Propeller aerodynamic modeling method based on physical information multiple fidelity proxy model

Abstract

The application provides a propeller aerodynamic modeling method based on a physical information multi-fidelity surrogate model, and belongs to the technical field of propeller aerodynamic optimization. The method adopts a Bezier curve to perform geometric parameterization on chord length and pitch angle distribution of a propeller; generates nested multi-fidelity data sets through a blade element momentum theory and a reconstruction viscous vortex particle method; constructs a multi-fidelity neural network, establishes physical constraints based on an actuator disk theory, extracts polynomial error correction coefficients, constructs a composite loss function for training, and obtains a physical information driven multi-fidelity surrogate model; performs Pareto front searching through an NSGA-II algorithm, and selects an optimal scheme and verifies the optimal scheme through a TOPSIS method. The application solves the problems of high-precision simulation high cost and insufficient physical consistency under a small sample, and is applied to an APC 10x7E propeller, so that the thrust coefficient and the weighted average efficiency are improved.

Description

Technical Field

[0001] This invention relates to the field of propeller aerodynamic optimization technology, and in particular to a propeller aerodynamic modeling method based on a physical information multifidelity proxy model. Background Technology

[0002] With the rapid popularization of urban air mobility (UAM), electric vertical takeoff and landing (eVTOL) aircraft, and various unmanned aerial vehicle (UAV) systems, aircraft propulsion systems are facing multiple requirements in terms of performance, safety, economy, and environmental friendliness. As the most important propulsion component of such aircraft, the propeller's aerodynamic efficiency and thrust performance directly affect the aircraft's endurance, mission payload capacity, energy utilization level, and operational safety.

[0003] In practical engineering, propeller optimization often involves multiple indicators such as thrust, efficiency, and structural strength, which are significantly coupled and even conflicting. For example, improving propulsion efficiency may exacerbate cavitation risk, while suppressing cavitation may sacrifice some efficiency. Propeller aerodynamic performance is influenced by multiple factors, including chord length distribution, pitch angle, blade shape, and rotational speed, resulting in a high-dimensional, highly nonlinear, and highly coupled design space. Small geometric changes can cause significant changes in thrust, torque, and efficiency. This complexity makes it difficult to obtain a globally optimal solution using traditional experience-based design or local trial-and-error methods.

[0004] Currently, evaluation methods for propeller aerodynamic performance have formed a multi-level system ranging from low-fidelity to high-fidelity. Blade element momentum theory (BEMT), relying on two-dimensional airfoil aerodynamic data, is the most widely used for rapid estimation, but its ability to accurately capture the three-dimensional rotational effects of propellers at low Reynolds numbers is limited. Computational fluid dynamics (CFD) methods based on the three-dimensional Reynolds-averaged Navier-Stokes equations, while accurately capturing flow field details, are extremely computationally intensive; a full-scale CFD solution for a single operating point typically takes tens of hours.

[0005] To overcome the contradiction between aerodynamic design efficiency and evaluation accuracy, multi-fidelity surrogate model technology has emerged. However, purely data-driven surrogate models are essentially "black box" fittings. When faced with the complex three-dimensional flow characteristics of propellers, if training samples are scarce, the model is prone to overfitting. Existing research has pointed out that even the most advanced machine learning models still struggle to guarantee physical consistency in their predictions, facing the risk of physical distortion in sparse data regions.

[0006] Therefore, it is necessary to propose a rapid optimization method for propeller aerodynamic shape that integrates physical constraints and multi-fidelity data, so as to ensure both computational economy and physical reliability of aerodynamic prediction. Summary of the Invention

[0007] The purpose of this invention is to provide a propeller aerodynamic modeling method based on a physical information multi-fidelity surrogate model, which solves the technical problems of high cost of high-precision simulation calculation and insufficient prediction accuracy and poor physical interpretability of pure data-driven surrogate models in small sample sizes in the prior art.

[0008] To achieve the above objectives, this invention provides a propeller aerodynamic modeling method based on a physical information multifidelity proxy model, comprising the following steps: Step S1: Use parametric curves to geometrically parameterize the chord length distribution and pitch angle distribution of the propeller to determine the optimal design variables; Step S2: Obtain the low-fidelity sample set and high-fidelity sample set of the propeller; Step S3: Construct a multi-fidelity neural network. Train the multi-fidelity neural network using low-fidelity and high-fidelity sample sets to obtain a multi-fidelity proxy model. The multi-fidelity neural network is used to fuse the correlation between data of different fidelity levels. Step S4: Construct a physical constraint model based on physical laws, and embed the physical constraint model into the training process of the multi-fidelity neural network to obtain a physical information-driven multi-fidelity proxy model; Step S5: Based on the physical information-driven multi-fidelity proxy model, construct a multi-objective optimization problem, and use a multi-objective optimization algorithm to perform Pareto front search to obtain a non-dominated solution set; Step S6: Select the optimal compromise solution from the non-dominated solution set using a multi-attribute decision-making method; Step S7: Perform geometric model restoration and simulation verification of the optimal compromise solution.

[0009] Preferably, in step S1, the parameterization curves are parameterized using a third-order Bézier curve to parameterize the chord length distribution, with 4 control points representing the chord length distribution; and the pitch angle distribution is parameterized using a sixth-order Bézier curve, with 7 control points representing the pitch angle distribution.

[0010] Preferably, in step S2, the low-fidelity sample set is generated by the leaf element momentum theory method, the high-fidelity sample set is generated by the reconstructed viscous vortex particle method, and the high-fidelity sample points are nested in the low-fidelity sample set; the ratio of the number of samples in the low-fidelity sample set to the number of samples in the high-fidelity sample set is 8:1.

[0011] Preferably, in step S3, the multi-fidelity neural network includes a low-fidelity approximation subnetwork and a high-fidelity correlation subnetwork. The high-fidelity correlation subnetwork captures the correlation between data of different fidelity levels through a weighted fusion of linear and nonlinear mapping components; the high-fidelity predicted value... The fusion formula is: ; in, The vector representing the input variables of the proxy model. For the output of the low-fidelity approximation subnetwork, The linear mapping component is the output of the linearly dependent subnetwork. The nonlinear mapping component is the output of the nonlinear correlation subnetwork. These are the trainable weight parameters.

[0012] Preferably, the physical law in step S4 is based on the actuation disk theory, and a theoretical analytical relationship is established between the thrust coefficient, torque coefficient, and forward ratio based on the actuation disk theory; torque coefficient The theoretical expression is: ; in, For thrust coefficient, For the forward ratio.

[0013] Preferably, the physical constraint model in step S4 also includes an error correction term; the specific process of error correction is as follows: based on experimental data, a fifth-order polynomial is constructed. Systematic deviations between theoretical predictions and experimental results: ; in, The fitting constant; the corrected physical prediction value. for: .

[0014] Preferably, the specific implementation method of embedding the physical constraint model into the training process of the multi-fidelity neural network is as follows: construct a composite loss function and use the composite loss function to jointly train the multi-fidelity neural network; Composite loss function for: ; in, This is the fitting error term for low-fidelity data. This is the high-fidelity data fitting error term. For regularization terms, For physical guidance loss terms; Physical guidance loss term The expression is: ; in, For physical constraint weights, This is the physical residual loss term. This is a physical boundary penalty term.

[0015] Preferably, the multi-objective optimization problem in step S5 includes two optimization objectives: the first objective is to maximize the thrust coefficient under low-speed climb conditions, and the second objective is to maximize the weighted average aerodynamic efficiency under multiple conditions; the forward ratio is 0.45 under climb conditions, 0.60 under cruise conditions, and 0.75 under sprint conditions, with corresponding weight coefficients of 0.2, 0.6, and 0.2, respectively.

[0016] Preferably, the design variables for the multi-objective optimization problem in step S5 are within ±15% of the corresponding geometric parameters of the baseline paddle shape; the multi-objective optimization algorithm is a non-dominated sorting genetic algorithm.

[0017] Preferably, in step S7, the simulation verification uses the multiple reference frame (MRF) method for quasi-steady calculation. The computational domain is divided into a rotating subdomain containing the propeller and an external stationary subdomain. The turbulence model selected is the SST k-ω model.

[0018] Therefore, the present invention employs the above-mentioned propeller aerodynamic modeling method based on a physical information multi-fidelity proxy model, and the beneficial technical effects are as follows: (1) The propeller chord length and pitch angle distribution are parameterized by Bézier curves to reduce the dimension of the design variables with a simplified set of control points, thus solving the high-dimensional problem of propeller shape representation.

[0019] (2) The leaf element momentum theory is used to generate a large number of low-fidelity samples to provide macroscopic performance profiles, while the reconstructed viscous eddy particle method is used to generate a small number of high-fidelity samples to accurately capture local flow field details. The two methods complement each other and achieve a good balance between accuracy and efficiency.

[0020] (3) By using the linear and nonlinear dual-channel weighted fusion mechanism in the multi-fidelity neural network architecture, the complex mapping relationship between data of different fidelity is adaptively captured, breaking through the accuracy ceiling of single data source modeling.

[0021] (4) The energy conservation relationship derived from the actuated disk theory is embedded as a physical constraint into the neural network loss function, and the polynomial correction coefficient is extracted in combination with experimental data to compensate for the systematic deviation between the ideal model and the real viscous dissipation. This fundamentally curbs the risk of overfitting in the sparse sample domain and improves the physical consistency and generalization ability of the model.

[0022] (5) A multi-condition weighted robust design strategy is adopted. The Pareto front search is performed by the NSGA-II algorithm and the optimal compromise scheme is selected by combining the TOPSIS method, which effectively balances the low-speed climb thrust and the full envelope cruise efficiency.

[0023] (6) High-precision computational fluid dynamics simulation was used as the final verification method, forming a complete closed loop from parametric modeling to surrogate model construction, and then to multi-objective optimization and simulation verification, which verified the engineering reliability of the optimization scheme. Attached Figure Description

[0024] Figure 1 The flowchart shows a propeller aerodynamic modeling method based on a physical information multifidelity proxy model according to the present invention. Figure 2 Front and top views of the APC 10×7E propeller; Figure 3 The network architecture diagram of the Multifidelity Neural Network (MFNN); Figure 4 A schematic diagram illustrating four implementation strategies for machine learning driven by physical information; Figure 5 A schematic diagram of the physical information loss function strategy; Figure 6 This is a comparison chart of torque coefficient predictions before and after polynomial correction. Figure 6 (a) in the text represents the original text before the correction. Figure 6 (b) in the text is the corrected version; Figure 7 This is a schematic diagram of the NSGA-II algorithm. Figure 8 Pareto frontier plot; Figure 9 The distribution of TOPSIS scores within the solution set; Figure 10 To optimize the comparison diagram of propeller geometry distribution before and after optimization, among which, Figure 10 (a) in the figure represents a comparison of chord length distribution. Figure 10 (b) shows a comparison of pitch angle distribution; Figure 11 A comparison chart of thrust coefficient and aerodynamic efficiency performance before and after propeller optimization is provided. Figure 11 (a) shows a comparison of thrust coefficients. Figure 11 (b) in the figure represents a comparison of aerodynamic efficiency. Detailed Implementation

[0025] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0026] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning as understood by one of ordinary skill in the art to which this invention pertains.

[0027] Example 1 like Figure 1As shown, this invention proposes a propeller aerodynamic modeling method based on a physical information multi-fidelity surrogate model. Taking the APC 10×7E propeller as the research object, it constructs a complete technical chain from geometric parameterization to multi-fidelity surrogate model training, and then to multi-objective optimization and simulation verification. The core idea of ​​this method is to reduce design variables through Bézier curve dimensionality reduction parameterization, fuse aerodynamic data of different precisions through a multi-fidelity neural network, embed the physical constraints derived from actuator disk theory into the model training process, and finally achieve efficient optimization of the propeller aerodynamic shape through a multi-objective evolutionary algorithm. The following is a detailed explanation of each step.

[0028] like Figure 2 As shown, this method takes the APC 10×7E propeller as the research object. The propeller is a two-bladed electric propeller with a diameter of 25.4 cm, a pitch of 17.78 cm, a hub diameter of 2.032 cm, and a hub-to-diameter ratio of 0.08. The front half of the cross-section is an E63 airfoil, and the rear half is a NACA 4412 airfoil.

[0029] In step S1, the APC 10×7E propeller geometry data publicly available from the UIUC University Laboratory is selected as the basis for modeling. This dataset fully covers... =0.15 to 1.0 radial stations, where, The radial distance from the rotation axis to the blade section. Where is the blade radius. Let be the independent variable in the domain of the Bézier curve. Data fitting of the propeller chord length distribution and pitch angle distribution is performed using Bézier curves of orders 1 to 8, respectively. The root mean square error (RMSE) and coefficient of determination are used as the data. As an evaluation index for fitting accuracy.

[0030] Through systematic comparative analysis, the accuracy improves rapidly when the chord length distribution is in the first or second order, but improves significantly after the third order. The result is close to 1, and the RMSE has dropped to a very small level. Continuing to increase the order, while the error continues to decrease, the magnitude is limited, and it has clearly entered the diminishing returns range. The underfit of the pitch angle distribution is more pronounced when using low-order curves, requiring higher orders to characterize the changing trend. At order six, the fitting effect has significantly improved and tended to stabilize; further increases in order also lead to diminishing returns. On the other hand, higher-order Bézier curves have more control points and greater degrees of freedom, making them prone to unnecessary fluctuations in local areas. At the same time, the increased dimensionality of variables also increases the difficulty of subsequent modeling and optimization, potentially leading to numerical instability.

[0031] Considering factors such as fitting accuracy, improvement magnitude, and model stability, this embodiment ultimately employs a third-order Bézier curve to parameterize the chord length distribution, using four control points P1~P4 to characterize the radial distribution of the chord length; and a sixth-order Bézier curve to parameterize the pitch angle distribution, using seven control points P5~P11 to characterize the radial distribution of the pitch angle. The above 11 Bézier curve control points and the advance ratio... J Together, these constitute the 12-dimensional input variables. The output variable is chosen as the propeller thrust coefficient. and torque coefficient Two dimensionless coefficients.

[0032] In step S2, this embodiment designs a nested multi-fidelity data acquisition scheme. The low-fidelity sample set is generated by the leaf element momentum theory (BEMT) method, and the high-fidelity sample set is generated by the reconstructed viscous eddy particle method (rVPM) method, and all high-fidelity sample points... Must be nested within a low-fidelity sample set In, that is .

[0033] Regarding low-fidelity data acquisition: The core idea of ​​the BEMT method is to decompose the complex blade hydrodynamics problem into infinitesimal elements for processing. Essentially, it combines the macroscopic analysis of momentum theory with the microscopic airfoil force analysis of blade element theory. This method first assumes the propeller is an infinitely thin "actuator disk" and discretizes the blade into several independent micro-rings along the radial direction. During the calculation, it is assumed that the individual blade elements do not interfere with each other, and that the aerodynamic forces depend only on the local geometric parameters of that section and the local flow field conditions. This dimensionality reduction greatly simplifies the complex three-dimensional turbulence problem, making it possible to complete the calculation of a single sample within a fraction of a second. Comparison with UIUC wind tunnel experimental data shows that the average relative error of the thrust coefficient using the BEMT method is 14.63%, and the average relative error of the aerodynamic efficiency is only 2.90%, enabling it to capture the global trend of aerodynamic performance changes with operating conditions at millisecond speeds.

[0034] Regarding high-fidelity data acquisition, this embodiment employs the rVPM simulation framework, a meshless large eddy simulation method. Its core idea is to solve the vorticity equations in Lagrangian form, using discrete vortex particles to characterize the vorticity distribution in the flow field. In the aerodynamic load calculation for the blades, an actuated line model (ALM) is used. The blades are discretized along the spanwise direction into multiple independent aerodynamic sections, and blade element theory is applied to solve for the local aerodynamic loads for each section. Comparison with UIUC wind tunnel experimental data shows that the rVPM method achieves an average relative error of 8.56% for the thrust coefficient across all operating conditions, an average relative error of only 1.69% for aerodynamic efficiency, and an average iterative convergence time of approximately 60 minutes for a single operating point, achieving a good balance between accuracy and efficiency.

[0035] Correlation analysis confirmed that the dataset constructed by this method exhibits good variable independence and low risk of multicollinearity, requiring no additional dimensionality reduction and making it suitable for direct use in subsequent regression modeling and neural network training.

[0036] like Figure 3 As shown, the multi-fidelity neural network (MFNN) constructed in step S3 consists of three fully connected neural networks. This framework first constructs a fully connected neural network for fitting low-fidelity data. , These are low-fidelity data points. Subsequently, a fully connected neural network... The output is not only used as a low-precision prediction, but also as prior knowledge and fed into the subsequent high-fidelity correlation network.

[0037] To adaptively capture the complex mapping relationships between low-fidelity and high-fidelity data, the correlation network is decoupled into a linear correlation subnetwork. and nonlinear correlation subnetwork The linear correlation subnetwork is used to capture the linear proportional or deviation relationship between the two, and outputs a linear mapping component. The nonlinear correlation subnetwork utilizes activation functions to mine deeper, higher-order nonlinear features and outputs nonlinear mapping components. Both are connected by a trainable weight parameter. This method performs dynamic weighted fusion. Fixed at 0.5, Given the input variable vector of the surrogate model, the final coupled prediction formula of the MFNN is: ; Regarding data allocation, systematic sensitivity analysis determined that the optimal ratio is 1 high-fidelity dataset to 8 low-fidelity datasets. This ratio maximizes the extraction of global spatial features from low-fidelity samples under limited high-fidelity sample conditions, achieving an optimal trade-off between information gain and sampling cost. In terms of data scale, a balance of 30 high-fidelity samples to 240 low-fidelity samples was selected as the best equilibrium point. This combination ensures high model accuracy while minimizing computational overhead.

[0038] like Figure 4 As shown, the core logic of physical information-driven machine learning lies in using domain knowledge to constrain the hypothesis space of the surrogate model, guiding the model from input features. Converging to the output prediction value that conforms to physical laws Based on the different stages of the physical information modeling lifecycle, existing implementation strategies can be mainly categorized into four types: physical information preprocessing based on input features, physical information model architecture based on network structure, physical information loss function based on objective function, and physical information model fusion based on hybrid systems. After comprehensively considering the characteristics of each strategy and its transferability and engineering applicability in multi-fidelity data coexistence scenarios, this solution ultimately adopts the strategy based on physical information loss function.

[0039] Regarding the establishment of theoretical constraints for the actuation disk. For example... Figure 5 As shown, the core idea of ​​the physical information loss function strategy is to simultaneously introduce data error terms and physical residual terms into the training objective of the neural network, forming a composite loss architecture. Specifically, the neural network uses the input feature vector... Input, output predicted value During training, the loss function consists of the data fitting error term. Physical constraint residuals It is composed of weighted combinations, and its general form is as follows: ,in These are the physical constraint weights, used to balance the weighting between data fit and physical consistency. This strategy does not change the network's basic architecture, but rather uses hyperparameters... Adjusting the guiding strength of the physical equations on the optimization direction to make the output prediction value While meeting the requirements for data fitting accuracy, it also adheres to physical laws. In this embodiment, Parameters of the 11 Bézier control points and advance ratio corresponding to the propeller , Corresponding thrust coefficient and torque coefficient Within this framework, the classical actuated disk theory is chosen as the source of macroscopic aerodynamic mechanism constraints. This theory abstracts the propeller as an infinitely thin disk that generates pressure jumps, focusing on the momentum and energy exchange of fluid flowing through the propeller disk under the assumptions of a steady, incompressible, and inviscid ideal axisymmetric flow field. An axial induction factor is introduced. To characterize the velocity increment of fluid flowing through the propeller disk, based on momentum theory, thrust Equal to the rate of change of momentum of the fluid flowing through the propeller disk, substituted into the feed rate ratio. Thrust coefficient and area Information about the inducing factor can be obtained. The quadratic equation in one variable, taking a physically plausible positive root: ; In an ideal state, the shaft power absorbed by the propeller is completely converted into fluid kinetic energy, with no energy dissipation whatsoever. (Combined with power coefficient) With torque coefficient Relationship Finally, the theoretical torque coefficient is derived: ; Regarding polynomial error correction. For example... Figure 6 As shown in the figure, the diagonal line represents the zero-error reference line where the predicted value and the experimental baseline value are in perfect agreement. Figure 6 In (a), the horizontal axis represents the torque coefficient of the experimental baseline data. The vertical axis represents the theoretically predicted torque coefficient before correction, derived from the actuation disc theory. The theoretical torque coefficient was checked point by point against the data in the APC official manual, and the feed rate ratio was... J Within the typical operating range, the average error of the theoretical model is approximately 24.36%. This systematic deviation mainly stems from the high degree of simplification of energy dissipation paths in the theoretical derivation—the actuated disk model essentially ignores blade drag and swirl losses. According to the regulations of the International Conference on Towed Pools regarding scale effects, there is typically a 10% to 30% power prediction error between ideal fluid models and real viscous flow fields; therefore, this level of deviation is within a reasonable range. More importantly, the error distribution exhibits a variation with the advance rate ratio. J The smooth evolution curve indicates that the physical constraint has successfully captured the core gradient of aerodynamic performance changes with operating conditions, providing a solid foundation for the subsequent introduction of semi-empirical mathematical corrections. Based on this, this scheme introduces a correction that depends solely on the advance ratio, building upon the original physical constraint. J The fifth-order polynomial correction term Corrected torque coefficient for: ; Figure 6(b) in the middle shows the introduction The effect after semi-empirical correction; the horizontal axis in the graph represents the torque coefficient of the experimental baseline data. The vertical axis represents the corrected predicted torque coefficient. The diagram is marked with The points represent the predicted values ​​after polynomial correction, and can be observed. All points have highly regressed to the diagonal, indicating a significant improvement in the prediction accuracy of the corrected model. Cross-model validation showed that the correction term extracted from the 10×7E benchmark was directly transferred to the 10×SF propeller in the same series, and this correction function still kept the average prediction error to 3.06%. This model faces... The slightly higher error within the range is due to the inherent misalignment of the aerodynamic designs of the two propellers within their respective operating conditions, rather than a failure of the generalization ability of the correction term. This result fully demonstrates that the extracted torque coefficient correction term can effectively compensate for unmodeled physical dissipation and exhibits good generalization ability among propellers of the same size.

[0040] Regarding the design of the composite loss function, the total loss function of the Physically Guided Multifidelity Neural Network (PG-MFNN) constructed in this scheme consists of four parts: ; in, and These are the fitting error terms for low-fidelity and high-fidelity data, respectively, with a weight coefficient of 1 for each term; The regularization term, used to prevent overfitting, has a weighting factor of 1. For physical guidance loss terms: ; Physical residual loss term Forced network predictions To the modified physical benchmark convergence: ; Physical boundary penalty Ensure that the prediction efficiency does not exceed the physically reasonable range: ; ; Sensitivity analysis determined the physical constraint weights. For optimal configuration, For propeller aerodynamic efficiency. Under this setting, PG-MFNN fully utilizes the generalization constraint of the physical equations while retaining the flexibility to fit high-fidelity experimental data.

[0041] Ablation experiments show that the baseline model MFNN has high fitting accuracy on the training set, but its prediction performance drops significantly after switching to the test set, exhibiting typical overfitting characteristics. In contrast, PG-MFNN, which introduces physically guided soft constraints, significantly reduces RMSE on the test set and maintains the same order of magnitude as the training set error, proving that physical constraints successfully guide the model from "data memorization" to "pattern learning." Comparison with six baseline models—Kriging, SVR, XGBoost, DNN, and Co-Kriging—shows that PG-MFNN exhibits overwhelming advantages in all comparisons: its box is compressed extremely flat and located in the top region, resulting in not only the highest accuracy but also extremely strong robustness.

[0042] In step S5, a multi-condition weighted robustness design strategy is proposed for typical mission scenarios of the APC 10×7E propeller. This strategy uses 11 geometric characteristic parameters affecting the propeller's aerodynamic performance as decision vectors to be optimized. The value range is ±15% of the reference propeller geometry parameters.

[0043] First objective function Focusing on thrust performance under low-speed conditions, the climbing operating point was selected. Thrust coefficient = 0.45 As an evaluation metric, its negative value is used to accommodate the minimization form of the optimization algorithm: ; Second objective function Focusing on the propeller's energy efficiency throughout the entire mission cycle, the climb rate was selected. =0.45, Cruise =0.60 and sprint =0.75 Three characteristic operating points are used to construct a weighted average efficiency index: ; in, =0.2, =0.6, =0.2, For aerodynamic efficiency, For thrust coefficient, The torque coefficient is denoted by . The constraints are that the torque coefficient under each operating condition does not exceed the allowable peak torque coefficient of the motor, and the aerodynamic efficiency is limited to the range of (0, 1).

[0044] like Figure 7As shown, the NSGA-II algorithm is used for Pareto front search. Considering the high-dimensional input features involving 12 parameters in this embodiment, the population size is set to 100, the maximum number of iterations is set to 200 generations, the crossover probability is 0.8, the mutation probability is 0.05, and the variable length is strictly limited to within 0.5% of the variable value range.

[0045] like Figure 8 , 9 As shown, after 200 generations of population evolution, the algorithm converged and output a set of Pareto non-dominated solutions containing multiple compromise schemes. From the macroscopic morphology of the Pareto front, it can be seen that the non-dominated solution set exhibits a clear convex function characteristic, and the thrust coefficient and aerodynamic efficiency show a significant negative correlation. Several visually perceptible discontinuities exist on the front surface; this discontinuity is a true mapping of the spatial physical constraints of complex aerodynamic design boundaries.

[0046] In step S6, the Top-Approximation-Ideal-Solution Ranking (TOPSIS) method is used for multi-attribute decision analysis. This method quantitatively evaluates the comprehensive performance of each scheme by calculating the relative closeness between each non-dominated solution and the ideal solution and negative ideal solution. Through TOPSIS analysis, scheme No. 14, with the highest relative closeness score of 0.6317, was determined as the optimal design scheme. This scheme has an aerodynamic efficiency of 73.98% and a thrust coefficient of 0.0873. A quantitative horizontal comparative analysis with schemes No. 18, No. 33, No. 74, and No. 25, which followed closely in the score, confirms that scheme No. 14 achieves the best trade-off between low-speed thrust reserve and full-envelope cruise efficiency, maintaining cruise performance comparable to the top-efficiency schemes while avoiding the degradation of other key performance characteristics caused by excessive pursuit of a single indicator.

[0047] like Figure 10 As shown, after inverse smooth fitting of the optimized chord length and pitch angle distributions, three-dimensional parametric construction was performed on the ANSYS Workbench platform. The optimized blade exhibits significant widening characteristics in the working core region from 0.2R to 0.8R, while the chord length curve from the outer section to the tip region where r / R>0.8 shows a more convergent taper change. Regarding the pitch angle distribution, the optimized model actively reduces the twist angle in the inner region where r / R<0.45, instead allocating a higher geometric angle of attack to the middle and outer main working section from 0.45R to 0.9R. In the extremely outer region, the twist angle decreases sharply, achieving reasonable aerodynamic unloading by reducing the local angle of attack at the tip. The optimized blade presents a planar shape similar to a "scimitar" in the top view, which, combined with the leading edge curvature and large twist, forms an efficient mechanism of high load in the mid-section and unloading at the tip.

[0048] In step S7, high-fidelity CFD simulation verification was performed using the ANSYS platform. The computational domain was cylindrical, divided into a rotating domain and a stationary domain. The inlet boundary was set at 5 times the upstream radius, using velocity inlet conditions; the outlet boundary was set at 10 times the downstream radius, using pressure outlet conditions; the distance from the cylinder side to the rotation axis was 10 times the radius, defined as the pressure far field. The SST k-ω model was selected as the turbulence model, and both the momentum equation and the turbulence equation were discretized using a second-order upwind scheme, with the dimensionless distance Y+ from the wall strictly controlled to be less than 4.

[0049] like Figure 11 As shown, at the core operating point J=0.45, the optimized propeller thrust coefficient achieved a significant increase of 13.12%; the multi-condition weighted aerodynamic efficiency improved by 6.79%. The relative errors between the surrogate model prediction and the CFD calculation were 3.31% and 2.92%, respectively, both strictly suppressed within the industry-recognized threshold of 5%, fully verifying the engineering confidence of the proposed strategy.

[0050] Flow field analysis shows that the optimized blade surface exhibits a fuller and smoother hydrostatic pressure distribution gradient, and the work-making capacity of the pressure difference between the windward and leeward sides is significantly enhanced. At the same time, the size and intensity of the low-pressure vortex core at the blade tip are significantly reduced and weakened. The uniformity of the slipstream velocity distribution is significantly improved after optimization, and the range of the deep blue low-speed region is greatly reduced, which more effectively converts energy into thrust. This verifies the effectiveness of the optimization strategy from the perspective of physical mechanisms.

[0051] This paper proposes a propeller aerodynamic modeling method based on a physical information multi-fidelity surrogate model, forming a complete closed loop from geometric parameterization to surrogate model construction, multi-objective optimization, and simulation verification. This method reduces design variables through Bézier curve dimensionality reduction parameterization, fuses BEMT low-fidelity data and rVPM high-fidelity data through a multi-fidelity neural network, embeds the energy conservation relationship derived from actuator disk theory as a physical constraint into the model training process, and combines fifth-order polynomial correction to compensate for systematic deviations between the ideal model and actual viscous dissipation. Finally, it achieves efficient optimization of the propeller aerodynamic shape using the NSGA-II algorithm and the TOPSIS method. Applied to the optimization of the APC 10×7E propeller, the thrust coefficient was improved by 13.12%, the weighted average efficiency was improved by 6.79%, and the prediction error of the surrogate model was controlled within 5%, fully verifying the engineering applicability of this method.

[0052] It is worth noting that all contents not described in detail in this invention are existing technologies and are well known to those skilled in the art.

[0053] Therefore, the propeller aerodynamic modeling method based on a multi-fidelity surrogate model of physical information adopted in this invention has significant advantages such as high computational efficiency, good prediction accuracy and strong physical consistency. It effectively solves the technical problems of high cost of high-precision simulation and easy overfitting of pure data-driven models under small sample conditions.

[0054] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A propeller aerodynamic modeling method based on a physical information multi-fidelity proxy model, characterized in that, Includes the following steps: Step S1: Use parametric curves to geometrically parameterize the chord length distribution and pitch angle distribution of the propeller to determine the optimal design variables; Step S2: Obtain the low-fidelity sample set and high-fidelity sample set of the propeller; Step S3: Construct a multi-fidelity neural network, train the multi-fidelity neural network using low-fidelity sample sets and high-fidelity sample sets to obtain a multi-fidelity proxy model; Step S4: Construct a physical constraint model based on physical laws, and embed the physical constraint model into the training process of the multi-fidelity neural network to obtain a physical information-driven multi-fidelity proxy model; Step S5: Based on the physical information-driven multi-fidelity proxy model, construct a multi-objective optimization problem, and use a multi-objective optimization algorithm to perform Pareto front search to obtain a non-dominated solution set; Step S6: Select the optimal compromise solution from the non-dominated solution set using a multi-attribute decision-making method; Step S7: Perform geometric model restoration and simulation verification of the optimal compromise solution.

2. The propeller aerodynamic modeling method based on a multi-fidelity proxy model of physical information according to claim 1, characterized in that, In step S1, the parameterization curves use a third-order Bézier curve to parameterize the chord length distribution, with 4 control points representing the chord length distribution; and a sixth-order Bézier curve to parameterize the pitch angle distribution, with 7 control points representing the pitch angle distribution.

3. The propeller aerodynamic modeling method based on a multi-fidelity proxy model of physical information according to claim 1, characterized in that, In step S2, the low-fidelity sample set is generated by the leaf element momentum theory method, and the high-fidelity sample set is generated by the reconstructed viscous eddy particle method. The high-fidelity sample points are nested in the low-fidelity sample set. The ratio of the number of samples in the low-fidelity sample set to the number of samples in the high-fidelity sample set is 8:

1.

4. The propeller aerodynamic modeling method based on a physical information multi-fidelity proxy model according to claim 1, characterized in that, In step S3, the multi-fidelity neural network includes a low-fidelity approximation subnetwork and a high-fidelity correlation subnetwork. The high-fidelity correlation subnetwork captures the correlation between data of different fidelity levels through a weighted fusion of linear and nonlinear mapping components; the high-fidelity predicted value... The fusion formula is: ； in, x For the input variable vector of the proxy model, For the output of the low-fidelity approximation subnetwork, The linear mapping component is the output of the linearly dependent subnetwork. The nonlinear mapping component is the output of the nonlinear correlation subnetwork. These are the trainable weight parameters.

5. The propeller aerodynamic modeling method based on a physical information multi-fidelity proxy model according to claim 1, characterized in that, In step S4, the physical law is the actuation disk theory, and a theoretical analytical relationship between the thrust coefficient, torque coefficient and forward ratio is established based on the actuation disk theory. Torque coefficient The theoretical expression is: ； in, For thrust coefficient, For the forward ratio.

6. The propeller aerodynamic modeling method based on a physical information multi-fidelity proxy model according to claim 5, characterized in that, Step S4 also includes an error correction term in the physical constraint model; the specific process of error correction is as follows: based on experimental data, a fifth-order polynomial is constructed. Systematic deviations between theoretical predictions and experimental results: ； in, The fitting constant; the corrected physical prediction value. for: 。 7. The propeller aerodynamic modeling method based on a physical information multi-fidelity proxy model according to claim 1, characterized in that, The specific implementation method of embedding the physical constraint model into the training process of the multi-fidelity neural network is as follows: construct a composite loss function and use the composite loss function to jointly train the multi-fidelity neural network; Composite loss function for: ； in, This is the fitting error term for low-fidelity data. This is the high-fidelity data fitting error term. For regularization terms, For physical guidance loss terms; Physical guidance loss term The expression is: ； in, For physical constraint weights, This is the physical residual loss term. This is a physical boundary penalty term.

8. The propeller aerodynamic modeling method based on a physical information multi-fidelity proxy model according to claim 1, characterized in that, The multi-objective optimization problem in step S5 includes two optimization objectives: the first objective is to maximize the thrust coefficient under low-speed climb conditions, and the second objective is to maximize the weighted average aerodynamic efficiency under multiple conditions; the forward ratio is 0.45 under climb conditions, 0.60 under cruise conditions, and 0.75 under sprint conditions, with corresponding weight coefficients of 0.2, 0.6, and 0.2, respectively.

9. The propeller aerodynamic modeling method based on a physical information multi-fidelity proxy model according to claim 1, characterized in that, In step S5, the design variables for the multi-objective optimization problem are within the range of ±15% of the corresponding geometric parameters of the baseline paddle shape; the multi-objective optimization algorithm is a non-dominated sorting genetic algorithm.

10. The propeller aerodynamic modeling method based on a physical information multi-fidelity proxy model according to claim 1, characterized in that, In step S7, the simulation verification uses the multiple reference frame (MRF) method for quasi-steady calculation. The computational domain is divided into a rotating subdomain containing the propeller and an external stationary subdomain. The SST k-ω model is selected as the turbulence model.

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