CN112597702B - Pneumatic modeling generation type confrontation network model training method based on radial basis function - Google Patents

Pneumatic modeling generation type confrontation network model training method based on radial basis function Download PDF

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CN112597702B
CN112597702B CN202011518083.5A CN202011518083A CN112597702B CN 112597702 B CN112597702 B CN 112597702B CN 202011518083 A CN202011518083 A CN 202011518083A CN 112597702 B CN112597702 B CN 112597702B
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张骏
汪文勇
向渝
王兵
胡力卫
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Abstract

The invention belongs to the technical field of generative confrontation networks, and particularly relates to a pneumatic modeling generative confrontation network model training method based on a radial basis function, which is used for designing the generation and regression of pneumatic data. The model introduces a radial basis function neural network on the basis of a traditional generative confrontation network model, so that the traditional fitting-based generative confrontation network is changed into a difference-based generative confrontation network, and meanwhile, regression and generation of nonlinear pneumatic data are achieved.

Description

Pneumatic modeling generation type confrontation network model training method based on radial basis function
Technical Field
The invention relates to the technical field of generative confrontation networks, in particular to a pneumatic modeling generative confrontation network model training method based on a radial basis function.
Background
With the development of economy and science and technology of China, the aerospace field is continuously advancing. The aerodynamic research directly influences the development and progress of aerospace industry, and at present, the aerodynamic research mainly adopts three technical means such as numerical calculation, wind tunnel experiment and flight test.
The numerical calculation method, namely the method for calculating the aerodynamics, can provide a high-precision flow field numerical simulation result, but the numerical solving difficulty of an aerodynamic partial differential equation set is high, the simulation precision is easily influenced by various factors such as a flow field grid and a turbulence model, and the method can consume a large amount of calculation resources and time resources; the wind tunnel experiment is the most basic research means for predicting the aerodynamic characteristics of the aircraft and evaluating the performance of the aircraft, but the wind tunnel experiment process is complex, the cost is high, the real flight environment is difficult to simulate, and various interference factors such as a bracket, a tunnel wall and the like exist; flight tests are the most important means for verifying the ground prediction result of the aircraft, the obtained data are most close to the real situation, and other two methods can be verified, but the application of the method is limited due to the problems of high test flight cost, high risk, difficult measurement, small data volume and the like.
With the development of new technologies, modern artificial neural networks are also widely applied to technical processing of function estimation or approximation, and Artificial Neural Networks (ANN), Neural Networks (NN) for short, are mathematical models or calculation models simulating the structure and function of biological neural networks.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a pneumatic modeling generation type confrontation network model training method based on a radial basis function, the radial basis function is introduced into a classical GAN (generic area network) discriminator to form a radial basis function-based discriminator, the regression problem and the generation problem of nonlinear pneumatic data can be simultaneously processed, and the defect of insufficient pneumatic data is overcome.
The invention discloses a pneumatic modeling generation type confrontation network model training method based on a radial basis function, which comprises the following steps:
a pneumatic data preprocessing step, namely extracting a pneumatic data set, determining design parameters and response parameters serving as input parameters and output parameters in the pneumatic data set, filtering and screening abnormal values and missing values in the pneumatic data set, normalizing all data in the pneumatic data set, and dividing the data into a training set, a verification set and a test set according to a preset proportion;
and a model construction step, namely setting the number of nodes of an input layer, the number of nodes of an output layer and the number of hidden nodes in a discriminator and a generator in the radial basis function-based generating confrontation network according to the dimension and data quantity information of the input and output pneumatic data sets determined in the pneumatic data preprocessing step, and constructing a radial basis function network model. The radial basis generation type countermeasure network is a novel generation type countermeasure network derivative model, is composed of a radial basis neural network and a generation type countermeasure network, and can achieve good effects in the field of pneumatic modeling.
And a model training step, namely training the generator and the discriminator in the neural network model constructed in the model construction step by adopting the training set obtained in the pneumatic data preprocessing step until the mean square error between the real data input into the discriminator and the generator and the generated data output by the discriminator and the generator meets a set convergence condition.
And a model verification step, namely, expanding or transforming the pneumatic data set in the pneumatic data preprocessing step, inputting the expanded or transformed pneumatic data set into the neural network model trained in the model training step for testing, and testing the prediction accuracy of the model so as to guide the modeling direction or the iterative optimization of the model.
Preferably, the aerodynamic data set may be obtained from CFD calculation software or wind tunnel tests, and subsequently it is determined which variables the design parameters and corresponding parameters in the aerodynamic data set specifically contain.
Further, the design parameters comprise Mach number, height and Reynolds number; the response parameters comprise lift coefficient, friction coefficient, resistance coefficient, pitching moment coefficient, yawing moment coefficient and rolling moment coefficient; the predetermined ratio is 8:1: 1.
Further, the number of input layer nodes of the generator is determined by the dimension of the input noise; the number of nodes of an input layer of the discriminator is determined by the dimensionality of the pneumatic data set; hidden nodes of the generator and the discriminator are determined according to a set threshold; the number of output layer nodes of the generator is the same as the dimensionality of the pneumatic data set; the number of output layer nodes of the discriminator is 1.
Correspondingly, the generator G is a fully-connected neural network and comprises an input layer, a hidden layer and an output layer; the input layer, the hidden layer and the output layer are all composed of a plurality of neurons, and the weights among the neurons are in a full-connection mode.
The discriminator D is a radial basis function neural network and comprises an input layer, a hidden layer and an output layer; the neurons of the hidden layer are radial basis hidden layers, namely the weights of the neurons between the input layer and the hidden layer are in the form of radial basis functions.
Further, the radial basis function is a Gaussian kernel function
Figure BDA0002848645080000031
Where x represents the input data, v represents the center of the radial basis function, and σ represents the width of the radial basis function.
The discriminator D is
Figure BDA0002848645080000032
Wherein, w0Representing the offset of the arbiter output node, wjRepresenting the weight between the jth hidden node of the discriminator and the output node, q representing the number of hidden nodes of the discriminator, xiRepresenting input data, vjAnd σjRespectively representing the center and width of the jth hidden node.
Preferably, the mean square error between the real data x and the generated data G (z) is 10-4Different application fields have different convergence indexes, and specific convergence conditions are set according to application scenes and industry-recognized precision/error standards.
The model training step specifically comprises the following steps:
training a discriminator, fixing the parameters of the generator according to the model
Figure BDA0002848645080000033
Training a discriminator;
training the generator, fixing the parameters of the discriminator according to the model
Figure BDA0002848645080000034
A training generator;
and repeating the training steps of the discriminator and the generator, and alternately training the discriminator and the generator until the mean square error between the real data input into the discriminator and the generator and the generated data output by the discriminator and the generator meets the set convergence condition.
Wherein D represents a discriminator, G represents a generator,
Figure BDA0002848645080000035
representing the distribution of real data, Pz(Z)Representing the distribution of random noise, D (x) representing a discriminant network, G (z) representing a generation network, LDLoss value, L, representing the discriminatorGRepresenting the loss value of the generator and equation E representing the expectation.
Compared with the prior art, the invention has the following beneficial effects:
the method introduces Radial Basis Function (RBF) in the classificator (Discriminator, D) of the classic GAN to form the Discriminator (RBF-D) based on the radial basis Function; the Generator (Generator, G) uses a fully connected neural Network (FCN), and the RBF-GAN can process a regression model and a generation model of nonlinear pneumatic data at the same time, so as to make up for the defect of insufficient pneumatic data.
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The foregoing and following detailed description of the invention will be apparent when read in conjunction with the following drawings, in which:
FIG. 1 is a diagram of a radial basis function based generative confrontation network model architecture;
fig. 2 is a flow chart of modeling a generative confrontation network based on radial basis functions.
Detailed Description
The technical solutions for achieving the objects of the present invention are further illustrated by the following specific examples, and it should be noted that the technical solutions claimed in the present invention include, but are not limited to, the following examples.
Referring to fig. 2, the embodiment discloses a pneumatic modeling generative confrontation network model training method based on the radial basis function as in fig. 1, which includes a pneumatic data preprocessing step, a model construction step, a model training step and a model verification step.
The method comprises the following steps of preprocessing pneumatic data, extracting a pneumatic data set, determining design parameters and response parameters serving as input parameters and output parameters in the pneumatic data set, filtering and screening abnormal values and missing values in the pneumatic data set, normalizing all data in the pneumatic data set, and dividing the data into a training set, a verification set and a test set according to a preset proportion;
preferably, the aerodynamic data set may be obtained from CFD calculation software or wind tunnel tests, and subsequently it is determined which variables the design parameters and corresponding parameters in the aerodynamic data set specifically contain.
Specifically, the design parameters include mach number, height and reynolds number, the response parameters include lift coefficient, friction coefficient, drag coefficient, pitch moment coefficient, yaw moment coefficient and roll moment coefficient, and the predetermined ratio is 8:1: 1.
That is, a pneumatic data set can be obtained through CFD calculation or wind tunnel test, and the main variables in the pneumatic data are extracted, including: position parameters, friction, lift, mach number, viscosity coefficient; firstly, preprocessing data including data cleaning and feature engineering, wherein abnormal values and null values exist in the data and need to be screened, meanwhile, certain transformation needs to be carried out on variables, the constructed feature variables can accelerate the optimization of a model, and then, a training set, a verification set and a test set need to be divided on the data.
And the model building step is to set the number of input layer nodes, the number of output layer nodes and the number of hidden layer nodes in a discriminator and a generator in the generation type countermeasure network based on the radial basis function according to the dimension and data volume information of the input and output pneumatic data sets determined in the pneumatic data preprocessing step, so as to build a radial basis function neural network model. The radial basis generation type countermeasure network is a novel generation type countermeasure network derivative model, is composed of a radial basis neural network and a generation type countermeasure network, and can achieve good effects in the field of pneumatic modeling.
Further, the number of input layer nodes of the generator is determined by the dimension of the input noise; the number of nodes of an input layer of the discriminator is determined by the dimensionality of the pneumatic data set; hidden nodes of the generator and the discriminator are determined according to a set threshold; the number of output layer nodes of the generator is the same as the dimensionality of the pneumatic data set; the number of output layer nodes of the discriminator is 1.
Specifically, the generator G is a fully-connected neural network, and includes an input layer, a hidden layer, and an output layer; the input layer, the hidden layer and the output layer are all composed of a plurality of neurons, and the weights among the neurons are in a full-connection mode.
The discriminator D is a radial basis function neural network and comprises an input layer, a hidden layer and an output layer; the neurons of the hidden layer are radial basis hidden layers, namely the weights of the neurons between the input layer and the hidden layer are in the form of radial basis functions.
Preferably, the radial basis function is a gaussian kernel function
Figure BDA0002848645080000051
Where x represents the input data, v represents the center of the radial basis function, and σ represents the width of the radial basis function.
Further, the discriminator D is
Figure BDA0002848645080000052
Wherein w0Representing the offset of the arbiter output node, wjRepresents the weight between the j-th hidden node and the output node of the discriminator, q represents the number of hidden nodes of the discriminator, xiRepresenting input data, vjAnd σjRespectively representing the center and width of the jth hidden node.
That is, information such as input/output dimensions and data size is obtained through the preprocessing process of the previous data. Therefore, a neural network model is preliminarily constructed, the input and output dimensions of the model are the same as those of the data set, and the complexity of the model is roughly matched with the size of the data set.
The method specifically comprises the following steps:
and in the random search, after the model is constructed, the better reference expression of the model on the data set is found by randomly searching the model parameters, so that the iterative optimization of the model is prepared.
The iterative optimization of the model is mainly a process of searching for optimal hyper-parameters, and lower training set errors and verification set errors are obtained by continuously adjusting parameters of the model and parameters of a training process, so that higher prediction accuracy can be finally obtained on a test set.
And the model training step is to train the generator and the discriminator in the neural network model constructed in the model construction step by adopting the training set obtained in the pneumatic data preprocessing step until the mean square error between the real data input into the discriminator and the generator and the generated data output by the discriminator and the generator meets the set convergence condition.
Preferably, the mean square error between the real data x and the generated data G (z) is 10-4Different application fields have different convergence indexes, and specific convergence conditions are set according to application scenes and industry-approved precision/error standards.
The model training step specifically includes the following steps:
training a discriminator, fixing the parameters of the generator according to the model
Figure BDA0002848645080000061
Training a discriminator;
training the generator, fixing the parameters of the discriminator according to the model
Figure BDA0002848645080000062
A training generator;
and repeating the training steps of the discriminator and the generator, and alternately training the discriminator and the generator until the mean square error between the real data input into the discriminator and the generator and the generated data output by the discriminator and the generator meets the set convergence condition.
Wherein D represents a discriminator, G represents a generator,
Figure BDA0002848645080000063
representing the distribution of real data, Pz(Z)Representing the distribution of random noise, D (x) representing a discriminant network, G (z) representing a generation network, LDRepresents the loss value of the discriminator, LGRepresenting the loss value of the generator and equation E representing the expectation.
And in the model verification step, the pneumatic data set in the pneumatic data preprocessing step is expanded or transformed and input to the neural network model trained in the model training step for testing, and the prediction accuracy of the model is tested, so that the modeling direction or the iterative optimization of the model is guided.
The method introduces Radial Basis Function (RBF) in the classificator (Discriminator, D) of the classic GAN to form the Discriminator (RBF-D) based on the radial basis Function; the Generator (Generator, G) uses a fully connected neural network (FCN), and the RBF-GAN can process a regression model and a generation model of nonlinear pneumatic data at the same time, so as to make up for the defect of insufficient pneumatic data.

Claims (6)

1. The method for training the pneumatic modeling generation type confrontation network model based on the radial basis function is characterized by comprising the following steps of:
the method comprises the steps of pneumatic data preprocessing, wherein a pneumatic data set is extracted, design parameters and response parameters which serve as input parameters and output parameters in the pneumatic data set are determined, abnormal values and missing values in the pneumatic data set are filtered and screened, all data in the pneumatic data set are subjected to normalization processing, and the data are divided into a training set, a verification set and a test set according to a preset proportion;
a model construction step, namely setting the number of input layer nodes, the number of output layer nodes and the number of hidden layer nodes in a discriminator and a generator in a generating type countermeasure network based on a radial basis function according to the dimension and data quantity information of the input and output pneumatic data sets determined in the pneumatic data preprocessing step, and constructing a radial basis function neural network model; the discriminator D is a radial basis function neural network and comprises an input layer, a hidden layer and an output layer; the neurons of the hidden layer are radial basis hidden layers, namely the weights of the neurons between the input layer and the hidden layer are in the form of radial basis functions, and the radial basis functions are Gaussian kernel functions
Figure FDA0003688265920000011
Wherein x represents the input data, v represents the center of the radial basis function, and σ represents the width of the radial basis function; the discriminator D is
Figure FDA0003688265920000012
Wherein, the first and the second end of the pipe are connected with each other,w0representing the offset of the arbiter output node, wjRepresents the weight between the j-th hidden node and the output node of the discriminator, q represents the number of hidden nodes of the discriminator, xiRepresenting input data, vjAnd σjRespectively representing the center and the width of a jth hidden layer node;
a model training step, in which a generator and a discriminator in the neural network model constructed in the model construction step are trained by adopting the training set obtained in the pneumatic data preprocessing step until the mean square error between real data input into the discriminator and the generator and generated data output by the discriminator and the generator meets a set convergence condition; specifically, the method comprises the following steps:
training the discriminator by fixing the parameters of the generator according to the model
Figure FDA0003688265920000013
Training a discriminator;
training the generator, fixing the parameters of the discriminator according to the model
Figure FDA0003688265920000014
A training generator;
repeating the training steps of the discriminator and the generator, and alternately training the discriminator and the generator until the mean square error between the real data input into the discriminator and the generator and the generated data output by the discriminator and the generator meets the set convergence condition;
wherein D represents a discriminator, G represents a generator, Pdata(x)Representing the distribution of real data, Pz(Z)Representing the distribution of random noise, D (x) representing a discriminant network, G (z) representing a generator network, LDRepresents the loss value of the discriminator, LGRepresents the loss value of the generator, and formula E represents the expectation
And a model verification step, namely, expanding or transforming the pneumatic data set in the pneumatic data preprocessing step, inputting the expanded or transformed pneumatic data set into the neural network model trained in the model training step for testing, and testing the prediction accuracy of the model so as to guide the modeling direction or the iterative optimization of the model.
2. The method of claim 1, wherein the method comprises: the pneumatic data set is extracted from CFD calculation software or wind tunnel tests.
3. The method of claim 1, wherein the method comprises: the design parameters comprise Mach number, height and Reynolds number; the response parameters comprise lift coefficient, friction coefficient, resistance coefficient, pitching moment coefficient, yawing moment coefficient and rolling moment coefficient; the predetermined ratio is 8:1: 1.
4. The radial basis function-based pneumatic modeling generative confrontation network model training method of claim 1, wherein: the number of input layer nodes of the generator is determined by the dimension of input noise; the number of nodes of an input layer of the discriminator is determined by the dimensionality of the pneumatic data set; hidden nodes of the generator and the discriminator are determined according to a set threshold; the number of output layer nodes of the generator is the same as the dimensionality of the pneumatic data set; the number of output layer nodes of the discriminator is 1.
5. The radial basis function-based pneumatic modeling generative confrontation network model training method according to claim 1 or 4, wherein: the generator G is a fully-connected neural network and comprises an input layer, a hidden layer and an output layer; the input layer, the hidden layer and the output layer are all composed of a plurality of neurons, and the weights among the neurons are in a full-connection mode.
6. The radial basis function-based pneumatic modeling generative confrontation network model training method of claim 1, wherein: in the model training step, the convergence condition index is that the mean square error of the real data and the generated data is 10-4。
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