CN109460599A - A kind of the transmitting quantization analysis method and system of assembly features deviation - Google Patents

A kind of the transmitting quantization analysis method and system of assembly features deviation Download PDF

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CN109460599A
CN109460599A CN201811272264.7A CN201811272264A CN109460599A CN 109460599 A CN109460599 A CN 109460599A CN 201811272264 A CN201811272264 A CN 201811272264A CN 109460599 A CN109460599 A CN 109460599A
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assembly
deviation
assembly features
transmitting
features deviation
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CN109460599B (en
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朱永国
霍正书
徐雪锋
付春林
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Nanchang Hangkong University
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    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00Computer-aided design [CAD]
    • G06F30/20Design optimisation, verification or simulation
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00Computer-aided design [CAD]
    • G06F30/10Geometric CAD
    • G06F30/15Vehicle, aircraft or watercraft design

Abstract

The transmitting that the present invention discloses a kind of assembly features deviation quantifies analysis method and system, the present invention first measure the assembly features deviation of different sortie aircraft assembly units, obtains the assembly features deviation of each assembly unit;Secondly transfer entropy is determined according to the assembly features deviation of two assembly units;Then assembly features deviation is constructed according to the assembly features deviation of each assembly unit and transmits network model;Finally carries out assembly features deviation according to the transfer entropy and assembly features deviation transmitting network model and transmit quantitative analysis, the topological relation between assembling deviation variable is determined using transfer entropy and measures the index of causality, the complex structure product assembling deviation mechanism of transmission and Coupling Rule under small lot development mode are disclosed, realizes the complex structure product build-up tolerance optimization under small lot production model.

Description

A kind of the transmitting quantization analysis method and system of assembly features deviation
Technical field
The present invention relates to aircraft assembly features deviations to digitize coordination technique field, inclined more particularly to a kind of assembly features The transmitting quantization analysis method and system of difference.
Background technique
Aircraft is that a kind of number of parts is numerous, assembly coordination relationship is complicated, Assembly veracity requirement is high, quality control is stringent Typical complex structure product, aircraft Product Assembly process belongs to multistage manufacturing process, has complexity, dynamic, non-thread The features such as property.Numerous deviations such as part manufacturing error, tool locating error, thin-wall part deformation resilience, rivet deformation, reference for assembling Source can all generate the accumulation of aircraft assembly features deviation, lead to off-gage phenomenon often occur in aircraft assembling process.Currently, advanced religion Practice machine, feeder liner, the emphasis new model aircraft such as large transport airplane to be in from small serial production to the key of batch production transition Stage has emerged in large numbers the more overproof difficult point of assembly urgently to be resolved, has seriously affected aircraft batch production process.In addition, assembly features are inclined Difference transmitting quantitative analysis is always problem of the Airplane Manufacturing Enterprise in dimensional accuracy lifting process.
In recent years, with the fast development of the digitized measurement equipments such as laser tracker, local GPS, CCD industrial camera, The common recognition that digitized measurement equipment has become domestic and international aircraft manufacturing company is introduced during aircraft development, utilizes digitlization Measuring device can measure fitted position data.Information included in these data is made full use of and excavated, assembly features are disclosed The mechanism of transmission of deviation, reduces assembling process unusual fluctuations, and control and improvement product assembly quality have great importance.
In previous research, many methods are had been proposed for the transmitting quantization point of assembly features deviation in researcher Analysis, that is, portray the interaction between two variables, such as traditional statistical analysis method, Granger causality method and mutual information method Deng, but due to the Aircraft Production batch factors such as small lead to not observe again all kinds of deviations inputs in assembling process, transmitting with it is defeated A large amount of complete detection datas out, measurement data show small sample, higher-dimension, it is incomplete the features such as, while also having ignored variable Between interactively, therefore, it is difficult to traditional statistical method to measurement data carry out assembly features deviation transmitting quantitative analysis. Relationship between Granger causality method hypothesis system is linear, therefore there is the problems such as quantization analysis precision is low;Mutual trust Breath method again cannot between expression system information transmitting directionality.
Summary of the invention
The object of the present invention is to provide a kind of transmitting of assembly features deviation quantization analysis method and systems, are realized with realizing Quantitative analysis is transmitted to assembly features deviation under small lot production model, improves quantitative analysis precision.
To achieve the above object, the present invention provides a kind of transmitting of assembly features deviation to quantify analysis method, the biography Passing quantitative analysis method includes:
The assembly features deviation of different sortie aircraft assembly units is measured, the assembly features of each assembly unit are obtained Deviation;
Transfer entropy is determined according to the assembly features deviation of two assembly units;
Assembly features deviation, which is constructed, according to the assembly features deviation of each assembly unit transmits network model;
The transmitting quantization of assembly features deviation is carried out according to the transfer entropy and assembly features deviation transmitting network model Analysis.
Optionally, the assembly features deviation according to two assembly units determines transfer entropy, specifically includes:
Determine assembly features deviation transfer entropy formula;
Using Density Estimator, according to the assembly of the assembly features deviation transfer entropy formula and two assembly units Feature deviation calculates transfer entropy.
Optionally, described inclined according to the transfer entropy and assembly features deviation transmitting network model progress assembly features Difference transmitting quantitative analysis, specifically includes:
The direction of transfer and delivery value of the assembly features deviation of two assembly units are determined according to the transfer entropy;
The transmitting of each assembly level assembly features deviation is carried out using assembly features deviation transmitting network model and is divided Solution.
Optionally, described to carry out each assembly level assembly features deviation using assembly features deviation transmitting network model Transmitting and decomposition, specifically include:
The transmitting of each assembly level assembly features deviation is carried out using assembly features deviation transmitting network model and is tired out Product;
It carries out each decomposition for assembling level assembly features deviation using assembly features deviation transmitting network model and traces back Source.
Optionally, described to utilize Density Estimator, according to the assembly features deviation transfer entropy formula and two dresses Assembly features deviation with unit calculates transfer entropy, specific formula are as follows:
Wherein, TJ→IThe transfer entropy transmitted by self-assembly unit J to assembly unit I, N are the length of detection data, For Density Estimator, xnAnd ynThe assembly features assembly features deviation of two assembly unit of respectively the n-th sortie aircraft, xn+1Indicate the The assembly features deviation of n+1 sortie, k and l are respectively the implantation dimension of x and y,
The present invention also provides a kind of transmitting of assembly features deviation to quantify analysis system, and the transmitting quantifies analysis system packet It includes:
Module is obtained, is measured for the assembly features deviation to different sortie aircraft assembly units, obtains each assembly The assembly features deviation of unit;
Transfer entropy determining module, for determining transfer entropy according to the assembly features deviation of two assembly units;
Assembly features deviation transmits network model determining module, for the assembly features deviation according to each assembly unit It constructs assembly features deviation and transmits network model;
Transmitting quantization analysis module, for being carried out according to the transfer entropy and assembly features deviation transmitting network model Assembly features deviation transmits quantitative analysis.
Optionally, the transfer entropy determining module, specifically includes:
Assembly features deviation transfer entropy formula determination unit, for determining assembly features deviation transfer entropy formula;
Transfer entropy determination unit, for utilizing Density Estimator, according to the assembly features deviation transfer entropy formula and two The assembly features deviation of a assembly unit calculates transfer entropy.
Optionally, the transmitting quantifies analysis module, specifically includes:
First analytical unit, the biography of the assembly features deviation for determining two assembly units according to the transfer entropy Pass direction and delivery value;
Second analytical unit assembles spy for carrying out each assembly level using assembly features deviation transmitting network model Levy the transmitting and decomposition of deviation.
Optionally, first analytical unit, specifically includes:
Transmitting and accumulation subelement, fill for carrying out each assembly level using assembly features deviation transmitting network model Transmitting and accumulation with feature deviation;
Decompose and trace to the source subelement, fills for carrying out each assembly level using assembly features deviation transmitting network model Decomposition with feature deviation with trace to the source.
Optionally, described to utilize Density Estimator, according to the assembly features deviation transfer entropy formula and two dresses Assembly features deviation with unit calculates transfer entropy, specific formula are as follows:
Wherein, TJ→IThe transfer entropy transmitted by self-assembly unit J to assembly unit I, N are the length of detection data, For Density Estimator, xnAnd ynThe assembly features assembly features deviation of two assembly unit of respectively the n-th sortie aircraft, xn+1Indicate the The assembly features deviation of n+1 sortie, k and l are respectively the implantation dimension of x and y,
The specific embodiment provided according to the present invention, the invention discloses following technical effects:
The present invention first measures the assembly features deviation of different sortie aircraft assembly units, obtains each assembly unit Assembly features deviation;Secondly transfer entropy is determined according to the assembly features deviation of two assembly units;Then according to each institute State the assembly features deviation building assembly features deviation transmitting network model of assembly unit;Finally according to the transfer entropy and described Assembly features deviation transmits network model and carries out the transmitting quantitative analysis of assembly features deviation, determines assembling deviation using transfer entropy The index of topological relation and measurement causality between variable, discloses the complex structure product assembling deviation under small lot development mode Mechanism of transmission and Coupling Rule realize the complex structure product build-up tolerance optimization under small lot production model.
Detailed description of the invention
It in order to more clearly explain the embodiment of the invention or the technical proposal in the existing technology, below will be to institute in embodiment Attached drawing to be used is needed to be briefly described, it should be apparent that, the accompanying drawings in the following description is only some implementations of the invention Example, for those of ordinary skill in the art, without any creative labor, can also be according to these attached drawings Obtain other attached drawings.
Fig. 1 is that the transmitting of assembly features of embodiment of the present invention deviation quantifies analysis method flow chart;
Fig. 2 is that assembly features of embodiment of the present invention deviation is layered transfer entropy network;
Fig. 3 is that the transmitting of assembly features of embodiment of the present invention deviation quantifies analysis system structure chart.
Specific embodiment
Following will be combined with the drawings in the embodiments of the present invention, and technical solution in the embodiment of the present invention carries out clear, complete Site preparation description, it is clear that described embodiments are only a part of the embodiments of the present invention, instead of all the embodiments.It is based on Embodiment in the present invention, it is obtained by those of ordinary skill in the art without making creative efforts every other Embodiment shall fall within the protection scope of the present invention.
The object of the present invention is to provide a kind of transmitting of assembly features deviation quantization analysis method and systems, are realized with realizing Quantitative analysis is transmitted to assembly features deviation under small lot production model, improves quantitative analysis precision.
In order to make the foregoing objectives, features and advantages of the present invention clearer and more comprehensible, with reference to the accompanying drawing and specific real Applying mode, the present invention is described in further detail.
Fig. 1 is that the transmitting of assembly features of embodiment of the present invention deviation quantifies analysis method flow chart, as shown in Figure 1, this hair Bright to provide a kind of transmitting quantization analysis method of assembly features deviation, the transmitting quantization analysis method includes:
Step S1: the assembly features deviation of different sortie aircraft assembly units is measured, each assembly unit is obtained Assembly features deviation;
Step S2: transfer entropy is determined according to the assembly features deviation of two assembly units;
Step S3: assembly features deviation is constructed according to the assembly features deviation of each assembly unit and transmits network model;
Step S4: assembly features deviation biography is carried out according to the transfer entropy and assembly features deviation transmitting network model Pass quantitative analysis.
Each step is discussed in detail below:
Step S1: the assembly features deviation of different sortie aircraft assembly units is measured, each assembly unit is obtained Assembly features deviation;Specifically, the present invention is using digitized measurements such as three coordinate measuring machine, laser tracker or laser scanners Equipment measures the assembly features deviation of different sortie aircraft assembly units, and the assembly features for obtaining each assembly unit are inclined Difference.
Step S2: the assembly features deviation according to two assembly units determines transfer entropy, specifically includes:
Transfer entropy is the new branch of information entropy theory, can not only describe the information of the information occurred between system transmitting Amount can also depict the directionality of Inter-System Information transmitting and the kinematic nonlinearity characteristic of Inter-System Information transmitting, can be effective Express interactively between variable in ground.By each assembling stage of complex product there are multi-source uncertain error source it is found that assembly features are inclined The transmission capacity of difference depends on the assembly accumulation error of the assembly unit after the assembly is completed, accordingly, it is determined that assembly features deviation is transmitted Entropy formula, specific formula are as follows:
Wherein, TJ→IThe transfer entropy transmitted by self-assembly unit J to assembly unit I, N are the length of detection data, xnWith ynThe assembly features assembly features deviation of two assembly unit of respectively the n-th sortie aircraft, xn+1Indicate that the assembly of the (n+1)th sortie is special Deviation is levied, k and l are respectively the implantation dimension of x and y, P () is conditional probability.
In order to calculate the transfer entropy of assembling deviation information, need to take detection data effective Multilayer networks, core Density estimation is a kind of method from data data distribution characteristics itself.It does not utilize the priori in relation to data distribution Knowledge does not add any hypothesis to data distribution.For this purpose, using Density Estimator, according to the assembly features deviation transfer entropy The assembly features deviation of formula and two assembly units calculates transfer entropy, specific formula are as follows:
Wherein, TJ→IThe transfer entropy transmitted by self-assembly unit J to assembly unit I, N are the length of detection data, For Density Estimator, xnAnd ynThe assembly features assembly features deviation of two assembly unit of respectively the n-th sortie aircraft, xn+1Indicate the The assembly features deviation of n+1 sortie, k and l are respectively the implantation dimension of x and y,
Fig. 2 is that assembly features of embodiment of the present invention deviation is layered transfer entropy network, as shown in Fig. 2, giving tier I dress Transfer entropy between assembly features deviation with unit and J layers of assembly unit.Wherein arrow is had from tier I to J layers of direction The line of head indicates that the assembling deviation relationship between different assembly levels, solid line grey arrow indicate tracing to the source for assembly features deviation, Dotted line grey arrow indicates the accumulative of assembling deviation.Dotted line black arrow indicates the decomposition direction of assembling deviation information, real Line black arrow indicates the assembly relation of same assembly level difference assembly unit.In Fig. 2Indicate assembly unit Pi1Assembling deviation and assembly unitAssembling deviation between transfer entropy.
Step S3: assembly features deviation is constructed according to the assembly features deviation of each assembly unit and transmits network model; Specifically, assembly features deviation transmitting network model is defined as G={ V, L, E, S, FV,FE, in which: the vertex of V expression network Set, L record hierarchical information, and E indicates the set of directed edge, and S is the set for recording assembly unit set membership, FVTo be defined on Feature on vertex, FETo be defined on the feature on side.With vertex representation assembly unit, assembly unit deviation is indicated with directed edge Between information transfering relation, if assembly unit I and assembly unit J have deviation transmit information, there is one and refer to from the vertex J To the side on the vertex I, the length transfer entropy T on sideJ→IQuantified.
Step S4: described inclined according to the transfer entropy and assembly features deviation transmitting network model progress assembly features Difference transmitting quantitative analysis, specifically includes:
Step S41: according to the transfer entropy determine the assembly features deviation of two assembly units direction of transfer and Delivery value;Specifically, utilizing transfer entropy TJ→IIt is emphasized to complete the assembling deviation of two assembly units in direction of transfer and transmitting Double grading evaluation, transfer entropy TJ→IThe size of value indicates that transmitting is emphasized, transfer entropy TJ→IThe positive and negative expression direction of transfer of value, it is real Now to the dynamic relationship quantificational description of deviation information between each assembly unit.
Step S42: each assembly level assembly features deviation is carried out using assembly features deviation transmitting network model Transmitting and decomposition, specifically include:
Step S421: each assembly level assembly features deviation is carried out using assembly features deviation transmitting network model Transmitting and accumulation;Utilize the interactively between assembly features deviation transmitting network model expression variable, it is indicated that respectively assemble layer Direction and the intensity that relationship is influenced between deviation complete the layer-by-layer transmitting and accumulation of assembling deviation.
Step S422: each assembly level assembly features deviation is carried out using assembly features deviation transmitting network model It decomposes and traces to the source.Network model is transmitted by transfer entropy T using the assembly features deviationJ→IJ to I is exchanged in formula, then can be obtained To the transfer entropy T from I to JI→J, using then achievable assembling deviation it is layer-by-layer decomposition and trace to the source.
Fig. 3 is that the transmitting of assembly features of embodiment of the present invention deviation quantifies analysis system structure chart, as shown in figure 3, this hair Bright also to provide a kind of transmitting quantization analysis system of assembly features deviation, the transmitting quantization analysis system includes:
Module 1 is obtained, is measured for the assembly features deviation to different sortie aircraft assembly units, obtains each assembly The assembly features deviation of unit;
Transfer entropy determining module 2, for determining transfer entropy according to the assembly features deviation of two assembly units;
Assembly features deviation transmits network model determining module 3, inclined for the assembly features according to each assembly unit Difference building assembly features deviation transmits network model;
Transmitting quantization analysis module 4, for according to the transfer entropy and the assembly features deviation transmit network model into Row assembly features deviation transmits quantitative analysis.
Modules are discussed in detail below:
The transfer entropy determining module 2, specifically includes:
Assembly features deviation transfer entropy formula determination unit, for determining assembly features deviation transfer entropy formula;
Transfer entropy determination unit, for utilizing Density Estimator, according to the assembly features deviation transfer entropy formula and two The assembly features deviation of a assembly unit calculates transfer entropy.
The transmitting quantifies analysis module 4, specifically includes:
First analytical unit, the biography of the assembly features deviation for determining two assembly units according to the transfer entropy Pass direction and delivery value;It specifically includes:
Transmitting and accumulation subelement, fill for carrying out each assembly level using assembly features deviation transmitting network model Transmitting and accumulation with feature deviation;
Decompose and trace to the source subelement, fills for carrying out each assembly level using assembly features deviation transmitting network model Decomposition with feature deviation with trace to the source.
Second analytical unit assembles spy for carrying out each assembly level using assembly features deviation transmitting network model Levy the transmitting and decomposition of deviation.
It is described to utilize Density Estimator, according to the assembly features deviation transfer entropy formula and two assembly units Assembly features deviation calculates transfer entropy, specific formula are as follows:
Wherein, TJ→IThe transfer entropy transmitted by self-assembly unit J to assembly unit I, N are the length of detection data, For Density Estimator, xnAnd ynThe assembly features assembly features deviation of two assembly unit of respectively the n-th sortie aircraft, xn+1Indicate the The assembly features deviation of n+1 sortie, k and l are respectively the implantation dimension of x and y,
Data mining is the effective technology that its implication relation model is found from data, is provided newly to solve this problem Approach.Present invention introduces Small Sample Database excavation and metrical information opinions, are embodied as aircraft Product Assembly characteristic error quantitative analysis New solution route is provided, can assist solving emphasis new model aircraft from small serial production to the assembly that emerges in large numbers when batch production transition Overproof problem instructs aircraft batch to produce and correctly carries out the overproof prevention work of assembly in time, is also other labyrinths such as space flight Product assembly quality control provides guidance.
The present invention first measures the assembly features deviation of different sortie aircraft assembly units, obtains each assembly unit Assembly features deviation;Secondly transfer entropy is determined according to the assembly features deviation of two assembly units;Then according to each institute State the assembly features deviation building assembly features deviation transmitting network model of assembly unit;Finally according to the transfer entropy and described Assembly features deviation transmits network model and carries out the transmitting quantitative analysis of assembly features deviation, determines assembling deviation using transfer entropy The index of topological relation and measurement causality between variable, discloses the complex structure product assembling deviation under small lot development mode Mechanism of transmission and Coupling Rule realize the complex structure product build-up tolerance optimization under small lot production model.
Each embodiment in this specification is described in a progressive manner, the highlights of each of the examples are with other The difference of embodiment, the same or similar parts in each embodiment may refer to each other.For system disclosed in embodiment For, since it is corresponded to the methods disclosed in the examples, so being described relatively simple, related place is said referring to method part It is bright.
Used herein a specific example illustrates the principle and implementation of the invention, and above embodiments are said It is bright to be merely used to help understand method and its core concept of the invention;At the same time, for those skilled in the art, foundation Thought of the invention, there will be changes in the specific implementation manner and application range.In conclusion the content of the present specification is not It is interpreted as limitation of the present invention.

Claims (10)

1. a kind of transmitting of assembly features deviation quantifies analysis method, which is characterized in that the transmitting quantifies analysis method and includes:
The assembly features deviation of different sortie aircraft assembly units is measured, the assembly features for obtaining each assembly unit are inclined Difference;
Transfer entropy is determined according to the assembly features deviation of two assembly units;
Assembly features deviation, which is constructed, according to the assembly features deviation of each assembly unit transmits network model;
It carries out assembly features deviation according to the transfer entropy and assembly features deviation transmitting network model and transmits quantitative analysis.
2. transmitting according to claim 1 quantifies analysis method, which is characterized in that described according to two assembly units Assembly features deviation determine transfer entropy, specifically include:
Determine assembly features deviation transfer entropy formula;
Using Density Estimator, according to the assembly features of the assembly features deviation transfer entropy formula and two assembly units Deviation calculates transfer entropy.
3. transmitting according to claim 1 quantifies analysis method, which is characterized in that described according to the transfer entropy and described Assembly features deviation transmits network model and carries out the transmitting quantitative analysis of assembly features deviation, specifically includes:
The direction of transfer and delivery value of the assembly features deviation of two assembly units are determined according to the transfer entropy;
The transmitting and decomposition of each assembly level assembly features deviation are carried out using assembly features deviation transmitting network model.
4. transmitting according to claim 3 quantifies analysis method, which is characterized in that described to utilize the assembly features deviation Transmitting network model carries out the transmitting and decomposition of each assembly level assembly features deviation, specifically includes:
The transmitting and accumulation of each assembly level assembly features deviation are carried out using assembly features deviation transmitting network model;
It carries out each decomposition for assembling level assembly features deviation using assembly features deviation transmitting network model and traces to the source.
5. transmitting according to claim 2 quantifies analysis method, which is characterized in that it is described to utilize Density Estimator, according to The assembly features deviation of the assembly features deviation transfer entropy formula and two assembly units calculates transfer entropy, specific formula Are as follows:
Wherein, TJ→IThe transfer entropy transmitted by self-assembly unit J to assembly unit I, N are the length of detection data,For core Density estimation, xnAnd ynThe assembly features assembly features deviation of two assembly unit of respectively the n-th sortie aircraft, xn+1Indicate (n+1)th The assembly features deviation of sortie, k and l are respectively the implantation dimension of x and y,
6. a kind of transmitting of assembly features deviation quantifies analysis system, which is characterized in that the transmitting quantifies analysis system and includes:
Module is obtained, is measured for the assembly features deviation to different sortie aircraft assembly units, obtains each assembly unit Assembly features deviation;
Transfer entropy determining module, for determining transfer entropy according to the assembly features deviation of two assembly units;
Assembly features deviation transmits network model determining module, for being constructed according to the assembly features deviation of each assembly unit Assembly features deviation transmits network model;
Transmitting quantization analysis module, for being assembled according to the transfer entropy and assembly features deviation transmitting network model Feature deviation transmits quantitative analysis.
7. transmitting according to claim 6 quantifies analysis system, which is characterized in that the transfer entropy determining module, specifically Include:
Assembly features deviation transfer entropy formula determination unit, for determining assembly features deviation transfer entropy formula;
Transfer entropy determination unit, for utilizing Density Estimator, according to the assembly features deviation transfer entropy formula and two institutes The assembly features deviation for stating assembly unit calculates transfer entropy.
8. transmitting according to claim 6 quantifies analysis system, which is characterized in that the transmitting quantifies analysis module, tool Body includes:
First analytical unit, the transmitting side of the assembly features deviation for determining two assembly units according to the transfer entropy To and delivery value;
Second analytical unit, it is inclined for carrying out each assembly level assembly features using assembly features deviation transmitting network model The transmitting and decomposition of difference.
9. transmitting according to claim 8 quantifies analysis system, which is characterized in that first analytical unit, it is specific to wrap It includes:
Transmitting and accumulation subelement, it is special for carrying out each assembly level assembly using assembly features deviation transmitting network model Levy the transmitting and accumulation of deviation;
Decompose and trace to the source subelement, assembles spy for carrying out each assembly level using assembly features deviation transmitting network model Levy deviation decomposition with trace to the source.
10. transmitting according to claim 7 quantifies analysis system, which is characterized in that it is described to utilize Density Estimator, according to The assembly features deviation of the assembly features deviation transfer entropy formula and two assembly units calculates transfer entropy, specific formula Are as follows:
Wherein, TJ→IThe transfer entropy transmitted by self-assembly unit J to assembly unit I, N are the length of detection data,For core Density estimation, xnAnd ynThe assembly features assembly features deviation of two assembly unit of respectively the n-th sortie aircraft, xn+1Indicate (n+1)th The assembly features deviation of sortie, k and l are respectively the implantation dimension of x and y,
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