Neural network modeling method and system for rapidly predicting aerodynamic performance of propeller

Abstract

The invention discloses a neural network modeling method and system for rapidly predicting aerodynamic performance of a propeller. The method comprises the following steps: acquiring initial data of the propeller through CFD numerical simulation; dividing CFD calculation data into a high-fidelity data set and a low-fidelity data set; dividing intervals of each physical variable for the low-fidelity data set, calculating a low-fidelity sample variance in each interval, and inserting the high-fidelity data set into a low-fidelity data space through a CLHS method to form a mixed sample data set; evaluating the training value of each sample in the mixed sample set; adjusting the sample training probability, and forming a training sample set; and sampling according to the specific training probability of each sample in the training sample set, and inputting the samples into the BP neural network for training. According to the method, by optimizing sample distribution and combining a neural network training mechanism embedded by physical information, collaborative improvement of calculation efficiency and prediction precision is achieved, and the requirement for real-time high-precision aerodynamic performance prediction under the complex working condition of the propeller is met.

Description

Technical Field

[0001] This invention relates to a neural network modeling method and system for rapidly predicting the aerodynamic performance of propellers under various incoming flow conditions, specifically a method and system for rapidly predicting the aerodynamic performance of propellers. Background Technology

[0002] As low-altitude, low-speed aircraft propulsion systems develop towards higher thrust density and higher energy efficiency, the rapid optimization design of the propeller, the core component of these systems, has become a critical bottleneck that urgently needs to be overcome. In practical engineering applications, propellers must adapt to changes in parameters such as rotational speed, pitch angle, and torque to maintain aerodynamic performance under complex operating conditions. This necessitates real-time and high-precision prediction of aerodynamic performance.

[0003] However, existing high-fidelity aerodynamic modeling methods have significant limitations. Conventional CFD calculations based on Navier-Stokes require multiple simulations for different geometric configurations in propeller design optimization. Each simulation requires high-resolution meshes and detailed turbulence models, resulting in a single full-scale blade simulation taking over 72 hours. Experimental measurements are also constrained by wind tunnel conditions, making it difficult to cover the entire operating range and incurring high experimental costs. These dual constraints limit the further development of iterative propeller optimization.

[0004] To overcome the aforementioned bottlenecks, machine learning-based alternative models have been widely developed in the field of aerodynamic design in recent years. Research shows that machine learning methods can solve problems in engineering that are difficult to address using simulation and experimental modeling alone, while effectively reducing the high costs associated with the modeling process. However, the modeling accuracy of machine learning-based aerodynamic simulation alternative models is closely related to the quality of the sample dataset. The massive amounts of high-precision sample data required to build high-fidelity models often bring engineering challenges such as an exponential increase in computational dimensionality and a surge in simulation resource consumption. To address this issue, researchers have proposed the variable-fidelity model (VFM), which offers an effective solution. As an advanced model integrating multiple precision data sources, VFM achieves synergistic optimization of computational efficiency by establishing a cross-fidelity correlation mechanism, thus balancing prediction accuracy and computational cost. Existing research has explored methods such as adaptive weighting mechanisms for multiple fidelities and hybrid surrogate models based on radial basis function neural networks, which have improved the accuracy of aerodynamic efficiency prediction to some extent. However, existing VFM methods still have two major limitations that restrict further improvement in their prediction accuracy and efficiency. First, the sampling strategy does not take into account the uncertainty distribution characteristics of the sample data, resulting in low utilization efficiency of high-fidelity samples. Second, the lack of an active utilization mechanism of prior physical information during model training leads to interference effects when fusing multi-fidelity data. Summary of the Invention

[0005] Therefore, to address the aforementioned shortcomings, this invention provides a neural network modeling method and system for rapidly predicting propeller aerodynamic performance. Based on prior physical information data fusion, this invention employs Conditional Latin Hypercube (LHS) sampling. By introducing a sampling mechanism based on variance information, it achieves active sampling with varying degrees of precision while retaining the spatial uniformity advantage of traditional LHS. Simultaneously, during the neural network training phase, the priority experience replay mechanism of reinforcement learning is combined with prior physical information to construct a multi-fidelity fusion model with autonomous sample value assessment capabilities, thereby enabling rapid and high-precision prediction of propeller aerodynamic performance.

[0006] Specifically, neural network modeling methods for rapidly predicting propeller aerodynamic performance include: A neural network modeling method for rapidly predicting propeller aerodynamic performance, characterized by comprising: Initial propeller data of different precisions were obtained through CFD numerical simulations with high and low computational costs, and compared with experimental results. The CFD computation data are divided into high-fidelity datasets with smaller experimental errors and low-fidelity datasets with larger experimental errors. For the low-fidelity dataset, the intervals of each physical variable are divided, the variance of the low-fidelity samples in each interval is calculated, and the sampling interval is selected according to the size of the variance. The high-fidelity dataset is inserted into the low-fidelity data space by the Conditional Latin Hypercube Sampling (CLHS) method to form a mixed sample dataset. Based on the mixed sample dataset, evaluate the training value of each sample in the mixed sample set; Adjust the training probability of the samples and form a training sample set; Samples are taken from each sample in the training sample set according to their specific training probability and fed into the BP neural network for training.

[0007] Furthermore, specific methods for evaluating the training value of each sample in a mixed dataset include: Calculate the Euclidean distance between each low-fidelity data point and the nearest high-fidelity data point; Calculate the training value of low-fidelity data and high-fidelity data separately.

[0008] Optionally, the Euclidean distance between each low-fidelity data point and the nearest high-fidelity data point can be calculated using the following formula: , i= 1… n, j=1 … m , in, Indicates the first iThe Euclidean distance between a low-fidelity data point and the nearest high-fidelity data point. C h,j Indicates the first j The coordinates of a high-fidelity data point in the data space. C l,i Indicates the first i The coordinates of low-fidelity data in the data space. n and m It is a positive integer.

[0009] Optionally, the training value of low-fidelity data and high-fidelity data can be calculated separately using the following formulas: , i =1… n ; V h,j =1+ f p ( C h,j ), j =1… m ; in, Indicates the first i The Euclidean distance between a low-fidelity data point and the nearest high-fidelity data point. C h,j Indicates the first j The coordinates of a high-fidelity data point in the data space. C l,i Indicates the first i The coordinates of low-fidelity data in the data space. n and m It is a positive integer; V l,i Indicates the first i The training value of low-fidelity data V h,j Indicates the first j The training value of high-fidelity data; f p ( C h,j ) is an additional value function.

[0010] Optionally, the method to adjust the sample training probability is: The probability of each sample being selected for training is calculated using the following value function: ,i =1… n , ,j =1… m , in, p tl,i Indicates the first i The probability that a low-fidelity dataset is selected for training. p th,j Indicates the first j The probability of selecting a high-fidelity dataset for training. V l,i Indicates the first i The training value of low-fidelity data V h,j Indicates the first j The training value of high-fidelity data.

[0011] Optionally, methods for training a BP neural network include forward propagation and backward propagation processes. Forward propagation involves going from the input layer through the hidden layer to the output layer, generating a predicted value, and using the error between the predicted value and the true value to measure the performance of the neural network. The backpropagation process involves using the error obtained from forward propagation to update the weights of the BP neural network.

[0012] On the other hand, the present invention provides a neural network modeling system for rapidly predicting propeller aerodynamic performance, comprising: The data generation module is used to obtain propeller initial data of different precision through high- and low-computational-cost CFD numerical simulations and compare them with experimental results. The data classification module is used to divide CFD computation data into high-fidelity datasets with smaller experimental errors and low-fidelity datasets with larger experimental errors. The data mixing module is used to divide the low-fidelity dataset into intervals for each physical variable, calculate the variance of the low-fidelity samples in each interval, select the sampling interval according to the size of the variance, and insert the high-fidelity dataset into the low-fidelity data space through the conditional Latin hypercube sampling method to form a mixed sample dataset. The data value training module is used to evaluate the training value of each sample in a mixed sample dataset. The data adjustment module is used to adjust the training probability of samples and form a training sample set; The neural network training module is used to sample each sample in the training sample set according to its specific training probability and feed it into the BP neural network for training.

[0013] The present invention has the following advantages: This invention is used to rapidly predict the aerodynamic performance of propellers under various incoming flow conditions. Addressing the problems of low utilization of high-fidelity samples and severe interference from low-fidelity data in traditional variable-fidelity models (VFM), this invention optimizes the distribution of high-fidelity samples through Conditional Latin Hypercube Sampling (CLHS). (That is, within the low-fidelity data space, the prediction error of the low-fidelity dataset with smaller variance meets the requirements, while regions with larger variance require high-fidelity sample data to be filled in using the CLHS method, ultimately forming a mixed sample dataset). Furthermore, a priori physical information embedding mechanism is introduced to regulate the training process. This achieves a synergistic improvement in computational efficiency and prediction accuracy, meeting the real-time, high-precision aerodynamic performance prediction requirements of propellers under complex operating conditions.

[0014] Simultaneously, the crucial step of sample probability weighting is embedded into the neural network training process, primarily affecting the preparation of training data and reflected in the loss function calculation. Unlike traditional BP neural networks that use all samples for uniform training, this invention introduces sample value evaluation results based on prior physical information into the standard training process to achieve adaptive training.

[0015] This invention can also be applied to rapid prediction of rotor blades or blade cascades. Attached Figure Description

[0016] Figure 1 This is a flowchart of the neural network modeling method for rapidly predicting propeller aerodynamic performance as described in this invention; Figure 2 This is a modular block diagram of the neural network modeling system for rapidly predicting propeller aerodynamic performance as described in this invention; Figure 3 This is a schematic diagram of a BP neural network structure; Figure 4 This is a schematic diagram of the propeller's geometric model; Figure 5 The mesh generation for propellers under different computational costs is shown, where (a) is a low-precision mesh and (b) is a high-precision mesh. Figure 6 It is a sample set of propeller aerodynamic parameters under different pitches; Figure 7 It is a sample error cloud map; Figure 8 It is a fitting error contour plot; Figure 9 This is a performance prediction diagram of a three-bladed propeller. Figure 10 This is a comparison chart with a single fidelity model. Detailed Implementation

[0017] The embodiments of this application are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain this application, and should not be construed as limiting this application.

[0018] In this document, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, without necessarily requiring or implying any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus.

[0019] As described in the background section, with the urgent need for high thrust density and high energy efficiency propeller propulsion systems in low-altitude, low-speed aircraft, propeller design urgently needs to overcome the bottleneck of rapid optimization. However, traditional high-fidelity aerodynamic performance prediction methods (such as high-precision CFD simulation and wind tunnel experiments) have significant limitations, including low computational efficiency, high cost, and difficulty in covering all operating conditions, which severely restrict the design iteration process. Although variable fidelity models (VFM) based on machine learning have shown potential in balancing computational cost and prediction accuracy by integrating data sources of different precision, existing methods still have two key drawbacks that limit further improvement in model prediction accuracy.

[0020] For the reasons mentioned above, this embodiment provides a neural network modeling method for rapidly predicting propeller aerodynamic performance, such as... Figure 1 The method includes: S100. Initial propeller data of different precisions were obtained through CFD numerical simulations with high and low computational costs, and compared with experimental results. S200. CFD computation data are divided into high-fidelity datasets with smaller experimental errors and low-fidelity datasets with larger experimental errors. S300. Divide the low-fidelity dataset into intervals for each physical variable, calculate the variance of the low-fidelity samples in each interval, select the sampling interval according to the size of the variance, and insert the high-fidelity dataset into the sample space using the Conditional Latin Hypercube Sampling (CLHS) method to form a mixed sample dataset. S400. Based on the mixed sample dataset, evaluate the training value of each sample in the mixed sample set; S500: Adjust the sample training probability and form a training sample set; S600: Sample each sample in the training sample set according to its specific training probability and feed it into the BP neural network for training.

[0021] The aforementioned technical features optimize sample distribution through Conditional Latin Hypercube Sampling (CLHS) and combine it with a neural network training mechanism that embeds physical information to achieve a synergistic improvement in computational efficiency and prediction accuracy, thus meeting the real-time high-precision aerodynamic performance prediction requirements of propellers under complex operating conditions.

[0022] Latin hypercube sampling (LHS) is a stratified sampling technique that effectively covers the parameter space by uniformly dividing the range of values ​​for each variable and randomly selecting samples within each range. Compared to traditional random sampling, LHS can achieve a more uniform parameter distribution with fewer samples.

[0023] The LHS method uniformly divides the value range of each variable into N sub-intervals (N being the number of sampling points), and randomly selects a value within each sub-interval of each variable. Then, by randomly permuting and combining the N values ​​(or sampling points) selected for each variable, N multidimensional sample points are formed. This combination method ensures that when all N sample points are projected onto any dimension, each sub-interval of that dimension contains exactly one sampling point, thus achieving uniform coverage of the parameter space and improving sample representativeness.

[0024] Traditional LHS (Latin Hypercube Sampling) achieves a uniform distribution of sampling points, avoiding concentration, but it has limitations in utilizing spatial and prior physical information. Due to the uneven distribution of uncertainty in the data domain, sampling in some areas has higher value, and global uniform sampling alone is insufficient for efficient resource utilization. To more accurately reflect uncertainty and address the problem of blind spatial distribution and low utilization efficiency of high-fidelity samples in traditional variable fidelity models, this embodiment employs the Conditional Latin Hypercube Sampling (CLHS) method based on variance information. This method divides the data domain into several sub-intervals and calculates the variance, prioritizing the allocation of limited, computationally expensive high-fidelity sampling resources to the regions with the highest prediction uncertainty in the parameter space. This maximizes the value of each high-fidelity sample, enabling the reasonable sampling of high-precision sample data.

[0025] In S200, the low-fidelity dataset is divided into intervals for each physical variable, the variance of the low-fidelity samples within each interval is calculated, and sampling intervals are selected based on the variance. The high-fidelity dataset is then inserted into the sample space using the Conditional Latin Hypercube Sampling (CLHS) method to form a mixed sample dataset. The methods include: S210. Calculate the variance of each interval of the low-fidelity dataset based on known prior physical information. For example, based on low-precision prior samples, the design space is divided into N sub-intervals in each dimension of the design space of the input variables. The variance of each interval based on known prior physical information is calculated. The larger the variance, the higher the prediction uncertainty of the low-fidelity data in that interval, and the more the region needs to be "corrected" with high-fidelity data.

[0026] S220. Select the interval with the largest variance for sampling.

[0027] S230. Exclude mutually exclusive intervals of the same dimension as the selected interval.

[0028] S240. Repeat the sampling steps for the remaining intervals until sampling is complete.

[0029] Among the aforementioned technical features, the resulting high-fidelity dataset is no longer random, but highly concentrated in the key regions that can best improve model performance. This CLHS method based on variance information can make full use of variance information, improve sampling efficiency and utilization of high-fidelity data, and make the distribution of sampling points more reasonable, thereby improving modeling accuracy and computational efficiency.

[0030] The VFM method based on prior physical information proposed in step S400: By calculating the Euclidean distance between high-fidelity and low-fidelity data and combining it with prior physical information, the value of training samples is evaluated, and the training sample selection stage in the BP network training process is optimized according to the training value of the samples, as follows: Specific methods for evaluating the training value of each sample in a mixed dataset include: Calculate the Euclidean distance between each low-fidelity data point and the nearest high-fidelity data point; Calculate the training value of low-fidelity data and high-fidelity data separately.

[0031] For example, the Euclidean distance between each low-fidelity data point and the nearest high-fidelity data point is calculated using the following formula: , i= 1… n, j=1 … m , in, Indicates the first i The Euclidean distance between a low-fidelity data point and the nearest high-fidelity data point. C h,j Indicates the first j The coordinates of a high-fidelity data point in the data space. C l,i Indicates the first i The coordinates of low-fidelity data in the data space. n and m It is a positive integer.

[0032] For example, the training value of low-fidelity data and high-fidelity data can be calculated using the following formulas respectively: , i =1… n ; V h,j =1+ f p ( C h,j ), j =1… m ; in, Indicates the first i The Euclidean distance between a low-fidelity data point and the nearest high-fidelity data point. C h,j Indicates the first j The coordinates of a high-fidelity data point in the data space. C l,i Indicates the first i The coordinates of low-fidelity data in the data space. n and m It is a positive integer; V l,i Indicates the first i The training value of low-fidelity data V h,j Indicates the first j The training value of high-fidelity data; f p ( C h,j ) is an additional value function.

[0033] In step S500, the method for adjusting the sample training probability is as follows: The probability of each sample being selected for training is calculated using the following value function: ,i =1… n , ,j =1… m , in, p tl,i Indicates the first i The probability that a low-fidelity dataset is selected for training. p th,j Indicates the first j The probability of selecting a high-fidelity dataset for training. V l,i Indicates the firsti The training value of low-fidelity data V h,j Indicates the first j The training value of high-fidelity data.

[0034] In step S600, the structure of the BP neural network is as follows: Figure 3 As shown, the training method for this BP neural network includes forward propagation and backward propagation processes. Forward propagation involves going from the input layer through the hidden layer to the output layer, generating a predicted value, and using the error between the predicted value and the true value to measure the performance of the neural network. The backpropagation process involves using the error obtained from forward propagation to update the weights of the BP neural network.

[0035] This training method embeds the crucial step of sample probability weighting into the neural network training process, primarily influencing the preparation of training data and reflecting this in the loss function calculation. Unlike traditional BP neural networks that use all samples for uniform training, this invention introduces sample value evaluation results based on prior physical information into the standard training process to achieve adaptive training. The specific implementation is as follows: The training batch is constructed not by using the entire dataset at the beginning of each training iteration, but by sampling each sample according to the pre-calculated training probability formula to form the training data for the current batch.

[0036] In the weighted calculation of the loss function, during backpropagation, when calculating the global error, this invention performs differentiated processing on the error of each sample according to its characteristics to further suppress the interference of low-fidelity samples: for high-fidelity samples, the error weight is high, and for low-fidelity samples, the error weight is related to their training value.

[0037] For example, the specific method of forward propagation is: Input layer to hidden layer: It includes an activation function layer to nonlinearize the activation units, enabling the neural network to learn from nonlinear datasets (i.e., the training sample set mentioned above), as shown in the following formula: ; h k = f 1( s k ); In the formula, s k Indicates the first k One hidden layer node, k=1, 2, 3... m , m It is the number of nodes in the hidden layer. x i Indicates the first i One input layer node, i =1,2,3... n , n It is the number of nodes in the input layer. w 1ik Indicates the first i The input layer node and the first k The connection weights of each hidden layer node h k This represents the th [unit] after the activation function. k One hidden layer node, f 1 represents the hidden layer activation function.

[0038] Hidden layer to output layer: ; ; In the formula, z j Indicates the first j One output layer node, w 2kj Indicates the hidden layer number 1 k The node and the output layer j The connection weight of each node j =1,2,3,... l , l It is the number of nodes in the output layer. This indicates the number of digits after the activation function. j One output layer node, f 2 represents the output layer activation function.

[0039] The specific method of backpropagation is as follows: First, the error between the predicted value and the true value of the output layer is calculated and quantified using a loss function. The error calculation is as follows: ; ; In the formula, E c Indicates the first c Individual sample error, c= 1,2,3 ...p， and y c They represent the first c The first sample j There are n output layer nodes, where E represents the sum of sample errors; The optimal parameter solution for the network weights is optimized iteratively using the following formula: , ; Using parameters w 1ik and w 2ik The optimal value is obtained by optimizing using the following gradient descent method: w 1ik =w 1ik -αΔw 1ik ; w 2ik =w 2ik -αΔw 2ik ; ; ; In the formula α Indicates the learning rate. Δw 1ik and Δw 2kj These represent the connection weights. w 1ik and w 2kj The gradient; The chain rule for differentiation is used to determine the distance from the output layer to the hidden layer: ; in: , , , From hidden layer to input layer: , in: , , get: , Finally, the following formula is used to... p The parameter update is obtained by summing all the gradients for each sample: , .

[0040] In another embodiment, such as Figure 2As shown, a neural network modeling system for rapidly predicting propeller aerodynamic performance is provided, including: The data generation module is used to obtain propeller initial data of different precision through high- and low-computational-cost CFD numerical simulations and compare them with experimental results. The data classification module is used to divide CFD computation data into high-fidelity datasets with smaller experimental errors and low-fidelity datasets with larger experimental errors. The data mixing module is used to divide the low-fidelity dataset into intervals for each physical variable, calculate the variance of the low-fidelity samples in each interval, select the sampling interval according to the size of the variance, and insert the high-fidelity dataset into the low-fidelity data space through the conditional Latin hypercube sampling method to form a mixed sample dataset. The data value training module is used to evaluate the training value of each sample in a mixed sample dataset. The data adjustment module is used to adjust the training probability of samples and form a training sample set; The neural network training module is used to sample each sample in the training sample set according to its specific training probability and feed it into the BP neural network for training.

[0041] The aforementioned technical features are used to realize the neural network modeling method for rapidly predicting propeller aerodynamic performance, achieving a synergistic improvement in computational efficiency and prediction accuracy, and meeting the real-time high-precision aerodynamic performance prediction requirements of propellers under complex operating conditions.

[0042] The following is a specific example of propeller aerodynamic performance prediction based on the neural network modeling method for rapid prediction of propeller aerodynamic performance described in the above embodiments: The sample set of propeller aerodynamic performance was obtained as follows; The method proposed in this invention was validated using a three-bladed variable-pitch propeller with a diameter of 47 inches and a variable pitch of 24 to 40 inches. Performance data was obtained through CFD calculations and experiments, and a sample set of propeller aerodynamic performance parameters was constructed. The propeller model is shown below. Figure 4 .

[0043] CFD calculations were performed using the commercial software ANSYS FLUENT to determine the propeller's aerodynamic characteristics. Numerical calculations were considered under two different computational cost scenarios, as shown in Figure 4, which illustrates the computational mesh generation for propellers at different precision levels. High-precision meshes corresponding to high computational cost and low-precision meshes corresponding to low computational cost were used respectively. The aerodynamic characteristics of the propeller were obtained using both methods and verified experimentally. Furthermore, compared to experimental results, a CFD propeller aerodynamic performance error between 10% and 20% was defined as a low-fidelity dataset; an error less than 10% was defined as a high-fidelity dataset.

[0044] Figure 6 As shown, the performance parameters of the propeller under different pitches were obtained. By comparing the calculations with experimental data using grids of different precision, the maximum error of the high-precision numerical calculation was 8.5%, and the maximum error of the low-precision calculation was 18.2%.

[0045] The following is a fusion of prior physical information; By combining the aerodynamic information of the propeller and the physical laws presented by the sample data, the training process of the multi-fidelity model is integrated to improve the performance prediction accuracy of the model without increasing the amount of sample computation. Figure 7 The error values ​​between CFD simulation samples of different fidelity and experimental data are given, with the horizontal and vertical axes representing the normalized values ​​of the incoming wind speed and propeller pitch, the input variables in the model built in this invention. It can be seen that the error values ​​increase with increasing incoming wind speed and propeller pitch.

[0046] Based on the above error distribution results with respect to pitch and incoming wind speed, the following quadratic polynomial is used to fit the error distribution: ; in: y Indicates sample error. x 1 indicates the propeller speed. x 2 indicates the propeller pitch.

[0047] Figure 8 The distribution cloud map of the fitting error is given. The overall data exhibits low-order nonlinear characteristics. The coefficient of determination R2 of the fitting error cloud map is 0.963. The fitting results are consistent with the characteristic distribution and trend of the error cloud map.

[0048] The propeller aerodynamic model predictions are validated as follows: Verification method: Substitute the quadratic polynomial of the fitting error as additional physical information into the equation. V (h,j) =1+ f p ( C h,j ), j =1... m middle f p ( C h,j The sample data for the three-bladed propeller was sampled, and the propeller thrust sample data was divided into a training set and an independent validation set at a ratio of 4:1, with a high-fidelity sample ratio of 1:4. The following four combination strategies were used for comparative testing: ① Traditional LHS sampling + traditional BP neural network; ② Traditional LHS sampling + VFM based on prior physical information; ③CLHS sampling with variance information + traditional BP neural network; ④ CLHS sampling with variance information + VFM based on prior physical information (the method described in the above embodiments); Performance comparison results are quantified using root mean square error (RMSE) and coefficient of determination (R²) to predict performance (see [link to relevant documentation]). Figure 9 ): 1. Improved sampling method effects (comparison of ① and ③, ② and ④): CLHS sampling with variance information reduced RMSE by 4.01% and 14.95%, respectively. The R² values ​​were improved by 0.53% and 0.83% respectively, indicating that CLHS optimized the spatial distribution of high-fidelity samples.

[0049] 2. Improved Modeling Methods (Comparison of ① and ②, ③ and ④): VFM based on prior physical information reduced RMSE by 22.09% and 30.96% respectively; R² increased by 2.22% and 2.52% respectively, verifying the ability of physical information embedding to suppress low-fidelity interference.

[0050] 3. Effects of the combined strategy (compare ① and ④): The RMSE decreased significantly by 33.73%, and the R² increased by 3.06%, demonstrating the synergistic effect of CLHS and physical information fusion.

[0051] Compared with a single fidelity model: Compare the optimal combination ④ with the single fidelity model (see...) Figure 10 ): Compared to a single low-fidelity model: RMSE A decrease of 44.4%, R² An increase of 4.72%; Compared to a single high-fidelity model: RMSE Only 7.8% higher, R² Slightly lower by 0.61%, but the high-fidelity sample size is reduced by 80%, significantly reducing computational costs.

[0052] Therefore, by fusing CLHS sampling with prior physical information, the method significantly reduces reliance on high-cost samples while ensuring prediction accuracy. This solves the problems of low utilization of high-fidelity samples and interference from multi-source data in traditional VFM, providing an efficient solution for real-time propeller aerodynamic performance prediction. The effectiveness of this method is verified through validation functions and a three-bladed propeller aerodynamic modeling example. Compared with the traditional VFM method, the prediction error is reduced by 33.73%.

[0053] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A neural network modeling method for fast prediction of propeller aerodynamic performance, characterized in that, The application relates to a method for training a BP neural network based on a mixed sample data set. The method comprises the following steps: Obtaining initial data of a propeller with different precisions through high and low cost CFD numerical simulation, and comparing the initial data with experimental results; Dividing CFD calculation data into a high-fidelity data set with small experimental error and a low-fidelity data set with large experimental error; Dividing intervals of each physical variable for the low-fidelity data set, calculating sample variances of the low-fidelity data set in each interval, selecting a sampling interval according to the variance size, inserting the high-fidelity data set into the low-fidelity data space through a conditional Latin hypercube sampling method, and forming a mixed sample data set; Evaluating the training value of each sample in the mixed sample data set; Adjusting the sample training probability and forming a training sample set; 2. The neural network modeling method for fast prediction of aerodynamic performance of propellers according to claim 1, characterized in that, Sampling according to the specific training probability of each sample in the training sample set and inputting the sample into a BP neural network for training. The specific method for evaluating the training value of each sample in the mixed sample data set comprises the following steps: Calculating the Euclidean distance between each low-fidelity data and the nearest high-fidelity data; 3. The neural network modeling method for fast prediction of the aerodynamic performance of a propeller according to claim 2, characterized in that, Respectively calculating the training value of the low-fidelity data and the high-fidelity data. ， i= 1… The Euclidean distance between each low-fidelity data and the nearest high-fidelity data is calculated through the following formula: … m ， wherein, denotes the Euclidean distance of the i th low-fidelity data to the nearest high-fidelity data, C h,j denotes the coordinates of the j th high-fidelity data in the data space, C l,i denotes the coordinates of the i th low-fidelity data in the data space, n and m is a positive integer.

4. The neural network modeling method for fast prediction of the aerodynamic performance of a propeller according to claim 2, characterized in that, n, j = 1 ， i =1… n ； V h,j =1+ f p ( C h,j )， j =1… m ； wherein, represents the Euclidean distance of the i th low-fidelity data to the nearest high-fidelity data, C h,j represents the coordinate of the j th high-fidelity data in the data space, C l,i represents the coordinate of the i th low-fidelity data in the data space, n and m is a positive integer; V l,i represents the training value of the i th low-fidelity data, V h,j represents the training value of the j th high-fidelity data; f p C h,j is an extra value function.​ 5. The neural network modeling method for fast prediction of the aerodynamic performance of a propeller according to claim 2, characterized in that, The training value of the low-fidelity data and the high-fidelity data is respectively calculated through the following formula: The method for adjusting the sample training probability comprises the following steps: ,i =1… n ， ,j =1… m ， wherein, p tl,i denotes the probability that the i th low-fidelity data is selected for training, p th,j denotes the probability that the j th high-fidelity data is selected for training, V l,i denotes the training value of the i th low-fidelity data, V h,j denotes the training value of the j th high-fidelity data.

6. The neural network modeling method for fast prediction of aerodynamic performance of propellers according to claim 2, characterized in that, The probability of each sample being selected for training is calculated through the following value function: The method for training the BP neural network comprises a forward propagation process and a backward propagation process, The forward propagation process is from the input layer to the hidden layer and then to the output layer, a predicted value is generated, and the error between the predicted value and the actual value is used to measure the performance of the neural network; 7. The neural network modeling method for fast prediction of the aerodynamic performance of a propeller according to claim 6, characterized in that, The backward propagation process is used to update the BP neural network weight value by using the error obtained through the forward propagation process. The specific method for the forward propagation process comprises the following steps: From the input layer to the hidden layer: ； h k = f 1( s k )； wherein s k denotes the k th hidden layer node, k= 1, 2, 3... m , m is the number of nodes of the hidden layer, x i denotes the i th input layer node, i = 1, 2, 3... n , n is the number of nodes of the input layer, w 1ik denotes the i th input layer node and the k th hidden layer node connection weight, h k denotes the k th hidden layer node after the activation function, f 1 denotes the hidden layer activation function; An activation function is included, the activation unit is nonlinearized, the neural network can learn the training sample set, and the formula is as follows: ； ； wherein z j denotes the j th output layer node, w 2kj denotes the connection weight of the k th node of the hidden layer and the j th node of the output layer, j = 1, 2, 3,... l , l is the number of nodes of the output layer, denotes the j th output layer node after the activation function, f 2 denotes the output layer activation function.

8. The neural network modeling method for fast prediction of the aerodynamic performance of a propeller according to claim 6, characterized in that, From the hidden layer to the output layer: The specific method for the backward propagation process comprises the following steps: ； ； In the formula, E c denotes the c sample error, c= 1,2,3 ...p， and y c denotes the c output layer node under the j sample error and; First, the error between the predicted value and the actual value of the output layer is calculated, the error is quantified through a loss function, and the error is calculated as follows: ， ； Utilizing parameters w 1ik And w 2ik The optimal value is obtained by optimizing the following gradient descent method: w 1ik =w 1ik The network weight value is iteratively optimized through the following formula to obtain the best parameter solution: 1ik ； w 2ik =w 2ik - alpha * delta * w 2ik ； ； ； In the formula α denotes the learning rate, - alpha * delta * w 1ik denotes the gradient of the connection weight Delta * w 2kj denotes the gradient of the connection weight w 1ik denotes the gradient of the connection weight w 2kj denotes the gradient of the connection weight Delta * w ； wherein: , ， ， From the output layer to the hidden layer, the chain rule is as follows: ， wherein: , ， From the hidden layer to the input layer: ， Finally, the update of the parameters is obtained by adding all the gradients of the samples with the following formula: p θ = θ - η * ∑ (δL / δθ) ， 。 9. A neural network modeling system for fast prediction of propeller aerodynamic performance, characterized by The following is obtained: The application further relates to a data forming module, a data classification module and a data mixing module. The data forming module is used for obtaining initial data of a propeller with different precisions through high and low cost CFD numerical simulation, and comparing the initial data with experimental results; The data classification module is used for dividing CFD calculation data into a high-fidelity data set with small experimental error and a low-fidelity data set with large experimental error; The data mixing module is used for dividing intervals of each physical variable for the low-fidelity data set, calculating sample variances of the low-fidelity data set in each interval, selecting a sampling interval according to the variance size, inserting the high-fidelity data set into the low-fidelity data space through a conditional Latin hypercube sampling method, and forming a mixed sample data set. The data value training module is configured to evaluate the training value of each sample in the mixed sample dataset based on the mixed sample dataset. The data adjustment module is configured to adjust the sample training probability and form a training sample set. The neural network training module is configured to sample and input each sample in the training sample set into the BP neural network for training according to the specific training probability of each sample.

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