Parafoil system analysis method, device, equipment and medium based on sparse identification

Abstract

The present application belongs to the technical field of accurate parafoil airdrop, and relates to a parafoil system analysis method, device, equipment and medium based on sparse identification. The method includes: according to the parafoil system, an initial model is established, and a coordinate system of the initial model is defined; system parameters of the parafoil system are obtained, the generalized mass and generalized inertia of the parafoil are calculated, and the dynamic model of the parafoil system is established in combination with the coordinate system; state variables and derivatives of state variables are obtained, the dynamic model is approximated, and a transition model of the parafoil system is obtained; a sparse identification method is used to solve the minimum problem transformation of the transition model to obtain a sparse model of the parafoil system; considering the actual control requirements of the parafoil system, a basic function library of the parafoil system is set according to the sparse model, and an identification model of the parafoil system is obtained to identify the key parameters of the parafoil system and analyze the parafoil system. The present application can meet the analysis needs of the parafoil system.

Description

Technical Field

[0001] The present application relates to the technical field of wing parachute precision airdrop, and in particular to a wing parachute system analysis method, device, equipment and medium based on sparse identification. Background Art

[0002] The Precision Aerial Delivery Systems (PADS) is one of the most effective airdrop methods in the world today. It is widely used in tasks such as long-distance deployment of troops, precise and lossless recovery of spacecraft, and high-altitude precise delivery of relief supplies. It has great military and civilian value.

[0003] The dynamic model of the parafoil system is the basis for studying the flight performance of the parafoil precision airdrop system and formulating control strategies. For example, in the process of parafoil system trajectory planning, it is necessary to establish a dynamic model oriented to control requirements to simulate the real state of the parafoil system.

[0004] In the prior art, parafoil system analysis is usually performed based on a simplified kinematic model, trajectory planning is performed, and then linearization processing is performed at the local working point of the parafoil, and finally trajectory tracking is performed.

[0005] However, the kinematic model used in the above analysis method has a high dimension, a complex form, and does not involve the nonlinear characteristics of the system, and cannot meet the analysis needs of the parafoil system. Summary of the invention

[0006] Based on this, it is necessary to provide a parafoil system analysis method, device, equipment and medium based on sparse identification to address the above technical problems, which can meet the analysis needs of the parafoil system.

[0007] The parafoil system analysis method based on sparse identification includes:

[0008] According to the parafoil system, an initial model is established, and a coordinate system of the initial model is defined;

[0009] Obtaining system parameters of the parafoil system, calculating the generalized mass and generalized inertia of the parafoil, and establishing a dynamic model of the parafoil system in combination with the coordinate system;

[0010] Acquire state variables and derivatives of the state variables, approximate the dynamic model, and obtain a transition model of the parafoil system;

[0011] The sparse identification method is used to transform the transition model into a minimum value problem, thereby obtaining a sparse model of the parafoil system.

[0012] Considering the actual control requirements of the parafoil system, the basic function library of the parafoil system is set according to the sparse model, and the identification model of the parafoil system is obtained to identify the key parameters of the parafoil system and analyze the parafoil system.

[0013] In one embodiment, the system parameters of the parafoil system are obtained, the generalized mass and the generalized inertia of the parafoil are calculated, and the dynamic model of the parafoil system is established in combination with the coordinate system, including:

[0014] Obtain the parafoil mass, parafoil additional mass and the moment of inertia of the parachute at the origin of the parafoil system, and calculate the generalized mass and generalized moment of inertia of the parafoil;

[0015] The aerodynamic force of the parafoil, the aerodynamic moment of the parafoil, the aerodynamic force of the load, the aerodynamic moment of the load, and the gravitational acceleration in the parafoil system are obtained, and the dynamic model of the parafoil system is established in combination with the generalized mass of the parafoil, the generalized inertia of the parafoil and the conversion relationship between the coordinate systems.

[0016] In one embodiment, the state variables and the derivatives of the state variables are obtained, the dynamic model is approximated, and a transition model of the parafoil system is obtained, including:

[0017] Get the state variables and their derivatives:

[0018]

[0019]

[0020] The dynamic model is approximated to obtain the transition model of the parafoil system:

[0021]

[0022] in,

[0023]

[0024] In the formula, [x1,x2…x m ] are state variables, t1, t2, …t n is a time series, is the derivative set of state variables, f(X,U) is the transition model of the parafoil system, Θ(X,U) is the basic function library, X is the state variable data set, U is the control variable data set, ξ=[ξ1ξ2…ξ p ] is the sparse vector coefficient, represents all product combinations of components in X, Represents all product combinations of X and U components.

[0025] In one embodiment, a sparse identification method is used to transform the transition model into a minimum value problem to obtain a sparse model of the parafoil system, including:

[0026] The sparse identification method is used to transform the transition model into a minimum value problem:

[0027]

[0028] Get the sparse model of the parafoil system:

[0029]

[0030] In the formula, is the optimal sparse vector coefficient, k is the kth column element of the data matrix, ξ k is the kth column of ξ, for The kth column of , λ is the weight coefficient of the regularization degree.

[0031] In one embodiment, considering the actual control requirements of the parafoil system, a basic function library of the parafoil system is set according to the sparse model to obtain an identification model of the parafoil system, including:

[0032] Considering the actual control requirements of the parafoil system, the basic function library of the parafoil system is set according to the sparse model:

[0033]

[0034] Get the identification model of the parafoil system:

[0035]

[0036]

[0037]

[0038]

[0039] in:

[0040] δ s =(δ l -δ r ) / 2

[0041] In the formula, is the parafoil yaw angle, δ l is the parafoil lower left deflection, δ r is the parafoil lower right deflection, They are the derivatives of displacement in three directions in the Cartesian coordinate system of the parafoil, and k1, k2, k3, and k4 are different sparse coefficients.

[0042] In one embodiment, a sparse coefficient matrix of key parameters of a parafoil system is identified, including:

[0043]

[0044] Where ξ is the matrix of sparse vector coefficients.

[0045] In one embodiment, the coordinate system of the initial model includes:

[0046] Earth coordinate system, parachute coordinate system, load coordinate system and airflow coordinate system.

[0047] The parafoil system analysis device based on sparse identification includes:

[0048] An initial module, used to establish an initial model according to the parafoil system and define a coordinate system of the initial model;

[0049] A power module is used to obtain system parameters of the parafoil system, calculate the generalized mass and generalized inertia of the parafoil, and establish a dynamic model of the parafoil system in combination with the coordinate system;

[0050] A transition module, used to obtain state variables and derivatives of the state variables, approximate the dynamic model, and obtain a transition model of the parafoil system;

[0051] A sparse module, used for converting the transition model into a minimum value problem by using a sparse identification method, so as to obtain a sparse model of the parafoil system;

[0052] The identification module is used to consider the actual control requirements of the parafoil system, set the basic function library of the parafoil system according to the sparse model, obtain the identification model of the parafoil system, identify the key parameters of the parafoil system, and analyze the parafoil system.

[0053] A computer device comprises a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, the following steps are implemented:

[0054] According to the parafoil system, an initial model is established, and a coordinate system of the initial model is defined;

[0055] Obtaining system parameters of the parafoil system, calculating the generalized mass and generalized inertia of the parafoil, and establishing a dynamic model of the parafoil system in combination with the coordinate system;

[0056] Acquire state variables and derivatives of the state variables, approximate the dynamic model, and obtain a transition model of the parafoil system;

[0057] The sparse identification method is used to transform the transition model into a minimum value problem, thereby obtaining a sparse model of the parafoil system.

[0058] Considering the actual control requirements of the parafoil system, the basic function library of the parafoil system is set according to the sparse model, and the identification model of the parafoil system is obtained to identify the key parameters of the parafoil system and analyze the parafoil system.

[0059] A computer-readable storage medium stores a computer program, which, when executed by a processor, implements the following steps:

[0060] According to the parafoil system, an initial model is established, and a coordinate system of the initial model is defined;

[0061] Obtaining system parameters of the parafoil system, calculating the generalized mass and generalized inertia of the parafoil, and establishing a dynamic model of the parafoil system in combination with the coordinate system;

[0062] Acquire state variables and derivatives of the state variables, approximate the dynamic model, and obtain a transition model of the parafoil system;

[0063] The sparse identification method is used to transform the transition model into a minimum value problem, thereby obtaining a sparse model of the parafoil system.

[0064] Considering the actual control requirements of the parafoil system, the basic function library of the parafoil system is set according to the sparse model, and the identification model of the parafoil system is obtained to identify the key parameters of the parafoil system and analyze the parafoil system.

[0065] The above-mentioned sparse identification-based parafoil system analysis method, device, equipment and medium adopt a data-driven strategy to establish a nine-degree-of-freedom dynamic model with the nonlinear dynamic characteristics of the system to approximate the flight trajectory motion characteristics of the parafoil, and combine with the sparse identification method to identify the four-degree-of-freedom dynamic model and key parameters suitable for the parafoil trajectory planning. While ensuring accuracy, it improves the computational efficiency, and has low dimension and relatively simple equations, which can meet the real-time and low-cost requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] Figure 1 This is an application scenario diagram of a parafoil system analysis method based on sparse identification in one embodiment;

[0067] Figure 2 It is a flowchart of a parafoil system analysis method based on sparse identification in one embodiment;

[0068] Figure 3 A schematic diagram of "parafoil-spherical joint-load" in one embodiment;

[0069] Figure 4 A schematic diagram of a rootless two-body model of "parafoil-spherical joint-load" in one embodiment;

[0070] Figure 5 A schematic diagram of a coordinate system of a two-body model of a parafoil system in an embodiment;

[0071] Figure 6 It is a schematic diagram showing the comparison results of the simulation values ​​of the X-direction displacement of the simplified model of the present application and the nine-degree-of-freedom model in the geodetic coordinate system in one embodiment;

[0072] Figure 7 It is a schematic diagram showing the comparison results of the simulation values ​​of the Y-direction displacement of the simplified model of the present application and the nine-degree-of-freedom model in the geodetic coordinate system in one embodiment;

[0073] Figure 8 It is a schematic diagram showing the comparison results of the simulation values ​​of the Z-direction displacement in the geodetic coordinate system of the simplified model of the present application and the nine-degree-of-freedom model in one embodiment;

[0074] Fig. 9 is a structural block diagram of a parafoil system analysis device based on sparse identification in one embodiment;

[0075] Fig.10 FIG. 4 is a diagram showing the internal structure of a computer device in one embodiment. DETAILED DESCRIPTION

[0076] In order to make the purpose, technical solutions and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not intended to limit the present application. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in the field without making creative work are within the scope of protection of the present application.

[0077] It should be noted that all directional indications in the embodiments of the present application (such as up, down, left, right, front, back, etc.) are only used to explain the relative position relationship, movement status, etc. between the components under a certain specific posture (as shown in the accompanying drawings). If the specific posture changes, the directional indication will also change accordingly.

[0078] In addition, the descriptions of "first", "second", etc. in this application are only for descriptive purposes and cannot be understood as indicating or implying their relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first" or "second" may explicitly or implicitly include at least one of the features. In the description of this application, "multiple groups" means at least two groups, such as two groups, three groups, etc., unless otherwise clearly and specifically defined.

[0079] In this application, unless otherwise clearly specified and limited, the terms "connection", "fixation", etc. should be understood in a broad sense. For example, "fixation" can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection, an electrical connection, a physical connection, or a wireless communication connection; it can be a direct connection, or an indirect connection through an intermediate medium, or it can be the internal connection of two elements or the interaction relationship between two elements, unless otherwise clearly defined. For ordinary technicians in this field, the specific meanings of the above terms in this application can be understood according to specific circumstances.

[0080] In addition, the technical solutions between the various embodiments of the present application can be combined with each other, but it must be based on the fact that ordinary technicians in the field can implement it. When the combination of technical solutions is contradictory or cannot be implemented, it should be deemed that such combination of technical solutions does not exist and is not within the scope of protection required by this application.

[0081] The parafoil system analysis method based on sparse identification provided in this application can be applied to Figure 1 In the application scenario diagram shown, the terminal 102 communicates with the server 104 through the network, and the terminal 102 may include but is not limited to various personal computers, laptops, smart phones, tablet computers and portable wearable devices, and the server 104 may be various portal websites, servers corresponding to the backend of the work system, etc.

[0082] This application provides a parafoil system analysis method based on sparse identification, such as Figure 2 The flowchart shown in FIG. 1 shows a method for applying the method to Figure 1 The following is an example of a terminal in the example, including:

[0083] Step 202: Establish an initial model based on the parafoil system and define the coordinate system of the initial model.

[0084] Specifically:

[0085] According to the parafoil system, the following basic assumptions are made to establish the initial model:

[0086] (1) The parafoil system and the load are considered as rigid bodies and connected at point O at the bottom of the load;

[0087] (2) The parafoil may yaw, pitch, or roll relative to the load;

[0088] (3) Since the materials used for parachute ropes, slings and connecting straps are usually strong and have little deformation, they can be regarded as ropes of constant length;

[0089] (4) The parachute body and the load are hinged together by slings and connecting straps, which are treated as ball joints;

[0090] (5) After the parafoil is fully deployed, the canopy maintains a fixed shape;

[0091] (6) The center of mass and pressure center of the parafoil canopy coincide and are located 1 / 4 of the distance from the leading edge in the chord direction;

[0092] (7) The changes in the parachute body's moment of inertia and center of mass position caused by the relative torsion between the two bodies, as well as the deformation time of the canopy's flexible deformation, are not considered.

[0093] like Figure 3 and Figure 4 As shown in the figure, because the shape of the parafoil does not change much, it can be approximately treated as a two-body rootless system consisting of the wing-shaped canopy and the load. The canopy and the parachute rope are rigid bodies A, the sling and the load are rigid bodies B, and the connecting rope at the intersection is a spherical joint M, with a total of nine degrees of freedom.

[0094] Define the coordinate system of the initial model, including:

[0095] 1) Geodetic coordinate system s d (o d x d y d z d ): origin o d It is arbitrary and fixed relative to the Earth's surface, usually related to the intended point of impact (IPI). d x d The axis points to due north, o d y d The axis points due east, o d z d The axis is towards the center of the earth. This coordinate system is called the North-East-Down (NED) coordinate system, which is an inertial system;

[0096] 2) Parachute coordinate system s p (o p x p y p z p ): origin o p The point is taken at the center of mass of the parafoil, o p x p The axis is along the positive direction of the longitudinal axis in the symmetry plane of the parafoil, and the axis o p z p Perpendicular to o p x p Axis, positive downward in the symmetry plane, axis o p y p It complies with the right-hand rule;

[0097] 3) Load coordinate system s t (ot x t y t z t ): origin o t At the load center, axis o t z t Along the symmetry axis of the load pointing downward, axis o t y t , axis o t x t It complies with the right-hand rule;

[0098] 4) Airflow coordinate system s w (o w x w y w z w ): origin o w At the center of mass of the system, axis o w x w The direction of the velocity vector relative to the air is positive, and the axis o w z w In the plane of symmetry of the system, perpendicular to the axis o w x w Pointing directly downward, axis o w y w Conforms to the right-hand rule.

[0099] Step 204, obtaining system parameters of the parafoil system, calculating the generalized mass and generalized inertia of the parafoil, and establishing a dynamic model of the parafoil system in combination with the coordinate system.

[0100] Specifically:

[0101] Calculate the transformation relationship between coordinate systems:

[0102] Using the pitch angle θ p , yaw angle and the roll angle γ p Describe the parachute coordinate system s p (o p x p y p z p ) to the geodetic coordinate system s d (o d x d y d z d ), the transformation matrix is

[0103] Euler angle θ t , γ t To describe the load coordinate system s t (o t xt y t z t ) to the geodetic coordinate system s d (o d x d y d z d ), the transformation matrix is

[0104] Denote the load coordinate system s t (o t x t y t z t ) to the parachute body coordinate system s p (o p x p y p z p ) is According to the transitivity of the transformation matrix, we can know that

[0105] Obtain the parafoil mass, parafoil additional mass and the rotational inertia of the parachute at the origin of the parafoil system;

[0106] According to the parafoil mass and parafoil attached mass of the parafoil system, the generalized mass of the parafoil is calculated:

[0107]

[0108] According to the parafoil added mass and the parachute's moment of inertia at the origin, calculate the generalized inertia of the parafoil:

[0109]

[0110] In the formula, m p is the generalized mass of the parafoil, m c is the parafoil mass, a 11 、a 33 、a 44 、a 66 is the additional mass of the parafoil (the parafoil moves under the influence of airflow, and the corresponding increment of aerodynamic force and torque caused by unsteadiness can be expressed by the additional mass), I p is the generalized inertia of the parafoil, I x ,I y and I z is the moment of inertia of the parachute at the origin;

[0111] The aerodynamic force of the parafoil, the aerodynamic moment of the parafoil, the aerodynamic force of the load, the aerodynamic moment of the load, and the gravitational acceleration in the parafoil system are obtained, and the dynamic model of the parafoil system is established at the hinge point O in combination with the generalized mass of the parafoil, the generalized inertia of the parafoil, and the conversion relationship between the coordinate systems:

[0112]

[0113]

[0114]

[0115] in:

[0116]

[0117]

[0118] Considering the motion relationship of the Euler angle of the parafoil system, it is derived that:

[0119]

[0120]

[0121]

[0122] in,

[0123]

[0124]

[0125] Introduce the following state variables:

[0126]

[0127] u=[δ r ,δ l ]

[0128] Where u is the left and right control input of the trailing edge of the parafoil;

[0129] Combining the above equations, we get the nonlinear dynamic model of the parafoil system:

[0130]

[0131] The aerodynamic force and moment on the parafoil are expressed as F p =[F px ,F py ,F pz ] T and M p The aerodynamic force and moment acting on the load are expressed as Ft =[F tx ,F ty ,F tz ] T and M t , the gravitational acceleration is expressed as g = [g, 0, 0] T , It means R = [x d ,y d ,z d ] T The derivative of , which represents the velocity of the hinge point O in the canopy coordinate system, is the parafoil Euler angle, is the load Euler angle, ω p =[ω px ,ω py ,ω pz ] T is the angular velocity of the parafoil, ω t =[ω tx ,ω ty ,ω tz ] T is the angular velocity of the load.

[0132] In this step, the nonlinear dynamic model of the parafoil system is a high-fidelity constrained nine-degree-of-freedom dynamic model, which can effectively describe the physical characteristics of the parafoil system. Based on the nine-degree-of-freedom dynamic model, the attitude, angular velocity and velocity of the parafoil-load system can be solved.

[0133] Step 206, obtaining state variables and derivatives of the state variables, approximating the dynamic model, and obtaining a transition model of the parafoil system.

[0134] Specifically:

[0135] The kinetic model is expressed as:

[0136]

[0137] Right now:

[0138]

[0139] Where x∈R m is the state variable of the system at time t, and the nonlinear function f(x,u) represents the dynamic equation of the system. Usually, in most systems, nonlinear functions consist of only a few terms, so they are sparse in the corresponding function space. For many systems of interest, the function f(x,u) has only a few key terms or factors (nonlinear terms), making it sparse in the possible function space.

[0140] Get the state variables and their derivatives:

[0141]

[0142]

[0143] According to the nine-degree-of-freedom dynamics model, the time series {t1, t2, …t n} The corresponding n sets of state quantities X and input signal U data sets are obtained, and two matrices X and U are arranged as follows:

[0144] X=[x1,x2…x m ]U=[u1,u2…u m ]

[0145] Where X = [x1, x2…x m ] is a set of state variables, is a set of state variable derivatives, U = [u1,u2…u m ] is a matrix of m snapshots of the input control quantity u.

[0146] Sparse regression can effectively identify a small number of non-zero terms instead of performing a brute-force search for nonlinear terms in the dynamics. Most physical systems contain only a few nonlinear terms in the dynamics, which are few compared to the other non-existent terms, i.e., zero terms, making the equation f(x,u) sparse in the high-dimensional nonlinear function space.

[0147] According to the two matrices X and U, the sparse vector coefficient ξ is introduced, that is, the dynamic model is approximated, and the transition model of the parafoil system represented as a generalized linear model is obtained:

[0148]

[0149] in,

[0150]

[0151] In the formula, [x1,x2…x m ] are state variables, t1, t2, …t n is a time series, is the set of derivatives of state variables, f(X,U) is the transition model of the parafoil system, Θ(X,U) is the basic function library, which is composed of the columns of X and U as nonlinear candidates, each column is the basis function of f(X,U), X is the state variable data set, U is the control variable data set, ξ=[ξ1ξ2…ξ p ] is the sparse vector coefficient, represents all product combinations of components in X, Represents all product combinations of X and U components.

[0152] In this step, each column of the basic function library Θ(X) represents a nonlinear element expressed by the function on the right side of the equation, and there is a lot of freedom of choice when constructing nonlinear elements.

[0153] Step 208, using a sparse identification method, the transition model is transformed into a minimum value problem to obtain a sparse model of the parafoil system.

[0154] Specifically:

[0155] In general, the coefficient ξ=[ξ1ξ2…ξ p ] There are multiple solutions with redundant terms. Especially for high-dimensional complex nonlinear systems, the number of solutions will increase exponentially and the optimal identification coefficient cannot be obtained. ξ=[ξ1ξ2…ξ p Each column in ] represents a sparse coefficient vector, which is used to determine the equation A row of is activated. After determining the kth row of the sparse coefficient matrix, the sparse model of the parafoil system can be obtained.

[0156] To determine the sparse vector coefficient ξ=[ξ1ξ2…ξ p ], which has been obtained through the nine-degree-of-freedom dynamic model and Θ(X,U), we can use the sparse concept: given a threshold range, we can force the items smaller than the threshold to be sparse, that is, to zero, in the sparse space, so as to ensure that the model is fitted with the least number of items, and finally transform it into solving the minimum problem, that is, use the sparse identification method to transform the transition model into solving the minimum problem.

[0157] The basic idea of ​​using the LASSO regression algorithm (LASSO is a linear regression algorithm used for feature selection and model regularization to solve "multicollinearity". By using the LASSO penalty to constrain the coefficients in the model and shrinking some coefficients to zero, the complexity of the model can be reduced. Sparse coefficients can be obtained to achieve the purpose of feature selection) to approximate the coefficients:

[0158]

[0159] In general, there are multiple solutions with redundant terms in the sparse coefficient vector. Especially for high-dimensional and complex nonlinear systems, the number of solutions will increase exponentially, and the optimal identification coefficient cannot be obtained. p Each column in ] represents a sparse coefficient vector, which is used to determine the equation A row of is activated. After the sparse coefficient matrix is ​​determined, the kth row of the control equation, that is, the sparse model of the parafoil system is:

[0160]

[0161] In the formula, is the optimal coefficient vector coefficient, k is the k-th column element of the data matrix, ξ k is the kth column of ξ, for The kth column of , λ is the weight coefficient of the regularization degree.

[0162] In this step, a sparse model is obtained after the nine-degree-of-freedom dynamic model is converted.

[0163] Step 210, considering the actual control requirements of the parafoil system, setting the basic function library of the parafoil system according to the sparse model, obtaining the identification model of the parafoil system, identifying the key parameters of the parafoil system, and analyzing the parafoil system.

[0164] Specifically:

[0165] The data set is constructed by using the numerical simulation results of the nine-degree-of-freedom multi-body dynamics model of the parafoil system, focusing on identifying the main characteristic relationships between the parafoil input control variables and the parafoil position, yaw angle and other state variables to obtain the basic database. Taking the parafoil airdrop system as an example, for the autonomous homing flight phase of the parafoil in the project, the main state components of the system concerned in trajectory planning are sought [x d ,y d ,z d ,ψ] and the control quantity is U=[δ r ,δ l ].

[0166] Considering the actual control requirements of the parafoil system, the basic function library of the parafoil system is set according to the sparse model:

[0167]

[0168] SINDYc is used to construct a fourth-order simplified dynamic model, and the identification model of the parafoil system is obtained:

[0169]

[0170]

[0171]

[0172]

[0173] in:

[0174] δ s =(δ l -δ r ) / 2

[0175] In the formula, is the parafoil yaw angle, δ lis the parafoil lower left deflection, δ r is the parafoil lower right deflection, They are the derivatives of displacement in three directions of the parafoil in the Cartesian coordinate system, i.e., the velocity components; k1, k2, k3, and k4 are different sparse coefficients, and the specific values ​​of the identified sparse coefficients k1 and k2 are approximately 28.205 and 28.175, which actually correspond to the horizontal velocity of the parafoil, the sparse coefficient k3 is approximately 11.293, which corresponds to the vertical falling velocity of the parafoil, and the sparse coefficient k4 is 0.032, which actually corresponds to the symmetrical pull-down control input. The results are consistent with the measured values ​​in the actual airdrop test.

[0176] Finally, the sparse coefficient matrix of the key parameters of the parafoil system is identified, including:

[0177]

[0178] Where ξ is the matrix of sparse vector coefficients.

[0179] In this step, the conventional four-DOF dynamics model was constructed using the existing SINDYc technology, and the nine-DOF dynamics model was used to provide The initial value of is combined with the basic function library to solve the fourth-order dynamic model and obtain k1, k2, k3, k4, so as to obtain the final identification model. Then, the parafoil system is analyzed according to the final identification model to obtain information such as position relationship and yaw angle.

[0180] like Figures 6 to 8 As shown in the figure, by comparing the dynamic simulation effects of the reduced-order model and the nine-DOF dynamics model, the feasibility of the reduced-order model is verified: the sparse identification model of the parafoil ignores the relative motion between the parafoil and the load for the nine-DOF model, removes the pitch angle and roll angle, and only retains the parafoil position information and the yaw angle, which is directly related to the controlled trajectory of the parafoil. Comparison of the position curves of the two models during flight. It can be seen that the kinematic model obtained by sparse identification is basically consistent with the existing nine-DOF dynamics model, and the former can be used as a simplified alternative model for the latter in the case of parafoil homing path planning, control quantity calculation, etc.

[0181] The above-mentioned parafoil system analysis method based on sparse identification adopts a data-driven strategy to establish a nine-degree-of-freedom dynamic model with the nonlinear dynamic characteristics of the system to approximate the flight trajectory motion characteristics of the parafoil. In combination with the sparse identification method, only the key parameters of the system are retained to identify a four-degree-of-freedom low-order dynamic model suitable for parafoil trajectory planning. The nine-degree-of-freedom model provides data for the four-degree-of-freedom model, which improves the computational efficiency while ensuring accuracy. It has low dimension and relatively simple equations, and can meet the requirements of real-time and low cost.

[0182] It should be understood that although Figure 2 The steps in the flowchart are shown in sequence as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified in this document, there is no strict order restriction for the execution of these steps, and these steps can be executed in other orders. Moreover, Figure 2 At least part of the steps may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily executed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed in turn or alternately with other steps or at least part of the sub-steps or stages of other steps.

[0183] The present application also provides a parafoil system analysis device based on sparse identification, such as Fig. 9 As shown, in one embodiment, it includes: an initial module 902, a power module 904, a transition module 906, a sparse module 908 and an identification module 910, wherein:

[0184] The initial module 902 is used to establish an initial model according to the parafoil system and define the coordinate system of the initial model;

[0185] The power module 904 is used to obtain the system parameters of the parafoil system, calculate the generalized mass and generalized inertia of the parafoil, and establish a dynamic model of the parafoil system in combination with the coordinate system;

[0186] A transition module 906 is used to obtain state variables and derivatives of the state variables, approximate the dynamic model, and obtain a transition model of the parafoil system;

[0187] A sparse module 908 is used to convert the transition model into a minimum value problem by using a sparse identification method to obtain a sparse model of the parafoil system;

[0188] The identification module 910 is used to consider the actual control requirements of the parafoil system, set the basic function library of the parafoil system for the sparse model, obtain the identification model of the parafoil system, identify the key parameters of the parafoil system, and analyze the parafoil system.

[0189] The specific definition of the parafoil system analysis device based on sparse identification can be found in the above definition of the parafoil system analysis method based on sparse identification, which will not be repeated here. Each module in the above device can be implemented in whole or in part by software, hardware and a combination thereof. Each of the above modules can be embedded in or independent of the processor in the computer device in the form of hardware, or can be stored in the memory of the computer device in the form of software, so that the processor can call and execute the operations corresponding to each of the above modules.

[0190] In one embodiment, a computer device is provided. The computer device may be a terminal, and its internal structure diagram may be as follows: Fig.10 As shown. The computer device includes a processor, a memory, a network interface, a display screen and an input device connected through a system bus. Among them, the processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and a computer program. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The network interface of the computer device is used to communicate with an external terminal through a network connection. When the computer program is executed by the processor, a parafoil system analysis method based on sparse identification is implemented. The display screen of the computer device can be a liquid crystal display screen or an electronic ink display screen, and the input device of the computer device can be a touch layer covering the display screen, or a key, trackball or touchpad set on the computer device housing, or an external keyboard, touchpad or mouse, etc.

[0191] Those skilled in the art will understand that Fig.10 The structure shown in the figure is only a block diagram of a part of the structure related to the solution of the present application, and does not constitute a limitation on the computer device to which the solution of the present application is applied. The specific computer device may include more or fewer components than those shown in the figure, or combine certain components, or have a different arrangement of components.

[0192] In one embodiment, a computer device is provided, including a memory and a processor, wherein the memory stores a computer program, and the processor implements the steps of the method in the above embodiment when executing the computer program.

[0193] In one embodiment, a computer-readable storage medium is provided, on which a computer program is stored. When the computer program is executed by a processor, the steps of the method in the above embodiment are implemented.

[0194] Those skilled in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be completed by instructing the relevant hardware through a computer program, and the computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to memory, storage, database or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM) or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. As an illustration and not limitation, RAM is available in many forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link (Synchlink) DRAM (SLDRAM), memory bus (Rambus) direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM).

[0195] The technical features of the above embodiments may be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0196] The above-mentioned embodiments only express several implementation methods of the present application, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the present application. It should be pointed out that, for a person of ordinary skill in the art, several variations and improvements can be made without departing from the concept of the present application, and these all belong to the protection scope of the present application. Therefore, the protection scope of the present application shall be subject to the attached claims.

Claims

1. A parafoil system analysis method based on sparse identification, characterized in that: include: According to the parafoil system, an initial model is established, and a coordinate system of the initial model is defined; Obtaining system parameters of the parafoil system, calculating the generalized mass and generalized inertia of the parafoil, and establishing a dynamic model of the parafoil system in combination with the coordinate system; Acquire state variables and derivatives of the state variables, approximate the dynamic model, and obtain a transition model of the parafoil system; The state variables and the derivatives of the state variables are obtained, and the dynamic model is approximated to obtain the transition model of the parafoil system, including: Get the state variables and their derivatives: ； The dynamic model is approximated to obtain the transition model of the parafoil system: ； in, ； In the formula, is the state variable, is a time series, is the set of derivatives of the state variables, is the transition model of the parafoil system, As a basic function library, is the state variable data set, is the control variable data set, is the sparse vector coefficient, X X represent X All product combinations of the components in X U represent X and U All product combinations of components; The sparse identification method is used to transform the transition model into a minimum value problem, thereby obtaining a sparse model of the parafoil system. Considering the actual control requirements of the parafoil system, the basic function library of the parafoil system is set according to the sparse model, and the identification model of the parafoil system is obtained to identify the key parameters of the parafoil system and analyze the parafoil system.

2. The parafoil system analysis method based on sparse identification according to claim 1 is characterized in that: Obtaining system parameters of the parafoil system, calculating the generalized mass and generalized inertia of the parafoil, and establishing a dynamic model of the parafoil system in combination with the coordinate system, including: Obtain the parafoil mass, parafoil additional mass and the moment of inertia of the parachute at the origin of the parafoil system, and calculate the generalized mass and generalized moment of inertia of the parafoil; The aerodynamic force of the parafoil, the aerodynamic moment of the parafoil, the aerodynamic force of the load, the aerodynamic moment of the load, and the gravitational acceleration in the parafoil system are obtained, and the dynamic model of the parafoil system is established in combination with the generalized mass of the parafoil, the generalized inertia of the parafoil and the conversion relationship between the coordinate systems.

3. The parafoil system analysis method based on sparse identification according to claim 2 is characterized in that: The sparse identification method is used to transform the transition model into a minimum value problem, and a sparse model of the parafoil system is obtained, including: The sparse identification method is used to transform the transition model into a minimum value problem: ； Get the sparse model of the parafoil system: ； In the formula, is the optimal sparse vector coefficient, The data matrix is Column elements, for No. List, for No. List, is the weight coefficient of the regularization degree.

4. The parafoil system analysis method based on sparse identification according to claim 3 is characterized in that: Considering the actual control requirements of the parafoil system, the basic function library of the parafoil system is set according to the sparse model to obtain the identification model of the parafoil system, including: Considering the actual control requirements of the parafoil system, the basic function library of the parafoil system is set according to the sparse model: ； Get the identification model of the parafoil system: ； in: ； In the formula, is the parafoil yaw angle, is the parafoil lower left deflection, is the parafoil lower right deflection, , , are the derivatives of the displacement in three directions of the parafoil in the Cartesian coordinate system, for different sparsity coefficients.

5. The parafoil system analysis method based on sparse identification according to claim 4 is characterized in that: The sparse coefficient matrix of the key parameters of the parafoil system is identified, including: ； In the formula, is the matrix of sparse vector coefficients.

6. The parafoil system analysis method based on sparse identification according to any one of claims 1 to 5, characterized in that: The coordinate system of the initial model includes: Earth coordinate system, parachute coordinate system, load coordinate system and airflow coordinate system.

7. A parafoil system analysis device based on sparse identification, characterized in that: include: An initial module, used to establish an initial model according to the parafoil system and define a coordinate system of the initial model; A power module is used to obtain system parameters of the parafoil system, calculate the generalized mass and generalized inertia of the parafoil, and establish a dynamic model of the parafoil system in combination with the coordinate system; A transition module, used to obtain state variables and derivatives of the state variables, approximate the dynamic model, and obtain a transition model of the parafoil system; The state variables and the derivatives of the state variables are obtained, and the dynamic model is approximated to obtain the transition model of the parafoil system, including: Get the state variables and their derivatives: ； ； The dynamic model is approximated to obtain the transition model of the parafoil system: ； in, ； In the formula, is the state variable, is a time series, is the set of derivatives of the state variables, is the transition model of the parafoil system, As a basic function library, is the state variable data set, is the control variable data set, is the sparse vector coefficient, X X represent X All product combinations of the components in X U represent X and U All product combinations of components; A sparse module, used for converting the transition model into a minimum value problem by using a sparse identification method, so as to obtain a sparse model of the parafoil system; The identification module is used to consider the actual control requirements of the parafoil system, set the basic function library of the parafoil system according to the sparse model, obtain the identification model of the parafoil system, identify the key parameters of the parafoil system, and analyze the parafoil system.

8. A computer device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 6 are implemented.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 6 are implemented.

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