An optimization generation method and system of open-loop excitation of aircraft aerodynamic parameter identification

Abstract

The application relates to the technical field of aircraft aerodynamic parameter identification, and discloses an optimization generation method and system for open-loop excitation of aircraft aerodynamic parameter identification, wherein the method comprises the following steps: constructing a maximum likelihood estimation function based on a six-degree-of-freedom dynamics equation and an observation model, and combining a Newton-Raphson iteration method to obtain an estimated value of to-be-identified aerodynamic parameters; constructing a target function according to an optimal criterion of a log maximum of a determinant of an information matrix based on the estimated value of the to-be-identified aerodynamic parameters, parameterizing control input into to-be-optimized variables through a Gauss pseudospectral method, and solving optimal open-loop excitation signals through a nonlinear programming method; and verifying the effectiveness of the optimal open-loop excitation signals through a multidimensional test method. The application can autonomously generate optimal open-loop excitation signals and improve the effect of aircraft aerodynamic parameter identification.

Description

Technical Field

[0001] This invention relates to the field of aerodynamic parameter identification technology for aircraft, and in particular to an optimized generation method and system for open-loop excitation of aerodynamic parameter identification for aircraft. Background Technology

[0002] Aircraft aerodynamic parameters are core foundational data for flight quality assessment, control system design, and flight simulation modeling. Obtaining aerodynamic parameters through parameter identification methods using flight test data has become an important supplementary means to theoretical analysis and wind tunnel experiments, capable of reflecting aerodynamic characteristics under real flight conditions.

[0003] In the field of aerodynamic parameter identification, maximum likelihood estimation (MLE) is one of the most widely used methods. It estimates unknown parameters by minimizing the error between the model output and the actual observed output. However, the identification accuracy depends not only on the estimation algorithm itself but also on the quality of the excitation input signal—the ideal excitation input should, under the premise of satisfying engineering constraints, fully excite the key motion modes of the aircraft, so that the observed data contains as much aerodynamic parameter information as possible. Regarding input design criteria, the D-optimality criterion (based on maximizing the logarithm of the determinant of the information matrix), which aims to maximize the determinant of the Fisher information matrix, is the most widely used optimal input design criterion. In terms of numerical optimization methods, the Gaussian pseudospectral method (GPM), which discretizes the time domain into Legendre-Gauss nodes and transforms it into a nonlinear programming (NLP) problem, has been successfully applied in areas such as aircraft trajectory optimization, but has not yet been introduced into the excitation input optimization design for aerodynamic parameter identification.

[0004] The existing technical solutions for excitation input optimization design for aerodynamic parameter identification are as follows: 1. Excitation signal design method based on engineering experience Currently, the field of aerodynamic parameter identification commonly employs excitation signals based on engineering experience, including the "3211" signal, multi-stage square waves, pulses, frequency sweeps, and multi-sine signals. The "3211" signal consists of multiple step sequences with alternating amplitudes; its name derives from the 3-2-1-1 time interval pattern it contains. The design concept is to generate excitation energy with a wide frequency range in the time domain through combinations of step sequences with different widths and amplitudes. In specific design, the elevator, starting from the trim position, sequentially undergoes a step sequence with alternating amplitudes and decreasing widths, with each segment having a width ratio of 3:2:1:1. Square wave and pulse signals construct open-loop rudder deflection commands by setting different amplitudes, pulse widths, and intervals. Frequency sweep signals (such as linear frequency modulation or exponential frequency modulation) excite a wide frequency band by continuously varying the frequency over time, while multi-sine signals superimpose multiple sinusoidal components, allowing for some control over the frequency band distribution of the excitation energy.

[0005] However, the design of the aforementioned signals mainly relies on the designer's engineering experience, repeatedly adjusting parameters such as amplitude, duration, and frequency components to meet engineering needs, lacking systematic theoretical guidance and quantitative evaluation mechanisms. These fixed waveforms cannot automatically adjust their energy distribution when facing different flight conditions and parameters to be identified. When some parameters are not sensitive enough to the observed output or when multiple parameters have a highly correlated effect on the output, the identification results are prone to significant dependence on measurement noise and initial algorithm values.

[0006] 2. D-Optimal Input Design Method Based on Particle Swarm Optimization Algorithm To overcome the shortcomings of the aforementioned empirical design methods, some scholars have introduced optimal input design theory into the field of aerodynamic parameter identification. Wang Qing et al. published related research in the *Journal of Astronautics* in 2008. This method, based on the Cramer-Rohr lower bound theorem, uses minimizing the determinant of the inverse of the Fisher information matrix as the optimization objective, transforming the control input design into a mathematical optimization problem, which is then solved using the particle swarm optimization algorithm. As a heuristic global search method, the particle swarm optimization algorithm does not rely on the gradient information of the objective function and possesses strong global search capabilities.

[0007] However, this method still has significant shortcomings in practical applications: The particle swarm optimization algorithm requires evaluating the objective function value of every particle in the entire swarm in each iteration, and a single objective function evaluation requires a complete six-degree-of-freedom simulation integration of the aircraft, resulting in extremely high overall computational costs. Furthermore, as a stochastic search method, its convergence lacks rigorous theoretical guarantees, and the optimization results are significantly affected by the random seed, making it difficult to guarantee a consistent optimal solution in each run. In addition, this method uses a penalty function approach to handle engineering constraints such as control surface deflection amplitude and deflection rate, requiring repeated adjustments of the penalty coefficient, and the optimization results cannot strictly guarantee that the constraints are precisely satisfied globally.

[0008] 3. Multi-step stimulus design method based on genetic algorithm In 2017, Lichota et al. published "Optimal Input Design for Aircraft System Identification" in the *Journal of Aircraft*, proposing a maneuver design method for aircraft system identification based on the D-optimal criterion, employing a genetic algorithm to optimize multi-step excitation sequences. This method, like particle swarm optimization, belongs to the category of heuristic stochastic search, limiting the control input to a piecewise constant form and searching for the optimal solution by optimizing the switching time and amplitude of each segment.

[0009] However, genetic algorithms also face problems such as heavy computational burden due to large population size, convergence dependence on parameter settings, and lack of theoretical guarantees. Furthermore, this method restricts the control input to a piecewise constant form, which, while reducing the dimensionality of the optimization problem, also limits the completeness of the search space, making it difficult to obtain the truly optimal control input. Summary of the Invention

[0010] To address the problems of low computational efficiency, lack of convergence guarantee, imprecise constraint handling, and limited optimality of solutions in existing methods, this invention proposes an optimized generation method and system for open-loop excitation of aerodynamic parameters identification for aircraft. This method can autonomously generate the optimal open-loop excitation signal, thereby improving the identification effect of aerodynamic parameters for aircraft.

[0011] The technical solution adopted in this invention is as follows: An optimized generation method for open-loop excitation of aerodynamic parameters identification of an aircraft includes: The maximum likelihood estimation function is constructed based on the six-degree-of-freedom dynamic equations of the aircraft and the observation model, and the estimated values ​​of the aerodynamic parameters to be identified are obtained by combining the Newton-Raphson iterative method. Based on the estimated values ​​of the aerodynamic parameters to be identified, an objective function is constructed according to the optimal criterion of maximizing the logarithm of the determinant of the information matrix. The control input parameter is parameterized into variables to be optimized by the Gaussian pseudospectral method, and the optimal open-loop excitation signal is obtained by solving the nonlinear programming method. The effectiveness of the optimal open-loop excitation signal is verified by a multi-dimensional verification method, which includes quantitative evaluation of the information matrix, comparison of parameter estimation errors, and comparison of output fitting errors.

[0012] Furthermore, the maximum likelihood estimation function constructed based on the six-degree-of-freedom dynamic equations of the aircraft and the observation model includes: A six-degree-of-freedom dynamic equation for an aircraft is constructed as a state prediction model. The state prediction model is used to describe the change of the aircraft's state vector over time. The state vector includes velocity components, angular rate components, attitude angle components, and position coordinate components. The input vector of the state prediction model is the control surface deflection angle. An observation model is constructed, and a maximum likelihood estimation function for the aerodynamic parameters to be identified is constructed based on the observation model. The observation model is used to describe the mapping relationship between the observation output vector of the aircraft and the state vector, control input vector and aerodynamic parameters to be identified. The observation output vector includes measurement noise.

[0013] It should be noted that by establishing dynamic equations and observation models that include complete state variables, the mathematical relationship between state variables and parameters to be identified is clarified, providing an accurate theoretical basis for subsequent sensitivity analysis and information matrix calculation. The construction of the maximum likelihood estimation function transforms the parameter estimation problem into an optimization problem, which is convenient for efficient solution using numerical optimization methods.

[0014] Furthermore, the optimization of the estimated values ​​of the aerodynamic parameters to be identified using the Newton-Raphson iterative method includes: Taking the negative logarithm of the maximum likelihood estimation function and ignoring the constant term, the identification criterion function is obtained; with the goal of minimizing the identification criterion function, the Newton-Raphson iterative method is used to iteratively solve for the aerodynamic parameters to be identified. During the iteration process, the gradient vector and Hessian matrix of the identification criterion function relative to the aerodynamic parameters to be identified are calculated, and the estimated values ​​of the aerodynamic parameters to be identified are updated accordingly.

[0015] It should be noted that taking the negative logarithm transforms the likelihood function maximization problem into an equivalent minimization problem, reducing computational complexity. The Newton-Raphson method utilizes the second derivative information of the objective function, which has the advantages of fast convergence speed and high estimation accuracy, and can effectively obtain the maximum likelihood estimates of aerodynamic parameters.

[0016] Furthermore, the method of combining the Newton-Raphson iterative method to optimize and obtain the estimated values ​​of the aerodynamic parameters to be identified also includes: During the iteration process, the sensitivity matrix of the observed output vector to the aerodynamic parameter to be identified is obtained, and the Fisher information matrix is ​​constructed using the sensitivity matrix and the observation noise covariance matrix. A damping correction strategy is introduced to regularize the Fisher information matrix to obtain a regularized information matrix. The iteration step size is then calculated by replacing the original Hessian matrix with the regularized information matrix.

[0017] It should be noted that the Fisher information matrix quantitatively characterizes the amount of information about the parameters to be identified contained in the observation data, and its inverse matrix gives the lower limit of the parameter estimation accuracy. The damping correction strategy can effectively suppress the numerical instability caused by matrix ill-conditioning during the iteration process, ensuring that the identification algorithm can converge stably under various flight conditions.

[0018] Furthermore, the construction of the objective function based on the optimal criterion of maximizing the logarithm of the determinant of the information matrix includes: Using the open-loop excitation signal to be optimized as the control input, and based on the Cramer-Rhodes lower bound theorem, with the goal of minimizing the volume of the uncertain ellipsoid of parameter estimation, an optimal input design objective function in the form of maximizing the logarithm of the determinant of the Fisher information matrix is ​​constructed. The engineering constraints that the optimal input design objective function must satisfy during the optimization process are determined. These engineering constraints include the control surface deflection angle magnitude constraint and the control surface deflection rate constraint.

[0019] It should be noted that using the logarithm of the determinant of the information matrix as the objective function has a clear physical meaning: minimizing the uncertain ellipsoidal volume of the parameter estimation so that the comprehensive estimation accuracy of each parameter to be identified reaches the optimal level. At the same time, engineering constraints such as the amplitude of the control surface deflection angle and the deflection rate are incorporated into the optimization framework to ensure that the excitation signal obtained by optimization is engineering feasible.

[0020] Furthermore, the step of parameterizing the control input into variables to be optimized using the Gaussian pseudospectral method includes: The physical time domain is mapped to the normalized time domain. Legendre-Gauss orthogonal nodes are selected as control input configuration points within the normalized interval. Corresponding control surface deflection angles are set as variables to be optimized at each Legendre-Gauss orthogonal node. The control surface deflection angles are fixed at the two endpoints of the normalized interval as the aircraft trim control deflection values ​​to form a complete sequence of control variable nodes. The centroid Lagrange interpolation method is used to reconstruct the continuous control input signal in the entire time domain based on the control variable node sequence; the control input change rate at each node is calculated using the pseudospectral differential matrix, and converted into the rudder deflection rate in the physical time domain according to the mapping relationship between the physical time domain and the normalized time domain.

[0021] It should be noted that using Legendre-Gaussian nodes to discretize the control input allows the complete excitation signal waveform to be described with a small number of variables, significantly reducing the dimensionality of the optimization problem; the centroid Lagrange interpolation has the characteristic of good numerical stability and can reconstruct a smooth continuous control signal; the pseudospectral differential matrix can accurately calculate the control rate, avoiding the numerical errors introduced by the finite difference method, which is conducive to accurately meeting the rate constraint.

[0022] Furthermore, the step of parameterizing the control input into variables to be optimized using the Gaussian pseudospectral method also includes: Amplitude constraints are applied to the rudder surface deflection angles at each Legendre-Gauss orthogonal node and at both ends of the normalized interval, and rate constraints are applied to the rudder surface deflection rate at each node. After the constraint check is completed at the Legendre-Gauss orthogonal node, the amplitude and rate at all time points are checked to see if the constraints are met on the complete time grid in the normalized time domain, forming a dual check mechanism that combines node constraints and grid constraints. A smoothing regularization term is added to the objective function of the optimal input design. The smoothing regularization term is in the form of the sum of squares of the differences between the variables to be optimized corresponding to adjacent Legendre-Gaussian orthogonal nodes. It is used to suppress the high-frequency oscillation of the optimized control input signal between adjacent nodes.

[0023] It should be noted that the dual-check mechanism ensures the precise satisfaction of constraints at discrete nodes on the one hand, and eliminates the risk of constraint overruns between nodes through grid traversal checks on the other hand, thus ensuring the engineering safety of the excitation signal across the entire time domain. The introduction of the smoothing regularization term effectively suppresses high-frequency oscillations caused by jumps in optimization variables between nodes, making the generated excitation signal smoother and easier to implement in engineering.

[0024] Furthermore, the step of obtaining the optimal open-loop excitation signal through nonlinear programming includes: The sequential quadratic programming method is used to solve the nonlinear programming problem formed after discretization by the Gaussian pseudospectral method. The rudder deflection angle at the Grégende-Gauss orthogonal nodes is used as the independent variable for optimization. The negative value of the logarithm of the determinant of the Fisher information matrix is ​​used as the objective function. The rudder deflection angle amplitude constraint and the rudder deflection rate constraint are used as constraints to construct a sequential quadratic programming subproblem. In each iteration, the objective function is approximated twice and the constraints are approximated linearly. The search direction of the current iteration step is obtained by solving the sequential quadratic programming subproblem. The optimization variables are updated along the search direction, and the update step size is determined by one-dimensional search until the preset convergence criterion is met. The optimization variables at convergence are mapped to the optimal open-loop excitation signal in the physical time domain.

[0025] It should be noted that the sequential quadratic programming method can make full use of the gradient information of the objective function and constraints, and has the advantages of fast convergence speed and accurate constraint handling. It usually only requires a finite number of iterations to converge to the optimal solution, and the computational cost is much lower than that of existing heuristic search methods. At the same time, its deterministic iterative process ensures the repeatability of the optimization results.

[0026] Furthermore, the validity verification of the optimal open-loop excitation signal using a multi-dimensional testing method includes: Using the same set of random noise sequences, the aircraft system with the reference excitation input and the optimal open-loop excitation signal are simulated and noisy observation data are obtained. Based on the two sets of noisy observation data, aerodynamic parameters are identified to obtain the corresponding parameter identification results. The determinant values ​​of the information matrices corresponding to the two excitation inputs are compared to measure the information gain; the estimated values ​​of the two identified aerodynamic parameters are compared with the true values ​​to measure the improvement in identification accuracy; the estimated values ​​of the two identified aerodynamic parameters are substituted into the observation model to calculate the model output and compared with the noisy observation data to measure the improvement in output prediction capability.

[0027] It should be noted that the use of the same noise sequence for comparison and verification eliminates the influence of noise randomness on the comparison results, ensuring the fairness of the evaluation. The comprehensive evaluation from three dimensions—information content, parameter estimation accuracy, and output fitting accuracy—can comprehensively and objectively reflect the performance improvement of the optimized input relative to the benchmark input.

[0028] An optimized generation system for open-loop excitation of aerodynamic parameters identification of an aircraft includes: The aerodynamic parameter identification module is configured to construct a maximum likelihood estimation function based on the six-degree-of-freedom dynamic equations of the aircraft and the observation model, and to obtain the estimated values ​​of the aerodynamic parameters to be identified by combining the Newton-Raphson iterative method. The optimal input design module is configured to construct an objective function based on the estimated values ​​of the aerodynamic parameters to be identified, according to the optimal criterion of maximizing the logarithm of the determinant of the information matrix, to convert the control input parameters into variables to be optimized using the Gaussian pseudospectral method, and to obtain the optimal open-loop excitation signal by solving the nonlinear programming method. The verification module is configured to verify the effectiveness of the optimal open-loop excitation signal through a multi-dimensional verification method, which includes quantitative evaluation of the information matrix, comparison of parameter estimation errors, and comparison of output fitting errors.

[0029] The beneficial effects of this invention are as follows: 1. This invention improves the aerodynamic parameter identification effect of aircraft by autonomously generating optimal open-loop excitation signals through aerodynamic parameter identification, optimal input design, and effectiveness verification. Compared with identification using engineering experience signals directly, this invention uses prior identification results as a basis, enabling the energy distribution of the excitation signal to be optimized in a targeted manner for the current aircraft model and the parameters to be identified, and quantitatively evaluates the optimization effect through multi-dimensional verification. Compared with existing optimization design methods based on heuristic algorithms, this invention transforms the optimal control problem into a nonlinear programming problem, uses gradient-based algorithms to solve it, and can complete the optimization in fewer iterations, significantly reducing computational costs. Furthermore, the optimization process is deterministic, and the results are stable and reproducible.

[0030] 2. This invention discretizes and parameterizes the control input using the Gaussian pseudospectral method, requiring only a small number of optimization variables to describe the complete excitation signal waveform, significantly reducing the dimensionality of the optimization problem. This invention reconstructs the continuous signal using centroid Lagrange interpolation and accurately calculates the control rate using the pseudospectral differential matrix, avoiding the numerical errors introduced by the finite difference method. Furthermore, this invention directly embeds the control surface deflection amplitude constraint and deflection rate constraint as explicit inequalities into the nonlinear programming framework, and ensures that the constraints are accurately satisfied throughout the entire time domain through a dual node and grid checking mechanism. This results in an optimized excitation signal with good engineering feasibility, allowing direct application to flight tests without subsequent manual adjustments.

[0031] 3. This invention employs a sequential quadratic programming method to solve nonlinear programming problems. This method fully utilizes the gradient information of the objective function and constraints, offering advantages such as fast convergence speed and accurate constraint handling. Compared to the penalty function method in existing technologies, which requires repeated adjustments of the penalty coefficient, this invention eliminates the need for cumbersome parameter tuning, exhibits lower sensitivity to algorithm parameters in the optimization results, and is more convenient for engineering implementation. Through comprehensive comparative verification across three dimensions—information matrix determinant value, parameter estimation error, and output fitting error—this invention can comprehensively and objectively evaluate the performance improvement of the optimized input compared to the baseline input, providing a systematic tool for optimizing excitation inputs in aerodynamic parameter identification experiments. Attached Figure Description

[0032] Figure 1 This is a flowchart of an optimized generation method for open-loop excitation of aerodynamic parameters identification of an aircraft, according to Embodiment 1 of the present invention.

[0033] Figure 2 This is a schematic diagram of the flight simulation data time history of Embodiment 2 of the present invention, wherein: sub-graph (a) shows the flight airspeed. Response curve, subplot (b) shows the angle of attack. The response curve, subplot (c) shows the pitch rate. Response curve.

[0034] Figure 3 This is a comparison diagram of the baseline 3211 signal input and the optimized signal input in Embodiment 2 of the present invention.

[0035] Figure 4 This is a comparison chart of the relative errors of parameters in Embodiment 2 of the present invention. Detailed Implementation

[0036] To provide a clearer understanding of the technical features, objectives, and effects of the present invention, specific embodiments are now described. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention; that is, the described embodiments are only a part of the embodiments of the invention, not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0037] Example 1 like Figure 1 As shown, this embodiment provides an optimized generation method for open-loop excitation of aerodynamic parameters identification of an aircraft, including: The maximum likelihood estimation function is constructed based on the six-degree-of-freedom dynamic equations of the aircraft and the observation model, and the estimated values ​​of the aerodynamic parameters to be identified are obtained by combining the Newton-Raphson iterative method. Based on the estimated values ​​of the aerodynamic parameters to be identified, an objective function is constructed according to the optimal criterion of maximizing the logarithm of the determinant of the information matrix. The control input parameter is parameterized into variables to be optimized by the Gaussian pseudospectral method, and the optimal open-loop excitation signal is obtained by solving the nonlinear programming method. The effectiveness of the optimal open-loop excitation signal is verified by a multi-dimensional verification method, which includes quantitative evaluation of the information matrix, comparison of parameter estimation errors, and comparison of output fitting errors.

[0038] Specifically, the method of this embodiment can be implemented by the following steps.

[0039] I. Identification of Aerodynamic Parameters The six-degree-of-freedom dynamic equations of an aircraft can be uniformly written in the following form:

[0040] In the formula: for The spacecraft state vector at time t. For the aircraft state vector Regarding time The first derivative; is the six-degree-of-freedom nonlinear dynamic mapping function for the aircraft, and is the vector-valued nonlinear function for a known structure; for The control input vector at time t must satisfy ,in for The elevator deflection angle of the aircraft at any given moment; The parameter vector to be identified; for The spacecraft state vector at time t. This is the initial state vector of the aircraft.

[0041] In this embodiment, the spacecraft state vector has 12 dimensions, and its specific expression is as follows:

[0042] In the formula: These are the three-axis velocity components of the aircraft in the body coordinate system. These are the roll, pitch, and yaw rates in the body coordinate system. This refers to the roll angle; The pitch angle; Yaw angle; These are the aircraft's position coordinates in the ground coordinate system.

[0043] In this embodiment, there are 12 aerodynamic parameters to be identified, which constitute a parameter vector. The specific expression is:

[0044] In the formula: The axial force has a zero angle of attack coefficient; This is the coefficient of the first term of the axial force angle of attack; The coefficient of the quadratic term of the axial force angle of attack; The axial force elevator efficiency coefficient; The normal force has a zero angle of attack coefficient; This is the normal force angle-of-attack linearization factor; The normal force elevator efficiency coefficient; The normal force pitch rate damping coefficient; The pitching moment has a zero angle of attack coefficient; This is the linearization factor for the pitching moment angle of attack; The pitch moment is the elevator control efficiency coefficient; is the pitch moment angular rate damping coefficient.

[0045] The longitudinal aerodynamic forces and pitching moment coefficients of the aircraft are modeled using a commonly used nonlinear fitting model in engineering, as follows:

[0046] In the formula: This is the axial force coefficient; Normal force coefficient; This is the pitch moment coefficient; For the angle of attack, Airspeed, The mean aerodynamic chord length is given.

[0047] The observation model at discrete time points The above is represented as:

[0048] In the formula: The discrete observation point number; This represents the total number of observed samples; for Time system observation vector; This is the system's nonlinear observation mapping function; for The noise vector observed at any given time follows a zero-mean Gaussian distribution and satisfies the following conditions: , To observe the noise covariance matrix.

[0049] Given a discrete observation dataset Parameters to be identified The likelihood function expression is:

[0050] In the formula: The dimension of the observation vector; output residual vector. Combining the observation equation, we can obtain Therefore, the residual satisfies .

[0051] Maximum likelihood estimation works by maximizing the likelihood function. To estimate the parameters, after taking the negative logarithm and ignoring the constant term, we obtain the simplified identification criterion function:

[0052] In the formula: abbreviation .

[0053] The identification of aerodynamic parameters of an aircraft is transformed into a minimum optimization problem, which involves solving for the vector of aerodynamic parameters to be identified. The optimal estimate:

[0054] In the formula: Vector of aerodynamic parameters to be identified The optimal estimate.

[0055] The Newton-Raphson iterative algorithm is used to solve the above minimum optimization problem. The iterative update formula is as follows:

[0056] In the formula: This represents the number of iteration steps. For the first The vector of aerodynamic parameters to be identified in the next iteration; The gradient vector of the objective function; Let Hessian matrix be the objective function.

[0057] The specific expression for the gradient vector is:

[0058] In the formula: abbreviation .

[0059] The exact expression for the Hessian matrix:

[0060] Near the optimal solution, the output residual is minimal, the second-order partial derivatives are negligible high-order quantities, and the Hessian matrix can be approximated as the Fisher information matrix. ,Right now:

[0061] Sensitivity matrix The central finite difference method is used for numerical solution. For the [missing information]... Parameters to be identified Apply small perturbations The approximate formula for partial derivatives is:

[0062] In the formula: For unit vectors, only the first One element is 1, and the rest are 0; For the first The small perturbations corresponding to each aerodynamic parameter. By traversing all parameter dimensions, the complete sensitivity matrix can be assembled.

[0063] To address the issues of matrix ill-conditioning and iterative divergence during iteration and improve numerical stability, a Levenberg-Marquardt (LM) damping correction strategy is introduced to regularize the Fisher information matrix.

[0064] In the formula: The damping coefficient is an adaptive factor that is adjusted in real time based on the iterative results. For Fisher's information matrix A diagonal matrix consisting of diagonal elements; This is the regularized information matrix after damping correction.

[0065] II. Optimal Input Design According to the Cramer-Rhodes lower bound theorem, maximum likelihood estimation is an unbiased estimation, and the parameter estimation covariance matrix... Satisfies matrix inequalities:

[0066] Determinant of the covariance matrix This represents the volume of the ellipsoid with uncertain parameter estimates. The D-optimality criterion aims to minimize this volume, which is equivalent to maximizing the determinant of the Fisher information matrix:

[0067] In the formula: For optimal stimulus input; The feasible region for control inputs that satisfy engineering constraints. Fisher information matrix. The calculation method is consistent with the aerodynamic parameter identification steps, namely:

[0068] This matrix depends on the control input. (Through status response) Affecting observation output Therefore, it can be used as the objective function for optimization. To avoid ill-conditioned Fisher information matrix during optimization, a regularization term is introduced:

[0069] in, The absolute regularization coefficient; The relative regularization coefficient; For matrix traces; To and An identity matrix of the same dimension. The optimization objective function is then changed to maximizing... .

[0070] The core idea of ​​the Gaussian pseudospectral method is to discretize the continuous-time optimal control problem into a nonlinear programming problem. The specific implementation steps are as follows: Step 1: Time Domain Mapping. Map the physical time domain... Linear mapping to normalized interval Mapping relationship:

[0071] In the formula: To excite the initial physical moment; To excite the termination of physical time; This is a dimensionless normalized time variable.

[0072] Step 2: Node selection. Select Legendre-Gauss orthogonal nodes within the normalized interval. ,in The number of Legendre-Gaussian interior points is preset to a fixed constant of 6 in this embodiment. These nodes are Legendre orthogonal polynomials. The root has high-order Gaussian quadrature accuracy. To fully cover the entire time domain, the left and right endpoints of the interval are supplemented. and This constitutes a complete interpolation node sequence containing 8 nodes.

[0073] Step 3: Parameterize control variables. Set the elevator deflection angles corresponding to the six Legendre-Gauss nodes as optimization variables. , For the first The elevator deflection angles corresponding to each internal node are to be optimized. To ensure the excitation signal is stable at the beginning and end and closely matches the initial trim state of the aircraft, the elevator deflection angles at both ends of the time domain are fixed as the trim rudder deflection angles of the aircraft. ,Right now:

[0074] The complete node vector is .

[0075] Step 4: Barycentric Lagrange Interpolation Continuous Signal Reconstruction. The continuous control signal on the full-time grid is reconstructed using barycentric Lagrange interpolation.

[0076] In the formula: For the first The barycentric Lagrange interpolation basis functions corresponding to each node; For the first The elevator deflection angle values ​​for each node. To improve numerical stability, the calculation is performed using the center of gravity method:

[0077] In the formula: For the first The centroid interpolation weights of each node.

[0078] Step 5: Precise calculation of control rate. This is achieved using the pseudospectral differential matrix. Precise calculation of the control rate avoids errors introduced by numerical differences. Differential matrix. The elements are:

[0079] In the formula: For the first Line number List the differential coefficients. The control rate at each node is:

[0080] elevator deflection rate in the physical time domain for:

[0081] After parameterization using the Gaussian pseudospectral method, the original optimal control problem is transformed into the following nonlinear programming (NLP) problem:

[0082] In the formula: The smoothing weighting coefficient is used to suppress over-vibration between nodes; Optimize the interpolation of rudder deflection variables for adjacent nodes; This is a constraint constant for the maximum amplitude of the elevator deflection angle; This is the maximum elevator deflection rate constraint constant. Constraint handling employs a dual-check mechanism: nodal constraints: magnitude and rate constraints are checked at Legendre-Gauss nodes; mesh constraints: magnitude and rate constraints are checked on the full time mesh to ensure constraints are satisfied globally.

[0083] This embodiment employs the Sequential Quadratic Programming (SQP) algorithm to solve the aforementioned nonlinear programming problem. In each iteration, this algorithm constructs a quadratic approximation subproblem of the objective function and constraints. By solving the quadratic programming subproblem, it obtains the search direction and performs a one-dimensional search along that direction to update the variables. This approach offers advantages such as fast convergence and accurate constraint handling.

[0084] III. Verification To eliminate the influence of noise randomness, this embodiment uses the same set of noise samples to identify the baseline input and the optimized input respectively:

[0085] In the formula: is a standard normal random number generation function, used to generate standard Gaussian random matrices with a mean of 0 and a variance of 1; This represents the total number of sampling points in the simulation, and 15 represents the total dimension of the observed vector. The Cholliski decomposition function is used to decompose the observation noise covariance matrix. The standard normal random matrix is ​​decomposed and mapped to an observed noise sequence that conforms to the statistical characteristics of true noise. This means using the exact same random noise sequence for both inputs to ensure fairness in the comparison.

[0086] Example 2 This embodiment is based on embodiment 1: This embodiment provides an optimized generation method for open-loop excitation of aerodynamic parameters identification of aircraft, and verifies it based on a standardized longitudinal dynamics simulation example of a fixed-wing aircraft. This method can be implemented according to the following steps.

[0087] Step 1: Construct a simulation dynamic model of a typical fixed-wing aircraft, given the overall parameters of the aircraft. Aircraft mass Reference area Mean aerodynamic chord length Reference length ; Directional moment of inertia ; Directional moment of inertia ; Directional moment of inertia Inertial product Engine thrust The remaining external forces / torques are Referring to the general longitudinal aerodynamic modeling of fixed-wing aircraft, a 12-parameter polynomial model including axial force, normal force, and pitch moment was constructed. The aerodynamic parameter values ​​are shown in Table 1. Trial calculations were performed under typical flight conditions (altitude 3000m, speed 170m / s) to obtain the initial state. And rudder deflection .

[0088] Table 1 - Aerodynamic Parameter Values

[0089] Step 2: Data Generation and Parameter Identification under Reference Excitation. A traditional "3211" multi-step signal is used as the elevator excitation input. The six-degree-of-freedom dynamic equations are solved using a fourth-order Runge-Kutta integral to obtain the state response. This result is then used by the observation model to generate simulated observation data containing Gaussian white noise, such as... Figure 2 As shown.

[0090] Figure 2 It contains 3 sub-images, of which: Sub-image (a) shows the airspeed. Response curve, unit: Sub-figure (b) shows the angle of attack. Response curve, unit: Subgraph (c) shows the pitch rate. Response curve, unit: The horizontal axis represents simulation time. The unit is value range In the figure, the solid blue line represents the actual state data of the noise-free system, and the dashed red line represents the observed data after Gaussian noise is added. As can be seen from the curve comparison, the overall trend of the observed data highly matches the actual state, but there are small random disturbances superimposed on the trajectory, simulating the noise characteristics of actual measurements by airborne sensors. Running the aerodynamic parameter identification steps of this invention, prior estimates of 12 longitudinal aerodynamic parameters are obtained through Newton-Raphson iteration. .

[0091] Step 3: Optimal input design based on the Gaussian pseudospectral method. Using the aerodynamic parameter baseline values ​​obtained in Step 2... As a priori parameter, the time domain is mapped to Six Legendre-Gauss interior points were selected to parameterize the elevator control input. With the objective of maximizing the logarithm of the determinant of the Fisher information matrix, amplitude constraints (±5°) and rate constraints (±60° / s) were directly embedded into a nonlinear programming framework. The optimal excitation signal was obtained by solving the problem using the Sequential Quadratic Programming (SQP) algorithm. Compared with the traditional "3211" reference excitation signal The comparison results are as follows Figure 3 As shown.

[0092] Figure 3 In the middle, the horizontal axis represents the simulation time. The unit is , range The vertical axis represents the elevator deflection angle. The unit is The blue solid line represents the traditional "3211" reference excitation input, while the red curve represents the optimized input obtained by this method. A comparison of the curves shows that the reference "3211" signal is a piecewise step signal, with the rudder deflection remaining constant for a long time, and the signal excitation form is singular. The optimized input obtained by this method is a continuous, smooth oscillating curve, fully utilizing the allowable amplitude range of the rudder deflection to continuously excite the longitudinal dynamics of the aircraft, and satisfying the rudder deflection amplitude and deflection rate constraints throughout the entire process.

[0093] Step 4: Verification and Comparison. Under the same initial conditions and the same set of fixed noise samples, the baseline "3211" signal and the optimized signal were used respectively. The excitation model, running the complete identification process, the identification results of aerodynamic parameters, and the comparison of relative errors are shown in Table 2 and... Figure 4 As shown.

[0094] Table 2 - Comparison of Identification Results of Aerodynamic Parameters

[0095] Figure 4 In the middle, the horizontal axis represents 12 aerodynamic parameters to be identified, in the following order: , , , , , , , , , , , The vertical axis uses a logarithmic scale to represent the relative error of the identified aerodynamic parameters relative to their true values. The blue dotted curve represents the identification result under the baseline "3211" excitation, while the red square curve represents the optimized identification result under the optimal excitation of this method. The curve comparison shows that for all 12 longitudinal aerodynamic parameters, the relative error of the parameters corresponding to the optimized excitation of this method is generally lower than that under the baseline "3211" excitation, proving that the optimal excitation can effectively improve the accuracy of parameter identification. Identification objective function. Depend on convergence to The algorithm converged after 10 iterations. The convergence speed of the optimized input condition was basically the same as that of the baseline input, which verified that the identification algorithm has good stability under the optimized excitation condition.

[0096] Example 3 This embodiment is based on embodiment 1: This embodiment provides a computer device, including a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the optimized generation method for open-loop excitation of aircraft aerodynamic parameter identification as described in Embodiment 1. The computer program can be in the form of source code, object code, executable file, or some intermediate form.

[0097] Example 4 This embodiment is based on embodiment 1: This embodiment provides a computer-readable storage medium storing a computer program. When executed by a processor, this computer program implements the optimized generation method for open-loop excitation of aircraft aerodynamic parameter identification as described in Embodiment 1. The computer program can be in the form of source code, object code, executable file, or some intermediate form. The storage medium includes any entity or device capable of carrying computer program code, a recording medium, a computer memory, a read-only memory (ROM), a random access memory (RAM), an electrical carrier signal, a telecommunication signal, and a software distribution medium, etc.

[0098] The above description is merely a preferred embodiment of the present invention. It should be understood that the present invention is not limited to the forms disclosed herein and should not be construed as excluding other embodiments. It can be used in various other combinations, modifications, and environments, and can be altered within the scope of the concept described herein through the above teachings or related technologies or knowledge. Modifications and variations made by those skilled in the art that do not depart from the spirit and scope of the present invention should be within the protection scope of the appended claims.

[0099] It should be noted that, for the sake of simplicity, the foregoing method embodiments are described as a series of actions. However, those skilled in the art should understand that this application is not limited to the described order of actions, as some steps may be performed in other orders or simultaneously according to this application. Furthermore, those skilled in the art should also understand that the embodiments described in the specification are preferred embodiments, and the actions and modules involved are not necessarily essential to this application.

Claims

1. An optimized generation method for open-loop excitation of aerodynamic parameters identification of an aircraft, characterized in that, include: The maximum likelihood estimation function is constructed based on the six-degree-of-freedom dynamic equations of the aircraft and the observation model, and the estimated values ​​of the aerodynamic parameters to be identified are obtained by combining the Newton-Raphson iterative method. Based on the estimated values ​​of the aerodynamic parameters to be identified, an objective function is constructed according to the optimal criterion of maximizing the logarithm of the determinant of the information matrix. The control input parameter is parameterized into variables to be optimized by the Gaussian pseudospectral method, and the optimal open-loop excitation signal is obtained by solving the nonlinear programming method. The effectiveness of the optimal open-loop excitation signal is verified by a multi-dimensional verification method, which includes quantitative evaluation of the information matrix, comparison of parameter estimation errors, and comparison of output fitting errors.

2. The optimized generation method for open-loop excitation of aerodynamic parameters identification of aircraft according to claim 1, characterized in that, The maximum likelihood estimation function constructed based on the six-degree-of-freedom dynamic equations of the aircraft and the observation model includes: A six-degree-of-freedom dynamic equation for an aircraft is constructed as a state prediction model. The state prediction model is used to describe the change of the aircraft's state vector over time. The state vector includes velocity components, angular rate components, attitude angle components, and position coordinate components. The input vector of the state prediction model is the control surface deflection angle. An observation model is constructed, and a maximum likelihood estimation function for the aerodynamic parameters to be identified is constructed based on the observation model. The observation model is used to describe the mapping relationship between the observation output vector of the aircraft and the state vector, control input vector and aerodynamic parameters to be identified. The observation output vector includes measurement noise.

3. The optimized generation method for open-loop excitation of aerodynamic parameters identification of aircraft according to claim 2, characterized in that, The method of combining Newton-Raphson iteration to obtain the estimated values ​​of the aerodynamic parameters to be identified includes: Taking the negative logarithm of the maximum likelihood estimation function and ignoring the constant term, the identification criterion function is obtained; with the goal of minimizing the identification criterion function, the Newton-Raphson iterative method is used to iteratively solve for the aerodynamic parameters to be identified. During the iteration process, the gradient vector and Hessian matrix of the identification criterion function relative to the aerodynamic parameters to be identified are calculated, and the estimated values ​​of the aerodynamic parameters to be identified are updated accordingly.

4. The optimized generation method for open-loop excitation of aircraft aerodynamic parameter identification according to claim 3, characterized in that, The method of combining the Newton-Raphson iterative method to optimize and obtain the estimated values ​​of the aerodynamic parameters to be identified also includes: During the iteration process, the sensitivity matrix of the observed output vector to the aerodynamic parameter to be identified is obtained, and the Fisher information matrix is ​​constructed using the sensitivity matrix and the observation noise covariance matrix. A damping correction strategy is introduced to regularize the Fisher information matrix to obtain a regularized information matrix. The iteration step size is then calculated by replacing the original Hessian matrix with the regularized information matrix.

5. The optimized generation method for open-loop excitation of aerodynamic parameters identification of aircraft according to claim 1, characterized in that, The objective function is constructed based on the optimal criterion of maximizing the logarithm of the determinant of the information matrix, including: Using the open-loop excitation signal to be optimized as the control input, and based on the Cramer-Rhodes lower bound theorem, with the goal of minimizing the volume of the uncertain ellipsoid of parameter estimation, an optimal input design objective function in the form of maximizing the logarithm of the determinant of the Fisher information matrix is ​​constructed. The engineering constraints that the optimal input design objective function must satisfy during the optimization process are determined. These engineering constraints include the control surface deflection angle magnitude constraint and the control surface deflection rate constraint.

6. The optimized generation method for open-loop excitation of aerodynamic parameters identification of aircraft according to claim 5, characterized in that, The process of parameterizing the control input into variables to be optimized using the Gaussian pseudospectral method includes: The physical time domain is mapped to the normalized time domain. Legendre-Gauss orthogonal nodes are selected as control input configuration points within the normalized interval. Corresponding control surface deflection angles are set as variables to be optimized at each Legendre-Gauss orthogonal node. The control surface deflection angles are fixed at the two endpoints of the normalized interval as the aircraft trim control deflection values ​​to form a complete sequence of control variable nodes. The centroid Lagrange interpolation method is used to reconstruct the continuous control input signal in the entire time domain based on the control variable node sequence; the control input change rate at each node is calculated using the pseudospectral differential matrix, and converted into the rudder deflection rate in the physical time domain according to the mapping relationship between the physical time domain and the normalized time domain.

7. The optimized generation method for open-loop excitation of aerodynamic parameter identification of aircraft according to claim 6, characterized in that, The step of parameterizing the control input into variables to be optimized using the Gaussian pseudospectral method also includes: Amplitude constraints are applied to the rudder surface deflection angles at each Legendre-Gauss orthogonal node and at both ends of the normalized interval, and rate constraints are applied to the rudder surface deflection rate at each node. After the constraint check is completed at the Legendre-Gauss orthogonal node, the amplitude and rate at all time points are checked to see if the constraints are met on the complete time grid in the normalized time domain, forming a dual check mechanism that combines node constraints and grid constraints. A smoothing regularization term is added to the objective function of the optimal input design. The smoothing regularization term is in the form of the sum of squares of the differences between the variables to be optimized corresponding to adjacent Legendre-Gaussian orthogonal nodes. It is used to suppress the high-frequency oscillation of the optimized control input signal between adjacent nodes.

8. The optimized generation method for open-loop excitation of aerodynamic parameter identification of an aircraft according to claim 7, characterized in that, The process of obtaining the optimal open-loop excitation signal through nonlinear programming includes: The sequential quadratic programming method is used to solve the nonlinear programming problem formed after discretization by the Gaussian pseudospectral method. The rudder deflection angle at the Grégende-Gauss orthogonal nodes is used as the independent variable for optimization. The negative value of the logarithm of the determinant of the Fisher information matrix is ​​used as the objective function. The rudder deflection angle amplitude constraint and the rudder deflection rate constraint are used as constraints to construct a sequential quadratic programming subproblem. In each iteration, the objective function is approximated twice and the constraints are approximated linearly. The search direction of the current iteration step is obtained by solving the sequential quadratic programming subproblem. The optimization variables are updated along the search direction, and the update step size is determined by one-dimensional search until the preset convergence criterion is met. The optimization variables at convergence are mapped to the optimal open-loop excitation signal in the physical time domain.

9. The optimized generation method for open-loop excitation of aerodynamic parameters identification of aircraft according to claim 2, characterized in that, The validity verification of the optimal open-loop excitation signal using a multi-dimensional testing method includes: Using the same set of random noise sequences, the aircraft system with the reference excitation input and the optimal open-loop excitation signal are simulated and noisy observation data are obtained. Based on the two sets of noisy observation data, aerodynamic parameters are identified to obtain the corresponding parameter identification results. The determinant values ​​of the information matrices corresponding to the two excitation inputs are compared to measure the information gain; the estimated values ​​of the two identified aerodynamic parameters are compared with the true values ​​to measure the improvement in identification accuracy; the estimated values ​​of the two identified aerodynamic parameters are substituted into the observation model to calculate the model output and compared with the noisy observation data to measure the improvement in output prediction capability.

10. An optimized generation system for open-loop excitation of aerodynamic parameters identification of an aircraft, characterized in that, include: The aerodynamic parameter identification module is configured to construct a maximum likelihood estimation function based on the six-degree-of-freedom dynamic equations of the aircraft and the observation model, and to obtain the estimated values ​​of the aerodynamic parameters to be identified by combining the Newton-Raphson iterative method. The optimal input design module is configured to construct an objective function based on the estimated values ​​of the aerodynamic parameters to be identified, according to the optimal criterion of maximizing the logarithm of the determinant of the information matrix, to convert the control input parameters into variables to be optimized using the Gaussian pseudospectral method, and to obtain the optimal open-loop excitation signal by solving the nonlinear programming method. The verification module is configured to verify the effectiveness of the optimal open-loop excitation signal through a multi-dimensional verification method, which includes quantitative evaluation of the information matrix, comparison of parameter estimation errors, and comparison of output fitting errors.

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