CN103678869A - Prediction and estimation method of flight parameter missing data - Google Patents

Abstract

The invention discloses a prediction and estimation method of flight parameter missing data. The method comprises the steps that firstly, the relevancy between all parameters is calculated to obtain a correlation matrix, all principal components reflecting the flying state of an airplane are determined by conducting principle component analysis on the correlation matrix, then, the parameters which have higher relevancy with the missing data are selected, loads, on all the parameters, of the principle components having higher relevancy with the missing data are compared, the parameters having higher relevancy with the missing data are further selected, time sequence modeling and order determining are conducted according to a time sequence modeling method, and testing is conducted on models according to a residual white noise analyzing method to obtain reasonable models, and then estimation and prediction of the missing data are conducted. By means of the prediction and estimation method, the prediction and estimation accuracy of the flight parameter missing data can be improved, and meanwhile, the number of dimensions of data processing can be reduced.

Description

A kind of prediction estimation method of flight parameter missing data

Technical field

The present invention relates to a kind of prediction estimation method of multivariate time series missing data, be specially adapted to flight parameter data.

Background technology

Along with improving constantly of scientific and technological level, in each field, all emerge multivariate time series data.Multivariate time series is not a plurality of monobasic seasonal effect in time series simple superposition, comprises a plurality of parameters in multivariate time series, and each parameter is determined the state of things jointly, and between each parameter, has certain incidence relation.

For multivariate time series data, researcher utilizes the technology such as neural network, support vector machine to predict estimation processing both at home and abroad.Said method is all the methods based on statistical learning, lays particular emphasis on the development trend of analyzing data from the statistical nature of data, is relatively applicable to not emphasize the multivariate time series data of sequential relationship.

Flight parameter data are a kind of in multivariate time series data, it is characterized in that: (1) parameter unit number is high, has certain correlativity between each yuan of parameter value; (2) the front and back data of each yuan of parameter value have certain sequential relationship, show as a kind of development trend; (3) data volume is large.

In utilization, fly to join in the process of registering instrument collection and record-setting flight supplemental characteristic, can be because interference such as noises, electronics, produce the abnormal conditions such as the improper beginning of some loss of datas, data distortion and record or end.These abnormal conditions will have a strong impact on the effect of carrying out flare maneuver assessment based on flight parameter data.Thereby, before carrying out the activities such as flight training assessment, need to estimate to replace to distortion data and missing data.

By technology such as neural network of the prior art, support vector machine, during for the treatment of flight parameter data, the accuracy that prediction is estimated is lower, and computation complexity is higher.Sequential character for flight parameter data, can applied time series analysis technology predict estimation, but current techniques of teime series analysis, although can consider the correlativity between a plurality of parameters as multivariate autoregressive modeling and analysis methods analyzes, but it is confined to the fewer situation of parameter unit's number, be not suitable for the high flight parameter data of parameter unit's number.

Summary of the invention

The technical problem to be solved in the present invention is: for the deficiencies in the prior art, the invention provides a kind of prediction estimation method of flight parameter missing data, utilize the maximally related parameter of principal component analysis (PCA) extraction and flare maneuver, the correlativity of these parameters is dissolved into the estimation procedure to distortion and missing data, thereby obtains rationally reflecting and reappearing the time series data of flight status.

For solving the problems of the technologies described above, concrete steps of the present invention are:

A kind of prediction estimation method of flight parameter missing data, it is characterized in that utilizing the maximally related parameter of principal component analysis (PCA) extraction and flare maneuver, and the correlativity of these parameters is dissolved into the estimation procedure to distortion and missing data, thereby the time series data that obtains rationally reflecting and reappearing aircraft flight action, concrete steps are:

(1) from given flight parameter extracting data part time series data collection complete, that there is no disappearance, and data set is carried out to standardization;

(2) set up the correlation matrix between each yuan of parametric data of data set;

(3) carry out principal component analysis (PCA): by correlation matrix being carried out to eigenmatrix calculating, try to achieve the load of each major component on each parameter, and by calculating the accumulation contribution rate of major component, determine the major component of reflection flight status;

(4) select the parameter larger with the parameter correlativity of missing data, and the load of the major component by more selected parameter on each parameter, the parameter with missing data correlativity maximum further selected;

(5) utilize that time series modeling analytical approach is that choose upper step carries out time series modeling, determines rank with the data of parameter missing data degree of correlation maximum;

(6) utilize the model that step (5) obtains to predict any time data of missing data parameter, the result of prediction and actual result compare, and obtain residual sequence;

(7) to predicting the outcome, test, judge whether described residual sequence is white noise, if white noise, the model that acceptance is set up, otherwise, need modeling again, determine rank, prediction and check;

(8) utilize by the model of check missing data is estimated.

As a further improvement on the present invention:

In step (4), determine that the process described and parameter that the missing data degree of correlation is larger is:

(4a) described load is taken absolute value and normalized obtains the degree of correlation weight of each parameter;

(4b) degree of correlation weight is arranged from big to small;

(4c) choose front m item parameter: front m item degree of correlation weight equal d with value, the scope of described d is 0.6≤J≤0.8, described m value≤5, parameter corresponding to front m item degree of correlation weight is m the parameter larger with missing data parameter correlativity.

Accumulation contribution rate described in step (3) is greater than 95%.

Time series modeling analytical approach in step (5) refers to multivariate autoregressive modeling.

The principle of determining rank described in step (5) is AIC function minimum principle.

Compared with prior art, the invention has the advantages that and the correlativity between each parameter of flight parameter can be dissolved into the estimation procedure to distortion and missing data, can rationally be reflected and reappear the time series data of flight status.It is little that the present invention is applicable to processing flight parameter data and predicated error that the many data volumes of parameter unit's number are large.

Accompanying drawing explanation

Fig. 1 is the prediction estimation method process flow diagram of a kind of flight parameter disappearance number pick;

Embodiment

Below with reference to the drawings and specific embodiments, the present invention is described in further detail.

Shown in Fig. 1, concrete steps of the present invention comprise:

Step 1: from given flight parameter extracting data part time series data collection X complete, that there is no disappearance _c, and to X _ccarry out standardization.

If given flight parameter data X, X relates to n parameter x _i(i=1,2 ..., n).Suppose that sampling number is T, i.e. each parameter x _i, all by T sampled data, formed parameter x _icomponent be x _ij, (i=1,2 ..., n, j=1,2 ..., T).Selected part time series data collection X complete, that there is no disappearance from X _c, establish X _ccomprise T in X _cindividual sampled data, i.e. each parameter x _iby T _cindividual sampled data forms.To X _ccarry out standardization, the component after standardization is in formula

and s _irespectively parameter x _imean value and standard deviation.

Step 2: for the data set X after standardization _c, set up the correlation matrix R between its each parametric data.

Calculate sample X _ccorrelation matrix

$R=\left[\begin{array}{cccc}1& r_{21}& ...& r_{1n}\\ r_{21}& 1& ...& r_{2n}\\ .& .& & .\\ .& .& & .\\ .& .& & .\\ r_{n1}& r_{n2}& ...& 1\end{array}\right]$

In formula $r_{\mathrm{ij}}=\frac{1}{T_c-1}\underset{k=1}{\overset{T_c}{\mathrm{\Σ}}}{z}_{\mathrm{ik}}{z}_{\mathrm{jk}}=r_{\mathrm{ji}},(i,j=\mathrm{1,2},...,n).$

Step 3: correlation matrix R is carried out to eigenmatrix calculating and try to achieve the load of each major component on each parameter, and determine front r major component by calculating the accumulation contribution rate of major component.

Major component y in the present invention _k, (k=1,2 ..., r) can be expressed as

y _k＝U _k1X ₁+u _k2x ₂+…+u _knx _n

In formula, u _kj, represent major component y _kat parameter x _ion load.

Correlation matrix R is carried out to eigenmatrix calculating, lists secular equation | R-λ I|=0,

$\left|\begin{array}{cccc}1-\mathrm{\λ}& r_{12}& ...& r_{1n}\\ r_{21}& 1-\mathrm{\λ}& ...& r_{2n}\\ .& .& & .\\ .& .& & .\\ .& .& & .\\ r_{n1}& r_{n2}& ...& 1-\mathrm{\λ}\end{array}\right|=0$

Obtain n the non-negative real root of equation, and by non-negative real root by arranging from big to small, i.e. λ ₁>=λ ₂>=...>=λ _n>=0.

By λ _k(k=1,2 ..., n) below substitution, equation is obtained proper vector, and this proper vector is major component y _kat parameter x _ion load u _ki.

$\left|\begin{array}{cccc}1-\mathrm{\λ}& r_{12}& ...& r_{1n}\\ r_{21}& 1-\mathrm{\λ}& ...& r_{2n}\\ .& .& & .\\ .& .& & .\\ .& .& & .\\ r_{n1}& r_{n2}& ...& 1-\mathrm{\λ}\end{array}\right|\left[\begin{array}{c}{u}_{k1}\\ u_{k2}\\ .\\ .\\ .\\ u_{\mathrm{kn}}\end{array}\right]=\left[\begin{array}{c}0\\ 0\\ .\\ .\\ .\\ 0\end{array}\right]$

In conjunction with u _kito parameter x _ilinear transformation obtains n major component y _k, (k=1,2 ..., n).

Definition

hook the contribution rate of each major component aspect reflection system state.By calculating the accumulation contribution rate of major component r major component before determining.If r major component of the reflection flight status drawing is y ₁, y ₂... y _r.

In order to reflect the state of flight of aircraft, the accumulation contribution rate of a front r major component is preferably more than 95%.

Step 4: select the parameter x with missing data _bthe parameter that correlativity is larger, and the load of the major component by more selected parameter on each parameter, further select m the parameter with missing data correlativity maximum;

If the parameter of missing data is x _b(b ∈ 1,2 ..., n}), compare x _bat r major component y _k(k=1,2 ..., r) middle load u _kbabsolute value (| u _kb|) size, find out maximal value | u _qb| (=max (| u _1b|, | u _2b| ... | u _rb|).Selected maximal value | u _qb| corresponding major component y _b=u _q1x ₁+ u _q2x ₂+ ... + u _qbx _p+ ... + u _qnx _n, and from y _qlinear transformation expression formula in, each parameter x relatively _i(i=1,2 ..., the load u on n) _qi, select and y _qthe m of a correlativity maximum parameter.As preferred embodiment, the definite concrete steps of this m parameter are:

(4.1) to load u _qitake absolute value and normalized, the degree of correlation weight that obtains n parameter is respectively | C| ₁, | C| ₂..., | C| _n, wherein

(4.2) by degree of correlation weight (| C| ₁, | C| ₂..., | C| _n) arrange from big to small;

(4.3) front m item degree of correlation weight should be greater than d with value, the scope of described d is O.6～0.8, from processing speed and accuracy, lower than the data that equal 5 dimensions, be applicable to utilizing time series modeling technique to carry out follow-up data processing, therefore the scope of described m value is 1～5, parameter corresponding to front m item degree of correlation weight is and y _qthe m of a correlativity maximum parameter.

The effect that this step is processed is like this, can select m the parameter with certain system state correlativity maximum, this m parametric data is estimated for missing data simultaneously, can improve the accuracy of estimation and reduce the dimension of data processing simultaneously, also be convenient to utilize time series modeling technique to carry out follow-up data processing.

Step 5: utilize that time series modeling analytical approach is that choose upper step carries out time series modeling, determines rank with the data of parameter missing data degree of correlation maximum.

Described time series modeling analytical approach has autoregressive modeling analysis, running mean modeling analysis and autoregression slip modeling analysis.Because the parameter estimation of autoregressive model is linear regression process, it calculates simply, speed is fast, actual physics system is full pole system often also, therefore the present invention preferably adopts multivariate autoregressive model, and comprehensive a plurality of related parameter values are carried out modeling analysis flight parameter data modeling is carried out to data estimator.

Use X _t=(x _1t, x _2t, x _mt) be illustrated in t constantly, the time series of m flight parameter, X _tthe general type of m dimension autoregressive model be:

X _t=a ₁X _t-1+a ₂X _t-2+…+a _px _t-p+ε _t

In formula, p is the exponent number of model, a ₁, a ₂... a _pall m * m rank solve for parameter matrixes, ε _t=(ε _1t, ε _2t..., e _mt) ^τbe m dimension white noise vector, also claim ε _tresidual error for model.

First Analysis of X _tstationarity, and it is carried out to tranquilization processing and normalize check.Seasonal effect in time series coefficient of autocorrelation after difference processing is decreased significantly trend, illustrates that the sequence through differential transformation has met the condition of regression modeling, then it is carried out to standardization normal state and processes and multivariate autoregressive modeling.The autoregressive model of m dimension can be expressed as:

$\left\{\begin{array}{c}{X}_{p+1}\left(i\right)={\mathrm{\Φ}}_{p+1}A\left(i\right)+{\mathrm{\ϵ}}_{n+1}\left(i\right)\\ .\\ .\\ .\\ X_N\left(i\right)={\mathrm{\Φ}}_{N}A\left(i\right)+{\mathrm{\ϵ}}_N\left(i\right)\end{array}\right.$

In formula: i=1,2 ... m,

t=p+1, p+2 ... N;

A(i)=[a ₁(i)，a ₂(i)…，a _p(i)] ^T。If IV is the final observation moment, and order

$L_N\left(i\right)=\left[\begin{array}{c}{x}_{p+1}\left(i\right)\\ ...\\ x_N\left(i\right)\end{array}\right],B_N=\left[\begin{array}{c}{\mathrm{\Φ}}_{p+1}\\ ...\\ {\mathrm{\Φ}}_N\end{array}\right],E_N=\left[\begin{array}{c}{\mathrm{\ϵ}}_{p+1}\left(i\right)\\ ...\\ {\mathrm{\ϵ}}_N\left(i\right)\end{array}\right]$

Autoregressive model can be converted into L _n(i)=B _na (i)+E _n(i).

Residual sum of squares (RSS) J can be expressed as

$\underset{t=p+1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\ϵ}}_t^T{\mathrm{\ϵ}}_t=\underset{t=p+1}{\overset{N}{\mathrm{\Σ}}}{(x_t-\underset{i=1}{\overset{p}{\mathrm{\Σ}}}{a}_i{x}_{t-i})}^T(x_t-\underset{i=1}{\overset{p}{\mathrm{\Σ}}}{a}_i{x}_{t-i})$

When J reaches minimal value, must have

$J_{\min }\left(i\right)=\underset{t=p+1}{\overset{N}{\mathrm{\Σ}}}{\left|E_N\left(i\right)\right|}^T\left|E_N\left(i\right)\right|$

The least-squares estimation value of the A of all observed readings based on moment N (i) like this

(i) be:

${\hat{A}}_N\left(i\right)={\left(B_N^T{B}_N\right)}^{-1}{B}^T{L}_N\left(i\right),i=\mathrm{1,2},...,m.$

For what meet data characteristics most, determine rank model, also need further model to be carried out determining rank.The principle of determining rank has a lot, and in the present invention, the exponent number p of model preferably adopts AIC function minimum principle to determine.

If a step of forecasting residual error of model

wherein

represent that prediction obtains t data constantly, X _trepresent t real data constantly,

be matching residual error variance, it is the function of model order p, and definition AIC criterion function is:

$\mathrm{AIC}\left(p\right)=\lg {\mathrm{\δ}}_E^2\left(p\right)+2p/N,p\∈(\mathrm{0,1},...n)$

In formula,

can be calculated as

${\mathrm{\δ}}_E^2\left(p\right)=\frac{{\mathrm{\δ}}_1^2}{{\left|C\right|}_1}+\frac{{\mathrm{\δ}}_2^2}{{\left|C\right|}_2}+...+\frac{{\mathrm{\δ}}_m^2}{{\left|C\right|}_m}$

Be in the present invention

the front m item degree of correlation weight that the descending order that can be obtained by step (4) is arranged (| C| ₁, | C| ₂..., | C| _m) can be calculated.

represent m dimension parameter time series X _t,=(x _1t, x _2t..., x _mt) ^τin) x _itmatching residual error variance.To criterion function AIC (p), the exponent number p of true model _odetermining rank meets

Step 7: to predicting the outcome, test, judge whether described residual sequence is white noise, if white noise, the model that acceptance is set up, otherwise, need modeling again, determine rank, prediction and check.

Step 8: utilize by the model of check missing data is estimated.

The above is only the preferred embodiment of the present invention, and protection scope of the present invention is also not only confined to above-described embodiment, and all technical schemes belonging under thinking of the present invention all belong to protection scope of the present invention.Should propose, for those skilled in the art, improvements and modifications without departing from the principles of the present invention, these improvements and modifications also should be considered as protection scope of the present invention.

Claims (5)

1. the prediction estimation method of a flight parameter missing data, it is characterized in that utilizing the maximally related parameter of principal component analysis (PCA) extraction and flare maneuver, and the correlativity of these parameters is dissolved into the estimation procedure to distortion and missing data, thereby the time series data that obtains rationally reflecting and reappearing aircraft flight action, concrete steps are:

(1) from given flight parameter extracting data part time series data collection complete, that there is no disappearance, and data set is carried out to standardization;

(2) set up the correlation matrix between each yuan of parametric data of data set;

(3) carry out principal component analysis (PCA): by correlation matrix being carried out to eigenmatrix calculating, try to achieve the load of each major component on each parameter, and by calculating the accumulation contribution rate of major component, determine the major component of reflection flight status;

(4) select the parameter larger with the parameter correlativity of missing data, and the load of the major component by more selected parameter on each parameter, the parameter with missing data correlativity maximum further selected;

(5) utilize that time series modeling analytical approach is that choose upper step carries out time series modeling, determines rank with the data of parameter missing data correlativity maximum;

(6) utilize the model that step (5) obtains to predict any time data of missing data parameter, the result of prediction and actual result compare, and obtain residual sequence;

(7) to predicting the outcome, test, judge whether described residual sequence is white noise, if white noise, the model that acceptance is set up, otherwise, need modeling again, determine rank, prediction and check;

(8) utilize by the model of check missing data is estimated.

2. the prediction estimation method of a kind of flight parameter missing data according to claim 1, is characterized in that determining in step (4) that the process of the parameter of described and missing data correlativity maximum is:

(4a) described load is taken absolute value and normalized obtains the degree of correlation weight of each parameter;

(4b) degree of correlation weight is arranged from big to small;

(4c) choose front m item parameter: front m item degree of correlation weight equal d with value, the scope of described d is O.6≤J≤O.8, described m value≤5, parameter corresponding to front m item degree of correlation weight is m the parameter with missing data parameter correlativity maximum.

3. the prediction estimation method of a kind of flight parameter missing data according to claim 1, is characterized in that the accumulation contribution rate described in step (3) is greater than 95%.

4. the prediction estimation method of a kind of flight parameter missing data according to claim 1, is characterized in that the time series modeling analytical approach in step (5) refers to multivariate autoregressive modeling.

5. the prediction estimation method of a kind of flight parameter missing data according to claim 1, is characterized in that the principle of determining rank described in step (5) is AIC function minimum principle.

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