CN110991051B - Remote guidance rocket projectile drop point prediction system based on experimental design and Kriging model - Google Patents
Remote guidance rocket projectile drop point prediction system based on experimental design and Kriging model Download PDFInfo
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Abstract
The invention belongs to the technical field of guided rocket drop point prediction, and particularly relates to a remote guided rocket drop point prediction system based on test design and a Kriging model. For the drop point prediction corresponding to the arc-rising section, the selected correlation functions include a Spline function, a Matern function and a Cubic function; for the drop point prediction corresponding to the arc-dropping segment, the selected correlation functions include a Spline function, a Matern function, a Gauss function and a Cubic function. The invention provides an effective scheme for the trajectory correction control system of the remotely guided rocket projectile to predict the drop point in real time.
Description
Technical Field
The invention belongs to the technical field of guided rocket drop point prediction, and particularly relates to a remote guided rocket drop point prediction system based on test design and a Kriging model.
Background
The core technology for realizing the accurate striking of the remotely guided rocket projectile is trajectory correction, and the drop point prediction guidance is one of the main methods of trajectory correction. The method for rapidly and accurately predicting the projectile drop point is one of key technologies of drop point prediction guidance, and the accuracy and the real-time performance of the method can directly influence the ballistic correction effect. Common methods for predicting the drop point include numerical integration, linearization and filter extrapolation.
The numerical integration method is a method for obtaining a drop point through an iterative ballistic program on the basis of an established ballistic model, and the most typical ballistic model is a six-degree-of-freedom model. Theoretically, the falling point obtained through calculation of the six-degree-of-freedom ballistic model is the most accurate, but in the calculation process, tedious iteration needs to consume a large amount of time, and the requirement on hardware is high, so that the numerical integration method generally adopts ballistic models with other degrees of freedom, such as a four-degree-of-freedom model, a three-degree-of-freedom model and a two-degree-of-freedom model.
The linearization method is a method for obtaining a linear ballistic equation system by approximately linearizing a nonlinear outer ballistic model, solving an analytical solution of the linear ballistic equation system, and predicting a projectile drop point by using the analytical solution. The linearization method can quickly predict the projectile landing point, but is insufficient in accuracy.
The filtering extrapolation method is a method for extrapolating a rocket drop point through an established filtering trajectory model. Since the theoretical basis of the filtering extrapolation method is established on a linear system and a Gaussian noise environment, certain errors are inevitably generated when the method is used for a nonlinear system of a flight trajectory, and even filtering divergence is caused when the noise is non-Gaussian noise.
Compared with the short-range guided rocket projectile, the long-range guided rocket projectile has the advantages of longer range, larger ballistic height and longer flight time. Under the condition, if the numerical integration method is still adopted to predict the drop point of the remotely guided rocket projectile, the real-time requirement cannot be met at all, and the linear method cannot meet the precision requirement. Meanwhile, compared with an outer ballistic model of a short-range guided rocket projectile, the relatively accurate outer ballistic model of the long-range guided rocket projectile needs to comprehensively consider the influences of gravity eccentricity, surface curvature, the change of gravity acceleration along with height and latitude, coriolis inertia force and other factors, and the influencing factors are determined by gun position latitude, elevation and direction, so that the influence of launching conditions needs to be considered when the drop point of the long-range guided rocket projectile is predicted. The method for predicting the drop point of the remotely guided rocket projectile under any launching condition has practical significance.
Disclosure of Invention
Technical problem to be solved
The technical problem to be solved by the invention is as follows: how to utilize the optimized Latin hypercube test design and the Kriging model to carry out high-precision rapid prediction on the drop point of the remotely guided rocket projectile.
(II) technical scheme
In order to solve the technical problem, the invention provides a remote guidance rocket projectile drop point prediction system based on experimental design and a Kriging model, which comprises: the system comprises an equation set establishing module, a mathematical model establishing module, a sample acquiring module, a training module and a loading module; the system comprises an equation set establishing module, an equation set establishing module and a data processing module, wherein the equation set establishing module is used for establishing a remote rocket projectile motion equation set;
the mathematical model building module is used for building a nonlinear mathematical model for the remote guidance rocket projectile drop point prediction;
the sample acquisition module is used for acquiring a training sample and a test sample;
the training module is used for selecting a proper correlation function of the Kriging model to train samples corresponding to the rising arc section and the falling arc section;
the loading module is used for loading the drop point prediction model meeting the requirements of precision and instantaneity into the missile-borne computer.
In the working process of the equation set establishing module, the remote guided rocket projectile is supposed to be predicted according to the landing point of the uncontrolled ballistic flight, and an uncontrolled ballistic mathematical model in the longitudinal plane of the remote guided rocket projectile is used as a remote rocket projectile motion equation set as follows:
in the formula: m is the flight quality of the remotely guided rocket projectile; t is time; v x And V y Two velocity components under a ground coordinate system; omega ix1 、ω iy1 And omega iz1 The three components of the rotating angular velocity vector of the projectile body relative to a translation coordinate system are in the projectile body coordinate system; j is a unit of x1 、J y1 And J z1 Respectively the polar moment of inertia, the equatorial moment of inertia and the equatorial moment of inertia of the remotely guided rocket projectile; omega e The angular speed of the rotation of the earth axis; omega ex 、ω ey And ω ez Is omega e Three components in a transmission coordinate system;
and θ is pitch angle and trajectory inclination angle, respectively; alpha is an attack angle;
p is engine thrust; q is dynamic pressure; s ref And L ref Respectively a reference area and a reference length; c x And C y Respectively a drag coefficient and a lift coefficient; x and y are two position components under a ground coordinate system; r is 0x And R 0y Two components of the emission point geocentric radial under an emission coordinate system are taken as the emission point; r is the model of the center-of-earth radial of any point on the trajectory; g is a radical of formula r 'is the component of the acceleration of the earth gravity along the direction of the earth's center sagittal;
is the component of the acceleration of the gravity along the earth axis direction; l is 0 The geocentric latitude of the transmitting point is taken as the center of the earth; a. The 0 Is the transmit azimuth;
the change rate of the static stability moment coefficient along with alpha;
to damp the moment coefficient
Of wherein
m c Is the rate of change of the mass of the engine over time.
Wherein, in the working process of the mathematical model establishing module, a nonlinear mathematical model for predicting the drop point of the remote guided rocket projectile under the standard meteorological condition is established, and the dependent variable of the nonlinear mathematical model is the drop point Y R And the independent variables are parameters of launching condition and flight state, including the latitude B of the gun position 0 Elevation of gun location H 0 Shoot to A T Elevation H of target point T 、V x 、V y 、x、y、
The basic form is:
in the working process of the sample acquisition module, the training sample and the test sample are acquired based on the optimized Latin hypercube test design and the remotely guided rocket projectile motion equation set.
Wherein, in the working process of the sample acquisition module,
because the training sample and the test sample are obtained by the same method, the method for obtaining the training sample only comprises the following steps:
s301: using optimized latin hypercube pairs including the latitude of the gun position B 0 Height H of gun position 0 Shoot to A T Distance X G Elevation H of target point T Medicine temperature T S Carrying out numerical test design on all the factors, wherein the value ranges of 6 factors are given according to the launching conditions and the range capability of the remotely guided rocket projectile;
s302: calculating a specific transmission condition B for each numerical test point in S301 0 、H 0 、A T 、H T And T S At a given range X G Corresponding shooting angle under standard meteorological conditionsEach test point corresponds to one trajectory;
s303: for each test point in S302, the flight data of the remote rocket projectile is output at regular intervals by taking the engine shutdown time as a starting point, wherein the flight data comprises V x 、V y 、x、y、
ω z1 An internal ballistic parameter;
s304: randomly generating a corresponding attack angle aiming at the flight data output each time in S303, giving out the variation range of the attack angle according to the variation range of the attack angle of the remotely guided rocket projectile at different stages in the actual flight process by using a formula
Recalculating the pitch angle in each flight data and comparing the pitch angle in each flight data in S303
Replacing the pitch angle with the latest pitch angle;
s305: and aiming at the flight data and the corresponding launching conditions in the S304, recalculating the drop points corresponding to the flight data under the standard meteorological conditions by using a ballistic simulation mode in a longitudinal plane, and dividing the drop points into two groups according to the modes of the arc rising section samples and the arc falling section samples.
Wherein, the training module is suitable for the correlation function of Kriging model of drop point prediction corresponding to ballistic rising arc section and drop arc section in the working process,
for the drop point prediction corresponding to the arc-rising section, the selected correlation function comprises: a Spline function, a Matern function and a Cubic function;
for the drop point prediction corresponding to the arc-dropping segment, the selected correlation function comprises: a Spline function, a Matern function, a Gauss function, and a Cubic function.
Wherein the value range of the non-negative integer q of the Matern function is 3-5.
The system can accurately and quickly predict the drop point of the remotely guided rocket projectile under any launching condition.
(III) advantageous effects
In order to solve the urgent need of rapid high-precision prediction of the drop point of the remote guidance rocket bomb, the invention provides a system for predicting the drop point of the remote guidance rocket bomb based on an optimized Latin hypercube test design and a Kriging model.
Drawings
FIG. 1 is a flow chart of remotely guided rocket projectile drop point prediction under standard meteorological conditions.
FIG. 2 is a graph of the prediction accuracy of a Kriging model with a correlation function of a Matern function on a drop point as a function of a non-negative integer q.
Detailed Description
In order to make the objects, contents, and advantages of the present invention clearer, the following detailed description of the embodiments of the present invention will be made in conjunction with the accompanying drawings and examples.
In order to solve the technical problem, the invention provides a remote guidance rocket projectile drop point prediction system based on test design and a Kriging model, which comprises: the system comprises an equation set establishing module, a mathematical model establishing module, a sample acquiring module, a training module and a loading module; the system comprises an equation set establishing module, an equation set establishing module and a data processing module, wherein the equation set establishing module is used for establishing a remote rocket projectile motion equation set;
the mathematical model building module is used for building a nonlinear mathematical model for the drop point prediction of the remotely guided rocket projectile;
the sample acquisition module is used for acquiring a training sample and a test sample;
the training module is used for selecting a proper correlation function of the Kriging model to train samples corresponding to the rising arc section and the falling arc section;
the loading module is used for loading the drop point prediction model meeting the requirements of precision and instantaneity into the missile-borne computer.
In the working process of the equation set establishing module, the remote guided rocket projectile is supposed to be predicted according to the landing point of the uncontrolled ballistic flight, and an uncontrolled ballistic mathematical model in the longitudinal plane of the remote guided rocket projectile is used as a remote rocket projectile motion equation set as follows:
in the formula: m is the flight quality of the remotely guided rocket projectile; t is time; v x And V y Two velocity components under a ground coordinate system; omega ix1 、ω iy1 And ω iz1 The three components of the rotating angular velocity vector of the projectile body relative to a translation coordinate system are in the projectile body coordinate system; j. the design is a square x1 、J y1 And J z1 Respectively the polar moment of inertia, the equatorial moment of inertia and the equatorial moment of inertia of the remotely guided rocket projectile; omega e The angular speed of the rotation of the earth axis; omega ex 、ω ey And ω ez Is omega e Three components in a transmission coordinate system;
and theta is a pitch angle and a ballistic inclination angle respectively; alpha is an attack angle;
p is engine thrust; q is dynamic pressure; s ref And L ref Respectively a reference area and a reference length; c x And C y Respectively a drag coefficient and a lift coefficient; x and y are two position components under a ground coordinate system; r 0x And R 0y Two components of the earth center radial of the emission point under an emission coordinate system are obtained; r is the model of the geocentric radial of any point on the trajectory; g r ' is the component of the acceleration of the earth's gravity along the radial direction of the earth's center;
is the component of the acceleration of the gravity along the earth axis direction; l is 0 Is the geocentric latitude of the transmitting point; a. The 0 Is the transmit azimuth;
the change rate of the static stability moment coefficient along with alpha;
for damping moment coefficient
Of wherein
m c Is the rate of change of the mass of the engine over time.
In the working process of the mathematical model establishing module, a nonlinear mathematical model for predicting the drop point of the remotely guided rocket projectile under the standard meteorological condition is established, and the dependent variable of the nonlinear mathematical model is the drop point Y R And the independent variables are parameters of launching conditions and flight states, including the latitude B of the gun position 0 Elevation of gun location H 0 Shoot to A T Elevation H of target point T 、V x 、V y 、x、y、
The basic form is:
in the working process of the sample acquisition module, the training sample and the test sample are acquired by the method based on optimized Latin hypercube test design and a remote guidance rocket projectile motion equation system.
Wherein, in the working process of the sample acquisition module,
as the acquisition method of the training sample and the test sample is the same, only the acquisition method of the training sample is given, and the method comprises the following steps:
s301: using optimized latin hypercube pairs including the latitude of the gun position B 0 Height H of gun position 0 Shoot to A T Distance X G Elevation of target pointH T Medicine temperature T S Carrying out numerical test design on all the factors, wherein the value ranges of 6 factors are given according to the launching conditions and the range capability of the remotely guided rocket projectile;
s302: calculating a specific transmission condition B for each numerical test point in S301 0 、H 0 、A T 、H T And T S At a given range X G Each test point corresponds to a trajectory at a corresponding shooting angle under the standard meteorological condition;
s303: for each test point in S302, the flight data of the remote rocket projectile is output at regular intervals by taking the engine shutdown time as a starting point, wherein the flight data comprises V x 、V y 、x、y、
ω z1 An internal ballistic parameter;
s304: randomly generating a corresponding attack angle aiming at the flight data output each time in S303, giving out the variation range of the attack angle according to the variation range of the attack angle of the remotely guided rocket projectile at different stages in the actual flight process by using a formula
Recalculating the pitch angle in each flight data, and comparing the pitch angle in each flight data in S303
Replacing with the latest pitch angle;
s305: and aiming at the flight data and the corresponding launching conditions in the S304, recalculating the drop points corresponding to the flight data under the standard meteorological conditions by using a ballistic simulation mode in a longitudinal plane, and dividing the drop points into two groups according to the modes of the arc rising section samples and the arc falling section samples.
Wherein, the training module is suitable for the correlation function of Kriging model of drop point prediction corresponding to ballistic rising arc section and drop arc section in the working process,
for the drop point prediction corresponding to the arc-rising section, the selected correlation function comprises: a Spline function, a Matern function and a Cubic function;
for the drop point prediction corresponding to the arc-dropping segment, the selected correlation function comprises: a Spline function, a Matern function, a Gauss function, and a Cubic function.
Wherein the value range of the non-negative integer q of the Matern function is 3-5.
The system can accurately and quickly predict the drop point of the remotely guided rocket projectile under any launching condition.
In addition, the invention also provides a remote guidance rocket projectile drop point prediction method based on the experimental design and the Kriging model, the method can be used for accurately and rapidly predicting the remote guidance rocket projectile drop point under any launching condition, and as shown in figure 1, the method comprises the following steps:
step 1: establishing a remote rocket projectile motion equation set;
step 2: establishing a nonlinear mathematical model for predicting the landing point of the remotely guided rocket projectile;
and step 3: acquiring a training sample and a test sample;
and 4, step 4: selecting a proper correlation function of the Kriging model to train samples corresponding to the rising arc section and the falling arc section;
and 5: and loading the drop point prediction model meeting the requirements of precision and real-time performance into the missile-borne computer.
In the step 1, it is assumed that the remotely guided rocket projectile is predicted according to a landing point of the uncontrolled ballistic flight, and an uncontrolled ballistic mathematical model in a longitudinal plane of the remotely guided rocket projectile is used as a motion equation set of the remotely guided rocket projectile, and the motion equation set comprises the following steps:
in the formula: m is the flight quality of the remotely guided rocket projectile; t is time; v x And V y Two velocity components under a ground coordinate system; omega ix1 、ω iy1 And ω iz1 The three components of the rotating angular velocity vector of the projectile body relative to a translation coordinate system are in the projectile body coordinate system; j. the design is a square x1 、J y1 And J z1 Respectively the polar moment of inertia, the equatorial moment of inertia and the equatorial moment of inertia of the remotely guided rocket projectile; omega e The angular velocity of the rotation of the earth axis; omega ex 、ω ey And omega ez Is omega e Three components in a transmission coordinate system;
and θ is pitch angle and trajectory inclination angle, respectively; alpha is an attack angle;
p is engine thrust; q is dynamic pressure; s ref And L ref Respectively a reference area and a reference length; c x And C y Respectively a drag coefficient and a lift coefficient; x and y are two position components under a ground coordinate system; r 0x And R 0y Two components of the emission point geocentric radial under an emission coordinate system are taken as the emission point; r is the model of the center-of-earth radial of any point on the trajectory; g r ' is the component of the acceleration of the earth's gravity along the radial direction of the earth's center;
is the component of the acceleration of the earth gravity along the direction of the earth axis; l is 0 Is the geocentric latitude of the transmitting point; a. The 0 Is the transmit azimuth;
the change rate of the static stability moment coefficient along with alpha;
for damping moment coefficient
Of wherein
m c Is the rate of change of the mass of the engine over time.
In the step 2, the nonlinear mathematical model for the remote guidance rocket projectile landing point prediction comprehensively considers launching condition factors and flight state parameters influencing the remote guidance rocket projectile landing point prediction precision under standard meteorological conditions, wherein the launching condition factors comprise a shot space latitude, a shot space elevation, a shot direction and a target point elevation, and the flight state parameters comprise the speed and the position in the x direction and the y direction and a pitch angle under a ground coordinate system;
a nonlinear mathematical model for predicting the drop point of the remotely guided rocket projectile under the standard meteorological condition is established, and the dependent variable is the drop point Y R And the independent variables are parameters of launching condition and flight state, including the latitude B of the gun position 0 Elevation of gun location H 0 Shoot to A T Elevation H of target point T 、V x 、V y 、x、y、
The basic form is:
in the step 3, the training samples and the test samples are obtained by the method based on the optimized Latin hypercube test design and the remotely guided rocket projectile motion equation set.
Wherein, in the step 3, the first step,
as the acquisition method of the training sample and the test sample is the same, only the acquisition method of the training sample is given, and the method comprises the following steps:
s301: using optimized Latin hypercube method to include the gun position latitude B 0 Height H of gun position 0 Shoot to A T Distance X G Elevation H of target point T Medicine temperature T S Carrying out numerical test design on all the factors, wherein the value ranges of 6 factors are given according to the launching conditions and the range capability of the remotely guided rocket projectile;
s302: calculating a specific transmission condition B for each numerical test point in S301 0 、H 0 、A T 、H T And T S At a given range X G Each test point corresponds to a trajectory at a corresponding shooting angle under the standard meteorological condition;
s303: for each test point in S302, the flight data of the remote rocket projectile, including V, are output at regular intervals by taking the engine shutdown time as a starting point x 、V y 、x、y、
ω z1 An internal ballistic parameter;
s304: randomly generating a corresponding attack angle aiming at the flight data output each time in the S303, giving the change range of the attack angle according to the change range of the attack angle of the remotely guided rocket projectile at different stages in the actual flight process, and utilizing a formula
Recalculating the pitch angle in each flight data and comparing the pitch angle in each flight data in S303
Replacing with the latest pitch angle;
s305: and aiming at the flight data and the corresponding launching conditions in the S304, recalculating the drop points corresponding to the flight data under the standard meteorological conditions by using a ballistic simulation mode in a longitudinal plane, and dividing the drop points into two groups according to the modes of the arc rising section samples and the arc falling section samples.
Wherein, in the step 4, the method is suitable for the correlation function of the Kriging model for predicting the drop points corresponding to the ballistic arc-rising section and the ballistic arc-falling section,
for the drop point prediction corresponding to the arc-rising section, the selected correlation function comprises: a Spline function, a Matern function and a Cubic function;
for the drop point prediction corresponding to the arc-dropping segment, the selected correlation function comprises: a Spline function, a Matern function, a Gauss function, and a Cubic function.
Wherein the value range of the non-negative integer q of the Matern function is 3-5.
Example 1
In the embodiment, a high-precision rapid prediction method for a remotely guided rocket projectile landing point based on an optimized latin hypercube test design and a Kriging model is provided, as shown in fig. 1, the method comprises the following steps:
s1: and establishing a motion equation set of the remotely guided rocket projectile. The drop point of a remotely guided rocket projectile is primarily determined by motion in the longitudinal plane. On the basis of carrying out stress analysis on the remotely guided rocket projectile, a relatively accurate motion model in a longitudinal plane of the remotely guided rocket projectile is established by combining the conventional ballistic model and based on the principle of being as accurate as possible, and the model comprehensively considers the influences of gravity eccentricity, surface curvature, gravity acceleration along with the change of height and latitude, coriolis inertia force and the like. Meanwhile, the invention mainly researches the remotely guided rocket projectile according to a drop point prediction method of the uncontrolled ballistic flight, so that only an uncontrolled ballistic mathematical model in a longitudinal plane is given:
in the formula: m is the flight quality of the remotely guided rocket projectile; t is time; v x And V y Two velocity components under a ground coordinate system; omega ix1 、ω iy1 And ω iz1 The three components of the rotating angular velocity vector of the projectile body relative to a translation coordinate system are in the projectile body coordinate system; j. the design is a square x1 、J y1 And J z1 Respectively the polar moment of inertia, the equatorial moment of inertia and the equatorial moment of inertia of the remotely guided rocket projectile; omega e The angular velocity of the rotation of the earth axis; omega ex 、ω ey And ω ez Is omega e Three components in a transmission coordinate system;
and θ is pitch angle and trajectory inclination angle, respectively; alpha is an attack angle;
S2: and establishing a nonlinear mathematical model for predicting the landing point of the remotely guided rocket projectile. Analyzing the motion equation set established in the step S1 to know that under the standard meteorological condition, after an engine of the remote guidance rocket is shut down, the falling point of the remote guidance rocket is mainly determined by the current flight state parameters and the stress condition, wherein the flight state parameters comprise the speed V under the ground coordinate system x And V y Position x and y under ground coordinate system, pitch angle
Pitch angle rate omega z1 . For remotely guided rocket projectilesThe pitch angle speed in the longitudinal plane of the rocket projectile is small, and the influence on the drop point is small, so that the influence of the pitch angle speed can be ignored when the drop point of the remotely guided rocket projectile is predicted. For the stress condition of the current flight state, besides the influence of the current flight state parameters, the stress condition is mainly influenced by the latitude of a gun position, the altitude of the gun position and the direction. Of course, the landing point of the remote rocket projectile is also related to the elevation of the target point. The analysis result is integrated to establish a nonlinear mathematical model for predicting the drop point of the remotely guided rocket projectile under the standard meteorological condition, and the dependent variable is the drop point Y R And the independent variables are parameters of launching condition and flight state, including the latitude B of the gun position 0 Altitude H of gun location 0 Shoot to A T Elevation H of target point T 、V x 、V y 、x、y、
The basic form is:
s3: training samples and test samples are obtained. Before establishing the nonlinear function relationship between the remote guided rocket falling point and each influence factor in the step S2, a training sample and a test sample need to be obtained. Because the training sample and the test sample are obtained by the same method, the method for obtaining the training sample is only provided, and mainly comprises the following steps:
s301: using optimized Latin hypercube method to measure various factors (including the latitude B of the gun position) 0 Height H of gun position 0 Shoot to A T Distance X G Target point elevation H T Medicine temperature T S ) Carrying out numerical test design, wherein the value range of 6 factors is given according to the launching condition and the range capability of the remotely guided rocket projectile;
s302: for each numerical test point in S301, a specific transmission condition (B) is calculated 0 、H 0 、A T 、H T And T S ) At a given range (X) G ) Corresponding standard meteorological conditionsEach test point corresponds to one trajectory;
s303: for each test point in S302, the flight data (including V) of the remote rocket projectile is output at regular intervals by taking the engine shutdown time as a starting point x 、V y 、x、y、
ω z1 Equal ballistic parameters);
s304: randomly generating a corresponding attack angle aiming at the flight data output each time in the S303, giving the change range of the attack angle according to the change range of the attack angle of the remotely guided rocket projectile at different stages in the actual flight process, and utilizing a formula
Recalculating the pitch angle in each flight data and comparing the pitch angle in each flight data in S303
Replacing the pitch angle with the latest pitch angle;
s305: and for the flight data and the corresponding launching conditions in the S304, recalculating the drop points corresponding to the flight data under the standard meteorological conditions by using a ballistic simulation program in a longitudinal plane, and dividing the drop points into two groups according to the mode of the rising arc section samples and the falling arc section samples.
S4: and selecting a correlation function to construct a Kriging model. And (4) selecting a proper Kriging model correlation function for training the training sample in the step (S3). Common correlation functions include Cubic function (Cubic), exponential function (Exp), gaussian function (Gauss), linear function (Lin), spherical function (sphere), spline function (Spline), and the like, as shown in table 1. In addition to the usual correlation functions described above, the Matern correlation function may be more efficient. When the positive parameter v takes a half integer, i.e. v = q +1/2, where q is a non-negative integer, the expression of the Matern correlation function becomes very simple. In this case, the Matern correlation function becomes the product of an exponential function and a polynomial of order q:
in the formula: r (theta, x) (i) ,x (j) ) Representing the training sample point x for the correlation function with the parameter theta (i) And x (j) Spatial correlation between them;
N Dv is x (i) Dimension (d) of (a).
For the drop point prediction corresponding to the rising arc section, the selectable correlation functions include a Spline function, a Matern function (the value of the non-negative integer q is 3-5) and a Cubic function, and for the drop point prediction corresponding to the falling arc section, the selectable correlation functions include a Spline function, a Matern function (the value of the non-negative integer q is 3-5), a Gauss function and a Cubic function. When the training error meets the requirement or the iteration reaches a certain number of times, extracting a drop point prediction model, testing the prediction precision and the real-time property by using a test sample, outputting the drop point prediction model if the drop point prediction model meets the precision and the real-time property requirement, modifying the type of a correlation function or properly increasing the number of training samples if the drop point prediction model cannot meet the precision or the real-time property requirement, training a new sample, and repeating the process until the drop point prediction model meets the precision and the real-time property requirement at the same time.
S5: and loading the non-linear functional relation between the drop point in the step S4 and each influence factor into the missile-borne computer.
S6: during actual flight of the remotely guided rocket projectile, for any given B 0 、H 0 、A T 、H T 、V x 、V y 、x、y、
The corresponding drop point can be obtained through the non-linear function relationship in step S5.
Example 2
In this embodiment, a long-distance guided rocket projectile is taken as an example, and for an ascending arc section after the shutdown of an engine and a descending arc section before the final guidance, kriging models with relevant functions of Cubic, exp, gauss, lin, matern, sphere and Spline are respectively used to verify the method. Aiming at all factors (gun position latitude, gun position elevation, shooting, range, target point elevation and chemical temperature), a test point is selected by adopting an optimized Latin hypercube test design, flight simulation data are output at regular intervals by taking the engine shutdown time as an initial point, and a training sample and a test sample are respectively flight simulation data generated on the basis of 1000 trajectories and 2000 trajectories. The training samples and the test samples are divided into two groups according to the mode of the arc rising section samples and the arc falling section samples.
For the rising arc section after the shutdown of the engine and the falling arc section before the end guidance, the change relation of the prediction precision of the Kriging model with the correlation function of the Matern function to the falling point along with the non-negative integer q is shown in FIG. 2, wherein the regression model part is a 4-order polynomial. When q belongs to [1,4], the drop point prediction accuracy corresponding to the rising arc section and the falling arc section is improved along with the increase of q, and when q belongs to [1,3], the falling point prediction accuracy corresponding to the rising arc section and the falling arc section is obviously improved along with the increase of q; when q belongs to [4,7], the drop point prediction accuracy corresponding to the rising arc section and the falling arc section is slightly reduced along with the increase of q. Taking the prediction of the falling point corresponding to the rising arc segment as an example, when q =1, the Maximum Absolute Error (MAE) and the Root Mean Square Error (RMSE) of the falling point are 356.49m and 40.83m, respectively; when q =3, both fall to 140.15m and 13.44m, respectively; when q =4, both dropped further to 102.11m and 11.76m; and when q =7, 178.45m and 18.51m, respectively. Compared with the drop point prediction precision corresponding to the arc rising section, the Kriging model with the correlation function being the Matern function has higher prediction precision for the drop point corresponding to the arc falling section.
When the regression model is a 4 th order polynomial, the influence of 7 correlation functions on the accuracy of the drop point prediction is shown in table 2, where Matern represents the optimal Matern correlation function (i.e., q = 4). When the number of training samples changes, the optimal nonnegative integer q of the Matern correlation function also changes, and a large amount of numerical simulation shows that the value of q is more suitable to be 3-5. For the rising arc section and the falling arc section, the related functions have larger influence on the prediction precision of the falling points, the related functions Cubic, matern and Spline have higher prediction precision on the falling points corresponding to the rising arc section and the falling arc section, a good interpolation result can be obtained mainly because the 3 related functions have good smoothness, the related functions Exp, gauss, lin and Spherical only have higher prediction precision on the falling points corresponding to the falling arc section, and the prediction precision of the related functions Exp, lin and Spherical on the falling points corresponding to the falling arc section is obviously lower than that of the related functions Cubic, matern and Spline on the falling points corresponding to the falling arc section. For the rising arc section and the falling arc section, the prediction accuracy of the 3 correlation function functions to the falling point is respectively Spline, matern and Cubic from high to low, wherein the falling point MAE and RMSE corresponding to the correlation function Spline are respectively 83.17m and 10.46m, and 37.76m and 3.13m. In summary, when the Kriging model is used to predict the drop points corresponding to the rising arc segment and the falling arc segment, the selected correlation functions include Spline, matern, and Cubic, and if only the drop points corresponding to the falling arc segment are predicted, the Gauss function may also be selected.
TABLE 1
In the table:
TABLE 2
The above description is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, it is possible to make various improvements and modifications without departing from the technical principle of the present invention, and those improvements and modifications should be considered as the protection scope of the present invention.
Claims (7)
1. A system for remotely guided rocket projectile drop point prediction based on design of experiments and Kriging modeling, said system comprising: the system comprises an equation set establishing module, a mathematical model establishing module, a sample acquiring module, a training module and a loading module; wherein, the first and the second end of the pipe are connected with each other,
the equation set establishing module is used for establishing a remote rocket projectile motion equation set;
the mathematical model building module is used for building a nonlinear mathematical model for the remote guidance rocket projectile drop point prediction;
the sample acquisition module is used for acquiring a training sample and a test sample;
the training module is used for selecting a proper correlation function of the Kriging model to train samples corresponding to the rising arc section and the falling arc section;
the loading module is used for loading the drop point prediction model meeting the requirements of precision and real-time performance into the missile-borne computer;
in the working process of the equation set establishing module, the remote guided rocket projectile is supposed to be predicted according to the landing point of the uncontrolled ballistic flight, and an uncontrolled ballistic mathematical model in a longitudinal plane of the remote guided rocket projectile is used as a remote rocket projectile motion equation set as follows:
in the formula: m is the flight quality of the remotely guided rocket projectile; t is time; v x And V y Two velocity components under a ground coordinate system; omega ix1 、ω iy1 And omega iz1 The three components of the rotating angular velocity vector of the projectile body relative to a translation coordinate system are in the projectile body coordinate system; j. the design is a square x1 、J y1 And J z1 Respectively the polar moment of inertia, the equatorial moment of inertia and the equatorial moment of inertia of the remotely guided rocket projectile; omega e The angular speed of the rotation of the earth axis; omega ex 、ω ey And omega ez Is omega e Three components in a transmission coordinate system;
and θ is pitch angle and trajectory inclination angle, respectively; alpha is an attack angle;
p is engine thrust; q is dynamic pressure; s ref And L ref Respectively a reference area and a reference length; c x And C y Respectively a drag coefficient and a lift coefficient; x and y are two position components under a ground coordinate system; r 0x And R 0y Two components of the emission point geocentric radial under an emission coordinate system are taken as the emission point; r is the model of the geocentric radial of any point on the trajectory; g r ' is the component of the acceleration of the earth's gravity along the radial direction of the earth's center;
is the component of the acceleration of the gravity along the earth axis direction; l is 0 Is the geocentric latitude of the transmitting point; a. The 0 Is the transmit azimuth;
the rate of change of the static stability moment coefficient with alpha;
for damping moment coefficient
Of wherein
m c Is the rate of change of the mass of the engine over time.
2. The trial design and Kriging model-based remotely guided rocket projectile drop point prediction system of claim 1 wherein during operation of said mathematical model building module, a non-linear mathematical model of remotely guided rocket projectile drop point prediction under standard meteorological conditions is built, and its dependent variable is drop point Y R And the independent variables are parameters of launching conditions and flight states, including the latitude B of the gun position 0 Altitude H of gun location 0 Shoot toward A T Target point elevation H T 、V x 、V y 、x、y、
The basic form is:
3. the trial design and Kriging model-based remotely guided rocket projectile drop point prediction system of claim 2, wherein during the operation of the sample acquisition module, the training sample and test sample acquisition method acquires the training sample and test sample based on the optimized Latin hypercube trial design and the remotely guided rocket projectile motion equation set.
4. The design-of-experiment and Kriging model based remotely guided rocket launch point prediction system of claim 3, wherein during operation of said sample acquisition module,
as the acquisition method of the training sample and the test sample is the same, only the acquisition method of the training sample is given, and the method comprises the following steps:
s301: using optimized Latin hypercube method to include the gun position latitude B 0 Height H of gun position 0 Shoot toward A T Distance X G Elevation H of target point T Medicine temperature T S Carrying out numerical test design on all the factors, wherein the value ranges of 6 factors are given according to the launching conditions and the range capability of the remotely guided rocket projectile;
s302: calculating a specific transmission condition B for each numerical test point in S301 0 、H 0 、A T 、H T And T S At a given range X G Each test point corresponds to a trajectory at a corresponding shooting angle under the standard meteorological condition;
s303: for each of S302The test point outputs the flight data of the remote rocket projectile at regular intervals by taking the engine shutdown time as the starting point, and the flight data comprises V x 、V y 、x、y、
ω z1 An internal ballistic parameter;
s304: randomly generating a corresponding attack angle aiming at the flight data output each time in the S303, giving the change range of the attack angle according to the change range of the attack angle of the remotely guided rocket projectile at different stages in the actual flight process, and utilizing a formula
Recalculating the pitch angle in each flight data, and comparing the pitch angle in each flight data in S303
Replacing with the latest pitch angle;
s305: and aiming at the flight data and the corresponding launching conditions in the S304, recalculating the drop points corresponding to the flight data under the standard meteorological conditions by using a ballistic simulation mode in a longitudinal plane, and dividing the drop points into two groups according to the modes of the arc rising section samples and the arc falling section samples.
5. The trial design and Kriging model-based remotely guided rocket projectile drop point prediction system of claim 4, wherein said training module, during operation, is adapted to the correlation function of Kriging model for drop point prediction corresponding to ballistic run-up and run-down segments,
for the drop point prediction corresponding to the arc-rising section, the selected correlation function comprises: a Spline function, a Matern function and a Cubic function;
for the drop point prediction corresponding to the arc-dropping segment, the selected correlation function comprises: a Spline function, a Matern function, a Gauss function, and a Cubic function.
6. The trial design and Kriging model-based remotely guided rocket launch point prediction system of claim 5, wherein the value of the non-negative integer q of the Matern function ranges from 3 to 5.
7. The trial design and Kriging model-based remotely guided rocket projectile landing point prediction system of claim 1, wherein said system can make accurate and rapid predictions of the remotely guided rocket projectile landing point under any firing conditions.
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| CN111504140B (en) * | 2020-04-28 | 2022-02-15 | 西北工业大学 | Remote solid rocket instantaneous orbit landing point closed-loop optimal feedback guidance method |
| CN111737815B (en) * | 2020-05-31 | 2024-02-20 | 南京航空航天大学 | Flight system drop point error correction method based on dimensionless form |
| CN112329131B (en) * | 2020-10-10 | 2024-04-05 | 中国运载火箭技术研究院 | Standard test model generation method, generation device and storage medium |
| CN112711816B (en) * | 2021-03-26 | 2021-06-29 | 南京信息工程大学 | Flight projectile trajectory correction method based on meteorological grid |
| CN117932793B (en) * | 2024-03-21 | 2024-06-14 | 西安现代控制技术研究所 | Guided rocket projectile inner-outer trajectory joint design method adopting coupling iteration optimization |
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