CN104915434B - A kind of multidimensional time-series sorting technique based on mahalanobis distance DTW - Google Patents
A kind of multidimensional time-series sorting technique based on mahalanobis distance DTW Download PDFInfo
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Abstract
A kind of multidimensional time-series sorting technique based on mahalanobis distance DTW, the present invention relates to multidimensional time-series sorting technique.The present invention is to solve for satellite telemetering data be fixed a subsection efect it is undesirable, due to correlation between multidimensional time-series be present and time series has minor shifts and makes measurement results not accurate enough and then the problem of cause classification results not accurate enough, and propose a kind of multidimensional time-series sorting technique based on mahalanobis distance DTW.This method is by 1, obtains multidimensional time-series X={ x for training1,x2,...,xj... xnAnd class label L={ l1,l2,…,ln}；2nd, multidimensional time-series X '={ x ' to be sorted is extracted1,x′2,...,x′m}；3rd, X '={ x ' is calculated1,x′2,...,x′mAnd X={ x1,x2,...,xj... xnBetween DTW distance sequences；4th, using the KNN sorting techniques of the DTW distances based on mahalanobis distance, according to the k nearest neighbor number of setting to multidimensional time-series X '={ x ' to be sorted1,x′2,...,x′mClassified, determine what the steps such as the generic of multidimensional time-series to be sorted were realized.The present invention is applied to multidimensional time-series classification field.
Description
Technical field
The present invention relates to the multidimensional time-series sorting technique based on mahalanobis distance DTW.
Background technology
By analyzing the yaw-position angle in satellite telemetering data, the overall variation trend at yaw-position angle is as schemed
Shown in 1, its variations in detail is as shown in Fig. 2 show that satellite telemetering data has significantly periodically, and the characteristic is distant with satellite
Data offer unit is surveyed to be confirmed.By analyzing each cycle of telemetry, it can be deduced that satellite is in this week
Whether the running status within the phase is normal, according to the fixing point situation undesirable to satellite telemetering data subsection efect, such as Fig. 3 institutes
Show, the degree of coupling between each time series obtained after segmentation is not high enough, certain deviation, and propulsion over time be present
This deviation can be more obvious.
It is that a critical function of data mining is carried out to satellite telemetering data that classification is carried out to satellite telemetering data, is being divided
A variety of data mining tasks, such as pattern-recognition, abnormality detection etc. can be completed on the basis of class.And satellite telemetering data
There is its own feature, such as：Parameter is more, dimension is high, drift etc. be present, and these features cause in point for satellite telemetering data
Class such as Euclidean distance, Pearson correlation coefficients, is embodied inadaptable using classical Time Series Similarity measure
Property.Classical Time Series Similarity measure, it is impossible to the interdependence effects between multidimensional time-series are excluded, meanwhile, pin
Minor shifts to time series be present can not realize that asynchronous measurement make it that measurement results are not accurate enough, and then cause to satellite telemetry
The classification results of data are not accurate enough.
The content of the invention
The invention aims to solve for satellite telemetering data be fixed a subsection efect it is undesirable, due to more
Correlation be present between dimension time series and time series has minor shifts and makes measurement results not accurate enough and then cause
The problem of classification results are not accurate enough, and propose a kind of multidimensional time-series sorting technique based on mahalanobis distance DTW.
Above-mentioned goal of the invention is achieved through the following technical solutions：
Step 1：Historical satellite telemetry Y under satellite normal operating condition is carried out by mark of argument catastrophe point
Segmentation, obtains normal multidimensional time-series X={ x1,x2,...,xj... xn, wherein, Y ndRow naThe historical satellite remote measurement of row
Data matrix, ndFor the dimension values of multidimensional time-series, naCounted for the data of all historical satellite telemetries, xjFor ndOK
nlenColumn data matrix represents X j-th of sequence, j=1,2 ..., n, nlenFor length of time series, n is the number of members in X；
Step 2: by the multidimensional time-series X={ x obtained by after segmentation1,x2,...,xj... xn, gathered by level
Class method sets cluster target class number and carries out cluster operation to sequence as c, so as to obtain the classification mark of multidimensional time-series
Sign L={ l1,l2,…,ln}；Wherein, c is the positive integer less than n, l more than 1sRepresent L sequences s-th of element, its value by
The determination of hierarchical clustering result, wherein s=1,2 ..., n；
Step 3：Extract adjacent m+1 argument catastrophe point in newest satellite telemetering data and correspond to test within time point
Data are that multidimensional time-series to be sorted are X '={ x '1,x′2,...,x′m, wherein, m is the positive integer more than 0；
Step 4: calculate multidimensional time-series X '={ x ' to be sorted1,x′2,...,x′mWith containing class label
Multidimensional time-series X={ x1,x2,...,xj... xnBetween DTW distance sequences
Wherein, dijCalculation it is as follows：
dij=DTWma(x'i,xj)
x'iRepresent X ' i-th of sequence, i=1,2 ..., m；DTWmaRepresent the DTW distance algorithms based on mahalanobis distance；
DTW, dijFor x'iWith xjBetween the DTW distances based on mahalanobis distance；
Step 5: using the KNN sorting techniques of the DTW distances based on mahalanobis distance, treated according to the k nearest neighbor number of setting
Multidimensional time-series X '={ x ' of classification1,x′2,...,x′mClassified, determine multidimensional time-series X ' to be sorted=
{x′1,x′2,...,x′mGeneric L '={ l '1,l′2,…,l′m, wherein, K=1,2 ..., n；Generic l' is 1,
Certain number determined in 2, L, c；KNN is K arest neighbors sorting algorithms；When completing a kind of multidimensional based on mahalanobis distance DTW
Between sequence sorting technique.
Invention effect
It is that a critical function of data mining is carried out to satellite telemetering data that classification is carried out to satellite telemetering data, is being divided
A variety of data mining tasks, such as pattern-recognition, abnormality detection etc. can be completed on the basis of class.And satellite telemetering data
There is its own feature, such as：Parameter is more, dimension is high, drift etc. be present, and these features cause in point for satellite telemetering data
Class such as Euclidean distance, Pearson correlation coefficients, is embodied inadaptable using classical Time Series Similarity measure
Property.Classical time series measure, it is impossible to the interdependence effects between multidimensional time-series are excluded, meanwhile, for the time
Sequence, which has minor shifts, can not realize that asynchronous measurement make it that measurement results are not accurate enough, and then cause to satellite telemetering data
Classification results are not accurate enough.Therefore, it is necessary to using more rational Time Series Similarity measure.For some it is complicated or
The satellite telemetering data that person's feature is not quite similar, choose reasonable time sequence similarity measure, it can be ensured that corresponding
Mode excavation obtains more good effect.The specific invention effect of each several part is as follows：
The present invention first against according to the fixing point situation undesirable to satellite telemetering data subsection efect as shown in figure 3,
It is the method that is segmented of mark to propose according to the argument catastrophe point in satellite telemetering data, its subsection efect as shown in figure 4,
More compact as the segmentation result that mark is segmented using argument, the degree of coupling between each fragment sequence is higher, more reasonable.
Then, using dynamic time warping (Dynamic Time Warping, DTW) distance based on mahalanobis distance to more
The distance between dimension satellite telemetering data time series is measured, and eliminates the interdependence effects between multidimensional time-series,
Asynchronous measurement is realized, solves the problems, such as to make measurement results not true enough because time series has minor shifts.
Finally, gone through with reference to K nearest-neighbors (K-Nearest Neighbor, KNN) sorting algorithm and satellite telemetering data
History multidimensional time-series are classified to newest remote measurement multidimensional time-series, and the running status current to satellite has been better achieved
Differentiation.
Brief description of the drawings
Fig. 1 is the yaw-position angle sequence example schematic diagram that background technology proposes；
Fig. 2 is that the yaw-position angle sequence details that background technology proposes change example schematic diagram；
Fig. 3 is the result being segmented using fixing point to satellite telemetering data that embodiment one proposes；
Fig. 4 is the result using argument catastrophe point as mark to satellite telemetering data segmentation that embodiment one proposes；
Fig. 5 is the example schematic diagram of Wafer parameters 1 that embodiment proposes；
Fig. 6 is the example schematic diagram of Wafer parameters 2 that embodiment proposes；
Fig. 7 is the example schematic diagram of Wafer parameters 3 that embodiment proposes；
Fig. 8 is the example schematic diagram of Wafer parameters 4 that embodiment proposes；
Fig. 9 is the example schematic diagram of Wafer parameters 5 that embodiment proposes；
Figure 10 is the example schematic diagram of Wafer parameters 6 that embodiment proposes；
Figure 11 (a) is the 1st class schematic diagram data of the satellite telemetering data dimension 1 that embodiment proposes；
Figure 11 (b) is the 2nd class schematic diagram data of the satellite telemetering data dimension 1 that embodiment proposes；
Figure 11 (c) is the 3rd class schematic diagram data of the satellite telemetering data dimension 1 that embodiment proposes；
Figure 11 (d) is the 4th class schematic diagram data of the satellite telemetering data dimension 1 that embodiment proposes；
Figure 12 (a) is the 1st class schematic diagram data of the satellite telemetering data dimension 2 that embodiment proposes；
Figure 12 (b) is the 2nd class schematic diagram data of the satellite telemetering data dimension 2 that embodiment proposes；
Figure 12 (c) is the 3rd class schematic diagram data of the satellite telemetering data dimension 2 that embodiment proposes；
Figure 12 (d) is the 4th class schematic diagram data of the satellite telemetering data dimension 2 that embodiment proposes；
Figure 13 (a) is the 1st class schematic diagram data of the satellite telemetering data dimension 3 that embodiment proposes；
Figure 13 (b) is the 2nd class schematic diagram data of the satellite telemetering data dimension 3 that embodiment proposes；
Figure 13 (c) is the 3rd class schematic diagram data of the satellite telemetering data dimension 3 that embodiment proposes；
Figure 13 (d) is the 4th class schematic diagram data of the satellite telemetering data dimension 3 that embodiment proposes；
Figure 14 (a) is the 1st class result schematic diagram of the satellite telemetering data dimension 1 that embodiment proposes；
Figure 14 (b) is the 2nd class result schematic diagram of the satellite telemetering data dimension 1 that embodiment proposes；
Figure 14 (c) is the 3rd class result schematic diagram of the satellite telemetering data dimension 1 that embodiment proposes；
Figure 14 (d) is the 4th class result schematic diagram of the satellite telemetering data dimension 1 that embodiment proposes；
Figure 15 (a) is the 1st class result schematic diagram of the satellite telemetering data dimension 2 that embodiment proposes；
Figure 15 (b) is the 2nd class result schematic diagram of the satellite telemetering data dimension 2 that embodiment proposes；
Figure 15 (c) is the 3rd class result schematic diagram of the satellite telemetering data dimension 2 that embodiment proposes；
Figure 15 (d) is the 4th class result schematic diagram of the satellite telemetering data dimension 2 that embodiment proposes；
Figure 16 (a) is the 1st class result schematic diagram of the satellite telemetering data dimension 3 that embodiment proposes；
Figure 16 (b) is the 2nd class result schematic diagram of the satellite telemetering data dimension 3 that embodiment proposes；
Figure 16 (c) is the 3rd class result schematic diagram of the satellite telemetering data dimension 3 that embodiment proposes；
Figure 16 (d) is the 4th class result schematic diagram of the satellite telemetering data dimension 3 that embodiment proposes.
Embodiment
Embodiment one：A kind of multidimensional time-series sorting technique based on mahalanobis distance DTW of present embodiment,
Specifically prepared according to following steps：
Step 1：Historical satellite telemetry Y under satellite normal operating condition is carried out by mark of argument catastrophe point
Segmentation, obtains normal multidimensional time-series X={ x1,x2,...,xj... xn, wherein, Y ndRow naThe historical satellite remote measurement of row
Data matrix, ndFor the dimension values of multidimensional time-series, naCounted for the data of all historical satellite telemetries, xjFor ndOK
nlenColumn data matrix represents X j-th of sequence, j=1,2 ..., n, nlenFor length of time series, n is the number of members in X；
Step 2: by the multidimensional time-series X={ x obtained by after segmentation1,x2,...,xj... xn, gathered by level
Class method sets cluster target class number and carries out cluster operation to sequence as c, so as to obtain the classification mark of multidimensional time-series
Sign L={ l1,l2,…,ln}；Wherein, c is the positive integer less than n, l more than 1sRepresent L sequences s-th of element, its value by
The determination of hierarchical clustering result, wherein s=1,2 ..., n；Classification assigned work herein, its method are not fixed, and can realize classification
Specify any existing method can, hierarchy clustering method is that by one of method that classification is specified；
Step 3：Extract adjacent m+1 argument catastrophe point in newest satellite telemetering data and correspond to test within time point
Data are that multidimensional time-series to be sorted are X '={ x '1,x′2,...,x′m, wherein, m is the positive integer more than 0；
Step 4: calculate multidimensional time-series X '={ x ' to be sorted1,x′2,...,x′mWith containing class label
Multidimensional time-series X={ x1,x2,...,xj... xnBetween DTW distance sequences
Wherein, dijCalculation it is as follows：
dij=DTWma(x'i,xj)
x'iRepresent X ' i-th of sequence, i=1,2 ..., m；DTWmaRepresent the DTW distance algorithms based on mahalanobis distance；
DTW (Dynamic Time Warping) is that one kind is reflected by bending time shaft preferably to carry out matching to time series form
The method for measuring similarity (existing theory) penetrated, dijFor x'iWith xjBetween the DTW distances based on mahalanobis distance；
Step 5: using the KNN sorting techniques of the DTW distances based on mahalanobis distance, treated according to the k nearest neighbor number of setting
Multidimensional time-series X '={ x ' of classification1,x′2,...,x′mClassified, determine multidimensional time-series X ' to be sorted=
{x′1,x′2,...,x′mGeneric L '={ l '1,l′2,…,l′m, wherein, K=1,2 ..., n；Generic l' is 1,
Certain number determined in 2, L, c；KNN (K-Nearest Neighbor) is K arest neighbors sorting algorithms；One kind is completed to be based on
Mahalanobis distance DTW multidimensional time-series sorting technique.
Present embodiment effect：
It is that a critical function of data mining is carried out to satellite telemetering data that classification is carried out to satellite telemetering data, is being divided
A variety of data mining tasks, such as pattern-recognition, abnormality detection etc. can be completed on the basis of class.And satellite telemetering data
There is its own feature, such as：Parameter is more, dimension is high, drift etc. be present, and these features cause in point for satellite telemetering data
Class such as Euclidean distance, Pearson correlation coefficients, is embodied inadaptable using classical Time Series Similarity measure
Property.Classical time series measure, it is impossible to the interdependence effects between multidimensional time-series are excluded, meanwhile, for the time
Sequence, which has minor shifts, can not realize that asynchronous measurement make it that measurement results are not accurate enough, and then cause to satellite telemetering data
Classification results are not accurate enough.Therefore, it is necessary to using more rational Time Series Similarity measure.For some it is complicated or
The satellite telemetering data that person's feature is not quite similar, choose reasonable time sequence similarity measure, it can be ensured that corresponding
Mode excavation obtains more good effect.The specific invention effect of each several part is as follows：
The present invention first against according to the fixing point situation undesirable to satellite telemetering data subsection efect as shown in figure 4,
It is the method that is segmented of mark to propose according to the argument catastrophe point in satellite telemetering data, its subsection efect as shown in figure 5,
More compact as the segmentation result that mark is segmented using argument, the degree of coupling between each fragment sequence is higher, more reasonable.
Then, using dynamic time warping (Dynamic Time Warping, DTW) distance based on mahalanobis distance to more
The distance between dimension satellite telemetering data time series is measured, and eliminates the interdependence effects between multidimensional time-series,
Asynchronous measurement is realized, solves the problems, such as to make measurement results not true enough because time series has minor shifts.
Finally, gone through with reference to K nearest-neighbors (K-Nearest Neighbor, KNN) sorting algorithm and satellite telemetering data
History multidimensional time-series are classified to newest remote measurement multidimensional time-series, and the running status current to satellite has been better achieved
Differentiation.
Embodiment two：Present embodiment is unlike embodiment one：Argument is satellite in step 1
One of test parameter of telemetry, argument changing rule are incremented by successively from 0 °~360 °, have obvious periodicity, argument
It is argument catastrophe point that value is changed into 0 ° from 360 °.Other steps and parameter are identical with embodiment one.
Embodiment three：Present embodiment is unlike embodiment one or two：By satellite in step 1
Historical satellite telemetry Y under normal operating condition is segmented using argument catastrophe point as mark, obtains normal multi-dimensional time
Sequence X={ x1,x2,...,xj... xnDetailed process is：
(1) after argument reaches 360 °, then it is changed into 0 ° and restarts to be incremented by, is changed into 0 ° of this point from 360 ° and is mutated for argument
Point；
(2) the corresponding time of argument catastrophe point is recorded；
(3) time according to corresponding to argument catastrophe point, extract two neighboring argument catastrophe point and correspond to test within the time
Data are time series；Wherein multidimensional time-series are made up of a plurality of time series；Wherein, test data is yaw-position
Angle, Speed of Reaction Wheels and busbar voltage.Other steps and parameter are identical with embodiment one or two.
Embodiment four：Unlike one of present embodiment and embodiment one to three：Step 4 is fallen into a trap
Calculate dijDetailed process be：
(1) the covariance matrix C between each dimension of multidimensional time-series to be sorted is calculatedcov, its calculation is：
Ccov=E { [Y-E (Y)] [Y-E (Y)]T}
Wherein, Y ndRow naThe historical satellite telemetry matrix of row, E are to represent to calculate desired value；
(2) the DTW distances based on mahalanobis distance are i.e. in two time seriesesWithBetween find optimal crooked route to obtain minimum mahalanobis distance metric DTWma(x'i,xj)；Adopt
Carried out that d (p are calculated with mahalanobis distancek), calculation is：
In crooked route, the total Least-cost of bending that an optimal path causes it be present, i.e.,：
Wherein, P={ p1,p2,…,pK'Crooked route is represented,pkExpression P k-th of member, k=1,
2 ..., K', and for representing x'iIn the i-th ' individual element x 'ii'kWith xjIn jth ' individual element xjj'kBetween corresponding relation i'
=1,2 ..., nlen, j'=1,2 ..., nlen, d (pk) represent x'ii'kWith xjj'kBending cost；
(3) in order to solveOne cost matrix is constructed by Dynamic Programming
R (i', j'), i.e.,：
R (i', j')=d (i', j')+min { R (i', j'-1), R (i'-1, j'-1), R (i'-1, j') }
Wherein, R (0,0)=0, R (i', 0)=R (0, j')=+ ∞；R(nlen,nlen) it is exactly DTW measuring period sequences x'i
And xjLowest distance value, that is, obtain DTWma(x'i,xj)=R (nlen,nlen).Other steps and parameter and embodiment one
It is identical to one of three.
Embodiment five：Unlike one of present embodiment and embodiment one to four：Adopted in step 5
With the KNN sorting techniques of the DTW distances based on mahalanobis distance, according to the k nearest neighbor number of setting to multi-dimensional time sequence to be sorted
Arrange X '={ x '1,x′2,...,x′mClassified, determine multidimensional time-series X '={ x ' to be sorted1,x′2,...,x′m
Generic L '={ l '1,l′2,…,l′mProcess be：
(1) determine and multidimensional time-series X '={ x ' to be sorted1,x′2,...,x′mIn each member between be based on horse
The K multidimensional time-series containing class label of the DTW distance minimums of family name's distance, that is, exist
In, per K minimum numerical value is taken out in row element, when determining the corresponding multidimensional containing class label of numerical value of this K minimum
Between sequence, corresponding class label is
(2) classification often row class label is countedMiddle frequency of occurrences highest classification, it is
Multidimensional time-series X '={ x ' of classification1,x′2,...,x′mGeneric be L '={ l '1,l′2,…,l′m}.Other steps
Rapid and parameter is identical with one of embodiment one to four.
Beneficial effects of the present invention are verified using following examples：
Embodiment：
Carry out the KNN classification emulation experiments based on different time sequence similarity measure for Wafer data sets,
Wafer data sets include 6 dimensions altogether, and for each dimension data as shown in Fig. 5 to Figure 10, its classification results is as shown in table 1.
Table 1 uses the classification results of different method for measuring similarity for Wafer data sets
By experimental result it can be found that the measurement results performance of traditional Euclidean distance is worst, and based on mahalanobis distance
DTW distances behave oneself best, wherein when setting limitation length of window as 5, effect reaches optimal rate of accuracy reached to 98.10%, relatively
10.85% is improved in the accuracy rate of Euclidean distance.
Satellite telemetering data classification experiments：
Carry out the KNN classification experiments based on different time sequence similarity measure for satellite telemetering data, wherein
Number of training is 50, and sample, which includes three dimension its corresponding relations, is respectively：Yaw-position angle corresponds to dimension 1, Speed of Reaction Wheels D
Corresponding dimension 2, busbar voltage correspond to dimension 3, and it is always divided into 4 classification data of all categories such as Figure 11 (a)~(d) to Figure 13
(a)~(d) shows that test sample 50, its classification results is as shown in table 2, Figure 14 (a)~(d), Figure 15 (a)~(d) and Figure 16
(a)~(d) is specifically to be classified situation using the KNN algorithms of the DTW distances based on mahalanobis distance, and its classification results is as shown in table 2.
Table 2 uses the classification results of different method for measuring similarity for satellite telemetering data
By experimental result it can be found that the measurement results of traditional Euclidean distance still show it is worst, and based on geneva away from
From DTW with a distance from behave oneself best, its rate of accuracy reached to 98.00%, 4.35%. is improved relative to the accuracy rate of Euclidean distance
The present invention can also have other various embodiments, in the case of without departing substantially from spirit of the invention and its essence, this area
Technical staff works as can make various corresponding changes and deformation according to the present invention, but these corresponding changes and deformation should all belong to
The protection domain of appended claims of the invention.
Claims (4)
1. a kind of multidimensional time-series sorting technique based on mahalanobis distance DTW, it is characterised in that one kind is based on mahalanobis distance DTW
Multidimensional time-series sorting techniques be specifically to follow the steps below：
Step 1：Historical satellite telemetry Y under satellite normal operating condition is segmented using argument catastrophe point as mark,
Obtain normal multidimensional time-series X={ x1,x2,...,xj... xn, wherein, it is width that argument value is changed into 0 ° of this point from 360 °
Cornicult height, Y ndRow naThe historical satellite telemetry matrix of row, ndFor the dimension values of multidimensional time-series, naGone through to be all
The data points of history satellite telemetering data, xjFor ndRow nlenColumn data matrix represents X j-th of sequence, j=1,2 ..., n, nlen
For length of time series, n is the number of members in X；
Step 2: by the multidimensional time-series X={ x obtained by after segmentation1,x2,...,xj... xn, pass through hierarchy clustering method
Set cluster target class number and cluster operation is carried out to sequence as c, so as to obtain the class label L=of multidimensional time-series
{l1,l2,…,ln}；Wherein, c is the positive integer less than n, l more than 1sS-th of element of L sequences is represented, its value is gathered by level
The determination of class result, wherein s=1,2 ..., n；
Step 3：Extract adjacent m+1 argument catastrophe point in newest satellite telemetering data and correspond to test data within time point
Multidimensional time-series i.e. to be sorted are X '={ x '1,x′2,...,x′m, wherein, m is the positive integer more than 0；
Step 4: calculate multidimensional time-series X '={ x ' to be sorted1,x′2,...,x′mAnd the multidimensional containing class label
Time series X={ x1,x2,...,xj... xnBetween DTW distance sequences
Wherein, dijCalculation it is as follows：
dij=DTWma(x'i,xj)
x'iRepresent X ' i-th of sequence, i=1,2 ..., m；DTWmaRepresent the DTW distance algorithms based on mahalanobis distance；dijFor
x'iWith xjBetween the DTW distances based on mahalanobis distance；
Calculate dijDetailed process be：
(1) the covariance matrix C between each dimension of multidimensional time-series to be sorted is calculatedcov, its calculation is：
Ccov=E { [Y-E (Y)] [Y-E (Y)]T}
Wherein, Y ndRow naThe historical satellite telemetry matrix of row, E are to represent to calculate desired value；
(2) the DTW distances based on mahalanobis distance are i.e. in two time seriesesWithBetween find optimal crooked route to obtain minimum mahalanobis distance metric DTWma(x'i,xj)；Adopt
Carried out that d (p are calculated with mahalanobis distancek), calculation is：
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<mo>&Sigma;</mo>
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<mi>k</mi>
<mo>=</mo>
<mn>1</mn>
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Wherein, P={ p1,p2,…,pK' crooked route is represented,pkExpression P k-th of member, k=1,2 ..., K',
And for representing x'iIn the i-th ' individual element x 'ii'kWith xjIn jth ' individual element x jj'kBetween corresponding relation i'=1,
2,…,nlen, j'=1,2 ..., nlen, d (pk) represent x'ii'kWith xjj'kBending cost；
(3) in order to solveBy Dynamic Programming come construct a cost matrix R (i',
J'), i.e.,：
R (i', j')=d (i', j')+min { R (i', j'-1), R (i'-1, j'-1), R (i'-1, j') }
Wherein, R (0,0)=0, R (i', 0)=R (0, j')=+ ∞；R(nlen,nlen) it is exactly DTW measuring period sequences x'iAnd xj
Lowest distance value, that is, obtain DTWma(x'i,xj)=R (nlen,nlen)；
Step 5: using the KNN sorting techniques of the DTW distances based on mahalanobis distance, according to the k nearest neighbor number of setting to be sorted
Multidimensional time-series X '={ x '1,x′2..., x ' m classified, determine multidimensional time-series X '={ x ' to be sorted1,
x′2,...,x′mGeneric L '={ l1′,l2′,…,l′m, wherein, K=1,2 ..., n；Generic l' is 1,2 ...,
Certain number determined in c；KNN is K arest neighbors sorting algorithms；Complete a kind of multi-dimensional time sequence based on mahalanobis distance DTW
Row sorting technique.
A kind of 2. multidimensional time-series sorting technique based on mahalanobis distance DTW according to claim 1, it is characterised in that：
Argument is one of test parameter of satellite telemetering data in step 1, and argument changing rule is, tool incremented by successively from 0 °~360 °
There is obvious periodicity.
A kind of 3. multidimensional time-series sorting technique based on mahalanobis distance DTW according to claim 1, it is characterised in that：
The historical satellite telemetry Y under satellite normal operating condition is segmented using argument catastrophe point as mark in step 1, obtained
To normal multidimensional time-series X={ x1,x2,...,xj... xnDetailed process is：
(1) after argument reaches 360 °, then it is changed into 0 ° and restarts to be incremented by, it is argument catastrophe point to be changed into 0 ° of this point from 360 °；
(2) the corresponding time of argument catastrophe point is recorded；
(3) time according to corresponding to argument catastrophe point, extract two neighboring argument catastrophe point and correspond to test data within the time
For time series；Wherein multidimensional time-series are made up of a plurality of time series；Wherein, test data is yaw-position angle, flown
Wheel speed and busbar voltage.
A kind of 4. multidimensional time-series sorting technique based on mahalanobis distance DTW according to claim 1, it is characterised in that：
The KNN sorting techniques of the DTW distances based on mahalanobis distance are used in step 5, according to the k nearest neighbor number of setting to be sorted
Multidimensional time-series X '={ x '1,x′2,...,x′mClassified, determine multidimensional time-series X '={ x ' to be sorted1,x
′2,...,x′mGeneric L '={ l '1,l′2,…,l′mProcess be：
(1) determine and multidimensional time-series X '={ x ' to be sorted1,x′2,...,x′mIn each member between based on geneva away from
From DTW with a distance from minimum K multidimensional time-series containing class label, that is, existIn, often
K minimum numerical value is taken out in row element, determines the multi-dimensional time sequence containing class label corresponding to this K minimum numerical value
Row, corresponding class label are
(2) classification often row class label is countedMiddle frequency of occurrences highest classification, as classifies
Multidimensional time-series X '={ x '1,x′2,...,x′mGeneric be L '={ l '1,l′2,…,l′m}。
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