CN112528417A - Aircraft semi-physical simulation evaluation method - Google Patents

Aircraft semi-physical simulation evaluation method Download PDF

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CN112528417A
CN112528417A CN202011507215.4A CN202011507215A CN112528417A CN 112528417 A CN112528417 A CN 112528417A CN 202011507215 A CN202011507215 A CN 202011507215A CN 112528417 A CN112528417 A CN 112528417A
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耿化品
闫英
佟佳慧
锁斌
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Beijing Research Institute of Mechanical and Electrical Technology
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Abstract

The invention relates to an evaluation method for aircraft semi-physical simulation, belongs to the technical field of simulation evaluation, and solves the problem that the semi-physical simulation effect cannot be accurately evaluated in the prior art. The method comprises the following steps: acquiring simulation data of all uncertain output variables; according to the simulation data, constructing a data distribution probability envelope of each uncertain output variable, and further determining corresponding random uncertainty and probability uncertainty; de-dimensionalizing the random uncertainty and the probability uncertainty, and constructing a comprehensive uncertainty vector of the whole aircraft semi-physical simulation; determining a weight coefficient for each element in the integrated uncertainty vector; according to the comprehensive uncertainty vector and the weight coefficient of each element in the comprehensive uncertainty vector, carrying out weighted average to obtain a comprehensive uncertainty metric value of the semi-physical simulation of the aircraft; and determining whether the semi-physical simulation result of the aircraft is credible according to whether the comprehensive uncertainty metric value is within a preset threshold range.

Description

Aircraft semi-physical simulation evaluation method
Technical Field
The invention relates to the technical field of simulation evaluation, in particular to an evaluation method for aircraft semi-physical simulation.
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 precision of the whole simulation test is influenced, and further the confidence coefficient of a simulation result is influenced.
Currently, in the prior art, the 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 the sample size and has dimensions, uncertainty measurement results given by different sample sizes are very different, and it is inconvenient to judge how much the uncertainty is good or how bad.
Aiming at the uncertainty measurement problem of the semi-physical simulation system under the condition of no reference data, a comprehensive uncertainty measurement index capable of describing key performance parameters of the semi-physical simulation system in a quantitative mode is lacked, the index is dimensionless and can provide a unified system-level uncertainty measurement result.
Disclosure of Invention
In view of the foregoing analysis, the embodiment of the present invention aims to provide an aircraft semi-physical simulation evaluation method, so as to solve the problem that the prior art cannot accurately evaluate the semi-physical simulation effect.
In one aspect, an embodiment of the present invention provides an aircraft semi-physical simulation assessment method, including the following steps:
acquiring simulation data of all uncertain output variables in the semi-physical simulation of the aircraft;
according to the simulation data, constructing a data distribution probability envelope of each uncertain output variable, and further determining the random uncertainty and the probability uncertainty of each uncertain output variable;
de-dimensionalizing 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 uncertain 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, carrying out weighted average to obtain a comprehensive uncertainty metric value of the semi-physical simulation of the aircraft;
and judging whether the comprehensive uncertainty metric value is within a preset threshold range, determining whether the semi-physical simulation result of the aircraft is credible, judging the aircraft to be credible if the comprehensive uncertainty metric value is within the preset threshold range, and otherwise, judging the aircraft to be credible.
The beneficial effects of the above technical scheme are as follows: whether the semi-physical simulation structure of the aircraft is credible can be quantitatively described through the comprehensive uncertainty metric value, the index of the comprehensive uncertainty metric value is dimensionless and normalized, a unified system-level uncertainty metric result can be given, and the method can be used for improving the current semi-physical simulation test of the aircraft.
In a further improvement of the above method, the uncertainty output variable comprises at least one of a drop point deviation, an aircraft attitude, an angle of attack, a sideslip angle, an aircraft position, an aircraft speed;
and obtaining simulation data of the uncertain output variables through multiple times of aircraft semi-physical simulation under the same set test condition.
The beneficial effects of the above further improved scheme are: the main factors influencing the uncertainty measurement of the semi-physical simulation of the aircraft can be positioned.
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, its simulation data a ═ a is obtained by the following formula1,a2,…,aMMean of samples of } sample
Figure BDA0002845282150000031
Figure BDA0002845282150000032
In the formula, M is the number of simulation data of an uncertain output variable x, namely the sample amount, and is the test times;
arranging the simulation data from small to large to obtain an interval set B
B＝{B1,B2,…,BM-1}
＝{[a(1),a(2)],[a(2),a(3)],…,[a(M-1),a(M)]}
In the formula, a(1)Is the minimum value in the simulation data, a(M)Is the maximum value in the simulation data;
obtaining each subinterval B in the interval set B by the following formulaj(j-1, 2, …, M-1) to
Figure BDA00028452821500000310
Euclidean distance of
Figure BDA0002845282150000033
Figure BDA0002845282150000034
Mixing the above
Figure BDA0002845282150000035
Normalization is performed according to the normalization result thetajB is obtained by the following formulajConfidence probability m (B)j)
Figure BDA0002845282150000036
Wherein
Figure BDA0002845282150000037
ξj＝1-θj
According to the aboveInterval set B and confidence probability m (B)j) Carrying out data fitting to obtain a data distribution probability envelope g (x) of the uncertain output variable;
determining an upper bound of the probability envelope by the following formula
Figure BDA0002845282150000038
Lower boundg(x)
Figure BDA0002845282150000039
And repeating the steps, and sequentially constructing the data distribution probability envelope of each uncertain output variable.
The beneficial effects of the above further improved scheme are: the data distribution probability envelopes of all the uncertainty output variables can be objectively obtained.
Further, the determining the random uncertainty and the probability uncertainty of each uncertainty output variable comprises:
according to the data distribution probability envelope g (x) of each uncertainty output variable, the random uncertainty of the uncertainty output variable is obtained by the following formula
Figure BDA0002845282150000041
Uncertainty of probability
Figure BDA0002845282150000042
Figure BDA0002845282150000043
Figure BDA0002845282150000044
In the formula, gk(x) The probability envelope of the data distribution for the kth uncertainty output variable x,
Figure BDA0002845282150000045
in order to achieve the upper bound,g k(x) Is the lower bound.
The beneficial effects of the above further improved scheme are: and acquiring the random uncertainty and cognitive uncertainty measurement result of each uncertainty output variable from the aspect of area.
Further, the de-dimensionalizing 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 includes:
random uncertainty for each uncertainty output variable by the following formula
Figure BDA0002845282150000046
Uncertainty of probability
Figure BDA0002845282150000047
Go on to descale
Figure BDA0002845282150000048
Dimensionless random uncertainty based on all uncertainty output variables after dimensioning
Figure BDA0002845282150000051
Dimensionless probability uncertainty
Figure BDA0002845282150000052
Establishing a random uncertainty measurement matrix u of the semi-physical simulation of the aircraft by the following formulaaAnd a cognitive uncertainty metric matrix ue
Figure BDA0002845282150000053
Figure BDA0002845282150000054
In the formula, r is the number of uncertain output variables;
according to the random uncertainty matrix u of the semi-physical simulation of the aircraftaAnd a cognitive uncertainty metric matrix ueObtaining the comprehensive uncertainty vector u of the semi-physical simulation of the whole aircraft by the following formula
Figure BDA0002845282150000055
The beneficial effects of the above further improved scheme are: a normalization method based on area uncertainty measurement is provided, possibility is provided for integration of system uncertainty measurement results, and an operator can be helped to know the source of the maximum uncertainty of the system and lock specific uncertainty output variables.
Further, the determining the correlation coefficients of any two variables in all the uncertainty output variables and establishing a correlation coefficient matrix includes:
acquiring simulation data of each uncertain output variable with data quantity M;
for any two variables of all the uncertain output variables, the simulation data A of each variable is1、A2Arranged from small to large to obtain the A1、A2Corresponding element rank vector S1、S2
Figure BDA0002845282150000056
Figure BDA0002845282150000057
A1＝{a1,a2,…,aM}
A2＝{b1,b2,…,bM}
In the formula (I), the compound is shown in the specification,
Figure BDA0002845282150000058
is represented by A1The ith element in the sequence from small to large,
Figure BDA0002845282150000059
is represented by A2The order of the ith element from small to large;
judgment S1、S2Whether they are equal to each other, and if they are not equal to each other, determining the correlation coefficient of the two variables by the following formula
Figure BDA0002845282150000061
Figure BDA0002845282150000062
Wherein
Figure BDA0002845282150000063
If they are equal, the correlation coefficient of the two variables is determined by the following formula
Figure BDA0002845282150000064
Figure BDA0002845282150000065
Wherein
Figure BDA0002845282150000066
In the formula (I), the compound is shown in the specification,
Figure BDA0002845282150000067
is A1The number of the same elements in the ith order from small to large,
Figure BDA0002845282150000068
is A2The number of the same elements in the ith order from small to large;
and repeating the steps to sequentially obtain the correlation coefficients of any two variables in all the uncertain output variables.
The beneficial effects of the above further improved scheme are: an effective calculation method of the correlation coefficient between the variables is limited, and a foundation is laid for the calculation of the weight between the variables.
Further, a correlation coefficient matrix ρ is established by the following formula
Figure BDA0002845282150000071
Wherein | ρ |i,jAnd | represents a correlation coefficient of the ith uncertainty output variable and the jth uncertainty output variable.
The beneficial effects of the above further improved scheme are: the method effectively measures the correlation of the uncertain output variables, defines the main factors influencing the uncertainty measurement of the system, and lays a foundation for determining the weight of each uncertain output variable in the system.
Further, the determining a weight coefficient of each element in the integrated uncertainty vector includes:
from the correlation coefficient matrix ρ, the uncorrelated matrix θ is obtained by the following formula
Figure BDA0002845282150000072
In the formula, 1 is a full 1 matrix of r × r dimensions;
all columns of the uncorrelated matrix theta are combined to obtain uncorrelated coefficient row vectors lambda ═ lambda1λ2…λr]
Figure BDA0002845282150000073
Normalizing the row vectors of the uncorrelated coefficients by the following formula to obtain the weight coefficient of each element in the comprehensive uncertainty vector
Figure BDA0002845282150000074
Figure BDA0002845282150000075
In the formula, r is the number of uncertainty output variables.
The beneficial effects of the above further improved scheme are: a data weight confirmation method based on data correlation is limited, and a foundation is laid for the calculation of the comprehensive uncertainty metric value of the system.
Further, the obtaining of the comprehensive uncertainty metric value of the semi-physical simulation of the aircraft according to the comprehensive uncertainty vector of the whole semi-physical simulation of the aircraft and the weight coefficient of each element of the comprehensive uncertainty vector includes:
the comprehensive uncertainty measurement value of the semi-physical simulation of the aircraft is obtained by a weighted average method in the following formula
Figure BDA0002845282150000081
Figure BDA0002845282150000082
The beneficial effects of the above further improved scheme are: a system comprehensive uncertainty measurement method based on data correlation is defined, and the uncertainty of the semi-physical simulation overall system of the aircraft is objectively measured.
Further, the evaluation method for the semi-physical simulation of the aircraft further comprises the following steps:
if the aircraft semi-physical simulation result is not credible, 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;
determining the semi-physical simulation condition of the aircraft causing the uncertainty of the uncertain output variable to be larger, correcting the semi-physical simulation condition of the aircraft, and acquiring the simulation data of all the uncertain output variables again until the semi-physical simulation result of the aircraft is judged to be credible.
The beneficial effects of the above further improved scheme are: the method for improving the system reliability (comprehensive uncertainty metric) is provided, and a user can obtain a credible simulation result meeting the actual requirement.
In the invention, the technical schemes can be combined with each other 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 will 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, wherein like reference numerals are used to designate like parts throughout.
Fig. 1 is a schematic step diagram 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 data distribution probability envelope g (x) of an uncertainty output variable x in embodiment 2 of the present invention;
FIG. 3 is a schematic diagram of the upper and lower bounds of a probability envelope in embodiment 2 of the present invention;
FIG. 4 shows example 2g of the present inventionk(x) 0.5 quantile point of (a).
Detailed Description
The accompanying drawings, which are incorporated in and constitute a part of this application, illustrate preferred embodiments of the invention and together with the description, serve to explain the principles of the invention and not to limit the scope of the invention.
Example 1
The invention discloses an evaluation method of aircraft semi-physical simulation, which comprises the following steps as shown in figure 1:
s1, acquiring simulation data of all uncertain output variables in semi-physical simulation of an aircraft;
s2, constructing a data distribution probability envelope of each uncertain output variable according to the simulation data, and further determining the random uncertainty and the probability uncertainty of each uncertain output variable;
s3, de-dimensionalizing the random uncertainty and the probability uncertainty of each uncertain 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 uncertain 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 metric 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;
and S6, judging whether the comprehensive uncertainty metric value is within a preset threshold range, determining whether the semi-physical simulation result of the aircraft is credible, judging the aircraft to be credible if the comprehensive uncertainty metric value is within the preset threshold range, and otherwise, judging the aircraft to be credible.
During implementation, whether the simulation result is credible or not can be judged according to the comprehensive uncertainty metric value, if the simulation result is not credible, the simulation condition or the simulation model of the aircraft semi-physical simulation is adjusted, and the steps S1-S6 are repeated again until the comprehensive uncertainty metric value is within the preset threshold value range and the judgment is credible. By the method, the existing semi-physical simulation of the aircraft can be modified.
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 by integrating the uncertainty metric value, the index of the integrated uncertainty metric value is dimensionless and normalized, and a uniform system-level uncertainty metric result can be given.
Example 2
Optimization is performed on the basis of embodiment 1, and the uncertainty output variables in step S1 include at least one of a drop point deviation, an aircraft attitude, an attack angle, a sideslip angle, an aircraft position, an aircraft speed, and the like.
Specifically, the landing point deviation is a deviation between the landing point position of the aircraft and the target position obtained through a semi-physical simulation test. The aircraft attitude comprises a pitch angle, a yaw angle, a roll angle and the like; aircraft positions include altitude, lateral, longitudinal position. For simple calculation, the aircraft attitude and the aircraft position at the landing point of each semi-physical simulation test can be taken.
And obtaining simulation data of all uncertain output variables through multiple times of aircraft semi-physical simulation under the same set test condition. The simulation data are directly obtained through a semi-physical simulation test.
Preferably, the uncertain output variables influencing the semi-physical simulation effect of the aircraft are the self-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 and obtain simulation data of an uncertain output variable.
Preferably, step S2 is to construct 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, its simulation data a ═ a is obtained by the following formula1,a2,…,aMMean of samples of } sample
Figure BDA0002845282150000111
Figure BDA0002845282150000112
In the formula, M is the number of simulation data of the uncertainty output variable x, and the sample size is also the number of tests.
S22, enabling the simulation data { a1,a2,…,aMArrange from small to large to obtain an interval set B
Figure BDA0002845282150000113
In the formula, a(1)Is the minimum value in the simulation data, a(M)Is the maximum value in the simulation data.
S23, obtaining each subinterval B in the interval set B through the following formulaj(j-1, 2, …, M-1) to sample mean
Figure BDA0002845282150000114
Euclidean distance of
Figure BDA0002845282150000115
Figure BDA0002845282150000116
S24, the above steps are carried out through the following formula
Figure BDA0002845282150000117
Normalizing to obtain a normalized result thetaj
Figure BDA0002845282150000121
According to the normalization result thetajB is obtained by the following formulajConfidence probability m (B)j)
Figure BDA0002845282150000122
Wherein
ξj＝1-θj
S25, according to the interval set B and the trust probability m (B)j) And performing data fitting to obtain a data distribution probability envelope g (x) of the uncertainty output variable.
Alternatively, a best approximation may be used for data fitting, with data points (a)(j)，m(Bj) As shown in fig. 2, such that any uncertainty output variable x falls within the envelope, with uncertainty output variable x range on the abscissa and confidence probability m (B) on the ordinatej). 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 by the following formula
Figure BDA0002845282150000123
Lower boundg(x) As shown in FIG. 3
Figure BDA0002845282150000124
S27, repeating the steps S21-S25, and sequentially constructing the data distribution probability envelope of each uncertain output variable.
Preferably, in step S2, the determining the random uncertainty and the probability uncertainty of each uncertainty output variable further comprises:
s28, according to the data distribution probability envelope g (x) of each uncertainty output variable, the random uncertainty of the uncertainty output variable is obtained through the following formula
Figure BDA0002845282150000125
Probability uncertainty (cognitive uncertainty)
Figure BDA0002845282150000126
Figure BDA0002845282150000131
Figure BDA0002845282150000132
In the formula, gk(x) The probability envelope of the data distribution for the kth uncertainty output variable x,
Figure BDA0002845282150000133
in order to achieve the upper bound,g k(x) Is the lower bound.
When the random uncertainty of the uncertainty output variable is small, gk(x) The dispersion of (A) is reduced, and the area metric index is reduced
Figure BDA0002845282150000134
And also decreases therewith; when the uncertainty output variable has no random uncertainty, gk(x) Degenerates to a vertical line (constant value), at which time the area metric index
Figure BDA0002845282150000135
Conversely, as the random uncertainty of the uncertainty output variable increases, the integration region will also increase, resulting in an area metric index
Figure BDA0002845282150000136
And also increases. Therefore, the temperature of the molten metal is controlled,
Figure BDA0002845282150000137
the random uncertainty of the uncertainty output variable (response) can be better reflected.
Preferably, in step S3, de-dimensionalizing 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, further includes:
s31, the random uncertainty of each uncertainty output variable is determined by the following formula
Figure BDA0002845282150000138
Uncertainty of probability
Figure BDA0002845282150000139
Go on to descale
Figure BDA00028452821500001310
In the formula, PkIs gk(x) 0.5 quantile Point of (1) (mean value μ for the normal distribution)k) The rectangular area enclosed with the coordinate axes is shown in fig. 4.
When g isk(x) In the case of a normal distribution, the distribution,
Figure BDA00028452821500001311
has a value range of [0,1 ]]. Although the cumulative probability distribution of the response is very complicated to analyze, it is generally the case that the nondimensionalized indicator is not required to be uniformly computed among different responses because the purpose of nondimensionalizing the uncertainty metric is to facilitate uniform computation among different responses
Figure BDA0002845282150000141
Strictly comprised in [0,1 ]]But only to eliminate differences in different dimensions.
S32, according to the dimensionless random uncertainty of all uncertainty output variables after dimension removal
Figure BDA0002845282150000142
Dimensionless probability uncertainty
Figure BDA0002845282150000143
Establishing a random uncertainty measurement matrix u of the semi-physical simulation of the aircraft by the following formulaaAnd a cognitive uncertainty metric matrix ue
Figure BDA0002845282150000144
Figure BDA0002845282150000145
In the formula, r is the number of uncertainty output variables.
S33, according to the random uncertainty matrix u of the semi-physical simulation of the aircraftaAnd a cognitive uncertainty metric matrix ueObtaining the comprehensive uncertainty vector u of the semi-physical simulation of the whole aircraft by the following formula
Figure BDA0002845282150000146
The integrated uncertainty vector comprises two items, namely random uncertainty (upper angle marked as a) and cognitive uncertainty (upper angle marked as e), and the uncertainty of each uncertain output variable also comprises the two items, and the integrated uncertainty vector is the integration of the uncertainties of all uncertain output variables of the semi-physical simulation of the aircraft.
For r response quantities, in order to obtain a uniform metric index, r uncertainty metric values need to be weighted and averaged. The weights of the degrees of contribution of the different responses to the system uncertainty are determined by the correlation coefficients. If all the response quantities are completely irrelevant, the weights are the same, and the uncertainty metric values of the r response quantities are directly averaged; otherwise, the higher the correlation degree of the response, the lower the assigned weight.
Preferably, the step S4 of determining correlation coefficients of any two variables of all the uncertainty output variables and establishing a correlation coefficient matrix further includes:
s41, acquiring simulation data of each uncertain output variable with M data quantity.
S42, regarding any two variables in all uncertain output variables, respectively simulating data A of the two variables1、A2Arranged from small to large to obtain the A1、A2Corresponding element rank vector S1、S2
Figure BDA0002845282150000151
Figure BDA0002845282150000152
A1＝{a1,a2,…,aM}
A2＝{b1,b2,…,bM} (11)
In the formula (I), the compound is shown in the specification,
Figure BDA0002845282150000153
is represented by A1The ith element in the sequence from small to large,
Figure BDA0002845282150000154
is represented by A2The ith element in the sequence from small to large.
S43, judging S1、S2Whether the two are equal or not, if the two are not equal, the determination is made by the following formula
Determining the correlation coefficient of the two variables
Figure BDA0002845282150000155
Figure BDA0002845282150000156
Wherein
Figure BDA0002845282150000157
If they are equal, the correlation coefficient of the two variables is determined by the following formula
Figure BDA0002845282150000158
Figure BDA0002845282150000159
Wherein
Figure BDA0002845282150000161
In the formula (I), the compound is shown in the specification,
Figure BDA0002845282150000162
is A1The number of the same elements in the ith order from small to large,
Figure BDA0002845282150000163
is A2The number of the same elements in the ith order from small to large; for example, assume A12.5,2.8,2.8,2.8,3.5,3.5,3.8, then
Figure BDA0002845282150000164
Correlation coefficient
Figure BDA0002845282150000165
Has a value between-1 and +1, i.e.
Figure BDA0002845282150000166
The properties are as follows:
when in use
Figure BDA0002845282150000167
When it is, it indicates that the two variables are positively correlated, i.e., when A1When the value of (A) is increased (decreased)2The value of (c) also increases (decreases).
Figure BDA0002845282150000168
When, it means that the two variables are negatively correlated, i.e. when A1When the value of (A) is increased (decreased)2The value of (b) is decreased (increased).
When in use
Figure BDA0002845282150000169
Time indicates that the two variables are fully correlated.
When in use
Figure BDA00028452821500001610
And (3) time, the method indicates that no correlation exists between two variables.
When in use
Figure BDA00028452821500001611
When, it means that there is a certain degree of correlation between the two variables, and | ρA,BThe closer the | is to 1, the more closely the linear relationship between the two variables is;
Figure BDA00028452821500001612
closer to 0, it means that the linear correlation of the two variables is weaker.
And S44, repeating the steps to sequentially obtain the correlation coefficients of any two variables in all the uncertain output variables.
Preferably, step S4 establishes the correlation coefficient matrix ρ by the following formula
Figure BDA00028452821500001613
Wherein | ρ |i,jAnd | represents a correlation coefficient of the ith uncertainty output variable and the jth uncertainty output variable.
Preferably, the step S4 of determining the weight coefficient of each element in the integrated uncertainty vector u further includes:
s45, obtaining an uncorrelated matrix theta through the following formula according to the correlation coefficient matrix rho
Figure BDA0002845282150000171
In the formula, 1 is a full 1 matrix of r × r dimensions;
s46, all columns of the uncorrelated matrix theta are combined to obtain uncorrelated coefficient row vectors lambda ═ lambda1λ2…λr]
Figure BDA0002845282150000172
S47, normalizing the uncorrelated coefficient row vectors through the following formula to obtain the weight coefficient of each element in the comprehensive uncertainty vector
Figure BDA0002845282150000173
Figure BDA0002845282150000174
In the formula, r is the number of uncertainty output variables.
Preferably, in step S5, obtaining 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, 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
Figure BDA0002845282150000175
Figure BDA0002845282150000176
The operator can know the total uncertainty level (comprehensive uncertainty measurement value) of the semi-physical simulation system and can master 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 credible, 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 S8, determining the semi-physical simulation condition of the aircraft causing the uncertainty of the uncertain output variable to be larger, correcting the semi-physical simulation condition of the aircraft, and acquiring the simulation data of all the uncertain output variables again until the semi-physical simulation result of the aircraft is judged to be credible.
Exemplarily, if the uncertain output variable corresponding to the maximum element is the deviation of the landing point, the aircraft semi-physical simulation condition causing the deviation of the landing point to be large is determined through the mechanism analysis of the aircraft, mainly the angular velocity error model of the detection device is inaccurate, the angular velocity error model can be improved, and the test is carried out again until the aircraft semi-physical simulation result is judged to be credible.
And after the aircraft semi-physical simulation condition is judged to be not credible, correcting the aircraft semi-physical simulation condition until the aircraft semi-physical simulation condition is credible. And determining main uncertainty output (uncertainty output variable) influencing the uncertainty of the system based on the magnitude sequence of the uncertainty measurement results of the data, and accordingly providing a system reliability improvement scheme based on the uncertainty key link.
On the basis of determining the main uncertainty output influencing the uncertainty, the model of the link such as the error is corrected by obtaining the test data of the real object corresponding to the link model and 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 the system is improved.
Compared with the method of the embodiment 1, the comprehensive uncertainty measurement value provided by the embodiment is a data uncertainty measurement method based on the area, and a normalization method of each output variable is provided, so that the uncertainty measurement of the system is supported, and the problem that the meaning of normalization results of various uncertainty measurement methods in the existing system is inconsistent is solved.
Those skilled in the art will appreciate that all or part of the flow of the method implementing the above embodiments may be implemented by a computer program, which is stored in a computer readable storage medium, to instruct related hardware. The computer readable storage medium is a magnetic disk, an optical disk, a read-only memory or a random access memory.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention.

Claims (10)

1. An evaluation method for aircraft semi-physical simulation is characterized by comprising the following steps:
acquiring simulation data of all uncertain output variables in the semi-physical simulation of the aircraft;
according to the simulation data, constructing a data distribution probability envelope of each uncertain output variable, and further determining the random uncertainty and the probability uncertainty of each uncertain output variable;
de-dimensionalizing 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 uncertain 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, carrying out weighted average to obtain a comprehensive uncertainty metric value of the semi-physical simulation of the aircraft;
and determining whether the semi-physical simulation result of the aircraft is credible according to whether the comprehensive uncertainty metric value is within a preset threshold range, judging the aircraft to be credible if the comprehensive uncertainty metric value is within the preset threshold range, and otherwise, judging the aircraft to be credible.
2. The method of claim 1, wherein the uncertainty output variables include at least one of a drop point deviation, an aircraft attitude, an angle of attack, a sideslip angle, an aircraft position, an aircraft speed;
and obtaining simulation data of the uncertain output variables through multiple times of aircraft semi-physical simulation under the same set test condition.
3. The method for evaluating semi-physical simulation of an aircraft according to claim 1 or 2, wherein said constructing a data distribution probability envelope for each uncertainty output variable from said simulation data further comprises:
for each uncertainty output variable x, its simulation data a ═ a is obtained by the following formula1,a2,…,aMMean of samples of } sample
Figure FDA0002845282140000011
Figure FDA0002845282140000012
In the formula, M is the number of simulation data of an uncertain output variable x;
arranging the simulation data from small to large to obtain an interval set B
B＝{B1,B2,…,BM-1}
＝{[a(1),a(2)],[a(2),a(3)],…,[a(M-1),a(M)]}
In the formula, a(1)Is the minimum value in the simulation data, a(M)Is the maximum value in the simulation data;
obtaining each subinterval B in the interval set B by the following formulaj(j-1, 2, …, M-1) euclidean distance to a
Figure FDA0002845282140000021
Figure FDA0002845282140000022
Mixing the above
Figure FDA0002845282140000023
Normalization according to normalizationChange result thetajB is obtained by the following formulajConfidence probability m (B)j)
Figure FDA0002845282140000024
Wherein
Figure FDA0002845282140000025
ξj＝1-θj
According to the interval set B and the trust probability m (B)j) Carrying out data fitting to obtain a data distribution probability envelope g (x) of the uncertain output variable;
determining an upper bound of the probability envelope by the following formula
Figure FDA0002845282140000026
Lower boundg(x)
Figure FDA0002845282140000027
And repeating the steps, and sequentially constructing the data distribution probability envelope of each uncertain output variable.
4. The method for evaluating semi-physical simulation of an aircraft according to claim 3, wherein said determining a random uncertainty and a probabilistic uncertainty for each uncertainty output variable further comprises:
according to the data distribution probability envelope g (x) of each uncertainty output variable, the random uncertainty of the uncertainty output variable is obtained by the following formula
Figure FDA0002845282140000031
Uncertainty of probability
Figure FDA0002845282140000032
Figure FDA0002845282140000033
Figure FDA0002845282140000034
In the formula, gk(x) The probability envelope of the data distribution for the kth uncertainty output variable x,
Figure FDA0002845282140000035
in order to achieve the upper bound,g k(x) Is the lower bound.
5. The method of claim 4, wherein said de-dimensionalizing the random uncertainty and the probability uncertainty of each of said uncertainty output variables to construct a comprehensive uncertainty vector for the entire aircraft semi-physical simulation further comprises:
random uncertainty for each uncertainty output variable by the following formula
Figure FDA0002845282140000036
Uncertainty of probability
Figure FDA0002845282140000037
Go on to descale
Figure FDA0002845282140000038
Dimensionless random uncertainty based on all uncertainty output variables after dimensioning
Figure FDA0002845282140000039
Dimensionless probability uncertainty
Figure FDA00028452821400000310
Establishing a random uncertainty measurement matrix u of the semi-physical simulation of the aircraft by the following formulaaAnd a cognitive uncertainty metric matrix ue
Figure FDA00028452821400000311
Figure FDA00028452821400000312
In the formula, r is the number of uncertain output variables;
according to the random uncertainty matrix u of the semi-physical simulation of the aircraftaAnd a cognitive uncertainty metric matrix ueObtaining the comprehensive uncertainty vector u of the semi-physical simulation of the whole aircraft by the following formula
Figure FDA0002845282140000041
6. The method of claim 5, wherein said determining correlation coefficients for any two of all uncertainty output variables and building a matrix of correlation coefficients, further comprises:
acquiring simulation data of each uncertain output variable with data quantity M;
for any two variables of all the uncertain output variables, the simulation data A of each variable is1、A2Arranged from small to large to obtain the A1、A2Corresponding element rank vector S1、S2
Figure FDA0002845282140000042
Figure FDA0002845282140000043
A1＝{a1,a2,…,aM}
A2＝{b1,b2,…,bM}
In the formula (I), the compound is shown in the specification,
Figure FDA0002845282140000044
is represented by A1The ith element in the sequence from small to large,
Figure FDA0002845282140000045
is represented by A2The order of the ith element from small to large;
judgment S1、S2Whether they are equal to each other, and if they are not equal to each other, determining the correlation coefficient of the two variables by the following formula
Figure FDA0002845282140000046
Figure FDA0002845282140000047
Wherein
Figure FDA0002845282140000048
If they are equal, the correlation coefficient of the two variables is determined by the following formula
Figure FDA0002845282140000049
Figure FDA0002845282140000051
Wherein
Figure FDA0002845282140000052
In the formula (I), the compound is shown in the specification,
Figure FDA0002845282140000053
is A1The number of the same elements in the ith order from small to large,
Figure FDA0002845282140000054
is A2The number of the same elements in the ith order from small to large;
and repeating the steps to sequentially obtain the correlation coefficients of any two variables in all the uncertain output variables.
7. The method for evaluating the semi-physical simulation of an aircraft according to claim 6, wherein the matrix of correlation coefficients p is established by the following formula
Figure FDA0002845282140000055
Wherein | ρ |i,jAnd | represents a correlation coefficient of the ith uncertainty output variable and the jth uncertainty output variable.
8. The method of claim 7, wherein said determining a weight coefficient for each element of said integrated uncertainty vector further comprises:
from the correlation coefficient matrix ρ, the uncorrelated matrix θ is obtained by the following formula
Figure FDA0002845282140000056
In the formula, 1 is a full 1 matrix of r × r dimensions;
all columns of the uncorrelated matrix theta are combined to obtain uncorrelated coefficient row vectors lambda ═ lambda1 λ2…λr]
Figure FDA0002845282140000061
Normalizing the row vectors of the uncorrelated coefficients by the following formula to obtain the weight coefficient of each element in the comprehensive uncertainty vector
Figure FDA0002845282140000064
Figure FDA0002845282140000062
In the formula, r is the number of uncertainty output variables.
9. The method of claim 8, wherein obtaining the integrated uncertainty measure for the aircraft semi-physical simulation based on the integrated uncertainty vector for the entire aircraft semi-physical simulation and the weight coefficients for each element of the integrated uncertainty vector further comprises:
the comprehensive uncertainty measurement value of the semi-physical simulation of the aircraft is obtained by a weighted average method in the following formula
Figure FDA0002845282140000065
Figure FDA0002845282140000063
10. Method for the evaluation of aircraft semi-physical simulations according to one of claims 1-2, 4-9, characterized in that it comprises the following further steps:
if the aircraft semi-physical simulation result is not credible, 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;
determining the semi-physical simulation condition of the aircraft causing the uncertainty of the uncertain output variable to be larger, correcting the semi-physical simulation condition of the aircraft, and acquiring the simulation data of all the uncertain output variables again until the semi-physical simulation result of the aircraft is judged to be credible.
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