain motion response sequence. In the model building stage S3, if a "dimensionality reduction followed by modeling" strategy is adopted, and the time-domain response is... The sample is set to a preprocessed time-domain sequence (such as a standard-length motion time history). The model then predicts the output. The predicted values ​​of the dimensionality-reduced principal components can be directly reconstructed by performing an inverse PCA transform on them to obtain the complete temporal motion sequence. This method achieves fast end-to-end prediction from input parameters to output time history.

[0049] To improve prediction speed and meet real-time requirements, in the calculation At that time, spatial indexing techniques (such as KD-Tree) can be used to quickly find results related to... The K nearest neighbors are used for calculation, and only the radial basis function terms of these K nearest neighbors are used to achieve fast prediction.

[0050] S6 Predictive Evaluation and Adaptive Correction: Predicting Motion Response The root mean square error (RMSE) and mean absolute percentage error (MAS) are calculated by comparing the results with a high-precision reference solution or measured values. This embodiment uses the RMSE. As a core evaluation indicator, its calculation formula is as follows:

[0051] Where M is the number of validation data points. and These are the predicted value and the reference value for the j-th data point, respectively.

[0052] If the error exceeds the preset threshold (e.g.) Trigger adaptive correction: Sample augmentation: Within the "low confidence interval", the parametric simulation tool is automatically invoked to generate a small number of new high-precision sample points and add them to the training sample set D.

[0053] Parameter optimization: Adaptively adjust the shape parameter σ based on the error distribution. The adjustment formula can be:

[0054] Where α is the learning rate. Subsequently, the interpolation prediction model is retrained using the updated sample library or parameters to achieve online performance improvement.

[0055] S7 Results Output and Decision Support The predicted ship motion response data is output in a standard engineering format, supporting import into ship maneuvering or control systems. For example, the output can be a frequency domain RAO spectrum curve, a time domain motion response sequence, or a table of key statistical indicators.

[0056] The system automatically generates visualization charts, including a two-dimensional response surface of wave direction angle-wave frequency; a response sensitivity analysis chart of ship speed-wave height; and a heatmap of prediction confidence under different parameter dimensions, to help engineers understand complex relationships.

[0057] The system compares the predicted motion response with preset safe operating thresholds in real time. If the predicted value exceeds the threshold, the system automatically triggers an early warning, highlights the "excessive motion risk condition," and provides decision-making basis for ship handling or operation planning.

[0058] Numerous specific details are set forth in the specification provided herein. However, it will be understood that embodiments of the invention may be practiced without these specific details. In some instances, well-known methods, structures, and techniques have not been shown in detail so as not to obscure the understanding of this specification.

[0059] Furthermore, those skilled in the art will understand that although some embodiments herein include certain features included in other embodiments but not others, combinations of features from different embodiments are intended to be within the scope of the invention and form different embodiments. Any of the claimed embodiments can be used in any combination.

Claims

1. A method for predicting ship motion response based on radial basis function multidimensional interpolation, characterized in that, Includes the following steps: S1. Data Acquisition and Construction of Training Sample Set: Collect data from model experiments, numerical simulations, and actual ship monitoring. Normalize, dimensionlessize, and remove outliers from the data to construct the training sample set D. Where N is the total number of samples, The input vector contains ship type parameters, sea state parameters, and mooring state parameters. This corresponds to the motion response; S2. Definition of Scaled Distance Metric: Based on the input vector, define a scaled distance function. Used to measure the relationship between any input vector x and the sample input vector. Distance between: S3. Construction of Radial Basis Function Interpolation Prediction Model: Selection of Radial Basis Functions Construct an interpolation prediction model: in, For the predicted motion response corresponding to the input vector x, These are the radial basis function weight coefficients corresponding to the j-th sample. These are polynomial terms used to ensure the stability of the model; S4. Solving for interpolation prediction model coefficients: Based on the training sample set, the weight coefficients are determined by solving the linear system. and the polynomial terms The coefficient; S5. Motion Response Prediction: Input vector of the target ship's operating condition parameters. The data is then input into the interpolation prediction model to calculate the predicted motion response of the ship. .

2. The ship motion response prediction method based on radial basis function multidimensional interpolation according to claim 1, characterized in that, A hybrid modeling approach based on physical constraints is adopted, specifically including: Introducing a baseline prediction model based on physical mechanisms The baseline prediction model is calculated using empirical formulas or a simplified potential flow model; Calculate the residuals of each sample in the training sample set. This constitutes the residual training sample set. ; Using the residual training sample set As a new training sample set, repeat steps S2 to S4 to construct a radial basis function interpolation prediction model for predicting residuals. ; Therefore, the final interpolation prediction model used in step S5 is a hybrid prediction model, which takes the following form: .

3. The ship motion response prediction method based on radial basis function multidimensional interpolation according to claim 1, characterized in that, In step S2, the scaled distance function Defined as: in, Let be the scale factor matrix, and d be the dimension of the input vector. This is a preset scaling factor used to scale the difference in the input vector along the k-th dimension.

4. The ship motion response prediction method based on radial basis function multidimensional interpolation according to claim 1, characterized in that, In step S3, the radial basis function ,in For shape parameters.

5. The ship motion response prediction method based on radial basis function multidimensional interpolation according to claim 1, characterized in that, In step S3, the multiple items With M basis functions It is a linear combination of (k=1,…,M): , These are the coefficients of the polynomial terms.

6. The ship motion response prediction method based on radial basis function multidimensional interpolation according to claim 5, characterized in that, In step S4, to satisfy the orthogonality constraint, the radial basis function weight coefficient vector is determined by solving the following regularized linear system. and the coefficient vector of the polynomial terms : in, For a symmetric matrix, its elements I is The identity matrix; Let be a polynomial matrix, its elements ; Let be the sample motion response vector; and the matrix equation c=0 corresponds to the orthogonality constraint.

7. The ship motion response prediction method based on radial basis function multidimensional interpolation according to claim 1, characterized in that, The motion response When the model is multidimensional, in step S3, when constructing the interpolation prediction model, any of the following methods may be used: a. Response to the motion For each dimension component, establish an interpolation prediction model as described in step S3; b. First, the motion response... Principal component analysis (PCA) is performed to reduce dimensionality. Then, an interpolation prediction model is established on the dimensionality-reduced principal components as described in step S3. Finally, the prediction results of the principal components are reconstructed into a complete motion response.

8. The ship motion response prediction method based on radial basis function multidimensional interpolation according to claim 1, characterized in that, In step S5, when calculating the predicted value, spatial indexing technology is used to accelerate the search for the target input vector. The radial basis function interpolation prediction model is calculated based on the neighboring training samples and only on the neighboring samples.

9. The ship motion response prediction method based on radial basis function multidimensional interpolation according to claim 1, characterized in that, It also includes step S6: evaluating the error of the predicted value. If the error exceeds a preset threshold, adaptive correction is triggered. The correction includes adding training samples in the neighborhood of the target parameter or adjusting the shape parameter σ of the radial basis function.

10. The ship motion response prediction method based on radial basis function multidimensional interpolation according to claim 1, characterized in that, It also includes step S7: visualizing the predicted motion response and comparing it with a preset safety threshold. If the safety threshold is exceeded, an excessive motion risk warning is generated.

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