An integrated deep neural network aerodynamic modeling method incorporating physical constraints

Abstract

The present invention relates to an integrated deep neural network aerodynamic modeling method that incorporates physical constraints to calculate the pressure coefficient C of the airfoil surface under different flow parameter conditions. p and the corresponding aerodynamic force (C L , C M ), the pressure coefficient C is calculated by the intrinsic orthogonal decomposition technique. p To reduce the dimension and integrate the deep neural network with physical constraints, two networks need to be constructed. The gradient back propagation method is used to adjust the weights and biases inside the neural network model after a certain number of iterations, so that the neural network can reduce the difference between the model prediction value and the true value under the constraint of distribution characteristics and improve the accuracy of the neural network. The integrated deep neural network model with physical constraints is built based on a multi-layer neural network, which has stronger nonlinear feature learning ability and stronger generalization ability to achieve high-precision prediction of aerodynamics.

Description

Technical Field

[0001] The present invention belongs to the technical field of aerodynamics and relates to an integrated deep neural network aerodynamic modeling method incorporating physical constraints. Background Art

[0002] In the field of aerodynamics, aerodynamic loads are one of the most important loads in aircraft design and use. They are the key inputs for aircraft aerodynamic shape design, structural design, strength verification, control system design, etc. It can be said that the prediction accuracy of aerodynamic loads is directly related to the performance and safety of aircraft. Traditionally, in the early stage of aircraft design, wind tunnel tests or computational fluid dynamics (CFD) simulations are generally used to obtain the aerodynamic coefficients of the airfoil. However, in the model design process, a large number of wind tunnel tests are difficult to bear in terms of funding costs and time cycles. CFD simulation is widely used in the aviation industry to analyze the aerodynamic performance of different aircraft during the design process. Compared with wind tunnel tests or flight tests, these simulations can reduce time and cost. However, in the aerodynamic design stage of modern aircraft, high-fidelity CFD simulation is usually a computationally intensive and time-consuming iterative process. Data-driven surrogate models are an effective method for estimating the approximate value of the distribution of a priori unknown functions, and are often applied to practical engineering problems. Therefore, surrogate models are currently beginning to be considered as a substitute for reasonable CFD tools for prediction.

[0003] Patent CN201610077146.5 proposed a dual-axis unsteady aerodynamic modeling method using support vector machine regression method, and patent CN201610863848.6 proposed an unsteady aerodynamic model parameter prediction method based on extreme learning machine ELM. Polynomial response surface method, Kriging model, support vector regression, radial basis function, neural network model, etc. are commonly used as proxy models and are widely used to solve black box problems with large amount of calculation and high calculation cost to reduce the calculation burden. The core of these methods is the mapping model between input and output. The parameters and structure of the model are adjusted through the learning of sample sets to make it have a better fitting effect.

[0004] The existing method has the following defects:

[0005] (1) In actual engineering applications, a black box model is used to construct an aerodynamic proxy model. This method has low interpretability and often requires a large amount of data for learning. However, the cost of obtaining samples is relatively high. Under small samples, the prediction accuracy of traditional direct modeling methods is insufficient and the generalization ability is low.

[0006] (2) CFD calculations or wind tunnel tests can obtain not only concentrated force information but also distributed force information. In the aerodynamic modeling process, researchers usually only focus on the integrated aerodynamic force and moment information, and the utilization rate of distributed force information is low.

[0007] The above defects show that aerodynamic modeling based on traditional black box models such as deep neural network models and Kriging models often requires a large number of samples. Under small samples, the model accuracy is insufficient, the generalization ability is low, and the utilization of distributed force information is low. At present, the proxy model that integrates distributed force information into the aerodynamic modeling process still needs to be developed. Summary of the invention

[0008] Technical issues to be solved

[0009] In order to avoid the shortcomings of the prior art, the present invention proposes an integrated deep neural network aerodynamic modeling method that incorporates physical constraints, making full use of the aerodynamic distribution information generated during the sampling process. In the modeling process, the distribution information characteristics are used as constraints to guide the neural network aerodynamic modeling process. This modeling method introduces the distributed load information generated by CFD calculations or wind tunnel tests into the aerodynamic modeling process, which can effectively reduce the model training samples, improve the accuracy, robustness and generalization of the model, and guide the subsequent work.

[0010] Technical Solution

[0011] An integrated deep neural network aerodynamic modeling method incorporating physical constraints is characterized by the following steps:

[0012] Step 1: Sample acquisition: Use numerical calculation methods to calculate the pressure coefficient C of the airfoil surface under different flow parameter conditions p and the corresponding aerodynamic force (C L , C M );

[0013] Step 2: Extraction of distributed force information features: The pressure coefficient C is extracted by using the intrinsic orthogonal decomposition technique. p The data set is reduced in dimension to obtain the corresponding POD modal features and the POD coefficients corresponding to different input parameters;

[0014] Step 3: Integrate the distribution information features into the neural network for aerodynamic modeling:

[0015] Construct two networks Net1 and Net2 to form an integrated deep neural network that incorporates physical constraints, and train the two networks uniformly;

[0016] The first network Net1 is constructed: the input is the flow parameters Ma, Re, AOA. If the airfoil shape changes, the CST parameters corresponding to the airfoil shape are added to the input parameters, and the output is the POD coefficient α of the distributed force information. POD ;

[0017] The second network Net2 is constructed by taking the input and output of the first network as the input of the second network, and the output is the aerodynamic force (C L , C M ), where Ma is the incoming Mach number, Re is the Reynolds number, AOA is the incoming angle of attack, and α POD is the POD coefficient obtained by feature extraction, C L is the lift coefficient, C M is the moment coefficient;

[0018] Step 4: Adopting the gradient back propagation method, after multiple iterations, the weights and bias items inside the neural network model are adjusted, so that the difference between the model prediction value and the true value is finally reduced under the constraint of the distribution characteristics, the accuracy of the neural network is improved, and the construction of the integrated deep neural network aerodynamic model is completed;

[0019] Where: The loss function of the neural network is given by α POD -α POD , the error of three parts, in which the POD coefficient obtained after the distribution information feature extraction is scaled by a factor γ, that is, γ×(α POD -α POD ).

[0020] Beneficial Effects

[0021] The present invention proposes an integrated deep neural network aerodynamic modeling method that incorporates physical constraints to calculate the pressure coefficient C of the airfoil surface under different flow parameter states. p and the corresponding aerodynamic force (C L , C M ), the pressure coefficient C is calculated by the intrinsic orthogonal decomposition technique. p To reduce the dimension and integrate the deep neural network with physical constraints, two networks need to be constructed. The gradient back propagation method is used to adjust the weights and biases inside the neural network model after a certain number of iterations, so that the neural network can reduce the difference between the model prediction value and the true value under the constraint of distribution characteristics and improve the accuracy of the neural network. The integrated deep neural network model with physical constraints is built based on a multi-layer neural network, which has stronger nonlinear feature learning ability and stronger generalization ability to achieve high-precision prediction of aerodynamics.

[0022] Compared with the traditional Kriging algorithm and deep neural network direct modeling method, the integrated deep neural network aerodynamic modeling method disclosed in the present invention can effectively improve the accuracy, robustness and generalization of aerodynamic modeling and increase the interpretability of the neural network model. At the same time, the integrated deep neural network aerodynamic modeling method based on the integration of physical constraints can effectively utilize the distributed load information generated during CFD calculations or wind tunnel tests, reduce the number of learning samples, and thus reduce the cost of sample acquisition, which is of great significance for guiding the subsequent work. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 Flowchart for modeling aerodynamic forces with integrated deep neural networks

[0024] Figure 2 Schematic diagram of the architecture for integrating deep neural network aerodynamic modeling DETAILED DESCRIPTION

[0025] The present invention will now be further described with reference to the embodiments and the accompanying drawings:

[0026] In this embodiment, the calculation data obtained by solving the Reynolds-Averaged Navier-Stokes (RANS) equation is specifically used to incorporate the characteristics of the distributed force information as constraints in the aerodynamic modeling process. The method is specifically as follows:

[0027] S1: Determine the flow state Ma, Re, AOA parameter space of CFD calculation, and obtain the pressure coefficient distribution C under each state p , lift coefficient C L , torque coefficient C M , where aerodynamic data (C L , C M ) as the training sample of the output part in the second network;

[0028] S2: Reduce the dimension of the pressure distribution data through the intrinsic orthogonal decomposition technology, and perform feature extraction to obtain the POD coefficient α corresponding to different input parameters POD ;

[0029] S3: Integrating distribution information features into neural networks for aerodynamic modeling

[0030] S301: The first network Net1 is constructed: the input is the flow parameters Ma, Re, AOA, and the output is the POD coefficient α of the distributed force information POD ; The second network Net2 is constructed by jumping the input parameters of the first network to the input layer of the second network, and the characteristic coefficient α of the distribution force information POD At the same time, it serves as the input of the second network, and the output is the aerodynamic force (CL , C M ). Finally, the two networks are trained uniformly to construct an integrated deep neural network model. The training samples of the neural network are Ma, Re, AOA, α POD , C L , C M Compared with the existing deep neural network direct modeling method, it can comprehensively utilize the distribution information generated during the sampling process, greatly improving the modeling accuracy and robustness of the existing aerodynamic modeling method.

[0031] S302: Construct a loss function of the integrated deep neural network through the training samples in step S301. The loss function is composed of α POD -α POD , the error of three parts, in which the POD coefficient obtained after the distribution force information feature extraction is scaled by a factor γ, that is, γ×(α POD -α POD ).

[0032] S303: The integrated deep neural network model is trained by the training samples in step S301 and the loss function in step S302. When training the neural network, the gradient back propagation method is used to continuously adjust the weights and bias items of the multi-layer neural network to minimize the loss function under the constraint of the distribution information characteristic coefficient while reducing the difference between the model prediction value and the true value, thereby improving the modeling accuracy of the neural network;

[0033] S4: After training, aerodynamic tests are performed. For states that are not in the design parameter space, an integrated deep neural network aerodynamic model with physical constraints is used to obtain efficient and high-precision lift coefficients. Moment coefficient

[0034] The integrated deep neural network aerodynamic modeling method incorporating physical constraints provided in this embodiment is compared to the prior art solution - aerodynamic modeling directly based on the deep neural network method. It can comprehensively utilize the distributed force data generated in the sampling process and introduce the distribution characteristic coefficients as physical constraints into the neural network modeling process, thereby improving the interpretability of the model and effectively improving the accuracy, robustness and generalization of the modeling, reducing the number of learning samples, and thus reducing the cost of sample acquisition.

Claims

1. An integrated deep neural network aerodynamic modeling method incorporating physical constraints, characterized by Here are the steps: Step 1: Sample acquisition: Use numerical calculation methods to calculate the pressure coefficient C of the airfoil surface under different flow parameter conditions p and the corresponding aerodynamic force (C L , C M ); Step 2: Extraction of distributed force information features: The pressure coefficient C is extracted by using the intrinsic orthogonal decomposition technique. p The data set is reduced in dimension to obtain the corresponding POD modal features and the POD coefficients corresponding to different input parameters; Step 3: Integrate the distribution information features into the neural network for aerodynamic modeling: Construct two networks Net1 and Net2 to form an integrated deep neural network that incorporates physical constraints, and train the two networks uniformly; The first network Net1 is constructed: the input is the flow parameters Ma, Re, AOA. If the airfoil shape changes, the CST parameters corresponding to the airfoil shape are added to the input parameters, and the output is the POD coefficient α of the distributed force information. POD ; The second network Net2 is constructed by taking the input and output of the first network as the input of the second network, and the output is the aerodynamic force (C L , C M );in Ma is the incoming flow Mach number, Re is the Reynolds number, AOA is the incoming flow angle of attack, α POD is the POD coefficient obtained by feature extraction, C L is the lift coefficient, C M is the moment coefficient; Step 4: Adopting the gradient back propagation method, after multiple iterations, the weights and bias items inside the neural network model are adjusted, so that the difference between the model prediction value and the true value is reduced under the constraint of the distribution characteristics, the accuracy of the neural network is improved, and the construction of the integrated deep neural network aerodynamic model is completed; Where: The loss function of the neural network is given by The error consists of three parts, in which the POD coefficient obtained after the distribution information feature extraction is scaled by a factor γ, that is,

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