CN115906719A - Wind tunnel test multi-source data quantitative comparison method based on complex type goodness of fit - Google Patents

Wind tunnel test multi-source data quantitative comparison method based on complex type goodness of fit Download PDF

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CN115906719A
CN115906719A CN202310222497.0A CN202310222497A CN115906719A CN 115906719 A CN115906719 A CN 115906719A CN 202310222497 A CN202310222497 A CN 202310222497A CN 115906719 A CN115906719 A CN 115906719A
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CN115906719B (en
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唐小伟
党雷宁
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Ultra High Speed Aerodynamics Institute China Aerodynamics Research and Development Center
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Ultra High Speed Aerodynamics Institute China Aerodynamics Research and Development Center
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Abstract

The invention discloses a wind tunnel test multi-source data quantitative comparison method based on complex type goodness of fit, belonging to the field of wind tunnel tests and comprising the following steps: carrying out quantitative calculation of dissimilarity, correlation and generalized included angle on multi-source data in a wind tunnel test to construct a complex number set and a corresponding integral composite complex number; the overall composite Euclidean distance and the overall composite correlation coefficient are obtained by calculating the modulus and the argument of the overall composite complex number, and the overall goodness of fit result of the multi-source data is evaluated by applying a complex goodness of fit formula. The invention provides a wind tunnel test multi-source data quantitative comparison method based on complex type goodness of fit, which is different from the traditional data group comparison between every two data groups.

Description

Wind tunnel test multi-source data quantitative comparison method based on complex type goodness of fit
Technical Field
The invention relates to the field of wind tunnel tests. More specifically, the invention relates to a wind tunnel test multi-source data quantitative comparison method based on the complex type goodness of fit.
Background
Data comparative analysis is an important recurrent work in scientific research work and engineering application. For a large amount of intricate and complex data, how to obtain valuable evaluation conclusions through comparative analysis or how to enlighten deep mechanism problems through comparative analysis results are all targets worth pursuing by scientific researchers.
Multi-source data comparisons often involve different condition states, and may also involve different study objects; since data to be compared by multisource data is usually an aggregate of multivariate attributes, it is necessary to perform a comprehensive data comparison by a necessary technical means. In the traditional data comparison and analysis process, the knowledge and experience in the aspect of professional technology are very important and indispensable, but quantitative comparison and analysis is relatively few, or is limited to local attributes, and the qualitative characteristics of data are more concerned.
In the basic algorithm of cluster analysis of data mining, a plurality of effective methods are provided for contrastive analysis between data groups, such as representing the difference between two groups of data through the distance between data samples; in probability theory, the correlation coefficient between two random variables (multidimensional) can characterize the correlation of regular trends between two sets of data.
The biggest limitation of the conventional comparative analysis method is that: often limited to quantitative comparisons between two sets of data; for the difference of multi-source data, the difference can be comprehensively analyzed only by comparing every two data. However, in many cases, it is necessary to compare a plurality of sets (more than 2) of data, and it is necessary to perform discriminant analysis on the overall consistency of the plurality of sets of data. For example, in the pneumatic data comparison, the overall matching degree of the aerodynamic characteristic curves (dispersion) obtained from different sources (such as calculation, wind tunnel test, flight test, equipment, personnel and the like) under the same condition state parameters is often evaluated. However, in the prior art, when the consistency of the whole plurality of sets of data is analyzed, the degree of coincidence of the aerodynamic characteristic curves is qualitatively described by using "better coincidence", "basically coincidence", and the like in technical reports and papers, and the qualitative description is not detailed enough in data analysis, that is, the prior art has no way of quantitatively evaluating the consistency of the whole plurality of sets of data.
Disclosure of Invention
An object of the present invention is to solve at least the above problems and/or disadvantages and to provide at least the advantages described hereinafter.
To achieve these objects and other advantages and in accordance with the purpose of the invention, as embodied and broadly described herein, there is provided a wind tunnel test multi-source data quantitative comparison method based on a complex number type goodness of fit, comprising:
s1, carrying out quantitative calculation on dissimilarity, correlation and generalized included angles on multi-source multi-group data in a wind tunnel test to construct a complex set representing dissimilarity and correlation;
s2, constructing integral composite complex numbers of integral quantitative comparison of multi-source multi-group data based on the complex set obtained in the S1;
s3, calculating the mode and the argument of the integral composite complex number in the S2 to obtain a corresponding integral composite Euclidean distance and an integral composite correlation coefficient;
s4, based on the values of the integral composite Euclidean distance and the integral composite argument obtained in the S3, a complex goodness of fit formula is applied to evaluate integral goodness of fit results of multiple sources of multiple groups of data;
the overall goodness of fit evaluation rule is that the smaller the goodness of fit value is, the higher the overall consistency of the multi-source multi-group data is.
Preferably, in S1, the quantitative calculation method of dissimilarity, correlation, and generalized angle includes:
s11, constructing a corresponding Euclidean distance data set based on Euclidean distances between every two multi-source multi-group data, and finishing the representation of dissimilarity between every two multi-source multi-group data;
s12, constructing a corresponding correlation coefficient data set based on correlation coefficients between each two of the multi-source multi-group data, and finishing the representation of the correlation between each two of the multi-source multi-group data;
and S13, calculating the generalized included angle between every two data groups based on the correlation coefficient in the correlation coefficient data set.
Preferably, in S11, the euclidean distance dataset is acquired in the following manner:
s110, is provided withmGrouping data from different sources
Figure SMS_1
，/>
Figure SMS_2
For any two groups of data->
Figure SMS_3
and />
Figure SMS_4
The euclidean distance between them,d k the calculation formula of (a) is as follows:
Figure SMS_5
wherein ,nfor the number of data set elements per set of data,
Figure SMS_6
、/>
Figure SMS_7
are respectively the data set->
Figure SMS_8
and />
Figure SMS_9
The elements of (1);
s111, in the step S110,mthe number of elements in the data set in the calculation result of Euclidean distance between two groups of data
Figure SMS_10
By number of data setsmIs determined by the binary combination calculation of:
Figure SMS_11
wherein ,
Figure SMS_12
，/>
Figure SMS_13
based on the number of data setsmBinary group sum formula。
Preferably, in S12, the correlation coefficient data set is constructed in a manner including:
for themGrouping data from different sources
Figure SMS_14
Is set based on>
Figure SMS_15
For any two groups of data->
Figure SMS_16
and />
Figure SMS_17
The calculation formula of the correlation coefficient is as follows:
Figure SMS_18
wherein the covariance
Figure SMS_19
Is defined as follows:
Figure SMS_20
Figure SMS_21
and />
Figure SMS_22
The mean square deviations of any two groups of data are respectively expressed as follows: />
Figure SMS_23
Figure SMS_24
and />
Figure SMS_25
Are the respective mean values of any two groups of data, and the expressions are respectively:
Figure SMS_26
。
preferably, in S13, the generalized included angle is calculated by:
formGrouping data from different sources
Figure SMS_27
Is set based on>
Figure SMS_28
For any two groups of data>
Figure SMS_29
and />
Figure SMS_30
The generalized angle therebetween is calculated as follows:
Figure SMS_31
wherein the generalized angle
Figure SMS_32
Is defined as ^ based on the value range>
Figure SMS_33
On the right side of the upper type is a pair->
Figure SMS_34
The inverse cosine function of (c).
Preferably, in S1, the complex set is obtained by:
formGrouping data from different sources
Figure SMS_35
Is set based on>
Figure SMS_36
For any two groups of data->
Figure SMS_37
and />
Figure SMS_38
The generalized complex number between, its calculation formula is as follows:
Figure SMS_39
wherein, the right side of the above formula is the exponential expression mode of complex numbers.
Preferably, in S2, the overall complex number is obtained by:
formGrouping data from different sources
Figure SMS_40
Is set based on>
Figure SMS_41
The overall composite complex number for overall quantitative comparison of multi-source multi-group data is calculated by the following formula:
Figure SMS_42
。
preferably, in S3, the overall composite euclidean distance is obtained by:
for themGrouping data from different sources
Figure SMS_43
Is provided withdThe composite Euclidean distance of the multi-source multi-group data is calculated according to the following formula:
Figure SMS_44
wherein, the right side of the upper formula is plural
Figure SMS_45
The mold of (4);
the overall composite correlation coefficient is obtained in the following mode:
for themGrouping data from different sources
Figure SMS_46
Is set based on>
Figure SMS_47
For the overall composite correlation coefficient of multi-source multi-group data, the calculation formula is as follows: />
Figure SMS_48
Wherein, the right denominator of the above formula is plural
Figure SMS_49
The number of the molecules is a plurality>
Figure SMS_50
The real part of (a).
Preferably, in S4, formGrouping data from different sources
Figure SMS_51
Is provided withFThe complex type goodness of fit of multi-source multi-group data is represented by the formula:
Figure SMS_52
wherein ,
Figure SMS_53
for the integral combination angle of multi-source data, the calculation formula is->
Figure SMS_54
To do soFHas a value range of
Figure SMS_55
。
Preferably, the composite euclidean distance is a functional parameter for quantitatively comparing the overall consistency of the multi-source multi-group data;
the overall composite correlation coefficient is a functional parameter for quantitatively comparing the overall correlation of the multi-source multi-group data;
the overall goodness of fit is a comprehensive comparative quantitative index for overall consistency of multi-source multi-group data;
the complex type goodness of fit is a scalar parameter which integrates Euclidean distances and correlation coefficients of a plurality of data pairs in multi-source multi-group data and is used for representing the whole goodness of fit.
The invention at least comprises the following beneficial effects:
first, the method is based on a new concept of goodness of fit, and has universal significance for guiding quantitative comparison and analysis of multi-source data, the concept of the overall goodness of fit is different from that of the traditional data group pair to pair comparison, and the method is a comprehensive method for comparing the traditional data group pair to pair and quantitative measurement of the overall consistency or difference of the data.
Secondly, the invention constructs an algorithm flow of the complex type goodness of fit, provides a means for revealing the difference of research data of different sources of the same research object and finds problems so as to inspire people to research the reasons causing the difference.
Thirdly, the multi-source data quantitative comparison of the invention can give the difference of research data among different research objects (model sequence/similar configuration/optimized design, etc.), thereby providing direct evidence for performance evaluation or optimized design.
Fourthly, the concept of 'goodness of fit' constructed in the invention has three basic attributes: one is compatibility, that is, when the goodness of fit is specified as a comparison between two sets of data, the traditional correlation (correlation coefficient) and dissimilarity (Euclidean distance) must be compatible and not contradictory; inheritance, namely constructing a specific calculation method of goodness of fit based on the correlation coefficient and Euclidean distance of two groups of data; thirdly, the method is innovative, and does not exclude other algorithm-based goodness of fit calculation methods.
Additional advantages, objects, and features of the invention will be set forth in part in the description which follows and in part will become apparent to those having ordinary skill in the art upon examination of the following or may be learned from practice of the invention.
Drawings
FIG. 1 is a flow chart of quantitative comparison of the degree of compliance of the complex form of the present invention;
FIG. 2 is a schematic diagram of aerodynamic force data of a model M1 at Mach 4 in different wind tunnels, wherein (a) is a schematic diagram of the change of an axial force coefficient CA with an attack angle, (b) is a schematic diagram of the change of a normal force coefficient CN with the attack angle, (c) is a schematic diagram of the change of a pitching moment coefficient Cmz with the attack angle, and (d) is a schematic diagram of the change of a pressure center coefficient Xcp with the attack angle;
FIG. 3 is a schematic representation of aerodynamic data for different models at Mach 4 in wind tunnel FD01, where (a) is a schematic representation of the variation of the axial force coefficient CA with angle of attack, (b) is a schematic representation of the variation of the normal force coefficient CN with angle of attack, (c) is a schematic representation of the variation of the pitch moment coefficient Cmz with angle of attack, and (d) is a schematic representation of the variation of the pressure center coefficient Xcp with angle of attack;
FIG. 4 is a schematic representation of aerodynamic data for different models at Mach 5 in wind tunnel FD01, where (a) is a schematic representation of the variation of the axial force coefficient CA with angle of attack, (b) is a schematic representation of the variation of the normal force coefficient CN with angle of attack, (c) is a schematic representation of the variation of the pitch moment coefficient Cmz with angle of attack, and (d) is a schematic representation of the variation of the pressure center coefficient Xcp with angle of attack;
FIG. 5 is a schematic representation of aerodynamic data of different models at Mach 6 in wind tunnel FD01, where (a) is a schematic representation of the variation of the axial force coefficient CA with angle of attack, (b) is a schematic representation of the variation of the normal force coefficient CN with angle of attack, (c) is a schematic representation of the variation of the pitch moment coefficient Cmz with angle of attack, and (d) is a schematic representation of the variation of the pressure center coefficient Xcp with angle of attack.
Detailed Description
The present invention is further described in detail below with reference to the attached drawings so that those skilled in the art can implement the invention by referring to the description text.
By means of a new concept and a new technology of modern data analysis, a quantifiable new method means is explored and provided for multi-source data comparison and analysis; in order to expand the universality of quantitative comparison and analysis of data, a new concept of 'goodness of fit' and a corresponding algorithm thereof are provided, the invention provides a quantitative comparison method of multi-source data based on complex goodness of fit, and the quantitative comparison method can be suitable for quantitative comprehensive comparison among multi-group data.
It should be noted that the multi-source multi-group data of the present invention are research data from different sources of the same research object, and each different source generates a group of data; or the multi-source multi-group data are research data among different research subjects under specific conditions, and each research subject generates one group of data.
The invention provides a multi-source data quantitative comparison method based on complex type goodness of fit, which comprises the following eight steps as shown in figure 1:
step one, calculating Euclidean distance data set between multi-source multi-group data pairwise
Firstly, euclidean distance data sets between a plurality of groups of data of multi-source data are needed to be obtained. Is provided withmGrouping data from different sources
Figure SMS_56
That is to say havemDifferent sources of data, eachjIs taken to indicate a source, each->
Figure SMS_57
A vector represents a series of data sets from one source. Before comparison, data sets from different sources are set, and except for different sources, the condition states of other determined vector element data are consistent, which is an important premise for calculation of Euclidean distance.
Is provided with
Figure SMS_58
For any two groups of data->
Figure SMS_59
and />
Figure SMS_60
The euclidean distance between them,d k the calculation formula of (a) is as follows:
Figure SMS_61
wherein ,nfor the number of data set elements per set of data,
Figure SMS_62
、/>
Figure SMS_63
are respectively the data set->
Figure SMS_64
and />
Figure SMS_65
The elements of (1);
as described abovemThe number of elements of the data set of the calculation result of the Euclidean distance between every two groups of data
Figure SMS_66
Is calculated as a scalar quantity ofmIs determined by the binary combination calculation of:
Figure SMS_67
/>
Figure SMS_68
i.e. in the Euclidean distance>
Figure SMS_69
The number of elements of the data set, namely:
Figure SMS_70
step two, calculating a correlation coefficient data set between each two multi-source multi-group data
Also before the correlation coefficient calculation, it is ensured that the conditional state of the other determining vector element data is consistent for data sets from different sources, except for the sources.
Is provided withmGrouping data from different sources
Figure SMS_71
. Device for combining or screening>
Figure SMS_72
For any two groups of data>
Figure SMS_73
and />
Figure SMS_74
The calculation formula is as follows:
Figure SMS_75
in the above formula, covariance
Figure SMS_76
Is defined as:
Figure SMS_77
in the above-mentioned formula,
Figure SMS_78
and />
Figure SMS_79
The mean square deviations of any two groups of data are respectively expressed as follows:
Figure SMS_80
in the above-mentioned formula,
Figure SMS_81
and />
Figure SMS_82
The data are respectively the mean values of any two groups of data, and the expressions are respectively:
Figure SMS_83
。
in the above-mentioned formula,nthe number of data set elements for each set of data. As described abovemCalculating result data set element number of correlation coefficient between group data and group data
Figure SMS_84
By a scalar quantitymIs determined by a binary combination calculation ofmThe calculation formulas of the Euclidean distance between every two groups of data are the same.
Step three, calculating generalized included angles between each two multi-source multi-group data
The concept of correlation coefficient is for any two groups of data, which can be regarded as two multidimensional vectors, and the function of the correlation coefficient is equivalent to the description of the generalized angle between the two multidimensional vectors: when the included angle is 0 degree, the two vectors are equivalent; when the included angle is 90 degrees, the two vectors are vertical; the two vectors are reversed when the included angle is 180 degrees. The value of the generalized angle reflects the degree of directional coincidence between the two multi-dimensional vectors; in other words, the correlation coefficient is equivalent to the generalized angle cosine function value. Accordingly, the generalized angle can be inversely calculated from the correlation coefficient.
Is provided withmGrouping data from different sources
Figure SMS_85
. Is arranged and/or is>
Figure SMS_86
For any two groups of data>
Figure SMS_87
and />
Figure SMS_88
The generalized included angle therebetween is calculated as follows:
Figure SMS_89
/>
in the above-mentioned formula,
Figure SMS_90
is the correlation coefficient between any two sets of data.
Generalized included angle
Figure SMS_91
Value range is defined as->
Figure SMS_92
(unit: radian) or [0,180](unit: degree).
In the first step, the second step and the third step, euclidean distance data sets and correlation coefficient data sets between multi-source multi-group data pairs are calculated, and generalized included angles between the data pairs are calculated according to the correlation coefficients, so that the data sets are an important basis for calculating the complex type goodness of fit. The two groups of data can be regarded as two data vectors, and the correlation coefficient can be regarded as the cosine of the generalized included angle of the two vectors.
Step four, constructing a plurality of characteristic dissimilarity and correlation between multi-source multi-group data based on Euclidean distance and generalized included angle
Carefully analyzing the concepts of the correlation coefficient and the Euclidean distance, the correlation coefficient can be regarded as the cosine of the generalized included angle of the two vectors, and the Euclidean distance can be regarded as the distance between the two vectors. Thus a complex number can be defined.
Is provided withmGrouping data from different sources
Figure SMS_93
. Is arranged and/or is>
Figure SMS_94
For any two groups of data->
Figure SMS_95
and />
Figure SMS_96
The generalized complex number between, its formula of calculation is as follows:
Figure SMS_97
in the above-mentioned formula,
Figure SMS_98
in the Euclidean distance between any two sets of data>
Figure SMS_99
For any two groups of data->
Figure SMS_100
And
Figure SMS_101
the generalized angle therebetween.
And fourthly, constructing complex numbers representing dissimilarity and correlation between multiple groups of multi-source data based on Euclidean distance and generalized included angles, wherein the complex numbers are the premise of constructing complex type goodness of fit.
Step five, calculating integral quantitative comparison composite complex numbers of multi-source data through arithmetic superposition of complex sets between every two
Is provided withmGrouping data from different sources
Figure SMS_102
. And calculating the integral quantitative comparison composite complex number of the multi-source data by arithmetically superposing the complex sets between every two complex sets. Device for combining or screening>
Figure SMS_103
The overall composite complex number for overall quantitative comparison of multi-source multi-group data is calculated by the following formula:
Figure SMS_104
。
in the above-mentioned formula,
Figure SMS_105
for any two groups of data->
Figure SMS_106
and />
Figure SMS_107
In a generalized plural, is present>
Figure SMS_108
Is composed ofmAnd the number of elements of the data set of the calculation result of the Euclidean distance between every two groups of data.
And fifthly, calculating the overall quantitative comparison composite complex number of the multi-source data by arithmetical superposition of the complex sets between every two multi-source data, which is an important link for representing the overall quantitative comparison complex type goodness of fit of the multi-source data.
Step six, calculating the integral composite Euclidean distance based on the integral composite complex number module;
on the basis of the composite complex numbers of the overall quantitative comparison of the multi-source data, the generalized Euclidean distance of the overall quantitative comparison of the multi-source data can be derived.
Is provided withmGrouping data from different sources
Figure SMS_109
。dThe calculation formula of the composite Euclidean distance of the multi-source multi-group data set is as follows: />
Figure SMS_110
In the above formula, the right side is complex number
Figure SMS_111
The complex number is the complex number of the overall quantization comparison of the multi-source data.
And step six, calculating the integral composite Euclidean distance based on the integral composite complex number module, wherein the integral consistency of the integral composite Euclidean distance to the multi-source data is a functional parameter with quantitative comparison.
Step seven, calculating an integral composite correlation coefficient based on an inverse cosine function of the integral composite complex argument;
similarly, on the basis of the composite complex numbers of the overall quantitative comparison of the multi-source data, generalized correlation coefficients of the overall quantitative comparison of the multi-source data can be derived.
Is provided withmGrouping data from different sources
Figure SMS_112
。/>
Figure SMS_113
The calculation formula of the overall composite correlation coefficient of the multi-source multi-group data is as follows:
Figure SMS_114
in the above formula, the right denominator is plural
Figure SMS_115
The number of the molecules is a plurality>
Figure SMS_116
The real part of (a). The plurality ofPNamely, the complex number is compared in the integral quantification of the multi-source data.
And step seven, calculating an integral composite correlation coefficient based on an inverse cosine function of the integral composite complex argument, wherein the integral correlation of the integral composite correlation coefficient to the multi-source data is a functional parameter with quantitative comparison.
And step eight, calculating to obtain an goodness-of-fit result of the overall consistency of the evaluated multi-source data based on the overall composite Euclidean distance and the overall composite argument.
For the sake of intuition, a scalar parameter is constructed to measure the overall consistency of the multi-source data.
Is provided withmGrouping data from different sources
Figure SMS_117
。FFor the goodness of fit of multi-source data multi-group data group to the overall consistency, the calculation formula is as follows:
Figure SMS_118
in the above-mentioned formula,
Figure SMS_119
and compounding Euclidean distance for the multi-source data.
In the above-mentioned formula,
Figure SMS_120
the calculation formula of the overall composite included angle of the multi-source data is as follows:
Figure SMS_121
wherein
Figure SMS_122
Namely the overall composite correlation coefficient of the multi-source data.
Integral composite included angle of the above formula
Figure SMS_123
And the aforementioned generalized angle>
Figure SMS_124
The ranges of values of (A) are the same and are all stated as: />
Figure SMS_125
(unit: radian) or [0,180](unit: degree) and thus the degree of coincidenceFThe range of values of (a) is: />
Figure SMS_126
. The smaller the value, the higher the goodness of fit, and the larger the value, the lower the goodness of fit.
And step eight, calculating to obtain the goodness of fit result of the overall consistency of the evaluated multi-source data based on the overall composite Euclidean distance and the overall composite argument. And integrating the integral composite Euclidean distance and the integral composite argument, and finally obtaining a simple scalar parameter representing the integral goodness of fit, namely the multi-source data complex goodness of fit, by a calculation method of an innovative structure.
Example (b):
the invention relates to a multi-source data quantitative comparison method based on complex type goodness of fit, which is explained by embodiments in order to more clearly explain the technical scheme of the invention. The embodiment is used for carrying out comparison and analysis on force measurement test data of an aircraft model (a model for short in the follow-up process) in aerodynamics in different wind tunnels or different condition parameters (namely different sources), and the quantitative calculation of dissimilarity (Euclidean distance), correlation (correlation coefficient) and goodness of fit (complex goodness of fit) is respectively carried out by adopting the method described by the invention, and meanwhile, the calculation result of quantitative comparison is analyzed.
The basic information of the study subject and the test condition status related to the force test data for comparative analysis is as follows:
configuration: model M1, model M2, model M3.
Wind tunnel: FD01, FD02, FD03.
Mach number: 4. 5, 6; angle of attack: -12 °; side slip angle: 0 degree and 3 degree
As shown in table 1, there are 14 groups of data, each group of data is a data set of a model changing with an attack angle in a wind tunnel, a mach number and a sideslip angle state; the independent variable of each group of data is an attack angle, and the dependent variable comprises an axial force coefficientCACoefficient of normal forceCNCoefficient of pitching momentCmzAnd center of gravity coefficientXcp。
Table 1 shows the data group numbers and the basic information, and in the model wind tunnel force measurement test data listed in table 1, the data are respectively selected according to two conditions for quantitative comparative analysis, wherein the two conditions are respectively 'different wind tunnels of the same model' and 'different models of the same wind tunnel', and simultaneously cover the state parameter range concerned in engineering. The calculation of the data dissimilarity and the data correlation aims at two groups of data, so the data for comparison and analysis are planned in groups and arranged in a data group pair mode to form two large-class dozens of groups of data, and the basic information of the data group pair for comparison and analysis is respectively the basic information of the data of the same model and different wind tunnels as shown in a table 2 and the basic information of the data of the same model and different models as shown in a table 3.
TABLE 1
Figure SMS_127
TABLE 2
Figure SMS_128
/>
TABLE 3
Figure SMS_129
Each data set is shown in the graph from 2 to 5 as each component of the contained aerodynamic test data changes with the attack angle; these data are the basic data set objects for comparative analysis of the embodiment.
Step one, calculating to obtain Euclidean distance data sets between multi-source multi-group data based on Euclidean distance formula
The euclidean distance characterizes the dissimilarity between the two sets of data. The data dissimilarity calculation results and analysis include two aspects, namely comparative analysis between test data obtained by the same model in different wind tunnels and comparative analysis between test data obtained by different models in the same wind tunnel, and Euclidean distance calculation results of each component data group pair of aerodynamic force shown in the table 4 are obtained:
TABLE 4
Figure SMS_130
/>
In table 4, the calculation results corresponding to the numbers (X1 to X3) are the euclidean distance between each two of the force measurement test data which are obtained by using the model M1, the mach number 4, and the sideslip angle 0 degree and are changed along with the attack angle under the conditions of different wind tunnels (FD 01/FD02/FD03, see tables 1 and 2). The different wind tunnel data dissimilarity analysis conditions of the same model are as follows:
under the same condition, the force measurement test data of the model M1 obtained on three different wind tunnels are not different integrally, which shows the basic consistency of the test results of the same model of each wind tunnel.
The Euclidean distance of each component aerodynamic coefficient is summarized according to a data set corresponding to the Euclidean distance from small to large as follows:
axial force coefficient: x3 < X1 ≈ X2
Normal force coefficient: x2 < X3 < X1
Pitching moment coefficient: x2 < X3 < X1
The core pressing coefficient is as follows: x2 < X1 ≈ X3
Overall, the data set numbered X2 was better differentiated, and the other two sets were ranked next.
In table 4, the calculation results corresponding to the numbers (W1 to W9) are mach numbers 4/5/6 and sideslip angles 0 degrees in the wind tunnel FD01, and the euclidean distance between each two of the force measurement test data which are obtained for different models (M1/M2/M3, see tables 1 and 3) and change with the angle of attack is consistent under the incoming flow conditions. The data dissimilarity analysis conditions of different models of the same wind tunnel are as follows:
under the same condition, the force measurement test data between every two three models obtained on the wind tunnel FD01 have larger dissimilarity integrally. The difference between the normal force coefficient (0.01 to 0.12 Euclidean distance), the pitching moment coefficient (0.17 to 0.51 Euclidean distance) and the core-pressing coefficient (0.03 to 0.14 Euclidean distance) is obvious except that the anisotropy of the axial force coefficient (0.001 to 0.01 Euclidean distance) is slightly small. These results give a quantitative balance of the difference in aerodynamic performance for different layout profiles.
The Euclidean distance of each component aerodynamic coefficient is summarized according to a data set corresponding to the Euclidean distance from small to large as follows:
axial force coefficient: w8 is more than W9 and more than W3 and more than W7 and more than W5 and more than W6 and more than W2 and more than W4 and more than W1
Normal force coefficient: w5 is more than W6 and more than W4 is more than W9 and more than W3 and more than W8 and more than W2 and more than W7 and more than W1
The pitching moment coefficient: w9 < W5 < W6 < W4 < W8 < W7 < W3 < W2 < W1
The core pressing coefficient is as follows: w9 is more than W8 and more than W7 and more than W4 and more than W5 and more than W6 and more than W3 and more than W2 and more than W1
Overall, the data sets of numbers W5, W6, W8, and W9 are more distinct, and the other data sets of numbers are less distinct. As can be seen from table 3, the dissimilarity result shows that the euclidean distances of mach numbers 5 and 6 are significantly smaller than the euclidean distance of mach number 4, which indicates that the difference between the axial forces of different shapes is smaller in the case of hypersonic velocity than in the case of supersonic velocity.
For the pitching moment coefficient, the dissimilarity between each group of data is very obvious. The longitudinal moment performances of the three models are almost different, and the evaluation analysis can be carried out by combining detailed pneumatic parameters.
Step two, calculating to obtain a correlation coefficient data set between each two multi-source multi-group data based on a correlation coefficient formula
The data correlation calculation results and analysis also include two aspects, namely comparison and analysis between test data obtained by the same model in different wind tunnels and comparison and analysis between test data obtained by different models in the same wind tunnel, so that correlation coefficient calculation results of all component data pairs of aerodynamic force shown in table 5 are obtained:
TABLE 5
Figure SMS_131
In table 5, the calculation results corresponding to the numbers (X1 to X3) are the correlation coefficient between the model M1, the mach number 4, and the sideslip angle 0 degree, and the force measurement test data which changes with the attack angle under different wind tunnels (FD 01/FD02/FD03, see tables 1 and 2). The correlation analysis conditions of different wind tunnel data of the same model are as follows:
under the same condition, the force measurement test data of the model M1 obtained on three different wind tunnels has better overall correlation except for the pressure center coefficient, and the correlation coefficients are all larger than 0.98, which shows that the aerodynamic coefficients of all components have more consistent change rule along with the attack angle.
The model M1 has very good correlation (the correlation coefficient is approximately equal to 1) in the force measurement test data (data group to number X2) of the wind tunnel FD01 and the wind tunnel FD03, mach 4 and the sideslip angle of 0 degree.
For the pressure center coefficient, the data set has poor correlation to X1 and X3, and it can be known from the comparison table 2 that the pressure center coefficient rule obtained by the wind tunnel FD02 and the pressure center coefficient rules obtained by the wind tunnel FD01 and the wind tunnel FD03 have obvious difference.
In table 5, the calculation results corresponding to the numbers (W1 to W9) are the mach numbers 4/5/6 and the sideslip angle 0 degrees in the wind tunnel FD01, the force measurement test data which is changed along with the attack angle and is obtained for different models (M1/M2/M3, see tables 1 and 3), and the correlation coefficient between each two is obtained under the condition that the incoming flow conditions are consistent. The different analysis conditions of different model data of the same wind tunnel are as follows:
under the same condition, the overall correlation of the force measurement test data among the three models obtained on the wind tunnel FD01 is good (the correlation coefficients are all larger than 0.98), and the change rule of each component aerodynamic coefficient along with the attack angle is consistent; however, the correlation of the core pressing coefficients is general (the correlation coefficient is between 0.47 and 0.98).
The correlation of the data group to the pressure center coefficient of W4/W5/W6 is better than that of other model combination comparison, which is also the reason that the model M1 and the model M3 are closer in appearance as a whole.
The quantitative results of the correlation of the different models indicate that the sensitivity of the centroid to the appearance layout is high.
Step three, calculating generalized included angles between each two multi-source multi-group data
Based on the correlation coefficient between each two multi-source multi-group data, the generalized included angle calculation result of each component data set of aerodynamic force shown in the table 6 is obtained by adopting a conversion formula of the generalized included angle and the correlation coefficient.
TABLE 6
Figure SMS_132
And step four to step eight, constructing the complex type goodness of fit, the corresponding composite Euclidean distance and the composite correlation coefficient.
Specifically, four types of data combinations are selected and respectively marked by numbers T1-T4. The numbered T1 data combination is test data obtained by the model M1 in three wind tunnels respectively; the serial numbers T2-T4 are combined into test data which are obtained by three different similar configuration models on the wind tunnel FD01 at Mach numbers 4, 5 and 6 respectively.
Firstly, constructing complex numbers representing dissimilarity and correlation between each two multi-source data of multiple groups based on Euclidean distance and generalized included angles, then calculating overall quantitative comparison composite complex numbers of the multi-source data through arithmetic superposition of complex sets between each two multi-source data, then calculating overall composite Euclidean distance based on a module of the overall composite complex numbers, calculating overall composite correlation coefficients based on an inverse cosine function of an overall composite complex argument, and finally calculating to obtain an goodness of fit result of the overall consistency of the evaluated multi-source data based on the overall composite Euclidean distance and the overall composite argument.
TABLE 7
Figure SMS_133
In table 7, the results of the complex goodness of fit and composite euclidean distance/composite correlation coefficient calculation are shown; the analysis was as follows: the data goodness of fit of different wind tunnels of the same model is integrally superior to that of the different models of the same wind tunnel. The complex type goodness of fit values are all small, because the data sets have certain similarity, namely the generalized included angles between the data sets are all small, the goodness of fit value range absolute value obtained by formula calculation is small. From the complex type goodness of fit results, it is also known that the data goodness of fit for judging mach numbers 5 and 6 is better than that for judging mach number 4. The composite correlation coefficient provides a new method for quantitative analysis of correlation of multi-source data, and the calculation result shows that the method has sufficient reasonability and applicability.
The above scheme is merely illustrative of a preferred example, and is not limiting. When the invention is implemented, appropriate replacement and/or modification can be carried out according to the requirements of users.
While embodiments of the invention have been disclosed above, it is not intended that they be limited to the applications set forth in the specification and examples. It can be applied to all kinds of fields suitable for the present invention. Additional modifications will readily occur to those skilled in the art. Therefore, the invention is not to be limited to the specific details and illustrations shown and described herein, without departing from the general concept as defined by the claims and their equivalents.

Claims (10)

1. A wind tunnel test multi-source data quantitative comparison method based on complex type goodness of fit is characterized by comprising the following steps:
s1, carrying out quantitative calculation on dissimilarity, correlation and generalized included angle on multi-source multi-group data in a wind tunnel test to construct a complex set representing dissimilarity and correlation;
s2, constructing an integral composite complex number for integral quantitative comparison of multi-source multi-group data based on the complex number set obtained in the S1;
s3, calculating the modulus and the argument of the integral composite complex number in the S2 to obtain a corresponding integral composite Euclidean distance and an integral composite correlation coefficient;
s4, based on the values of the integral composite Euclidean distance and the integral composite argument obtained in the S3, evaluating the integral goodness-of-fit result of the multi-source multi-group data by applying a complex goodness-of-fit formula;
the overall goodness of fit evaluation rule is that the smaller the goodness of fit value is, the higher the overall consistency of the multi-source multi-group data is.
2. The wind tunnel test multi-source data quantitative comparison method based on the complex type goodness of fit as claimed in claim 1, wherein in S1, the quantitative calculation mode of dissimilarity, correlation, and generalized included angle includes:
s11, constructing a corresponding Euclidean distance data set based on Euclidean distances between every two multi-source multi-group data, and finishing the representation of dissimilarity between every two multi-source multi-group data;
s12, constructing a corresponding correlation coefficient data set based on correlation coefficients between each two of the multi-source multi-group data, and finishing the representation of the correlation between each two of the multi-source multi-group data;
and S13, calculating the generalized included angle between every two data groups based on the correlation coefficient in the correlation coefficient data set.
3. The wind tunnel test multi-source data quantitative comparison method based on the complex type goodness of fit as claimed in claim 2, wherein in S11, the euclidean distance data set is obtained by:
s110, is provided withmGrouping data from different sources
Figure QLYQS_1
，/>
Figure QLYQS_2
For any two groups of data>
Figure QLYQS_3
and />
Figure QLYQS_4
The Euclidean distance between the two electrodes,d k the calculation formula of (a) is as follows:
Figure QLYQS_5
wherein ,nfor the number of data set elements per set of data,
Figure QLYQS_6
、/>
Figure QLYQS_7
respectively a data set>
Figure QLYQS_8
and />
Figure QLYQS_9
The elements of (1);
s111, in S110,mthe number of elements in the data set in the calculation result of Euclidean distance between two groups of data
Figure QLYQS_10
By number of data setsmIs determined by the binary combination calculation of:
Figure QLYQS_11
wherein ,
Figure QLYQS_12
，/>
Figure QLYQS_13
based on the number of data setsmBinary group sum formula。
4. The wind tunnel test multi-source data quantitative comparison method based on the complex number goodness of fit according to claim 2, wherein in S12, the construction mode of the correlation coefficient data set comprises:
for themGrouping data from different sources
Figure QLYQS_14
Is set based on>
Figure QLYQS_15
For any two groups of data>
Figure QLYQS_16
and />
Figure QLYQS_17
The calculation formula of the correlation coefficient is as follows: />
Figure QLYQS_18
Wherein the covariance
Figure QLYQS_19
Definition of (2)Comprises the following steps:
Figure QLYQS_20
Figure QLYQS_21
and />
Figure QLYQS_22
The mean square deviations of any two groups of data are respectively shown as the following expressions:
Figure QLYQS_23
Figure QLYQS_24
and />
Figure QLYQS_25
The data are respectively the mean values of any two groups of data, and the expressions are respectively:
Figure QLYQS_26
。
5. the wind tunnel test multi-source data quantitative comparison method based on the complex type goodness of fit as claimed in claim 2, wherein in S13, the generalized included angle is calculated in a manner that:
for themGrouping data from different sources
Figure QLYQS_27
Is set based on>
Figure QLYQS_28
For any two groups of data>
Figure QLYQS_29
and />
Figure QLYQS_30
The generalized included angle therebetween is calculated as follows:
Figure QLYQS_31
wherein the generalized angle
Figure QLYQS_32
Is defined as a value range of->
Figure QLYQS_33
Right side of the above formula is a pair>
Figure QLYQS_34
And (5) solving an inverse cosine function.
6. The wind tunnel test multi-source data quantitative comparison method based on the complex number goodness of fit as claimed in claim 1, wherein in S1, the complex number set is obtained in a manner that:
formGrouping data from different sources
Figure QLYQS_35
Is set based on>
Figure QLYQS_36
For any two groups of data->
Figure QLYQS_37
and />
Figure QLYQS_38
The generalized complex number between, its calculation formula is as follows:
Figure QLYQS_39
wherein, the right side of the above formula is the exponential expression mode of complex numbers.
7. The wind tunnel test multi-source data quantitative comparison method based on the complex number goodness of fit of claim 1, characterized in that in S2, the overall composite complex number is obtained in a manner that:
for themGrouping data from different sources
Figure QLYQS_40
Is/are>
Figure QLYQS_41
The overall composite complex number for overall quantitative comparison of multi-source multi-group data is calculated according to the following formula:
Figure QLYQS_42
。/>
8. the wind tunnel test multi-source data quantitative comparison method based on the complex number goodness of fit as claimed in claim 1, wherein in S3, the overall composite euclidean distance is obtained by:
formGrouping data from different sources
Figure QLYQS_43
Is provided withdThe composite Euclidean distance of the multi-source multi-group data is calculated according to the following formula:
Figure QLYQS_44
wherein, the right side of the upper formula is plural
Figure QLYQS_45
The mold of (4);
the overall composite correlation coefficient is obtained in the following mode:
formGrouping data from different sources
Figure QLYQS_46
Is set based on>
Figure QLYQS_47
The calculation formula of the overall composite correlation coefficient of the multi-source multi-group data is as follows:
Figure QLYQS_48
wherein, the right denominator of the above formula is plural
Figure QLYQS_49
The number of the molecules is a plurality>
Figure QLYQS_50
The real part of (a).
9. The wind tunnel test multi-source data quantitative comparison method based on complex type goodness of fit of claim 1, characterized in that in S4, formGrouping data from different sources
Figure QLYQS_51
Is provided withFThe complex type goodness of fit of multi-source multi-group data is represented by the formula:
Figure QLYQS_52
wherein ,
Figure QLYQS_53
the calculation formula is ^ based on the integral combined included angle of multi-source data>
Figure QLYQS_54
To do soFHas a value range of->
Figure QLYQS_55
。
10. The wind tunnel test multi-source data quantitative comparison method based on the complex type goodness of fit as claimed in claim 1, wherein the composite euclidean distance is a functional parameter for quantitatively comparing the overall consistency of multi-source multi-group data;
the overall composite correlation coefficient is a functional parameter for quantitatively comparing the overall correlation of the multi-source multi-group data;
the integral goodness of fit is a comprehensive comparative quantitative index of integral consistency of multi-source multi-group data;
the complex type goodness of fit is a scalar parameter which integrates Euclidean distances and correlation coefficients of a plurality of data pairs in multi-source multi-group data and is used for representing the whole goodness of fit.
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