Aerodynamic parameter estimation method based on outlier adaptive detection removal strategy

Abstract

The invention belongs to the technical field of aerospace, and particularly relates to an aerodynamic parameter estimation method based on an outlier adaptive detection removal strategy. A traditional scheme, such as a Rauch-Tung-Striebel (RTS) smoother, for estimating the optimal performance of aerodynamic parameters is often based on the assumption that measurement noise meets Gaussian distribution. However, in practical application, noise distribution often deviates from Gaussian hypothesis, and performance is remarkably reduced when aerodynamic parameters are estimated based on a filter or smoother method. In order to solve the problems, the invention provides the aircraft aerodynamic parameter estimation method based on the adaptive outlier detection removal strategy, self-detection and self-diagnosis of outliers in measured data are realized in the aerodynamic parameter estimation process, and the precision of the aerodynamic parameter estimation value is greatly improved under the condition that the measured value is disturbed by the outliers. A simulation result verifies the feasibility of the robust aerodynamic data estimation scheme in a real flight environment.

Description

Technical Field

[0001] The present invention belongs to the field of aerospace technology, and in particular relates to an aerodynamic parameter estimation method based on an outlier adaptive detection and removal strategy. Background Art

[0002] In the field of aviation industry, accurate aircraft dynamics models are crucial for the design of control laws, performance verification and flight simulation. These models are usually described by coefficients or parameters, and the determination of these parameters needs to be based on different flight conditions. Among the many parameters, the aerodynamic coefficients related to aerodynamic forces and moments are particularly important. The values ​​of these coefficients are usually derived from wind tunnel test data or computational fluid dynamics (CFD) technology. However, wind tunnel tests and CFD simulations often cannot fully simulate the actual flight environment. Therefore, it is necessary to use parameter estimation technology to directly extract aerodynamic coefficients from flight test data. Common parameter estimation methods include equation error method, output error method, filter error method, filter method and neural network-based methods. Among them, the filter method has been widely used because of its simple operation. This method transforms the parameter estimation problem into a state estimation problem through state augmentation, and then can use a variety of filters for systematic solution. However, when estimating the state at a certain moment, these filters often only use the measured values ​​at the current moment, and fail to make full use of the measurement data in the entire sampling history. In contrast, smoothing methods such as the Rauch-Tung-Striebel (RTS) smoother are able to use the entire sampled data to estimate the state, and therefore generally provide higher accuracy. When real-time estimation is not required, smoothing methods become the best choice for aerodynamic parameter estimation. Whether it is a filter method or a smoother method, their optimal performance in estimating aerodynamic parameters is often based on the assumption that the measurement noise satisfies a Gaussian distribution. However, in practical applications, the noise distribution often deviates from the Gaussian assumption for various reasons, for example, heavy-tailed density may appear in applications involving flicker noise, air turbulence; outliers caused by clutter, and model mismatch caused by linearization, etc. These factors will cause the Gaussian assumption of measurement noise to fail, which may lead to a significant decrease in performance when estimating aerodynamic parameters based on filter or smoother methods. Summary of the invention

[0003] In view of the above problems, the present invention proposes a method for estimating aircraft aerodynamic parameters based on an adaptive outlier detection and removal strategy, which realizes self-detection and self-diagnosis of outliers in the measurement data during the aerodynamic parameter estimation process, and greatly improves the accuracy of aerodynamic parameter estimation when the measurement values ​​are disturbed by outliers. This is of vital importance for establishing a high-precision aircraft motion model.

[0004] The purpose of the present invention is to design an aerodynamic parameter estimation algorithm suitable for the presence of wild values ​​in the measured values, to adaptively detect and remove wild values ​​in the measured data, and to achieve accurate estimation of aerodynamic parameters. Specifically, with the help of the solution ideas and algorithms for classification problems in the field of artificial intelligence, a novel, simple and adaptive wild value detection and removal measurement model is proposed for the problem of estimating the aerodynamic parameters of aircraft. On this basis, an aerodynamic parameter estimation method is designed to meet the needs of high-precision estimation of aircraft aerodynamic parameters.

[0005] The technical solution of the present invention is:

[0006] An extended state-based aerodynamic parameter modeling method is used to simplify the aerodynamic parameter estimation process, including:

[0007] The state evolution model of the aerodynamic parameter estimation problem is established as:

[0008] x t =f(x t-1 ,θ)+v t

[0009] Among them, x t Contains the state of the aircraft dynamic system, including attitude angle, speed, altitude, etc., θ contains the aerodynamic parameters to be estimated, such as lift coefficient, drag coefficient, etc., v t The noise is composed of all sensor noises, which has a mean of 0 and a variance of the diagonal matrix Q t Gaussian distribution, f(·,·) is a function (linear or nonlinear) used to describe the evolution of state quantities. In order to estimate aerodynamic parameters, a random walk model is first introduced for aerodynamic parameters, and then aerodynamic force and state quantities are established together into an extended state, so that the aerodynamic parameter estimation problem can be transformed into a state estimation problem. Specifically, the aerodynamic parameters are modeled as the following random walk model:

[0010] θ t =θ t-1 +η t

[0011] Among them, η t is a random noise with zero mean. The extended state is further defined as The T in the above table represents the transposition operation. Using the newly defined extended state, the following new state evolution model can be established:

[0012]

[0013] in, represents the extended process noise.

[0014] A strategy model based on an outlier adaptive detection and removal strategy is provided for realizing adaptive detection and removal of outliers in measured values, including:

[0015] The measurement model for the aerodynamic parameter estimation problem is established as:

[0016] y t =h(x t ,θ t )+w t

[0017] Among them, y t Contains all measurements of the aircraft dynamic system, x t Contains the state of the aircraft dynamic system, including attitude angle, speed, altitude, etc., θ t Contains the aerodynamic parameters to be estimated, such as lift coefficient, drag coefficient, etc., w t is the noise composed of all sensor noises, which has a mean of 0 and a variance of the diagonal matrix R t Gaussian distribution of , h(·,·) is a function (linear or nonlinear) used to describe the relationship between the measured value and the state quantity and aerodynamic parameters.

[0018] Based on this measurement model, an adaptive outlier detection and removal strategy is used to obtain a measurement model that can adaptively detect and remove outliers, specifically:

[0019] For the observed value y t The i-th component introduces a binary indicator variable z it To characterize its properties, if y it is a valid observation value, then z it =1, otherwise y it is an outlier, then z it =0, that is:

[0020]

[0021] Among them, h i (·,·) is the i-th component of the function h(·,·). it is the effective observation value, i.e. z it =1, y it The likelihood function is σ ii,t is the diagonal matrix R t The i-th main diagonal element of it = 0, y it The likelihood function value of is a constant, so y t The likelihood function is unified as:

[0022]

[0023] Where M represents the observed value y t Dimension.

[0024] The indicator variable z it Modeled as a random variable following a Beta-Bernoulli distribution:

[0025]

[0026]

[0027] Among them, Beta(·,·) represents the beta function, e it and f it is the parameter of the Beta-Bernoulli distribution.

[0028] An extended state estimation method based on variational Bayesian estimation theory and a method for obtaining aerodynamic parameter estimation values ​​from the extended state are designed, including:

[0029] definition Then all unknown quantities involved in the aerodynamic parameter estimation problem can be obtained through the following maximum a posteriori probability estimation problem:

[0030]

[0031] The variational Bayesian inference method is used to approximate the solution:

[0032]

[0033] According to the VBI theory, the distribution of different factors is solved through the following sequential iterative process:

[0034]

[0035]

[0036]

[0037] Where k is the iteration index of the VBI inference process, is the total probability density function, Solved by the solution of Kalman smoothing theory, q k (z 1:T ) and q k (π 1:T ) Because of the relationship between the conjugate prior distribution, there is a closed solution; after a certain iterative process, the VBI process converges. Approximately a Gaussian distribution, use its expectation as the estimated value of the extended state, that is,

[0038]

[0039] Based on the estimated values ​​of the extended state, the estimated values ​​of the aerodynamic parameters can be estimated as

[0040]

[0041] The beneficial effect of the present invention is that the aerodynamic parameter estimation method proposed in the present invention can provide a robust estimation of aerodynamic parameters when the measured values ​​are disturbed by wild values, providing a guarantee for the establishment of a high-precision model of the aircraft. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 is the elevator input signal (unit: δ e / deg);

[0043] Figure 2 The response of the vehicle system to the elevator input (unit: α / deg). DETAILED DESCRIPTION

[0044] The present invention is described in detail below with reference to the accompanying drawings and simulation examples, and the identification of aerodynamic parameters of short-period longitudinal motion of an aircraft is taken as an example to demonstrate the practicability of the present invention.

[0045] A method for modeling aerodynamic parameters based on extended states is used to simplify the estimation process of aerodynamic parameters. The system equation for the short-period longitudinal motion of an aircraft is:

[0046]

[0047] Where α is the angle of attack; q is the pitch rate; δ e is the elevator input signal. Let the state of the system be x t =[α t ,q t ] T , the input is u t =d e,t , the continuous system can be obtained by discretizing it with sampling time △t

[0048] x t =Fx t-1 +Bu t +w t

[0049] in,

[0050]

[0051] Define the variables to be estimated Further define the extended state The expanded state equation can be described as

[0052]

[0053] Among them, f(·,·) is related to F, B, and u t The nonlinear function involved, is the augmented process noise function.

[0054] A strategy model based on the outlier adaptive detection and removal strategy is used to realize the adaptive detection and removal of outliers in the measured values. Assuming that the aircraft is equipped with an angle of attack sensor and a pitch angle sensor, the measurement equation for the aerodynamic parameter estimation problem is established as follows:

[0055]

[0056] Where H = diag[I2,O6] is a block diagonal matrix, where I2 is the identity matrix and O6 is an all-zero matrix; v t =[v α,t ,v p,t ] T is the measurement noise. Usually, the angle of attack sensor and pitch angle sensor will give wild values ​​due to intermittent failures. To simulate this scenario, a mixed Gaussian model is used to model the noise of these two sensors, namely

[0057]

[0058]

[0059] The goal of the aerodynamic parameter identification task of the aircraft is to operate the elevator δ e Excite the aircraft and according to the measured value y 1:T To estimate the aerodynamic parameters of the aircraft contained in F and B. Based on this measurement model, an adaptive outlier detection and removal strategy is used to obtain a measurement model that can adaptively detect and remove outliers. t The i-th component introduces a binary indicator variable z it To characterize its properties, if y it is a valid observation value, then z it =1, otherwise y it is an outlier, then z it =0, that is:

[0060]

[0061] Among them, h i (·,·) is the i-th component of the function h(·,·). In this case, h1(·,·)=α t , h2(·,·)=q t When y it is the effective observation value, i.e. z it=1, y it The likelihood function is σ ii,t is the diagonal matrix R t The i-th main diagonal element of it = 0, y it The likelihood function value of is a constant, so y t The likelihood function is unified as:

[0062]

[0063] In this case, M = 2 represents the observed value y t The indicator variable z it Modeled as a random variable following a Beta-Bernoulli distribution:

[0064]

[0065]

[0066] Among them, Beta(·,·) represents the beta function, e it and f it is the parameter of the Beta-Bernoulli distribution.

[0067] An extended state estimation method based on variational Bayesian estimation theory and a method for obtaining aerodynamic parameter estimates from the extended state. Definition Then all unknown quantities involved in the aerodynamic parameter estimation problem can be obtained through the following maximum a posteriori probability estimation problem:

[0068]

[0069] The variational Bayesian inference method is used to approximate the solution:

[0070]

[0071] According to the VBI theory, the distribution of different factors is solved through the following sequential iterative process:

[0072]

[0073]

[0074]

[0075] Where k is the iteration index of the VBI inference process, is the total probability density function, Solved by the solution of Kalman smoothing theory, q k (z 1:T) and q k (π 1:T ) Because of the relationship between the conjugate prior distribution, there is a closed solution; after a certain iterative process, the VBI process converges. Approximately a Gaussian distribution, use its expectation as the estimated value of the state, that is,

[0076]

[0077] Based on the estimated values ​​of the extended state, the estimated values ​​of the aerodynamic parameters can be estimated as

[0078]

[0079] Considering the flight altitude of 30,000ft and airspeed of 750fps, the aerodynamic parameters of the F-16 aircraft's longitudinal short-period motion are:

[0080]

[0081] Assume that the initial state of the aircraft is x0 = [0,0] T ,use Figure 1 The signal shown is used as the input signal of the elevator, and the response of the longitudinal short-period model is as follows Figure 2 The input signal is a combined input signal, including a double step signal, a "3-2-1-1" signal, and a "2-1-1" signal, which can fully excite each mode of the aircraft. In the simulation, the system process noise variance matrix Q t =0.01I2, the measurement noise variance of the two sensors without wild value is 0.05. The number of iterations of VBI in the method proposed in this scheme (denoted as VB-OD) is set to 15. The traditional aerodynamic parameter identification method based on Kalman smoothing algorithm and EM algorithm (denoted as KS-EM) is used as a comparison algorithm. The performance of the algorithm is evaluated by the mean square error obtained from the results of 1000 MC simulations, that is,

[0082]

[0083] Table 1 shows the NMSE values ​​of the aerodynamic parameter estimation results calculated by the two identification algorithms when λ=0.1 and α is 100, 200, and 300 respectively. As can be seen from the figure, the accuracy of the identification result given by VB-OD is higher than that of KS-EM, indicating that when solving the aerodynamic identification problem, the wild value detection and removal method proposed in the present invention can effectively solve the system identification problem when there are wild values ​​in the measured values. This preliminarily proves the effectiveness and feasibility of the robust aerodynamic parameter estimation method based on the wild value adaptive detection and removal strategy proposed in the present invention.

[0084] Table 1 NMSE values ​​of aerodynamic parameter estimation results calculated by two identification algorithms under different scenarios

[0085]

[0086] In summary, the present invention has developed a robust aerodynamic parameter estimation method based on outlier detection and removal strategy. The outlier self-detection and self-removal in the measured data are adaptively implemented to achieve accurate estimation of aerodynamic parameters. The simulation results verify the feasibility of the proposed robust aerodynamic data estimation scheme in a real flight environment.

Claims

1. A method for estimating aerodynamic parameters based on an outlier adaptive detection and removal strategy, characterized in that: The following steps are involved: S1. The state evolution model of aerodynamic parameter estimation problem is established as: x t =f(x t-1 ,θ)+v t Among them, x t Contains the state of the aircraft dynamic system, θ contains the aerodynamic parameters to be estimated, and v t The noise is composed of all sensor noises, which has a mean of 0 and a variance of the diagonal matrix Q t The Gaussian distribution of , the function f(·,·) is used to describe the evolution relationship of the state quantity; In order to estimate the aerodynamic parameters, a random walk model is first introduced for the aerodynamic parameters, and then the aerodynamic force and the state quantity are established together into an extended state, thereby transforming the aerodynamic parameter estimation problem into a state estimation problem; wherein, the aerodynamic parameters are modeled into the following random walk model: i t =θ t-1 +n t Among them, η t is random noise with zero mean; Define the extended state as The above table T represents the transposition operation; the following state evolution model is established: in, represents the extended process noise; S2. A strategy model based on an outlier adaptive detection and removal strategy is used to achieve adaptive detection and removal of outliers in measured values, specifically including: The measurement model for the aerodynamic parameter estimation problem is established as: y t =h(x t ,θ t )+w t Among them, y t Contains all measurements of the aircraft dynamic system, w t is the noise composed of all sensor noises, which has a mean of 0 and a variance of the diagonal matrix R t The Gaussian distribution of , the function h(·,·) is used to describe the relationship between the measured value and the state quantity and aerodynamic parameters; Based on the measurement model t , through the adaptive outlier detection and removal strategy, a measurement model that can adaptively detect and remove outliers is obtained, specifically: for the observed value y t The i-th component introduces a binary indicator variable z it To characterize its properties, if y it is a valid observation value, then z it =1, otherwise y it is an outlier, then z it =0, that is: Among them, h i (·,·) is the i-th component of the function h(·,·); when y it is the effective observation value, i.e. z it =1, y it The likelihood function is σ ii,t is the diagonal matrix R t The i-th main diagonal element of it = 0, y it The likelihood function value of is a constant, so y t The likelihood function is unified as: Where M represents the observed value y t Dimensions; The indicator variable z it Modeled as a random variable following a Beta-Bernoulli distribution: Among them, Beta(·,·) represents the beta function, e it and f it is the parameter of the Beta-Bernoulli distribution; S3. Definition and π t ={π it }, all unknown quantities involved in the aerodynamic parameter estimation problem are obtained through the following maximum a posteriori probability estimation problem: The variational Bayesian inference method is used to approximate the solution: According to the VBI theory, the distribution of different factors is solved through the following sequential iterative process: in, k is the iteration index of the VBI inference process, is the total probability density function, Solved by the solution of Kalman smoothing theory, q k (z 1:T ) and q k (π 1:T ) Because of the relationship between conjugate prior distributions, there are closed solutions; After the iteration process, the VBI process converges. Approximately a Gaussian distribution, use its expectation as the estimated value of the extended state, that is, Based on the estimated values ​​of the extended state, the estimated values ​​of the aerodynamic parameters are:

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