Mach number correction method based on aerodynamic parameter identification

Abstract

The present application belongs to the technical field of aviation. Disclosed is a Mach number correction method based on aerodynamic parameter identification. The method comprises: taking wind tunnel test data as an initial value of an aerodynamic parameter to be identified, and identifying the aerodynamic parameter by using test flight data under a determined flight state point; performing linear regression processing on the aerodynamic parameter identified under the current Mach number, and compiling statistics to obtain a final aerodynamic parameter identification result corresponding to the Mach number; and performing parameter expansion and correction on the identified aerodynamic parameter that has been subjected to linear regression. In the present application, full-envelope aerodynamic characteristic parameters are obtained according to the above Mach number expansion and correction method and from aerodynamic data that has been subjected to parameter identification, and are regressed to an aerodynamic model; and simulation verification results are compared with test flight test data, and the results show that consistency with real flight data can be better realized according to the Mach number expansion and correction method in the present application.

Description

A Mach number correction method based on aerodynamic parameter identification Technical Field

[0001] The invention belongs to the field of aviation technology and relates to a method for correcting Mach number, and in particular to a method for correcting Mach number based on aerodynamic parameter identification. Background Art

[0002] To improve the accuracy of aerodynamic models, obtaining basic aerodynamic parameters of aircraft models from flight test data using aerodynamic parameter identification is currently the most common and effective method. However, due to limitations in flight test data sample size and the flight envelope, flight test state points are limited. When using flight test data for aerodynamic parameter identification, aerodynamic parameters can only be obtained within a specific linear range of Mach numbers, and aerodynamic parameters across the entire envelope cannot be obtained from flight test data. Therefore, to obtain aerodynamic parameters across the entire envelope, a Mach number correction extension method suitable for aerodynamic parameter identification is needed.

[0003] Summary of the Invention

[0004] In order to solve the above problems, the present invention proposes a Mach number correction method based on aerodynamic parameter identification. After parameter identification and regression of limited test flight sample points, the aerodynamic parameters are expanded to the full envelope range using the Mach number correction method, thereby providing accurate full envelope aerodynamic parameters for the flight performance simulation model.

[0005] The technical solutions of the present invention are as follows:

[0006] A Mach number correction method based on aerodynamic parameter identification includes the following steps:

[0007] Step 1: Using wind tunnel test data as the initial values ​​of the aerodynamic parameters to be identified, the aerodynamic parameters are identified using the test flight data at a certain flight state point;

[0008] Step 2: Perform linear regression on the aerodynamic parameters identified in step 1 at the current Mach number, and calculate the final aerodynamic parameter results corresponding to the Mach number;

[0009] Step 3: Parameter expansion and correction of the identified aerodynamic parameters after linear regression are performed as follows:

[0010] a) Within the linear range, the identified aerodynamic parameters are expanded using linear interpolation at different flap angles and Mach numbers;

[0011] b) In the nonlinear range, the incremental method is used, retaining the first-order and second-order coefficients and only calculating the constant part of the translation method, that is, incremental superposition is performed at the inflection point of linear and nonlinear.

[0012] Furthermore, in the above step 3, some small nonlinear correction quantities of the second order or above are not directly involved in the identification, and are manually adjusted after the identification.

[0013] Furthermore, in the above step 3, the nonlinear correction amount caused by the large angle of attack and sideslip angle is not directly involved in the identification, and manual adjustment is performed after the identification.

[0014] Furthermore, in the above step 2, linear regression is used to remove values ​​with large deviations, and according to the law of change of the original aerodynamic derivative Mach number, the linear regression method is used to statistically calculate the final identification aerodynamic parameter results corresponding to the Mach number.

[0015] Furthermore, in step 1, the maximum likelihood method is used to identify the aerodynamic parameters.

[0016] Furthermore, the wind tunnel test data is used as the initial value of the aerodynamic parameters to be identified. Since the aerodynamic derivatives are three-dimensional interpolation tables of different altitudes, Mach numbers Ma and flap angles, according to the aircraft's airspeed Ma(t), flap Flag(t), and altitude history H(t) during the flight test data, the initial values ​​of the parameters are obtained by linear interpolation from the wind tunnel data table: θ1(t) = f(Ma(t) Flag(t) H(t)) (1)

[0017] The time-domain identification method based on state space is used to identify the aerodynamic parameters in real time in stages.

[0018] Furthermore, in step 1, the state space-based time domain identification method specifically includes using the aircraft small perturbation linear equation, as shown below:

[0019] Where: A, B, C, D matrices represent the aircraft's stability derivative and control derivative matrices, which contain unknown parameters that need to be identified; u represents the aircraft's input matrix, which includes the aircraft's control surface deflection angle δ e , δ a , δ r , and throttle deflection δ p ; x represents the state variable of the n-dimensional aircraft; y and z represent the observation vector and actual measurement vector of the m-dimensional aircraft respectively; v represents the noise in the aircraft observation variable, that is, the difference between the measurement vector z and the observation vector y.

[0020] Furthermore, the maximum likelihood principle is used to process the parameters in the aircraft's small perturbation linear equation:

[0021] Where θ represents the unknown parameter values ​​contained in matrices A, B, C, and D, and R is the covariance matrix of the measurement noise. When the statistical value of the measurement noise is unknown, the optimal estimate of R is used, that is, J is used to find the extreme value of R:

[0022] J finds the extreme value of θ and obtains the optimal estimate of the parameter to be identified θ; the Newton-Raphson algorithm is used to solve it, and the formula is as follows

[0023] θ k represents the estimated value of the parameter to be identified in the kth iteration calculation; Dθ is the parameter update value; θ k+1 represents the estimated value of the k+1th iteration;

[0024] Represents the sensitivity of the observed value to the parameters to be identified, where h, l = 1, 2, ... p. The dynamic state equations of the aircraft are transformed to θ k Taking the derivative, we get the sensitivity equations, |(J k+1 -J k ) / J k |≤0.01 (6)

[0025] Use θ k+1 Update θ k Iterate until the likelihood criterion function J satisfies formula (6), and the obtained θ converges, which is the desired parameter value.

[0026] The beneficial effects of the present invention are as follows:

[0027] The aerodynamic data after parameter identification are corrected and extended according to the above-mentioned Mach number method to obtain the full envelope aerodynamic characteristic parameters, which are then regressed to the aerodynamic model, as shown in Figure 5. The simulation verification results are compared with the flight test data. The results show that the Mach number correction and extension method in the present invention can achieve good consistency with the actual flight data. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following is a brief introduction to the drawings required for use in the embodiments. It should be understood that the following drawings only show certain embodiments of the present invention and should not be regarded as limiting the scope. For ordinary technicians in this field, other relevant drawings can be obtained based on these drawings without creative work.

[0029] Figure 1 shows the discrete points of the identified aerodynamic parameters.

[0030] Figure 2 C Lα Comparison chart of wind tunnel test results and Mach number correction results after identification.

[0031] Figure 3 shows C mδe Comparison chart of wind tunnel test results and Mach number correction results after identification.

[0032] Figure 4 shows C yβ Comparison chart of wind tunnel test results and Mach number correction results after identification.

[0033] Figure 5 is a comparison of the simulation results after Mach number correction and the test flight data. DETAILED DESCRIPTION

[0034] This section is an embodiment of the present invention, which is used to explain and illustrate the technical solution of the present invention. In the absence of conflict, the embodiments of the present invention and the features in the embodiments can be combined with each other.

[0035] In the description of the present invention, it should be understood that the terms "center", "longitudinal", "lateral", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside" and the like indicate directions or positional relationships based on the orientations or positional relationships in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or case referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as limiting the present invention. In addition, the terms "first", "second" and the like are used for descriptive purposes only, and cannot be understood as indicating or implying relative importance or implying the number of technical features indicated. Thus, features defined as "first", "second" and the like may explicitly or implicitly include more of the features. In the description of the present invention, unless otherwise specified, "multiple" means two or more.

[0036] In the description of the present invention, it should be noted that, unless otherwise expressly specified or limited, the terms "mounted," "connected," and "connected" should be interpreted broadly. For example, they may refer to fixed, detachable, or integrated connections; mechanical or point connections; direct or indirect connections through an intermediary; and internal communication between two components. Those skilled in the art will understand the specific meanings of the above terms in the present invention based on specific circumstances.

[0037] Example 1:

[0038] A Mach number correction method based on aerodynamic parameter identification includes the following steps:

[0039] Step 1: Using wind tunnel test data as the initial values ​​of the aerodynamic parameters to be identified, the aerodynamic parameters are identified using the test flight data at a certain flight state point;

[0040] Step 2: Perform linear regression on the aerodynamic parameters identified in step 1 at the current Mach number, and calculate the final aerodynamic parameter results corresponding to the Mach number;

[0041] Step three: perform parameter expansion and correction on the identified aerodynamic parameters after linear regression.

[0042] (1) Aerodynamic parameter identification

[0043] The aerodynamic parameter identification algorithm mainly adopts the maximum likelihood method, and the wind tunnel test data is used as the initial value of the aerodynamic parameters to be identified. Since the aerodynamic derivative is a three-dimensional interpolation table of different altitudes, Mach numbers Ma and flap angles, according to the aircraft's airspeed Ma(t), flap Flag(t), and altitude history H(t) during the flight test data, the initial value of the parameter is obtained by linear interpolation from the wind tunnel data table: θ1(t)=f(Ma(t) Flag(t) H(t)) (1)

[0044] The time domain identification method based on state space is used to identify the aerodynamic parameters in real time in stages. The linear equation of the aircraft small disturbance is as follows:

[0045] Where:

[0046] The A, B, C, and D matrices represent the aircraft's stability derivative and control derivative matrices, which contain unknown parameters that need to be identified; u represents the aircraft's input matrix, which includes the aircraft's control surface deflection angle δ e , δ a , δ r , and throttle deflection δ p ; x represents the state variable of the n-dimensional aircraft; y and z represent the observation vector and actual measurement vector of the m-dimensional aircraft respectively; v represents the noise in the aircraft observation variable, that is, the difference between the measurement vector z and the observation vector y.

[0047] Using the maximum likelihood principle:

[0048] Where θ represents the unknown parameter values ​​contained in matrices A, B, C, and D, and R is the covariance matrix of the measurement noise. When the statistical value of the measurement noise is unknown, the optimal estimate of R is used, that is, J is used to find the extreme value of R:

[0049] J finds the extreme value of θ and obtains the optimal estimate of the parameter to be identified θ. The Newton-Raphson algorithm is used to solve the problem. The formula is as follows

[0050] θ k represents the estimated value of the parameter to be identified in the kth iteration calculation; Dθ is the parameter update value; θ k+1 Indicates the estimated value of the k+1th iteration.

[0051] Represents the sensitivity of the observed value to the parameters to be identified, where h, l = 1, 2, ... p. The dynamic state equations of the aircraft are transformed to θ k By taking the derivative, we can get the sensitivity equations. k+1 Update θ k Iterate until the likelihood criterion function J satisfies Equation (6), and the obtained θ converges, which is the desired parameter value. k+1 -J k ) / J k |≤0.01 (6)

[0052] (2) Parametric regression statistics

[0053] Since atmospheric disturbances and measurement noise cannot be accurately estimated, the aerodynamic parameters obtained after identification of different sorties, different times, and different subjects are not the same. In fact, they are discrete point diagrams with certain rules as shown in Figure 1. They need to be processed by linear regression to eliminate values ​​with large deviations. According to the law of change of the original aerodynamic derivative Mach number, the final identification aerodynamic parameter results corresponding to the Mach number are statistically calculated through linear regression and other methods.

[0054] 1) Mach number correction

[0055] Since the flight test state points are limited and cannot cover the entire flight envelope, in order to obtain more accurate aerodynamic parameters within the entire flight envelope, it is necessary to expand and correct the identified aerodynamic parameters after linear regression. The methods and principles used for parameter expansion are as follows:

[0056] a) Within the linear range, the identified aerodynamic parameters are expanded using linear interpolation at different flap angles and Mach numbers;

[0057] b) In the nonlinear range, the incremental method is used, retaining the first-order and second-order coefficients and only calculating the constant part of the translation method, that is, incremental superposition is performed at the inflection point of linear and nonlinear;

[0058] c) Some small quantities above the second order, as well as nonlinear correction quantities caused by large angles of attack and sideslip angles, are not directly involved in the identification and are manually adjusted after identification.

[0059] According to the above method, the identified aerodynamic parameters are corrected and expanded according to the Mach number. The results of some aerodynamic parameters after correction and expansion are shown in Figure 2-4.

[0060] Example 2:

[0061] The specific implementation steps of the present invention are shown in the figure:

[0062] Step 1: Perform aerodynamic parameter identification based on flight test data. Select high-quality flight test data and use aerodynamic parameter identification software to perform aerodynamic parameter identification.

[0063] Step 2: Perform regression statistics on the identified sample points

[0064] The output error method is used to perform regression statistics on the identified sample points. The statistical results are shown in Table 1.

[0065] Table 1 Regression statistical results

[0066] C Dmin Minimum drag coefficient, CLα is the derivative of lift with respect to angle of attack α, Cmδe is the derivative of pitching moment with respect to elevator deflection angle;

[0067] Step 3: Perform Mach number correction and expansion on the regressed aerodynamic parameters

[0068] 1) Within the linear range, the identified aerodynamic parameters are expanded using linear interpolation at different flap angles and Mach numbers.

[0069] Table 2 Correction expansion within the linear range

[0070] 2) In the nonlinear range, the incremental method is used to retain the first-order and second-order coefficients and only calculate the constant part of the translation.

[0071] Table 3 Correction and expansion of parameters within the nonlinear range

[0072] 3) After identifying some small quantities of the second order and above, as well as nonlinear correction quantities caused by large angles of attack and sideslip angles, manual parameter adjustment is performed.

[0073] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, but the scope of protection of the present invention is not limited thereto. Any technician familiar with the field can easily think of various equivalent modifications or replacements within the technical scope disclosed by the present invention, and these modifications or replacements should all be covered by the scope of protection of the present invention.

Claims

1. A Mach number correction method based on aerodynamic parameter identification, characterized in that: The following steps are involved: Step 1: Using wind tunnel test data as the initial values ​​of the aerodynamic parameters to be identified, and using the test flight data at a certain flight state point to identify the aerodynamic parameters; Step 2: Perform linear regression processing on the aerodynamic parameters identified in step 1 at the current Mach number, and calculate the final identification aerodynamic parameter results corresponding to the Mach number; Step 3: Parameter expansion and correction of the identified aerodynamic parameters after linear regression are performed as follows: a) Within the linear range, the identified aerodynamic parameters are expanded using linear interpolation at different flap angles and different Mach numbers; b) Within the nonlinear range, the incremental method is used, retaining the first-order and second-order coefficients and only calculating the constant part. That is, incremental superposition is performed at the inflection point of linear and nonlinear.

2. The Mach number correction method based on aerodynamic parameter identification according to claim 1 is characterized in that: In the above step three, some small nonlinear correction quantities of the second order or above are not directly involved in the identification, and are manually adjusted after the identification.

3. The Mach number correction method based on aerodynamic parameter identification according to claim 1 is characterized in that: In the above step three, the nonlinear correction caused by the large angle of attack and sideslip angle is not directly involved in the identification, and manual adjustment is performed after the identification.

4. The Mach number correction method based on aerodynamic parameter identification according to claim 1 is characterized in that: In the above step 2, linear regression is used to remove the values ​​with large deviations, and according to the law of change of the original aerodynamic derivative Mach number, the linear regression method is used to statistically calculate the final identification aerodynamic parameter results corresponding to the Mach number.

5. The Mach number correction method based on aerodynamic parameter identification according to claim 1, characterized in that: In step 1, the maximum likelihood method is used to identify the aerodynamic parameters.

6. The Mach number correction method based on aerodynamic parameter identification according to claim 5 is characterized in that: The wind tunnel test data is used as the initial value of the aerodynamic parameters to be identified. Since the aerodynamic derivative is a three-dimensional interpolation table of different altitudes, Mach numbers Ma and flap angles, according to the aircraft's airspeed Ma(t), flap Flag(t), and altitude history H(t) during the flight test data, the initial value of the parameter is obtained by linear interpolation from the wind tunnel data table: θ1(t) = f(Ma(t) Flag(t) H(t)) (1) The aerodynamic parameters are identified in real time in stages using a time-domain identification method based on state space.

7. The Mach number correction method based on aerodynamic parameter identification according to claim 6 is characterized in that: In step 1, the time domain identification method based on state space specifically includes using the aircraft small disturbance linear equation, as follows: Where: A, B, C, D matrices represent the aircraft's stability derivative and control derivative matrices, which contain unknown parameters that need to be identified; u represents the aircraft's input matrix, which includes the aircraft's control surface deflection angle δ e , δ a , δ r , and throttle deflection δ p ; x represents the state variable of the n-dimensional aircraft; y and z represent the observation vector and the actual measurement vector of the m-dimensional aircraft respectively; v represents the noise in the aircraft observation variable, that is, the difference between the measurement vector z and the observation vector y.

8. The Mach number correction method based on aerodynamic parameter identification according to claim 7, characterized in that: The maximum likelihood principle is used to process the parameters in the linear equation of small disturbance of the aircraft: Where θ represents the unknown parameter values ​​contained in matrices A, B, C, and D, and R is the covariance matrix of the measurement noise. When the statistical value of the measurement noise is unknown, the optimal estimate of R is used, that is, J is used to find the extreme value of R: J finds the extreme value of θ and obtains the optimal estimate of the parameter θ to be identified; the Newton-Raphson algorithm is used to solve it, and the formula is as follows θ k represents the estimated value of the parameter to be identified in the kth iteration calculation; Dθ is the parameter update value; θ k+1 represents the estimated value of the k+1th iteration; represents the sensitivity of the observed value to the parameter to be identified, where h,l=1,2,...p. k Taking the derivative, we get the sensitivity equations, |(J k+1 -J k ) / J k |≤0.01 (6) Use θ k+1 Update θ k Iterate until the likelihood criterion function J satisfies equation (6), then the obtained θ converges, which is the desired parameter value.

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