Online heaven and earth data fusion method based on physical information neural network

Abstract

The invention discloses an online heaven and earth data fusion method based on a physical information neural network. The online heaven and earth data fusion method comprises the following steps: constructing a full-connection neural network model; performing physical constraint on an output value of the full-connection neural network model to obtain a physical information neural network model, and performing back propagation on an error obtained by physical constraint through a loss function; wind tunnel test data and test flight data are selected as features to be input into the physical information neural network model, the test flight data are selected as labels, heaven and earth data are fused, the data are continuously updated and input in a time domain at a given step length, and online fusion is achieved. According to the method, high-precision fusion data can be obtained through a small amount of high-precision test flight data and a large amount of low-precision test data.

Description

Technical Field

[0001] The present invention belongs to the technical field of intelligent fluid mechanics, and in particular relates to an online sky-ground data fusion method based on a physical information neural network. Background Art

[0002] In recent years, multi-source aerodynamic data fusion technology has received extensive attention in related fields due to the difficulty in obtaining ground aerodynamic data of spacecraft and the poor consistency between the ground and the sky. The academic community has developed some aerodynamic data fusion methods based on classical methods, such as weighted average method, Kalman filter method, Kriging model, etc. This type of method uses clear algebraic formulas to effectively fuse aerodynamic data from different sources. The principle is simple and clear, but it is difficult to meet the modeling requirements of high-dimensional, nonlinear, and complex data.

[0003] With the rapid development of artificial intelligence, intelligent algorithms such as fuzzy logic, support vector machines, extreme learning machines, and various neural network structures are increasingly being used in the field of unsteady aerodynamic modeling. These intelligent algorithms do not rely on prior physical cognition and can be applied to the unsteady aerodynamic modeling process of various configurations of aircraft while ensuring sufficient nonlinear mapping accuracy. However, due to the "black box" properties, researchers cannot understand the physical laws inside the model, which limits its development to a certain extent.

[0004] Physics-Informed Neural Networks (PINNs) are a type of neural network that encodes the governing equations of a problem, such as partial differential equations (PDEs), as part of the neural network, alleviating to some extent the “black box” property of traditional neural networks.

[0005] The shortcomings of the prior art are summarized as follows:

[0006] 1. The existing aerodynamic prediction methods have serious inadequacies in simulating unsteady aerodynamic forces during large-scale maneuvers, which directly affects the control accuracy.

[0007] 2. General flight data lacks active excitation and effective information, and is also affected by errors such as signal acquisition noise, making it difficult to meet the needs of high-precision aerodynamic parameter identification or correction of ground-ground data differences.

[0008] 3. Traditional neural networks have “black box” properties when used for unsteady aerodynamic modeling.

[0009] 4. Most existing modeling methods process existing data, and there is little research on online recognition of data that is being generated. Summary of the invention

[0010] In view of the above-mentioned deficiencies in the prior art, the purpose of the present invention is to provide an online space-ground data fusion method based on physical information neural network to solve the problems in the prior art of mismatch between wind tunnel test data and flight test data and difficulty in online identification of flight test data.

[0011] To achieve the above object, the technical solution adopted by the present invention is as follows:

[0012] The present invention provides an online space-ground data fusion method based on a physical information neural network, comprising the following steps:

[0013] 1) Build a fully connected neural network model;

[0014] 2) Physically constrain the output value of the fully connected neural network model through the flight dynamics equation to obtain a physical information neural network model, and back-propagate the error obtained by the physical constraint through the loss function Smooth_L1;

[0015] 3) Select wind tunnel test data with x1 dimensions and flight test data with x2 dimensions as feature inputs to the physical information neural network model, 1≤x1 and x1∈N + , 1≤x2 and x2∈N + ; Select y dimensions of test flight data as labels, 1≤y≤6 and y∈N + ,Fusing the sky and earth data, the data is continuously updated in the time domain with a given step size to achieve online fusion.

[0016] Furthermore, the step 1) specifically includes:

[0017] 11) Construct the input layer, hidden layer, and output layer of the fully connected neural network model; the number of neurons in the input layer is x1+x2, and the hidden layer has M layers, with the number of neurons being n1, n2, n3,…, n respectively. M , M and n are adjustable hyperparameters, and the number of neurons in the output layer is y;

[0018] 12) Each neuron in the fully connected neural network model processes input through a weighted sum operation and a nonlinear activation function and generates output. Assuming that the current fully connected layer is the lth layer of the fully connected neural network model, the calculation formula of the neuron is expressed as:

[0019]

[0020] In the formula, is the weighted sum of the jth neuron in the lth layer, s l-1 is the number of neurons in the l-1th layer, is the weight from the i-th neuron in the l-1th layer to the j-th neuron in the lth layer, is the output of the i-th neuron in the l-1th layer, is the bias term of the jth neuron in the lth layer;

[0021] 13) The weighted sum is passed through a nonlinear activation function to produce the final output, which is expressed as follows:

[0022]

[0023] In the formula, is the output of the jth neuron in the lth layer, f is the activation function, and the activation function is the Sigmoid function, the hyperbolic tangent function, or the ReLU function.

[0024] Furthermore, the step 2) specifically includes:

[0025] 21) The output value of the fully connected neural network model is physically constrained by the six-degree-of-freedom flight dynamics equation, so that it converges to the label data under the constraint of boundary conditions, thereby obtaining a physical information neural network model. The physical constraint expression is:

[0026]

[0027]

[0028] c5=(I z -I x ) / I y

[0029] c6=I xz / I y

[0030] c7=1 / I y

[0031]

[0032] Where, f1, f2, f3, f4, f5, f6 are the residuals of the six constraint equations; p, q, r are the roll angular velocity, pitch angular velocity, and yaw angular velocity respectively; V xb ,V yb ,V zb They are the X-axis speed, Y-axis speed, and Z-axis speed in the body coordinate system respectively; is the air dynamic pressure; S is the reference area; m is the body mass; g is the gravity coefficient; θ is the pitch angle; φ is the roll angle; a x ,a y ,a z are the X-axis acceleration, Y-axis acceleration, and Z-axis acceleration in the body coordinate system; dp, dq, and dr are the roll angular acceleration, pitch angular acceleration, and yaw angular acceleration, respectively; C X ,C Y ,CZ They are respectively the X-axis prediction force coefficient, the Y-axis prediction force coefficient, and the Z-axis prediction force coefficient; C l ,C m ,C n They are respectively the roll prediction moment coefficient, the pitch prediction moment coefficient, and the yaw prediction moment coefficient, I xz is the product of inertia between the X-axis and the Z-axis, I x ,I y ,I z They are the X-axis moment of inertia, the Y-axis moment of inertia, and the Z-axis moment of inertia;

[0033] 22) The error obtained by the physical constraint is converged to 0 through the loss function Smooth_L1, and the expression is as follows:

[0034]

[0035] Where, L i is the sum of errors of the i-th loss function, N is the amount of data for each feature, Δ i is f in step 21) i ,i=1,2,…,6;

[0036] 23) The six loss functions of the physical information neural network model are integrated into a total loss function using the linear weighted superposition method, and the error is back-propagated. The expression is as follows:

[0037]

[0038] In the formula, Loss i is the total loss of the updated data in the i-th batch, β1, β2, β3, β4, β5, β6 are the weighted values ​​of the loss in the six dimensions respectively, Update the loss of data for the i-th batch in six dimensions respectively.

[0039] Furthermore, the step 3) specifically includes:

[0040] 31) Use normal distribution to normalize the data values ​​of each dimension to eliminate the adverse effects caused by singular sample data. The expression is:

[0041]

[0042] In the formula, x′ ij is the jth data point of the normalized i-th dimension feature, x ij is the jth data point of the i-th dimension feature before normalization, μ i is the mean of the i-th feature, σ i is the standard deviation of the i-th feature, and n is the number of data points for each feature;

[0043] 32) The normalized feature data is input into the physical information neural network model, and the stochastic gradient descent method is used to make the output value gradually approach the label data during continuous training. The label data is the aerodynamic parameters of the test flight data. That is, by correcting the wind tunnel test data in the feature, the output value of the physical information neural network model is close to the aerodynamic parameters of the test flight data, thereby realizing the fusion of ground and space data; the expression is:

[0044]

[0045] In the formula, θ is the parameter of the physical information neural network model, η is the learning rate, which is used to control the update step size. is the gradient of the loss function J(θ) with respect to the parameter θ, (x j ,y j ) is a sample randomly selected from all training samples;

[0046] 33) Realize online identification in the entire time domain, set the aerodynamic identification step value to s, so that each feature continuously updates s input data under the movement of the aerodynamic identification step, the expression is as follows:

[0047] Input i ={[R1 i ,R2 i ,...,R 16 i ],...,[R1 i+S R2 i+s ,...,R 16 i+s ]},i=0,1,2,..n

[0048] In the formula, R1, R2, …, R 16 is the feature data of each dimension. When the data volume of each dimension is greater than / equal to s, online identification starts. i is the update batch of training data, and n is equal to the input data volume of each dimension minus the aerodynamic identification step value s.

[0049] Beneficial effects of the present invention:

[0050] 1. The method of the present invention can obtain high-precision fusion data through a small amount of high-precision test flight data and a large amount of low-precision test data.

[0051] 2. In the present invention, the six-degree-of-freedom dynamic equation of flight mechanics is used as the physical constraint, which reduces the "black box" property of the neural network to a certain extent and enhances the interpretability of the fused data.

[0052] 3. The present invention performs online identification and data fusion in the entire time domain, and by giving an initial step length, points whose number is greater than the initial step length can be fitted individually, thereby improving the accuracy of data fusion. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 Schematic diagram of the method of the present invention. DETAILED DESCRIPTION

[0054] In order to facilitate the understanding of those skilled in the art, the present invention is further described below in conjunction with embodiments and drawings. The contents mentioned in the implementation modes are not intended to limit the present invention.

[0055] Reference Figure 1 As shown, an online space-ground data fusion method based on physical information neural network of the present invention comprises the following steps:

[0056] 1) Construct a fully connected neural network model; specifically including:

[0057] 11) Construct the input layer, hidden layer, and output layer of the fully connected neural network model; the number of neurons in the input layer is x1+x2, and the hidden layer has M layers, with the number of neurons being n1, n2, n3,…, n respectively. M , M and n are adjustable hyperparameters, and the number of neurons in the output layer is y;

[0058] 12) Each neuron in the fully connected neural network model processes input through a weighted sum operation and a nonlinear activation function and generates output. Assuming that the current fully connected layer is the lth layer of the fully connected neural network model, the calculation formula of the neuron is expressed as:

[0059]

[0060] In the formula, is the weighted sum of the jth neuron in the lth layer, s l-1 is the number of neurons in the l-1th layer, is the weight from the i-th neuron in the l-1th layer to the j-th neuron in the lth layer, is the output of the i-th neuron in the l-1th layer, is the bias term of the jth neuron in the lth layer;

[0061] 13) The weighted sum is passed through a nonlinear activation function to produce the final output, which is expressed as follows:

[0062]

[0063] In the formula, is the output of the jth neuron in the lth layer, f is the activation function, and the activation function is the Sigmoid function, the hyperbolic tangent function, or the ReLU function.

[0064] 2) Physically constrain the output value of the fully connected neural network model through the flight dynamics equation to obtain a physical information neural network model, and back-propagate the error obtained by the physical constraint through the loss function Smooth_L1; specifically,

[0065] 21) The output value of the fully connected neural network model is physically constrained by the six-degree-of-freedom flight dynamics equation, so that it converges to the label data under the constraint of boundary conditions, thereby obtaining a physical information neural network model. The physical constraint expression is:

[0066]

[0067]

[0068] c5=(I z -I x ) / I y

[0069] c6=I xz / I y

[0070] c7=1 / I y

[0071]

[0072] Where, f1, f2, f3, f4, f5, f6 are the residuals of the six constraint equations; p, q, r are the roll angular velocity, pitch angular velocity, and yaw angular velocity respectively; V xb ,V yb ,V zb are the X-axis velocity, Y-axis velocity, and Z-axis velocity in the body coordinate system respectively; q is the air dynamic pressure; S is the reference area; m is the body mass; g is the gravity coefficient; θ is the pitch angle; φ is the roll angle; a x ,a y ,a z are the X-axis acceleration, Y-axis acceleration, and Z-axis acceleration in the body coordinate system; dp, dq, and dr are the roll angular acceleration, pitch angular acceleration, and yaw angular acceleration, respectively; C X ,C Y ,C Z They are respectively the X-axis prediction force coefficient, the Y-axis prediction force coefficient, and the Z-axis prediction force coefficient; C l ,C m ,C n They are respectively the roll prediction moment coefficient, the pitch prediction moment coefficient, and the yaw prediction moment coefficient, I xz is the product of inertia between the X-axis and the Z-axis, I x ,I y ,I zThey are the X-axis moment of inertia, the Y-axis moment of inertia, and the Z-axis moment of inertia;

[0073] 22) The error obtained by the physical constraint is converged to 0 through the loss function Smooth_L1, and the expression is as follows:

[0074]

[0075] Where, L i is the sum of errors of the i-th loss function, N is the amount of data for each feature, Δ i is f in step 21) i ,i=1,2,…,6;

[0076] 23) The six loss functions of the physical information neural network model are integrated into a total loss function using the linear weighted superposition method, and the error is back-propagated. The expression is as follows:

[0077]

[0078] In the formula, Loss i is the total loss of the updated data in the i-th batch, β1, β2, β3, β4, β5, β6 are the weighted values ​​of the loss in the six dimensions respectively, Update the loss of data for the i-th batch in six dimensions respectively.

[0079] 3) Select the trajectory parameters of the wind tunnel test data with x1 dimensions and the flight test data with x2 dimensions as the feature input physical information neural network model, 1≤x1 and x1∈N + , 1≤x2 and x2∈N + , N + is a positive integer; the aerodynamic parameters of the flight test data in y dimensions are selected as labels, 1≤y≤6 and y∈N + , integrating the earth and sky data, the data is continuously updated in the time domain with a given step size to achieve online fusion; specifically including:

[0080] 31) Use normal distribution to normalize the data values ​​of each dimension to eliminate the adverse effects caused by singular sample data. The expression is:

[0081]

[0082] In the formula, x′ ij is the jth data point of the normalized i-th dimension feature, x ij is the jth data point of the i-th dimension feature before normalization, μ i is the mean of the i-th feature, σ i is the standard deviation of the i-th feature, and n is the number of data points for each feature;

[0083] 32) The normalized feature data is input into the physical information neural network model, and the stochastic gradient descent method is used to make the output value gradually approach the label data during continuous training. The label data is the aerodynamic parameters of the test flight data. That is, by correcting the wind tunnel test data in the feature, the output value of the physical information neural network model is close to the aerodynamic parameters of the test flight data, thereby realizing the fusion of ground and space data; the expression is:

[0084]

[0085] In the formula, θ is the parameter of the physical information neural network model, η is the learning rate, which is used to control the update step size. is the gradient of the loss function J(θ) with respect to the parameter θ, (x j ,y j ) is a sample randomly selected from all training samples;

[0086] 33) Realize online identification in the entire time domain, set the aerodynamic identification step value to s, so that each feature continuously updates s input data under the movement of the aerodynamic identification step, the expression is as follows:

[0087] Input i ={[R1 i ,R2 i ,...,R 16 i ],...,[R1 i+S R2 i+s ,..,R 16 i+s ]}, i = 0, 1, 2, .. n

[0088] In the formula, R1, R2, …, R 16 is the feature data of each dimension. When the data volume of each dimension is greater than / equal to s, online identification starts. i is the update batch of training data, and n is equal to the input data volume of each dimension minus the aerodynamic identification step value s.

[0089] The present invention has many specific application paths. The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements can be made without departing from the principle of the present invention. These improvements should also be regarded as the protection scope of the present invention.

Claims

1. An online space-ground data fusion method based on physical information neural network, characterized in that: Here are the steps: 1) Build a fully connected neural network model; 2) Physically constrain the output value of the fully connected neural network model to obtain a physical information neural network model, and back-propagate the error obtained by the physical constraint; 3) Select wind tunnel test data with x1 dimensions and flight test data with x2 dimensions as feature inputs to the physical information neural network model, 1≤x1 and x1∈N + , 1≤x2 and x2∈N + ; Select y dimensions of test flight data as labels, 1≤y≤6 and y∈N + ,Fusing the sky and earth data, the data is continuously updated in the time domain with a given step size to achieve online fusion.

2. The online space-ground data fusion method based on physical information neural network according to claim 1 is characterized in that: The step 1) specifically includes: 11) Construct the input layer, hidden layer, and output layer of the fully connected neural network model; the number of neurons in the input layer is x1+x2, and the hidden layer has M layers, with the number of neurons being n1, n2, n3,…, n respectively. M , M and n are adjustable hyperparameters, and the number of neurons in the output layer is y; 12) Each neuron in the fully connected neural network model processes input through a weighted sum operation and a nonlinear activation function and generates output. Assuming that the current fully connected layer is the lth layer of the fully connected neural network model, the calculation formula of the neuron is expressed as: In the formula, is the weighted sum of the jth neuron in the lth layer, s l-1 is the number of neurons in the l-1th layer, is the weight from the i-th neuron in the l-1th layer to the j-th neuron in the lth layer, is the output of the i-th neuron in the l-1th layer, is the bias term of the jth neuron in the lth layer; 13) The weighted sum is passed through a nonlinear activation function to produce the final output, which is expressed as follows: In the formula, is the output of the jth neuron in the lth layer, f is the activation function, and the activation function is the Sigmoid function, the hyperbolic tangent function, or the ReLU function.

3. The online space-ground data fusion method based on physical information neural network according to claim 1 is characterized in that: The step 2) specifically includes: 21) The output value of the fully connected neural network model is physically constrained by the six-degree-of-freedom flight dynamics equation, so that it converges to the label data under the constraint of boundary conditions, thereby obtaining a physical information neural network model. The physical constraint expression is: c5=(I z -I x ) / I y c6=I xz / I y c7=1 / I y Where, f1, f2, f3, f4, f5, f6 are the residuals of the six constraint equations; p, q, r are the roll angular velocity, pitch angular velocity, and yaw angular velocity respectively; V xb ,V yb ,V zb They are the X-axis speed, Y-axis speed, and Z-axis speed in the body coordinate system respectively; is the air dynamic pressure; S is the reference area; m is the body mass; g is the gravity coefficient; θ is the pitch angle; φ is the roll angle; a x ,a y ,a z are the X-axis acceleration, Y-axis acceleration, and Z-axis acceleration in the body coordinate system; dp, dq, and dr are the roll angular acceleration, pitch angular acceleration, and yaw angular acceleration, respectively; C X ,C Y ,C Z They are respectively the X-axis prediction force coefficient, the Y-axis prediction force coefficient, and the Z-axis prediction force coefficient; C l ,C m ,C n They are respectively the roll prediction moment coefficient, the pitch prediction moment coefficient, and the yaw prediction moment coefficient, I xz is the product of inertia between the X-axis and the Z-axis, I x ,I y ,I z They are the X-axis moment of inertia, the Y-axis moment of inertia, and the Z-axis moment of inertia; 22) The error obtained by the physical constraint is converged to 0 through the loss function Smooth_L1, and the expression is as follows: Where, L i is the sum of errors of the i-th loss function, N is the amount of data for each feature, Δ i is f in step 21) i ,i=1,2,…,6; 23) The six loss functions of the physical information neural network model are integrated into a total loss function using the linear weighted superposition method, and the error is back-propagated. The expression is as follows: In the formula, Loss i is the total loss of the updated data for the i-th batch, β1, β2, β3, β4, β5, β6 are the loss weighted values ​​of the six dimensions respectively, Update the loss of data for the i-th batch in six dimensions respectively.

4. The online space-ground data fusion method based on physical information neural network according to claim 1 is characterized in that: The step 3) specifically includes: 31) Use normal distribution to normalize the data values ​​of each dimension to eliminate the adverse effects caused by singular sample data. The expression is: In the formula, x′ ij is the jth data point of the normalized i-th dimension feature, x ij is the jth data point of the i-th dimension feature before normalization, μ i is the mean of the i-th feature, σ i is the standard deviation of the i-th feature, and n is the number of data points for each feature; 32) The normalized feature data is input into the physical information neural network model, and the stochastic gradient descent method is used to make the output value gradually approach the label data during continuous training. The label data is the aerodynamic parameters of the test flight data. That is, by correcting the wind tunnel test data in the feature, the output value of the physical information neural network model is close to the aerodynamic parameters of the test flight data, thereby realizing the fusion of ground and space data; the expression is: In the formula, θ is the parameter of the physical information neural network model, η is the learning rate, is the gradient of the loss function J(θ) with respect to the parameter θ, (x j ,y j ) is a sample randomly selected from all training samples; 33) Realize online identification in the entire time domain, set the aerodynamic identification step value to s, so that each feature continuously updates s input data under the movement of the aerodynamic identification step, the expression is as follows: Input i ={[R1 i ,R2 i ,…,R 16 i ],…,[R1 i+s ,R2 i+s ,…,R 16 i+s ]},i=0,1,2,..n In the formula, R1, R2, …, R 16 is the feature data of each dimension. When the data volume of each dimension is greater than / equal to s, online identification starts. i is the update batch of training data, and n is equal to the input data volume of each dimension minus the aerodynamic identification step value s.

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