A method for predicting the impact point of booster debris using ISABO-BP neural network

Abstract

This application discloses an ISABO-BP neural network method for predicting the impact point of booster debris. The method may include: establishing a booster debris dynamics model that includes complex factors; performing random deflection simulation on the state of the wreckage from booster separation to landing to construct a booster debris impact point database; obtaining an improved subtraction average optimizer, namely the ISABO algorithm, through a lens imaging reverse learning strategy; preprocessing the booster debris impact point database; and obtaining an ISABO-BP neural network debris impact point prediction model through the ISABO algorithm. The present invention is applied to the prediction of booster debris impact points, achieving both high solution accuracy and extremely high solution speed, significantly improving the numerical solution compared to traditional integral methods.

Description

Technical Field

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

[0002] With the increase in rocket or ballistic missile flight test missions, the safety issues arising from these tests are increasingly attracting the attention of commanders and mission managers. The impact of booster debris on ground personnel and facilities is significant and difficult to predict, making it a key focus of flight test area planning. After fuel exhaustion or separation conditions are met, the booster separates from the upper stage. After separation, the booster is subject to a variety of complex conditions, including gravity, aerodynamics, and its initial state. After a period of uncontrolled flight, the booster debris falls to the ground. Currently, commonly used test launch sites all take into account the safety of the debris fall area, but further research is needed to predict the range of debris fall during temporary or mobile launches.

[0003] Existing research on booster debris impact prediction has mostly used more traditional numerical simulation methods, and the algorithms have varying emphases. For cases where debris possesses autonomous navigation and positioning capabilities, there are debris impact calculation models that implement predictions. However, in actual flight tests, navigation and positioning systems are expensive, and most booster debris lacks this capability. Some algorithms, based on the particle dynamics model, further consider factors such as the attitude motion of the rocket debris and the Earth's gravity, predicting impact points based on a six-degree-of-freedom model and reducing the theoretical impact zone, but their solution efficiency is poor. Meanwhile, some algorithms employ numerical integration methods, using Monte Carlo and unscented sampling methods to predict the impact points of rocket sub-stages. The latter method uses fewer sampling points and offers improved computational efficiency. All of the above booster impact prediction studies based on traditional numerical methods suffer from low computational efficiency and a large predicted impact zone.

[0004] In summary, the existing methods still have the following problems: requiring a 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 impact 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 an admission or any form of suggestion 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 points, achieving both high solution accuracy and extremely high solution speed, and significantly improving the numerical solution compared to the traditional integration method.

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

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

[0010] Perform random deflection simulations on the state of the booster debris from separation to landing to build a database of booster debris landing points.

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

[0012] Pre-process the booster debris impact point database;

[0013] The ISABO-BP neural network debris impact 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 atmospheric density, aerodynamic coefficients, and true debris velocity, and then establish a wind field and atmospheric model to incorporate 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 unified into a 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; the thrust, control force and drag force terms are omitted;

[0021] Taking the damping torque into consideration, 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 state of the wreckage from the separation of the booster to the landing, and constructing the booster wreckage landing point database includes:

[0025] Monte Carlo numerical simulation is used to construct a debris impact point database, where the debris state at the separation point includes 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 deflection simulations to obtain the state data of the falling process;

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

[0028] Preferably, the ISABO algorithm includes:

[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 ​​to obtain the optimal search agent, and calculate the scaling factor and perturbation probability;

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

[0033] Step 305: Calculate the new position of the search agent based on 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 impact point database is divided into training, validation, and test sets. During the training process, the training results are monitored through cross-validation based on the validation set.

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

[0038] Preferably, obtaining the ISABO-BP neural network debris impact 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 using the preprocessed data from 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 participating in the training.

[0046] Its beneficial effects are:

[0047] The present invention addresses the problem of booster landing point debris prediction. By considering complex conditions such as wind fields, atmospheric models, 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 lens imaging reverse learning principle are made. The resulting ISABO algorithm further enhances the ability of the algorithm to escape from the local optimal solution in the later iterative stage, 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 less time-consuming than the six-degree-of-freedom numerical simulation.

[0048] The method of the present invention has other features and advantages that will be apparent from or will be described in detail in the accompanying drawings and subsequent detailed description incorporated herein, which together serve to explain the specific principles of the 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 with reference to 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 debris impact point prediction method according to an embodiment of the present invention.

[0051] Figure 2 A schematic diagram of axial force 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.

[0052] Figure 3 A schematic diagram showing pitching 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 falling 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 average 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] Figure 9 A schematic diagram showing the x-coordinate prediction errors of various model emission systems according to an embodiment of the present invention is shown.

[0059] Figure 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] Figure 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] Figure 12 A schematic diagram showing relative errors of the y-coordinates of the emission systems of various models according to an embodiment of the present invention is shown.

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

[0063] Figure 14 A schematic diagram showing relative errors of z coordinates of various model emission 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 solutions 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 debris impact point prediction method according to an embodiment of the present invention.

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

[0069] Step 1: Establish a booster debris dynamics model that includes complex factors;

[0070] Step 2: Perform random deflection simulation on the state of the wreckage from booster separation to landing to build a booster wreckage landing point database;

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

[0072] Step 4: Preprocess the booster debris impact point database;

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

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

[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 atmospheric density, aerodynamic coefficients, and true debris velocity, and then establish a wind field and atmospheric model to incorporate 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 motion model around the center of mass are established, and the models are unified into a ground launch system. 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; the thrust, control force and drag force terms are omitted;

[0081] Taking the damping torque into consideration, 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 booster debris from separation to landing. Building a database of booster debris landing points includes:

[0085] Monte Carlo numerical simulation is used to construct a debris impact point database, where the debris state at the separation point includes 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 deflection simulations to obtain the state data of the falling process;

[0087] The debris state parameters are collected from separation to 0.5s before landing, with a collection interval of 0.5s. The collected data are matched with the landing point launch system coordinates to form a booster debris 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 ​​to obtain the optimal search agent, and calculate the scaling factor and perturbation probability;

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

[0093] Step 305: Calculate the new position of the search agent based on 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 a booster debris impact point database includes:

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

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

[0098] In one example, obtaining an ISABO-BP neural network debris impact prediction model using 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 using the preprocessed data from the booster debris impact point database.

[0101] In one example, improving the objective function of the BP neural network using 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 participating in the training.

[0106] Figure 2 A schematic diagram of axial force 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.

[0107] Figure 3 A schematic diagram showing pitching 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 falling booster debris in a database according to an embodiment of the present invention is shown.

[0109] Specifically, taking the debris 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, it is approximately a body of rotation, but the transition section is usually determined by the upper stage shape due to its connection with the upper stage. The aerodynamic coefficients of the wreckage are modeled as functions with 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 as follows: Figures 3 and 4 As shown in the figure, since the debris is in an uncontrolled state after separation, the range of angle of attack and sideslip angle in the database needs to cover all states, that is, angle of attack α∈[-180°,180°], sideslip angle β∈[-90°,90°].

[0110] Since there is no guidance 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 atmospheric model and wind field on the landing point. The sounding balloon released by the weather station can obtain data such as temperature, pressure, humidity, wind speed and direction that vary with altitude. The atmospheric density is calculated 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 during 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] To facilitate subsequent numerical simulations, the model is unified with the ground launch system. The model is basically consistent with rockets and other aircraft. The dynamic model of the 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 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 motion model 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 debris after separation is often in a statically unstable configuration. In an uncontrolled state, its attitude will diverge rapidly, generating a large angular velocity. The damping torque in this state is a non-negligible item. Existing research and modeling on debris landing point prediction often ignores this item, thus affecting the accuracy of 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 The simulation consists of 12 state variables, starting with a separation condition as the initial state. In addition to randomly deflecting the initial state, the Monte Carlo simulation also applies proportional deflections to the aerodynamic force and moment coefficients, wind field, and atmospheric density. The initial state and deflection settings for the separation point are shown in Table 1. The simulation uses a fourth-order fixed-step Runge-Kutta algorithm with a step size of 0.001. A total of 1000 deflection simulations are performed to obtain state data for 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 debris state parameters is from separation to 0.5s before landing, with a collection interval of 0.5s. The collected data are mapped to the coordinates (x, y, z) of the landing point launch system to form a database, which contains a total of 63,828 sets of data.

[0135] Heuristic algorithms are characterized by not relying on gradient information when searching for optimal results, making them less likely to fall into local optima and more adaptable. In related fields, heuristic algorithms such as PSO, GA, and SSA have been used to optimize BP neural networks. The present invention improves the subtractive average optimizer algorithm and further applies it to optimize traditional BP neural network algorithms.

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

[0137] The SABO algorithm uses the arithmetic mean of all search agents to update their positions, rather than the optimal or worst value in the population. The most critical aspect is the "-v" arithmetic mean calculation method used, as shown below, which is the subtraction of v from 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 arithmetic mean of v is obtained by subtracting it, that is, the search agent X i The position of is updated by:

[0141]

[0142] Where: is the search agent X at iteration i 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's worth noting that the "-v" arithmetic mean search mechanism has both an "exploration" phase and an "exploitation" phase. The exploration phase is achieved through v subtraction, while the exploitation phase is achieved through the arithmetic mean after v subtraction. However, as the algorithm iterates, the "exploration" capability becomes less effective in the later stages, and there's still a risk that the optimization results will fall into a local optimum.

[0147] Therefore, the present invention improves the subtraction averaging optimizer by adopting 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 solution is better than X, the reverse search agent replaces the original search agent as the current optimal solution. However, improving the effectiveness of reverse learning during the search process is key to the algorithm's ability to escape the local optimal solution. The scaling factor based on the lens imaging principle enhances 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, then according to the imaging principle, the real image P* can be obtained. 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 * Backward 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. This improves the later "exploration" capability while ensuring the early "development" capability.

[0158]

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

[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.

[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 average 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 and ub 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 iteration number 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 average 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 of 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 this 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 to map the original data into the interval [-1, 1]:

[0178]

[0179] In the formula: x max and x min are respectively the maximum and minimum values of the sample data; x and x norm are respectively the sample data before and after normalization; 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. Therefore, this patent adopts a single hidden layer. Regarding the number of nodes in the hidden layer, the "three-part method" is adopted to conduct a search and inspection within the hidden layer node number interval [3,93]. The network structure during the trial calculation is kept consistent with the training state except for the number of hidden layer nodes, and the trial calculation step size is 10. The optimal number of hidden layer nodes for this patent model is 17. At the same time, the input and output layer nodes of the network are determined to have 12 parameters for the separation point debris and 3 parameters for 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. This means there are a total of 12 × 17 + 17 + 17 × 3 + 3 = 275 weights and thresholds to be optimized for the ISABO algorithm. Furthermore, the activation function used to calculate the neural network output error remains the same as the BP network described 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 participating in the training.

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

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

[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 BP neural network are as follows: Figures 7 and 8 The results shown are for any one of 100 algorithm runs. Analysis shows that the output error of the traditional BP neural network rapidly decreases, approaching the set error, with an exponential downward trend. Ultimately, the output error reaches 0.04219 when the upper limit of 1000 iterations is reached, and the algorithm is stopped to avoid overfitting. However, the output error of the ISABO-BP neural network remains essentially at the same order of magnitude throughout the training process, ultimately reaching 0.03821, lower than the traditional BP network. This phenomenon demonstrates that the ISABO algorithm conducts a comprehensive search of the search space formed by the weight and threshold parameters, resulting in a relatively optimal initial parameter. Overall, compared to traditional algorithms that are trapped in local optimal solutions and cannot escape, this algorithm achieves a global optimal solution.

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

[0196] Figure 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] Figure 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] Figure 12 A schematic diagram showing relative errors of the y-coordinates of the emission systems of various models according to an embodiment of the present invention is shown.

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

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

[0201] The results of BP, ISABO-BP, SABO-BP, SSA-BP and PSO-BP models for 100 samples of predicted landing points of booster debris are as follows: Figures 9 to 14 Analysis Figures 9 to 14 The results show that the ISABO-BP model performs relatively stably in all prediction errors, with minimal fluctuations in both prediction error and relative error. The traditional BP model exhibits the largest error among the above models, and the PSO-BP model also exhibits relatively poor stability. Furthermore, the minimum and maximum errors of each model across all test results (ranked by Euclidean distance error) are shown in Table 3. The ISABO-BP model outperforms the other models, reducing the minimum Euclidean distance error by 78.5% and the maximum Euclidean distance error by 37.1% compared to the traditional BP algorithm.

[0202] Table 3 Comparison of maximum values ​​of emission system coordinate prediction errors

[0203]

[0204]

[0205] The calculation output errors of each model in the 100 rounds of simulation results were statistically analyzed, and their mean and standard deviation were calculated. The results are shown in Table 4. The italics in the table are the worst values, and the bold ones are the best values. All of them 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, its mean is 63.8% higher and its 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 are the smallest, indicating that both models are highly stable and not susceptible to 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 may "overfit".

[0209] In terms of algorithmic efficiency, models based on BP neural networks far outperformed six-degree-of-freedom numerical simulations. For 100 separation states, the BP neural network model averaged only 3.5 milliseconds per state, while the six-degree-of-freedom numerical simulation required 19.958 seconds. When constructing the BP neural network model, the BP model took the shortest time because it did not require a heuristic algorithm for global optimization. The ISABO-BP model also took slightly longer, achieving acceptable construction efficiencies for all models.

[0210] Those skilled in the art should understand that the above description of the embodiments of the present invention is only for the purpose of illustrative purposes only to 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] While various embodiments of the present invention have been described above, the above description is intended to be illustrative, not exhaustive, and not limited to the disclosed embodiments. Many modifications and variations 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 impact point prediction method, characterized in that: include: Establish a booster debris dynamics model that includes complex factors; Perform random deflection simulations on the state of the booster debris from separation to landing to build a database of booster debris landing points. The improved subtraction average optimizer is obtained through the lens imaging reverse learning strategy, which is the ISABO algorithm; Pre-process the booster debris impact point database; The ISABO-BP neural network debris impact prediction model is obtained through the ISABO algorithm; The establishment of a booster debris dynamics model with complex factors includes: 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 atmospheric density, aerodynamic coefficients, and true debris velocity, and then establish a wind field and atmospheric model to incorporate into the debris dynamics model; Unify the model to the ground launch system to obtain the final dynamic model; Among them, 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 ​​to obtain the optimal search agent, and calculate the scaling factor and perturbation probability; Step 304: Calculate the reverse search agent and update; Step 305: Calculate the new position of the search agent based on 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.

2. The ISABO-BP neural network booster debris impact prediction method according to claim 1, wherein: The center-of-mass dynamics model and the center-of-mass motion model are established and 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; the thrust, control force and drag force terms are omitted; According to 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.

3. The ISABO-BP neural network booster debris impact prediction method according to claim 1, wherein: Random deflection simulation is performed on the debris state from booster separation to landing, and the booster debris landing point database is constructed, including: Monte Carlo numerical simulation is used to construct a debris impact point database, where the debris state at the separation point includes 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 deflection simulations to obtain the state data of the falling process; The debris state parameters are collected from separation to 0.5s before landing, with a collection interval of 0.5s. The collected data are matched with the landing point launch system coordinates to form a booster debris landing point database.

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

5. The ISABO-BP neural network booster debris impact prediction method according to claim 1, wherein: The ISABO-BP neural network debris impact 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 using the preprocessed data from the booster debris impact point database.

6. The ISABO-BP neural network booster debris impact point prediction method according to claim 5, wherein: The objective functions of the BP neural network improved by the ISABO algorithm include: The calculation output error of BP neural network is used as the objective function of ISABO algorithm.

7. The ISABO-BP neural network booster debris impact point prediction method according to claim 6, 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 participating in the training.

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