CN106909532A - A kind of method and system of the relevance of analysis ground total electric field and airborne particle thing Size - Google Patents

A kind of method and system of the relevance of analysis ground total electric field and airborne particle thing Size Download PDF

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CN106909532A
CN106909532A CN201710035258.9A CN201710035258A CN106909532A CN 106909532 A CN106909532 A CN 106909532A CN 201710035258 A CN201710035258 A CN 201710035258A CN 106909532 A CN106909532 A CN 106909532A
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data
total electric
particle diameter
ground total
canonical correlation
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鞠勇
谢莉
王秋生
谷晓岚
袁海文
赵录兴
陆家榆
杨晓洪
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State Grid Corp of China SGCC
Beihang University
China Electric Power Research Institute Co Ltd CEPRI
State Grid Beijing Electric Power Co Ltd
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State Grid Corp of China SGCC
Beihang University
China Electric Power Research Institute Co Ltd CEPRI
State Grid Beijing Electric Power Co Ltd
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Publication of CN106909532A publication Critical patent/CN106909532A/en
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    • GPHYSICS
    • G06COMPUTING; CALCULATING; COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10Complex mathematical operations
    • G06F17/15Correlation function computation including computation of convolution operations
    • GPHYSICS
    • G06COMPUTING; CALCULATING; COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10Complex mathematical operations
    • G06F17/16Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization

Abstract

The invention discloses a kind of analysis ground total electric field and the method for the relevance of airborne particle thing Size, it is characterised in that methods described includes:Ground total electric field data and airborne particle thing particle diameter modal data are obtained respectively, and the ground total electric field data and the airborne particle thing particle diameter modal data are standardized respectively;Decorrelative transformation is carried out to the ground total electric field data and the airborne particle thing particle diameter modal data respectively;Canonical correlation analysis are carried out to the ground total electric field data by decorrelative transformation and airborne particle thing particle diameter modal data respectively, the canonical correlation coefficient of ground total electric field data and the canonical correlation coefficient of airborne particle thing particle diameter modal data is obtained;And canonical correlation coefficient respectively to the ground total electric field data and the canonical correlation coefficient of the airborne particle thing particle diameter modal data are analyzed, and judge the relevance of the ground total electric field data and airborne particle thing particle diameter modal data.

Description

A kind of method of the relevance of analysis ground total electric field and airborne particle thing Size And system
Technical field
The present invention relates to technical field of HVDC transmission, and more particularly, to one kind analysis ground total electric field With the method and system of the relevance of airborne particle thing Size.
Background technology
With the economic sustained and rapid development of China, particularly energy demand, the sustainable growth of electric power resource demand.But China Electric power resource generally Xi Duodong is few, northern many south are few, with distribution and the unbalanced feature of demand.Therefore it is to realize electric power resource Distribute rationally, China is by " transferring electricity from the west to the east, north and south supply mutually, national network " as the strategic objective of power network development.This means need Build extensive, remote, efficient power transmission engineering, high voltage dc transmission technology turn into realize this target it is only it Choosing.
During HVDC transmission line transmission electric energy, because wire electrical discharge inevitably results from corona current, wireless Electrical interference, audible noise and total electric field etc., cause electric energy loss and other environmental problems.In order to by UHVDC Transmission Lines Ground total electric field is controlled in the reasonable scope, and urgent need researching DC circuit ground total electric field is associated with airborne particle thing System, is subsequently to carry out airborne particle thing to study ready to the Influencing Mechanism of ground total electric field.
The content of the invention
In order to solve the above problems, according to an aspect of the invention, there is provided a kind of analysis ground total electric field and sky The method of the relevance of middle particle size spectrum, methods described includes:
Ground total electric field data and airborne particle thing particle diameter modal data are obtained respectively, and respectively to ground synthesis electricity Field data and the airborne particle thing particle diameter modal data are standardized;
Decorrelative transformation is carried out to the ground total electric field data and the airborne particle thing particle diameter modal data respectively;
Typical case is carried out to the ground total electric field data by decorrelative transformation and airborne particle thing particle diameter modal data respectively Correlation analysis, obtain the canonical correlation coefficient of ground total electric field data and the canonical correlation of airborne particle thing particle diameter modal data Coefficient;
Canonical correlation coefficient respectively to the ground total electric field data and the airborne particle thing particle diameter modal data Canonical correlation coefficient is analyzed, and judges the relevance of the ground total electric field data and airborne particle thing particle diameter modal data.
Preferably, wherein described enter to the ground total electric field data and the airborne particle thing particle diameter modal data respectively Row decorrelative transformation includes:
The ground total electric field data and the corresponding matrix data of the airborne particle thing particle diameter modal data are entered respectively Line translation or rank transformation, obtain corresponding stepped matrix;
Calculate the correlation matrix R=[r of the ground total electric field data or the particle size modal dataij], And strong correlation weight matrix A=[a are calculated according to the correlation matrix Rij],
Wherein, τ is strong correlation coefficient threshold, is strong correlation if two coefficient correlations of variable are more than τ;If two changes The coefficient correlation of amount is less than τ, then for weak related or uncorrelated;
The corresponding variable of the maximum weight of the often capable weight sum of strong correlation weight matrix A is proposed respectively, obtain through Cross the ground total electric field data and airborne particle thing particle diameter modal data of decorrelative transformation.
Preferably, wherein described respectively to the ground total electric field data and airborne particle thing particle diameter by decorrelative transformation Modal data carries out canonical correlation analysis, obtains the canonical correlation coefficient and airborne particle thing Size of ground total electric field data The canonical correlation coefficient of data includes:
By by the ground total electric field data of decorrelative transformation and airborne particle thing particle diameter modal data respectively by sample set X Represented with Y, wherein the ground total electric field data are made up of the ground total electric field of p various location, it is described aerial Particle size modal data is made up of the particle size spectrum of q different-grain diameter size, has N number of observation for each variable Value, the sample set X and Y is expressed as:
Order vector α=[α12,…,αp]TWith β=[β12,…,βq]TThe allusion quotation of sample set X and Y linear combination is represented respectively Type coefficient correlation, then linear combinationAndMaximize relevance function:
Canonical correlation analysis is expressed as following optimization problem:
Using Lagrange multiplier methods, the Lagrange functions for obtaining are as follows:
Partial derivative is asked to α and β respectively, is madeObtain:
The covariance matrix Σ of marker samples collection X and Y11=XXT22=YYTAnd Cross-covariance Σ12=XYT, Σ21=YXT, α and β is calculated respectively.
Preferably, wherein described respectively to the canonical correlation coefficient and the airborne particle of the ground total electric field data The canonical correlation coefficient of thing particle diameter modal data is analyzed, and judges the ground total electric field data and airborne particle thing Size The relevance of data includes:
Canonical correlation coefficient respectively to the ground total electric field data and the airborne particle thing particle diameter modal data Canonical correlation coefficient takes absolute value;
The absolute value is compared with canonical correlation coefficient threshold value respectively, and the ground is judged according to comparative result The relevance of total electric field data and airborne particle thing particle diameter modal data, if the absolute value of canonical correlation coefficient is more than canonical correlation Coefficient threshold, then illustrate that the corresponding variable of the canonical correlation coefficient is strong with the relevance of another data;If canonical correlation coefficient Absolute value be less than canonical correlation coefficient threshold value, then illustrate associating for the corresponding variable of the canonical correlation coefficient and another data Property is weak.
According to another aspect of the present invention, there is provided a kind of analysis ground total electric field and airborne particle thing Size The system of relevance, the system includes:Standardization unit, decorrelative transformation unit, canonical correlation coefficient computing unit With relevance determining unit.
The standardization unit, obtains ground total electric field data and airborne particle thing particle diameter modal data respectively, and The ground total electric field data and the airborne particle thing particle diameter modal data are standardized respectively;
The decorrelative transformation unit, respectively to the ground total electric field data and the airborne particle thing Size number According to carrying out decorrelative transformation;
The canonical correlation coefficient computing unit, respectively to the ground total electric field data by decorrelative transformation and in the air Particle size modal data carries out canonical correlation analysis, obtain ground total electric field data canonical correlation coefficient and aerial The canonical correlation coefficient of grain thing particle diameter modal data;
The relevance determining unit, the respectively canonical correlation coefficient to the ground total electric field data and described aerial The canonical correlation coefficient of particle size modal data is analyzed, and judges the ground total electric field data and airborne particle thing grain The relevance of footpath modal data.
Preferably, wherein described enter to the ground total electric field data and the airborne particle thing particle diameter modal data respectively Row decorrelative transformation includes:
The ground total electric field data and the corresponding matrix data of the airborne particle thing particle diameter modal data are entered respectively Line translation or rank transformation, obtain corresponding stepped matrix;
Calculate the correlation matrix R=[r of the ground total electric field data or the particle size modal dataij], And strong correlation weight matrix A=[a are calculated according to the correlation matrix Rij],
Wherein, τ is strong correlation coefficient threshold, is strong correlation if two coefficient correlations of variable are more than τ;If two changes The coefficient correlation of amount is less than τ, then for weak related or uncorrelated;
The corresponding variable of the maximum weight of the often capable weight sum of strong correlation weight matrix A is proposed respectively, obtain through Cross the ground total electric field data and airborne particle thing particle diameter modal data of decorrelative transformation.
Preferably, wherein described respectively to the ground total electric field data and airborne particle thing particle diameter by decorrelative transformation Modal data carries out canonical correlation analysis, obtains the canonical correlation coefficient and airborne particle thing Size of ground total electric field data The canonical correlation coefficient of data includes:
By by the ground total electric field data of decorrelative transformation and airborne particle thing particle diameter modal data respectively by sample set X Represented with Y, wherein the ground total electric field data are made up of the ground total electric field of p various location, it is described aerial Particle size modal data is made up of the particle size spectrum of q different-grain diameter size, has N number of observation for each variable Value, the sample set X and Y is expressed as:
Order vector α=[α12,…,αp]TWith β=[β12,…,βq]TThe allusion quotation of sample set X and Y linear combination is represented respectively Type coefficient correlation, then linear combinationAndMaximize relevance function:
Canonical correlation analysis is expressed as following optimization problem:
Using Lagrange multiplier methods, the Lagrange functions for obtaining are as follows:
Partial derivative is asked to α and β respectively, is madeObtain:
The covariance matrix Σ of marker samples collection X and Y11=XXT22=YYTAnd Cross-covariance Σ12=XYT, Σ21=YXT, α and β is calculated respectively.
Preferably, wherein described respectively to the canonical correlation coefficient and the airborne particle of the ground total electric field data The canonical correlation coefficient of thing particle diameter modal data is analyzed, and judges the ground total electric field data and airborne particle thing Size The relevance of data includes:
Canonical correlation coefficient respectively to the ground total electric field data and the airborne particle thing particle diameter modal data Canonical correlation coefficient takes absolute value;
The absolute value is compared with canonical correlation coefficient threshold value respectively, and the ground is judged according to comparative result The relevance of total electric field data and airborne particle thing particle diameter modal data, if the absolute value of canonical correlation coefficient is more than canonical correlation Coefficient threshold, then illustrate that the corresponding variable of the canonical correlation coefficient is strong with the relevance of another data;If canonical correlation coefficient Absolute value be less than canonical correlation coefficient threshold value, then illustrate associating for the corresponding variable of the canonical correlation coefficient and another data Property is weak.
The beneficial effects of the present invention are:
1. the present invention employs decorrelation method to the variable of some strong incidence relations of data inside, and data are eliminated with this Internal strong incidence relation is on another group of relevance influence of data.
2. the present invention using canonical correlation analysis analysis two groups of abilities of variable to carry out data incidence relation divide Analysis, have effectively achieved the correlation analysis between amount data complicated and changeable.
3. technical scheme only considers data in itself, to experiment condition and every group of data variable number etc. without specific It is required that, highly versatile.
Brief description of the drawings
By reference to the following drawings, illustrative embodiments of the invention can be more fully understood by:
Fig. 1 is the analysis ground total electric field and the relevance of airborne particle thing Size according to embodiment of the present invention The flow chart of method 100;
Fig. 2 is the signal of the ground total electric field data and airborne particle thing particle diameter modal data according to embodiment of the present invention Figure;
Fig. 3 is the schematic diagram of the correlation matrix of the ground total electric field data according to embodiment of the present invention;
Fig. 4 is the schematic diagram of the correlation matrix of the airborne particle thing particle diameter modal data according to embodiment of the present invention;
Fig. 5 is the ground total electric field data and airborne particle thing Size after the decorrelation according to embodiment of the present invention The schematic diagram of data;
Fig. 6 is the strong phase of the canonical variable in the ground total electric field data according to embodiment of the present invention and its dependent variable The schematic diagram of pass relation;
Fig. 7 is canonical variable and its dependent variable in the airborne particle thing particle diameter modal data according to embodiment of the present invention The schematic diagram of strong correlation relation;
Fig. 8 is the canonical correlation system of the ground total electric field data of four various locations according to embodiment of the present invention Several schematic diagrames;
Fig. 9 is the typical case of the airborne particle thing particle diameter modal data of five kinds of different-grain diameter sizes according to embodiment of the present invention The schematic diagram of coefficient correlation;
Figure 10 be according to the ground total electric field data and airborne particle thing particle diameter modal data of embodiment of the present invention most The corresponding scatter diagram of excellent linear combination;
Figure 11 is the analysis ground total electric field and the relevance of airborne particle thing Size according to embodiment of the present invention System 1100 structural representation.
Specific embodiment
With reference now to accompanying drawing, illustrative embodiments of the invention are introduced, however, the present invention can use many different shapes Formula is implemented, and is not limited to embodiment described herein, there is provided these embodiments are to disclose at large and fully The present invention, and fully pass on the scope of the present invention to person of ordinary skill in the field.For showing for being illustrated in the accompanying drawings Term in example property implementation method is not limitation of the invention.In the accompanying drawings, identical cells/elements are attached using identical Icon is remembered.
Unless otherwise indicated, term (including scientific and technical terminology) used herein has to person of ordinary skill in the field It is common to understand implication.Further it will be understood that the term limited with usually used dictionary, is appreciated that and it The linguistic context of association area has consistent implication, and is not construed as Utopian or excessively formal meaning.
A kind of analysis ground total electric field and the method for the relevance of airborne particle thing Size that the present invention is provided are bases Proposed in canonical correlation analysis, associated making full use of canonical correlation analysis two groups of abilities of variable of analysis to carry out data The analysis of relation.Wherein, by the method for decorrelation, the internal strong incidence relation of data is eliminated to another group of association of data Property influence, finally have effectively achieved the correlation analysis between amount data complicated and changeable.
Fig. 1 is the analysis ground total electric field and the relevance of airborne particle thing Size according to embodiment of the present invention The flow chart of method 100.As indicated with 1, the method for the relevance of shown analysis ground total electric field and airborne particle thing Size 100 since step 101 place, and ground total electric field data and airborne particle thing particle diameter modal data are obtained respectively in step 101, and The ground total electric field data and the airborne particle thing particle diameter modal data are standardized respectively.According to Fig. 2 The ground total electric field data of embodiment of the present invention and the schematic diagram of airborne particle thing particle diameter modal data.As shown in Fig. 2 described The upper figure of schematic diagram is 12 sample set X of the ground total electric field data of diverse location, wherein, abscissa represents that 500 are adopted At the sample moment, ordinate is electric field intensity value, and the broken line of different colours represents under diverse location that electric field changes with time situation;Under Figure is 17 kinds of sample set Y of the airborne particle thing particle diameter modal data of different-grain diameter size, wherein, the sampling instant shown in abscissa Corresponding with the sampling instant of sample set X identical, ordinate is particle size modal data, and the broken line of different colours represents different grains The particulate matter of footpath size changes with time situation.First have to ground total electric field data and airborne particle thing particle diameter modal data It is standardized respectively so that all variables have zero-mean and standard variance characteristic.Assuming that for electric field data or particulate matter A certain variable x in data, it is assumed that N number of observation of variable is x=[x1,x2,…,xN]T.Then the data after standardization are:
Wherein,It is the average of variable,It is the variance of variable.
Preferably, in step 102 respectively to the ground total electric field data and the airborne particle thing particle diameter modal data Carry out decorrelative transformation.Preferably, wherein described respectively to the ground total electric field data and the airborne particle thing particle diameter Modal data carries out decorrelative transformation to be included:Respectively to the ground total electric field data and the airborne particle thing particle diameter modal data Corresponding matrix data enters line translation or rank transformation, obtains corresponding stepped matrix;Calculate the ground total electric field data Or the correlation matrix R=[r of the particle size modal dataij], and strong correlation is calculated according to the correlation matrix R Weight matrix A=[aij],
Wherein, τ is strong correlation coefficient threshold, is strong correlation if two coefficient correlations of variable are more than τ;If two changes The coefficient correlation of amount is less than τ, then for weak related or uncorrelated;And respectively by the often capable weight of strong correlation weight matrix A it Variable corresponding with maximum weight is proposed, obtained by ground total electric field data and airborne particle the thing grain of decorrelative transformation Footpath modal data.Fig. 3 is the schematic diagram of the correlation matrix of the ground total electric field data according to embodiment of the present invention.As schemed Shown in 3, the electric-field intensity under corresponding two positions in 12 diverse locations is represented respectively, strength factor is from 0.75 to 1.Wherein color The color of block is deeper, and the relevance of the electric-field intensity under corresponding two positions of expression is stronger;The color of color lump is more shallow, and it is right to represent The relevance of the electric-field intensity under two positions answered is weaker.Fig. 4 is the airborne particle thing particle diameter according to embodiment of the present invention The schematic diagram of the correlation matrix of modal data.As shown in figure 4, representing two kinds of particle sizes in 17 in different-grain diameter respectively The corresponding coefficient correlation of particulate matter.Wherein, the color of color lump is deeper, represents the particle size spectrum of corresponding two kinds of particle sizes The relevance of data is stronger;The color of color lump is more shallow, represents the pass of the particle size modal data of corresponding two kinds of particle sizes Connection property is weaker.Decorrelation operation is carried out to the strong correlation amount in ground total electric field data or particle size modal data, specifically Comprise the following steps:Given strong correlation coefficient threshold τ, when two coefficient correlations of variable are more than τ, then regards as strong correlation, Otherwise it is weak related or uncorrelated;Calculate the correlation matrix R=of ground total electric field data or particle size modal data [rij], strong correlation weight matrix A=[a are calculated according to correlation matrix Rij], wherein:
The often capable weight sum of strong correlation weight matrix A is calculated, weight limit and corresponding variable are canonical variable And propose, and the variable of strong correlation is rejected therewith;Repeat the above steps, until all of variable is suggested or is rejected, then The data set that all variables being suggested are constituted is then the data after decorrelation.Fig. 5 is going according to embodiment of the present invention The schematic diagram of ground total electric field data and airborne particle thing particle diameter modal data after correlation.As shown in figure 5, upper figure is to extract 4 exemplary positions under ground total electric field data, wherein, abscissa represents 500 sampling instants, and ordinate is electric-field intensity Value, the broken line of different colours represents after decorrelation under 4 exemplary positions that electric field changes with time situation;Figure below is extracted 5 kinds of particle size modal datas of typical particle diameter size, wherein, during the sampling of sampling instant and electric field data shown in abscissa Carve correspondence identical, ordinate is particle size modal data, the broken line of different colours represents 5 kinds of typical particle diameter sizes after decorrelation Particulate matter change with time situation.Fig. 6 is the typical case's change in the ground total electric field data according to embodiment of the present invention The schematic diagram of the strong correlation relation of amount and its dependent variable.As shown in fig. 6, the schematic diagram is the allusion quotation of position 3,7,10 and 12 4 The strong correlation relation of type position and its dependent variable, wherein each exemplary position one color lump color of correspondence, each position correspondence one Individual color lump color, representing the ground total electric field of the position that the position represents with color lump has very strong dependency relation.According to Fig. 7 The signal of the strong correlation relation of canonical variable and its dependent variable in the airborne particle thing particle diameter modal data of embodiment of the present invention Figure.As shown in fig. 7, the schematic diagram be in particle size modal data 6,11,13,15 and 17 5 kind of canonical variable and other The strong correlation relation of variable, wherein each canonical variable correspondence one color lump color, each particle size all with a color lump Correspondence, representing the particle size spectrum of the particle size that the position represents with color lump has very strong dependency relation.
Preferably, in step 103 respectively to ground total electric field data and airborne particle the thing grain by decorrelative transformation Footpath modal data carries out canonical correlation analysis, obtains the canonical correlation coefficient and airborne particle thing particle diameter of ground total electric field data The canonical correlation coefficient of modal data.Preferably, wherein it is described respectively to the ground total electric field data by decorrelative transformation and Airborne particle thing particle diameter modal data carries out canonical correlation analysis, obtains the canonical correlation coefficient and sky of ground total electric field data The canonical correlation coefficient of middle particle size modal data includes:
By by the ground total electric field data of decorrelative transformation and airborne particle thing particle diameter modal data respectively by sample set X Represented with Y, wherein the ground total electric field data are made up of the ground total electric field of p various location, it is described aerial Particle size modal data is made up of the particle size spectrum of q different-grain diameter size, has N number of observation for each variable Value, the sample set X and Y is expressed as:
Order vector α=[α12,…,αp]TWith β=[β12,…,βq]TThe allusion quotation of sample set X and Y linear combination is represented respectively Type coefficient correlation, then linear combinationAndMaximize relevance function:
Canonical correlation analysis is expressed as following optimization problem:
Using Lagrange multiplier methods, the Lagrange functions for obtaining are as follows:
Partial derivative is asked to α and β respectively, is madeObtain:
The covariance matrix Σ of marker samples collection X and Y11=XXT22=YYTAnd Cross-covariance Σ12=XYT, Σ21=YXT, α and β is calculated respectively.Fig. 8 is the ground synthesis electricity of four various locations according to embodiment of the present invention The schematic diagram of the canonical correlation coefficient of field data.As shown in figure 8, open circle represents the position given up during decorrelation, it is real Numerical value where heart circle represents the absolute value of the corresponding canonical correlation coefficient in the position, i.e., the ground synthesis at position 3,7,10 and 12 The absolute value of the canonical correlation coefficient α of electric field data, the scope of coefficient correlation absolute value is 0 to 1.Fig. 9 is according to of the invention real Apply the schematic diagram of the canonical correlation coefficient of the airborne particle thing particle diameter modal data of five kinds of different-grain diameter sizes of mode.Such as Fig. 9 institutes Show, numerical value where open circle represents the particle diameter given up during decorrelation, solid rim represents the corresponding canonical correlation of the particle diameter The absolute value of coefficient, i.e., 6,11,13,15 and the corresponding canonical correlation coefficient β of 17 5 kind of particle size modal data absolute value, The scope of coefficient correlation absolute value is 0 to 1.
Figure 10 be according to the ground total electric field data and airborne particle thing particle diameter modal data of embodiment of the present invention most The corresponding scatter diagram of excellent linear combination.As shown in Figure 10, it is linear combinationWith Distribution on two dimensional surface, abscissa represents that, by the electric field data after linear combination, ordinate is represented by linear combination Particulate count evidence afterwards, electric field data is corresponding with particulate count evidence under each discrete point represents a certain sampling instant.Wherein, from Scatterplot is distributed near the angular bisector of one or three quadrants, illustrates that linear combination x, y have strong correlation.
Preferably, in step 104 canonical correlation coefficient respectively to the ground total electric field data and described aerial The canonical correlation coefficient of grain thing particle diameter modal data is analyzed, and judges the ground total electric field data and airborne particle thing particle diameter The relevance of modal data.Preferably, wherein the canonical correlation coefficient respectively to the ground total electric field data and described The canonical correlation coefficient of airborne particle thing particle diameter modal data is analyzed, and judges the ground total electric field data and airborne particle The relevance of thing particle diameter modal data includes:
Canonical correlation coefficient respectively to the ground total electric field data and the airborne particle thing particle diameter modal data Canonical correlation coefficient takes absolute value;
The absolute value is compared with canonical correlation coefficient threshold value respectively, and the ground is judged according to comparative result The relevance of total electric field data and airborne particle thing particle diameter modal data, if the absolute value of canonical correlation coefficient is more than canonical correlation Coefficient threshold, then illustrate that the corresponding variable of the canonical correlation coefficient is strong with the relevance of another data;If canonical correlation coefficient Absolute value be less than canonical correlation coefficient threshold value, then illustrate associating for the corresponding variable of the canonical correlation coefficient and another data Property is weak.
The variable got rid of in for being operated in decorrelation, they are not examined due to strong correlation in canonical variable Consider, thus their influences to another data set are identical with the influence degree of its correspondence canonical variable.
Figure 11 is the analysis ground total electric field and the relevance of airborne particle thing Size according to embodiment of the present invention System 1100 structural representation.As shown in figure 11, the pass of analysis ground total electric field and airborne particle thing Size The system 1100 of connection property includes:Standardization unit 1101, decorrelative transformation unit 1102, canonical correlation coefficient computing unit 1103 and relevance determining unit 1104.Preferably, ground total electric field is obtained respectively in the standardization unit 1101 Data and airborne particle thing particle diameter modal data, and respectively to the ground total electric field data and the airborne particle thing Size Data are standardized.
Preferably, in the decorrelative transformation unit 1102 respectively to ground total electric field data and described aerial Grain thing particle diameter modal data carries out decorrelative transformation.Preferably, wherein described respectively to ground total electric field data and described Airborne particle thing particle diameter modal data carries out decorrelative transformation to be included:
The ground total electric field data and the corresponding matrix data of the airborne particle thing particle diameter modal data are entered respectively Line translation or rank transformation, obtain corresponding stepped matrix;
Calculate the correlation matrix R=[r of the ground total electric field data or the particle size modal dataij], And strong correlation weight matrix A=[a are calculated according to the correlation matrix Rij],
Wherein, τ is strong correlation coefficient threshold, is strong correlation if two coefficient correlations of variable are more than τ;If two changes The coefficient correlation of amount is less than τ, then for weak related or uncorrelated;
The corresponding variable of the maximum weight of the often capable weight sum of strong correlation weight matrix A is proposed respectively, obtain through Cross the ground total electric field data and airborne particle thing particle diameter modal data of decorrelative transformation.
Preferably, electricity is synthesized to the ground by decorrelative transformation respectively in the canonical correlation coefficient computing unit 1103 Field data and airborne particle thing particle diameter modal data carry out canonical correlation analysis, obtain the canonical correlation of ground total electric field data The canonical correlation coefficient of coefficient and airborne particle thing particle diameter modal data.Preferably, wherein described respectively to by decorrelative transformation Ground total electric field data and airborne particle thing particle diameter modal data carry out canonical correlation analysis, obtain ground total electric field number According to canonical correlation coefficient and the canonical correlation coefficient of airborne particle thing particle diameter modal data include:
By by the ground total electric field data of decorrelative transformation and airborne particle thing particle diameter modal data respectively by sample set X Represented with Y, wherein the ground total electric field data are made up of the ground total electric field of p various location, it is described aerial Particle size modal data is made up of the particle size spectrum of q different-grain diameter size, has N number of observation for each variable Value, the sample set X and Y is expressed as:
Order vector α=[α12,…,αp]TWith β=[β12,…,βq]TThe allusion quotation of sample set X and Y linear combination is represented respectively Type coefficient correlation, then linear combinationAndMaximize relevance function:
Canonical correlation analysis is expressed as following optimization problem:
Using Lagrange multiplier methods, the Lagrange functions for obtaining are as follows:
Partial derivative is asked to α and β respectively, is madeObtain:
The covariance matrix Σ of marker samples collection X and Y11=XXT22=YYTAnd Cross-covariance Σ12=XYT, Σ21=YXT, α and β is calculated respectively.
Preferably, in the relevance determining unit 1104 respectively to the canonical correlation system of the ground total electric field data Number and the canonical correlation coefficient of the airborne particle thing particle diameter modal data are analyzed, judge the ground total electric field data with The relevance of airborne particle thing particle diameter modal data.Preferably, wherein described respectively to the typical case of the ground total electric field data The canonical correlation coefficient of coefficient correlation and the airborne particle thing particle diameter modal data is analyzed, and judges the ground total electric field The relevance of data and airborne particle thing particle diameter modal data includes:Respectively to the canonical correlation system of the ground total electric field data The canonical correlation coefficient of number and the airborne particle thing particle diameter modal data takes absolute value;And by the absolute value respectively with typical case Correlation coefficient threshold is compared, and judges the ground total electric field data and airborne particle thing Size according to comparative result The relevance of data, if the absolute value of canonical correlation coefficient is more than canonical correlation coefficient threshold value, illustrates the canonical correlation system The corresponding variable of number is strong with the relevance of another data;If the absolute value of canonical correlation coefficient is less than canonical correlation coefficient threshold value, Then illustrate that the corresponding variable of the canonical correlation coefficient is weak with the relevance of another data.
The present invention is described by reference to a small amount of implementation method.However, it is known in those skilled in the art, as What subsidiary Patent right requirement was limited, except the present invention other embodiments disclosed above equally fall of the invention In the range of.
Normally, all terms for using in the claims are all solved according to them in the usual implication of technical field Release, unless clearly defined in addition wherein.It is all of to be all opened ground with reference to " one/described/be somebody's turn to do [device, component etc.] " At least one of described device, component etc. example is construed to, unless otherwise expressly specified.Any method disclosed herein Step need not all be run with disclosed accurate order, unless explicitly stated otherwise.

Claims (8)

1. the method for the relevance of a kind of analysis ground total electric field and airborne particle thing Size, it is characterised in that the side Method includes:
Ground total electric field data and airborne particle thing particle diameter modal data are obtained respectively, and respectively to the ground total electric field number It is standardized according to the airborne particle thing particle diameter modal data;
Decorrelative transformation is carried out to the ground total electric field data and the airborne particle thing particle diameter modal data respectively;
Canonical correlation is carried out to the ground total electric field data by decorrelative transformation and airborne particle thing particle diameter modal data respectively Property analysis, obtain the canonical correlation coefficient of ground total electric field data and the canonical correlation system of airborne particle thing particle diameter modal data Number;
Canonical correlation coefficient respectively to the ground total electric field data and the typical case of the airborne particle thing particle diameter modal data Coefficient correlation is analyzed, and judges the relevance of the ground total electric field data and airborne particle thing particle diameter modal data.
2. method according to claim 1, it is characterised in that described respectively to ground total electric field data and described Airborne particle thing particle diameter modal data carries out decorrelative transformation to be included:
The ground total electric field data and the corresponding matrix data of the airborne particle thing particle diameter modal data are become respectively Change or rank transformation, obtain corresponding stepped matrix;
Calculate the correlation matrix R=[r of the ground total electric field data or the particle size modal dataij], and root Strong correlation weight matrix A=[a are calculated according to the correlation matrix Rij],
a i j = r i j , i f r i j > τ 0 , o t h e r w i s e ,
Wherein, τ is strong correlation coefficient threshold, is strong correlation if two coefficient correlations of variable are more than τ;
If two coefficient correlations of variable are less than τ, for weak related or uncorrelated;
The corresponding variable of the maximum weight of the often capable weight sum of strong correlation weight matrix A is proposed respectively, was obtained through the past The ground total electric field data and airborne particle thing particle diameter modal data of relevant treatment.
3. method according to claim 1, it is characterised in that described that electricity is synthesized to the ground by decorrelative transformation respectively Field data and airborne particle thing particle diameter modal data carry out canonical correlation analysis, obtain the canonical correlation of ground total electric field data The canonical correlation coefficient of coefficient and airborne particle thing particle diameter modal data includes:
By by the ground total electric field data of decorrelative transformation and airborne particle thing particle diameter modal data respectively by sample set X and Y To represent, wherein the ground total electric field data are made up of the ground total electric field of p various location, the airborne particle Thing particle diameter modal data is made up of the particle size spectrum of q different-grain diameter size, has N number of observation, institute for each variable Sample set X and Y is stated to be expressed as:
Order vector α=[α12,…,αp]TWith β=[β12,…,βq]TThe typical phase of sample set X and Y linear combination is represented respectively Relation number, then linear combinationAndMaximize relevance function:
C o r r ( x ~ , y ~ ) = E [ x ~ y ~ T ] E [ x ~ x ~ T ] E [ y ~ y ~ T ] = α T XY T β α T XX T α · β T YY T β ;
Canonical correlation analysis is expressed as following optimization problem:
max α , β f ( α , β ) = α T XY T β s . t . α T XX T α = 1 β T YY T β = 1 ;
Using Lagrange multiplier methods, the Lagrange functions for obtaining are as follows:
L ( α , β ) = α T XY T β - λ 2 ( α T XX T α - 1 ) - μ 2 ( β T YY T β - 1 ) ,
Partial derivative is asked to α and β respectively, is madeObtain:
∂ L ∂ α = XY T β - λ · XX T α = 0
∂ L ∂ β = YX T α - μ · YY T β = 0 ;
The covariance matrix Σ of marker samples collection X and Y11=XXT22=YYTAnd Cross-covariance Σ12=XYT21= YXT, α and β is calculated respectively.
4. method according to claim 1, it is characterised in that described respectively to the typical case of the ground total electric field data The canonical correlation coefficient of coefficient correlation and the airborne particle thing particle diameter modal data is analyzed, and judges the ground total electric field The relevance of data and airborne particle thing particle diameter modal data includes:
Canonical correlation coefficient respectively to the ground total electric field data and the typical case of the airborne particle thing particle diameter modal data Coefficient correlation takes absolute value;
The absolute value is compared with canonical correlation coefficient threshold value respectively, and the ground synthesis is judged according to comparative result The relevance of electric field data and airborne particle thing particle diameter modal data, if the absolute value of canonical correlation coefficient is more than canonical correlation coefficient Threshold value, then illustrate that the corresponding variable of the canonical correlation coefficient is strong with the relevance of another data;If canonical correlation coefficient is exhausted Canonical correlation coefficient threshold value is less than to value, then illustrates the relevance of the corresponding variable of the canonical correlation coefficient and another data It is weak.
5. the system of the relevance of a kind of analysis ground total electric field and airborne particle thing Size, it is characterised in that the system System includes:Standardization unit, decorrelative transformation unit, canonical correlation coefficient computing unit and relevance determining unit,
The standardization unit, obtains ground total electric field data and airborne particle thing particle diameter modal data respectively, and respectively The ground total electric field data and the airborne particle thing particle diameter modal data are standardized;
The ground total electric field data and the airborne particle thing particle diameter modal data are entered by the decorrelative transformation unit respectively Row decorrelative transformation;
The canonical correlation coefficient computing unit, respectively to the ground total electric field data and airborne particle by decorrelative transformation Thing particle diameter modal data carries out canonical correlation analysis, obtains the canonical correlation coefficient and airborne particle thing of ground total electric field data The canonical correlation coefficient of particle diameter modal data;
The relevance determining unit, respectively to the canonical correlation coefficient and the airborne particle of the ground total electric field data The canonical correlation coefficient of thing particle diameter modal data is analyzed, and judges the ground total electric field data and airborne particle thing Size The relevance of data.
6. system according to claim 5, it is characterised in that described respectively to ground total electric field data and described Airborne particle thing particle diameter modal data carries out decorrelative transformation to be included:
The ground total electric field data and the corresponding matrix data of the airborne particle thing particle diameter modal data are become respectively Change or rank transformation, obtain corresponding stepped matrix;
Calculate the correlation matrix R=[r of the ground total electric field data or the particle size modal dataij], and root Strong correlation weight matrix A=[a are calculated according to the correlation matrix Rij],
a i j = r i j , i f r i j > τ 0 , o t h e r w i s e ,
Wherein, τ is strong correlation coefficient threshold, is strong correlation if two coefficient correlations of variable are more than τ;If two variables Coefficient correlation is less than τ, then for weak related or uncorrelated;
The corresponding variable of the maximum weight of the often capable weight sum of strong correlation weight matrix A is proposed respectively, was obtained through the past The ground total electric field data and airborne particle thing particle diameter modal data of relevant treatment.
7. system according to claim 5, it is characterised in that described that electricity is synthesized to the ground by decorrelative transformation respectively Field data and airborne particle thing particle diameter modal data carry out canonical correlation analysis, obtain the canonical correlation of ground total electric field data The canonical correlation coefficient of coefficient and airborne particle thing particle diameter modal data includes:
By by the ground total electric field data of decorrelative transformation and airborne particle thing particle diameter modal data respectively by sample set X and Y To represent, wherein the ground total electric field data are made up of the ground total electric field of p various location, the airborne particle Thing particle diameter modal data is made up of the particle size spectrum of q different-grain diameter size, has N number of observation, institute for each variable Sample set X and Y is stated to be expressed as:
Order vector α=[α12,…,αp]TWith β=[β12,…,βq]TThe typical phase of sample set X and Y linear combination is represented respectively Relation number, then linear combinationAndMaximize relevance function:
C o r r ( x ~ , y ~ ) = E [ x ~ y ~ T ] E [ x ~ x ~ T ] E [ y ~ y ~ T ] = α T XY T β α T XX T α · β T YY T β ;
Canonical correlation analysis is expressed as following optimization problem:
max α , β f ( α , β ) = α T XY T β s . t . α T XX T α = 1 β T YY T β = 1 ;
Using Lagrange multiplier methods, the Lagrange functions for obtaining are as follows:
L ( α , β ) = α T XY T β - λ 2 ( α T XX T α - 1 ) - μ 2 ( β T YY T β - 1 ) ,
Partial derivative is asked to α and β respectively, is madeObtain:
∂ L ∂ α = XY T β - λ · XX T α = 0
∂ L ∂ β = YX T α - μ · YY T β = 0 ;
The covariance matrix Σ of marker samples collection X and Y11=XXT22=YYTAnd Cross-covariance Σ12=XYT21= YXT, α and β is calculated respectively.
8. system according to claim 5, it is characterised in that described respectively to the typical case of the ground total electric field data The canonical correlation coefficient of coefficient correlation and the airborne particle thing particle diameter modal data is analyzed, and judges the ground total electric field The relevance of data and airborne particle thing particle diameter modal data includes:
Canonical correlation coefficient respectively to the ground total electric field data and the typical case of the airborne particle thing particle diameter modal data Coefficient correlation takes absolute value;
The absolute value is compared with canonical correlation coefficient threshold value respectively, and the ground synthesis is judged according to comparative result The relevance of electric field data and airborne particle thing particle diameter modal data, if the absolute value of canonical correlation coefficient is more than canonical correlation coefficient Threshold value, then illustrate that the corresponding variable of the canonical correlation coefficient is strong with the relevance of another data;If canonical correlation coefficient is exhausted Canonical correlation coefficient threshold value is less than to value, then illustrates the relevance of the corresponding variable of the canonical correlation coefficient and another data It is weak.
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Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US4329053A (en) * 1975-02-26 1982-05-11 Nasa Frequency-scanning particle size spectrometer
CN102967541A (en) * 2012-11-22 2013-03-13 中国石油大学(北京) Device and method suitable for on-line detection of particulate matters in high-temperature gas pipeline
CN103454203A (en) * 2013-09-09 2013-12-18 中国科学院合肥物质科学研究院 Real-time online measurement system and method of particle size and chemical components of atmospheric particulate
CN106226842A (en) * 2016-07-13 2016-12-14 成都信息工程大学 A kind of city underlying surface aerosol method of testing to thunder and lighting process Influencing Mechanism

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US4329053A (en) * 1975-02-26 1982-05-11 Nasa Frequency-scanning particle size spectrometer
CN102967541A (en) * 2012-11-22 2013-03-13 中国石油大学(北京) Device and method suitable for on-line detection of particulate matters in high-temperature gas pipeline
CN103454203A (en) * 2013-09-09 2013-12-18 中国科学院合肥物质科学研究院 Real-time online measurement system and method of particle size and chemical components of atmospheric particulate
CN106226842A (en) * 2016-07-13 2016-12-14 成都信息工程大学 A kind of city underlying surface aerosol method of testing to thunder and lighting process Influencing Mechanism

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