Hydrofoil proxy model optimization method and hydrofoil ship

Abstract

The invention provides a hydrofoil proxy model optimization method and a hydrofoil ship, and the hydrofoil proxy model optimization method comprises the steps that a two-stage adding point Kriging proxy model is used for accurately predicting the hydrofoil performance, then a NSGA II algorithm is used for hydrofoil optimization, the calculation efficiency is ensured, the prediction precision of the hydrofoil strong nonlinear working condition performance is remarkably improved, and the hydrofoil performance is optimized. And dynamic balance between global optimization and local refinement is realized.

Description

Technical Field

[0001] This invention relates to the field of hydrofoil technology, and in particular to a hydrofoil proxy model optimization method and a hydrofoil. Background Technology

[0002] A hydrofoil is an energy-saving hydrodynamic device that generates lift based on Bernoulli's principle. By raising the hull of the hydrofoil above the water surface, it significantly reduces the ship's sailing resistance and is the core component of a hydrofoil vessel.

[0003] Currently, hydrofoil performance optimization mainly relies on two approaches: computational fluid dynamics (CFD) simulation and physical experiments. However, CFD-based optimization design, especially in global optimization processes involving multiple operating conditions and design variables, incurs a huge computational burden due to the need to perform numerous numerical simulations, a problem particularly prominent in the preliminary design and parameter sensitivity analysis stages. Physical experimental methods, on the other hand, are constrained by high costs and long development cycles, making it difficult to support rapid iteration.

[0004] A new approach has emerged to utilize surrogate models to construct an approximate mapping between design parameters and performance responses, combined with global optimization strategies such as evolutionary algorithms, for hydrofoil performance optimization. This framework uses a limited number of high-fidelity CFD samples as a benchmark, achieving rapid performance prediction for large-scale design schemes through surrogate models, thereby significantly shortening the optimization cycle. While this approach alleviates computational cost pressures to some extent, existing surrogate model techniques still have the following key shortcomings when dealing with strongly nonlinear, multi-parameter coupled flow problems in hydrofoil systems:

[0005] 1) Traditional surrogate models generally adopt a one-time static sampling strategy. After the model is built, there is a lack of active learning and updating mechanism for the sample space, which results in weak fitting ability in strong nonlinear regions and difficulty in balancing prediction accuracy and modeling efficiency.

[0006] 2) Existing optimization frameworks lack a systematic adaptive sampling guidance strategy, which cannot dynamically coordinate global exploration and local development during the optimization process, thus limiting the algorithm's ability and robustness to find the global optimal solution.

[0007] Therefore, it is necessary to invent a hydrofoil proxy model performance optimization scheme to address the problems of insufficient prediction accuracy and efficiency in optimizing hydrofoil performance using existing proxy models. Summary of the Invention

[0008] This invention provides a hydrofoil surrogate model optimization method and a hydrofoil boat, which can overcome the problem of insufficient prediction accuracy and efficiency of surrogate models in existing hydrofoil optimization methods.

[0009] To address the above problems, this invention provides a hydrofoil proxy model optimization method, comprising the following steps:

[0010] S1. Determine the number of design variables for the hydrofoil and the value range of each design variable; all the design variables take values ​​within their respective value ranges and are combined to construct the sample space of the hydrofoil; randomly select a preset number of training samples and test samples within the sample space;

[0011] S2. Based on the training samples and the test samples, calculate the performance response values ​​of the corresponding hydrofoil;

[0012] S3. Construct the first Kriging proxy model using the training samples and their performance response values;

[0013] S4. Verify the accuracy of the first Kriging proxy model using the test samples and their performance response values;

[0014] S5. If the accuracy meets the standard, use a multi-objective genetic algorithm to perform multi-objective optimization on the first Kriging surrogate model to obtain the Pareto front, and use the two-base point method to select the final optimal solution from the Pareto front;

[0015] S6. If the accuracy does not meet the standard, a two-level addition strategy is adopted to correct the first Kriging surrogate model. This includes adopting a two-level addition strategy to obtain samples from the sample space, adding them to the training samples, returning to steps S2 to S4, until the accuracy meets the standard, and then running step S5. The two-level addition strategy includes primary addition based on the expectation improvement criterion and secondary addition based on the prediction variance criterion.

[0016] In the technical solution of this invention, a sample space for hydrofoils is constructed through the design variables of the hydrofoil. A portion of the samples are selected to construct a Kriging surrogate model, while the other portion is used to verify the model. After verification, a multi-objective genetic algorithm is used to perform multi-objective optimization to obtain the Pareto front. Finally, the two-base-point method is used to select the optimal solution from the Pareto front, providing a systematic and reusable solution for the actual design and operation control of hydrofoil systems.

[0017] In an optional embodiment of the present invention, in step S1, the design variables include the angle of attack, immersion depth, and speed of the hydrofoil.

[0018] In an optional embodiment of the present invention, in step S2, the performance response value includes the lift coefficient, drag coefficient, and lift-to-drag ratio of the hydrofoil.

[0019] In an optional embodiment of the present invention, step S6, the initial addition of points based on the expected improvement criterion, includes:

[0020] S6.1.1 Construct a second kriging proxy model based on all samples in the sample space;

[0021] S6.1.2. Use a genetic algorithm to obtain the sample that maximizes the expected improvement value in the second Kriging surrogate model, and remove the sample from the second Kriging surrogate model.

[0022] S6.1.3 Repeat S6.1.2, with the number of repetitions set to the third preset value; construct the second kriging proxy model with all the samples taken out as the third kriging proxy model, and all the samples taken out constitute the design point library.

[0023] In an optional embodiment of the present invention, in step S6.1.2, a genetic algorithm is used to obtain the sample that maximizes the expected improvement value in the second Kriging surrogate model, wherein the initial population of the decision variables of the genetic algorithm is set to 180-220 and the number of iterations is set to 100-140.

[0024] In an optional embodiment of the present invention, step S6, the secondary addition of points based on the prediction variance criterion, includes:

[0025] S6.2.1. For the samples in the design point library, a genetic algorithm is used to simulate the binary crossover operator to process them and generate a secondary candidate point library;

[0026] S6.2.2 Based on the third Kriging surrogate model, calculate the mean square error of all samples in the secondary candidate point library, and take the sample with the maximum value of the mean square error as the final sample and add it to the training samples.

[0027] In an optional embodiment of the present invention, step S6.2.2, the process of obtaining the sample with the maximum value in the mean square error, includes:

[0028] Among all the mean squared errors of the samples, the four samples with the largest fourth preset values ​​are selected to form the fourth Kriging surrogate model. A multi-objective genetic algorithm is then used to obtain the sample with the largest mean squared error, which is then used as the final sample.

[0029] In an optional embodiment of the present invention, in step S1, the preset number of training samples is set to a first preset value, and the preset number of test samples is set to a second preset value, wherein the first preset value is greater than the second preset value.

[0030] In an optional embodiment of the present invention, the number of design variables is set to n, and n≥3; the first preset value is set to 45n-60n, and the second preset value is set to 8n-12n; and / or,

[0031] The third preset value is set to 20-30; and / or,

[0032] The fourth preset value is set to 13-18.

[0033] To address the aforementioned problems, the present invention also provides a hydrofoil boat, comprising a hydrofoil obtained according to the hydrofoil proxy model optimization method described above.

[0034] The present invention has the following beneficial effects:

[0035] 1. This invention employs a two-stage adaptive sampling mechanism. In the initial stage, the Expectation Improvement (EI) criterion is used to orient and lock in high-potential sample regions. Then, in the secondary stage, the Prediction Variance criterion is used to precisely locate the local space with the greatest model uncertainty, achieving a progressive sample deployment from global exploration to local refinement. This strategy significantly enhances the fitting ability of the surrogate model in regions with drastic changes in lift-drag characteristics and nonlinear sensitive areas. Simultaneously, it fully leverages the hybrid modeling advantages of combining the Kriging surrogate model with high-fidelity computational fluid dynamics (CFD) simulation. While ensuring prediction accuracy, it significantly reduces the frequency of CFD calls, fundamentally resolving the typical contradiction in traditional optimization where accuracy and efficiency are difficult to balance.

[0036] 2. In the initial point-addition stage, a global kriging surrogate model based on the full sample and a genetic algorithm work together to explore a wide range of regions. The secondary stage, through cross-reconstruction of candidate points and local modeling, achieves in-depth development of key regions. This two-stage structure achieves an automatic trade-off between global optimization and refined local search, effectively suppressing premature convergence and enhancing the search process's adaptability to complex performance landscapes, thereby significantly improving the reliability and convergence speed of obtaining the global optimum.

[0037] 3. This invention clarifies the entire technical path from experimental design, simulation modeling, surrogate model training, adaptive sampling to multi-objective decision-making. The process is highly standardized, facilitating implementation and promotion. Furthermore, by introducing the NSGA-II multi-objective optimization algorithm and the TOPSIS decision evaluation system, it can output the optimal combination of operating parameters with clear engineering guidance under the condition of considering multiple competitive performance indicators, providing a systematic and reusable solution for the actual design and operation control of hydrofoil systems. Attached Figure Description

[0038] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the accompanying drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without any creative effort.

[0039] Figure 1 This is an overall flowchart of the hydrofoil operation condition optimization method based on the two-level point-addition Kriging proxy model of the present invention;

[0040] Figure 2 This is a detailed step diagram of the two-stage adaptive sampling process in an embodiment of the present invention;

[0041] Figure 3 This is a schematic diagram of the hydrofoil used in Embodiment 1 of the present invention;

[0042] Figure 4 This is a front view of the hydrofoil in Embodiment 1 of the present invention;

[0043] Figure 5 This is a left view of the hydrofoil in Embodiment 1 of the present invention;

[0044] Figure 6 This is a top view of the hydrofoil in Embodiment 1 of the present invention;

[0045] Figure 7 This is a schematic diagram of the V-shaped hydrofoil structure used in Embodiment 2 of the present invention;

[0046] Figure 8 This is a schematic diagram of the trapezoidal hydrofoil structure used in Embodiment 3 of the present invention;

[0047] Figure 9 This is a schematic diagram of the airfoil cross-section structure of the FX60-100 according to an embodiment of the present invention;

[0048] Figure 10 This is a schematic diagram of the NACA0012 airfoil cross-section structure according to an embodiment of the present invention;

[0049] Figure 11 This is a schematic diagram of the NACA4415 airfoil cross-section structure according to an embodiment of the present invention;

[0050] Figure 12 This is a spatial distribution diagram of the training samples for Latin hypercube sampling in an embodiment of the present invention;

[0051] Figure 13 This is a spatial distribution diagram of the test samples obtained by Latin hypercube sampling in an embodiment of the present invention;

[0052] Figure 14 This is a graph showing the variation of the proxy model error with the number of adaptive sampling points in an embodiment of the present invention;

[0053] Figure 15 This is a schematic diagram illustrating the location of the Pareto front, the optimal solution, and solutions with different preferences in an embodiment of the present invention.

[0054] Illustration:

[0055] 1. Vertical wing; 2. Horizontal wing. Detailed Implementation

[0056] In the description of this specification, the terms "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that the specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0057] See Figures 1-15 As shown, this invention provides a hydrofoil proxy model optimization method, including the following steps:

[0058] S1. Determine the number of design variables for the hydrofoil and the value range of each design variable; all the design variables take values ​​within their respective value ranges and are combined to construct the sample space of the hydrofoil; randomly select a preset number of training samples and test samples within the sample space;

[0059] S2. Based on the training samples and the test samples, calculate the performance response values ​​of the corresponding hydrofoil;

[0060] S3. Construct the first Kriging surrogate model using the training samples and their performance response values;

[0061] S4. Verify the accuracy of the first Kriging proxy model using the test samples and their performance response values;

[0062] S5. If the accuracy meets the standard, use a multi-objective genetic algorithm to perform multi-objective optimization on the first Kriging surrogate model to obtain the Pareto front, and use the two-base point method to select the final optimal solution from the Pareto front;

[0063] S6. If the accuracy does not meet the standard, a two-level addition strategy is adopted to correct the first Kriging surrogate model. This includes adopting a two-level addition strategy to obtain samples from the sample space, adding them to the training samples, returning to steps S2 to S4, until the accuracy meets the standard, and then running step S5. The two-level addition strategy includes primary addition based on the expectation improvement criterion and secondary addition based on the prediction variance criterion.

[0064] In the technical solution of this invention, a sample space for hydrofoils is constructed through the design variables of the hydrofoil. A portion of the samples are selected to construct a Kriging surrogate model, while the other portion is used to verify the model. After verification, a multi-objective genetic algorithm is used to perform multi-objective optimization to obtain the Pareto front. Finally, the two-base-point method is used to select the optimal solution from the Pareto front, providing a systematic and reusable solution for the actual design and operation control of hydrofoil systems.

[0065] This invention primarily uses a two-level Kriging surrogate model to accurately predict hydrofoil performance, and then employs a multi-objective genetic algorithm (NSGA II algorithm) for optimization to obtain the optimal solutions for key design variables of hydrofoils of different models and structures, thereby ensuring that the resulting hydrofoils have the best operational performance in use.

[0066] In this embodiment of the invention, the preset number of training samples and test samples refers to samples that cover the entire sample space. In other words, the samples drawn from the sample space are drawn evenly and dispersedly, and are representative.

[0067] The first Kriging proxy model is constructed using training samples that occupy only a portion of the sample space. If the model is validated by the other portion of the test samples, the hydrofoil optimization process can be completed. Compared to the samples in the entire sample space, this reduces the number of operations and increases efficiency.

[0068] In an optional embodiment of the present invention, in step S1, the design variables include the angle of attack, immersion depth, and speed of the hydrofoil.

[0069] In an optional embodiment of the present invention, in step S2, the performance response value includes the lift coefficient, drag coefficient, and lift-to-drag ratio of the hydrofoil.

[0070] In an optional embodiment of the present invention, in step S6,

[0071] The initial point allocation based on the expectation enhancement criterion includes:

[0072] S6.1.1 Construct a second kriging proxy model based on all samples in the sample space;

[0073] S6.1.2. Use a genetic algorithm to obtain the sample that maximizes the expected improvement value in the second Kriging surrogate model, and remove the sample from the second Kriging surrogate model.

[0074] S6.1.3 Repeat S6.1.2, with the number of repetitions set to the third preset value; construct the second kriging proxy model with all the samples taken out as the third kriging proxy model, and all the samples taken out constitute the design point library;

[0075] In an optional embodiment of the present invention, in step S6.1.2, a genetic algorithm is used to obtain the sample that maximizes the expected improvement value in the second Kriging surrogate model, wherein the initial population of the decision variables of the genetic algorithm is set to 180-220 and the number of iterations is set to 100-140.

[0076] In an optional embodiment of the present invention, step S6, the secondary addition of points based on the prediction variance criterion, includes:

[0077] S6.2.1. For the samples in the design point library, a genetic algorithm is used to simulate the binary crossover operator to process them and generate a secondary candidate point library;

[0078] S6.2.2 Based on the third Kriging surrogate model, calculate the mean square error of all samples in the secondary candidate point library, and take the sample with the maximum value of the mean square error as the final sample and add it to the training samples.

[0079] Regarding the adjustment method of the first Kriging proxy model, this embodiment of the invention adopts a two-stage addition adaptive sampling process, which sequentially goes through the primary addition stage, the secondary addition stage, and the data update stage to correct the first Kriging proxy model, so that the first Kriging proxy model is at its optimal value and the hydrofoil has the best operating effect.

[0080] In an optional embodiment of the present invention,

[0081] In step S6.2.2, the process of obtaining the sample with the maximum value in the mean square error includes:

[0082] Among all the mean squared errors of the samples, the four samples with the largest fourth preset values ​​are selected to form the fourth Kriging surrogate model. A multi-objective genetic algorithm is then used to obtain the sample with the largest mean squared error, which is then used as the final sample.

[0083] In an optional embodiment of the present invention, in step S1, the preset number of training samples is set to a first preset value, and the preset number of test samples is set to a second preset value, wherein the first preset value is greater than the second preset value.

[0084] In an optional embodiment of the present invention, the number of design variables is set to n, and n≥3; the first preset value is set to 45n-60n, and the second preset value is set to 8n-12n; and / or,

[0085] The third preset value is set to 20-30; and / or,

[0086] The fourth preset value is set to 13-18.

[0087] The following specific examples illustrate the above-mentioned hydrofoil proxy model optimization method:

[0088] Example 1:

[0089] Taking the T-shaped hydrofoil as the optimization target, such as Figures 3-10 As shown, the horizontal wing 2 of the T-shaped hydrofoil is an FX60-100 airfoil, and the vertical wing 1 is a NACA0012 airfoil, with the goal of improving its overall hydrodynamic performance (high lift-to-drag ratio, low drag) during cruise.

[0090] The specific implementation steps are as follows:

[0091] Step 1: Experimental Design and Initial Sampling

[0092] Determining Design Variables and Ranges: In this embodiment, three key operating parameters that significantly affect the performance of the T-shaped hydrofoil are selected as design variables, including angle of attack α (range: -5° to 20°), immersion depth h (range: 0.05m to 0.5m), and speed v (0 to 20m / s). Therefore, the number of design variables n=3.

[0093] Sample point generation: Using the Latin hypercube sampling method, 50×3=150 training sample points and 10×3=30 test sample points were generated within the range of angle of attack, immersion depth, and speed. Figure 12 and Figure 13 The sample points shown are evenly distributed in the three-dimensional design space, covering the key value regions of each variable.

[0094] Step 2: CFD Simulation and Data Acquisition

[0095] Parametric modeling and mesh generation: Based on the design variable combination (α, h, v) for each sample point, a corresponding 3D geometric model of the T-shaped hydrofoil is generated using parametric modeling software (such as 3D modeling software or computer-aided design software). The model is then imported into mesh generation software (such as a mesh generation tool) for mesh generation, and boundary layer refinement is performed on the near-wall region of the hydrofoil to ensure that the y+ value is within the range required by the turbulence model.

[0096] Flow field simulation calculation: Import the mesh file into the CFD solver (Computational Fluid Dynamics Solver or CFD Simulation Platform). Set the solution conditions, select the VOF two-phase flow model, with air as the first phase and water as the second phase; set the turbulence model to the DES model, using velocity inlet and pressure outlet boundary conditions; use the PISO pressure-velocity coupling algorithm and activate the second-order discretization scheme; perform unsteady calculations for each sample point, setting the time step to adaptive, satisfying a global Courant number less than 2, and a total duration equal to the time required for the current velocity to flow through 5 times the fluid domain; extract the lift coefficient C of the hydrofoil from the calculation results. L and drag coefficient C D And calculate its lift-to-drag ratio (C) L / C D() is used as a performance response value.

[0097] Step 3: Proxy Model Construction and Validation

[0098] Model construction: The immersion depth and speed in 150 training sample points are converted into dimensionless relative immersion depth h / c (where c is the average chord length of the hydrofoil) and Reynolds number Re ( , where μ is the dynamic viscosity); using (α, h / c, Re) as the input to the surrogate model, (C L、 C D The first Kriging surrogate model is constructed using the Kriging toolbox (such as mathematical modeling tools) of a numerical computation platform. This model establishes a path from the design variables (α, h, v) to the target response (C). L、 C D Approximate mapping relationship of ).

[0099] Model Validation: The model is validated using 30 reserved test sample points. The maximum relative error between the model's predicted values ​​and the CFD simulation values ​​is calculated. In this embodiment, the calculated maximum prediction error is 78%, which is greater than 5%. Therefore, the first Kriging surrogate model fails validation and enters the adaptive update phase.

[0100] Step 4: Two-stage adaptive sampling

[0101] This step is the core of improving model accuracy, and its parameters are set as follows: primary loop count N=25, secondary filter count M=15.

[0102] This process includes the following stages:

[0103] 4.1 Initial Skill Point Allocation Stage:

[0104] a. First, based on all the data in the current master database, construct a second kriging agent model.

[0105] b. Use a genetic algorithm (population size 200, iterations 150) to find a new sample point X_new_EI that maximizes the expected improvement (EI) function value on the second Kriging surrogate model.

[0106] c. Store X_new_EI in the design point library.

[0107] d. Repeat step ac a total of 25 times. During this stage, the main database remains unchanged, and points added to the design point library will be removed from the initial population. Each optimization will find a different maximum EI point due to the model's updated spatial understanding, thereby accumulating a batch of potential candidate points.

[0108] 4.2 Secondary Stat Allocation Stage:

[0109] a. The 25 points in the design point library are processed using the simulated binary crossover operator of the genetic algorithm to generate a new secondary candidate point library containing more sample points.

[0110] b. Construct a third kriging proxy model based on the current master database again, and calculate the prediction mean square error (MSE) of all points in the secondary candidate point library.

[0111] c. Sort the MSE values ​​from largest to smallest and select the top 15 points.

[0112] d. Construct a local fourth Kriging surrogate model based on these 15 points, and find the point with the largest prediction variance on this model as the final new sample point X_final for this round of adaptive sampling.

[0113] 4.3 Data Update Phase: Perform CFD simulation on X_final to obtain its true lift and drag coefficients, and add the new data pairs of X_final to the main database.

[0114] Then, return to step three to rebuild and validate the revised first Kriging agent model using the updated master database.

[0115] Repeat steps 3-4. After 21 model updates, the main database contains 171 sets of training sample data. At this point, the maximum prediction error of the model for the test sample points is 4.1%, which is less than 5%, and the model is validated.

[0116] Step 5: Multi-objective optimization and decision-making

[0117] Multi-objective optimization: After 21 model updates, the main database contains 171 sets of training sample data. At this time, the maximum prediction error of the model for the test sample points is 4.1%, which is less than 5%, and the model is validated.

[0118] A validated Kriging surrogate model was used as the objective function evaluator, and the multi-objective genetic algorithm NSGA-II (population size 200, 300 generations) was invoked for optimization. This embodiment sets two objectives: maximizing the lift coefficient and minimizing the drag coefficient. After the algorithm runs, it outputs a set of 70 non-dominated Pareto fronts that achieve the best trade-off between the two objectives.

[0119] Optimal decision: The TOPSIS (Topology of Ideal Solutions) method is used to select the final optimal solution from the Pareto solution set. This method sorts each solution by calculating its relative distance to the ideal solution and the negative ideal solution. The solution that is closest to the ideal solution and furthest from the negative ideal solution is the combination of operating parameters with the best overall performance.

[0120] The final optimal operating condition: angle of attack 7.6°, immersion depth 0.242m, speed 17.5m / s. This condition effectively balances lift and drag (C). L =0.857, C D =0.063, C L / C D =13.6), providing a robust and efficient configuration for general cruising conditions. For example... Figure 7 As shown, the optimal lift-to-drag ratio solution and the maximum lift solution can also be obtained from the Pareto front, which correspond to the optimal economic operating condition and the high load operating condition, respectively.

[0121] The specific data for the three operating conditions in this embodiment are shown in Table 1.

[0122] Table 1. Specific numerical values ​​corresponding to different preference solutions

[0123] Example 2:

[0124] This embodiment selects a V-shaped hydrofoil (NACA0012 airfoil) as the optimization target, such as... Figure 7 and Figure 10 As shown.

[0125] Step 1: Experimental Design and Initial Sampling

[0126] Similar to Example 1, the design variables include angle of attack α (range: -5° to 20°), immersion depth h (range: 0.05m to 0.5m), and speed v (range: 0 to 20m / s), and training and test samples are generated using the Latin hypercube sampling method.

[0127] Step 2: CFD Simulation and Data Acquisition

[0128] The process is similar to that in Example 1, but the mesh generation strategy is adjusted according to the geometric characteristics of the V-shaped hydrofoil to ensure that the volume mesh quality is greater than 0.2 to ensure calculation accuracy.

[0129] Step 3: Proxy Model Construction and Validation

[0130] Construct a system with input (α, h / c, Re) and output (C). L C D The Kriging surrogate model was used. The initial model validation maximum error was 59%, and adaptive sampling optimization was continued.

[0131] Step 4: Two-stage adaptive sampling

[0132] The two-level adaptive sampling strategy described in this invention was applied for model updating. After 18 iterations, the maximum prediction error of the surrogate model was reduced to 4.3%, meeting the accuracy requirements.

[0133] Step 5: Multi-objective optimization and decision-making

[0134] Multi-objective optimization was performed using NSGA-II, and the optimal operating condition was obtained through TOPSIS decision-making: angle of attack 9.2°, immersion depth 0.225m, and speed 16.8m / s. Under this condition, C L =0.845, C D =0.072, C L / C D =11.7.

[0135] Example 3:

[0136] This embodiment further optimizes the trapezoidal hydrofoil (NACA4415 airfoil), such as... Figure 8 and Figure 11 As shown.

[0137] The implementation process of steps one through five is similar to that of Example 1 described above, adjusting the design variable range and CFD settings according to the characteristics of the trapezoidal hydrofoil. After optimization using the method of this invention, the optimal operating conditions are obtained: angle of attack 7.8°, immersion depth 0.235m, and speed 17.2m / s. Under these conditions, C L =0.853, C D =0.068, C L / C D =12.5.

[0138] To fully illustrate the superiority of the technical solution of this invention, a systematic comparative analysis is conducted below between this invention and conventional optimization schemes. The comparison results are shown in Table 2. The conventional optimization scheme refers to the method of constructing a surrogate model using only initial sample points and employing a conventional genetic algorithm for optimization, without using the two-stage adaptive sampling strategy described in this invention. As shown in Table 2, for all tested hydrofoil configurations, the optimal operating condition obtained by the solution of this invention yields the optimal lift coefficient (C). L The coefficients of drag (C) are all higher than those of conventional schemes. D The efficiency of the proposed invention is significantly reduced. This demonstrates that the invention is not simply about parameter optimization, but rather that it fundamentally improves the reliability of the surrogate model through an innovative adaptive modeling method, thereby guiding the optimization algorithm to discover a design scheme with significantly better overall performance. This advantage has been consistently verified in the optimization of various hydrofoils, such as V-shaped and trapezoidal hydrofoils, fully demonstrating the versatility, advancement, and significant technological progress of the invention.

[0139] Table 2 Performance Comparison of the Invention Scheme and Conventional Optimization Schemes

[0140] In the above embodiments,

[0141] 1. The multi-objective genetic algorithm NSGA-II is one of the most popular multi-objective genetic algorithms. It reduces the complexity of non-dominated sorting genetic algorithms and has the advantages of fast running speed and good convergence of solution sets, making it the benchmark for the performance of other multi-objective optimization algorithms.

[0142] 2. TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution) is a ranking method that approximates the ideal solution. First proposed by CLHwang and K. Yoon in 1981, TOPSIS ranks a finite number of evaluation objects based on their proximity to the ideal goal. It evaluates the relative merits of existing objects, requiring only that each utility function is monotonically increasing (or decreasing). TOPSIS is a commonly used and effective method in multi-objective decision analysis, also known as the distance method between best and worst solutions. Its basic principle is to rank the evaluation objects by detecting their distances to the optimal and worst solutions. If an evaluation object is closest to the optimal solution and furthest from the worst solution, it is considered the best; otherwise, it is not optimal. In the optimal solution, all indicator values ​​reach their optimal values ​​for each evaluation indicator. In the worst solution, all indicator values ​​reach their worst values ​​for each evaluation indicator.

[0143] 3. Expected Improvement (EI): A core acquisition function in Bayesian optimization, used to guide the search process and select the next most promising sampling point in each iteration. For a candidate point x, its expected improvement is defined as:

[0144] EI(x)=E[max(0,f(x)−f(x+))]

[0145] in:

[0146] f(x) is the Gaussian process's prediction of the objective function at point x (usually a random variable).

[0147] f(x+)) is the currently known and observed maximum objective function value (i.e. the current optimal value).

[0148] The `max(0,⋅)` method ensures that only positive improvements are considered; that is, `f(x)` must be strictly greater than the current optimal value to be meaningful.

[0149] 4. Mean-square error (MSE) is a statistical measure of the difference between an estimator and the true value of a parameter, or between a predicted value and the actual value. It is defined as the expected value of the squared deviation or the mean of the squared error. The formula is MSE = 1 / n∑(yi−ŷi)². By squaring, it amplifies the effect of larger errors, reflecting the overall error level.

[0150] To address the aforementioned problems, the present invention also provides a hydrofoil boat, comprising a hydrofoil obtained according to the hydrofoil proxy model optimization method described above.

[0151] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention.

Claims

1. A method for optimizing a hydrofoil proxy model, characterized in that, Includes the following steps: S1. Determine the number of design variables for the hydrofoil and the value range of each design variable; all the design variables take values ​​within their respective value ranges and are combined to construct the sample space of the hydrofoil; randomly select a preset number of training samples and test samples within the sample space; S2. Based on the training samples and the test samples, calculate the performance response values ​​of the corresponding hydrofoil; S3. Construct the first Kriging proxy model using the training samples and their performance response values; S4. Verify the accuracy of the first Kriging proxy model using the test samples and their performance response values; S5. If the accuracy meets the standard, use a multi-objective genetic algorithm to perform multi-objective optimization on the first Kriging surrogate model to obtain the Pareto front, and use the two-base point method to select the final optimal solution from the Pareto front; S6. If the accuracy does not meet the standard, a two-level addition strategy is adopted to correct the first Kriging surrogate model. This includes adopting a two-level addition strategy to obtain samples from the sample space, adding them to the training samples, returning to steps S2 to S4, until the accuracy meets the standard, and then running step S5. The two-level addition strategy includes primary addition based on the expectation improvement criterion and secondary addition based on the prediction variance criterion.

2. The hydrofoil proxy model optimization method according to claim 1, characterized in that, In step S1, the design variables include the hydrofoil's angle of attack, immersion depth, and speed.

3. The hydrofoil proxy model optimization method according to claim 2, characterized in that, In step S2, the performance response values ​​include the lift coefficient, drag coefficient, and lift-to-drag ratio of the hydrofoil.

4. The hydrofoil proxy model optimization method according to claim 1, characterized in that, In step S6, the initial point addition based on the expected improvement criterion includes: S6.1.1 Construct a second kriging proxy model based on all samples in the sample space; S6.1.

2. Use a genetic algorithm to obtain the sample that maximizes the expected improvement value in the second Kriging surrogate model, and remove the sample from the second Kriging surrogate model. S6.1.3 Repeat S6.1.2, with the number of repetitions set to the third preset value; construct the second kriging proxy model with all the samples taken out as the third kriging proxy model, and all the samples taken out constitute the design point library.

5. The hydrofoil proxy model optimization method according to claim 4, characterized in that, In step S6.1.2, a genetic algorithm is used to obtain the sample that maximizes the expected improvement value in the second Kriging surrogate model. The initial population of the decision variables of the genetic algorithm is set to 180-220 and the number of iterations is set to 100-140.

6. The hydrofoil proxy model optimization method according to any one of claims 1-5, characterized in that, In step S6, the secondary addition of points based on the prediction variance criterion includes: S6.2.

1. For the samples in the design point library, a genetic algorithm is used to simulate the binary crossover operator to process them and generate a secondary candidate point library; S6.2.2 Based on the third Kriging surrogate model, calculate the mean square error of all samples in the secondary candidate point library, and take the sample with the maximum mean square error as the final sample and add it to the training samples.

7. The hydrofoil proxy model optimization method according to claim 6, characterized in that, In step S6.2.2, the process of obtaining the sample with the maximum value in the mean square error includes: Among all the mean squared errors of the samples, the four samples with the largest fourth preset value are selected to form the fourth Kriging surrogate model. The sample with the largest mean squared error is obtained by using a multi-objective genetic algorithm and is used as the final sample.

8. The hydrofoil proxy model optimization method according to claim 7, characterized in that, In step S1, the preset number of training samples is set to a first preset value, and the preset number of test samples is set to a second preset value, wherein the first preset value is greater than the second preset value.

9. The hydrofoil proxy model optimization method according to claim 8, characterized in that, The number of design variables is set to n, and n≥3; the first preset value is set to 45n-60n, and the second preset value is set to 8n-12n; and / or, The third preset value is set to 20-30; and / or, The fourth preset value is set to 13-18.

10. A hydrofoil, characterized in that, This includes hydrofoils obtained using the hydrofoil proxy model optimization method as described in any one of claims 1-9.

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