CN112528417B - Assessment method for semi-physical simulation of aircraft - Google Patents
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Abstract
The invention relates to an evaluation method of semi-physical simulation of an aircraft, belongs to the technical field of simulation evaluation, and solves the problem that the prior art cannot accurately evaluate the semi-physical simulation effect. The method comprises the following steps: acquiring simulation data of all uncertainty output variables; according to the simulation data, constructing a data distribution probability envelope of each uncertainty output variable, and further determining corresponding random uncertainty and probability uncertainty; the random uncertainty and the probability uncertainty are dimensionalized, and a comprehensive uncertainty vector of the whole aircraft semi-physical simulation is constructed; determining a weight coefficient of each element in the comprehensive uncertainty vector; according to the comprehensive uncertainty vector and the weight coefficient of each element in the comprehensive uncertainty vector, obtaining the comprehensive uncertainty value of the semi-physical simulation of the aircraft by weighted average; and determining whether the semi-physical simulation result of the aircraft is credible according to whether the comprehensive uncertainty measurement value is within a preset threshold range.
Description
Technical Field
The invention relates to the technical field of simulation evaluation, in particular to an evaluation method of semi-physical simulation of an aircraft.
Background
In the semi-physical simulation process of the aircraft, because simulation equipment such as a simulation turntable, a target simulator, a load simulator, an area array, an altimeter simulator and the like have errors, the accuracy of the whole simulation test is affected, and the confidence of a simulation result is further affected.
Currently, in the prior art, uncertainty of a semi-physical simulation system under the condition of no reference data is usually measured by adopting a standard deviation, but the standard deviation is sensitive to sample size, and has dimensions, uncertainty measurement results given by different sample sizes are quite different, so that it is inconvenient to judge whether a specific size is the same or the specific size is the best.
Aiming at the problem of uncertainty measurement of the semi-physical simulation system under the condition of no reference data, a comprehensive uncertainty measurement index capable of quantitatively describing key performance parameters of the semi-physical simulation system is lacking, the index is dimensionless, and a unified system-level uncertainty measurement result can be given.
Disclosure of Invention
In view of the above analysis, the embodiment of the invention aims to provide an evaluation method for semi-physical simulation of an aircraft, which is used for solving the problem that the prior art cannot accurately evaluate the semi-physical simulation effect.
In one aspect, an embodiment of the present invention provides a method for evaluating semi-physical simulation of an aircraft, including the following steps:
Acquiring simulation data of all uncertainty output variables in the semi-physical simulation of the aircraft;
According to the simulation data, constructing a data distribution probability envelope of each uncertainty output variable, and further determining the random uncertainty and probability uncertainty of each uncertainty output variable;
Carrying out dimensionality removal on the random uncertainty and the probability uncertainty of each uncertainty output variable to construct a comprehensive uncertainty vector of the whole aircraft semi-physical simulation;
determining the correlation coefficient of any two variables in all uncertainty output variables, establishing a correlation coefficient matrix, and further determining the weight coefficient of each element in the comprehensive uncertainty vector;
According to the comprehensive uncertainty vector and the weight coefficient of each element in the comprehensive uncertainty vector, obtaining the comprehensive uncertainty value of the semi-physical simulation of the aircraft by weighted average;
And judging whether the comprehensive uncertainty measurement value is within a preset threshold range, determining whether the semi-physical simulation result of the aircraft is credible, if so, judging that the semi-physical simulation result is credible, otherwise, judging that the semi-physical simulation result is not credible.
The beneficial effects of the technical scheme are as follows: the method can quantitatively describe whether the semi-physical simulation structure of the aircraft is credible or not through the comprehensive uncertainty measurement value, the index of the comprehensive uncertainty measurement value is dimensionless and normalized, and a unified system-level uncertainty measurement result can be given, so that the method can be used for improving the current semi-physical simulation test of the aircraft.
Based on a further improvement of the above method, the uncertainty output variable includes at least one of a landing point deviation, an aircraft attitude, an angle of attack, a sideslip angle, an aircraft position, an aircraft speed;
and obtaining simulation data of the uncertainty output variable through repeated aircraft semi-physical simulation under the same set test condition.
The beneficial effects of the further improved scheme are as follows: the main factors affecting the measurement of uncertainty of semi-physical simulation of the aircraft can be located.
Further, the constructing a data distribution probability envelope of each uncertainty output variable according to the simulation data includes:
For each uncertainty output variable x, the sample mean of its simulation data a= { a 1,a2,…,aM } is obtained by the following formula
Wherein M is the number of simulation data of the uncertainty output variable x, namely the sample size, and is also the test times;
Arranging the simulation data from small to large to obtain a section set B
B＝{B1,B2,…,BM-1}
＝{[a(1),a(2)],[a(2),a(3)],…,[a(M-1),a(M)]}
Wherein a (1) is the minimum value in the simulation data, and a (M) is the maximum value in the simulation data;
Each subinterval B j (j=1, 2, …, M-1) to in the interval set B is obtained by the following formula Euclidean distance of (2)
The above-mentioned materials are mixedNormalization, the trust probability m (B j) of B j is obtained from the normalization result θ j by the following formula
Wherein the method comprises the steps of
ξj＝1-θj
Performing data fitting according to the interval set B and the trust probability m (B j) to obtain a data distribution probability envelope g (x) of the uncertainty output variable;
Determining the upper bound of the probability envelope by the following formula Lower bound g (x)
Repeating the steps to sequentially construct the data distribution probability envelope of each uncertainty output variable.
The beneficial effects of the further improved scheme are as follows: the data distribution probability envelope of all uncertainty output variables can be objectively obtained.
Further, the determining the random uncertainty and the probability uncertainty for each uncertainty output variable includes:
from the data distribution probability envelope g (x) for each uncertainty output variable, the random uncertainty for that uncertainty output variable is obtained by the following equation Probability uncertainty/>
Where g k (x) is the data distribution probability envelope of the kth uncertainty output variable x,G k (x) is the upper bound and g k (x) is the lower bound.
The beneficial effects of the further improved scheme are as follows: from an area perspective, a random uncertainty and a cognitive uncertainty metric result for each uncertainty output variable are obtained.
Further, the step of performing dimensionality removal on the random uncertainty and the probability uncertainty of each uncertainty output variable to construct a comprehensive uncertainty vector of the whole aircraft semi-physical simulation comprises the following steps:
random uncertainty for each uncertainty output variable is determined by the following formula Probability uncertainty/>Performing dimensionalization
Dimensionless random uncertainty of all uncertainty output variables after dimensionality removalDimensionless probability uncertainty/>Establishing a random uncertainty metric matrix u a, and a cognitive uncertainty metric matrix u for aircraft semi-physical simulation by the following formula e
Wherein r is the number of uncertainty output variables;
According to the random uncertainty matrix u a and the cognitive uncertainty metric matrix u e of the aircraft semi-physical simulation, the comprehensive uncertainty vector u of the whole aircraft semi-physical simulation is obtained through the following formula
The beneficial effects of the further improved scheme are as follows: the normalization method based on the area uncertainty measurement provides possibility for the combination of the system uncertainty measurement results, and can help an operator to know the source of the maximum uncertainty of the system and lock specific uncertainty output variables.
Further, the determining the correlation coefficient of any two variables in all uncertainty output variables, and establishing a correlation coefficient matrix includes:
Acquiring simulation data of each uncertainty output variable with the data quantity of M;
For any two variables in all uncertainty output variables, arranging respective simulation data A 1、A2 from small to large to obtain an element rank order vector S corresponding to the A 1、A2 1、S2
A1＝{a1,a2,…,aM}
A2＝{b1,b2,…,bM}
In the method, in the process of the invention,Representing the order in which the i-th element in A 1 is arranged from small to large,/>Representing the order in which the i-th element in A 2 is arranged from small to large;
judging whether S 1、S2 are equal or not, if not, determining the correlation coefficients of the two variables by the following formula
Wherein the method comprises the steps of
If they are equal, the correlation coefficients of the two variables are determined by the following formula
Wherein the method comprises the steps of
In the method, in the process of the invention,For the number of identical elements in the ith order of the A 1 from small to large,/>The number of the same elements in the ith order of the arrangement from small to large for A 2;
Repeating the steps to sequentially obtain the correlation coefficients of any two variables in all the uncertainty output variables.
The beneficial effects of the further improved scheme are as follows: an effective calculation method of the correlation coefficient between the variables is limited, and a foundation is laid for the calculation of the weights between the variables.
Further, a correlation coefficient matrix ρ is established by the following formula
Where ρ i,j represents the correlation coefficient of the i-th uncertainty output variable and the j-th uncertainty output variable.
The beneficial effects of the further improved scheme are as follows: the correlation of the uncertainty output variables is effectively measured, the main factors influencing the uncertainty measurement of the system are defined, and a foundation is laid for the weight determination of each uncertainty output variable in the system.
Further, the determining the weight coefficient of each element in the integrated uncertainty vector includes:
the uncorrelated matrix θ is obtained from the correlation coefficient matrix ρ by the following formula
Wherein 1 is an all 1 matrix in r x r dimension;
All columns of the uncorrelated matrix θ are combined to obtain an uncorrelated coefficient row vector λ= [ λ 1λ2…λr ]
Normalizing the uncorrelated coefficient row vector by the following formula to obtain the weight coefficient of each element in the comprehensive uncertainty vector
Where r is the number of uncertainty output variables.
The beneficial effects of the further improved scheme are as follows: a data weight confirmation method based on data correlation is defined, and a foundation is laid for calculating the comprehensive uncertainty metric value of the system.
Further, the obtaining the comprehensive uncertainty measurement value of the aircraft semi-physical simulation according to the comprehensive uncertainty vector of the whole aircraft semi-physical simulation and the weight coefficient of each element of the comprehensive uncertainty vector comprises the following steps:
The comprehensive uncertainty measurement value of the aircraft semi-physical simulation is obtained by a weighted average method in the following formula
The beneficial effects of the further improved scheme are as follows: a system comprehensive uncertainty measurement method based on data correlation is defined, and the uncertainty of the whole system of the semi-physical simulation of the aircraft is objectively measured.
Further, the assessment method of the semi-physical simulation of the aircraft further comprises the following steps:
If the aircraft semi-physical simulation result is not reliable, sequencing all elements in the comprehensive uncertainty vector of the aircraft semi-physical simulation, and searching an uncertainty output variable corresponding to the largest element;
And determining an aircraft semi-physical simulation condition causing the uncertainty of the uncertainty output variable to be larger, correcting the aircraft semi-physical simulation condition, and acquiring simulation data of all the uncertainty output variables again until the reliability of the aircraft semi-physical simulation result is determined.
The beneficial effects of the further improved scheme are as follows: the method for improving the reliability (comprehensive uncertainty measurement) of the system is beneficial to users to obtain a reliable simulation result meeting actual demands.
In the invention, the technical schemes can be mutually combined to realize more preferable combination schemes. Additional features and advantages of the invention will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. The objectives and other advantages of the invention may be realized and attained by the structure particularly pointed out in the written description and drawings.
Drawings
The drawings are only for purposes of illustrating particular embodiments and are not to be construed as limiting the invention, like reference numerals being used to refer to like parts throughout the several views.
FIG. 1 is a schematic diagram showing the steps of an evaluation method for semi-physical simulation of an aircraft according to embodiment 1 of the present invention.
FIG. 2 is a schematic diagram of a probability envelope g (x) of data distribution of an uncertainty output variable x according to embodiment 2 of the present invention;
FIG. 3 is a diagram illustrating upper and lower bounds of a probability envelope according to embodiment 2 of the present invention;
FIG. 4 shows the response at the 0.5 minute point of example 2g k (x) of the present invention.
Detailed Description
The following detailed description of preferred embodiments of the application is made in connection with the accompanying drawings, which form a part hereof, and together with the description of the embodiments of the application, are used to explain the principles of the application and are not intended to limit the scope of the application.
Example 1
The invention discloses an evaluation method of semi-physical simulation of an aircraft, which is shown in fig. 1 and comprises the following steps:
s1, acquiring simulation data of all uncertainty output variables in semi-physical simulation of an aircraft;
S2, constructing a data distribution probability envelope of each uncertainty output variable according to the simulation data, and further determining the random uncertainty and the probability uncertainty of each uncertainty output variable;
S3, carrying out dimensionality removal on the random uncertainty and the probability uncertainty of each uncertainty output variable to construct a comprehensive uncertainty vector of the whole aircraft semi-physical simulation;
S4, determining correlation coefficients of any two variables in all uncertainty output variables, establishing a correlation coefficient matrix, and further determining a weight coefficient of each element in the comprehensive uncertainty vector;
s5, obtaining a comprehensive uncertainty measurement value of the semi-physical simulation of the aircraft by weighted average according to the comprehensive uncertainty vector and the weight coefficient of each element in the comprehensive uncertainty vector;
S6, judging whether the comprehensive uncertainty measurement value is within a preset threshold range, determining whether the semi-physical simulation result of the aircraft is credible, if so, judging that the semi-physical simulation result is credible, otherwise, judging that the semi-physical simulation result is not credible.
When the method is implemented, whether the simulation result is credible or not can be judged according to the comprehensive uncertainty measurement value, if not, the simulation conditions or the simulation model of the semi-physical simulation of the aircraft are adjusted, and the steps S1 to S6 are repeated again until the comprehensive uncertainty measurement value is within the range of a preset threshold value, and the credibility is judged. By the method, the current semi-physical simulation of the aircraft can be corrected.
Compared with the prior art, the method provided by the embodiment can quantitatively describe whether the semi-physical simulation structure of the aircraft is credible or not through the comprehensive uncertainty measurement value, the index of the comprehensive uncertainty measurement value is dimensionless, normalization is carried out, and a unified system-level uncertainty measurement result can be given.
Example 2
The optimization is performed on the basis of embodiment 1, and the uncertainty output variables in step S1 include at least one of landing point deviation, aircraft attitude, angle of attack, sideslip angle, aircraft position, aircraft speed, and the like.
Specifically, the landing point deviation is the deviation between the landing point position and the target position of the aircraft obtained by the semi-physical simulation test. The attitude of the aircraft comprises a pitch angle, a yaw angle, a roll angle and the like; aircraft position includes altitude, lateral, longitudinal position. For the sake of simple calculation, the attitude and the position of the aircraft at the landing point of each semi-physical simulation test can be taken.
And obtaining simulation data of all uncertainty output variables through repeated aircraft semi-physical simulation under the same set test condition. The simulation data are directly obtained through a semi-physical simulation test.
Preferably, the uncertainty output variable affecting the semi-physical simulation effect of the aircraft is the uncertainty of natural environment factors, simulation equipment, simulation models and the like. In order to measure the uncertainty of the semi-physical simulation system, an orthogonal/uniform test design method can be adopted to design a simulation test, so that simulation data of an uncertainty output variable can be obtained.
Preferably, step S2 constructs a data distribution probability envelope of each uncertainty output variable according to the simulation data, and further includes:
S21, for each uncertainty output variable x, obtaining a sample mean value of simulation data A= { a 1,a2,…,aM } of the uncertainty output variable x through the following formula
Where M is the number of simulation data of the uncertainty output variable x, and the sample size is also the number of trials.
S22, arranging the simulation data { a 1,a2,…,aM } from small to large to obtain a section set B
Where a (1) is the minimum value in the simulation data and a (M) is the maximum value in the simulation data.
S23. obtaining the sample mean value for each subinterval B j (j=1, 2, …, M-1) in interval set B by the following formulaEuclidean distance/>
S24, the following formula is adopted to carry out the above stepsNormalizing to obtain normalized result theta j
Based on the normalization result θ j, the trust probability m (B j) of B j is obtained by the following formula
Wherein the method comprises the steps of
ξj＝1-θj
S25, performing data fitting according to the interval set B and the trust probability m (B j) to obtain a data distribution probability envelope g (x) of the uncertainty output variable.
Alternatively, a best approximation may be used for data fitting, data points (a (j),m(Bj)), as shown in FIG. 2, such that any uncertainty output variable x falls within the envelope, with the uncertainty output variable x range on the abscissa and the confidence probability m on the ordinate (B j). The data fitting may also be performed using a least squares method, as will be appreciated by those skilled in the art.
S26, determining the upper bound of the probability envelope through the following formulaLower bound g (x), as shown in FIG. 3
S27, repeating the steps S21-S25, and sequentially constructing the data distribution probability envelope of each uncertainty output variable.
Preferably, in step S2, the determining the random uncertainty and the probability uncertainty of each uncertainty output variable further includes:
s28, obtaining random uncertainty of each uncertainty output variable according to the data distribution probability envelope g (x) of the uncertainty output variable through the following formula Probability uncertainty (cognitive uncertainty)/>
Where g k (x) is the data distribution probability envelope of the kth uncertainty output variable x,G k (x) is the upper bound and g k (x) is the lower bound.
When the random uncertainty of the uncertainty output variable is small, the dispersibility of g k (x) is reduced, and the area measurement index is obtainedAnd also decreases; when the uncertainty output variable has no random uncertainty, g k (x) is degenerated to a vertical line (fixed value), at which time the area metric/>Conversely, as the random uncertainty of the uncertainty output variable increases, the integration area will also increase, resulting in an area metric/>And also increases. Thus,/>The random uncertainty of the uncertainty output variable (response quantity) can be reflected well.
Preferably, step S3 includes performing dimensionality reduction on the random uncertainty and the probability uncertainty of each uncertainty output variable to construct a comprehensive uncertainty vector of the whole aircraft semi-physical simulation, and further includes:
s31, random uncertainty of each uncertainty output variable is calculated by the following formula Probability uncertaintyPerforming dimensionalization
Wherein P k is the rectangular area surrounded by the response quantity (average value mu k for normal distribution) corresponding to the 0.5 quantile of g k (x) and the coordinate axis, as shown in FIG. 4.
When g k (x) is normally distributed,The value range of (C) is [0,1]. In the case where the cumulative probability distribution of the response is not normal, the analysis is significantly complicated, but in general, the nondimensional measurement index is not required because the purpose of nondimensional measurement is to facilitate unified operation between different response amountsStrictly included between [0,1], but only if the difference in the different dimensions can be eliminated.
S32, outputting the dimensionless random uncertainty of the variable according to all uncertainty after dimensionality removalDimensionless probability uncertainty/>Establishing a random uncertainty metric matrix u a, and a cognitive uncertainty metric matrix u for aircraft semi-physical simulation by the following formula e
Where r is the number of uncertainty output variables.
S33, obtaining a comprehensive uncertainty vector u of the whole aircraft semi-physical simulation according to the random uncertainty matrix u a and the cognitive uncertainty metric matrix u e of the aircraft semi-physical simulation through the following formula
The comprehensive uncertainty vector comprises two items of random uncertainty (upper corner marked as a) and cognitive uncertainty (upper corner marked as e), the uncertainty of each uncertainty output variable also comprises the two items, and the comprehensive uncertainty vector is the combination of the uncertainties of all uncertainty output variables of the semi-physical simulation of the aircraft.
For r responses, in order to obtain a unified metric, a weighted average of r uncertainty metrics is required. And determining the weight of the contribution degree of different response amounts to the uncertainty of the system through the correlation coefficient. If all the response amounts are completely uncorrelated, the weights are the same, and the uncertainty measurement values of the r response amounts are directly averaged; otherwise, the higher the degree of correlation, the lower the assigned weight.
Preferably, determining the correlation coefficient of any two variables in all the uncertainty output variables in step S4, and establishing a correlation coefficient matrix further includes:
s41, acquiring simulation data of all uncertainty output variables with data quantity M.
S42, for any two variables in all uncertainty output variables, arranging respective simulation data A 1、A2 from small to large to obtain an element rank order vector S corresponding to the A 1、A2 1、S2
A1＝{a1,a2,…,aM}
A2＝{b1,b2,…,bM} (11)
In the method, in the process of the invention,Representing the order in which the i-th element in A 1 is arranged from small to large,/>Representing the order in which the i-th element in a 2 is arranged from small to large.
S43, judging whether the two are equal or not, if not, determining by the following formula
Determining the correlation coefficient of the two variables
Wherein the method comprises the steps of
If they are equal, the correlation coefficients of the two variables are determined by the following formula
Wherein the method comprises the steps of
In the method, in the process of the invention,For the number of identical elements in the ith order of the A 1 from small to large,/>The number of the same elements in the ith order of the arrangement from small to large for A 2; for example, assume a 1 = {2.5,2.8,2.8,2.8,3.5,3.5,3.8}, then
Correlation coefficientThe value of (2) is between-1 and +1, i.e./>The properties are as follows:
When (when) When two variables are positively correlated, the value of a 2 increases (decreases) as the value of a 1 increases (decreases).
When two variables are represented as being inversely related, i.e., the value of a 2 decreases (increases) when the value of a 1 increases (decreases).
When (when)When two variables are indicated as fully correlated.
When (when)When the two variables are related, the two variables are not related.
When (when)When the two variables are related to a certain degree, the closer the |ρ A,B | is to 1, the closer the linear relationship between the two variables is; /(I)The closer to 0, the weaker the linear correlation of the two variables.
S44, repeating the steps to obtain the correlation coefficients of any two variables in all uncertainty output variables in sequence.
Preferably, step S4 establishes the correlation coefficient matrix ρ by the following formula
Where ρ i,j represents the correlation coefficient of the i-th uncertainty output variable and the j-th uncertainty output variable.
Preferably, the determining the weight coefficient of each element in the integrated uncertainty vector u in step S4 further includes:
S45, obtaining an uncorrelated matrix theta according to a correlation coefficient matrix rho through the following formula
Wherein 1 is an all 1 matrix in r x r dimension;
s46, combining all columns of the uncorrelated matrix theta to obtain an uncorrelated coefficient row vector lambda= [ lambda 1λ2…λr ]
S47, normalizing the uncorrelated coefficient row vector by the following formula to obtain the weight coefficient of each element in the comprehensive uncertainty vector
Where r is the number of uncertainty output variables.
Preferably, step S5 obtains a comprehensive uncertainty metric value of the aircraft semi-physical simulation according to the comprehensive uncertainty vector of the entire aircraft semi-physical simulation and the weight coefficient of each element of the comprehensive uncertainty vector, and further includes:
S51, obtaining the comprehensive uncertainty measurement value of the semi-physical simulation of the aircraft by a weighted average method in the following formula
The operator can know the total uncertainty level (comprehensive uncertainty measurement) of the semi-physical simulation system, and can grasp the source of uncertainty through random and cognitive uncertainty values.
Preferably, the method further comprises:
S7, if the aircraft semi-physical simulation result is not reliable, sequencing all elements in the comprehensive uncertainty vector of the aircraft semi-physical simulation, and searching an uncertainty output variable corresponding to the largest element;
s8, determining an aircraft semi-physical simulation condition causing the uncertainty of the uncertainty output variable to be larger, correcting the aircraft semi-physical simulation condition, and acquiring simulation data of all the uncertainty output variables again until the reliability of the aircraft semi-physical simulation result is judged.
If the uncertainty output variable corresponding to the maximum element is the landing point deviation, and the aircraft semi-physical simulation condition causing the landing point deviation to be larger is determined to be mainly that the angular velocity error model of the detection device is inaccurate through the mechanism analysis of the aircraft, the angular velocity error model can be improved, and the test is carried out again until the reliability of the aircraft semi-physical simulation result is determined.
And after the judgment of the credibility, correcting the semi-physical simulation condition of the aircraft until the credibility is achieved. Based on the size ordering of uncertainty measurement results of each data, determining main uncertainty output (uncertainty output variable) affecting the uncertainty of the system, and accordingly, providing a system reliability improvement scheme based on an uncertainty key link.
On the basis of determining main uncertainty output affecting uncertainty, the test data of a corresponding entity of the link model is obtained, and the error and other models of the link are corrected by adopting methods such as approximate modeling, so that the uncertainty of the link is reduced, the reliability of the link model is improved, and the reliability of a system is improved.
Compared with the method in embodiment 1, the comprehensive uncertainty measurement value provided by the embodiment is an area-based data uncertainty measurement method, and a normalization method of each output variable is provided, so that uncertainty measurement of a system is supported, and the problem that the normalization result meanings of various uncertainty measurement methods in the existing system are inconsistent is solved.
Those skilled in the art will appreciate that all or part of the flow of the methods of the embodiments described above may be accomplished by way of a computer program to instruct associated hardware, where the program may be stored on a computer readable storage medium. Wherein the computer readable storage medium is a magnetic disk, an optical disk, a read-only memory or a random access memory, etc.
The present invention is not limited to the above-mentioned embodiments, and any changes or substitutions that can be easily understood by those skilled in the art within the technical scope of the present invention are intended to be included in the scope of the present invention.
Claims (3)
1. The assessment method of the semi-physical simulation of the aircraft is characterized by comprising the following steps of:
Acquiring simulation data of all uncertainty output variables in the semi-physical simulation of the aircraft;
According to the simulation data, constructing a data distribution probability envelope of each uncertainty output variable, and further determining the random uncertainty and probability uncertainty of each uncertainty output variable;
The constructing a data distribution probability envelope of each uncertainty output variable according to the simulation data further comprises:
For each uncertainty output variable x, the sample mean of its simulation data a= { a 1,a2,L,aM } is obtained by the following formula
Wherein M is the number of simulation data of the uncertainty output variable x;
Arranging the simulation data from small to large to obtain a section set B
B＝{B1,B2,L,BM-1}
＝{[a(1),a(2)],[a(2),a(3)],L,[a(M-1),a(M)]}
Wherein a (1) is the minimum value in the simulation data, and a (M) is the maximum value in the simulation data;
Each subinterval B j (j=1, 2, l, m-1) to in the interval set B is obtained by the following formula Euclidean distance/>
The above-mentioned materials are mixedNormalization, the trust probability m (B j) of B j is obtained from the normalization result θ j by the following formula
Wherein the method comprises the steps of
ξj＝1-θj
Performing data fitting according to the interval set B and the trust probability m (B j) to obtain a data distribution probability envelope g (x) of the uncertainty output variable;
Determining the upper bound of the probability envelope by the following formula Lower bound g (x)
Repeating the steps to sequentially construct the data distribution probability envelope of each uncertainty output variable;
The determining the random uncertainty and the probability uncertainty for each uncertainty output variable further comprises:
from the data distribution probability envelope g (x) for each uncertainty output variable, the random uncertainty for that uncertainty output variable is obtained by the following equation Probability uncertainty/>
Where g k (x) is the data distribution probability envelope of the kth uncertainty output variable x,G k (x) is the upper bound and g k (x) is the lower bound;
The method comprises the steps of carrying out dimensionalization on the random uncertainty and the probability uncertainty of each uncertainty output variable to construct a comprehensive uncertainty vector of the whole aircraft semi-physical simulation, and further comprising the following steps:
random uncertainty for each uncertainty output variable is determined by the following formula Probability uncertainty/>Performing dimensionalization
Dimensionless random uncertainty of all uncertainty output variables after dimensionality removalDimensionless probability uncertainty/>Establishing a random uncertainty metric matrix u a, and a cognitive uncertainty metric matrix u for aircraft semi-physical simulation by the following formula e
Wherein r is the number of uncertainty output variables;
According to the random uncertainty matrix u a and the cognitive uncertainty metric matrix u e of the aircraft semi-physical simulation, the comprehensive uncertainty vector u of the whole aircraft semi-physical simulation is obtained through the following formula
The determining the correlation coefficient of any two variables in all uncertainty output variables, establishing a correlation coefficient matrix, further comprises:
Acquiring simulation data of each uncertainty output variable with the data quantity of M;
For any two variables in all uncertainty output variables, arranging respective simulation data A 1、A2 from small to large to obtain an element rank order vector S corresponding to the A 1、A2 1、S2
A1＝{a1,a2,L,aM}
A2＝{b1,b2,L,bM}
In the method, in the process of the invention,Representing the order in which the i-th element in A 1 is arranged from small to large,/>Representing the order in which the i-th element in A 2 is arranged from small to large;
judging whether S 1、S2 are equal or not, if not, determining the correlation coefficients of the two variables by the following formula
Wherein the method comprises the steps of
If they are equal, the correlation coefficients of the two variables are determined by the following formula
Wherein the method comprises the steps of
In the method, in the process of the invention,For the number of identical elements in the ith order of the A 1 from small to large,/>The number of the same elements in the ith order of the arrangement from small to large for A 2;
repeating the steps to sequentially obtain the correlation coefficients of any two variables in all uncertainty output variables;
the correlation coefficient matrix ρ is established by the following formula
Where ρ i,j represents the correlation coefficient of the i-th uncertainty output variable and the j-th uncertainty output variable;
The determining the weight coefficient of each element in the integrated uncertainty vector further comprises:
the uncorrelated matrix θ is obtained from the correlation coefficient matrix ρ by the following formula
Wherein 1 is an all 1 matrix in r x r dimension;
All columns of the uncorrelated matrix θ are combined to obtain an uncorrelated coefficient row vector λ= [ λ 1 λ2 L λr ]
Normalizing the uncorrelated coefficient row vector by the following formula to obtain the weight coefficient of each element in the comprehensive uncertainty vector
Wherein r is the number of uncertainty output variables;
The method for obtaining the comprehensive uncertainty measurement value of the aircraft semi-physical simulation according to the comprehensive uncertainty vector of the whole aircraft semi-physical simulation and the weight coefficient of each element of the comprehensive uncertainty vector further comprises the following steps:
The comprehensive uncertainty measurement value of the aircraft semi-physical simulation is obtained by a weighted average method in the following formula
Carrying out dimensionality removal on the random uncertainty and the probability uncertainty of each uncertainty output variable to construct a comprehensive uncertainty vector of the whole aircraft semi-physical simulation;
determining the correlation coefficient of any two variables in all uncertainty output variables, establishing a correlation coefficient matrix, and further determining the weight coefficient of each element in the comprehensive uncertainty vector;
According to the comprehensive uncertainty vector and the weight coefficient of each element in the comprehensive uncertainty vector, obtaining the comprehensive uncertainty value of the semi-physical simulation of the aircraft by weighted average;
and determining whether the semi-physical simulation result of the aircraft is credible according to whether the comprehensive uncertainty measurement value is in a preset threshold range, if so, judging that the semi-physical simulation result is credible, otherwise, judging that the semi-physical simulation result is not credible.
2. The method of assessing a semi-physical simulation of an aircraft according to claim 1, wherein said uncertainty output variables include at least one of landing point deviation, aircraft attitude, angle of attack, sideslip angle, aircraft position, aircraft speed;
and obtaining simulation data of the uncertainty output variable through repeated aircraft semi-physical simulation under the same set test condition.
3. Method for the assessment of semi-physical simulation of an aircraft according to one of claims 1 to 2, characterized in that it further comprises the steps of:
If the aircraft semi-physical simulation result is not reliable, sequencing all elements in the comprehensive uncertainty vector of the aircraft semi-physical simulation, and searching an uncertainty output variable corresponding to the largest element;
And determining an aircraft semi-physical simulation condition causing the uncertainty of the uncertainty output variable to be larger, correcting the aircraft semi-physical simulation condition, and acquiring simulation data of all the uncertainty output variables again until the reliability of the aircraft semi-physical simulation result is determined.
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