CN113126643A - Intelligent robust reentry guidance method and system for hypersonic aircraft - Google Patents
Intelligent robust reentry guidance method and system for hypersonic aircraft Download PDFInfo
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Abstract
The invention belongs to the technical field of hypersonic gliding aircraft reentry trajectory planning guidance and discloses a hypersonic aircraft intelligent robust reentry guidance method and a hypersonic aircraft intelligent robust reentry guidance system, wherein the hypersonic aircraft intelligent reentry guidance method comprises the following steps: based on uncertainty system modeling, judging uncertainty and types thereof existing in the gliding reentry process of the hypersonic aerocraft, and determining an uncertainty parameter distribution form and a distribution interval; carrying out uncertainty quantitative analysis, and establishing a robust dynamic trajectory optimization model containing the statistical moment characteristics of a random system; establishing a robust track optimization numerical sample set; designing a deep neural network model architecture, carrying out model training and verifying the effectiveness of the model; and loading a deep neural network model, and intelligently updating the robust trajectory planning guidance instruction in real time. The method can reduce the robust track design time, enhance the active defense capability of the guidance instruction to the complex uncertainty, and reduce the design burden of an aircraft guidance control system.
Description
Technical Field
The invention belongs to the technical field of hypersonic gliding aircraft reentry trajectory planning and guidance, and particularly relates to an intelligent robust reentry guidance method and system for a hypersonic gliding aircraft.
Background
At present, the hypersonic gliding aircraft is one of main types of hypersonic gliding aircraft in an adjacent space, is generally transported to a preset height by a carrier rocket or released by a space-based platform, enters the atmosphere at hypersonic speed, realizes long-distance unpowered gliding by means of self high lift-drag ratio and pneumatic control, and finally completes tasks such as accurate striking of a target. The hypersonic gliding aircraft is regarded as a technical high point of adjacent space resource competition and national strategic safety guarantee by various countries because the hypersonic gliding aircraft breaks through the conventional ballistic reentry mode and has the advantages of high response speed, long flight distance, large space span, strong maneuvering penetration capability, high hitting precision and the like.
The track design is a core problem in the field of guidance and control of the hypersonic aircraft, needs to undertake overall analysis tasks in the overall design stage of the aircraft, provides theoretical basis for multidisciplinary design such as guidance, control, penetration and thermal protection and almost runs through the whole aircraft design process. The inherent property of hypersonic gliding aircraft of unpowered gliding reentry makes the challenge of trajectory design more severe. The ideal target of the hypersonic aircraft track design is to obtain a global optimal track on line under the condition of meeting all constraints by exceeding the precision of navigation errors and exceeding the efficiency of a guidance period.
At present, limited missile-borne computing processing capacity is adopted, and a track design framework of off-line track optimization and on-line tracking guidance is generally adopted in engineering: in the off-line design stage, a reference track is optimized based on a particle dynamics model and is stored in an missile-borne computer; and in the online flight process, the guidance control system tracks the reference track and guides the aircraft to the terminal position according to the pre-planned track. The traditional offline trajectory optimization is based on deterministic nominal model expansion, uncertainty in the aircraft and the environment is ignored, so that the reference trajectory often lacks robustness, unpredictable fluctuation or deviation from the design direction is easily caused in the flight process, the task execution effect is obviously influenced, and even the safety of the aircraft is threatened. The deficiency of the deterministic reference trajectory can be compensated to a certain extent by using technologies such as online trajectory optimization, online tracking guidance or prediction-correction guidance, but new design difficulties still exist: in order to meet the real-time requirement, the online track optimization usually costs partial track optimality, but the track optimality design is still necessary in consideration of the limitation of missile-borne consumable quantity; the online tracking guidance has high calculation speed but low guidance precision, the prediction-correction guidance precision is higher but seriously depends on the calculation capability, the mixed guidance of the two methods is an improved method under the existing framework, but the track robust design and the calculation resource configuration are lack of fundamental improvement, and the performance of the aircraft is limited by the limited correction capability.
Intelligent trajectory planning guidance-related research has shown that a trajectory controller based on deep learning has the potential to take over all or part of a missile-borne trajectory generation and guidance system, but robust intelligent trajectory planning guidance research considering uncertainty has not yet received attention. Because the missile-borne computing power is difficult to support the online learning process, the deep neural network flight controller is mainly realized in an off-line training and online application mode. In the face of the problem of complex multi-source uncertainty reentry trajectory optimization, a high-fidelity robust dynamic trajectory optimization model and multi-working-condition robust trajectory design data support are lacked.
Aiming at the problems, the traditional trajectory optimization and guidance technology framework of the hypersonic aircraft is broken through, and the research of the hypersonic aircraft intelligent reentry guidance method based on robust trajectory optimization is developed, so that the hypersonic aircraft intelligent reentry guidance method has important scientific significance and engineering application value.
Through the above analysis, the problems and defects of the prior art are as follows:
(1) the traditional offline trajectory optimization is based on deterministic nominal model expansion, uncertainty in the aircraft and the environment is ignored, so that the reference trajectory often lacks robustness, unpredictable fluctuation or deviation from the design direction is easily caused in the flight process, the task execution effect is obviously influenced, and even the safety of the aircraft is threatened.
(2) The deficiency of the deterministic reference trajectory can be compensated to a certain extent by using technologies such as online trajectory optimization, online tracking guidance or prediction-correction guidance, but new design difficulties still exist: in order to meet the real-time requirement, the online trajectory optimization usually comes at the expense of partial trajectory optimality, but in consideration of the missile-borne consumable quantity limit, the trajectory optimality design is still necessary.
(3) The online tracking guidance has high calculation speed but low guidance precision, the prediction-correction guidance precision is higher but seriously depends on the calculation capability, the mixed guidance of the two methods is an improved method under the existing framework, but the track robust design and the calculation resource configuration are lack of fundamental improvement, and the performance of the aircraft is limited by the limited correction capability.
(4) In the prior art, the robust intelligent track planning guidance research considering uncertainty still does not give attention, and in the face of the problem of complex multi-source uncertainty reentry track optimization, a high-fidelity robust dynamic track optimization model and multi-working-condition robust track design data support are lacked.
The difficulty in solving the above problems and defects is:
(1) under the traditional track design architecture, the track numerical solving efficiency is often in a contradiction relation with other key indexes such as modeling complexity, discretization precision and global optimality, and the demand of high-speed supersonic aircraft for flexibility and rapidity which is urgently needed in the field of track design and guidance is still not met. For the problem of robust reentry trajectory optimization facing complex uncertainty, due to the introduction of various uncertain factors and random optimization models, the number of model constraints and design variables is multiplied, and the numerical solution is more difficult.
(2) Because the missile-borne computing power is difficult to support the online learning process, the deep neural network flight controller is mainly realized in an off-line training and online application mode, and the reliability of the deep neural network flight controller highly depends on a training model and training data. In the face of the problem of complex multi-source uncertainty reentry trajectory optimization, a high-fidelity robust dynamic trajectory optimization model and multi-working-condition robust trajectory design data support are lacked.
The significance of solving the problems and the defects is as follows:
(1) the robust track design facing multi-source uncertainty is developed, reverse information flow of off-line track optimization and on-line guidance control can be constructed on the basis of a traditional architecture, a bridge of track control instructions and a real reentry scene is indirectly erected, original relatively independent design steps on a time axis become an interactive whole, and reliability and safety of overall design are effectively improved.
(2) Based on the mode recognition capability of artificial intelligence, an uncertain nonlinear dynamics model is approximated by utilizing a deep learning technology, a robust track planning and guidance optimization strategy is learned, an intelligent robust optimal track and guidance model is established, online track prediction and path selection can be realized, and flight problems such as target change, terminal combat change, uncertainty disturbance and the like can be effectively solved, so that the flexibility of reentry flight is improved.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides an intelligent robust reentry guidance method and system for a hypersonic aircraft, and particularly relates to an intelligent reentry guidance method and system for the hypersonic aircraft based on robust trajectory optimization.
The invention is realized in such a way, and the hypersonic aircraft intelligent robust reentry guidance method comprises the following steps:
the method comprises the steps that firstly, modeling is carried out based on an uncertainty system, uncertainty and types of the hypersonic aircraft in the gliding reentry process are judged according to data mining and expert experience, and the distribution form and the distribution interval of uncertainty parameters are determined, so that a foundation is laid for robust modeling and design of reentry trajectories;
step two, carrying out uncertainty quantitative analysis based on a non-embedded polynomial chaos theory according to the uncertainty factors obtained in the step one, and establishing a robust dynamic trajectory optimization model containing random system targets and state variable statistical moment characteristics; by changing uncertain parameter values and designing a numerical solving strategy, a robust track optimization numerical sample set aiming at multisource uncertain factors is established, and reliability basis and data support are provided for intelligent robust guidance model design;
thirdly, designing a deep neural network model architecture by taking the track state vector as input and the track control vector as output; performing model training by using the robust track optimization numerical sample set aiming at the multi-source uncertain factors obtained in the step two, verifying the effectiveness of the model and providing feasibility analysis for the online application of the intelligent robust guidance model;
and step four, loading the deep neural network model which is completely trained in the step three, and finally realizing intelligent real-time updating of the robust trajectory planning guidance instruction according to flight state information output by a missile-borne control system including the navigation positioning system and the attitude control system in the reentry process of the aircraft.
Further, in the first step, the modeling based on the uncertainty system, the uncertainty and the type thereof existing in the glide reentry process of the hypersonic flight vehicle are judged according to data mining and expert experience, and the distribution form and the distribution interval of the uncertainty parameters are determined, including:
carrying out classification modeling aiming at cognitive uncertainty, random uncertainty and numerical uncertainty in a high-speed flight dynamics system, researching uncertainty sources and types in a robust trajectory optimization design process on the basis, and carrying out uncertainty modeling around initial reentry conditions, pneumatic model data, atmospheric model parameters and perturbation parameters of an aircraft in the unpowered reentry process of the hypersonic glide aircraft;
wherein the uncertain factor types are:
wherein xi is a random variable vector; subscript y0、θ0、
V0、γ0、ψ0Respectively representing the initial reentry states of the aircraft state variables such as the earth's center distance, longitude, latitude, speed, track angle and course angle, CL、CDRespectively represents the lift coefficient and the drag coefficient of the aircraft, rho represents the atmospheric density, mVRepresenting the aircraft's own mass.
Further, in the first step, the distribution form of the uncertain factors is assumed to be uniformly distributed and independent, and the distribution range of the system random model and the uncertain factors is as follows:
wherein the content of the first and second substances,
respectively representing the random initial reentry state of the aircraft;
representing a random lift coefficient and a random drag coefficient;
is a random atmospheric density;
is a random aircraft mass.
Further, in step two, the aircraft random trajectory optimization model includes a random dynamics differential equation, a random dimensionless aerodynamic force, a random process constraint, a random initial value constraint, a terminal constraint and a control variable, and includes:
(1) differential equation of stochastic dynamics
Wherein y, theta,
V, gamma and psi respectively represent the geocentric distance, longitude, latitude, speed, track angle and heading angle of the aircraft state variables; omega is the rotation angular rate of the earth; y, V, t and omega are dimensionless variables, R is the dimensionless parameter0、Vc＝(g0R0)0.5、(R0/g0)0.5And (g)0/R0)0.5，R0Is the mean radius of the earth, g0Is the sea level gravitational acceleration.
Respectively random dimensionless lift force and resistance force, and dimensionless parameters of 2mV·g0。
(2) Random aerodynamic force
Wherein S isVIs the aerodynamic reference area of the aircraft.
(3) Random process constraints
Wherein the content of the first and second substances,
is the heat flow density, qrIs dynamic pressure, nrIs overloaded;
qmax、nmaxrespectively, corresponding process constraint maxima.
(4) Random initial value constraint
Wherein the content of the first and second substances,
is the initial value of the random state.
(5) Terminal constraints
Wherein, XfIs in the terminal state, yf、θf、
VfRespectively, corresponding terminal state design values.
(6) Controlled variable
U＝[α σ]T；
Where α is the angle of attack and σ is the angle of inclination.
(7) Optimizing an objective function
J＝tf；
Wherein, tfIs the terminal time.
Further, in the second step, a non-embedded polynomial chaotic algorithm is adopted to carry out uncertainty quantitative analysis, statistical moment information of a flight system state variable, a target variable, a process constraint and a boundary constraint is obtained, meanwhile, a stochastic dynamics differential equation is converted into a high-dimensional deterministic differential equation to be solved, and a robust dynamic trajectory optimization model is established; wherein the robust dynamic trajectory optimization model is in the form of:
wherein U (t) is a control variable, and t is a time variable; j. the design is a squareAFor robust optimization of the objective, JμAnd JσSeparately optimizing the target statistical moment, k, for randomμAnd k isσIs the corresponding coefficient;
is a random state vector;
deterministic differential equations transformed from stochastic state differential equations with n-1 … mqWherein q is the dimension of a random variable vector xi, and m is the number of orthogonal integration points adopted by the polynomial chaotic expansion; cμAnd CσStatistical moments that are respectively random process constraints; b isμAnd BσStatistical moments, t, respectively, of random boundary constraints0Is the starting time.
Further, in the second step, according to the system random model and the uncertain factor distribution shown in the first step, the uncertain factor values are changed randomly, the corresponding robust dynamic trajectory optimization model is solved, a trajectory data set facing the multisource uncertainty is obtained, and a sufficient offline robust optimal trajectory is obtained.
Further, in step three, the trajectory state and control data pairs on the numerical discrete points are used as training data to form a robust trajectory training data set, including:
wherein the content of the first and second substances,
for the track state variable, U ═ α σ]TIs a trajectory control variable; l is 1,2, …, L represents different track labels, D is 1,2 …, and D represents track number discrete points. On the basis, an uncertain nonlinear dynamics model is approximated by using a deep learning technology, a robust track planning and guidance optimization strategy is learned, and an intelligent robust optimal track and guidance model (f (X) is established(d)):→U(d))。
Further, in the third step, the track state vector is used as the input of the deep neural network, the track control vector is used as the output of the deep neural network, the training and the testing of the deep neural network are carried out, and the uncertain nonlinear flight dynamics model state and control optimality mapping is established, which comprises the following steps:
under a Python environment, using a Keras deep learning package to create DNN, and operating a Keras framework by taking Tensorflow accelerated based on a GPU as a back end; dividing a track data set into a training set and a testing set according to a proper proportion; the deep neural network consists of an input layer, an output layer and a plurality of hidden layers, the created DNN network is a sequential model, and adjacent layers are connected with each other; adopting an Adam optimization algorithm with excellent performance, adopting a mean square error as a loss function, adopting a ReLU function as a hidden layer activation function, transmitting a certain batch of data each time to calculate loss and update network parameters to obtain an optimal training result; and finally, comparing the track generated by the optimal control with the track generated by the state quantity generated by the DNN drive, and verifying the validity of the model.
Further, in the fourth step, the loading of the deep neural network model with complete training realizes intelligent real-time update of the robust trajectory planning guidance instruction according to flight state information output by a missile-borne control system including the navigation positioning system and the attitude control system in the reentry process of the aircraft, and includes:
loading the deep neural network model which is completely trained on the aircraft, and using the real-time flight state quantity output by the missile-borne control system including the navigation positioning system and the attitude control system in the reentry process of the aircraft
As network input, to control the quantity U(d)＝[α σ]TAnd as output, intelligent real-time updating of the robust track planning guidance instruction is realized.
Another object of the present invention is to provide a hypersonic aircraft intelligent robust reentry guidance system using the hypersonic aircraft intelligent robust reentry guidance method, the hypersonic aircraft intelligent robust reentry guidance system comprising:
the uncertainty modeling module is used for judging uncertainty and types thereof existing in the gliding reentry process of the hypersonic flight vehicle according to data mining and expert experience based on uncertainty system analysis and determining the distribution form and the distribution interval of uncertainty parameters;
an uncertainty quantitative analysis module for developing uncertainty quantitative analysis based on non-embedded polynomial chaos theory according to the obtained uncertainty factors,
the track optimization model building module is used for building a robust dynamic track optimization model containing the random system target and the state variable statistical moment characteristics;
the numerical sample set establishing module is used for establishing a robust track optimization numerical sample set aiming at the multi-source uncertain factors by changing uncertain parameter values and designing a numerical solving strategy;
the neural network model architecture design module is used for designing a deep neural network model architecture by taking the track state vector as input and taking the track control vector as output;
the model training module is used for performing model training by using the obtained robust track optimization numerical sample set aiming at the multi-source uncertain factors and verifying the effectiveness of the model;
and the instruction real-time updating module is used for loading a deep neural network model with complete training and realizing intelligent real-time updating of the robust track planning guidance instruction according to flight state information output by a missile-borne control system including the navigation positioning system and the attitude control system in the reentry process of the aircraft.
By combining all the technical schemes, the invention has the advantages and positive effects that: the hypersonic aircraft intelligent reentry guidance method based on robust trajectory optimization provided by the invention comprises the steps of firstly modeling based on an uncertainty system, judging uncertainty and types thereof existing in the process of gliding reentry of a hypersonic aircraft according to data mining and expert experience, and determining the distribution form and distribution interval of uncertainty parameters; secondly, carrying out uncertainty quantitative analysis based on a non-embedded polynomial chaos theory, establishing a robust dynamic trajectory optimization model containing target and state variable statistical moment information, and establishing a robust trajectory optimization numerical sample set aiming at multi-source uncertain factors by changing uncertain parameter values and designing a numerical solving strategy; then, a track state vector is used as input, a track control vector is used as output, a deep neural network model is designed, and a sample set is used for training and verifying; and finally, loading a deep neural network model with complete training, and realizing intelligent real-time updating of the robust trajectory planning guidance instruction according to flight state information output by missile-borne control systems such as a navigation positioning system and an attitude control system. The method can realize intelligent online planning of the robust reentry trajectory aiming at multisource uncertain factors, greatly reduce the design time of the robust trajectory, and effectively enhance the active defense capability of the guidance instruction on the complex uncertainty, thereby effectively reducing the design burden of an aircraft guidance control system.
The method analyzes the distribution form and the distribution interval of uncertainty parameters in the reentry process, is used for realizing the intelligent online planning of the robust reentry trajectory aiming at the multisource uncertainty factors, then solves the corresponding robust dynamic trajectory optimization model to obtain the enough offline robust optimal trajectory, takes the trajectory state and control data pair on the numerical discrete point as training data to finish the training of the neural network, and obtains the nonlinear mapping relation between the state quantity and the control quantity.
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In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the embodiments of the present invention will be briefly described below, and it is obvious that the drawings described below are only some embodiments of the present invention, and it is obvious for those skilled in the art that other drawings can be obtained according to the drawings without creative efforts.
Fig. 1 is a flowchart of an intelligent robust reentry guidance method for a hypersonic aircraft according to an embodiment of the invention.
FIG. 2 is a schematic diagram of an intelligent robust reentry guidance method for a hypersonic aircraft according to an embodiment of the invention.
FIG. 3 is a structural block diagram of an intelligent robust reentry guidance system of a hypersonic aircraft provided by an embodiment of the invention.
In the figure: 1. an uncertainty modeling module; 2. an uncertainty quantitative analysis module; 3. a trajectory optimization model construction module; 4. a numerical sample set establishing module; 5. a neural network model architecture design module; 6. a model training module; 7. and the instruction real-time updating module.
FIG. 4 is a schematic diagram for verifying the robustness of the reentry flight altitude of the intelligent guidance model provided by the embodiment of the invention.
Fig. 5 is a schematic diagram of verification of the reentry flight longitude robustness of the intelligent guidance model provided by the embodiment of the invention.
Fig. 6 is a schematic diagram illustrating the verification of the robustness of the reentry flight latitude of the intelligent guidance model provided by the embodiment of the invention.
Fig. 7 is a schematic diagram of verification of the reentry flight speed robustness of the intelligent guidance model provided by the embodiment of the invention.
FIG. 8 is a schematic diagram for verifying the robustness of the reentry flight path angle of the intelligent guidance model provided by the embodiment of the invention.
FIG. 9 is a schematic diagram for verifying the robustness of the reentry flight heading angle of the intelligent guidance model provided by the embodiment of the invention.
FIG. 10 is a schematic diagram of an application of intelligent robust reentry guidance of a hypersonic aircraft provided by an embodiment of the invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
Aiming at the problems in the prior art, the invention provides an intelligent robust reentry guidance method and system for a hypersonic aircraft, and the invention is described in detail below with reference to the accompanying drawings.
As shown in fig. 1, the hypersonic aircraft intelligent robust reentry guidance method provided by the embodiment of the invention comprises the following steps:
s101, modeling based on an uncertainty system, judging uncertainty and types thereof existing in the gliding reentry process of the hypersonic aerocraft according to data mining and expert experience, and determining an uncertainty parameter distribution form and a distribution interval;
s102, carrying out uncertainty quantitative analysis based on a non-embedded polynomial chaos theory according to the uncertainty factors obtained in the S101, and establishing a robust dynamic trajectory optimization model containing random system targets and state variable statistical moment characteristics; establishing a robust track optimization numerical sample set aiming at the multi-source uncertain factors by changing uncertain parameter values and designing a numerical solving strategy;
s103, designing a deep neural network model architecture by taking the track state vector as input and the track control vector as output; performing model training by using the robust track optimization numerical sample set aiming at the multi-source uncertain factors obtained in the step S102, and verifying the effectiveness of the model;
and S104, loading the deep neural network model which is completely trained in the S103, and realizing intelligent real-time updating of the robust trajectory planning guidance instruction according to flight state information output by a missile-borne control system including the navigation positioning system and the attitude control system in the reentry process of the aircraft.
The schematic diagram of the hypersonic aircraft intelligent robust reentry guidance method provided by the embodiment of the invention is shown in fig. 2.
As shown in fig. 3, the hypersonic aircraft intelligent robust reentry guidance system provided by the embodiment of the invention comprises:
the uncertainty modeling module 1 is used for judging uncertainty and types thereof existing in the gliding reentry process of the hypersonic flight vehicle according to data mining and expert experience based on uncertainty system analysis, and determining the distribution form and the distribution interval of uncertainty parameters;
an uncertainty quantitative analysis module 2 for developing uncertainty quantitative analysis based on the non-embedded polynomial chaos theory according to the obtained uncertainty factors,
the track optimization model building module 3 is used for building a robust dynamic track optimization model containing the characteristics of the random system target and the state variable statistical moment;
the numerical sample set establishing module 4 is used for establishing a robust track optimization numerical sample set aiming at the multi-source uncertain factors by changing uncertain parameter values and designing a numerical solving strategy;
the neural network model architecture design module 5 is used for designing a deep neural network model architecture by taking the track state vector as input and taking the track control vector as output;
the model training module 6 is used for performing model training by using the obtained robust track optimization numerical sample set aiming at the multi-source uncertain factors and verifying the effectiveness of the model;
and the instruction real-time updating module 7 is used for loading a deep neural network model with complete training and realizing intelligent real-time updating of the robust track planning guidance instruction according to flight state information output by a missile-borne control system including the navigation positioning system and the attitude control system in the reentry process of the aircraft.
The technical solution of the present invention will be further described with reference to the following examples.
The technical scheme of the invention is explained in detail by taking a CAV-H aircraft as a specific embodiment.
As shown in fig. 2, the hypersonic aircraft intelligent reentry guidance method based on robust trajectory optimization comprises the following steps:
the method comprises the following steps: based on uncertainty system modeling, the uncertainty and the type of the hypersonic flight vehicle in the gliding reentry process are judged according to data mining and expert experience, and the distribution form and the distribution interval of uncertainty parameters are determined.
The method is used for carrying out classification modeling aiming at cognitive uncertainty, random uncertainty, numerical uncertainty and the like in a high-speed flight dynamics system, researching uncertainty sources and types in a robust track optimization design process on the basis, and carrying out uncertainty modeling around initial reentry conditions, aerodynamic model data, atmospheric model parameters, perturbation parameters of an aircraft and the like in a hypersonic glide aircraft unpowered reentry process. The specifically adopted uncertain factor types are as follows:
xi is a random variable vector and is subjected to uniform distribution; subscript y0、θ0、
V0、γ0、ψ0Respectively representing the initial reentry states of the aircraft state variables such as the earth's center distance, longitude, latitude, speed, track angle and course angle, CL、CDRespectively represents the lift coefficient and the drag coefficient of the aircraft, rho represents the atmospheric density, mVRepresenting the aircraft's own mass.
The uncertain factor distribution form specifically adopted in this embodiment is assumed to be uniformly distributed and independent from each other, and the system random model and the uncertain factor distribution range are:
wherein the content of the first and second substances,
respectively representing the random initial reentry state of the aircraft;
representing a random lift coefficient and a random drag coefficient;
is a random atmospheric density;
is a random aircraft mass;
initial reentry state y of aircraft0＝100km+R0，θ0＝160°，
V0＝7200m·s-1，γ0＝-2°，ψ058 °, itMean radius of the middle earth R0＝6378000m；
Fitting and calculating the lift coefficient and the drag coefficient of the aircraft by adopting a bivariate aerodynamic coefficient model and a nonlinear least square method, wherein the expression is
Wherein
Mach number
Speed of sound vSAbout 295.188m/s, alpha is the angle of attack;
using a general exponential atmosphere model, atmospheric density
Wherein the sea level atmospheric density ρ0＝1.2258kg/m3Altitude h-y-R0Coefficient of beta0＝1.3785×10-4m-1；
Aircraft mass mV＝907.2kg。
Step two: carrying out uncertainty quantitative analysis based on a non-embedded polynomial chaos theory, establishing a robust dynamic trajectory optimization model containing random system target and state variable statistical moment characteristics, designing a numerical solving strategy, and establishing a robust trajectory optimization numerical sample set aiming at multi-source uncertain factors.
The adopted aircraft random trajectory optimization model comprises a random dynamics differential equation, random dimensionless aerodynamic force, random process constraint, random initial value constraint, terminal constraint, control variables and the like, and specifically comprises the following steps:
the stochastic dynamics differential equation is:
wherein y, theta,
V, gamma and psi respectively represent the geocentric distance, longitude, latitude, speed, track angle and heading angle of the aircraft state variables; omega 7.2722 × 10-5rad/s is the rotation angular rate of the earth; y, V, t and omega are dimensionless variables, R is the dimensionless parameter0、Vc＝(g0R0)0.5、(R0/g0)0.5And (g)0/R0)0.5Mean radius of the earth R06378000m, sea level acceleration of gravity g0＝9.80665m/s2。
Respectively random dimensionless lift force and resistance force, and dimensionless parameters of 2mV·g0。
The random aerodynamic force is:
wherein the aerodynamic reference area S of the aircraftV＝0.4839m2。
The random process constraints are:
wherein the content of the first and second substances,
is the heat flow density, qrIs dynamic pressure, nrIs overloaded;
qmax、nmaxrespectively the corresponding process constraint maximum value,
qmax＝400kPa，nmax＝6。
the random initial value constraint is:
the terminal constraints are:
wherein, yf＝20km+R0、θf＝236°、
Vf＝1000m·s-1。
The control variables are:
U＝[ασ]T (8)
wherein the angle of attack α ∈ [10 °, 20 ° ], the angle of inclination σ ∈ [ 80 °, 80 ° ].
The optimization objective function is:
J＝tf (9)
wherein, tfIs the terminal time.
Then, performing uncertainty quantitative analysis by adopting a non-embedded polynomial chaotic algorithm to obtain statistical moment information of a state variable, a target variable, a process constraint and a boundary constraint of a flight system, simultaneously converting a stochastic dynamics differential equation into a high-dimensional certainty differential equation to solve, and finally establishing a robust dynamic trajectory optimization model in the following form:
wherein U (t) is a control variable, and t is a time variable; j. the design is a squareAFor robust optimization of the objective, JμAnd JσSeparately optimizing the target statistical moment, k, for randomμAnd k isσIs the corresponding coefficient;
is a random state vector;
deterministic differential equations transformed from stochastic state differential equations with n-1 … mqWherein q is the dimensionality of a random variable vector xi, in the example, q is 10, m is the number of orthogonal integration points adopted by polynomial chaotic expansion, and in the example, m is 6; cμAnd CσStatistical moments that are respectively random process constraints; b isμAnd BσStatistical moments, t, respectively, of random boundary constraints0Is the starting time.
The requirements of two aspects of calculation precision and calculation burden are comprehensively considered, and 2-order non-embedded polynomial chaotic expansion of 6 Gaussian sampling points is adopted in simulation analysis; and solving the robust dynamic optimization model by adopting a particle swarm algorithm, wherein the particle swarm size is 50, the maximum iteration frequency is 100, the number of discrete nodes is 100, and the number of integral points is 500.
And (3) randomly changing the value of the uncertain factors and solving a corresponding robust dynamic trajectory optimization model according to the system random model and the uncertain factor distribution shown in the formula (1) and the formula (2) to obtain 4000 offline robust optimal trajectories.
Step three: and (4) designing a deep neural network model architecture by taking the track state vector as input and the track control vector as output, performing model training by using the robust track optimization numerical sample set aiming at the multi-source uncertain factors obtained in the step two, and verifying the effectiveness of the model.
Specifically, a track state and control data pair on a numerical discrete point is used as training data to form a robust track training data set, and the robust track training data set is formed by collecting the state and control pair in the robust track training data set
Wherein the content of the first and second substances,
is a railTrace state variable, U ═ αcσc]TIs a trajectory control variable; l is 1,2, …, L represents different track labels, D is 1,2 …, and D represents track number discrete points. On the basis, an uncertain nonlinear dynamics model is approximated by using a deep learning technology, a robust track planning and guidance optimization strategy is learned, and an intelligent robust optimal track and guidance model (f (X) is established(d)):→U(d))。
In this embodiment, 4000 robust optimal trajectories are optimized in MATLAB, each trajectory includes 500 discrete points of numerical value, so as to obtain an optimized numerical sample set of robust trajectories for multi-source uncertain factors, and the number of robust state and control data pairs in a data set is 4000 × 500 pairs.
Before deep neural network training, in order to improve the network training efficiency and enable the neural network to train and converge faster and better, track state variables in a data set are normalized, and the size of data is compressed to the range of [0, 1], wherein the normalization method comprises the following steps:
in the embodiment, a data set is randomly divided according to the proportion of a 75% training set and a 25% testing set, wherein the training set is used for training a deep neural network, and after multiple iterations, when the value of a loss function reaches a required error or the maximum iteration times, the network training is completed; the test set is used for verifying and testing the trained network performance, and the evaluation indexes comprise Mean Square Error (MSE), Mean Absolute Error (MAE) and accuracy.
The deep neural network is constructed by using a Keras2.3.1 deep learning package in a Python3.8.3 environment, a Keras framework runs by taking Tensorflow2.2.0 accelerated based on a GPU as a rear end, a network model is defined as a sequential model, and adjacent layers are mutually and completely connected.
An input layer: state quantity of aircraft at time d
Includes 6 state parameters, y, theta,
V, gamma and psi respectively represent the center distance, longitude, latitude, speed, track angle and heading angle of the state variables of the aircraft.
Hiding the layer: determining the number of proper hidden layers and the number of nodes of each layer through general experience and experimental results of repeated training; the activation function is selected as a ReLU function which can avoid the gradient disappearance problem in most cases and has higher convergence speed, and the expression is as follows:
an output layer: due to the outputted control quantity U(d)＝[ασ]TAnd the classification problem is not involved, only the network prediction value is output, and the output layer does not need to call an activation function additionally.
The measure of the network output error is a loss function, the larger the loss value is, the worse the prediction accuracy of the network is represented, the present embodiment adopts the mean square error as the loss function, and the expression is:
wherein C represents the error size of each batch, XdRepresenting the input state quantity, UsRepresenting the true value of the controlled variable, UpRepresenting the network output value, NbRepresenting a batch of data sizes each time it is provided for network training.
The embodiment is used for data set of training and testing network, and the number of robust state and control data pairs is 2 multiplied by 106For the above reasons, considering that the data set is large, the computing resources of the computer are limited, the data cannot be transmitted into the network at one time, and each time only one data is relied on to update the parameters, the loss in the training process can be causedThe variation of the function is large, which results in non-convergence of the model, so that each time a certain batch of data sets are transmitted into the network for training, N is selected in the embodimentb＝1024。
When the model is configured, an Adam optimization algorithm with excellent performance is selected to train the network so as to enable the network to converge more quickly and better, and the parameter setting of the algorithm follows the default value.
The setting of the number of network training rounds also influences the prediction capability of the model. Considering the problem of computational complexity, the more rounds of training, the more accurate the result may be, but the corresponding training time is also increasing. In the example, the training round number is set to be 200 times to select a proper hidden layer structure, the training round number is increased under an optimal structure, so that the network is sufficiently converged, and the model is stored to realize the prediction of the aircraft control quantity.
In the selection of the network hidden layer structure, the influence of different hidden layer structures on the network prediction precision is compared by fixing the batch value of each training to be 1024 and the number of training rounds to be 200. Table 1 compares the magnitude and accuracy of Mean Square Error (MSE) values on training sets and test sets obtained by analyzing the number of different hidden layers and the number of nodes.
TABLE 1 MSE and accuracy results for different hidden layer structures
As can be seen from table 1, a relatively shallow network with a limited number of cells reduces the ability of the network to approach the optimal control structure, resulting in under-training; increasing the number of cells will have a positive effect on reducing the values of Tr-MSE and Te-MSE and increasing the accuracy, and more layers of the network will also provide more benefits. However, when the network scale is too large, the calculation complexity is correspondingly improved, the network convergence speed is reduced, the improvement of the training result index is not obvious, and finally, after the network is carried on an aircraft, the calculation amount of forward prediction is increased along with the increase of the depth, so that the real-time performance is deteriorated; in addition, the network is oversized, which may result in the network being over-trained, resulting in an overfitting. In this embodiment, a structure with a hidden layer of 6/64 is selected according to the computing power of the computer and the training index of the network.
To determine the influence of different training rounds on the accuracy of the deep neural network, table 2 lists the results of the evaluation indexes of the training set and the test set obtained by different training rounds under the same hidden layer structure, that is, the number of hidden layers is 6, the number of nodes of each layer is 64, and the size of the same batch is 1024.
TABLE 2 network evaluation index results under different training rounds
As can be seen from table 2, in the initial stage, as the number of training rounds is continuously increased, the errors and the accuracy of the training set and the test set are on the whole in an improvement trend, but when the number of training rounds is large, the goodness of the training result on the test set is no longer obvious, but rather, the training result is continuously fluctuated within a certain error range. In addition, the training time of the network also increases as the number of rounds increases. The DNN model with 1000 training rounds is finally selected for saving in this example for calling and testing.
Step four: the performance of the DNN drive control scheme was tested. Under the environment of a Windows 10 operating system 8G memory i5-7300HQ CPU, the DNN only needs 0.04s to complete the track prediction of 500 discrete points, and the capability of satisfying the intelligent real-time update of the robust track planning guidance instruction is achieved.
In order to verify the robustness of the robust track planning guidance instruction, the numerical range of uncertain factors such as reentry initial values and atmospheric parameters adopted in the off-line robust optimization design stage is considered, and a DNN (Dempster-Ny) model is used for predicting the robust track control vector UCSolving a kinetic equation based on a fourth-order Runge Kutta integral algorithm, and calculating a corresponding track state vector XC. On the basis, the original uncertain factor value range is respectively enlarged by 15%, 20% and 25%, and corresponding DNN control vectors and state vectors are sequentially calculated to obtain the DNN control vectors and the state vectors
For the reentry trajectory states obtained under the four conditions, the robustness of the DNN model trajectory planning guidance is analyzed, and the obtained aircraft trajectory state variable results are respectively shown in fig. 4 to 9. It can be seen that, as the robust track optimization numerical sample set aiming at the multi-source uncertain factors is adopted for training, after the value range of the original uncertain factors is sequentially increased by 15%, 20% and 25%, the track state vectors driven by the DNN model are almost overlapped together, and the guidance instruction keeps good robustness.
In summary, an application schematic diagram of the hypersonic aircraft intelligent reentry guidance method based on robust trajectory optimization provided by the invention is shown in fig. 10. Compared with the traditional track optimization method, the method can enhance the active defense capability of the guidance instruction on complex multi-source uncertainty, and meanwhile effectively reduces the design burden of the aircraft guidance control system.
In the above embodiments, the implementation may be wholly or partially realized by software, hardware, firmware, or any combination thereof. When used in whole or in part, can be implemented in a computer program product that includes one or more computer instructions. When loaded or executed on a computer, cause the flow or functions according to embodiments of the invention to occur, in whole or in part. The computer may be a general purpose computer, a special purpose computer, a network of computers, or other programmable device. The computer instructions may be stored in a computer readable storage medium or transmitted from one computer readable storage medium to another, for example, the computer instructions may be transmitted from one website site, computer, server, or data center to another website site, computer, server, or data center via wire (e.g., coaxial cable, fiber optic, Digital Subscriber Line (DSL), or wireless (e.g., infrared, wireless, microwave, etc.)). The computer-readable storage medium can be any available medium that can be accessed by a computer or a data storage device, such as a server, a data center, etc., that includes one or more of the available media. The usable medium may be a magnetic medium (e.g., floppy Disk, hard Disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., Solid State Disk (SSD)), among others.
The above description is only for the purpose of illustrating the present invention and the appended claims are not to be construed as limiting the scope of the invention, which is intended to cover all modifications, equivalents and improvements that are within the spirit and scope of the invention as defined by the appended claims.
Claims (10)
1. An intelligent robust reentry guidance method for a hypersonic aircraft is characterized by comprising the following steps:
based on uncertainty system modeling, judging uncertainty and types thereof existing in the gliding reentry process of the hypersonic aerocraft according to data mining and expert experience, and determining the distribution form and distribution interval of uncertainty parameters;
carrying out uncertainty quantitative analysis based on a non-embedded polynomial chaos theory according to the obtained uncertainty factors, and establishing a robust dynamic trajectory optimization model containing the statistical moment characteristics of a random system; establishing a robust track optimization numerical sample set aiming at the multi-source uncertain factors by changing uncertain parameter values and designing a numerical solving strategy;
designing a deep neural network model architecture by taking the track state vector as input and the track control vector as output; performing model training by using the obtained robust track optimization numerical sample set aiming at the multi-source uncertain factors, and verifying the effectiveness of the model;
and loading a deep neural network model with complete training, and intelligently updating the robust trajectory planning guidance instruction in real time according to flight state information output by a missile-borne control system including a navigation positioning system and an attitude control system in the reentry process of the aircraft.
2. The hypersonic aircraft intelligent robust reentry guidance method of claim 1, wherein the modeling based on the uncertainty system, judging the uncertainty and the type thereof existing in the process of hypersonic aircraft gliding reentry according to data mining and expert experience, and determining the distribution form and the distribution interval of the uncertainty parameters comprises:
carrying out classification modeling aiming at cognitive uncertainty, random uncertainty and numerical uncertainty in a high-speed flight dynamics system, researching uncertainty sources and types in a robust trajectory optimization design process on the basis, and carrying out uncertainty modeling around initial reentry conditions, pneumatic model data, atmospheric model parameters and perturbation parameters of an aircraft in the unpowered reentry process of the hypersonic glide aircraft;
wherein the uncertain factor types are:
wherein xi is a random variable vector; subscript y0、θ0、
V0、γ0、ψ0Respectively representing the initial reentry states of the aircraft state variables such as the earth's center distance, longitude, latitude, speed, track angle and course angle, CL、CDRespectively represents the lift coefficient and the drag coefficient of the aircraft, rho represents the atmospheric density, mVRepresenting the aircraft's own mass.
3. The hypersonic aircraft intelligent robust reentry guidance method according to claim 1, wherein the uncertainty distribution form is assumed to be uniformly distributed and independent from each other, and the system stochastic model and the uncertainty distribution range are as follows:
wherein the content of the first and second substances,
respectively representing the random initial reentry state of the aircraft;
representing a random lift coefficient and a random drag coefficient;
is a random atmospheric density;
is a random aircraft mass.
4. The hypersonic aircraft intelligent robust reentry guidance method of claim 1, wherein the aircraft random trajectory optimization model comprises random dynamical differential equations, random dimensionless aerodynamic forces, random process constraints, random initial value constraints, terminal constraints and control variables, including:
(1) differential equation of stochastic dynamics
Wherein y, theta,
V, gamma and psi respectively represent the geocentric distance, longitude, latitude, speed, track angle and heading angle of the aircraft state variables; omega is the rotation angular rate of the earth; y, V, t and omega are dimensionless variables, R is the dimensionless parameter0、Vc＝(g0R0)0.5、(R0/g0)0.5And (g)0/R0)0.5，R0Is the mean radius of the earth, g0Is seaPlanar gravitational acceleration;
respectively random dimensionless lift force and resistance force, and dimensionless parameters of 2mV·g0；
(2) Random aerodynamic force
Wherein S isVAn aerodynamic reference area for the aircraft;
(3) random process constraints
Wherein the content of the first and second substances,
is the heat flow density, qrIs dynamic pressure, nrIs overloaded;
qmax、nmaxrespectively corresponding process constraint maximum values;
(4) random initial value constraint
Wherein the content of the first and second substances,
is a random state initial value;
(5) terminal constraints
Wherein, XfIs in the terminal state, yf、θf、
VfRespectively corresponding terminal state design values;
(6) controlled variable
U＝[ασ]T；
Wherein alpha is an attack angle and sigma is an inclination angle;
(7) optimizing an objective function
J＝tf；
Wherein, tfIs the terminal time.
5. The hypersonic aircraft intelligent robust reentry guidance method according to claim 1, characterized in that a non-embedded polynomial chaotic algorithm is adopted for uncertainty quantitative analysis to obtain statistical moment information of flight system state variables, target variables, process constraints and boundary constraints, and meanwhile, a stochastic dynamics differential equation is converted into a high-dimensional deterministic differential equation to be solved, and a robust dynamic trajectory optimization model is established; wherein the robust dynamic trajectory optimization model is in the form of:
wherein U (t) is a control variable, and t is a time variable; j. the design is a squareAFor robust optimization of the objective, JμAnd JσSeparately optimizing the target statistical moment, k, for randomμAnd k isσIs the corresponding coefficient;
is a random state vector;
derived for random state differential equation transformationQualitative differential equation with n being 1 … mq(ii) a Wherein q is the dimension of a random variable vector xi, and m is the number of orthogonal integration points adopted by the polynomial chaotic expansion; cμAnd CσStatistical moments that are respectively random process constraints; b isμAnd BσStatistical moments, t, respectively, of random boundary constraints0Is the starting time.
6. The hypersonic aircraft intelligent robust reentry guidance method according to claim 1 is characterized in that according to the system random model and uncertainty factor distribution shown in claims 2 and 3, uncertainty factor values are changed randomly and a corresponding robust dynamic trajectory optimization model is solved to obtain a trajectory data set and obtain a sufficient offline robust optimal trajectory.
7. The hypersonic aircraft intelligent robust reentry guidance method of claim 1, wherein the trajectory state and control data pairs on the numerical discrete points are used as training data to form a robust trajectory training data set, and the robust trajectory training data set comprises:
wherein the content of the first and second substances,
for the track state variable, U ═ α σ]TIs a trajectory control variable; l is 1,2, …, L represents different track labels, D is 1,2 …, and D represents track numerical discrete points; on the basis, an uncertain nonlinear dynamics model is approximated by using a deep learning technology, a robust track planning and guidance optimization strategy is learned, and an intelligent robust optimal track and guidance model (f (X) is established(d)):→U(d))。
8. The hypersonic aircraft intelligent robust reentry guidance method of claim 1, wherein the deep neural network is trained and tested by taking a track state vector as the input of the deep neural network and a track control vector as the output of the deep neural network, and uncertain nonlinear flight dynamics model state and control optimality mapping is established, comprising:
under a Python environment, using a Keras deep learning package to create DNN, and operating a Keras framework by taking Tensorflow accelerated based on a GPU as a back end; dividing a track data set into a training set and a testing set according to a proper proportion; the deep neural network consists of an input layer, an output layer and a plurality of hidden layers, the created DNN network is a sequential model, and adjacent layers are connected with each other; adopting an Adam optimization algorithm with excellent performance, adopting a mean square error as a loss function, adopting a ReLU function as a hidden layer activation function, transmitting a certain batch of data each time to calculate loss and update network parameters to obtain an optimal training result; and finally, comparing the track generated by the optimal control with the track generated by the state quantity generated by the DNN drive, and verifying the validity of the model.
9. The hypersonic aircraft intelligent robust reentry guidance method of claim 1, wherein the loading of the deep neural network model with complete training realizes intelligent real-time updating of the robust trajectory planning guidance instruction according to flight state information output by a missile-borne control system including a navigation positioning system and an attitude control system in the reentry process of the aircraft, and comprises the following steps:
loading the deep neural network model which is completely trained on the aircraft, and using the real-time flight state quantity output by the missile-borne control system including the navigation positioning system and the attitude control system in the reentry process of the aircraft
As network input, to control the quantity U(d)＝[α σ]TAnd as output, intelligent real-time updating of the robust track planning guidance instruction is realized.
10. A hypersonic aircraft intelligent robust reentry guidance system for executing the hypersonic aircraft intelligent robust reentry guidance method according to any one of claims 1 to 9, wherein the hypersonic aircraft intelligent robust reentry guidance system comprises:
the uncertainty modeling module is used for judging uncertainty and types thereof existing in the gliding reentry process of the hypersonic flight vehicle according to data mining and expert experience based on uncertainty system analysis and determining the distribution form and the distribution interval of uncertainty parameters;
the uncertainty quantitative analysis module is used for developing uncertainty quantitative analysis based on a non-embedded polynomial chaos theory according to the obtained uncertainty factors;
the track optimization model building module is used for building a robust dynamic track optimization model containing the random system target and the state variable statistical moment characteristics;
the numerical sample set establishing module is used for establishing a robust track optimization numerical sample set aiming at the multi-source uncertain factors by changing uncertain parameter values and designing a numerical solving strategy;
the neural network model architecture design module is used for designing a deep neural network model architecture by taking the track state vector as input and taking the track control vector as output;
the model training module is used for performing model training by using the obtained robust track optimization numerical sample set aiming at the multi-source uncertain factors and verifying the effectiveness of the model;
and the instruction real-time updating module is used for loading a deep neural network model with complete training and realizing intelligent real-time updating of the robust track planning guidance instruction according to flight state information output by a missile-borne control system including the navigation positioning system and the attitude control system in the reentry process of the aircraft.
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Application publication date: 20210716 |