ISABO-BP neural network booster wreckage drop point prediction method

Abstract

The invention discloses a booster wreckage drop point prediction method based on an ISABO-BP neural network. The method comprises the following steps: establishing a booster wreckage dynamic model containing complex factors; random pulling deviation simulation is carried out on the wreckage state of the booster after separation and before landing, and a booster wreckage landing point database is constructed; an improved subtraction average optimizer, namely an ISABO algorithm, is obtained through a lens imaging reverse learning strategy; preprocessing the booster wreckage drop point database; and obtaining an ISABO-BP neural network wreckage drop point prediction model through an ISABO algorithm. The method is applied to prediction of the booster wreckage drop point, high solving precision is achieved, the extremely high solving speed is achieved, and compared with a traditional integration method for numerical solving, the method is remarkably improved.

Description

Technical Field

[0001] The present invention relates to the field of debris fall point prediction and neural network in aerospace technology, and more specifically, to an ISABO-BP neural network booster debris fall point prediction method. Background Art

[0002] With the increase in rocket or ballistic missile flight test missions, the safety issues arising during the test process have also attracted more and more attention from commanders and mission responsible personnel. Among them, the booster debris landing area has a great impact on ground personnel and facilities and is difficult to predict, becoming the focus of flight test area planning. After the fuel is exhausted or the separation conditions are met, the rocket engines of each stage separate from the upper stage. After separation, the booster is affected by a variety of complex conditions such as the earth's gravity, aerodynamics, and its own initial state of separation. After a certain period of uncontrolled flight, the booster debris falls to the ground. The current commonly used test launch sites have taken into account the safety of the debris landing area, but further research is still needed on the prediction method of the debris landing range in temporary or mobile launch situations.

[0003] Existing research on the prediction of the landing point of booster debris mostly uses more traditional numerical simulation methods, and the algorithms have different focuses. For the case where some debris has autonomous navigation and positioning capabilities, there are debris landing point calculation models to achieve prediction, but the cost of navigation and positioning systems in actual flight tests is high, and most booster debris do not have this capability. On the basis of the particle dynamics model, some algorithms further consider the attitude movement of rocket debris and factors such as the earth's gravity, and predict the landing point based on the six-degree-of-freedom model and reduce the theoretical landing area, but the performance in solution efficiency is poor. At the same time, some algorithms use numerical integration methods to solve the predicted landing point of the rocket sub-stage based on the Monte Carlo method and the unscented sampling method, respectively. The latter has fewer sampling points and a certain improvement in calculation efficiency. The above booster landing point prediction studies based on traditional numerical methods all have the problems of low calculation efficiency and a large predicted landing area.

[0004] In summary, the existing methods still have the following problems: requiring large amount of calculation, taking a long time to calculate, and having a large prediction area.

[0005] Therefore, it is necessary to develop an ISABO-BP neural network booster debris fall point prediction method.

[0006] The information disclosed in the background technology section of the present invention is only intended to deepen the understanding of the general background technology of the present invention, and should not be regarded as acknowledging or suggesting in any form that the information constitutes the prior art already known to those skilled in the art. Summary of the invention

[0007] The present invention proposes an ISABO-BP neural network booster debris impact point prediction method, which is applied to the prediction of booster debris impact point, and achieves both high solution accuracy and extremely high solution speed, which is significantly improved compared with the traditional integral method for numerical solution.

[0008] The ISABO-BP neural network booster debris fall point prediction method includes:

[0009] Establish a booster debris dynamics model that includes complex factors;

[0010] A random deflection simulation is performed on the wreckage state from booster separation to landing, and a booster wreckage landing point database is constructed;

[0011] The improved subtraction average optimizer is obtained through the lens imaging reverse learning strategy, which is the ISABO algorithm.

[0012] Preprocess the booster debris landing point database;

[0013] The ISABO-BP neural network debris fall point prediction model is obtained through the ISABO algorithm.

[0014] Preferably, establishing a booster debris dynamics model including complex factors includes:

[0015] A function with angle of attack, sideslip angle and Mach number as independent variables is constructed as the aerodynamic coefficient of the wreckage, and the axial force, normal force and lateral force are obtained through three-dimensional linear interpolation.

[0016] Calculate the atmospheric density, aerodynamic coefficients, and true velocity of debris, and then establish a wind field and atmospheric model, which is then incorporated into the debris dynamics model;

[0017] The model is unified to the ground launch system to obtain the final dynamic model.

[0018] Preferably, a center of mass dynamics model and a center of mass motion model are established, and the models are unified to the ground launch system, wherein the center of mass dynamics model is:

[0019]

[0020] Where: R is the aerodynamic term; mg is the gravitational term; -mω e ×(ω e ×r) is the centrifugal inertia force; is the Coriolis inertial force term; r is the radius of the booster debris; ω e is the angular velocity of the earth's rotation; t is the flight time; thrust, control force and drag force terms are omitted;

[0021] Considering the damping torque, the motion model around the center of mass is established as:

[0022]

[0023] Where: I is the inertia tensor; ω T is the angular velocity in the projectile coordinate system; M st is the stabilizing torque; M d is the damping torque; the control torque, additional relative torque and additional Coriolis torque terms are omitted.

[0024] Preferably, performing random deflection simulation on the wreckage state from booster separation to landing, and constructing a booster wreckage landing point database includes:

[0025] Monte Carlo numerical simulation is used to construct a database of debris impact points, in which the debris states at the separation point include velocity, launch system coordinates, three-axis angular velocity, attitude angle, trajectory inclination angle, and trajectory deviation angle.

[0026] Monte Carlo simulation uses the fourth-order fixed-step Runge-Kutta algorithm to perform multiple pull-off simulations to obtain the state data of the falling process;

[0027] The collection time of the wreckage status parameters is from separation to 0.5s before landing, with a collection interval of 0.5s. The collected data are matched with the coordinates of the landing point launch system to form a booster wreckage landing point database.

[0028] Preferably, the ISABO algorithm comprises:

[0029] Step 301: Determine the total number of search agents N, the maximum number of iterations T, and the search space dimension m;

[0030] Step 302: Generate a random initial population and calculate the objective function value;

[0031] Step 303: sort the objective function values, obtain the optimal search agent, and calculate the scaling factor and disturbance probability;

[0032] Step 304: Calculate the reverse search agent and update it;

[0033] Step 305: Calculate the new position of the search agent according to the arithmetic mean of v subtraction and update;

[0034] Step 306: If the number of iterations reaches the maximum number of iterations, the optimal search agent position of the objective function is the optimization result, otherwise return to step 303.

[0035] Preferably, preprocessing the booster debris impact point database includes:

[0036] The data in the booster debris drop point database are divided into a training set, a validation set, and a test set. During the training process, the training results are monitored by cross-validation based on the validation set.

[0037] The data is normalized by the mapminmax function and the original data is mapped to the interval [-1,1].

[0038] Preferably, obtaining the ISABO-BP neural network debris fall point prediction model through the ISABO algorithm includes:

[0039] Improve the objective function of BP neural network through ISABO algorithm;

[0040] The ISABO-BP neural network debris impact point prediction model was obtained by training the BP neural network with the preprocessed data in the booster debris impact point database.

[0041] Preferably, the objective function of the BP neural network improved by the ISABO algorithm includes:

[0042] The calculation output error of BP neural network is used as the objective function of ISABO algorithm.

[0043] Preferably, the objective function is:

[0044]

[0045] Where: y and are the actual value and predicted value of the output respectively; N is the number of samples involved in the training.

[0046] Its beneficial effects are:

[0047] The present invention aims at the problem of booster landing point debris prediction. By considering complex conditions such as wind field, atmospheric model and aerodynamic damping torque, a booster debris dynamic model with authenticity and accuracy is constructed. At the same time, based on the emerging heuristic algorithm SABO, improvements based on the principle of lens imaging reverse learning are carried out. The formed ISABO algorithm further enhances the ability of the algorithm to jump out of the local optimal solution in the later iterative period, and balances the "exploration" and "development" nature of the algorithm. In addition, the booster debris landing point prediction model of the ISABO-BP neural network formed in combination with the BP algorithm makes up for the global defects of the traditional BP model, greatly improves the accuracy and stability, and is much shorter in running time than the six-degree-of-freedom numerical simulation.

[0048] The method of the present invention has other characteristics and advantages, which will be apparent from the accompanying drawings and subsequent detailed descriptions incorporated herein, or will be described in detail in the accompanying drawings and subsequent detailed descriptions incorporated herein, which together serve to explain the specific principles of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] The above and other objects, features and advantages of the present invention will become more apparent through a more detailed description of exemplary embodiments of the present invention in conjunction with the accompanying drawings, wherein like reference numerals generally represent like components throughout the exemplary embodiments of the present invention.

[0050] Figure 1 A flowchart showing the steps of an ISABO-BP neural network booster wreckage fall point prediction method according to an embodiment of the present invention.

[0051] Figure 2 A schematic diagram of the axial force coefficient at different angles of attack, sideslip angles and Mach numbers in a typical flight condition according to an embodiment of the present invention is shown.

[0052] Figure 3 A schematic diagram of pitch moment coefficients at different angles of attack, sideslip angles and Mach numbers in a typical flight condition according to an embodiment of the present invention is shown.

[0053] Figure 4 A schematic diagram of the three-dimensional trajectory of the fall of booster debris in a database according to an embodiment of the present invention is shown.

[0054] Figure 5 A one-dimensional schematic diagram of a lens imaging reverse learning strategy according to an embodiment of the present invention is shown.

[0055] Figure 6 A flow chart of an improved subtraction mean optimizer algorithm according to an embodiment of the present invention is shown.

[0056] Figure 7 A schematic diagram showing the training results of a traditional BP neural network.

[0057] Figure 8 A schematic diagram showing the training results of the ISABO-BP neural network.

[0058] Fig. 9 A schematic diagram showing the x-coordinate prediction errors of the emission systems of various models according to an embodiment of the present invention is shown.

[0059] Fig.10 A schematic diagram showing relative errors of x-coordinates of various model emission systems according to an embodiment of the present invention is shown.

[0060] Fig.11 A schematic diagram showing the y-coordinate prediction errors of the emission systems of various models according to an embodiment of the present invention is shown.

[0061] Fig.12 A schematic diagram showing relative errors of y coordinates of various model emission systems according to an embodiment of the present invention is shown.

[0062] Fig.13 A schematic diagram showing the z-coordinate prediction errors of the emission systems of various models according to an embodiment of the present invention is shown.

[0063] Fig.14 A schematic diagram showing relative errors of z coordinates of various model launch systems according to an embodiment of the present invention is shown. DETAILED DESCRIPTION

[0064] The preferred embodiments of the present invention will be described in more detail below. Although the preferred embodiments of the present invention are described below, it should be understood that the present invention can be implemented in various forms and should not be limited to the embodiments set forth herein.

[0065] To facilitate understanding of the solution and effects of the embodiments of the present invention, a specific application example is given below. Those skilled in the art should understand that this example is only for facilitating understanding of the present invention, and any specific details thereof are not intended to limit the present invention in any way.

[0066] Example 1

[0067] Figure 1 A flowchart showing the steps of an ISABO-BP neural network booster wreckage fall point prediction method according to an embodiment of the present invention.

[0068] like Figure 1 As shown, the ISABO-BP neural network booster debris fall point prediction method includes:

[0069] Step 1, establish a booster debris dynamics model including complex factors;

[0070] Step 2, performing random deflection simulation on the wreckage state from booster separation to landing, and building a booster wreckage landing point database;

[0071] Step 3, obtaining an improved subtraction average optimizer through the lens imaging reverse learning strategy, which is the ISABO algorithm;

[0072] Step 4, preprocessing the booster debris landing point database;

[0073] Step 5: Obtain the ISABO-BP neural network debris landing point prediction model through the ISABO algorithm.

[0074] In one example, modeling the dynamics of a booster debris complex included:

[0075] A function with angle of attack, sideslip angle and Mach number as independent variables is constructed as the aerodynamic coefficient of the wreckage, and the axial force, normal force and lateral force are obtained through three-dimensional linear interpolation.

[0076] Calculate the atmospheric density, aerodynamic coefficients, and true velocity of debris, and then establish a wind field and atmospheric model, which is then incorporated into the debris dynamics model;

[0077] The model is unified to the ground launch system to obtain the final dynamic model.

[0078] In one example, a center of mass dynamics model and a center of mass motion model are established, and the models are unified to the ground launch system, where the center of mass dynamics model is:

[0079]

[0080] Where: R is the aerodynamic term; mg is the gravitational term; -mω e ×(ω e ×r) is the centrifugal inertia force; is the Coriolis inertial force term; r is the radius of the booster debris; ω e is the angular velocity of the earth's rotation; t is the flight time; thrust, control force and drag force terms are omitted;

[0081] Considering the damping torque, the motion model around the center of mass is established as:

[0082]

[0083] Where: I is the inertia tensor; ω T is the angular velocity in the projectile coordinate system; M st is the stabilizing torque; M d is the damping torque; the control torque, additional relative torque and additional Coriolis torque terms are omitted.

[0084] In one example, a random deflection simulation is performed on the state of the wreckage after the booster is separated and before it lands, and the booster wreckage landing point database is constructed, including:

[0085] Monte Carlo numerical simulation is used to construct a database of debris impact points, in which the debris states at the separation point include velocity, launch system coordinates, three-axis angular velocity, attitude angle, trajectory inclination angle, and trajectory deviation angle.

[0086] Monte Carlo simulation uses the fourth-order fixed-step Runge-Kutta algorithm to perform multiple pull-off simulations to obtain the state data of the falling process;

[0087] The collection time of the wreckage status parameters is from separation to 0.5s before landing, with a collection interval of 0.5s. The collected data are matched with the coordinates of the landing point launch system to form a booster wreckage landing point database.

[0088] In one example, the ISABO algorithm includes:

[0089] Step 301: Determine the total number of search agents N, the maximum number of iterations T, and the search space dimension m;

[0090] Step 302: Generate a random initial population and calculate the objective function value;

[0091] Step 303: sort the objective function values, obtain the optimal search agent, and calculate the scaling factor and disturbance probability;

[0092] Step 304: Calculate the reverse search agent and update it;

[0093] Step 305: Calculate the new position of the search agent according to the arithmetic mean of v subtraction and update;

[0094] Step 306: If the number of iterations reaches the maximum number of iterations, the optimal search agent position of the objective function is the optimization result, otherwise return to step 303.

[0095] In one example, preprocessing the booster debris impact point database includes:

[0096] The data in the booster debris drop point database are divided into a training set, a validation set, and a test set. During the training process, the training results are monitored by cross-validation based on the validation set.

[0097] The data is normalized by the mapminmax function and the original data is mapped to the interval [-1,1].

[0098] In one example, obtaining the ISABO-BP neural network debris fall point prediction model through the ISABO algorithm includes:

[0099] Improve the objective function of BP neural network through ISABO algorithm;

[0100] The ISABO-BP neural network debris impact point prediction model was obtained by training the BP neural network with the preprocessed data in the booster debris impact point database.

[0101] In one example, the objective function of improving the BP neural network by the ISABO algorithm includes:

[0102] The calculation output error of BP neural network is used as the objective function of ISABO algorithm.

[0103] In one example, the objective function is:

[0104]

[0105] Where: y and are the actual value and predicted value of the output respectively; N is the number of samples involved in the training.

[0106] Figure 2 A schematic diagram of the axial force coefficient at different angles of attack, sideslip angles and Mach numbers in a typical flight condition according to an embodiment of the present invention is shown.

[0107] Figure 3 A schematic diagram of pitch moment coefficients at different angles of attack, sideslip angles and Mach numbers in a typical flight condition according to an embodiment of the present invention is shown.

[0108] Figure 4 A schematic diagram of the three-dimensional trajectory of the fall of booster debris in a database according to an embodiment of the present invention is shown.

[0109] Specifically, taking the wreckage of a first-stage booster as an example, in addition to the engine, it also includes the transition section, tail cabin and booster rudder system, such as Figure 2 As shown in the figure, it is approximately a body of rotation, but the transition section is usually determined by the shape of the upper stage because it is connected to the upper stage. The aerodynamic coefficients of the wreckage are modeled as a function of the angle of attack, sideslip angle and Mach number as independent variables. During the numerical simulation, the axial force, normal force and lateral force under the specified state are obtained by three-dimensional linear interpolation. The aerodynamic coefficients under different angles of attack, sideslip angles and Mach numbers in typical flight conditions are shown in the figure below. Figure 3-4 As shown in the figure, since the wreckage is in an uncontrolled state after separation, the range of the angle of attack and sideslip angle in the database needs to cover all states, that is, the angle of attack α∈[-180°,180°], and the sideslip angle β∈[-90°,90°].

[0110] Since there is no guidance and control law to correct the flight trajectory of the booster debris, the landing point of the debris is more susceptible to environmental influences during the fall process.

[0111] The present invention mainly considers the influence of the atmospheric model and wind field on the landing point. The sounding balloon released by the meteorological station can obtain data such as temperature, air pressure, humidity, wind speed and wind direction that vary with altitude, and calculate the atmospheric density according to the empirical formula:

[0112] ρ=1.293·(p / p st )·(273.15 / T)

[0113] Where: p st =101325Pa is the standard physical atmospheric pressure; p is the measured pressure; T is the thermodynamic temperature.

[0114] At the same time, the speed of sound a can be calculated based on the measured temperature. sonic Calculate and then interpolate the aerodynamic coefficients after obtaining the Mach number:

[0115]

[0116] Where: γ = 1.4 is the air adiabatic index; R is the gas constant.

[0117] The wind field of the falling process is calculated based on the wind speed and wind direction, and the velocity vector a at the measurement point is wind , the true speed of the debris is the sum of the wind speed and the speed of the debris launching system:

[0118] a wind =[a wind cosλ wind ,0,a wind sinλ wind ] T

[0119] Where: wind speed is a wind The wind direction is λ wind .

[0120] The atmospheric model and wind field are brought into the calculation of the aerodynamic related parts of the wreckage, and the standard atmospheric table and no wind conditions are corrected to improve the accuracy of the model numerical simulation.

[0121] In order to facilitate subsequent numerical simulation, the model is unified into the ground launch system. The model is basically consistent with rockets and other aircraft. The dynamic model of booster debris is reasonably simplified and the following assumptions are made:

[0122] 1) The booster has been completely exhausted and shut down, with no thrust;

[0123] 2) After separation, the booster servo loses control and the rudder surface is locked at 0°.

[0124] The center of mass dynamics model is established as follows:

[0125]

[0126] Where: R is the aerodynamic term; mg is the gravitational term; -mω e ×(ω e ×r) is the centrifugal inertia force; is the Coriolis inertial force term; r is the radius of the booster debris; ω e is the angular velocity of the earth's rotation; t is the flight time; thrust, control force and drag force terms are omitted.

[0127] The model of motion around the center of mass is as follows:

[0128]

[0129] Where: I is the inertia tensor; ω T is the angular velocity in the projectile coordinate system; M st is the stabilizing torque; M d is the damping torque; the control torque, additional relative torque and additional Coriolis torque terms are omitted.

[0130] It should be emphasized that the wreckage after separation is often in a statically unstable configuration. In an uncontrolled state, its attitude will diverge rapidly, resulting in a large angular velocity. The damping torque in this state is a non-negligible item. Existing research and modeling on the prediction of wreckage landing point often ignores this item, thus affecting the accuracy of the landing point prediction.

[0131] After establishing a relatively accurate booster debris fall simulation model, the Monte Carlo numerical simulation method is used to construct a debris fall point database. The debris state at the separation point is determined by: velocity V, launch system coordinates (x, y, z), three-axis angular velocity (ω x ,ω y ,ω z ), attitude angle Ballistic inclination angle θ and ballistic deviation angle ψ V It consists of 12 state quantities in total, and the simulation starts with a certain separation condition as the initial state. In addition to randomly pulling the initial state, the Monte Carlo simulation also pulls the aerodynamic force and moment coefficient, wind field and atmospheric density proportionally. The initial state and pull-off settings of the separation point are shown in Table 1. The simulation uses the fourth-order fixed-step Runge-Kutta algorithm with a step size of 0.001. A total of 1000 pull-off simulations are performed to obtain the state data of the fall process.

[0132] Table 1 Separation point status and pull deviation setting

[0133]

[0134] The three-dimensional trajectory curve of the booster debris is as follows Figure 4 As shown in the figure, the collection time of the wreckage state parameters is from separation to 0.5s before landing, the collection interval is 0.5s, and the collected data are matched with the coordinates (x, y, z) of the landing point launch system to form a database, which contains 63828 sets of data in total.

[0135] The heuristic algorithm has the characteristic of not relying on gradient information when searching for the best result, so it is not easy to fall into the local optimum and has better applicability. In the related field, there are applications of optimizing BP neural network by using heuristic algorithms such as PSO, GA and SSA. The present invention improves the subtraction average optimizer optimization algorithm and further uses it to optimize the traditional BP neural network algorithm.

[0136] The core idea of ​​the Subtraction-Average-Based Optimizer (SABO) is to use the subtraction average of the search agent to update the position of the population members in the search space. The algorithm steps are simple and the effect is excellent. The details are as follows:

[0137] The SABO algorithm uses the arithmetic mean of all search agents to update the position, rather than the best or worst value in the population. The most critical part is the "-v" arithmetic mean calculation method used, as shown below, which is the v subtraction of search agent B relative to search agent A.

[0138]

[0139] Where: is an m-dimensional row vector whose components are randomly generated from the set {1,2}; the operator “*” represents the Hadamard product of two vectors (i.e., the multiplication of corresponding components); sign is the sign function; F(A) and F(B) are the objective function values ​​of the search agents A and B, respectively.

[0140] In the search space, all search agents X i The displacement of each search agent X is calculated by j Relative to the search agent X i The search agent X is obtained by subtracting the arithmetic mean of v. i The position is updated by:

[0141]

[0142] Where: is the search agent X at the i-th iteration i The updated position; N is the total number of search agents; is an m-dimensional row vector whose components are random numbers that follow a standard normal distribution in the interval [0,1].

[0143] If the updated position has a better objective function value, then this position can replace the original search agent's position according to the following formula:

[0144]

[0145] Where: and F(X i ) are search agents respectively and X i The objective function value of .

[0146] It is worth noting that the arithmetic mean search mechanism of "-v" has both an "exploration" stage and a "development" stage. The exploration stage is achieved through v subtraction, and the development stage is achieved through the arithmetic mean after v subtraction. However, as the algorithm is iterated, the "exploration" ability in the later stage is not obvious, and there is still the possibility that the optimization result falls into the local optimum.

[0147] Therefore, the present invention improves the subtraction average optimizer by using a reverse learning strategy based on lens imaging.

[0148] Reverse learning means that for a search agent X in the search space, there is always a corresponding reverse search agent X in the current space. * , if X * If the value is better than X, the reverse search agent is used to replace the original search agent as the current optimal solution. However, how to improve the effect of reverse learning during the search process is the key to the algorithm jumping out of the local optimal solution, and the scaling factor based on the lens imaging principle improves the algorithm's "exploration" ability.

[0149] Figure 5 A one-dimensional schematic diagram of a lens imaging reverse learning strategy according to an embodiment of the present invention is shown.

[0150] like Figure 5 As shown, in the one-dimensional problem, the x-axis search space is [a, b], and y represents a convex lens. Assuming that the coordinate of the object P on the x-axis is ζ and the height is h, the real image P* can be obtained according to the imaging principle. Correspondingly, the reverse individual coordinate is ζ * , height h * . Individual coordinate ζ and reverse individual coordinate ζ * Taking O as the base point, we have:

[0151]

[0152] Let the scaling factor k = h / h * , can be rewritten as

[0153]

[0154] Extended to m dimensions:

[0155]

[0156] Where: j The component of the current search agent in the jth dimension, j = 1, 2, ..., m; a j and b j are the upper and lower bounds of the j-th dimension in the search space respectively; ζ j * Reverse search agent for lens imaging.

[0157] In addition, according to the principle of lens imaging, the larger the scaling factor k, the smaller the range of the reverse search agent generated by the algorithm, and the smaller k, the larger the range of the reverse search agent. Therefore, an adaptive scaling factor adjustment strategy is designed to control the k value to increase nonlinearly with the increase in the number of iterations, as shown below, thereby improving the later "exploration" ability while ensuring the early "development" ability.

[0158]

[0159] Where: t is the current iteration number; T is the maximum iteration number.

[0160] In order to balance the contradiction between the algorithm's running time and effect, the adaptive function perturbation probability is designed as follows. By adjusting the probability of reverse learning, the probability of reverse learning in the early stage of the algorithm is designed to be higher, thereby controlling the algorithm's energy efficiency ratio.

[0161]

[0162] Where: η is the nonlinear decreasing adjustment coefficient η>1, and η=1.3 is taken.

[0163] If the position after reverse learning has a better objective function value, the position and objective function value of the search agent are updated, otherwise they are not updated.

[0164] Figure 6 A flow chart of an improved subtraction mean optimizer algorithm according to an embodiment of the present invention is shown.

[0165] like Figure 6 As shown, the specific steps of the improved subtraction average optimizer formed by the above improvements are as follows:

[0166] Step 1: Parameter initialization (total number of search agents N, maximum number of iterations T, search space dimension m, etc.);

[0167] Step 2: Generate a random initial population and calculate the objective function value:

[0168] x i,d =lb d +r i,d (ub d -lb d )

[0169] Where: x i,d is the component of the i-th search agent in the d-dimensional search space, i = 1, 2, ..., N, d = 1, 2, ..., m; lb d andub d are the upper and lower bounds of the d-dimensional search space respectively; r i,d ∈[0,1] is a random number;

[0170] Step 3: Sort the objective function values, get the optimal search agent and and Calculate the scaling factor k and the perturbation probability δ;

[0171] Step 4: If rand(0,1)<δ, then Compute the reverse search agent and renew;

[0172] Step 5: Use Equation to calculate the new position of the search agent using the v subtraction arithmetic mean, which is also updated by ;

[0173] Step 6: If the number of iterations t < T is satisfied, the position of the search agent with the optimal objective function is the optimization result; otherwise, return to Step 3.

[0174] The core idea of the traditional BP neural network algorithm is to determine the objective function to be solved and adjust the parameters of each layer of the network based on the steepest descent method to make it reach the minimum value. However, calculating the adjustment amount of each network parameter in the negative gradient direction of the objective function has the problem of easily falling into local minima. To solve the above problems, an improved subtraction mean optimizer algorithm is introduced into the traditional BP neural network to form an ISABO - BP neural network model for fast and accurate prediction of the booster debris landing point.

[0175] After the construction of the booster debris landing point database, operations such as data partitioning and normalization need to be performed on the data before using the BP neural network, so as to avoid problems such as overfitting and large prediction errors caused by unreasonable partitioning and large differences in data magnitudes.

[0176] When training a neural network, the database is usually divided into three subsets: a training set, a validation set, and a test set. In the present invention, the data is divided in the ratio of 0.7:0.15:0.15. During the training process, the training results are monitored through cross - validation based on the validation set to prevent the occurrence of network overfitting.

[0177] The mapminmax function is used for data normalization, mapping the original data into the interval [-1, 1]:

[0178]

[0179] In the formula: x max and x min are the maximum and minimum values of the sample data respectively; x and x norm are the sample data before and after normalization respectively; y min = -1, y max = 1 are the upper and lower bounds of the interval.

[0180] The structure of the BP neural network will directly affect its performance. Too many hidden layers are likely to cause "overfitting" in network training, and the number of nodes in the hidden layer is also the main cause of "overfitting".

[0181] Existing theories have proven that a single hidden layer BP neural network can approximate any continuous function within a closed interval, so this patent adopts a single hidden layer. For the problem of the number of nodes in the hidden layer, the "three-part method" is used to search and inspect in the hidden layer node number interval [3,93], and keep the network structure during the trial calculation consistent with the training state except for the number of hidden layer nodes, and the trial calculation step length is 10. Through trial calculation, the optimal number of hidden layer nodes of this patent model is 17. At the same time, the input layer and output layer nodes of the network are determined to be 12 parameters of the separation point debris and 3 parameters of the landing point position, respectively. The hidden layer activation function uses the logsig function, and the output layer activation function uses the pureline function.

[0182] In the application of heuristic algorithms, the most critical part is the selection of the objective function. This patent uses the calculation output error of the BP neural network under certain weights and thresholds as the objective function of the ISABO algorithm optimization.

[0183] The input layer has 12 nodes, the hidden layer has 17 nodes, and the output layer has 3 nodes, so there are a total of 12×17+17+17×3+3=275 weights and thresholds as parameters to be optimized and input into the ISABO algorithm. At the same time, the activation function for calculating the output error of the neural network is also consistent with the BP network in the previous section.

[0184] Here we choose MSE mean square error as the output error, that is, the objective function is

[0185]

[0186] Where: y and are the actual value and predicted value of the output respectively; N is the number of samples involved in the training.

[0187] In addition to the BP neural network structure and database, other parameter settings of the model will also have a great impact on the training results. After simulation test comparison, the BP neural network training is determined as follows: the maximum number of iterations is 1000, the learning rate is 0.001, and the expected training error is 1×10 -5 .

[0188] In order to verify the effectiveness of this algorithm, under the same parameter settings, in addition to comparing with the traditional BP neural network algorithm, the unimproved SABO algorithm, PSO algorithm and SSA algorithm are used as references, and the parameter settings of the heuristic algorithm are shown in Table 2. In addition, in order to reduce the simulation result deviation caused by randomness in the numerical simulation process, such as data set division and random numbers within the algorithm, each algorithm is simulated 100 times and the results are analyzed. Different algorithms use the same data set allocation in each test.

[0189] Table 2 Heuristic algorithm parameter settings

[0190]

[0191]

[0192] Figure 7 A schematic diagram showing the training results of a traditional BP neural network.

[0193] Figure 8 A schematic diagram showing the training results of the ISABO-BP neural network.

[0194] Under the above conditions, the results of training the BP neural network are as follows: Figure 7-Figure 8 As shown, the results are any one of the 100 algorithms. Analysis shows that the output error of the traditional BP neural network drops rapidly to approach the set error, and the downward trend conforms to the exponential form. Finally, when the upper limit of the iteration is reached 1000 times, the output error is 0.04219. In order to avoid the "overfitting" phenomenon, the algorithm is stopped. During the whole training process, the output error of the ISABO-BP neural network basically remains at the same order of magnitude, and finally is 0.03821, which is lower than the traditional BP network. This phenomenon proves that ISABO in the algorithm conducts a more comprehensive search of the search space composed of weights and threshold parameters, so that the initial parameters are already the best results. On the whole, compared with the traditional algorithm that is trapped in the local optimal solution and cannot jump out, this algorithm solves the global optimal solution.

[0195] Fig. 9 A schematic diagram showing the x-coordinate prediction errors of the emission systems of various models according to an embodiment of the present invention is shown.

[0196] Fig.10 A schematic diagram showing relative errors of x-coordinates of various model emission systems according to an embodiment of the present invention is shown.

[0197] Fig.11 A schematic diagram showing the y-coordinate prediction errors of the emission systems of various models according to an embodiment of the present invention is shown.

[0198] Fig.12 A schematic diagram showing relative errors of y coordinates of various model emission systems according to an embodiment of the present invention is shown.

[0199] Fig.13 A schematic diagram showing the z-coordinate prediction errors of the emission systems of various models according to an embodiment of the present invention is shown.

[0200] Fig.14 A schematic diagram showing relative errors of z coordinates of various model launch systems according to an embodiment of the present invention is shown.

[0201] The results of 100 samples of predicted landing points of booster debris by BP, ISABO-BP, SABO-BP, SSA-BP and PSO-BP models are as follows: Figures 9 to 14 Analysis Figures 9 to 14 The results show that in the prediction errors in all directions, the ISABO-BP model is relatively stable, and the fluctuations of the prediction error and relative error are small. The traditional BP model has the largest error among the above models, and the stability of the PSO-BP model is relatively poor. In addition, the minimum and maximum errors of each model in all test results (sorted by Euclidean distance error) are shown in Table 3. The ISABO-BP model performs better than other models, and the minimum Euclidean distance error is reduced by 78.5% and the maximum Euclidean distance error is reduced by 37.1% compared with the traditional BP algorithm.

[0202] Table 3 Comparison of the maximum values ​​of the prediction errors of the launch system coordinates

[0203]

[0204]

[0205] The calculation output errors of each model in the 100 rounds of simulation results are statistically analyzed, and their mean and standard deviation are calculated. The results are shown in Table 4. The italics in the table are the worst values, and the bolds are the best values, all of which are the results before normalization.

[0206] Table 4 Results of 100 rounds of model training

[0207]

[0208] The analysis results show that after multiple rounds of tests, the ISABO-BP model is the best except for the minimum value. Compared with the traditional BP model, the mean is 63.8% higher and the standard deviation is 94.2% higher. At the same time, the standard deviations of the ISABO-BP and SSA-BP models are basically the same at 0.0017 and the smallest, indicating that the two models are highly stable and not easily affected by randomness. For the minimum value item, the PSO-BP model is the best, but its stability is poor, it is easily affected by randomness, and "overfitting" may occur.

[0209] In terms of algorithm operation efficiency, the models based on BP neural network are far superior to the six-degree-of-freedom numerical simulation. For the prediction of the landing point of 100 separation states, the BP neural network model only takes 3.5ms per state on average, while the six-degree-of-freedom numerical simulation takes 19.958s. When constructing the BP neural network model, the BP model takes the shortest time because it does not require the heuristic algorithm to search for global optimization; the ISABO-BP model takes a shorter time, slightly higher than the SABO-BP model, and the construction efficiency of each model is within an acceptable range.

[0210] Those skilled in the art should understand that the purpose of the above description of the embodiments of the present invention is only to exemplarily illustrate the beneficial effects of the embodiments of the present invention, and is not intended to limit the embodiments of the present invention to any given examples.

[0211] The embodiments of the present invention have been described above, and the above description is exemplary, not exhaustive, and is not limited to the disclosed embodiments. Many modifications and changes will be apparent to those skilled in the art without departing from the scope and spirit of the described embodiments.

Claims

1. An ISABO-BP neural network booster debris fall point prediction method, characterized in that: include: Establish a booster debris dynamics model that includes complex factors; A random deflection simulation is performed on the wreckage state from booster separation to landing, and a booster wreckage landing point database is constructed; The improved subtraction average optimizer is obtained through the lens imaging reverse learning strategy, which is the ISABO algorithm. Preprocess the booster debris landing point database; The ISABO-BP neural network debris fall point prediction model is obtained through the ISABO algorithm.

2. The ISABO-BP neural network booster debris fall point prediction method according to claim 1, wherein: The dynamics model of booster debris is built with complex factors including: A function with angle of attack, sideslip angle and Mach number as independent variables is constructed as the aerodynamic coefficient of the wreckage, and the axial force, normal force and lateral force are obtained through three-dimensional linear interpolation. Calculate the atmospheric density, aerodynamic coefficients, and true velocity of debris, and then establish a wind field and atmospheric model, which is then incorporated into the debris dynamics model; The model is unified to the ground launch system to obtain the final dynamic model.

3. The ISABO-BP neural network booster debris fall point prediction method according to claim 2, wherein: The center-of-mass dynamics model and the center-of-mass motion model are established, and the models are unified into the ground launch system. The center-of-mass dynamics model is: Where: R is the aerodynamic term; mg is the gravitational term; -mω e ×(ω e ×r) is the centrifugal inertia force; is the Coriolis inertial force term; r is the radius of the booster debris; ω e is the angular velocity of the earth's rotation; t is the flight time; thrust, control force and drag force terms are omitted; Considering the damping torque, the motion model around the center of mass is established as: Where: I is the inertia tensor; ω T is the angular velocity in the projectile coordinate system; M st is the stabilizing torque; M d is the damping torque; the control torque, additional relative torque and additional Coriolis torque terms are omitted.

4. The ISABO-BP neural network booster debris fall point prediction method according to claim 1, wherein: Random deflection simulation is performed on the wreckage state from booster separation to landing, and the booster wreckage landing point database is constructed, including: Monte Carlo numerical simulation is used to construct a database of debris impact points, in which the debris states at the separation point include velocity, launch system coordinates, three-axis angular velocity, attitude angle, trajectory inclination angle, and trajectory deviation angle. Monte Carlo simulation uses the fourth-order fixed-step Runge-Kutta algorithm to perform multiple pull-off simulations to obtain the state data of the falling process; The collection time of the wreckage status parameters is from separation to 0.5s before landing, with a collection interval of 0.5s. The collected data are matched with the coordinates of the landing point launch system to form a booster wreckage landing point database.

5. The ISABO-BP neural network booster debris fall point prediction method according to claim 1, wherein: The ISABO algorithm includes: Step 301: Determine the total number of search agents N, the maximum number of iterations T, and the search space dimension m; Step 302: Generate a random initial population and calculate the objective function value; Step 303: sort the objective function values, obtain the optimal search agent, and calculate the scaling factor and disturbance probability; Step 304: Calculate the reverse search agent and update it; Step 305: Calculate the new position of the search agent according to the arithmetic mean of v subtraction and update; Step 306: If the number of iterations reaches the maximum number of iterations, the optimal search agent position of the objective function is the optimization result, otherwise return to step 303.

6. The ISABO-BP neural network booster debris fall point prediction method according to claim 1, wherein: Preprocessing of the booster debris fall point database includes: The data in the booster debris drop point database are divided into a training set, a validation set, and a test set. During the training process, the training results are monitored by cross-validation based on the validation set. The data is normalized by the mapminmax function and the original data is mapped to the interval [-1,1].

7. The ISABO-BP neural network booster debris fall point prediction method according to claim 1, wherein: The ISABO-BP neural network debris fall point prediction model obtained through the ISABO algorithm includes: Improve the objective function of BP neural network through ISABO algorithm; The ISABO-BP neural network debris impact point prediction model was obtained by training the BP neural network with the preprocessed data in the booster debris impact point database.

8. The ISABO-BP neural network booster debris fall point prediction method according to claim 7, wherein: The objective function of improving the BP neural network by the ISABO algorithm includes: The calculation output error of BP neural network is used as the objective function of ISABO algorithm.

9. The ISABO-BP neural network booster debris fall point prediction method according to claim 8, wherein: The objective function is: Where: y and are the actual value and predicted value of the output respectively; N is the number of samples involved in the training.

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