Spin feature analysis method

Abstract

The present invention relates to a method for analyzing tailspin characteristics. The time history of tailspin characteristics is obtained by solving tailspin dynamics differential equations, and the tailspin characteristics of simulation examples under conditions of multi-parameter changes such as weight, moment of inertia, and entry mode are predicted, and the influence of multi-variable parameters on the tailspin characteristics is analyzed; a machine learning model is built using an XGBoost regression algorithm based on decision tree analysis, and the multi-variable parameters of the simulation example are analyzed for feature importance with tailspin characteristics such as average angle of attack, average rotation rate, and sinking speed as targets; the influence ratio of multi-variable parameters on the same tailspin characteristics is analyzed, and the influence of key factors on the tailspin is completed in a quantitative manner. The tailspin feature analysis method of the present invention takes tailspin characteristics as targets, performs feature importance analysis on three multi-variable parameters of weight, moment of inertia, and entry mode, gives the degree of influence of each variable parameter on the corresponding target in the form of quantitative weights, and completes the multi-dimensional global feature analysis of the simulation example.

Description

Technical Field

[0001] The invention relates to the field of aircraft spin dynamics, and in particular to a spin characteristic analysis method. Background Art

[0002] A tailspin, also known as a spiral, refers to the phenomenon that an aircraft rotates around its longitudinal axis when the critical angle of attack is exceeded. Under the combined effects of aerodynamic force, inertial force and gravity, the aircraft performs a compound rotation around its three-axis system on the one hand, and performs a spontaneous descent along a spiral trajectory with a smaller radius on the other hand. The tailspin phenomenon usually occurs after the aircraft stalls, at which time the aircraft's maneuverability is significantly reduced, and may even fail completely. The tailspin movement is mainly manifested in rolling movement around the longitudinal axis and continuous yaw rotation movement.

[0003] The rotational motion in an aircraft tailspin is mainly caused by the wings. As the main source of lift, the airflow separation between the left and right wings is asymmetric when the aircraft is in a stalled state, resulting in uneven lift generated by the wings on both sides. Due to the inconsistent degree of lift loss on the two wings, the wing with a larger lift loss will sink and roll around the longitudinal axis. This rolling motion further causes additional speed in the wing section, causing the angle of attack of each section of the sinking half wing to increase, while the angle of attack of each section of the rising half wing to decrease. The change in angle of attack causes the aerodynamic force to be redistributed along the wingspan, and generates tilt and yaw aerodynamic forces. Under the action of this yaw moment, the aircraft yaws and rotates, and then enters a tailspin state.

[0004] In current engineering practice, the method of predicting tailspin characteristics based on differential equation theory is dominant, and this method can describe the phenomenon of aircraft tailspin to a certain extent. The prediction of tailspin characteristics based on differential equation theory requires data support from a high angle of attack aerodynamic database, and the content of the high angle of attack aerodynamic database mainly involves the aerodynamic parameters of the aircraft under different angles of attack and airspeed conditions, such as lift, drag and static stability. These data are usually derived from a variety of methods such as wind tunnel tests, computer simulations and flight tests. Since the aerodynamic forces borne by an aircraft when performing arbitrary maneuvers in space can be decomposed into static aerodynamic forces (caused by the attitude of the aircraft relative to the oncoming airflow), oscillating aerodynamic forces (caused by the angular motion of the aircraft around its center of gravity) and rotational aerodynamic forces (caused by the rotational motion of the aircraft around the spatial axis), the high angle of attack database of the aircraft should be composed of the data of these three aspects, and the corresponding wind tunnel tests are also divided into static force measurement tests, oscillating balance tests and rotating balance tests.

[0005] However, the existing research on spin characteristics prediction still has certain limitations. The main manifestation is that the analysis of aircraft spin characteristics mostly remains at the qualitative level, lacking precise quantification of the prediction results. This makes us lack understanding of the specific laws of how each parameter variable affects the spin characteristics, resulting in difficulty in accurately grasping the occurrence, development and control of the spin phenomenon in practical applications. In order to overcome this defect, it is necessary to conduct in-depth research and expansion on the spin characteristics prediction technology, in order to achieve the goals of improving the quantification of the prediction results, clarifying the influence of each parameter variable on the spin characteristics, and clarifying the interaction between various factors. Summary of the invention

[0006] In view of the above-mentioned deficiencies in the prior art, the present invention provides a method for analyzing tail spin characteristics, which improves the quantification degree of the results of tail spin characteristic prediction, clarifies the influence of various parameter variables on the tail spin characteristics, and clarifies the interaction between various factors.

[0007] The technical solution adopted by the present invention is:

[0008] A method for analyzing tailspin characteristics, which obtains the time history of tailspin characteristics by solving the tailspin dynamics differential equation, predicts the tailspin characteristics of the simulation example under the conditions of multiple parameters such as weight, moment of inertia, and entry mode, and analyzes the influence of multiple variable parameters on the tailspin characteristics;

[0009] The XGBoost regression algorithm based on decision tree analysis is used to build a machine learning model. Taking the average angle of attack, average rotation rate, sinking speed and other spin characteristics as the target, the feature importance analysis of the multi-variable parameters of the simulation example is performed; the influence ratio of the multi-variable parameters on the same spin characteristics is analyzed, and the influence of key factors on the spin is completed in a quantitative way;

[0010] Including multi-variable spin characteristic prediction and multi-dimensional global feature analysis based on feature importance;

[0011] The prediction of multi-variable spin characteristics is based on the dynamic model, motion model and large angle of attack unsteady aerodynamic model. With the physics-driven analysis strategy, the simulation platform is built through MATLAB to solve the spin dynamics differential equation with clear physical meaning, realize the real-time simulation of the entire dynamic process of stall / spin entry and recovery, and complete the prediction of multi-variable spin characteristics.

[0012] Based on the body axis coordinate system, dynamic equations including axial force, lateral force, normal force, rolling moment, pitching moment and yaw moment were established to describe the force conditions of the aircraft during the tailspin.

[0013] By using numerical simulation methods, such as the fourth-order Runge-Kutta integration method, the dynamic differential equations are solved to analyze the force conditions of the aircraft during the tailspin, including the changes of axial force, lateral force, normal force, rolling moment, pitching moment and yaw moment over time.

[0014] The changing trends of the angle of attack and sideslip angle over time, as well as their influence on the spin entry and recovery process can be analyzed; the changing trends of the roll angular velocity and yaw angular velocity over time, as well as their influence on the spin motion can be analyzed; the changing trends of the sideslip angle over time, as well as its influence on the spin motion can be analyzed.

[0015] Establish kinematic equations including roll angular velocity, pitch angular velocity and yaw angular velocity to describe the motion state of the aircraft during the tailspin;

[0016] The motion state of an aircraft during a spin is described by describing how the center of mass position, attitude angle, and angular velocity of the aircraft change with time.

[0017] The motion state data includes attitude angles (pitch angle, roll angle, yaw angle) and three-axis angular velocity (pitch angular velocity, roll angular velocity, yaw angular velocity). By analyzing the changing patterns of attitude angles and angular velocity, we can understand the process of entering, developing and recovering from a spin, as well as the characteristic parameters of the spin mode, such as angle of attack, yaw angular rate, period, trajectory radius, etc.

[0018] The dynamic derivative model is used to combine the static aerodynamic data, the aerodynamic data caused by forced oscillation motion and the aerodynamic data caused by rotation motion in the high angle of attack wind tunnel test to describe the aerodynamic characteristics of the aircraft at high angles of attack.

[0019] The static aerodynamic data provides the force of the aircraft in a static state, the aerodynamic data caused by forced oscillation motion provides the aerodynamic changes of the aircraft when the state variables such as angle of attack, sideslip angle and rudder deflection change, and the aerodynamic data caused by rotational motion provides the aerodynamic changes of the aircraft during rotational motion. These three parts of aerodynamic data are linearly superimposed to form a dynamic derivative model.

[0020] In the high angle of attack wind tunnel test, the static aerodynamic data, aerodynamic data caused by forced oscillatory motion, and aerodynamic data caused by rotational motion jointly determine the model's ability to describe the aircraft's high angle of attack flight characteristics. Static aerodynamic data are used to calculate the aircraft's aerodynamic coefficients in a static state, such as the lift coefficient, drag coefficient, and pitch moment coefficient. These coefficients determine the force conditions of the aircraft when it is stationary or in a uniform straight flight state. The aerodynamic data caused by forced oscillatory motion are used to calculate the dynamic derivatives of the aircraft in a forced oscillatory motion state, such as the derivative of the pitch moment coefficient to the angle of attack, the derivative of the yaw moment coefficient to the sideslip angle, and the derivative of the rolling moment coefficient to the rudder deflection angle. These dynamic derivatives describe the changes in the aircraft's aerodynamic forces when state variables such as the angle of attack, sideslip angle, and rudder deflection change. The aerodynamic data caused by rotational motion is used to calculate the aerodynamic coefficients of the aircraft in rotational motion, such as the derivative of the lift coefficient to the dimensionless rotational angular velocity, the derivative of the drag coefficient to the dimensionless rotational angular velocity, the derivative of the pitch moment coefficient to the dimensionless rotational angular velocity, etc. These coefficients describe the changes in the aerodynamic force of the aircraft during rotational motion.

[0021] Use MATLAB's powerful numerical calculation and graphics display capabilities to build a simulation platform.

[0022] The present invention uses Simulink in MATLAB to build a simulation platform for simulating and analyzing the motion state and stress condition of an aircraft during a tailspin, and predicting the development process of the aircraft during a tailspin. The platform integrates a dynamic model, a motion model, and a large angle of attack unsteady aerodynamic model, and can achieve real-time simulation of the entire dynamic process of entering and exiting a stall / tailspin. During operation, a simulation toolbar is used to run the simulation, such as starting, pausing, and stopping the simulation. The simulation results can be displayed in a model window, such as a waveform diagram, a state diagram, and the like.

[0023] Input the aerodynamic parameter database required for simulation and perform multi-dimensional interpolation processing; including high angle of attack data input, data fitting, and control law data input;

[0024] Organize the required input data into a format suitable for Simulink, such as a CSV file or a MATLAB file; import the data into the signal source module or the data reading module, and input the fitted model parameters into the transfer function module or the custom module, and set the parameters of the signal source module, transfer function module, and custom module.

[0025] The numerical simulation method is used to calculate the time history of the tailspin and obtain the tailspin calculation results, including balanced flight calculation, speed and density calculation, and six-degree-of-freedom motion equation calculation. The six-degree-of-freedom motion equation calculation adopts the fourth-order Runge-Kutta integration method.

[0026] The balanced flight calculation can use MATLAB's ode45 function to simulate the aircraft's balanced flight process and calculate the corresponding coefficients based on the dynamic equations and initial conditions; the speed and density are calculated using the following formulas respectively; select a suitable solver, such as MATLAB's ode45 or ode15s function, and use the fourth-order Runge-Kutta integration method to solve the dynamic equations and kinematic equations.

[0027]

[0028] In the formula, m Indicates the aircraft mass in kg; S Indicates the wing area in m 2 ; V Indicates the flight speed in m / s; g Indicates the acceleration due to gravity, in m / s 2 ; Indicates the air density in kg / m³; H Indicates the flight altitude in meters; C L represents the lift coefficient. Since aircraft stall spin generally occurs in the troposphere, it is only necessary to calculate the density below an altitude of 11 kilometers.

[0029] By analyzing the calculation results, we can understand the forces and motion states of the aircraft during the tailspin, and how these factors interact to cause the formation and development of the tailspin; we can evaluate the risk of the aircraft entering a tailspin under different parameter conditions; and we can understand the dynamic response of the aircraft during the tailspin recovery process. Among them, the calculation results of the balanced flight calculation and the speed and density calculation provide the initial state for the subsequent six-degree-of-freedom motion equation calculation. The six-degree-of-freedom motion equation calculation obtains the changes of system parameters (such as speed, altitude, angle of attack, sideslip angle, etc.) over time.

[0030] The spatial motion trajectory and attitude changes of the aircraft tailspin are displayed statically or dynamically through images, and sub-modules such as data result output module, two-dimensional curve output module and three-dimensional dynamic display module are provided to facilitate users to view and analyze simulation results.

[0031] The purpose of displaying the spatial motion trajectory and attitude changes of an aircraft tailspin statically or dynamically through images is to gain a deeper understanding of the tailspin phenomenon. The spatial motion trajectory image can intuitively display the spatial motion trajectory of the aircraft during the tailspin process, such as spiral lines, spiral descents, etc. Analyzing the trajectory shape can help understand the stability of the tailspin and the difficulty of entering / exiting, and help understand the motion characteristics of the tailspin; the attitude change image can display the attitude changes of the aircraft during the tailspin process, such as changes in pitch angle, roll angle, and yaw angle, which can help understand the dynamic mechanism and influencing factors of the tailspin and help understand the dynamic characteristics of the tailspin.

[0032] The data result output module includes data storage, file writing, and a user reading interface; the two-dimensional curve output module includes a two-dimensional drawing function, parameter setting, and a user reading interface; the three-dimensional dynamic display module includes a three-dimensional drawing function, an animation function, and a user reading interface.

[0033] The modules work in a collaborative way as follows: the data result output module stores the simulation result data in the data storage structure, and exports it in the form of a matrix or external table file according to user requirements; the two-dimensional curve output module reads data from the data storage structure, and uses the drawing function to draw a two-dimensional curve graph; the three-dimensional dynamic display module reads data from the data storage structure, and uses the three-dimensional drawing function and animation function to draw a three-dimensional dynamic graph; the user selects the output data, drawing parameters and display parameters through the user interface, and triggers the data result output module, the two-dimensional curve output module and the three-dimensional dynamic display module to work collaboratively.

[0034] Mass, moment of inertia and entry method are selected as multi-variable parameters, representing the weight characteristics, inertia characteristics and the method of entering the tailspin of the aircraft respectively;

[0035] Design different simulation examples, including dual-parameter analysis and triple-parameter analysis, and compare the variable parameter results with the original parameter results to analyze the impact of multiple variable parameters on the spin characteristics;

[0036] Based on the two-parameter analysis and the three-parameter analysis, we can comprehensively analyze the influence of multiple parameters on the spin characteristics and observe the complex interactions between them; by comparing the spin characteristics under different parameter combinations, we can more accurately determine which parameters have the greatest influence on the spin characteristics and quantify their influence. Due to the limitation of space and data volume, only the two-parameter analysis and the three-parameter analysis are used as representatives for simulation analysis.

[0037] In the present invention, the dual variable parameter analysis mainly studies the influence of two parameters changing at the same time on the tailspin characteristics, and determines the influence degree of the two parameters on the tailspin characteristics. The process includes: selecting two parameters to be changed, such as weight and moment of inertia; setting two different states of the two parameters, such as weight 1 and weight 2, moment of inertia 1 and moment of inertia 2; performing simulation calculations to obtain tailspin characteristic data under different parameter combinations, such as curves of angle of attack, sideslip angle, height, etc. changing with time; comparing and analyzing the simulation results under different parameter combinations with the simulation results under the original parameter state, observing the changing trend and law of the tailspin characteristics; through comparative analysis, determining the influence degree of the two parameters on the tailspin characteristics, and analyzing the interaction relationship between them.

[0038] In the present invention, the three-variable parameter analysis mainly studies the influence of the simultaneous change of three parameters on the tailspin characteristics, and determines the influence degree of the three parameters on the tailspin characteristics. The process includes: selecting three parameters to be changed, such as weight, moment of inertia and entry mode; setting two different states of the three parameters, such as weight 1 and weight 2, moment of inertia 1 and moment of inertia 2, entry mode 1 and entry mode 2; performing simulation calculations to obtain tailspin characteristic data under different parameter combinations, such as curves of angle of attack, sideslip angle, height, etc. changing with time; comparing and analyzing the simulation results under different parameter combinations with the simulation results under the original parameter state, observing the changing trend and law of the tailspin characteristics; through comparative analysis, determining the influence degree of the three parameters on the tailspin characteristics, and analyzing the interaction relationship between them.

[0039] When comparing and analyzing the simulation results, curve comparison and parameter comparison are adopted, including: comparing the simulation curves under different parameter combinations with the simulation curves under the original parameter state to observe the changing trends and laws of the spin characteristics; comparing the spin modal parameters (such as average angle of attack, sinking speed, etc.) under different parameter combinations with the spin modal parameters under the original parameter state to analyze the influence of parameter changes on the spin characteristics.

[0040] Taking the results of three-variable parameter analysis as an example, in the present invention, the influence of weight on the spin characteristics is mainly reflected in the average angle of attack. As the weight increases, the average angle of attack of the aircraft after entering the spin will increase; the influence of the moment of inertia on the spin characteristics is mainly reflected in the sinking speed. As the moment of inertia increases, the sinking speed of the aircraft after entering the spin will increase; the influence of the entry method on the spin characteristics is more complicated, it will affect the initial attitude and speed of the aircraft, and then affect the development of the spin characteristics.

[0041] Output the real-time curves of the angle of attack, sideslip angle, altitude and other parameters changing with time, and draw the prediction curves, including the angle of attack characteristic curve, sideslip angle characteristic curve and altitude characteristic curve;

[0042] By observing the simulation curves and parameter changes, the influence trend and law of multi-variable parameters on spin characteristics are analyzed;

[0043] In the present invention, by observing the simulation curve, the difference between the spin characteristics after the parameter change and the spin characteristics in the original state is analyzed to determine whether there are obvious abnormal fluctuations and whether there are abnormal development trends. Through parameter changes, it can be confirmed whether key parameters (such as average angle of attack, sinking speed) are gradually increasing, whether oscillations occur, whether the aircraft attitude becomes favorable and whether the spin can be recovered.

[0044] The multi-dimensional global feature analysis based on feature importance combines the influence of multi-variable parameters on the spin characteristics with feature importance analysis, takes multi-variable parameters as each feature in the machine learning model, takes the spin characteristics as the prediction result, and uses feature importance analysis to obtain the contribution of multi-variable parameters to the spin characteristics.

[0045] The weight, moment of inertia and entry mode are used as feature variables in the machine learning model; the average angle of attack, average rotation rate and sinking speed are used as target variables in the machine learning model; since the entry mode contains multiple rudder deflection parameters, data dimensionality reduction processing is required;

[0046] When performing data dimensionality reduction, first input the original data into the dimensionality reduction model and ensure that the data has been standardized, that is, the mean value of each feature is 0 and the standard deviation is 1; select the target dimension for dimensionality reduction, such as reducing 2-dimensional data to 1-dimensional, and set other parameters, such as learning rate, number of iterations, etc.; the dimensionality reduction model will learn a mapping based on the input data, map high-dimensional data to low-dimensional space, and finally output the reduced-dimensional data. The coordinates of each data point in the low-dimensional space represent its features;

[0047] For example, the t-SNE (t-Distributed Stochastic Neighbor Embedding) nonlinear dimensionality reduction method is used to reduce the elevator and rudder deflections to one-dimensional data for feature importance analysis;

[0048] Select the XGBoost regression algorithm as the machine learning model; use the processed training data set, including the feature matrix X and the target vector Y, to train the XGBoost model; the XGBoost model measures the importance of features by calculating the total gain of the features in the model. The total gain of each feature in the model can be obtained by calculating the sum of the gains of the nodes split by the feature in all trees; based on the total gain of the feature, the contribution of each feature to the tailspin characteristic can be calculated, that is, the degree of influence of the feature on the tailspin characteristic;

[0049] Assume that an XGBoost model is used to predict the average angle of attack of an aircraft tailspin, which contains the following features:

[0050] X1: Weight (kg)

[0051] X2: Moment of inertia (kg·s²)

[0052] X3: Entry method (1-dimensional data)

[0053] After the model training is completed, the total gain of each feature is calculated as follows:

[0054]

[0055] Then the contribution of each feature to the average angle of attack is:

[0056] Contribution of X1 = 0.5 / (0.5+0.3+0.2) = 0.5

[0057] Contribution of X2 = 0.3 / (0.5+0.3+0.2) = 0.3

[0058] Contribution of X3 = 0.2 / (0.5+0.3+0.2) = 0.2

[0059] It can be seen that weight (X1) has the greatest impact on the average angle of attack, followed by moment of inertia (X2), and finally the entry method (X3). This means that when predicting the average angle of attack of an aircraft spin, weight is the most critical factor, followed by moment of inertia, and finally the entry method.

[0060] By observing the prediction deviation of some test sets, the prediction accuracy of the model can be evaluated; by observing the importance ratio of each feature, it is possible to analyze which feature has the greatest impact on the spin characteristics and the contribution of each feature to the spin characteristics.

[0061] Divide the data set into a training set and a test set, use the model to predict the data in the test set, calculate the deviation between the predicted value and the true value, and statistically analyze the distribution of the deviation or calculate the evaluation index (such as MSE, MAE, etc.). By observing the size of the prediction deviation or the evaluation index, you can judge whether the prediction accuracy of the model meets the requirements. You can draw a distribution diagram of the prediction deviation of the test data points, such as a scatter plot or a box plot, to visually observe the distribution of the deviation; according to the size of the evaluation index, judge whether the prediction accuracy of the model meets the requirements. Generally, the smaller the evaluation index, the higher the prediction accuracy of the model.

[0062] By observing the importance ratio of each feature, we can analyze which feature has the greatest impact on the spin characteristics and the contribution of each feature to the spin characteristics. For example, if weight is the most important feature affecting the average angle of attack, it can be explained that increased weight will increase the inertia of the aircraft, making it difficult to quickly recover from the spin, and thus requiring a larger angle of attack to maintain lift.

[0063] Preferably, the simulation platform includes a data processing module, a tailspin calculation module and a calculation result output module; the function of the data processing module is to input the database used in the simulation calculation, and perform multi-dimensional interpolation processing on the aerodynamic data, including processing processes such as high angle of attack data input, data fitting, and control law data input; the function of the tailspin calculation module is to calculate the tailspin time history through a numerical simulation method to obtain the tailspin calculation result, including processing processes such as balanced flight calculation, speed (true speed and indicated speed) and density calculation, and calculation of six-degree-of-freedom motion equations, wherein the calculation of the six-degree-of-freedom motion equations adopts fourth-order Runge-Kutta integration; the function of the calculation result output module is to statically or dynamically display the spatial motion trajectory and attitude changes of the aircraft tailspin through images, and can also call the result data file, including three sub-modules such as the data result output module, the two-dimensional curve output module, and the three-dimensional dynamic display module.

[0064] The dynamic model is established based on the body axis coordinate system, and the units of all parameters are international standard units, so that the model has sufficient versatility; the dynamic model expression is:

[0065]

[0066] in, It represents the axial force coefficient of the body shaft system; represents the lateral force coefficient of the body axis system; represents the normal force coefficient of the body axis system; represents the rolling moment coefficient; represents the pitching moment coefficient; represents the yaw moment coefficient; Represents the axis around the body The roll angular velocity is in rad / s; Represents the axis around the body The pitch angular velocity, in rad / s; Represents the axis around the body The yaw rate is in rad / s; b represents the wingspan, in m; c represents the mean aerodynamic chord length, in m; g Indicates the acceleration due to gravity, in m / s 2 ; 、 、 Respectively represent the x , y , z Axis moment of inertia, in ; represents the cross product of inertia about the center of mass, in units of ;m Indicates the aircraft mass in kg; Q Indicates dynamic pressure, the unit is Pa; S Indicates the wing area in m2; V Indicates the flight speed in m / s; It represents the angle of attack, in rad; Represents the sideslip angle, in rad; Indicates the pitch angle, the unit is rad; represents the roll angle, the unit is rad; V represents the flight speed, the unit is m / s; represents the product of inertia correction factor, and:

[0067] .

[0068] The model is constructed based on the following assumptions;

[0069] The mass of the aircraft is constant; an irrotational flat Earth with a fixed atmosphere; the aircraft is considered to be a rigid body; constant gravity; the aircraft has a longitudinal plane of symmetry, i.e.: the aircraft has a longitudinal plane of symmetry ,Right now ;

[0070] The above assumptions are based on simplified considerations of the main forces and motions that an aircraft is subject to during flight, and they are derived from classical mechanics and aircraft design theory. In actual flight, the fuel consumption of an aircraft will cause a change in mass, but this change is usually secondary to analyzing the dynamic behavior of an aircraft in a short period of time. In order to simplify the problem, the assumption that the mass of the aircraft remains unchanged can make the dynamic equations easier to handle; the assumption of an irrotational flat earth with a fixed atmosphere means that the atmosphere is stationary, there are no atmospheric disturbances such as wind and turbulence, and the surface of the earth is flat, and the curvature of the earth is not considered. In order to simplify the atmospheric dynamics model and make the problem easier to describe with mathematical equations, the irrotational assumption means that there is no vortex motion in the atmosphere, which simplifies the calculation of lift and drag, and the fixed atmosphere assumption excludes the effects of time and space on the dynamics of the atmosphere. The spatially varying atmospheric density and pressure make aerodynamic calculations simpler; treating the aircraft as a rigid body means ignoring the deformation of the aircraft structure when subjected to force. This assumption is reasonable when analyzing the tailspin motion of an aircraft because the effect of structural deformation on the tailspin motion is relatively small; in near-ground flight, the gravitational acceleration can be approximated as a constant value because the radius of the earth is very large relative to the aircraft's flight altitude, so the effect of gravity changes on aircraft performance can be ignored; most aircraft designs are symmetrical about the longitudinal symmetry plane, that is, the left and right sides of the aircraft are geometrically and structurally symmetrical, so the aircraft is assumed to have a longitudinal symmetry plane.

[0071] The units related to degrees in the dynamic model and the motion model are all in radians, such as rad, rad / s; the dynamic model ignores engine-related items.

[0072] The purpose of establishing the kinetic model is to:

[0073] The dynamic model describes the force conditions of the aircraft during the tailspin by establishing mathematical expressions for the axial force, lateral force, normal force, rolling moment, pitching moment and yaw moment that the aircraft is subjected to during the tailspin, providing an important theoretical basis for analyzing the tailspin phenomenon.

[0074] The combination of dynamic model and motion model can analyze the motion state of the aircraft during the tailspin, such as the aircraft's speed, acceleration, attitude angle and angular velocity, which provides an important reference for understanding the dynamic mechanism of the tailspin phenomenon.

[0075] By solving the dynamic model, the aircraft's spin characteristics, such as motion trajectory, attitude change, and sinking speed, after entering a spin under different parameter conditions can be predicted, providing important data support for assessing the aircraft's spin risk and formulating flight safety measures.

[0076] Preferably, the motion model is:

[0077]

[0078] In the formula, Represents the axis around the body The roll angular velocity is in rad / s; Represents the axis around the body The pitch angular velocity, in rad / s; Represents the axis around the body The yaw rate is in rad / s; Indicates the pitch angle, the unit is rad; Indicates the roll angle, the unit is rad; Represents the yaw angle in rad.

[0079] The purpose of establishing the motion model is to:

[0080] The motion model describes the motion state of the aircraft during the tailspin by establishing mathematical expressions of the aircraft's roll angular velocity, pitch angular velocity, and yaw angular velocity, providing an important theoretical basis for analyzing the tailspin phenomenon.

[0081] The motion model can analyze the changes in the aircraft's attitude angles during a tailspin, such as changes in roll angle, pitch angle, and yaw angle, providing an important reference for understanding the dynamic mechanism of the tailspin phenomenon;

[0082] The combination of the motion model and the dynamic model can more comprehensively describe the force conditions and motion state of the aircraft during a tailspin, calculate the changes in the aircraft's attitude during a tailspin, and provide an important theoretical tool for analyzing the tailspin phenomenon.

[0083] Preferably, the high angle of attack unsteady aerodynamic model adopts a dynamic derivative model with clear physical meaning, and the expression is:

[0084]

[0085] in,

[0086] , ; represents the axial force coefficient of the body shaft system, represents the lateral force coefficient of the body axis system, represents the normal force coefficient of the body axis system, represents the rolling moment coefficient, represents the pitching moment coefficient, Represents the yaw moment coefficient. represents the angle of attack, represents the sideslip angle, , , They represent the aileron, pitch and yaw angles respectively, and the unit is degree.

[0087] In the above formula, It represents the static aerodynamic data item in the high angle of attack wind tunnel test, including the static aerodynamic item when the rudder deflection is zero and the static aerodynamic increment item caused by the rudder surface deflection;

[0088] The aerodynamic terms caused by the forced oscillatory motion in the high angle of attack wind tunnel test;

[0089] It is the aerodynamic term caused by rotational motion in high angle of attack wind tunnel test.

[0090] Preferably, representative factors are selected in the simulation examples, including: weight, moment of inertia, and entry method;

[0091] Data output includes real-time curves of parameters such as angle of attack, sideslip angle, and altitude changing over time.

[0092] Preferably, the feature importance refers to the degree of influence of each feature of the model on the prediction result in machine learning;

[0093] The XGBoost regression algorithm is used to perform feature importance analysis on multi-variable parameters;

[0094] The steps are summarized into three aspects: building a regression model, calculating feature importance, and evaluating model performance.

[0095] Preferably, the establishment of the regression model requires preparation of training set data, and the processed training data set is used to establish and train the XGBoost model;

[0096] The training set data usually includes features (independent variables) and targets (dependent variables);

[0097] The training data used defines single variables and multivariate variables as features, and tailspin characteristics as targets;

[0098] For the XGBoost algorithm, the training set data contains a feature matrix X and a target vector Y ,in:

[0099]

[0100]

[0101] in, n is the sample size, p is the characteristic value;

[0102] When the dataset contains missing values ​​or the features of the samples need to be scaled, data preprocessing steps must be performed;

[0103] If the data is already in a state suitable for training, it is directly used for model training;

[0104] The goal of the XGBoost model is to minimize an objective function composed of a loss function and a regularization term;

[0105] In XGBoost, the loss function is defined as the squared loss function:

[0106]

[0107] In the formula, is the true target value of the i-th sample, is the target value predicted by the model;

[0108] The regularization term consists of two parts: the number of leaf nodes in the tree T and the L2 norm of the fraction of leaf nodes w:

[0109]

[0110] in, and is a hyperparameter used to control the regularization strength;

[0111] Get the objective function of the XGBoost model:

[0112]

[0113] In the formula k Indicates k A decision tree.

[0114] Preferably, the calculation of feature importance refers to determining the influence of each feature (or variable, attribute) in the data set on the output result of the prediction model through a specific algorithm or method;

[0115] In XGBoost, feature importance is measured by calculating the total gain of the feature in the model;

[0116] The total gain of each feature in the model can be obtained by calculating the sum of the gains of the feature in splitting nodes in all trees;

[0117] Specifically, for the jth feature, its gain in the kth tree is It can be expressed as:

[0118]

[0119] in, and Respectively represent the sum of the gradients of the left and right child nodes after segmentation, and Represents the sum of the second-order derivatives of the left and right child nodes, is the coefficient of the L2 regularization term;

[0120] Therefore, the total gain of the jth feature is It can be expressed as:

[0121]

[0122] In the formula, K is the total number of decision trees.

[0123] Preferably, the performance of the model is evaluated by calculating the evaluation indicators of the model according to the prediction results and the true target value of the test set after the model training is completed. These evaluation indicators include mean square error (MSE), determination coefficient (R²), mean absolute error (MAE), and root mean square error (RMSE).

[0124] MSE measures the average of the squares of the differences between the predicted values ​​and the true values. It is one of the most commonly used evaluation metrics in regression analysis because it is simple to calculate and has good mathematical properties (for example, it is a convex function, which is easy to optimize). Generally, the lower the MSE value, the closer the model's predicted values ​​are to the true values, and the better the model's performance.

[0125] R² represents the proportion of variability explained by the model, that is, the accuracy of the model's predictions. Its value ranges from 0 to 1, with 1 indicating a perfect fit and 0 indicating that the model cannot explain any variability. The closer R² is to 1, the better the model fit and the higher the performance.

[0126] MAE is the average of the absolute values ​​of the differences between the predicted values ​​and the true values. It is an intuitive measure of the model's prediction error and is not affected by extreme values. The lower the MAE value, the more accurate the model's predictions.

[0127] RMSE is the square root of MSE. It provides the average magnitude of the prediction error and its unit is consistent with the original data, so it is easier to interpret. The lower the RMSE value, the higher the prediction accuracy of the model.

[0128] The calculation formula of the evaluation index is:

[0129]

[0130] in n is the sample size, It is i The true value of the samples, It is i The predicted value of samples, , are the residual sum of squares and the total sum of squares respectively, and:

[0131] In the formula, is the average of the true values.

[0132] The smaller the values ​​of mean square error, mean absolute error, and root mean square error, the more accurate the model is; the closer the coefficient of determination is to 1, the more accurate the model is.

[0133] Since the difference between entry method 1 and entry method 2 is mainly reflected in the elevator deflection and rudder deflection, it is necessary to express it with a single feature when predicting the feature importance.

[0134] The t-SNE (t-Distributed Stochastic Neighbor Embedding) nonlinear dimensionality reduction method is selected to reduce the data dimension of the elevator and rudder deflections, and reflect the similarity of the two-dimensional data in the form of one-dimensional data.

[0135] The beneficial effects of the present invention compared with the prior art are as follows:

[0136] The spin characteristic analysis method of the present invention focuses on the shortcoming that the analysis results of the existing spin characteristic prediction have not been quantified, and develops a multi-dimensional global characteristic analysis method for studying the influence of multiple variables on the aircraft spin dynamic characteristics. The data set generated by the aircraft variables is studied from multiple dimensions, and the common characteristics of all samples or data points in the data set are deeply explored and analyzed, so as to better understand the inherent structure and relationship of the data, and then analyze the influence characteristics and influence degree of key factors on the spin characteristics, providing a new research logic for studying the influence of key parameters on the aircraft spin characteristics. Compared with the prior art, the beneficial effects of the present invention include but are not limited to:

[0137] Quantitative analysis, accurate prediction. This paper uses a machine learning model to quantitatively analyze the influence of three key parameters, namely weight, moment of inertia, and entry mode, on the average angle of attack, average rotation rate, sinking speed and other spin characteristics in the form of feature importance. This quantitative analysis goes beyond the traditional qualitative analysis and provides a more accurate basis for flight control law design, flight safety assessment, etc., which helps us to have a deeper understanding of the spin phenomenon and reduce flight risks.

[0138] Optimize design and reduce risk. Based on the prediction results of the spin characteristics, the present invention can help designers more clearly understand the impact of different aerodynamic layout parameters on the spin characteristics, thereby performing more effective aerodynamic optimization design and reducing the risk of the aircraft entering a spin. In addition, the present invention can also help designers better understand the dynamic characteristics of the aircraft at high angles of attack, thereby designing an aircraft with good high angle of attack characteristics and improving flight performance.

[0139] Test flights, escort. The multi-dimensional global feature analysis method (MGFA) provided by the present invention can provide important technical support for test flights. Through MGFA, we can have a deeper understanding of the dynamic characteristics of the aircraft at large angles of attack, so as to formulate a more reasonable test flight plan, select more appropriate test flight parameters, and evaluate the test flight results to improve the safety and effectiveness of the test flight. In terms of airworthiness certification, MGFA can provide a more accurate basis for the safety assessment of the aircraft, help the airworthiness certification department to have a more comprehensive understanding of the performance of the aircraft, optimize the compliance verification method, ensure that the aircraft meets the airworthiness standards, and ensure flight safety.

[0140] At the same time, with the continuous development of technology, the multi-dimensional global feature analysis method (MGFA) provided by the present invention can be applied to multiple fields. The following are some specific application scenarios:

[0141] Control law optimization based on MGFA. MGFA is used to analyze the key characteristics of the aircraft under different flight conditions, such as angle of attack, pitch rate, throttle opening, etc., and use them as input variables of the control law. The response of the aircraft is predicted through a machine learning model, and the corresponding control strategy is designed to improve the performance and robustness of the flight control system.

[0142] Health status monitoring based on MGFA. Use MGFA to analyze aircraft sensor data, such as engine vibration, oil temperature, etc., and use them as characteristic variables for health status monitoring. Use machine learning models to predict the health status of the aircraft and warn of potential failures in advance to improve aircraft reliability.

[0143] MGFA-based path optimization. MGFA is used to analyze the environmental characteristics of the drone's flight path, such as terrain, obstacles, weather, etc., and use them as characteristic variables for path optimization. The machine learning model is used to predict the performance and risks of the drone on different paths, and the optimal path is planned to improve the flight efficiency and safety of the drone.

[0144] Accident analysis based on MGFA: Use MGFA to analyze aircraft accident data, such as black box data, flight data, ground radar data, etc., and use them as feature variables for accident analysis. Use machine learning models to analyze the causes and processes of accidents, and provide corresponding improvement suggestions to prevent similar accidents from happening again. BRIEF DESCRIPTION OF THE DRAWINGS

[0145] Figure 1 This is a multi-dimensional global feature analysis flow chart of a preferred embodiment of the present application;

[0146] Figure 2 It is a prediction curve diagram of tailspin characteristics under multi-variable parameter state of a preferred embodiment of the present application;

[0147] Figure 3 A comparison diagram of the representation value after dimensionality reduction and the original feature of the tailspin characteristic data of a preferred embodiment of the present application;

[0148] Figure 4 This is a prediction diagram of the characteristic importance of multiple variable parameters to the average angle of attack of a preferred embodiment of the present application. DETAILED DESCRIPTION

[0149] The present invention is described in detail below with reference to the accompanying drawings and embodiments:

[0150] During the analysis, aircraft aerodynamic parameter data are collected, including high angle of attack wind tunnel test data, forced oscillation motion data and rotational motion data; research parameters such as weight, moment of inertia and entry method are determined; and the weight, moment of inertia and entry method are changed respectively to conduct double-variable parameter analysis and three-variable parameter analysis.

[0151] During the analysis, the aircraft dynamics model, motion model and high angle of attack unsteady aerodynamic model were established; the simulation platform was built using MATLAB, the aerodynamic parameter database was input, and multi-dimensional interpolation processing was performed; the numerical simulation method was used to calculate the time history of the spin and obtain the spin characteristic data, including curves of parameters such as angle of attack, sideslip angle, and altitude changing with time.

[0152] During the analysis, the XGBoost regression algorithm was selected as the machine learning model; weight, moment of inertia and entry mode after dimensionality reduction were used as feature variables, and the tailspin characteristics were used as the target variable; the XGBoost model was trained using the training data set, and the feature importance was calculated.

[0153] During the analysis, the influence of each feature on the spin characteristics is analyzed, such as the average angle of attack, average rotation rate, sinking speed, etc.; the simulation results and feature importance analysis are combined to deeply understand the relationship between the aircraft spin characteristics and influencing factors; the model performance is evaluated, such as the mean square error, determination coefficient, etc., to ensure the reliability of the prediction results.

[0154] The data processing module imports high angle of attack wind tunnel test data (static, forced oscillation, rotational motion data) into the platform; fits the imported data to obtain mathematical expressions or functions of aerodynamic parameters; inputs control law related data, such as rudder deflection angle, etc.; uses interpolation algorithms to interpolate the data to obtain the aerodynamic parameters required at any time and in any state during the simulation process.

[0155] The tailspin calculation module simulates the balanced flight process of the aircraft according to the dynamic equations and initial conditions, and calculates the corresponding coefficients; uses the formula to calculate the flight speed and air density; based on the body axis coordinate system, establishes dynamic equations including axial force, lateral force, normal force, rolling moment, pitching moment and yaw moment to describe the force conditions of the aircraft during the tailspin; establishes kinematic equations including rolling angular velocity, pitching angular velocity and yaw angular velocity to describe the motion state of the aircraft during the tailspin; adopts the dynamic derivative model to combine the high angle of attack wind tunnel test data with the interpolation data to describe the aerodynamic characteristics of the aircraft at a large angle of attack; selects a suitable numerical integration method (such as the fourth-order Runge-Kutta integration method) to solve the dynamic equations and kinematic equations to obtain the changes of the aircraft's speed, altitude, angle of attack, sideslip angle and other parameters over time during the tailspin.

[0156] The calculation result output module stores the simulation result data in a data structure; exports the data in the form of a matrix or external table file according to user needs; reads data from the data structure and uses drawing functions to draw two-dimensional curve graphs, such as angle of attack characteristic curves, sideslip angle characteristic curves, and altitude characteristic curves; reads data from the data structure and uses three-dimensional drawing functions and animation functions to draw three-dimensional dynamic graphics, such as the spatial motion trajectory and attitude changes of the aircraft tailspin.

[0157] The multi-variable parameter state has different degrees of influence on the spin characteristics, specifically: Figure 2 It can be seen that the influence of weight on the spin characteristics is mainly reflected in the average angle of attack. As the weight increases, the average angle of attack of the aircraft after entering the spin will increase. This may be because the increase in weight causes the aircraft to sink faster, requiring a larger angle of attack to maintain lift.

[0158] from Figure 2 It can be seen that the influence of rotational inertia on the spin characteristics is mainly reflected in the sinking speed. As the rotational inertia increases, the sinking speed of the aircraft after entering the spin will increase. This may be because the increase in rotational inertia increases the inertia of the aircraft, making it difficult to quickly recover from the spin.

[0159] from Figure 2 It can be seen that the impact of the entry method on the spin characteristics is relatively complex. The change of the entry method will affect the initial attitude and speed of the aircraft, and then affect the development of the spin characteristics. For example, the entry method of Case E is "pull the stick first, then push the rudder", which may cause the average angle of attack of the aircraft to increase after entering the spin and reduce the sinking speed.

[0160] By observing the graph, we can see that there is a certain correlation between the representation value after dimensionality reduction and the original feature, and the features of the original data can be reconstructed by similarity. By comparing the original features and the representation values ​​after dimensionality reduction, we can find that the representation values ​​after dimensionality reduction can retain some important information of the original features. For example, there is a significant difference in the representation values ​​of entry mode 1 and entry mode 2 after dimensionality reduction, which is consistent with the difference in rudder deviation in the original features. This shows that the t-SNE nonlinear dimensionality reduction method can effectively reduce the dimensions of the features of entry mode 1 and entry mode 2 and retain important information; the representation values ​​after dimensionality reduction can reconstruct the features of the original data by similarity, providing necessary data support for subsequent feature importance analysis.

[0161] Figure 3 The relationship between the representation value and the original feature after dimensionality reduction of entry method 1 and entry method 2 is shown.

[0162] Figure 4 The prediction results of the XGBoost model for the average angle of attack are shown. The prediction deviations of some test sets are shown. The deviation values ​​are small, indicating that the XGBoost model has a high prediction accuracy for the average angle of attack.

[0163] Mass has the greatest impact on the average angle of attack, indicating that the weight of the aircraft has a significant impact on the spin characteristics. Increased weight will increase the inertia of the aircraft, making it difficult for the aircraft to quickly recover from a spin, resulting in an increase in the average angle of attack. Increased moment of inertia will increase the inertia of the aircraft, making it difficult for the aircraft to quickly recover from a spin, resulting in an increase in the average angle of attack. Different entry methods will result in different initial attitudes and speeds of the aircraft, which in turn affects the development of spin characteristics.

[0164] The embodiment of the present application provides a multidimensional global feature analysis (MGFA) for studying the influence of multiple variables on the dynamic characteristics of aircraft spins, to solve the problem that the analysis results in the existing prediction of spin characteristics have not been quantified. The so-called multidimensional global feature analysis refers to a comprehensive analysis of the global characteristics caused by multiple variable parameters from a multidimensional perspective of qualitative analysis and quantitative analysis, with a research paradigm driven by "physics + data", through a research carrier that combines aerodynamic derivative models and machine learning algorithms. The specific technical route can be summarized as:

[0165] Firstly, with a physics-driven analysis strategy, the time history of the spin characteristics is obtained by solving the differential equation of spin dynamics, and the spin characteristics of the simulation example under the conditions of multi-parameter changes such as weight, moment of inertia, and entry method are predicted, and the influence of multi-variable parameters on the spin characteristics is analyzed; secondly, with "data-driven" as the research idea, the XGBoost regression algorithm based on decision tree analysis is used to build a machine learning model, and the multi-variable parameters of the simulation example are analyzed with the average angle of attack, average rotation rate, sinking speed and other spin characteristics as the target; finally, the influence ratio of multi-variable parameters on the same spin characteristics is analyzed, and the research on the characteristics and degree of influence of key factors on the spin is completed in a quantitative way.

[0166] Figure 1 It can be seen that a method for analyzing tailspin characteristics obtains the time history of tailspin characteristics by solving the tailspin dynamics differential equation, predicts the tailspin characteristics of the simulation example under the conditions of multiple parameter changes such as weight, moment of inertia, and entry mode, and analyzes the influence of multiple variable parameters on the tailspin characteristics;

[0167] A machine learning model was built using the XGBoost regression algorithm based on decision tree analysis. Taking the spin characteristics such as the average angle of attack, average rotation rate, and sinking speed as the target, the feature importance analysis of the multi-variable parameters of the simulation example was performed. The influence of the multi-variable parameters on the same spin characteristics was analyzed, and the influence of key factors on the spin was completed in a quantitative way.

[0168] A method for analyzing tailspin characteristics, including multi-variable parameter tailspin characteristic prediction and multi-dimensional global characteristic analysis based on characteristic importance,

[0169] The prediction of multi-variable spin characteristics is based on the dynamic model, motion model and large angle of attack unsteady aerodynamic model. With the physics-driven analysis strategy, the simulation platform is built through MATLAB to solve the spin dynamics differential equation with clear physical meaning, realize the real-time simulation of the entire dynamic process of stall / spin entry and recovery, and complete the prediction of multi-variable spin characteristics.

[0170] Based on the body axis coordinate system, a dynamic equation including axial force, lateral force, normal force, rolling moment, pitching moment and yaw moment was established to describe the force conditions of the aircraft during the tailspin; a kinematic equation including rolling angular velocity, pitching angular velocity and yaw angular velocity was established to describe the motion state of the aircraft during the tailspin; a dynamic derivative model was used to combine the static aerodynamic data in the high angle of attack wind tunnel test, the aerodynamic data caused by forced oscillation motion and the aerodynamic data caused by rotational motion to describe the aerodynamic characteristics of the aircraft at high angles of attack;

[0171] The simulation platform is built by using the powerful numerical calculation and graphic display functions of MATLAB. The aerodynamic parameter database required for the simulation is input, and multi-dimensional interpolation processing is performed, including high angle of attack data input, data fitting, control law data input, etc. The numerical simulation method is used to calculate the time history of the tailspin and obtain the tailspin calculation results, including balanced flight calculation, speed and density calculation, six-degree-of-freedom motion equation calculation, etc., among which the six-degree-of-freedom motion equation calculation adopts the fourth-order Runge-Kutta integration method. The spatial motion trajectory and attitude changes of the aircraft tailspin are displayed statically or dynamically through images, and sub-modules such as data result output module, two-dimensional curve output module and three-dimensional dynamic display module are provided to facilitate users to view and analyze the simulation results.

[0172] Weight, moment of inertia and entry method are selected as multi-variable parameters, representing the mass, inertia characteristics and entry method of the aircraft respectively; different simulation examples are designed, including double-variable parameter analysis and three-variable parameter analysis, and the variable parameter results are compared with the original parameter results to analyze the influence of multi-variable parameters on the spin characteristics; real-time curves of parameters such as angle of attack, sideslip angle, and altitude changing with time are output, and prediction curves are drawn, including angle of attack characteristic curves, sideslip angle characteristic curves, and altitude characteristic curves; by observing the simulation curves and parameter changes, the influence trends and laws of multi-variable parameters on the spin characteristics are analyzed.

[0173] The multi-dimensional global feature analysis based on feature importance combines the influence of multi-variable parameters on the tailspin characteristics with the feature importance analysis, uses the multi-variable parameters as the various features in the machine learning model, and uses the tailspin characteristics as the prediction results. The contribution of the multi-variable parameters to the tailspin characteristics can be obtained by using the feature importance analysis.

[0174] The weight, moment of inertia and entry method are used as feature variables in the machine learning model; the average angle of attack, average rotation rate and sinking speed are used as target variables in the machine learning model; since the entry method contains multiple rudder deflection parameters, data dimensionality reduction processing is required, for example, using the t-SNE (t-Distributed Stochastic NeighborEmbedding) nonlinear dimensionality reduction method to reduce the elevator deflection and rudder deflection into one-dimensional data for feature importance analysis.

[0175] Select the XGBoost regression algorithm as the machine learning model; use the processed training data set, including the feature matrix X and the target vector Y, to train the XGBoost model; the XGBoost model measures the importance of features by calculating the total gain of the features in the model. The total gain of each feature in the model can be obtained by calculating the sum of the gains of the nodes split by the feature in all trees; based on the total gain of the feature, the contribution of each feature to the tailspin characteristic can be calculated, that is, the degree of influence of the feature on the tailspin characteristic;

[0176] By observing the prediction deviation of some test sets, the prediction accuracy of the model can be evaluated; by observing the importance ratio of each feature, it is possible to analyze which feature has the greatest impact on the spin characteristics and the contribution of each feature to the spin characteristics.

[0177] Preferably, the simulation platform includes a data processing module, a tailspin calculation module and a calculation result output module; the function of the data processing module is to input the database used in the simulation calculation, and perform multi-dimensional interpolation processing on the aerodynamic data, including processing processes such as high angle of attack data input, data fitting, and control law data input; the function of the tailspin calculation module is to calculate the tailspin time history through a numerical simulation method to obtain the tailspin calculation result, including processing processes such as balanced flight calculation, speed (true speed and indicated speed) and density calculation, and calculation of six-degree-of-freedom motion equations, wherein the calculation of the six-degree-of-freedom motion equations adopts fourth-order Runge-Kutta integration; the function of the calculation result output module is to statically or dynamically display the spatial motion trajectory and attitude changes of the aircraft tailspin through images, and can also call the result data file, including three sub-modules such as the data result output module, the two-dimensional curve output module, and the three-dimensional dynamic display module.

[0178] The dynamic model is established based on the body axis coordinate system, and the units of all parameters are international standard units, so that the model has sufficient versatility; the dynamic model expression is:

[0179]

[0180] in, It represents the axial force coefficient of the body shaft system; represents the lateral force coefficient of the body axis system; represents the normal force coefficient of the body axis system; represents the rolling moment coefficient; represents the pitching moment coefficient; represents the yaw moment coefficient; Represents the axis around the body The roll angular velocity is in rad / s; Represents the axis around the body The pitch angular velocity, in rad / s; Represents the axis around the body The yaw rate is in rad / s; b represents the wingspan, in m; c represents the mean aerodynamic chord length, in m; g Indicates the acceleration due to gravity, in m / s 2 ; 、 、 Respectively represent the x , y , z Axis moment of inertia, in ; represents the cross product of inertia about the center of mass, in units of ; m Indicates the aircraft mass in kg; Q Indicates dynamic pressure, the unit is Pa; S Indicates the wing area in m2; V Indicates the flight speed in m / s; It represents the angle of attack, in rad; Represents the sideslip angle, in rad; Indicates the pitch angle, the unit is rad; represents the roll angle, the unit is rad; V represents the flight speed, the unit is m / s; represents the product of inertia correction factor, and:

[0181] .

[0182] The model is constructed based on the following assumptions;

[0183] The mass of the aircraft is constant; an irrotational flat Earth with a fixed atmosphere; the aircraft is considered to be a rigid body; constant gravity; the aircraft has a longitudinal plane of symmetry, i.e.: the aircraft has a longitudinal plane of symmetry ,Right now;

[0184] The above assumptions are based on simplified considerations of the main forces and motions that an aircraft is subject to during flight, and they are derived from classical mechanics and aircraft design theory. In actual flight, the fuel consumption of an aircraft will cause a change in mass, but this change is usually secondary to analyzing the dynamic behavior of an aircraft in a short period of time. In order to simplify the problem, the mass of the aircraft is assumed to be constant, which makes the dynamic equations easier to handle; the assumption of an irrotational flat earth with a fixed atmosphere means that the atmosphere is stationary, there are no atmospheric disturbances such as wind and turbulence, and the surface of the earth is flat, and the curvature of the earth is not considered. In order to simplify the atmospheric dynamics model and make the problem easier to describe with mathematical equations, the irrotational assumption means that there is no vortex motion in the atmosphere, which simplifies the calculation of lift and drag, and the fixed atmosphere assumption excludes the effects of time and space. The atmospheric density and pressure that change over time make aerodynamic calculations simpler; treating the aircraft as a rigid body means ignoring the deformation of the aircraft structure when subjected to force. This assumption is reasonable when analyzing the tailspin motion of the aircraft because the effect of structural deformation on the tailspin motion is relatively small; in near-ground flight, the gravitational acceleration can be approximated as a constant value because the radius of the earth is very large relative to the flight altitude of the aircraft, so the effect of gravity changes on aircraft performance can be ignored; most aircraft designs are symmetrical about the longitudinal symmetry plane, which means that the left and right sides of the aircraft are geometrically and structurally symmetrical, so the aircraft is assumed to have a longitudinal symmetry plane.

[0185] The units related to degrees in the dynamic model and the motion model are all in radians, such as rad, rad / s; the dynamic model ignores engine-related items.

[0186] The purpose of establishing the kinetic model is to:

[0187] The dynamic model describes the force conditions of the aircraft during the tailspin by establishing mathematical expressions for the axial force, lateral force, normal force, rolling moment, pitching moment and yaw moment that the aircraft is subjected to during the tailspin, providing an important theoretical basis for analyzing the tailspin phenomenon.

[0188] The combination of dynamic model and motion model can analyze the motion state of the aircraft during the tailspin, such as the aircraft's speed, acceleration, attitude angle and angular velocity, which provides an important reference for understanding the dynamic mechanism of the tailspin phenomenon.

[0189] By solving the dynamic model, the aircraft's spin characteristics, such as motion trajectory, attitude change, and sinking speed, after entering a spin under different parameter conditions can be predicted, providing important data support for assessing the aircraft's spin risk and formulating flight safety measures.

[0190] Preferably, the motion model is:

[0191]

[0192] In the formula, Represents the axis around the body The roll angular velocity is in rad / s; Represents the axis around the body The pitch angular velocity, in rad / s; Represents the axis around the body The yaw rate is in rad / s; Indicates the pitch angle, the unit is rad; Indicates the roll angle, the unit is rad; Represents the yaw angle in rad.

[0193] The purpose of establishing the motion model is to:

[0194] The motion model describes the motion state of the aircraft during the tailspin by establishing mathematical expressions of the aircraft's roll angular velocity, pitch angular velocity, and yaw angular velocity, providing an important theoretical basis for analyzing the tailspin phenomenon.

[0195] The motion model can analyze the changes in the aircraft's attitude angles during a tailspin, such as changes in roll angle, pitch angle, and yaw angle, providing an important reference for understanding the dynamic mechanism of the tailspin phenomenon;

[0196] The combination of the motion model and the dynamic model can more comprehensively describe the force conditions and motion state of the aircraft during a tailspin, calculate the changes in the aircraft's attitude during a tailspin, and provide an important theoretical tool for analyzing the tailspin phenomenon.

[0197] Preferably, the high angle of attack unsteady aerodynamic model adopts a dynamic derivative model with clear physical meaning, and the expression is:

[0198]

[0199] in, , ; represents the axial force coefficient of the body shaft system, represents the lateral force coefficient of the body axis system, represents the normal force coefficient of the body axis system, represents the rolling moment coefficient, represents the pitching moment coefficient, Represents the yaw moment coefficient. represents the angle of attack, represents the sideslip angle, , , They represent the aileron, pitch and yaw angles respectively, and the unit is degree.

[0200] In the above formula, It represents the static aerodynamic data item in the high angle of attack wind tunnel test, including the static aerodynamic item when the rudder deflection is zero and the static aerodynamic increment item caused by the rudder surface deflection;

[0201] The aerodynamic terms caused by the forced oscillatory motion in the high angle of attack wind tunnel test;

[0202] It is the aerodynamic term caused by rotational motion in high angle of attack wind tunnel test.

[0203] Preferably, representative factors are selected in the simulation examples, including: weight, moment of inertia, and entry method;

[0204] Data output includes real-time curves of parameters such as angle of attack, sideslip angle, and altitude changing over time.

[0205] Due to space limitations, only two variations of each parameter are selected here, including weight 1, weight 2, moment of inertia 1, moment of inertia 2, entry method 1, entry method 2.

[0206] Weight 1 and weight 2 represent the two weight states of single-person full fuel and multi-person full fuel respectively;

[0207] The moment of inertia 1 and moment of inertia 2 represent the different inertia characteristics under the two center of gravity states;

[0208] The action to enter method 1 is "first push the rudder, then pull the stick", and the action to enter method 2 is "first pull the stick, then push the rudder".

[0209] The simulation examples include dual-parameter analysis and triple-parameter analysis, and the variable parameter results are compared with the original parameter results. The calculation characteristics of different simulation examples are shown in Table 1.

[0210] Table 1 Simulation examples based on different variable parameter states

[0211]

[0212] The simulation results show the influence of the multi-variable parameters of the simulation example on the spin characteristics, and draw the prediction curve, including Figure 2 The angle of attack characteristic curve of a in Figure 2 Side slip angle characteristic curve of b, Figure 2 The height characteristic curve of c in the figure. It can be seen from the figure that the multi-variable parameter state has different degrees of influence on the tailspin characteristics. The numerical results of the influence on the tailspin modal parameters are shown in Table 2.

[0213] Table 2. Characteristics of spin modes under multi-variable parameters

[0214]

[0215] Although the influence of multi-variable parameters on some spin characteristics in the simulation example was predicted through simulation calculation, and the numerical changes of key characteristics were obtained, the overall analysis still remained at the qualitative level, the weight of the influence of multi-variable parameters on the spin characteristics was not clear, and there was a lack of quantitative analysis of the influence of specific parameters on the structure. Therefore, it is necessary to carry out quantitative analysis of the influence of multi-variable parameters on the spin characteristics based on qualitative analysis.

[0216] Preferably, the feature importance refers to the degree of influence of each feature of the model on the prediction result in machine learning;

[0217] The XGBoost regression algorithm is used to perform feature importance analysis on multi-variable parameters;

[0218] The steps are summarized into three aspects: building a regression model, calculating feature importance, and evaluating model performance.

[0219] Preferably, the establishment of the regression model requires preparation of training set data, and the processed training data set is used to establish and train the XGBoost model;

[0220] The training set data usually includes features (independent variables) and targets (dependent variables);

[0221] The training data used defines single variables and multivariate variables as features, and tailspin characteristics as targets;

[0222] For the XGBoost algorithm, the training set data contains a feature matrix X and a target vector Y ,in:

[0223]

[0224]

[0225] in, n is the sample size, p is the characteristic value;

[0226] When the dataset contains missing values ​​or the features of the samples need to be scaled, data preprocessing steps must be performed;

[0227] If the data is already in a state suitable for training, it is directly used for model training;

[0228] The goal of the XGBoost model is to minimize an objective function composed of a loss function and a regularization term;

[0229] In the XGBoost model, the loss function is defined as the squared loss function:

[0230]

[0231] In the formula, is the true target value of the i-th sample, is the target value predicted by the model;

[0232] The regularization term consists of two parts: the number of leaf nodes in the tree T and the L2 norm of the fraction of leaf nodes w:

[0233]

[0234] in, and is a hyperparameter used to control the regularization strength;

[0235] Get the objective function of the XGBoost model:

[0236]

[0237] In the formula k Indicates k A decision tree.

[0238] Preferably, the calculation of feature importance refers to determining the influence of each feature (or variable, attribute) in the data set on the output result of the prediction model through a specific algorithm or method;

[0239] In XGBoost, feature importance is measured by calculating the total gain of the feature in the model;

[0240] The total gain of each feature in the model can be obtained by calculating the sum of the gains of the feature in splitting nodes in all trees;

[0241] Specifically, for the jth feature, its gain in the kth tree is It can be expressed as:

[0242]

[0243] in, and Respectively represent the sum of the gradients of the left and right child nodes after segmentation, and Represents the sum of the second-order derivatives of the left and right child nodes, is the coefficient of the L2 regularization term;

[0244] Therefore, the total gain of the jth feature is It can be expressed as:

[0245]

[0246] In the formula, Kis the total number of decision trees.

[0247] Preferably, the performance of the model is evaluated by calculating the evaluation indicators of the model according to the prediction results and the true target value of the test set after the model training is completed. These evaluation indicators include mean square error (MSE), determination coefficient (R²), mean absolute error (MAE), and root mean square error (RMSE).

[0248] MSE measures the average of the squares of the differences between the predicted values ​​and the true values. It is one of the most commonly used evaluation metrics in regression analysis because it is simple to calculate and has good mathematical properties (for example, it is a convex function, which is easy to optimize). Generally, the lower the MSE value, the closer the model's predicted values ​​are to the true values, and the better the model's performance.

[0249] R² represents the proportion of variability explained by the model, that is, the accuracy of the model's predictions. Its value ranges from 0 to 1, with 1 indicating a perfect fit and 0 indicating that the model cannot explain any variability. The closer R² is to 1, the better the model fit and the higher the performance.

[0250] MAE is the average of the absolute values ​​of the differences between the predicted values ​​and the true values. It is an intuitive measure of the model's prediction error and is not affected by extreme values. The lower the MAE value, the more accurate the model's predictions.

[0251] RMSE is the square root of MSE. It provides the average magnitude of the prediction error and its unit is consistent with the original data, so it is easier to interpret. The lower the RMSE value, the higher the prediction accuracy of the model.

[0252] The calculation formula of the evaluation index is:

[0253]

[0254] in n is the sample size, It is i The true value of the samples, It is i The predicted value of samples, , are the residual sum of squares and the total sum of squares respectively, and:

[0255]

[0256] In the formula, is the average of the true values.

[0257] The smaller the values ​​of mean square error, mean absolute error, and root mean square error, the more accurate the model is; the closer the coefficient of determination is to 1, the more accurate the model is.

[0258] Since the difference between entry method 1 and entry method 2 is mainly reflected in the elevator deflection and rudder deflection, it is necessary to express it with a single feature when predicting the feature importance.

[0259] The t-SNE (t-Distributed Stochastic Neighbor Embedding) nonlinear dimensionality reduction method is selected to reduce the data dimension of the elevator and rudder deflections, and reflect the similarity of the two-dimensional data in the form of one-dimensional data.

[0260] from Figure 3 It can be seen that whether it is Figure 3 The entry method of medium a is 1 or Figure 3 In b’s entry method 2, the representation value after dimensionality reduction can reconstruct the features of the original data by similarity, providing necessary data support for subsequent feature importance analysis.

[0261] Through preliminary analysis, the impact of the entry method on the target is far greater than that of other variables. Therefore, it is necessary to conduct a comprehensive analysis of the feature importance of the remaining variables, and analyze the feature importance of the entry method based on the influence of the remaining variables.

[0262] The prediction results of feature importance based on the XGBoost algorithm include the prediction accuracy of some test sets in the form of prediction deviation, and the importance ratio of each feature (variable parameter).

[0263] At the same time, the evaluation results of the model are listed in Table 3. The model has a high prediction accuracy, indicating that the prediction results are highly credible.

[0264] On this basis, the importance analysis of the entry methods shows that entry method 2 has the largest impact on the average angle of attack, reaching 95.3%, while entry method 1 only accounts for 4.7%. This is because the action of "pull the stick first, then push the rudder" in entry method 2 has a greater impact on the angle of attack. The prediction deviation is also within a small range, with the maximum deviation being only 1.5.

[0265]

[0266] The spin characteristic analysis method of the present invention focuses on the shortcoming that the analysis results in the existing spin characteristic prediction have not been quantified, and develops a multidimensional global characteristic analysis method for studying the influence of multiple variables on the aircraft spin dynamic characteristics. The data set generated by the aircraft variables is studied from multiple dimensions, and the common characteristics of all samples or data points in the data set are deeply explored and analyzed, so as to better understand the inherent structure and relationship of the data, and then analyze the influence characteristics and influence degree of key factors on the spin characteristics, providing a new research logic for studying the influence of variables on the aircraft spin characteristics.

[0267] The tailspin characteristic analysis method of the present invention takes the tailspin characteristic as the target, performs characteristic importance analysis on three multi-variable parameters, namely weight, moment of inertia, and entry mode, gives the influence degree of each variable parameter on the corresponding target in the form of quantitative weight, and completes the multi-dimensional global characteristic analysis of the simulation example. Taking the three tailspin characteristics, namely the average angle of attack, the average rotation rate, and the sinking speed, as the targets, the characteristic importance of weight, moment of inertia, and entry mode, a total of three multi-variable parameters, to each tailspin characteristic is calculated respectively.

[0268] The above is only a preferred embodiment of the present invention, and does not limit the structure of the present invention in any form. Any simple modification, equivalent change and modification made to the above embodiment according to the technical essence of the present invention are within the scope of the technical solution of the present invention.

Claims

1. A method for analyzing tailspin characteristics, characterized in that: The time history of the tailspin characteristics is obtained by solving the tailspin dynamics differential equation, and the tailspin characteristics of the simulation example under the conditions of weight, moment of inertia, and entry mode multi-parameter changes are predicted, and the influence of multi-variable parameters on the tailspin characteristics is analyzed; The XGBoost regression algorithm based on decision tree analysis was used to build a machine learning model. The average angle of attack, average rotation rate, sinking speed and other spin characteristics were used as targets to perform feature importance analysis on the multi-variable parameters of the simulation example. Analyze the influence ratio of multiple variable parameters on the same spin characteristics, and quantify the influence of key factors on the spin; Including multi-variable spin characteristic prediction and multi-dimensional global feature analysis based on feature importance; The prediction of multi-variable spin characteristics is based on the dynamic model, motion model and large angle of attack unsteady aerodynamic model. With the physics-driven analysis strategy, the simulation platform is built through MATLAB to solve the spin dynamics differential equation with clear physical meaning, realize the real-time simulation of the entire dynamic process of stall / spin entry and recovery, and complete the prediction of multi-variable spin characteristics. Based on the body axis coordinate system, the dynamic equations including axial force, lateral force, normal force, rolling moment, pitching moment and yaw moment are established to describe the force conditions of the aircraft during the tailspin; Establish kinematic equations including roll angular velocity, pitch angular velocity and yaw angular velocity to describe the motion state of the aircraft during the tailspin; The dynamic derivative model is used to combine the static aerodynamic data, the aerodynamic data caused by forced oscillation motion and the aerodynamic data caused by rotation motion in the high angle of attack wind tunnel test to describe the aerodynamic characteristics of the aircraft at high angles of attack. Input the aerodynamic parameter database required for simulation and perform multi-dimensional interpolation processing; The numerical simulation method is used to calculate the time history of the tailspin and obtain the tailspin calculation result; By observing the simulation curves and parameter changes, the influence trend and law of multi-variable parameters on spin characteristics are analyzed; Based on the multi-dimensional global feature analysis of feature importance, the influence of multi-variable parameters on the spin characteristics is combined with the feature importance analysis. The multi-variable parameters are used as the features in the machine learning model, and the spin characteristics are used as the prediction results. The contribution of the multi-variable parameters to the spin characteristics can be obtained by feature importance analysis.

2. The method for analyzing tailspin characteristics according to claim 1, characterized in that: The simulation platform includes a data processing module, a spin calculation module and a calculation result output module; The data processing module is used to input the database used in the simulation calculation and perform multi-dimensional interpolation processing on the aerodynamic data, including the high angle of attack data input, data fitting, and control law data input processing; The tailspin calculation module is used to calculate the tailspin time history through numerical simulation methods to obtain the tailspin calculation results, including balanced flight calculation, speed and density calculation, and calculation and processing of six-degree-of-freedom motion equations; The calculation result output module is used to display the spatial motion trajectory and attitude changes of the aircraft tailspin statically or dynamically through images; it retrieves the result data file and includes three sub-modules: data result output module, two-dimensional curve output module, and three-dimensional dynamic display module.

3. The method for analyzing tailspin characteristics according to claim 1, characterized in that: The dynamic model is established based on the body axis coordinate system, and the units of all parameters are international standard units; the dynamic model expression is: in, It represents the axial force coefficient of the body shaft system; represents the lateral force coefficient of the body axis system; represents the normal force coefficient of the body axis system; represents the rolling moment coefficient; represents the pitching moment coefficient; represents the yaw moment coefficient; Represents the axis around the body The roll angular velocity is in rad / s; Represents the axis around the body The pitch angular velocity, in rad / s; Represents the axis around the body The yaw rate is in rad / s; b represents the wingspan, in m; c represents the mean aerodynamic chord length, in m; g Indicates the acceleration due to gravity, in m / s 2 ; 、 、 Respectively represent the x , y , z Axis moment of inertia, in ; represents the cross product of inertia about the center of mass, in units of ; m Indicates the mass of the aircraft in kg; Q Indicates dynamic pressure, the unit is Pa; S Indicates the wing area in m2; V Indicates the flight speed in m / s; It represents the angle of attack, in rad; Represents the sideslip angle, in rad; Indicates the pitch angle, the unit is rad; represents the roll angle, the unit is rad; V represents the flight speed, the unit is m / s; represents the product of inertia correction factor, and: 。 4. The method for analyzing tailspin characteristics according to claim 1, characterized in that: The motion model is: In the formula, Represents the axis around the body The roll angular velocity is in rad / s; Represents the axis around the body The pitch angular velocity, in rad / s; Represents the axis around the body The yaw rate is in rad / s; Indicates the pitch angle, the unit is rad; Indicates the roll angle, the unit is rad; Represents the yaw angle in rad.

5. The method for analyzing tailspin characteristics according to claim 1, characterized in that: The high angle of attack unsteady aerodynamic model adopts a dynamic derivative model with clear physical meaning, and the expression is: in, , ; represents the axial force coefficient of the body shaft system, represents the lateral force coefficient of the body axis system, represents the normal force coefficient of the body axis system, represents the rolling moment coefficient, represents the pitching moment coefficient, represents the yaw moment coefficient, represents the angle of attack, represents the sideslip angle, , , Respectively represent the aileron, pitch, and yaw rudder deflection angles, the unit is degree; In the above formula, It represents the static aerodynamic data item in the high angle of attack wind tunnel test, including the static aerodynamic item when the rudder deflection is zero and the static aerodynamic increment item caused by the rudder surface deflection; The aerodynamic terms caused by the forced oscillatory motion in the high angle of attack wind tunnel test; It is the aerodynamic term caused by rotational motion in high angle of attack wind tunnel test.

6. The method for analyzing tailspin characteristics according to claim 1, characterized in that: The feature importance refers to the degree of influence of each feature of the model on the prediction result in machine learning; The XGBoost regression algorithm is used to perform feature importance analysis on multi-variable parameters; The steps are summarized into three aspects: building a regression model, calculating feature importance, and evaluating model performance.

7. The method for analyzing tailspin characteristics according to claim 6, characterized in that: The establishment of the regression model requires the preparation of training set data, and the processed training data set is used to establish and train the XGBoost model; The training set data usually includes features and targets; The training data used defines single variables and multivariate variables as features, and tailspin characteristics as targets; For the XGBoost algorithm, the training set data contains a feature matrix X and a target vector Y ,in: in, n is the sample size, p is the characteristic value; When the dataset contains missing values ​​or the features of the samples need to be scaled, data preprocessing steps must be performed; If the data is already in a state suitable for training, it is directly used for model training; The goal of the XGBoost model is to minimize an objective function composed of a loss function and a regularization term; In XGBoost, the loss function is defined as the squared loss function: In the formula, is the true target value of the i-th sample, is the target value predicted by the model; The regularization term consists of two parts: the number of leaf nodes in the tree T and the L2 norm of the fraction of leaf nodes w: in, and is a hyperparameter used to control the regularization strength; Get the objective function of the XGBoost model: In the formula k Indicates k A decision tree.

8. The method for analyzing tailspin characteristics according to claim 6, characterized in that: The calculation of feature importance refers to determining the influence of each feature in the data set on the output result of the prediction model through an algorithm or method; In XGBoost, feature importance is measured by calculating the total gain of the feature in the model; The total gain of each feature in the model is obtained by calculating the sum of the gains of the feature splitting nodes in all trees; Specifically, for the jth feature, its gain in the kth tree is It can be expressed as: in, and Respectively represent the sum of the gradients of the left and right child nodes after segmentation, and Represents the sum of the second-order derivatives of the left and right child nodes, is the coefficient of the L2 regularization term; Therefore, the total gain of the jth feature is It can be expressed as: Where K is the total number of decision trees.

9. The method for analyzing tailspin characteristics according to claim 6, characterized in that: The evaluation model performance is to evaluate the performance of the model by calculating the evaluation indicators of the model according to the prediction results and the true target value of the test set after completing the model training. These evaluation indicators include mean square error (MSE), determination coefficient (R²), mean absolute error (MAE), and root mean square error (RMSE); MSE measures the average of the squared differences between the predicted values ​​and the true values; R² represents the proportion of variability explained by the model, that is, the accuracy of the model's predictions; Its value ranges from 0 to 1, with 1 indicating a perfect fit and 0 indicating that the model cannot explain any variability; MAE is the average of the absolute values ​​of the differences between the predicted values ​​and the true values; RMSE is the square root of MSE, which provides the average magnitude of the prediction error, and the unit is consistent with the original data; The calculation formula of the evaluation index is: in n is the sample size, It is i The true value of the samples, It is i The predicted value of samples, , are the residual sum of squares and the total sum of squares respectively, and: In the formula, is the average of the true values.

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