Method for calculating distance-average coefficient related to landing parameters of shipboard aircraft

Abstract

The invention belongs to the technical field of shipboard aircraft landing gear ship surface load calculation, and particularly relates to a shipboard aircraft landing gear ship surface load calculation method, which comprises the following steps: obtaining an average value, a standard deviation and a skewness coefficient in shipboard aircraft landing gear sinking speed distribution, and calculating an override probability of Pearson III type distribution through a gamma function; obtaining an integral point tp of an override probability of Pearson III-type distribution, and replacing the standard gamma distribution function through the integral point tp to obtain a distance-average coefficient algebraic formula; and substituting the integral point tp into an average separation coefficient algebraic formula, solving a gamma probability distribution inverse function to obtain an average separation coefficient # imgabs0 #, performing parameter replacement on a probability formula to obtain an algebraic formula of the average separation coefficient on the basis of the existing calculation of the maximum value of the landing and sinking speed of the airplane, and finally solving the average separation coefficient through Matlab tool software to obtain the maximum value of the landing and sinking speed of the airplane. And programming integral operation is not needed, so that the calculation speed is improved, and the learning cost is reduced.

Description

Technical Field

[0001] The present application belongs to the technical field of calculation of carrier-based aircraft landing gear deck loads, and in particular relates to a method for calculating a deviation coefficient related to carrier-based aircraft landing parameters. Background Art

[0002] In GJB67.4A-2008, the multivariate distribution chapter of landing impact requires that the sinking velocity distribution conforms to the Pearson III distribution; and the Pearson III distribution function is mainly determined by the mean, standard deviation, and skewness coefficient. If the skewness coefficient is 0, then the deviation coefficient can be determined according to the normal distribution, and then the distribution value is calculated by the mean, standard deviation, and deviation coefficient. However, if the skewness coefficient is not 0, then how to determine the corresponding deviation coefficient becomes the key to determining the landing parameters.

[0003] In the paper "Method for Determining the Maximum Aircraft Landing Sinking Speed" (Li Bo et al.) in the first issue of "Journal of Applied Mechanics" (March 2008), the Pearson III distribution was analyzed. Finally, the gamma function representation of the Pearson III distribution was given, and the final deviation coefficient calculation result was obtained through programming integral operation.

[0004] The final gamma function representation of the Pearson III distribution is as follows:

[0005]

[0006] The final numerical solution of the deviation coefficient фp is obtained through programming integration; this method requires the use of programming software to integrate the given 0 to the assumed distribution domain, and when the given exceedance probability is finally obtained, the corresponding integral upper limit can replace the deviation coefficient value. This method is the only paper that proposes the Pearson III distribution deviation coefficient, but its inconvenience is reflected in the need for programming operations, and the integral density of the integration interval will also affect the accuracy of the numerical solution.

[0007] Therefore, how to improve the convenience of calculating the deviation coefficient related to carrier-based aircraft landing parameters is a problem that needs to be solved. Summary of the invention

[0008] The purpose of the present application is to provide a method for calculating a deviation coefficient related to carrier-based aircraft landing parameters, so as to solve the problem of inconvenience in calculating the deviation coefficient related to carrier-based aircraft landing parameters.

[0009] The technical solution of the present application is: a method for calculating a deviation coefficient related to carrier-based aircraft landing parameters, comprising:

[0010] The mean, standard deviation and skewness coefficient of the carrier-based aircraft landing gear sinking speed distribution are obtained, and the exceedance probability of the Pearson III distribution is calculated by the gamma function;

[0011] Get the integral point t of the exceedance probability of the Pearson type III distribution p , through the integration point t p By permuting the standard gamma distribution function, we can obtain the algebraic formula of the deviation coefficient;

[0012] The integration point t p Substitute into the algebraic formula of the deviation coefficient and solve the inverse function of the gamma probability distribution to obtain the deviation coefficient

[0013] Preferably, the specific calculation steps of the algebraic formula of the deviation coefficient are:

[0014] The exceedance probability formula for the standard gamma function distribution is:

[0015]

[0016] To obtain the exceedance probability calculation formula of the Pearson III distribution, we only need to set β·(x-α0)=t to convert it into the standard gamma distribution exceedance probability formula.

[0017] Therefore, for the integration point t p , let t p =β·(x p -α0), substitute the exceedance probability calculation formula of Pearson III distribution into the conformity formula to obtain:

[0018]

[0019] because To find the dissociation coefficient The standard deviation is taken as 1; we get:

[0020]

[0021] After conversion, the algebraic formula of the deviation coefficient is:

[0022]

[0023] Preferably, the integration point t p Found by integrating the standard gamma distribution.

[0024] Preferably, the calculation formula of the inverse gamma distribution integral is: p =gaminv(1-p, α, 1), where gaminv is the inverse gamma distribution calculation.

[0025] Preferably, the calculation formula for the exceedance probability of the Pearson III distribution is:

[0026]

[0027] Where: is the mean; σ is the standard deviation; C s is the skewness coefficient.

[0028] Preferably, the integration point t p The inverse gamma distribution integral is obtained by directly calculating it by inputting relevant instructions in Matlab.

[0029] The method for calculating the deviation coefficient related to the carrier-based aircraft landing parameters of the present application, based on the existing maximum value calculation of the aircraft landing sinking speed, obtains the algebraic formula of the deviation coefficient by replacing the parameters of the probability formula, and finally solves the deviation coefficient through Matlab tool software, without the need for programming integral operation, thereby improving the calculation speed and reducing the learning cost. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] In order to more clearly illustrate the technical solution provided by the present application, the following is a brief introduction to the accompanying drawings. Obviously, the accompanying drawings described below are only some embodiments of the present application.

[0031] Figure 1 This is a schematic diagram of the overall process of this application DETAILED DESCRIPTION

[0032] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0033] A method for calculating the deviation coefficient related to carrier-based aircraft landing parameters, such as Figure 1 As shown, the following steps are included:

[0034] Step S100, obtaining the mean value, standard deviation and skewness coefficient of the carrier aircraft landing gear sinking speed distribution, and calculating the exceedance probability of the Pearson III distribution by the gamma function, the calculation formula is:

[0035]

[0036] in:

[0037] Where: is the mean; σ is the standard deviation; C s is the skewness coefficient.

[0038] Step S200, obtaining the integral point t of the exceedance probability of the Pearson III distribution p , through the integration point t p By permuting the standard gamma distribution function, we can obtain the algebraic formula of the coefficient of deviation from the mean.

[0039] The specific calculation steps of the algebraic formula of the deviation coefficient are as follows:

[0040] The exceedance probability formula for the standard gamma function distribution is:

[0041]

[0042] To obtain the exceedance probability calculation formula of the Pearson III distribution, we only need to set β·(x-α0)=t, and then convert it into the standard gamma distribution exceedance probability formula (2).

[0043] Therefore, for the integration point t p , let t p =β·(x p -α0), substitute the exceedance probability calculation formula of Pearson III distribution into the conformity formula to obtain:

[0044]

[0045] because To find the dissociation coefficient The standard deviation is taken as 1. We get:

[0046]

[0047] After conversion, the algebraic formula of the deviation coefficient is:

[0048]

[0049] Preferably, the integration point t p It can be obtained by integrating the standard gamma distribution.

[0050] Step S300: set the integral point t p Substitute into the algebraic formula of the deviation coefficient and solve the inverse function of the gamma probability distribution to obtain the deviation coefficient Preferably, the integration point t p The inverse gamma distribution integral is directly calculated by inputting relevant instructions in Matlab, and its calculation formula is: p =gaminv(1-p, α, 1), where gaminv is the inverse gamma distribution calculation. No need to perform integral calculations through programming, greatly improving the calculation efficiency.

[0051] In summary, based on the existing calculation of the maximum landing sinking speed of an aircraft, this application obtains the algebraic formula of the deviation coefficient by replacing the parameters of the probability formula, and finally solves the deviation coefficient through Matlab tool software, without the need for programming integral operations, thereby improving the calculation speed and reducing the learning cost.

[0052] As a specific implementation, the calculation is performed in a specific manner as follows:

[0053] Taking GJB67.4A-2008 as an example, it is required that during normal takeoff and landing of carrier-based aircraft, the maximum landing sinking speed should be solved according to the univariate distribution method;

[0054] Requirements: The exceedance probability is 0.0001 and the skewness coefficient is 0.5;

[0055] From this we can know: P = 0.0001, Cs = 0.5;

[0056] In Matlabs, enter: tp = gaminv (1-0.0001, 16, 1);

[0057] We get: tp = 35.2856;

[0058] Substituting this value into formula (3), we can quickly get

[0059] On this basis, the GJB specification gives the average sinking speed of 1.0973 and the standard deviation of 0.4054 in this case, thus obtaining the maximum sinking speed:

[0060]

[0061] This sinking speed value is consistent with the maximum sinking speed for land-based aircraft landing given in the national military standard.

[0062] This method can solve any non-zero skewness coefficient and any deviation from the mean coefficient under any combination of exceedance probability. When the skewness coefficient is zero, the standard normal distribution method can be used to solve it.

[0063] Finally, it should be noted that: the drawings of the embodiments disclosed in the present invention only involve structures related to the embodiments disclosed in the present invention, and other structures can refer to the general design. In the absence of conflict, the same embodiment and different embodiments of the present invention can be combined with each other;

[0064] Finally: The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for calculating deviation coefficients related to carrier-based aircraft landing parameters, characterized in that: include: The mean, standard deviation and skewness coefficient of the carrier-based aircraft landing gear sinking speed distribution are obtained, and the exceedance probability of the Pearson III distribution is calculated by the gamma function; Obtain the integral point tp of the exceedance probability of the Pearson III distribution, permute the standard gamma distribution function through the integral point tp, and obtain the algebraic formula of the deviation coefficient; The integration point t p Substitute into the algebraic formula of the deviation coefficient and solve the inverse function of the gamma probability distribution to obtain the deviation coefficient 2. The method for calculating the deviation coefficient related to carrier-based aircraft landing parameters according to claim 1, characterized in that: The specific calculation steps of the algebraic formula of the deviation coefficient are: The exceedance probability formula for the standard gamma function distribution is: To obtain the exceedance probability calculation formula of the Pearson III distribution, we only need to set β·(x-α0)=t to convert it into the standard gamma distribution exceedance probability formula. Therefore, for the integration point t p , let t p =t·(x p -α0), substitute the exceedance probability calculation formula of Pearson III distribution into the conformity formula to obtain: because To find the dissociation coefficient The standard deviation is taken as 1; get: After conversion, the algebraic formula of the deviation coefficient is:

3. The method for calculating the deviation coefficient related to carrier-based aircraft landing parameters according to claim 2, characterized in that: The integral point tp is obtained by integrating the standard gamma distribution.

4. The method for calculating the deviation coefficient related to carrier-based aircraft landing parameters according to claim 3, characterized in that: The calculation formula of the inverse gamma distribution integral is: p =gaminv(1-p, α, 1), where gaminv is the inverse gamma distribution calculation.

5. The method for calculating the deviation coefficient related to carrier-based aircraft landing parameters according to claim 1, characterized in that: The calculation formula for the exceedance probability of the Pearson type III distribution is: Where: is the mean; σ is the standard deviation; c s is the skewness coefficient.

6. The method for calculating the deviation coefficient related to carrier-based aircraft landing parameters according to claim 1, characterized in that: The integration point t p The inverse gamma distribution integral is obtained by directly calculating it by inputting relevant instructions in Matlab.

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