Rotor aerodynamic shape optimization method and system based on airfoil geometry feasibility constraints

Abstract

This invention belongs to the field of rotor optimization technology and discloses a rotor aerodynamic shape optimization method and system based on airfoil geometric feasibility constraints. It transforms the high-dimensional, complex three-dimensional rotor shape into low-dimensional mathematical vectors using CST and SVD parameterization methods; constructs a large-scale aerodynamic database using the low-fidelity but extremely fast XROTOR tool; utilizes a deep neural network MLP to learn the nonlinear mapping relationship between design variables and aerodynamic performance, constructing a high-precision surrogate model to replace expensive CFD simulations; and finally introduces airfoil geometric feasibility constraints based on modal space Euclidean distance into the SLSQP gradient optimization algorithm, rapidly searching for the global optimal solution within the surrogate model space while ensuring the geometric rationality and manufacturability of the optimization results.

Description

Technical Field

[0001] This invention belongs to the field of rotor optimization technology, specifically relating to a rotor aerodynamic shape optimization method and system based on airfoil geometric feasibility constraints. Background Technology

[0002] Since the rotor propulsion system of unmanned aerial vehicles has been widely used in many fields such as civilian, industrial and scientific research, researchers have been committed to optimizing its design in a complete three-dimensional shape design space. The three-dimensional shape design space includes three core design dimensions: airfoil, chord length and torsion. The optimization goal is to balance aerodynamic efficiency, noise level and engineering manufacturability, and to have the ability to quickly iterate the design.

[0003] Currently, the industry widely adopts the surrogate-based optimization (SBO) method to achieve the above design requirements. This method can effectively solve the technical problems of low computational efficiency and high simulation cost in traditional optimization design. Its basic process is as follows: First, reasonable sampling is carried out in the three-dimensional shape design space through the design of experiments (DOE) method to obtain a series of design sample points; Second, the aerodynamic performance of each sample point is accurately calculated using computational fluid dynamics (CFD) simulation technology to obtain the aerodynamic performance data corresponding to the sample point; Next, based on the sample points and their aerodynamic performance data, a surrogate model (such as Kriging model, radial basis function (RBF) neural network, polynomial response surface model, etc.) is constructed to fit the complex mapping relationship between design variables and aerodynamic performance; Finally, the constructed surrogate model is coupled with the optimization algorithm, and the optimization algorithm efficiently optimizes the surrogate model to quickly obtain the optimal rotor three-dimensional shape design scheme that meets the requirements of aerodynamic efficiency, noise level and engineering manufacturability. However, the following problems still exist:

[0004] (1) Data-driven optimization lacks geometric feasibility constraints, making it impossible to form a reliable automated design process: In recent years, work has begun to use machine learning or surrogate models to assist propeller / wind turbine design. However, these methods generally only focus on prediction accuracy and optimization convergence, lacking systematic constraints on the rationality and manufacturability of airfoil geometry. Senior designers often need to manually screen and correct the results extensively, making it difficult to truly close the loop in the automated design process. How to ensure that the airfoil geometry does not deviate too far from the mature airfoil family, has stable aerodynamic characteristics and manufacturability at the mathematical model level in data-driven optimization is a long-standing but unresolved core problem.

[0005] (2) High-precision CFD optimization computation cost is too high: the initial sample points required to build the surrogate model still need to be obtained through high-cost CFD simulation. When the number of design variables increases, the required sample size increases sharply (another manifestation of the curse of dimensionality). The early data preparation stage takes a long time.

[0006] (3) Three-dimensional shape co-optimization is difficult to implement and has long remained at the level of step-by-step parameter tuning: Most existing studies only optimize the planar shape (chord length, torsion) or airfoil step by step, or only explore a few degrees of freedom. In actual engineering, it is generally still at the level of empirical selection and local fine-tuning combination. Some studies adopt a strategy of decoupling the design process to reduce the design difficulty: first optimize the airfoil family with the adjoint method, and then optimize the torsion angle and chord length distribution step by step with the parameter perturbation method and flow field reconstruction method. The airfoil and planar shape parameters are always processed independently in mutually isolated optimization loops, and true three-dimensional co-optimization has not been achieved. Some studies select only one fixed reference airfoil at the blade root and blade tip to control the dimension of design variables. The middle section of the blade span is transitioned by interpolation. The airfoil itself is not the optimization object. Some studies only include chord length and torsion distribution in the design variables. The overall airfoil geometry is fixed. It is mentioned that the computational cost of introducing airfoil coordinates as optimization variables under the surrogate model framework is too high. Existing technologies systematically reveal that true synergistic optimization of three types of parameters—airfoil, chord length, and torsion—has long been lacking in engineering practice in the field of rotor / propeller aerodynamic optimization.

[0007] In summary, within the existing technological framework, achieving rapid rotor optimization design that balances efficiency, noise, and manufacturability using data-driven methods in a high-dimensional three-dimensional shape design space has remained a comprehensive technical challenge that has yet to be successfully solved. Summary of the Invention

[0008] To address the core deficiency in existing technologies where the optimization solution of airfoil geometry cannot be automatically guaranteed by proxy models, this invention provides a method and system for optimizing rotor aerodynamic shape based on airfoil geometry feasibility constraints.

[0009] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0010] The first aspect: provides a rotor aerodynamic shape optimization method based on airfoil geometric feasibility constraints, including the following steps:

[0011] A shape transformation-like method is used to parametrically model the rotor planar shape, and the parameters of the shape transformation-like method are used as the first design variable.

[0012] The singular value decomposition method is used to reduce the dimensionality of the airfoil library. The modal coefficients representing the airfoil are used as the second design variable. The first and second design variables together constitute the design space.

[0013] Random sampling was performed within the design space, and aerodynamic performance simulation was conducted at each sampling point using a low-order aerodynamic model rotor analysis tool. After data cleaning and normalization, an aerodynamic performance training database was constructed.

[0014] The multilayer perceptron neural network is trained offline using the aerodynamic performance training database, and then solidified as a surrogate model after training is completed.

[0015] A gradient-based sequential least squares programming algorithm is introduced. Based on the current design variables in the iteration, the surrogate model is called to complete the aerodynamic performance inference, obtain the gradient information associated with the objective function and constraint functions, update the design variables based on the gradient information and carry out iterative optimization until the iterative convergence condition is met, output the optimal design variables, and obtain the optimal rotor aerodynamic shape. The constraint function includes the minimum Euclidean distance between the current design variables and the corresponding design variables of several known feasible airfoils being less than the geometric feasibility threshold.

[0016] Several alternative methods are provided below, but they are not intended as additional limitations on the overall solution above. They are merely further additions or optimizations. Provided there are no technical or logical contradictions, each alternative method can be combined individually with respect to the overall solution above, or multiple alternative methods can be combined with each other.

[0017] Preferably, the method of parametrically modeling the rotor planar shape using a shape transformation-like method, and using the parameters of the shape transformation-like method as the first design variable, includes:

[0018] For the radial chord length distribution and torsion angle distribution of the rotor, a shape transformation-like method is used for parametric modeling;

[0019] The shape function orders of the chord length distribution and the torsion angle distribution are respectively set to be... Therefore, the chord length distribution Each control parameter and torsion angle distribution One control parameter is used as the first design variable.

[0020] Preferably, the method of using singular value decomposition to reduce the dimensionality of the airfoil library, and using the modal coefficients representing the airfoils as the second design variable, includes:

[0021] Incorporating the airfoil section into the design variables, and employing singular value decomposition to reduce the dimensionality of the airfoil coordinates in the airfoil library, the preceding section is truncated. The airfoil will be reconstructed using the principal modes, therefore the airfoil will be reconstructed using the... The modal coefficients are used as the second design variables.

[0022] Preferably, the objective function is to maximize rotor propulsion efficiency or minimize rotor noise performance.

[0023] The constraint functions include thrust constraints, geometric constraints, and airfoil geometric feasibility constraints. The airfoil geometric feasibility constraint is that the minimum Euclidean distance between the current design variable and the corresponding design variables of several known feasible airfoils is less than the geometric feasibility threshold.

[0024] Preferably, the minimum Euclidean distance between the current design variable and the corresponding design variables of several known feasible airfoils is less than the geometric feasibility threshold, including:

[0025] Take the second design variable from the current design variables in the iteration, and calculate the standardized value of the second design variable;

[0026] Iterate through the standardized values ​​of the second design variable corresponding to each feasible airfoil in the airfoil feasibility database, calculate the standardized value of the second design variable in the current design variable, and the Euclidean distance between it and the standardized values ​​of each traversed second design variable;

[0027] If the minimum Euclidean distance is less than or equal to the geometric feasibility threshold, it means that the current design variables meet the airfoil geometric feasibility constraints; otherwise, the current design variables do not meet the airfoil geometric feasibility constraints.

[0028] As a preferred embodiment, the airfoil feasibility database is constructed as follows:

[0029] Obtain rotor aerodynamic shape data for known feasible airfoils;

[0030] The second design variable is obtained by using singular value decomposition on the rotor aerodynamic shape data;

[0031] The second design variable is standardized to obtain its standardized value.

[0032] An airfoil feasibility database is constructed based on the standardized values ​​of the second design variables corresponding to all feasible airfoils.

[0033] Preferably, the geometric feasibility threshold is determined as follows:

[0034] Calculate the Euclidean distance between two adjacent feasible airfoils in the airfoil feasibility database;

[0035] Determine the Euclidean distance between each feasible airfoil and the nearest feasible airfoil, and use it as the nearest neighbor distance;

[0036] Calculate the average distance of all nearest neighbors. and standard deviation And calculate the geometric feasibility threshold as ,in This is the proportionality coefficient.

[0037] Preferably, obtaining the optimal rotor aerodynamic shape includes:

[0038] The optimal design variables are subjected to the inverse process of shape transformation method and singular value decomposition method to reconstruct rotor plane shape data and airfoil geometric coordinate data;

[0039] If the reconstructed rotor plane shape data and airfoil geometric coordinate data satisfy geometric consistency, the corresponding aerodynamic performance is output using the low-order aerodynamic model rotor analysis tool, and the reconstructed rotor plane shape data and airfoil geometric coordinate data are output as the optimal rotor aerodynamic shape; otherwise, the gradient-based sequential least squares programming algorithm is executed.

[0040] As a preferred option, it also includes:

[0041] If the aerodynamic performance output by the low-order aerodynamic model rotor analysis tool and the aerodynamic performance predicted by the surrogate model corresponding to the optimal design variables are within a preset tolerance range, then the surrogate model is determined to be unnecessary to correct; otherwise, the optimal design variables and the aerodynamic performance output by the low-order aerodynamic model rotor analysis tool are combined into a new sample, the new sample is added to the aerodynamic performance training database, and incremental training or parameter fine-tuning of the surrogate model is triggered.

[0042] Secondly, a rotor aerodynamic shape optimization system based on airfoil geometric feasibility constraints is provided, including:

[0043] The parameterization module is used to perform parameterized modeling of the rotor plane shape using a shape transformation-like method, and uses the parameters of the shape transformation-like method as the first design variable; it is also used to reduce the dimensionality of the airfoil library using a singular value decomposition method, and uses the modal coefficients representing the airfoil as the second design variable. The first design variable and the second design variable together constitute the design space.

[0044] The surrogate model training module is used to randomly sample within the design space, perform aerodynamic performance simulation on each sampling point using a low-order aerodynamic model rotor analysis tool, and construct an aerodynamic performance training database after data cleaning and normalization. The aerodynamic performance training database is used to train the multilayer perceptron neural network offline, and the trained model is then solidified into a surrogate model.

[0045] The online optimization module introduces a gradient-based sequential least squares programming algorithm. Based on the current design variables in the iteration, it calls a surrogate model to complete aerodynamic performance inference, obtains gradient information associated with the objective function and constraint functions, updates the design variables based on the gradient information, and performs iterative optimization until the iterative convergence condition is met, outputs the optimal design variables, and obtains the optimal rotor aerodynamic shape. The constraint functions include the minimum Euclidean distance between the current design variables and the corresponding design variables of several known feasible airfoils being less than the geometric feasibility threshold.

[0046] This invention provides a rotor aerodynamic shape optimization method and system based on airfoil geometric feasibility constraints. It proposes an airfoil geometric feasibility constraint method based on Euclidean distance in modal space, embedding it into the optimization model as a hard constraint. This mathematically ensures the geometric rationality and manufacturability of the optimized solution, enabling an automated design process that allows for "optimization followed by use." Specifically, compared with existing technologies, this invention has the following advantages:

[0047] (1) Significantly improves the efficiency of optimization design and shortens the R&D cycle: Traditional optimization methods based on high-precision CFD require several hours for a single simulation, and completing a round of optimization often takes several weeks or even months, which seriously restricts the rapid iteration of products. This invention introduces a deep learning proxy model to compress the time of a single aerodynamic performance evaluation to the millisecond level. Experimental results show that this invention can shorten the cycle of the entire rotor aerodynamic shape optimization from the traditional "week / month" level to the "minute / hour" level, achieving an order-of-magnitude efficiency leap, which is particularly suitable for the agile development mode of modern UAV products.

[0048] (2) Achieving true three-dimensional shape co-optimization and tapping performance potential: Existing technologies typically employ a step-by-step optimization strategy (i.e., selecting the airfoil first and then optimizing the plane, or optimizing only the chord length and torsion) to reduce computational difficulty, neglecting the strong nonlinear coupling effect between the aerodynamic characteristics of the airfoil section and the plane torsion distribution. This invention simultaneously adjusts the chord length, torsion, and airfoil modes within a unified 29-dimensional design space. This global optimization strategy can capture variable coupling gains that traditional methods cannot detect, thereby obtaining a globally optimal design scheme with higher propulsion efficiency or lower noise level than traditional designs under the same thrust constraint.

[0049] (3) This invention solves the problem of data-driven design being unusable in engineering and ensures manufacturability: Existing pure data-driven or mathematical optimization methods often produce geometrically strange, unmanufacturable, or aerodynamically unstable design results due to a lack of physical constraints, which is known as black-box optimization. This invention introduces airfoil similarity distance constraints, adding constraints to the optimizer from a mathematical level, forcing the generated results to resemble a real airfoil. This makes the optimized rotor blades have smooth and reasonable surface features, eliminating the need for extensive post-design manual modifications by designers, and directly achieving engineering practicality and manufacturability.

[0050] (4) Reduced computational costs and hardware barriers: The data generation of this invention adopts a fast low-order rotor analysis tool based on blade element momentum theory. The model training and optimization process involves little computation and does not rely on expensive high-performance computing clusters. It achieves engineering design effects comparable to high-precision simulation, and the entire design process can be completed on ordinary graphics workstations or even personal computers. This significantly reduces the financial barriers and hardware costs of UAV aerodynamic research and development, and has broad application value.

[0051] (5) Excellent mission adaptability and flexibility: The optimization system constructed by this invention has strong versatility. For different design requirements (such as pursuing the maximum efficiency design for the ultimate long flight time, or pursuing the low noise design for urban logistics) and different operating conditions (such as heavy load or light load), there is no need to redevelop the model. Simply adjust the objective function and thrust constraint values ​​in the system, and the system can automatically search for the airfoil and plane parameter combination that best matches the mission operating conditions, realizing customized intelligent design. Attached Figure Description

[0052] Figure 1 This is a framework diagram of the rotor aerodynamic shape optimization method based on airfoil geometric feasibility constraints of the present invention;

[0053] Figure 2 This is a flowchart of the rotor aerodynamic shape optimization method based on airfoil geometric feasibility constraints according to the present invention;

[0054] Figure 3 This is a flowchart illustrating the data preparation and database construction process for this invention.

[0055] Figure 4 This is a flowchart of the data-driven agent model training process of the present invention;

[0056] Figure 5 This is a flowchart illustrating the construction and solution process of the intelligent optimization system of this invention.

[0057] Figure 6 This is a diagram showing the optimized fore-wing geometry used in the experiments of this invention.

[0058] Figure 7 This is a diagram showing the optimized airfoil geometry for maximizing propulsion efficiency, as described in this invention.

[0059] Figure 8 This is an optimized airfoil geometry diagram for the present invention, with the goal of minimizing noise. Detailed Implementation

[0060] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0061] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used herein in the description of the invention is for the purpose of describing particular embodiments only and is not intended to limit the invention.

[0062] Existing optimization methods based on surrogate models lack an inherent guarantee mechanism for the feasibility of the optimized airfoil geometry. Specifically, the mathematical models of existing technologies typically only include objective functions (such as maximizing efficiency) and simple physical constraints (such as thrust lower limit and variable boundaries), lacking systematic constraints on the rationality of the airfoil geometry itself. Traditional approaches include: post-processing manual screening and modification: after optimization, senior designers check the results one by one, eliminating geometrically abnormal designs and manually modifying usable designs. This method is inefficient, highly subjective, and may compromise the optimality of the optimization; design variable boundary constraints: setting upper and lower limits for each design variable in the optimization model. This method only constrains the value range of a single variable and cannot guarantee the overall rationality of the airfoil geometry after combining multiple variables. For high-dimensional design spaces (such as 29 dimensions), it cannot effectively cover the complex boundaries of the feasible region. This deficiency makes it difficult for existing methods to truly achieve an automated design process that is "optimized and usable".

[0063] Furthermore, existing technologies generally use CFD simulation as the primary means of aerodynamic performance evaluation. While this method offers high computational accuracy, it consumes enormous computational resources per simulation, the overall optimization time is unacceptable, and it struggles to support large-scale searches in high-dimensional design spaces. These shortcomings severely restrict the rapid design and engineering application of rotors.

[0064] Meanwhile, existing surrogate model optimization methods lack an effective closed-loop correction mechanism. When the optimization result is located in an area where the surrogate model training data is insufficient, it cannot automatically identify and correct the prediction bias, resulting in the reliability of the optimization result being compromised.

[0065] To address the problems existing in the prior art, this invention provides a rotor aerodynamic shape optimization method based on airfoil geometric feasibility constraints. For example... Figure 1 As shown, the method mainly consists of three core stages: data preparation and database construction (offline), data-driven agent model training (offline), and intelligent optimization system construction and solution (online).

[0066] The working principle of this invention is as follows: A high-dimensional, complex three-dimensional rotor shape is transformed into a low-dimensional mathematical vector using Class Shape Transformation (CST) and Singular Value Decomposition (SVD) parameterization methods; a large-scale aerodynamic database is constructed using the low-fidelity but extremely fast XROTOR rotor aerodynamic analysis tool; a high-precision surrogate model is constructed to replace expensive CFD simulations by learning the nonlinear mapping relationship between design variables and aerodynamic performance using a deep multilayer perceptron (MLP) neural network; finally, an airfoil geometric feasibility constraint based on Euclidean distance in modal space is introduced into the Sequential Least Squares Programming (SLSQP) algorithm to quickly search for the global optimal solution in the surrogate model space, while ensuring the geometric rationality and manufacturability of the optimization results.

[0067] like Figure 2 As shown in the figure, the rotor aerodynamic shape optimization method based on airfoil geometric feasibility constraints in this embodiment has the following specific implementation steps:

[0068] Phase 1: Data Preparation and Database Construction: The goal of this phase is to establish a high-dimensional rotor geometry parameterization model and use rapid simulation tools to generate large-scale, high-quality aerodynamic performance training data.

[0069] Step S1: Establish a high-dimensional rotor geometric parameterization model (design space definition). The key is to establish a unified mathematical description, transforming the three-dimensional geometric features of the rotor into computer-optimizable design variables.

[0070] The three-dimensional design of rotors (including airfoil, chord length, and torsion) involves a large number of parameters and a complex design space (extremely high dimensionality; complex variable coupling relationships; and highly nonlinear search space). Traditional optimization methods are prone to problems such as decreased search efficiency, weak computational convergence, and optimization localization in such high-dimensional nonlinear spaces, making it difficult to obtain stable and efficient optimization solutions.

[0071] To address the challenges of handling high-dimensional design spaces, this invention proposes: functional modeling of rotor chord length and torsion based on the CST parametric method; and low-dimensional representation of the airfoil based on the SVD modal dimensionality reduction method. This unifies the cross-dimensional heterogeneous parameters of the rotor's three-dimensional shape (radial plane distribution (chord length / torsion) and cross-sectional airfoil modes) into a low-dimensional, continuous, and differentiable 29-dimensional collaborative design space. The SVD airfoil modal coefficients simultaneously serve as both design variables and geometric feasibility constraint inputs, and are a necessary prerequisite for constructing the airfoil feasibility database (DB) and calculating the minimum Euclidean distance constraint.

[0072] (1) The rotor plane shape is parametrically modeled using a shape transformation method, and the parameters of the shape transformation method are used as the first design variable.

[0073] For the radial chord length distribution of the rotor and twist angle distribution This embodiment uses the CST method for modeling. The normalized radius is defined. ,in The current cross-sectional radius, The rotor radius is... .

[0074] The general mathematical expression for the CST method is:

[0075]

[0076] In the formula, Dimensionless geometric coordinates For class functions, It is a shape function. It is a dimensionless correction quantity for the trailing edge.

[0077] Among them, class functions : This is used to define the basic category of geometry. Considering the physical characteristics of rotor chord length and torsional distribution, this embodiment uses an exponent. The formula for characterizing the aerodynamic shape of a rounded head and pointed tail is:

[0078]

[0079] Where the shape function Used to describe specific geometric changes in detail. Bernstein polynomials are represented as follows:

[0080]

[0081] In the formula, The coefficients are binomial coefficients. The weight coefficients to be optimized are: This is the order index.

[0082] In this embodiment, the shape function orders of the chord length distribution and the torsional distribution are respectively set as follows: That is, each requires 7 control coefficients. The chord length control parameter is denoted as... The torsional control parameter is denoted as Therefore, the rotor plane shape is uniquely determined by 14 primary design variables.

[0083] (2) The singular value decomposition method is used to reduce the dimension of the airfoil library. The modal coefficients representing the airfoil are used as the second design variable. The first design variable and the second design variable together constitute the design space.

[0084] To achieve three-dimensional collaborative optimization, this embodiment incorporates the airfoil section into the design variables. Addressing the high-dimensional redundancy of airfoil coordinate data, the SVD method is used to reduce the dimensionality of the UIUC standard airfoil library (in other embodiments, other airfoil libraries, such as the NASA airfoil library, NACA airfoil library, etc., can be selected).

[0085] Decomposition process: Constructing a system containing... Coordinate matrix of a standard airfoil Decompose .in For a left singular matrix, its column vectors These are the airfoil's primary modes (Basis Modes).

[0086] Reconstructed formula: Before truncation Reconstructing arbitrary airfoils using a single dominant mode:

[0087]

[0088] In the formula, For the reconstructed airfoil, For average airfoil coordinates, For the first The weighting coefficients of each principal mode. The primary modality index.

[0089] Thus, any airfoil is compressed into 15 modal coefficients. This invention constructs a 29-dimensional unified design space comprising 14 planar parameters and 15 airfoil parameters.

[0090] Step S2: Construct a large-scale aerodynamic performance training database.

[0091] like Figure 3As shown, this step focuses on automatic sampling of a unified parameter space, low-fidelity high-efficiency aerodynamic simulation, and intelligent cleaning of abnormal samples to build an aerodynamic performance training database covering a high-dimensional design space.

[0092] To replace expensive online CFD calculations, this embodiment pre-constructs a high-capacity aerodynamic knowledge base. Using Python automated scripts, Latin hypercube sampling or random sampling is performed within the aforementioned 29-dimensional design space to generate a massive number of geometric sampling points. Subsequently, a low-order aerodynamic model rotor analysis tool (in this embodiment, XROTOR, a fast aerodynamic analysis tool based on blade element momentum theory), is invoked to perform batch calculations on the sampling points.

[0093] XROTOR is based on leaf element momentum theory and calculates overall performance through integration:

[0094] thrust:

[0095] power:

[0096] In the formula, The total thrust of the rotor, air density, For the rate of leaf nutrient synthesis, The number of rotor blades, For the length of the leaf string, The lift coefficient of leaf element. For the angle of entry, The leaf element drag coefficient, For dimensionless radial coordinates, For rotor shaft power, This represents the rotor angular velocity.

[0097] Data cleaning: Outlier samples were removed using the interquartile range method. If a certain sample's performance index... satisfy or If a value is found to be a divergence point, it is considered a data point and removed to ensure database quality; otherwise, the data is retained. The lower quartile, Interquartile range, It is the upper quartile.

[0098] Normalization: The 29-dimensional design variables are mapped to the interval [-1,1], and the normalized sampling points and the corresponding aerodynamic performance indicators are combined to form a sample.

[0099] Through the integrated automated process of random sampling, automatic geometric reconstruction, XROTOR batch simulation, outlier cleaning and normalization, this embodiment finally established a high-dimensional rotor aerodynamic performance database with approximately 500,000 valid samples. This database fully covers the entire design space involved in the collaborative optimization, providing a reliable and sufficient data foundation for the subsequent construction of a high-precision multi-output neural network surrogate model and the implementation of gradient collaborative optimization solutions.

[0100] Phase Two: Data-Driven Agent Model Training.

[0101] Traditional rotor optimization design based on high-precision computational fluid dynamics (CFD) offers advantages in prediction accuracy, but single simulations are extremely time-consuming. When performing iterative optimization in a multi-dimensional design space: each optimization round requires numerous costly CFD calculations; the number of optimization iterations is severely limited; and the overall design cycle typically lasts for weeks or even months. This results in a limited number of optimization iterations and a lengthy design cycle, failing to meet the rapid iterative design requirements of unmanned aerial vehicles (UAVs). This embodiment employs a data-driven surrogate model to replace expensive CFD simulations, achieving extremely rapid prediction of aerodynamic performance.

[0102] This embodiment addresses a specific engineering scenario of rotor 3D shape optimization by constructing an MLP aerodynamic performance prediction model that is deeply adapted to the 29-dimensional unified parameterized design space. This model serves as a core means for rapid rotor performance evaluation, replacing high-cost CFD simulation. Specifically, it involves: constructing a neural network surrogate model trained on sample data; using the surrogate model to rapidly predict rotor aerodynamic performance indicators; and running the optimization search entirely within the surrogate model space, thereby significantly reducing the computational cost of a single evaluation.

[0103] Step S3: Construct a multilayer perceptron (MLP) neural network to replace the CFD solver.

[0104] Network structure: It consists of an input layer (29 nodes), hidden layer 1 (128 nodes, ReLU / Tanh activation), hidden layer 2 (128 nodes), hidden layer 3 (64 nodes), and output layer (1 node) connected in sequence. Independent prediction models are trained for different metrics such as thrust, efficiency, and noise to avoid interference from weights.

[0105] Training configuration: The optimizer used is Adam, the loss function is mean squared error (MSE), and L2 regularization is introduced. To prevent overfitting.

[0106] Results: The model's average prediction error on the test set is less than 5%, and the time taken for a single inference is only in the milliseconds.

[0107] like Figure 4As shown, the training process involves simultaneously dividing the training set and the test set. Backpropagation is used to iteratively solve the network weight parameters through the training set, and real-time error verification is performed based on the test set. When the prediction error exceeds the preset accuracy threshold, the process automatically backtracks to the retraining loop until the surrogate model meets the accuracy evaluation index on the test dataset. In this embodiment, the error threshold is set to an average prediction error of less than 5%. Once the above error control target is achieved, the surrogate model is deemed to have completed training and is stored as a real-time aerodynamic performance evaluation kernel for the subsequent online optimization stage.

[0108] After the above training and closed-loop optimization, the obtained MLP surrogate model maintains high prediction accuracy while controlling the time consumption of a single inference calculation to the order of milliseconds. Compared with traditional CFD or high-precision numerical simulation methods, the computational efficiency is improved by several orders of magnitude, enabling it to meet the engineering application requirements of large-scale collaborative search and real-time optimization solution in high-dimensional design space.

[0109] Phase 3: Construction and solution of intelligent optimization system.

[0110] Step S4: Intelligent optimization solution based on airfoil geometric feasibility constraints.

[0111] After completing the construction and solidification of the high-precision MLP neural network surrogate model in step S3, the surrogate model is used as the real-time calculation kernel for rotor aerodynamic performance evaluation. The sequential least squares programming gradient optimization algorithm (also known as gradient-based sequential least squares programming algorithm) is introduced to carry out the coordinated optimization search of planar configuration parameters and airfoil modal parameters in a unified 29-dimensional continuous design space.

[0112] To address the geometric feasibility problem of surrogate model optimization solutions, this embodiment proposes an airfoil geometric feasibility constraint method based on modal space Euclidean distance, specifically including:

[0113] (1) Construction of the airfoil feasibility database DB.

[0114] This embodiment constructs an airfoil feasibility database (DB) to characterize the geometric distribution features of known feasible airfoils:

[0115]

[0116] In the formula, For the first in the database The 15-dimensional modal coefficient vector of a feasible airfoil after SVD decomposition This represents the total number of feasible airfoils in the airfoil feasibility database. This is an index of feasible airfoils. In this embodiment, the feasible airfoils are sourced from the UIUC standard airfoil library. The airfoils in the airfoil feasibility database are all mature airfoil designs that have been used in the aviation field for a long time and have been verified by engineering, possessing good aerodynamic characteristics and manufacturability.

[0117] (2) Real-time measurement method for the feasibility of candidate solutions.

[0118] For the airfoil modal coefficients at any candidate design point during the optimization process The present invention uses the following steps to measure its geometric feasibility:

[0119] (2.1) Z-score standardization.

[0120] First, the modal coefficients are standardized:

[0121]

[0122] In the formula, and These are the mean and standard deviation of each modal coefficient in the airfoil feasibility database.

[0123] (2.2) Calculation of minimum Euclidean distance.

[0124] Calculate the minimum Euclidean distance between the standardized candidate airfoil modal coefficients and all known feasible airfoils in the airfoil feasibility database. :

[0125]

[0126] In the formula, For the first in the database The standardized vector of modal coefficients corresponding to each feasible airfoil This represents the Euclidean norm (L2 norm).

[0127] Minimum Euclidean distance Quantitatively reflects the degree to which candidate airfoils deviate from the known feasible airfoil distribution: minimum Euclidean distance. The smaller the value, the closer the candidate airfoil is to a known feasible airfoil, and the higher its geometric feasibility; minimum Euclidean distance The larger the value, the further the candidate airfoil is from all known feasible airfoils, and the higher the risk of geometric feasibility.

[0128] When using surrogate models such as neural networks to replace high-precision CFD simulations for rotor aerodynamic shape optimization design, the surrogate model, being essentially a mathematical fit to finite sample data, often lacks physical basis for its extrapolation predictions in the design space boundary region and sparse sample region. When the optimization algorithm searches for the optimal solution on the surrogate model's response surface, it is highly prone to converging to the following types of pseudo-optimal solutions:

[0129] Geometric non-existent type: The combination of airfoil modal coefficients is far from the data distribution characteristics of known airfoils, and the corresponding airfoil geometry does not exist in reality and cannot be manufactured by traditional processing methods;

[0130] Non-smooth surface type: The curvature of the airfoil surface changes abruptly, resulting in non-smooth features such as wavy wrinkles, local depressions or sharp corners, which do not meet the requirements of continuity and smoothness of aerodynamic shape;

[0131] Aerodynamically unstable type: The airfoil thickness distribution is unreasonable (too thin or too thick), which leads to problems such as aerodynamic stall, boundary layer separation or insufficient structural strength under actual working conditions.

[0132] The essence of the above problem is that existing technologies lack an effective method to evaluate the geometric feasibility of candidate airfoil designs in real time during the optimization iteration process and embed it as a hard constraint into the optimization model.

[0133] To address the aforementioned issues, this embodiment introduces the minimum Euclidean distance as an inequality constraint embedded in the optimization model. The advantage of this constraint mechanism is that it does not simply restrict the range of values ​​for a single design variable, but rather performs an overall feasibility assessment of the airfoil geometry formed by the combination of variables, ensuring from a mathematical perspective that the optimization solution lies within the geometric neighborhood of the known feasible airfoils.

[0134] (3) Optimization of feasibility constraints.

[0135] This embodiment uses the minimum Euclidean distance. Embedded as an inequality constraint in the optimization model:

[0136]

[0137] In the formula, This is a geometric feasibility threshold. This embodiment provides a threshold. The determination method is specifically an adaptive determination method based on the statistical characteristics within the airfoil library: 1. Calculate the Euclidean distance between two adjacent feasible airfoils in the airfoil feasibility database; 2. Determine the Euclidean distance between each feasible airfoil and the nearest feasible airfoil, as the nearest neighbor distance; 3. Calculate the average of all nearest neighbor distances. and standard deviation And calculate the geometric feasibility threshold as ,in This is a proportionality coefficient. In this embodiment, it is taken as... This value is approximately 1.5 times the average nearest neighbor distance in the database.

[0138] like Figure 5As shown, after completing the construction and solidification of the high-precision MLP neural network surrogate model in step S3, the surrogate model is used as the real-time calculation kernel for rotor aerodynamic performance evaluation. The SLSQP algorithm is introduced to carry out the collaborative optimization search of planar configuration parameters and airfoil modal parameters in a unified 29-dimensional continuous design space.

[0139] The initial solution is set by the user based on empirical configuration or random strategy. After initialization, the SLSQP algorithm calls the surrogate model to perform fast aerodynamic performance inference calculation based on the current design vector in each iteration step, obtains gradient information associated with the objective function and constraint function, and thus constructs a local quadratic approximate shear constraint optimization subproblem, solves the optimal iteration step size and updates the design parameter vector for the next round, thereby realizing continuous differentiable search and fast convergence in the high-dimensional joint design variable space.

[0140] In this embodiment, the objective function can be flexibly set to maximize rotor propulsion efficiency according to design requirements. Alternatively, set it to minimize rotor noise. ,in To improve efficiency, This is a noise index.

[0141] Constraint functions include thrust constraints Geometric constraints And airfoil geometric feasibility constraints, where airfoil geometric feasibility constraints are defined as the minimum Euclidean distance between the current design variable and the corresponding design variables of several known feasible airfoils being less than the geometric feasibility threshold.

[0142] To prevent the generation of unmanufacturable deformed airfoils, this invention introduces Euclidean distance based on modal space to construct airfoil geometric feasibility constraints. Specifically, this involves calculating the modal parameters of candidate airfoils. The Z-score normalized value. Calculate its minimum Euclidean distance with all real airfoils in the database:

[0143]

[0144] The airfoil geometric feasibility constraint is set as follows: (This embodiment takes) ),in The rotor thrust predicted by the surrogate model. The preset minimum rotor thrust value, The radial position predicted by the surrogate model chord length at the point, The preset minimum chord length, This is the minimum Euclidean distance. For the candidate airfoil One modal parameter, For the first in the airfoil feasibility database The first feasible airfoil Each mode parameter. The forced optimization result of the airfoil geometry feasibility constraint must be within the neighborhood of existing mature airfoil designs, automatically ensuring the smoothness and physical rationality of the airfoil.

[0145] Throughout the SLSQP search process, the optimization workflow maintains a closed-loop iterative mechanism encompassing surrogate model prediction, objective / constraint evaluation, gradient update, configuration correction, error assessment, and either continuing the search or terminating convergence. When the change in the objective function caused by the design variables falls below the set convergence threshold, or when both the accuracy error threshold and various constraint convergence conditions are simultaneously met, the optimization search is considered complete, and the final optimal 29-dimensional rotor design parameter vector is output. The iterative process of the SLSQP algorithm is a conventional process and will not be elaborated upon in this embodiment.

[0146] Step S5: Result reconstruction and verification.

[0147] The optimized 29-dimensional parameter vector is reconstructed into a 3D geometric model through the reverse process of step S1. This model is then visualized using the PyGeo (Geometry Package for Multidisciplinary Design Optimization) geometric parameterization tool and input into the XROTOR tool for final verification. After completing step S4 and obtaining the final optimized design parameter vector, the results of step S5 are reconstructed and aerodynamically verified. Specifically, the 29-dimensional optimal parameters are input into the reverse geometry mapping module of step S1. Based on the CST geometric parameterization function and the SVD modal reconstruction relationship, the complete 3D geometric outline of the rotor is restored, and the chord length distribution, torsion distribution, and airfoil geometric coordinate data of each radial section are reconstructed. Subsequently, the PyGeo geometric parameterization tool is used to perform 3D visualization and geometric consistency checks on the reconstructed rotor model to confirm that the obtained configuration meets the requirements for surface continuity, aerodynamic compliance, and manufacturing dimensions.

[0148] If the reconstructed rotor plane shape data and airfoil geometric coordinate data satisfy geometric consistency, the corresponding aerodynamic performance (obtaining aerodynamic performance indicators such as thrust, power, and efficiency under real physical conditions) is output using a low-order aerodynamic model rotor analysis tool (in this embodiment, the fast aerodynamic analysis tool XROTOR) and the reconstructed rotor plane shape data and airfoil geometric coordinate data are output as the optimal rotor aerodynamic shape; otherwise, return to step S4 to execute the gradient-based sequential least squares programming algorithm.

[0149] This embodiment further proposes the definition of the correction sample and a closed-loop correction mechanism: If the aerodynamic performance output by the low-order aerodynamic model rotor analysis tool and the aerodynamic performance predicted by the surrogate model corresponding to the optimal design variables are within a preset tolerance range (in this embodiment, the error is set to be less than or equal to 5%), then it is determined that the surrogate model does not need to be corrected and the optimized design result is true and effective; otherwise, the online correction process of the surrogate model is executed: the optimal design variables and the aerodynamic performance output by the low-order aerodynamic model rotor analysis tool are combined into a new sample (called the correction sample, the data structure is: input: 29-dimensional design variable vector = [CST chord length parameter (7-dimensional), CST torsion parameter (7-dimensional), SVD airfoil modal coefficient (15-dimensional)], output: the true aerodynamic performance calculated by XROTOR = [thrust T, efficiency η, noise SPL]), the correction sample is fed back into the aerodynamic performance training database of step S2, and the incremental training or parameter fine-tuning of the surrogate model in step S3 is triggered, forming a dynamic closed-loop mechanism of simulation verification, incremental data regression and surrogate model correction, thereby further improving the global generalization accuracy of the surrogate model and the reliability of subsequent optimization results. It should be noted that after incremental training or parameter fine-tuning of the surrogate model, the current online solution phase can be restarted to output new optimal parameters; alternatively, the optimal parameters obtained before incremental training or parameter fine-tuning can be taken as the final result, and the surrogate model after incremental training or parameter fine-tuning can be used for the next airfoil optimization.

[0150] In the surrogate model-driven optimization process, when the optimization result exceeds the coverage of the surrogate model's training data, the model prediction may be significantly biased, leading to a discrepancy between the actual performance of the optimization result and the prediction. To address this, this embodiment proposes the aforementioned closed-loop correction mechanism based on corrected samples, which offers the following advantages:

[0151] (1) Precisely defined data structure: The input of the corrected sample is a 29-dimensional vector of [CST chord length parameter (7-dimensional) + CST torsion parameter (7-dimensional) + SVD airfoil modal coefficient (15-dimensional)], and the output is a three-dimensional performance vector of [thrust T, efficiency η, noise SPL]. This data structure is deeply bound to the parameterization system of this application and has a clear engineering definition.

[0152] (2) Clear automatic triggering conditions: The correction process is automatically triggered when the relative error between the XROTOR verification calculation and the surrogate model prediction exceeds 5%, without the need for manual intervention, and has engineering operability and determinism.

[0153] (3) Deep integration with the main optimization process: The corrected samples are directly fed back into the aerodynamic performance training database in step S2 and trigger the incremental training in step S3, forming an adaptive accuracy improvement closed loop linked with the main optimization process, rather than an independent post-processing step.

[0154] To verify the effectiveness of the method of the present invention, this embodiment built a complete optimization system in a Python computing environment and conducted multiple sets of experiments for two typical design scenarios: maximizing propulsion efficiency and minimizing aerodynamic noise.

[0155] (1) Experimental environment setup:

[0156] Design variables: 29-dimensional unified space (including 14 CST plane geometry parameters and 15 SVD airfoil modal parameters).

[0157] Operating conditions: Rotor speed is constant at 6000 RPM.

[0158] Physical constraints: All optimizations applied airfoil similarity distance constraints. This is to ensure manufacturability.

[0159] Effect verification: The effectiveness of the airfoil geometric feasibility constraint mechanism is shown in Table 1.

[0160] Table 1 Verification results of airfoil geometric feasibility constraint mechanism

[0161]

[0162] The above results demonstrate that the airfoil geometric feasibility constraint mechanism proposed in this invention can significantly reduce the risk of geometric anomalies in the optimization solution and improve the engineering usability of the optimization results.

[0163] (2) Optimization with the goal of maximizing propulsion efficiency, the rotor geometry and chord length and twist angle distribution before optimization are given as follows: Figure 6 As shown.

[0164] (2.1) Optimize scene definition:

[0165] Design goal: To maximize propulsion efficiency.

[0166] Constraints: Required rotor thrust It simultaneously satisfies the airfoil geometric similarity constraint and the chord length distribution constraint.

[0167] This embodiment aims to verify the system's ability to improve rotor aerodynamic efficiency while meeting high thrust requirements.

[0168] (2.2) Performance improvement results:

[0169] The optimization results after SLSQP algorithm iteration are shown in Table 2.

[0170] Table 2 Optimization Results

[0171]

[0172] (2.3) Comparison of rotor geometry evolution, for example Figure 7 As shown, the optimized rotor shape, chord length, and torsion distribution are displayed. By comparing the rotor shape before and after optimization, the geometric features are analyzed as follows:

[0173] Chord length distribution: The optimized rotor has a significantly wider chord length in the middle section of the blade. This is because this area is the core work area where the rotating blades generate lift, and widening the chord length can effectively increase the lift area and adapt to heavy-load requirements.

[0174] Airfoil characteristics: The system automatically converged to the rc12b3.dat airfoil type. Geometrically, this airfoil has a large camber and relative thickness. This geometric feature has a high lift coefficient in aerodynamics. This airfoil feature is beneficial to improving the rotor's aerodynamic load capacity and enhancing propulsion efficiency while meeting thrust constraints.

[0175] (3) Optimization with the goal of minimizing noise, the rotor geometry and chord length and twist angle distribution before optimization are given as follows: Figure 6 As shown.

[0176] (3.1) Optimize scene definition:

[0177] Design goal: Minimize aerodynamic noise (sound pressure level SPL).

[0178] Constraints: Required rotor thrust It simultaneously satisfies the airfoil geometric similarity constraint and the chord length distribution constraint.

[0179] Comparison objects: initial design and optimized design.

[0180] (3.2) Performance improvement results: The optimization results are shown in Table 3.

[0181] Table 3 Optimization Results

[0182]

[0183] (3.3) Comparison of rotor geometry evolution, for example Figure 8 As shown, the rotor optimized for quiet operation exhibits geometric characteristics completely different from those optimized for maximum propulsion efficiency. The geometric characteristic analysis is as follows:

[0184] Sharpened blade tip: Unlike the width chord length of the optimization result aimed at maximizing propulsion efficiency, Figure 8 The silent rotor on the right is located at the tip of the blade ( The blade exhibits a distinct nonlinear contraction with a very sharp trailing edge. This geometric modification can significantly reduce the intensity of tip vortices, which are one of the main sources of rotor aerodynamic noise.

[0185] Airfoil characteristics: The system automatically selected the fx78k161.dat type airfoil. This airfoil is characterized by its slender shape and relatively small thickness. The thinner airfoil cross-section reduces the thickness noise generated by the air being expelled during blade rotation, thus achieving a quieter operation.

[0186] Comparing the optimization results for different optimization objectives, it can be seen that the optimization method proposed in this invention can generate differentiated rotor aerodynamic shapes according to different design goals. Taking the initial baseline scheme composed of the raf19.dat airfoil as an example, its predicted thrust is 124.624 N, efficiency is 0.2001, and noise is 65.188. This initial scheme does not meet the 200 N thrust design requirement and exhibits characteristics of low efficiency and high noise.

[0187] When the optimization objective is maximum thrust efficiency, the system obtains an optimized rotor with an airfoil similar to rc12b3.dat as the matching result, under the conditions of thrust not less than 200N, airfoil geometric similarity constraints, and chord length distribution constraints. This scheme predicts a thrust of 348.258N, an efficiency of 0.4181, and a noise level of 59.649. Compared to the baseline scheme, the thrust is increased by approximately 179.5%, the efficiency is increased by approximately 108.9%, and the noise is reduced by approximately 5.539.

[0188] When the optimization objective is to minimize noise, the system obtains an optimized rotor with the fx78k161.dat airfoil as the matching result. This scheme predicts a thrust of 374.252 N, an efficiency of 0.2266, and a noise of 54.938. Compared with the baseline scheme, the thrust is increased by approximately 200.3%, the efficiency is increased by approximately 13.2%, and the noise is reduced by approximately 10.25.

[0189] The above results show that the method of the present invention does not generate a single fixed configuration, but can automatically adjust the chord length distribution, twist angle distribution and airfoil geometry parameters according to different optimization objectives within a unified 29-dimensional design space, and obtain an engineering-usable rotor aerodynamic shape under the premise of satisfying thrust and airfoil geometry feasibility constraints.

[0190] The advantages of the method of this invention are:

[0191] (1) Improvement in design space dimension: Existing technologies typically employ low-dimensional or decoupled optimization strategies, such as optimizing only the chord length and torsion distribution, or selecting the airfoil first and then optimizing the planar parameters. This approach ignores the three-dimensional coupling effect of the rotor. In contrast, this invention constructs a unified high-dimensional collaborative design space of 29 dimensions, which can simultaneously optimize the chord length, torsion distribution, and airfoil cross-section. This invention breaks down the design barriers between the planar and cross-sectional dimensions, and can capture the strong nonlinear coupling relationship between the airfoil and the torsion distribution, thereby uncovering the global optimal solution that traditional decoupling methods cannot find.

[0192] (2) Improvements in computational efficiency: Existing technologies mainly rely on iterative solutions in computational fluid dynamics, which often takes hours for a single evaluation and weeks for global optimization, resulting in extremely low efficiency. This invention adopts a data-driven surrogate model, achieving extremely high computational efficiency. A single inference takes only milliseconds, and the overall optimization process can be completed in just minutes. By implementing a strategy that combines low-fidelity large-scale data with deep learning correction, this invention achieves an order-of-magnitude efficiency improvement while ensuring the accuracy of engineering design, greatly shortening the design cycle.

[0193] (3) Improvement in Feasibility of Results In existing technologies, pure mathematical optimization often suffers from uncontrollable results, easily generating deformed, wavy, or unmanufacturable airfoils, posing a black box risk. This invention ensures high feasibility of the design results by introducing airfoil similarity distance constraints. This invention mathematically mandates that the optimization results fall within the neighborhood of mature airfoils, fundamentally eliminating the possibility of deformed airfoils entering the final solution set, automatically guaranteeing the physical rationality and engineering manufacturability of the optimization results, and completely eliminating the need for subsequent manual modification.

[0194] (4) Improvements in optimization mechanism: Commonly used global search algorithms (such as genetic algorithms and particle swarm optimization algorithms) often have slow convergence speed in high-dimensional spaces and are prone to getting trapped in local optima. This invention adopts the SLSQP gradient optimization algorithm, which makes full use of the differentiability of the neural network model and achieves fast and accurate convergence.

[0195] In another embodiment, the invention replaces the prediction module with a different surrogate model. In a preferred embodiment, the invention employs a multilayer perceptron neural network to construct the surrogate model. Alternatively, other types of machine learning regression models can be used to establish the mapping relationship between design variables and aerodynamic performance.

[0196] The Kriging model uses Gaussian process regression to fit the aerodynamic response surface. Compared to the MLP, the Kriging model can provide an estimate of the uncertainty (variance) of the prediction, which is beneficial for adaptive sampling. However, its training and prediction time complexity increases cubically with the sample size. In large-scale datasets (such as the 500,000 samples in this invention), its computational efficiency is much lower than that of the MLP, and training is extremely slow.

[0197] RBF neural networks or support vector regression: Modeling is performed using RBF networks or kernel-based support vector regression. These methods perform reasonably well with small samples, but when dealing with 29-dimensional high-dimensional inputs and strongly nonlinear aerodynamic problems, their generalization ability and fitting accuracy are generally weaker than deep neural network MLPs, and they are more sensitive to hyperparameters.

[0198] Deep generative models: These use variational autoencoders or generative adversarial networks to directly learn airfoil manifolds and predict performance. The model structure is more complex, training is more difficult, and they are less efficient than direct MLPs for simple numerical regression tasks (predicting thrust / efficiency).

[0199] In another embodiment, the present invention replaces the solution module based on different optimization algorithms. In a preferred embodiment, the present invention employs the SLSQP gradient optimization algorithm. Alternatively, non-gradient or heuristic optimization algorithms can be used.

[0200] Genetic algorithms or particle swarm optimization (PSO) use global optimization algorithms that simulate natural evolution or swarm behavior to find the optimal solution. These algorithms do not require differentiability of the surrogate model (gradient information), possess global search capabilities, and are less prone to getting trapped in local optima. However, in high-dimensional spaces (29-dimensional), their convergence speed is extremely slow, requiring far more calls to the surrogate model than gradient algorithms, leading to a decrease in overall optimization efficiency. Furthermore, their ability to handle complex nonlinear constraints (such as airfoil similarity constraints) is weaker than SLSQP.

[0201] Differential evolution or simulated annealing: stochastic search algorithms based on population differences or thermodynamic principles. They also face the problems of low efficiency and slow convergence in high-dimensional spaces, and the stability of the results is not as good as deterministic gradient algorithms.

[0202] In step S4 of this invention, the optimization algorithm is not limited to the SLSQP gradient optimization algorithm. For scenarios seeking the global optimum, non-gradient optimization algorithms, such as genetic algorithms and particle swarm optimization algorithms, can be used instead. Although the computational cost will increase, the global optimization search can still be completed within an acceptable timeframe due to the extremely fast evaluation speed of the surrogate model.

[0203] In another embodiment, the present invention provides a rotor aerodynamic shape optimization system based on airfoil geometric feasibility constraints, comprising:

[0204] The parameterization module is used to perform parameterized modeling of the rotor plane shape using a shape transformation-like method, and uses the parameters of the shape transformation-like method as the first design variable; it is also used to reduce the dimensionality of the airfoil library using a singular value decomposition method, and uses the modal coefficients representing the airfoil as the second design variable. The first design variable and the second design variable together constitute the design space.

[0205] The surrogate model training module is used to randomly sample within the design space, perform aerodynamic performance simulation on each sampling point using a low-order aerodynamic model rotor analysis tool, and construct an aerodynamic performance training database after data cleaning and normalization. The aerodynamic performance training database is used to train the multilayer perceptron neural network offline, and the trained model is then solidified into a surrogate model.

[0206] The online optimization module introduces a gradient-based sequential least squares programming algorithm. Based on the current design variables in the iteration, it calls a surrogate model to complete aerodynamic performance inference, obtains gradient information associated with the objective function and constraint functions, updates the design variables based on the gradient information, and performs iterative optimization until the iterative convergence condition is met, outputs the optimal design variables, and obtains the optimal rotor aerodynamic shape. The constraint functions include the minimum Euclidean distance between the current design variables and the corresponding design variables of several known feasible airfoils being less than the geometric feasibility threshold.

[0207] For specific limitations on rotor aerodynamic shape optimization systems based on airfoil geometric feasibility constraints, please refer to the limitations on rotor aerodynamic shape optimization methods based on airfoil geometric feasibility constraints mentioned above, which will not be repeated here.

[0208] In another embodiment, the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of a rotor aerodynamic shape optimization method based on airfoil geometric feasibility constraints.

[0209] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), Rambus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.

[0210] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0211] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the appended claims.

Claims

1. A method for optimizing rotor aerodynamic shape based on airfoil geometric feasibility constraints, characterized in that, Includes the following steps: A shape transformation-like method is used to parametrically model the rotor planar shape, and the parameters of the shape transformation-like method are used as the first design variable. The singular value decomposition method is used to reduce the dimensionality of the airfoil library. The modal coefficients representing the airfoil are used as the second design variable. The first and second design variables together constitute the design space. Random sampling was performed within the design space, and aerodynamic performance simulation was conducted at each sampling point using a low-order aerodynamic model rotor analysis tool. After data cleaning and normalization, an aerodynamic performance training database was constructed. The multilayer perceptron neural network is trained offline using the aerodynamic performance training database, and then solidified as a surrogate model after training is completed. A gradient-based sequential least squares programming algorithm is introduced. Based on the current design variables in the iteration, the surrogate model is called to complete the aerodynamic performance inference, obtain the gradient information associated with the objective function and constraint functions, update the design variables based on the gradient information and carry out iterative optimization until the iterative convergence condition is met, output the optimal design variables, and obtain the optimal rotor aerodynamic shape. The constraint function includes the minimum Euclidean distance between the current design variables and the corresponding design variables of several known feasible airfoils being less than the geometric feasibility threshold.

2. The rotor aerodynamic shape optimization method based on airfoil geometric feasibility constraints according to claim 1, characterized in that, The method employs a shape transformation-like approach to parametrically model the rotor's planar shape, and uses the parameters of this shape transformation-like approach as the first design variable, including: For the radial chord length distribution and torsion angle distribution of the rotor, a shape transformation-like method is used for parametric modeling; The shape function orders of the chord length distribution and the torsion angle distribution are respectively set to be... Therefore, the chord length distribution Each control parameter and torsion angle distribution One control parameter is used as the first design variable.

3. The rotor aerodynamic shape optimization method based on airfoil geometric feasibility constraints according to claim 1, characterized in that, The method of using singular value decomposition to reduce the dimensionality of the airfoil library, and using the modal coefficients representing the airfoils as the second design variable, includes: Incorporating the airfoil section into the design variables, and employing singular value decomposition to reduce the dimensionality of the airfoil coordinates in the airfoil library, the preceding section is truncated. The airfoil will be reconstructed using the principal modes, therefore the airfoil will be reconstructed using the... The modal coefficients are used as the second design variables.

4. The rotor aerodynamic shape optimization method based on airfoil geometric feasibility constraints according to claim 1, characterized in that, The objective function is to maximize the rotor propulsion efficiency or minimize the rotor noise index. The constraint functions include thrust constraints, geometric constraints, and airfoil geometric feasibility constraints. The airfoil geometric feasibility constraint is that the minimum Euclidean distance between the current design variable and the corresponding design variables of several known feasible airfoils is less than the geometric feasibility threshold.

5. The rotor aerodynamic shape optimization method based on airfoil geometric feasibility constraints according to claim 1, characterized in that, The minimum Euclidean distance between the current design variable and the corresponding design variables of several known feasible airfoils is less than the geometric feasibility threshold, including: Take the second design variable from the current design variables in the iteration, and calculate the standardized value of the second design variable; Iterate through the standardized values ​​of the second design variable corresponding to each feasible airfoil in the airfoil feasibility database, calculate the standardized value of the second design variable in the current design variable, and the Euclidean distance between it and the standardized values ​​of each traversed second design variable; If the minimum Euclidean distance is less than or equal to the geometric feasibility threshold, it means that the current design variables meet the airfoil geometric feasibility constraints; otherwise, the current design variables do not meet the airfoil geometric feasibility constraints.

6. The rotor aerodynamic shape optimization method based on airfoil geometric feasibility constraints according to claim 5, characterized in that, The airfoil feasibility database is constructed as follows: Obtain rotor aerodynamic shape data for known feasible airfoils; The second design variable is obtained by using singular value decomposition on the rotor aerodynamic shape data; The second design variable is standardized to obtain its standardized value. An airfoil feasibility database is constructed based on the standardized values ​​of the second design variables corresponding to all feasible airfoils.

7. The rotor aerodynamic shape optimization method based on airfoil geometric feasibility constraints according to claim 5, characterized in that, The geometric feasibility threshold is determined as follows: Calculate the Euclidean distance between two adjacent feasible airfoils in the airfoil feasibility database; Determine the Euclidean distance between each feasible airfoil and the nearest feasible airfoil, and use it as the nearest neighbor distance; Calculate the average distance of all nearest neighbors. and standard deviation And calculate the geometric feasibility threshold as ,in This is the proportionality coefficient.

8. The rotor aerodynamic shape optimization method based on airfoil geometric feasibility constraints according to claim 1, characterized in that, The process of obtaining the optimal rotor aerodynamic shape includes: The optimal design variables are subjected to the inverse process of shape transformation method and singular value decomposition method to reconstruct rotor plane shape data and airfoil geometric coordinate data; If the reconstructed rotor plane shape data and airfoil geometric coordinate data satisfy geometric consistency, the corresponding aerodynamic performance is output using the low-order aerodynamic model rotor analysis tool, and the reconstructed rotor plane shape data and airfoil geometric coordinate data are output as the optimal rotor aerodynamic shape; otherwise, the gradient-based sequential least squares programming algorithm is executed.

9. The rotor aerodynamic shape optimization method based on airfoil geometric feasibility constraints according to claim 8, characterized in that, Also includes: If the aerodynamic performance output by the low-order aerodynamic model rotor analysis tool and the aerodynamic performance predicted by the surrogate model corresponding to the optimal design variables are within a preset tolerance range, then the surrogate model is determined to be unnecessary to correct; otherwise, the optimal design variables and the aerodynamic performance output by the low-order aerodynamic model rotor analysis tool are combined into a new sample, the new sample is added to the aerodynamic performance training database, and incremental training or parameter fine-tuning of the surrogate model is triggered.

10. A rotor aerodynamic shape optimization system based on airfoil geometric feasibility constraints, characterized in that, include: The parameterization module is used to perform parametric modeling of the rotor planar shape using a shape transformation-like method, and uses the parameters of the shape transformation-like method as the first design variable; It is also used to reduce the dimensionality of the airfoil library using the singular value decomposition method, taking the modal coefficients representing the airfoil as the second design variable, and the first and second design variables together constitute the design space; The surrogate model training module is used to randomly sample within the design space, perform aerodynamic performance simulation on each sampling point using a low-order aerodynamic model rotor analysis tool, and construct an aerodynamic performance training database after data cleaning and normalization. The aerodynamic performance training database is used to train the multilayer perceptron neural network offline, and the trained model is then solidified into a surrogate model. The online optimization module introduces a gradient-based sequential least squares programming algorithm. Based on the current design variables in the iteration, it calls a surrogate model to complete aerodynamic performance inference, obtains gradient information associated with the objective function and constraint functions, updates the design variables based on the gradient information, and performs iterative optimization until the iterative convergence condition is met, outputs the optimal design variables, and obtains the optimal rotor aerodynamic shape. The constraint functions include the minimum Euclidean distance between the current design variables and the corresponding design variables of several known feasible airfoils being less than the geometric feasibility threshold.

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