CN115951585B - Hypersonic aircraft reentry guidance method based on deep neural network - Google Patents
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Abstract
Embodiments of the present disclosure provide a depth-based godThe network hypersonic aircraft reentry guidance method belongs to the technical field of control, and specifically comprises the following steps: determining the input quantity of the deep neural network and simultaneously determining the inclination angle amplitude profile parameters
Determining a deep neural network structure by adopting a 5-fold cross validation method for output quantity, and training the deep neural network by using training data generated based on a prediction correction method; the trained deep neural network output quantity
The longitudinal guidance is completed by bringing the inclination angle amplitude section into cooperation with three process constraints of heat flow rate, overload and dynamic pressure and quasi-equilibrium gliding condition constraint; and determining a tilting angle sign based on the deviation of the course angle and the line of sight angle, and completing transverse guidance. By the scheme, the depth neural network can be predicted by utilizing the characteristic that the depth neural network can approximate any nonlinear mapping
As a longitudinal guidance main body, the calculation efficiency, the precision and the stability of guidance instructions of reentry guidance of the hypersonic aircraft are improved.
Description
Technical Field
The embodiment of the disclosure relates to the technical field of control, in particular to a hypersonic aircraft reentry guidance method based on a deep neural network.
Background
The guidance technology is one of core technologies for controlling reentry flight of hypersonic aircrafts, and has important influence on realizing stable flight of reentry sections and reaching a desired terminal state. The hypersonic aircraft reentry guidance aims to safely guide the hypersonic aircraft from the reentry initial state to a certain designated area without violating a plurality of process constraints. The common reentry guidance method can be divided into a nominal track guidance method and a predictive correction guidance method. The nominal track guidance method is used for completing guidance tasks by tracking pre-designed nominal tracks meeting various constraint conditions, has the advantages of small calculated amount and high instantaneity, but has insufficient autonomy to tasks and adaptability and robustness to complex environments, so that the actual track deviates from the pre-designed nominal track after the aircraft is affected by unpredictable disturbance in the flight process. The predictive correction guidance method is used for completing a guidance task by predicting a landing point or a voyage and correcting a track control quantity in real time, is not dependent on a pre-designed reference track and track tracking method, has higher autonomy of the task, but needs to carry out numerical integration on a motion equation for a plurality of times, and has higher requirements on the calculation and storage capacity of an missile-borne computer.
With the breakthrough of the performance of computer hardware and the continuous development of high-efficiency algorithms, a new generation of artificial intelligence technology represented by machine learning has a strong application potential in the field of guidance control. Compared with the traditional technology, the artificial intelligence has obvious advantages in the aspects of calculation precision, efficiency and the like. Many students utilize artificial intelligence technology to carry out a lot of improvement to traditional reentry guidance method, literature "reentry aircraft guidance method based on Q-Learning algorithm" is to reentry aircraft guidance method need according to the problem that the manual experience adjustment parameter can adapt to different distance and near, azimuth target points, put forward the concept of "intelligent prediction correction guidance", construct the flight environment as the state space that contains tens of millions of magnitude state points, adopt reinforcement Learning algorithm training guidance model parameter, vertical guidance still adopts the roll angle iteration method based on fixed attack angle section, horizontal guidance is then utilized Q-Learning algorithm training horizontal flip decision maker. Aiming at the fault-tolerant guidance problem of the hypersonic aircraft under the fault condition, the document hypersonic aircraft reentry prediction correction fault-tolerant guidance based on deep learning constructs an extended state observer to estimate the variation of aerodynamic parameters, inputs the variation into a deep neural network in real time, and then trains the deep neural network to predict landing points so as to avoid a large amount of integral operation in a prediction correction guidance algorithm. The document hypersonic aircraft reentry prediction guidance based on a self-adaptive neural fuzzy system proposes a reentry prediction correction guidance algorithm based on a self-adaptive neural fuzzy system (AN-FIS), longitudinal guidance mainly comprises a prediction link and AN ANFIS controller, the prediction link obtains terminal landing point deviation information through prediction calculation, the ANFIS controller adjusts the value of the camber angle according to the deviation information and related parameters, circulates until the landing point deviation is within a preset range, and then outputs corrected camber angle values. According to the reentry prediction correction guidance method based on the BP neural network prediction course, the BP neural network is trained to fit with a prediction link in a prediction correction algorithm, the BP neural network outputs the course to be flown, and then a secant method iteration of the correction link is performed, so that a certain numerical operation process is reduced.
However, the existing method aims at the reentry guidance problem, and the main body of the longitudinal guidance still comprises a prediction correction process, so that the numerical integration or iteration process is unavoidable, and the guidance instruction calculation efficiency still has room for improvement. Therefore, a high-efficiency, accurate and stable hypersonic speed aircraft reentry guidance method based on a deep neural network is needed.
Disclosure of Invention
In view of the above, embodiments of the present disclosure provide a hypersonic aircraft reentry guidance method based on a deep neural network, and the application of the method can effectively solve the problem in the prior art that guidance instruction calculation efficiency, accuracy and stability are poor
In a first aspect, an embodiment of the present disclosure provides a hypersonic vehicle reentry guidance method based on a deep neural network, including:
step 1, establishing a hypersonic aircraft reentry section three-degree-of-freedom mass center motion model to obtain normalized energy
Determining the input quantity of the depth neural network according to factors affecting the roll angle amplitude as an independent variable motion equation, and simultaneously determining the roll angle amplitude profile parameters
Presetting a plurality of deep neural networks with different network structures for output quantity, determining the deep neural network structure by adopting a 5-fold cross validation method, and training the deep neural network by using training data generated based on a prediction correction method, wherein the expression of the motion equation is
wherein ,
for longitudinal plane voyage->
Is earth sea level gravitational acceleration->
Is round in earth radius>
For aircraft mass>
For tilting angle>
Normalized energy;
step 2, presetting reentry terminal information, obtaining the input quantity of the trained deep neural network according to the flight state quantity at the current moment, and outputting the trained deep neural network
Bringing a section of the tilting angle amplitude, and obtaining the tilting angle amplitude by matching with three process constraints of heat flow rate, overload and dynamic pressure and the constraint of quasi-equilibrium gliding conditions to finish longitudinal guidance;
the step 2 specifically includes:
step 2.1, presetting reentry terminal information, and obtainingThe re-entry terminal information includes terminal point height
Speed of end point
Target point longitude->
Target point latitude->
Residual course of the terminal point from the target point +.>
Setting a guidance period
；
Step 2.2, obtaining the flying state quantity at any moment in the flying process through measurement and calculation, wherein the flying state quantity comprises the ground center distance
Speed->
Longitude->
Latitude->
Track angle->
Course angle->
；
Step 2.3, from the reentry initiation time
Initially, every interval time +.>
Obtaining an input quantity of the deep neural network based on the current time flight state quantity +. >
, wherein ,
for the difference between the current time height and the end point height,
For the difference between the current time speed and the terminal point speed, < >>
Is a circular shape of the radius of the earth,
obtaining a roll angle amplitude profile parameter +.>
；
Step 2.4, each time during the flight
Based on the roll angle amplitude profile parameter +.>
Obtaining the current moment roll angle amplitude +.>
The calculation formula is as follows:
wherein ,
the energy is normalized for the current moment of time,
normalizing the energy for the re-entry of the initial moment +.>
Normalizing energy for re-entry termination point, +.>
For preset parameters +.>
To reenter the initial moment ground centre distance +.>
For re-entering the initial time speed +.>
Is the gravitational acceleration of the earth sea level;
and step 3, determining a roll angle sign based on the deviation of the course angle and the sight angle, and finishing transverse guidance.
According to a specific implementation manner of the embodiment of the present disclosure, the step 1 specifically includes:
step 1.1, comprehensively considering factors influencing the roll angle amplitude, and selecting the input quantity of the deep neural network as
The output of the deep neural network is the roll angle amplitude profile parameter +.>
, wherein ,
For distance between the earth and heart, add>
Longitude->
Latitude,>
for speed->
For the track angle>
In order to be the heading angle,
for the current time height +>
Height from end point->
Is used for the difference in (a),
for the current time speed +.>
Speed +.>
Is used for the difference in (a),
the remaining range of the current time position from the target point;
step 1.2, presetting a plurality of deep neural networks with different network structures, and evaluating the advantages and disadvantages of the different network structures by using a 5-fold cross validation method, wherein the specific flow is as follows: randomly dividing training samples into 5 parts, sequentially taking the 5 parts of training samples as verification samples, taking the rest 4 parts of training samples as training samples to train a deep neural network with a preset network structure, recording training loss and verification loss after each training, and finally calculating the average value of the training loss and the verification loss as an evaluation standard of the network structure;
step 1.3, according to the result of 5-fold cross validation, selecting a network structure with minimum training loss and validation loss under the condition that the complexity of the network structure accords with a preset condition as a deep neural network, wherein the deep neural network structure is a forward feedback neural network, the forward feedback neural network comprises an input layer, a plurality of hidden layers and an output layer which are sequentially connected, each hidden layer comprises a plurality of neurons, and an activation function of the neurons in the hidden layers uses the following hyperbolic tangent Tanh function:
And step 1.4, training the deep neural network by adopting the deep neural network structure determined by the step, and using all training data generated based on a prediction correction method.
According to a specific implementation manner of the embodiment of the present disclosure, the step 2 specifically further includes:
limiting roll angle magnitude by thermal flow rate, overload and dynamic pressure process constraints, and quasi-equilibrium glide condition constraints
At->
And if the distance exceeds the range, taking an interval extreme value, and ending the longitudinal guidance.
According to a specific implementation manner of the embodiment of the present disclosure, the step 3 specifically includes:
step 3.1, based on the target point longitude
Target point latitude->
Longitude +.>
And the latitude at the current moment
Calculating the sight angle of the aircraft and the target point at the current moment>
The calculation formula is as follows:
step 3.2, from the current moment line of sight angle
And heading angle->
Calculating the deviation between the course angle and the line of sight angle, namely, the transverse guidance control quantity is +.>
；
Step 3.3, designing a transverse guidance control quantity corridor, wherein the upper boundary of the corridor
And lower border->
The calculation formulas of (a) are respectively as follows:
wherein ,
the parameters are preset;
step 3.4, the deviation between the required course angle and the line of sight angle in the flying process is between the upper and lower boundaries of the corridor of the transverse guidance control quantity, and when the deviation exceeds the upper or lower boundary of the corridor from within the corridor, the sign of the tilting angle is reversed, namely 
And ending the transverse guidance.
The hypersonic aircraft reentry guidance scheme based on the deep neural network in the embodiment of the disclosure comprises: step 1, establishing a hypersonic aircraft reentry section three-degree-of-freedom mass center motion model to obtain normalized energy
Determining the input quantity of the depth neural network according to factors affecting the roll angle amplitude as an independent variable of a motion equation, and simultaneously determining the roll angle amplitude profile parameter +.>
Presetting a plurality of deep neural networks with different network structures for output quantity, determining the deep neural network structure by adopting a 5-fold cross validation method, and training the deep neural network by using training data generated based on a prediction correction method; step 2, presetting reentry terminal information, obtaining the input quantity of the trained deep neural network according to the flight state quantity at the current moment, and obtaining the output quantity of the trained deep neural network +.>
Bringing a section of the tilting angle amplitude, and obtaining the tilting angle amplitude by matching with three process constraints of heat flow rate, overload and dynamic pressure and the constraint of quasi-equilibrium gliding conditions to finish longitudinal guidance; and step 3, determining a roll angle sign based on the deviation of the course angle and the sight angle, and finishing transverse guidance.
The beneficial effects of the embodiment of the disclosure are that: according to the scheme, in longitudinal guidance, the deep neural network is trained offline based on the track data set data generated by the prediction correction guidance method, the tilting angle amplitude is directly obtained by the deep neural network in cooperation with the tilting angle amplitude profile, the deep neural network is used as a main algorithm of longitudinal guidance instead of an auxiliary tool, the numerical integration and iteration process of the prediction correction guidance method are avoided, the calculation time of guidance instructions is effectively shortened, and the real-time performance of the algorithm is improved; the track data set generated by the prediction correction guidance method trains the deep neural network, so that the advantage that the prediction correction guidance method can adapt to complex task distribution is reserved, the parameter information of the deep neural network is distributed and stored in neurons in the network, and when the input information or the network has limited perturbation, the deep neural network can still keep a normal input-output mapping relation, so that the method has the advantage of strong robustness, and the coping capability of the guidance method to complex multisource uncertainty of an aircraft body and a flight environment is enhanced.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present disclosure, the drawings that are needed in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present disclosure, and other drawings may be obtained according to these drawings without inventive effort to a person of ordinary skill in the art.
Fig. 1 is a schematic flow chart of a hypersonic aircraft reentry guidance method based on a deep neural network according to an embodiment of the disclosure;
FIG. 2 is a flowchart of a guidance method based on a deep neural network for a reentry segment according to an embodiment of the present disclosure;
FIG. 3 is a flowchart of a method for reentry segment predictive correction guidance according to an embodiment of the present disclosure;
FIG. 4 is a schematic view of an angle of attack-velocity profile provided by an embodiment of the present disclosure;
FIG. 5 is a heading angle deviation corridor design diagram provided by an embodiment of the present disclosure;
FIG. 6 is a block diagram of a deep neural network according to an embodiment of the present disclosure;
FIG. 7 is a histogram of absolute error between a deep neural network output and a test sample provided by an embodiment of the present disclosure;
fig. 8 is a longitude and latitude distribution diagram of a monte carlo simulation terminal point according to an embodiment of the present disclosure.
Detailed Description
Embodiments of the present disclosure are described in detail below with reference to the accompanying drawings.
Other advantages and effects of the present disclosure will become readily apparent to those skilled in the art from the following disclosure, which describes embodiments of the present disclosure by way of specific examples. It will be apparent that the described embodiments are merely some, but not all embodiments of the present disclosure. The disclosure may be embodied or practiced in other different specific embodiments, and details within the subject specification may be modified or changed from various points of view and applications without departing from the spirit of the disclosure. It should be noted that the following embodiments and features in the embodiments may be combined with each other without conflict. All other embodiments, which can be made by one of ordinary skill in the art without inventive effort, based on the embodiments in this disclosure are intended to be within the scope of this disclosure.
It is noted that various aspects of the embodiments are described below within the scope of the following claims. It should be apparent that the aspects described herein may be embodied in a wide variety of forms and that any specific structure and/or function described herein is merely illustrative. Based on the present disclosure, one skilled in the art will appreciate that one aspect described herein may be implemented independently of any other aspect, and that two or more of these aspects may be combined in various ways. For example, an apparatus may be implemented and/or a method practiced using any number of the aspects set forth herein. In addition, such apparatus may be implemented and/or such methods practiced using other structure and/or functionality in addition to one or more of the aspects set forth herein.
It should also be noted that the illustrations provided in the following embodiments merely illustrate the basic concepts of the disclosure by way of illustration, and only the components related to the disclosure are shown in the drawings and are not drawn according to the number, shape and size of the components in actual implementation, and the form, number and proportion of the components in actual implementation may be arbitrarily changed, and the layout of the components may be more complicated.
In addition, in the following description, specific details are provided in order to provide a thorough understanding of the examples. However, it will be understood by those skilled in the art that the aspects may be practiced without these specific details.
The embodiment of the disclosure provides a hypersonic aircraft reentry guidance method based on a deep neural network, which can be applied to hypersonic aircraft reentry flight control process of an aerospace scene.
Referring to fig. 1, a schematic flow chart of a hypersonic aircraft reentry guidance method based on a deep neural network is provided in an embodiment of the disclosure. As shown in fig. 1 and 2, the method mainly comprises the following steps:
step 1, establishing a hypersonic aircraft reentry section three-degree-of-freedom mass center motion model to obtain normalized energy 
Determining the input quantity of the depth neural network according to factors affecting the roll angle amplitude as an independent variable of a motion equation, and simultaneously determining the roll angle amplitude profile parameter +.>
Presetting a plurality of deep neural networks with different network structures for output quantity, determining the deep neural network structure by adopting a 5-fold cross validation method, and training the deep neural network by using training data generated based on a prediction correction method;
further, the step 1 specifically includes:
step 1.1, establishing a hypersonic aircraft reentry section three-degree-of-freedom mass center motion model to obtain normalized energy
An equation of motion being an argument, wherein the equation of motion has an expression +.>
wherein ,
for longitudinal plane voyage->
Is earth sea level gravitational acceleration->
Is a circular shape of the radius of the earth,
for aircraft mass>
For tilting angle>
Normalized energy;
further, the step 1 specifically includes:
step 1.1, comprehensively considering factors influencing the roll angle amplitude, and selecting the input quantity of the deep neural network as
The output of the deep neural network is the roll angle amplitude profile parameter +.>
, wherein ,
For distance between the earth and heart, add>
Longitude->
Latitude,>
for speed->
For the track angle >
In order to be the heading angle,
for the current time height +>
Height from end point->
Is used for the difference in (a),
for the current time speed +.>
Speed +.>
Is used for the difference in (a),
the remaining range of the current time position from the target point;
step 1.2, presetting a plurality of deep neural networks with different network structures, and evaluating the advantages and disadvantages of the different network structures by using a 5-fold cross validation method, wherein the specific flow is as follows: randomly dividing training samples into 5 parts, sequentially taking the 5 parts of training samples as verification samples, taking the rest 4 parts of training samples as training samples to train a deep neural network with a preset network structure, recording training loss and verification loss after each training, and finally calculating the average value of the training loss and the verification loss as an evaluation standard of the network structure;
step 1.3, according to the result of 5-fold cross validation, selecting a network structure with minimum training loss and validation loss under the condition that the complexity of the network structure accords with a preset condition as a deep neural network, wherein the deep neural network structure is a forward feedback neural network, the forward feedback neural network comprises an input layer, a plurality of hidden layers and an output layer which are sequentially connected, each hidden layer comprises a plurality of neurons, and an activation function of the neurons in the hidden layers uses the following hyperbolic tangent Tanh function:
And step 1.4, training the deep neural network by adopting the deep neural network structure determined by the step, and using all training data generated based on a prediction correction method.
Can take a general aviation aircraft CAV-H as a research object to establish the three-degree-of-freedom centroid of the reentry section of the hypersonic aircraftMotion model, get time
The equation of motion as an argument is as follows:
in the formula (1), the calculation formulas of the lift force L and the drag force D are:
in the formula (2), the amino acid sequence of the compound,
air density for the altitude of the aircraft, +.>
Is the feature area.
and
The lift coefficient and drag coefficient are respectively, generally, functions of attack angle and speed of the aircraft, and are specific to the working condition of the embodiment:
the stop condition of reentry guidance is that energy stops when reaching the energy value set by the terminal, so that the integration by taking the energy as an independent variable is convenient, and the independent variable conversion is carried out on the formula (1). The normalized energy can be calculated as follows:
the normalized energy can be obtained by differentiating the formula (4) and substituting the derivative into the formula (1)
Equation of motion as an independent variable, equation (11). />
In order to ensure that hypersonic aircraft successfully completes the reentry mission, the aircraft is required to meet various condition constraints, including terminal constraints, reentry process constraints, quasi-equilibrium glide condition constraints, and roll angle control constraints, for the core.
Reentry flight terminal constraints include a terminal point altitude constraint, a terminal point velocity constraint, and a terminal point distance target point residual range constraint, and the expressions are:
the heat flow rate constraints, overload constraints and dynamic pressure constraints are process constraints that must be met during the re-entry of the aircraft, expressed as:
the quasi-equilibrium gliding condition constraint can ensure that the flying height of the hypersonic aircraft does not generate long-period oscillation. The track angle and derivative thereof in the three-degree-of-freedom mass center motion equation are simultaneously zero, and the expression of the quasi-equilibrium gliding condition constraint is as follows:
when the constraint of the quasi-equilibrium gliding condition is met, the resultant force of gravity and lift force borne by the aircraft is exactly balanced with the centripetal force borne by the aircraft, at the moment, the change of the flight path height is small, and the track angle is kept small. After the amplitude of the roll angle is added to the correction of the formula (7), the height change rate of the track is close to that of the quasi-equilibrium glide track, so that the long-period oscillation is eliminated.
Because of the limitation of the control mechanism in the aircraft, the change of the control quantity needs to meet certain constraint, and because the attack angle adopts the designed standard attack angle profile, the constraint of the control quantity is reflected on the amplitude of the limiting roll angle, and the expression is as follows:
In the reentry flight process, the process constraint condition and the quasi-equilibrium glide condition constraint are converted into the constraint on the roll angle so as to be convenient to realize, and therefore, the process constraint condition and the quasi-equilibrium glide condition constraint are required to be correspondingly converted.
The process constraints translate into:
the quasi-equilibrium glide condition constraint translates into:
specifically, in the establishment and training of the deep neural network in longitudinal guidance, the embodiment includes the following steps:
determining the input and output of deep neural network
The following assumptions are made within the range allowed by the accuracy: the earth is a homogeneous circular sphere without considering rotation, the aircraft is always in an instantaneous moment balance state and the sideslip angle is limited to be zero, and then a hypersonic aircraft reentry section three-degree-of-freedom mass center motion model is built, so that normalized energy is obtained
The equation of motion as an argument is as follows:
in the formula (11), the amino acid sequence of the compound,
for distance between the earth and heart, add>
Longitude->
Latitude,>
for speed->
For the track angle>
For course angle->
For longitudinal plane voyage->
Is earth sea level gravitational acceleration->
Is round in earth radius>
For aircraft mass>
For tilting angle>
Is normalized energy.
Comprehensively considering factors influencing the roll angle amplitude, and selecting the input quantity of the deep neural network as 
The output of the deep neural network is the roll angle amplitude profile parameter +.>
, wherein ,
For distance between the earth and heart, add>
Longitude->
Latitude,>
for speed->
For the track angle>
For course angle->
For the current time height +>
Height from end point->
Difference of->
For the current time speed +.>
Speed +.>
Is used for the difference in (a),
the remaining range of the current time position from the target point; longitude +.>
Latitude at present moment->
Target point longitude +>
Target point latitude->
Related to the following.
(II) determining deep neural network structure
The structure of the network is a very important super parameter of the deep neural network, too few hidden layers and neurons will lead to under-fitting, i.e. the loss function on both the test sample and the training sample will be high, and too many hidden layers and neurons will lead to over-fitting. The invention uses a 5-fold cross validation method to select the structure of the deep neural network, namely, firstly, a network structure is selected, training samples are randomly divided into 5 samples, the 5 samples are sequentially used as validation samples, the rest 4 samples are used as training samples to train the deep neural network of the network structure, training loss and validation loss after training is completed are recorded each time, and finally, the average value of the training loss and the validation loss is calculated and used as an evaluation standard of the network structure. According to the result of 5-fold cross validation, a deep neural network structure with minimum training loss and validation loss under the condition of moderate network structure complexity is selected, and the deep neural network structure comprises 5 hidden layers, wherein each layer comprises 10 neurons.
The activation function of neurons in the hidden layer of the deep neural network uses the hyperbolic tangent Tanh function as follows:
the hyperbolic tangent function can compress any number from [ -1,1] by an "S" type function, which has the advantage of being smooth and easily derivable as an activation function.
(III) Generation of training data and training of deep neural networks
(1) Generating training samples and test samples based on predictive correction guidance methods
As shown in fig. 3, given a state parameter range of the reentry initial point, randomly setting reentry initial point parameters in the given range, obtaining a large number of flight tracks by a prediction correction guidance method, mixing sample points of each track to form training data, randomly taking 80% of the training data as training samples of the deep neural network, and 20% of the training data as test samples of the deep neural network.
In particular, the longitudinal guidance of the predictive correction guidance method, in the reentry guidance of the aircraft, the control quantity includes the angle of attack and the roll angle. In the case of angle-of-attack profile determination, the longitudinal guidance of the aircraft only focuses on the magnitude of the roll angle.
(1.1) As shown in FIG. 4, the angle of attack is typically generated by a designed speed-angle of attack profile. The large attack angle is adopted in the early reentry stage to meet the heat flow rate constraint, and the attack angle corresponding to the maximum lift-drag ratio is adopted in the middle and later stages to meet the range requirement. The attack angle profile adopted by the invention is as follows:
(1.2) longitudinal guidance mainly includes a prediction link and a correction link. And (3) predicting the landing point by integrating the values of the motion equation of the aircraft according to the current state quantity and the control quantity to obtain the information of the to-be-flown range from the current position to the predicted landing point, which is a prediction link. And adjusting the parameter of the roll angle amplitude by utilizing the deviation information of the to-be-flown range from the current position to the predicted landing point and the terminal landing point until the deviation of the parameter of the roll angle amplitude updated twice is within a preset range, and substituting the deviation of the parameter of the roll angle amplitude into the section of the roll angle amplitude to obtain the corrected roll angle amplitude, which is a correction link. The method comprises the following specific steps:
(a) From the current roll angle magnitude parameter
Starting, numerical integration of the mathematical model of the aircraft movement is carried out to obtain the predicted range to be flown>
And calculate +.>
；
(b) Calculating an objective function
；
(c) By means of
Updating the roll angle amplitude parameter;
(d) Repeating the three steps until the difference between the amplitude parameters of the two adjacent roll angles is smaller than the set threshold value. Then substituting the roll angle amplitude parameter into
Obtaining the tilting angle amplitude value;
(e) Limiting the amplitude of the roll angle by a process constraint and a quasi-equilibrium glide condition constraint, and substituting the roll angle amplitude obtained in (d) into equations (9) and (10) in order to obtain a final roll angle amplitude instruction.
Lateral guidance of predictive correction guidance method
As shown in fig. 5, the design of the lateral guidance mainly includes the design of the lateral control amount and the control amount corridor, and when the lateral control amount passes beyond the corridor boundary from the inside of the control amount corridor, the roll angle sign is reversed, so that the lateral control amount is kept within the control amount corridor at all times. The transverse control quantity used by the invention is the deviation of the course angle and the line of sight angle, and the transverse guidance is carried out by setting a proper deviation corridor of the course angle and the line of sight angle.
The sample data of the present invention is generated by a predictive correction guidance method. The initial state parameters are randomly selected in the range given in the table 1, 2000 reentrant flight tracks are calculated by using a predictive correction guidance method, sample points in each track are mixed, 80% of the initial state parameters are randomly selected as training samples of the deep neural network, and 20% of the initial state parameters are used as test samples of the deep neural network.
TABLE 1
(2) Training data preprocessing
The magnitude order of each variable in the input quantity of the deep neural network is very different, and the obtained training sample is directly input into the network and possibly causes a phenomenon that convergence is difficult to occur, so the invention uses a characteristic scaling method shown in the following formula to normalize the training sample data:
In the formula (14), the amino acid sequence of the compound,
for the minimum value of a variable in the input quantity in the sample set, +.>
Is the maximum value of a variable in the input quantity in the sample set. Normalization parameters based on training samples +>
and
And carrying out the same data normalization processing on the test sample to complete the pretreatment of all training data.
(3) Training deep neural network using normalized training data
As shown in fig. 6, the deep neural network adopted by the invention is a fully-connected feed-forward neural network, and consists of 1 input layer, 5 hidden layers and 1 output layer. Using the above-determined network structure, a training method is selected as a Levenberg-Marquardt back propagation algorithm, a loss function is a mean square error (Mean Squared Error, MSE for short), and a model training-related hyper-parameter learning rate (learning rate) and learning times (Epoch) are specified. The training process is to send training samples into the deep neural network in turn according to the actual output of the network
And (2) desired output->
The difference between the two sets adjusts the weight coefficient and the offset value among the neurons, and the weight value is adjusted by using the input and output sample set continuously in a circulating way so as to reduce the output errors of all the input samples to the preset precision, and the method comprises the following specific operations:
(a) Randomly initializing a weight coefficient and a bias value of a deep neural network;
(b) Forward propagation: the values of the input layer are firstly transmitted to the hidden layer through network calculation and then transmitted to the output layer in the same mode, and the actual output value of the deep neural network is obtained. Will input samples
Incoming from the input layer, the input layer-hidden layer nodes are weighted and summed and Sigmoid activation is performed:
in the formula (15), the amino acid sequence of the compound,
is->
Layer->
Activation value of individual neurons, < >>
Is->
Layer->
The output values of the individual neurons are then,
to activate the function +.>
Is->
Layer->
Neurons to->
Layer->
Weight coefficient of individual neurons, +.>
Is->
Layer->
Offset values of the individual neurons.
After each hidden layer is processed layer by layer, the hidden layer is transmitted to an output layer, and the hidden layer-output layer nodes are weighted and summed and Sigmoid activation is executed to obtain the actual output of the network
；
(c) Back propagation: calculate the actual output
And (2) desired output->
Updating the weight coefficient and the offset value according to the result;
(d) Repeating the processes (a) and (c) until the loss function value is reduced to a preset value or training is performed for a preset number of learning times.
Considering that the order of magnitude of the input of deep neural networks varies greatly, the direct input into the network is thatThe method of feature scaling is used to normalize the training samples. Normalization parameters based on training samples
and
And carrying out the same data normalization processing on the test sample to complete the pretreatment of all training data. The training samples and the test samples are processed separately, the training samples are normalized first, and then the test samples are processed by using the normalization parameters of the training samples, instead of normalizing the training samples together, so that the information of the test samples is not leaked, thereby obtaining real test loss and accurately judging whether the network is good or bad.
FIG. 7 is a histogram of absolute error between the output of the deep neural network and the test sample, with about 66% of the output of the deep neural network having an absolute error of less than 0.009, about 50% having an absolute error of less than 0.006, about 26.7% having an absolute error of less than 0.03, an average value of 0.01088, and a variance of
The standard deviation was 0.03096. The loss of deep neural network on the test sample was 0.001077. It follows that the trained deep neural network model can estimate the optimal roll angle magnitude parameter +_with high accuracy >
。
Step 2, presetting reentry terminal information, obtaining the input quantity of the trained deep neural network according to the flight state quantity at the current moment, and outputting the trained deep neural network
Bringing a section of the tilting angle amplitude, and obtaining the tilting angle amplitude by matching with three process constraints of heat flow rate, overload and dynamic pressure and the constraint of quasi-equilibrium gliding conditions to finish longitudinal guidance;
on the basis of the above embodiment, the step 2 specifically includes:
step 2.1, presetting re-entry terminal information, wherein the re-entry terminal information comprises terminal point height
Speed of end point
Target point longitude->
Target point latitude->
Residual course of the terminal point from the target point +.>
Setting a guidance period
；
Step 2.2, obtaining the flying state quantity at any moment in the flying process through measurement and calculation, wherein the flying state quantity comprises the ground center distance
Speed->
Longitude->
Latitude->
Track angle->
Course angle->
；
Step 2.3, from the reentry initiation time
Initially, every interval time +.>
Obtaining an input quantity of the deep neural network based on the current time flight state quantity +.>
, wherein ,
for the difference between the current time height and the end point height,
For the difference between the current time speed and the terminal point speed, < > >
Is a circular shape of the radius of the earth,
obtaining a roll angle amplitude profile parameter +.>
；
Step 2.4, each time during the flight
Based on the roll angle amplitude profile parameter +.>
Obtaining the current moment roll angle amplitude +.>
The calculation formula is as follows:
wherein ,
the energy is normalized for the current moment of time,
normalizing the energy for the re-entry of the initial moment +.>
Normalizing energy for re-entry termination point, +.>
For preset parameters +.>
To reenter the initial moment ground centre distance +.>
For re-entering the initial time speed +.>
Is the gravitational acceleration of the earth sea level;
on the basis of the foregoing embodiment, the step 2 further includes:
limiting roll angle magnitude by thermal flow rate, overload and dynamic pressure process constraints, and quasi-equilibrium glide condition constraints
At->
And if the distance exceeds the range, taking an interval extreme value, and ending the longitudinal guidance.
For example, the information of the reentry terminal can be preset, the guidance period can be set, then the flying state quantity at any moment can be obtained by measurement and calculation in the flying process, and then the reentry initial moment can be obtained
Initially, every interval time +.>
Based on the current time flight state quantity, obtaining the input quantity of the deep neural network, and further obtaining the roll angle amplitude section parameter through the output quantity of the deep neural network >
. Every moment in the flight->
Based on the roll angle amplitude profile parameter +.>
Obtaining the current moment roll angle amplitude +.>
Limiting the roll angle magnitude +_by three process constraints (as shown in formula (9)) of heat flow rate, overload and dynamic pressure and a Quasi-equilibrium glide condition (Quasi-Equilibrium Glide Condition, QEGC) constraint (as shown in formula (10)) +.>
At->
And if the range is exceeded, taking an interval extremum, and thus, determining the longitudinal guidance of the roll angle amplitude based on the deep neural network to finish.
And step 3, determining a roll angle sign based on the deviation of the course angle and the sight angle, and finishing transverse guidance.
On the basis of the above embodiment, the step 3 specifically includes:
step 3.1, based on the target point longitude
Target point latitude->
Longitude +.>
And latitude at the current moment->
Calculating the sight angle of the aircraft and the target point at the current moment>
The calculation formula is as follows:
step 3.2, from the current moment line of sight angle
And heading angle->
Calculating the deviation between the course angle and the line of sight angle, namely, the transverse guidance control quantity is +.>
；
Step 3.3, designing a transverse guidance control quantity corridor, wherein the upper boundary of the corridor
And lower border->
The calculation formulas of (a) are respectively as follows:
wherein ,
、
、
、
The parameters are preset;
step 3.4, the deviation between the required course angle and the line of sight angle in the flying process is between the upper and lower boundaries of the corridor of the transverse guidance control quantity, and when the deviation exceeds the upper or lower boundary of the corridor from within the corridor, the sign of the tilting angle is reversed, namely
And ending the transverse guidance.
In particular, the design of the transverse guidance mainly comprises the design of the transverse control quantity and the control quantity corridor, and when the transverse control quantity exceeds the corridor boundary from the interior of the control quantity corridor, the tilting angle sign is reversed, so that the transverse control quantity is always kept in the control quantity corridor. The transverse control quantity used by the invention is the deviation of the course angle and the line of sight angle, and the transverse guidance is carried out by setting a proper deviation corridor of the course angle and the line of sight angle. The method comprises the following specific steps:
(1) Based on the longitude of the target point
Target point latitude->
Longitude +.>
And latitude at the current moment->
Calculating the sight angle of the aircraft and the target point at the current moment>
The calculation formula is as follows: />
(2) From the current moment angle of view
And heading angle->
The deviation of the course angle and the sight angle, namely the transverse guidance control quantity is calculated as follows:
(3) Designing a transverse guidance control amount corridor, and the upper boundary of the corridor 
And lower border->
The calculation formulas of (a) are respectively as follows:
(4) The deviation of the required course angle and the line of sight angle is between the upper boundary and the lower boundary of the transverse guidance control quantity corridor in the flying process, and when the deviation exceeds the upper boundary or the lower boundary of the corridor from the inside of the corridor, the sign of the tilting angle is reversed, namely:
the transverse guidance ends.
The invention will be described with reference to a specific embodiment, and the superiority of the reentry guidance method based on the deep neural network provided by the invention is verified by comparing and analyzing the reentry guidance method based on the deep neural network and the prediction correction guidance method.
Basic parameters such as hypersonic aircraft quality, reference area and the like and aerodynamic parameters refer to the CAV-H aircraft:
(1) Aircraft parameters: quality of
Reference area
Maximum allowable heat flow rate
Coefficient of heat flow rate model->
Maximum allowable overload->
Maximum allowable dynamic pressure->
。
(2) Lift coefficient and drag coefficient parameters:
，
，
，
，
，
，
，
。
(3) Control amount constraint: maximum roll angle magnitude
。
Digital simulation is carried out based on MATLAB software, and simulation parameters are as follows:
(1) Initial value of flight state parameter: height of (1)
Longitude->
Latitude->
Speed->
Track angle->
Course angle->
Voyage->
。
(2) Reenter terminal information: terminal point height 
Target point longitude->
Latitude of target point
Terminal speed->
Residual course of the terminal point from the target point +.>
。
(3) Angle of attack profile parameters: maximum angle of attack
The attack angle corresponding to the maximum lift-drag ratio +.>
Adjustable speed parameter->
，
。
(4) Transverse guidance control corridor parameters: adjustable speed parameter
，
。
(5) Motion equation integration step size: the integration step length with time as an independent variable is 0.1s, and the integration step length with nondimensional energy as an independent variable is 0.00001.
(6) Guidance cycle: when the voyage is left
When (I)>
The method comprises the steps of carrying out a first treatment on the surface of the When (when)
When (I)>
The method comprises the steps of carrying out a first treatment on the surface of the When->
When (I)>
。
TABLE 2
The deviation of the initial state parameter range and the aerodynamic parameter of the reentry of the aircraft is shown in table 2, 500 groups of Monte Carlo simulation are respectively carried out by using a prediction correction guidance method and a reentry guidance method based on a deep neural network, the guidance period modes of the two are the same, and the longitude and latitude distribution diagram of the reentry section terminal calculated by the two methods is shown in fig. 8. The longitude and latitude distribution conditions of the reentry section terminals obtained by the two methods are approximately the same, and it can be seen that the reentry guidance method based on the deep neural network has the same good precision as the prediction correction guidance method.
TABLE 3 Table 3
The statistical parameters of the course absolute error, the altitude absolute error and the speed absolute error of the reentry terminal obtained by Monte Carlo simulation are shown in the table 3, and it can be seen that the average value of the final course, altitude and speed absolute error of the intelligent reentry guidance method is lower than the prediction correction guidance. The neural network can learn the flight state and the nonlinear mapping hidden behind the optimal control under the simulation condition, and has good stability and robustness under the deviation of pneumatic parameters in the parameter range of the initial state of the reentry section set by the invention.
The average time required by the prediction correction guidance method to finish the calculation of the once guidance instruction is 0.57s, the average simulation time to finish the once complete reentry flight is 18.82s, the average time required by the reentry guidance method based on the deep neural network to finish the calculation of the once guidance instruction is 0.0089s, the average simulation time to finish the once complete reentry flight is 0.62s, and therefore, the calculation speed of the method to finish the once guidance is much faster than that of the prediction correction guidance method.
The units involved in the embodiments of the present disclosure may be implemented by means of software, or may be implemented by means of hardware.
It should be understood that portions of the present disclosure may be implemented in hardware, software, firmware, or a combination thereof.
The foregoing is merely specific embodiments of the disclosure, but the protection scope of the disclosure is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the disclosure are intended to be covered by the protection scope of the disclosure. Therefore, the protection scope of the present disclosure shall be subject to the protection scope of the claims.
Claims (4)
1. The hypersonic aircraft reentry guidance method based on the deep neural network is characterized by comprising the following steps of:
step 1, establishing a hypersonic aircraft reentry section three-degree-of-freedom mass center motion model to obtain normalized energy
Determining the input quantity of the depth neural network according to factors affecting the roll angle amplitude as an independent variable of a motion equation, and simultaneously determining the roll angle amplitude profile parameter +.>
Presetting a plurality of deep neural networks with different network structures for output quantity, determining the deep neural network structure by adopting a 5-fold cross validation method, and training the deep neural network by using training data generated based on a prediction correction method, wherein the expression of the motion equation is
wherein ,
for longitudinal plane voyage->
Is earth sea level gravitational acceleration->
Is round in earth radius>
For aircraft mass>
For tilting angle>
Normalized energy;
step 2, presetting reentry terminal information, obtaining the input quantity of the trained deep neural network according to the flight state quantity at the current moment, and outputting the trained deep neural network
Bringing a section of the tilting angle amplitude, and obtaining the tilting angle amplitude by matching with three process constraints of heat flow rate, overload and dynamic pressure and the constraint of quasi-equilibrium gliding conditions to finish longitudinal guidance;
The step 2 specifically includes:
step 2.1, presetting re-entry terminal information, wherein the re-entry terminal information comprises terminal point height
Terminal speed->
Target point longitude->
Target point latitude->
Residual course of the terminal point from the target point +.>
Setting guidance period +.>
；
Step 2.2, passing during flightMeasuring and calculating to obtain flying state quantity at any moment, wherein the flying state quantity comprises the earth center distance
Speed->
Longitude->
Latitude->
Track angle->
Course angle->
；
Step 2.3, from the reentry initiation time
Initially, every interval time +.>
Obtaining an input quantity of the deep neural network based on the current time flight state quantity +.>
, wherein ,
For the difference between the current time height and the end point height,
For the difference between the current time speed and the terminal point speed, < >>
Is a round earth halfDiameter (diameter) and (diameter) of (diameter>
Obtaining a roll angle amplitude profile parameter +.>
；
Step 2.4, each time during the flight
Based on the roll angle amplitude profile parameter +.>
Obtaining the current moment roll angle amplitude +.>
The calculation formula is as follows:
wherein ,
normalizing the energy for the current moment,/- >
Normalizing the energy for the re-entry of the initial moment +.>
Normalizing energy for re-entry termination point, +.>
For preset parameters +.>
To reenter the initial timeDistance between the earth and heart>
For re-entering the initial time speed +.>
Is the gravitational acceleration of the earth sea level;
and step 3, determining a roll angle sign based on the deviation of the course angle and the sight angle, and finishing transverse guidance.
2. The method according to claim 1, wherein the step 1 comprises,
step 1.1, comprehensively considering factors influencing the roll angle amplitude, and selecting the input quantity of the deep neural network as
The output of the deep neural network is the roll angle amplitude profile parameter +.>
, wherein ,
For distance between the earth and heart, add>
Longitude->
Latitude,>
for speed->
For the track angle>
In order to be the heading angle,
for the current time height +>
Height from end point->
Difference of->
For the current time speed +.>
Speed +.>
Is used for the difference in (a),
the remaining range of the current time position from the target point;
step 1.2, presetting a plurality of deep neural networks with different network structures, and evaluating the advantages and disadvantages of the different network structures by using a 5-fold cross validation method, wherein the specific flow is as follows: randomly dividing training samples into 5 parts, sequentially taking the 5 parts of training samples as verification samples, taking the rest 4 parts of training samples as training samples to train a deep neural network with a preset network structure, recording training loss and verification loss after each training, and finally calculating the average value of the training loss and the verification loss as an evaluation standard of the network structure;
Step 1.3, according to the result of 5-fold cross validation, selecting a network structure with minimum training loss and validation loss under the condition that the complexity of the network structure accords with a preset condition as a deep neural network, wherein the deep neural network structure is a forward feedback neural network, the forward feedback neural network comprises an input layer, a plurality of hidden layers and an output layer which are sequentially connected, each hidden layer comprises a plurality of neurons, and an activation function of the neurons in the hidden layers uses the following hyperbolic tangent Tanh function:
and step 1.4, training the deep neural network by adopting the deep neural network structure determined by the step, and using all training data generated based on a prediction correction method.
3. The method according to claim 2, wherein the step 2 further comprises:
limiting roll angle magnitude by thermal flow rate, overload and dynamic pressure process constraints, and quasi-equilibrium glide condition constraints
At->
And if the distance exceeds the range, taking an interval extreme value, and ending the longitudinal guidance.
4. A method according to claim 3, wherein said step 3 comprises:
step 3.1, based on the target point longitude
Target point latitude->
Longitude +.>
And latitude at the current moment- >
Calculating the sight angle of the aircraft and the target point at the current moment>
The calculation formula is as follows:
step 3.2, from the current moment line of sight angle
And heading angle->
Calculating the deviation between the course angle and the line of sight angle, namely, the transverse guidance control quantity is +.>
；
Step 3.3, designing a transverse guidance control quantity corridor, wherein the upper boundary of the corridor
And lower border->
The calculation formulas of (a) are respectively as follows:
wherein ,
、
、
、
the parameters are preset;
step 3.4, the deviation between the required course angle and the sight angle in the flying process is between the upper boundary and the lower boundary of the transverse guidance control quantity corridor, whenThe sign of the roll angle being reversed when the deviation exceeds the upper or lower boundary of the corridor from within the corridor, i.e.
And ending the transverse guidance. />
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