CN104915434A - Multi-dimensional time sequence classification method based on mahalanobis distance DTW - Google Patents

Abstract

The invention discloses a multi-dimensional time sequence classification method based on mahalanobis distance DTW, and relates to the multi-dimensional time sequence classification method. In order to solve the problems that aiming at satellite telemetry data, a fixed point segmentation effect is non-ideal, due to the facts that relativity exists between multi-dimensional time sequences and small deviation exists between the time sequences, a measuring result is not accurate, therefore a classification result is not accurate, and the multi-dimensional time sequence classification method based on the mahalanobis distance DTW is provided. The method comprises the steps that 1 a multi-dimensional time sequence X={x <1>, x <2>, ..., x<j>, ..., x<n>} used for training and a classification label L={l<1>, l<2>, ..., l<n>}are obtained; 2 a to-be-classified multi-dimensional time sequence X'={x' <1>, x' <2>, ..., x'<j>, ..., x'<n>} is extracted; 3 a DTW distance sequence between the X'={x' <1>, x' <2>, ..., x'<j>, ..., x'<n>} and the X={x <1>, x <2>, ..., x<j>, ..., x<n>} is calculated; 4 classification is conducted on the to-be-classified multi-dimensional time sequence X'={x' <1>, x' <2>, ..., x'<j>, ..., x'<m>} according to neighboring numbers of K which is set by using a KNN classification method based on the mahalanobis DTW distance, and the classification of the to-be-classified multi-dimensional time sequence is determined. The method is applied to the field of multi-dimensional time sequence classification.

Description

A kind of multidimensional time-series sorting technique based on mahalanobis distance DTW

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 as shown in Figure 1, its variations in detail as shown in Figure 2, show that satellite telemetering data has significantly periodically, and this characteristic provides unit to confirm with satellite telemetering data.By analyzing each cycle of telemetry, can show that whether the running status of satellite within this cycle be normal, according to the situation that point of fixity is undesirable to satellite telemetering data subsection efect, as shown in Figure 3, the degree of coupling between each time series obtained after segmentation is not high enough, there is certain deviation, and along with this deviation of propelling of time can be more obvious.

Classifying to satellite telemetering data is critical function satellite telemetering data being carried out to data mining, can complete several data mining task, such as pattern-recognition, abnormality detection etc. on the basis of classification.And satellite telemetering data has himself feature, such as: parameter is many, dimension is high, there is drift etc., these features cause and adopt classical Time Series Similarity measure in the classification for satellite telemetering data, as Euclidean distance, Pearson correlation coefficients etc., embody inadaptability.Classical Time Series Similarity measure, the interdependence effects between multidimensional time-series can not be got rid of, meanwhile, there is minor shifts for time series and can not realize asynchronous tolerance and make measurement results not accurate enough, and then cause the classification results of satellite telemetering data not accurate enough.

Summary of the invention

The object of the invention is in order to solve for satellite telemetering data be fixed a subsection efect undesirable, owing to there is correlativity between multidimensional time-series and time series exists minor shifts and makes the problem that measurement results is not accurate enough and then cause classification results 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 one: the historical satellite telemetry Y under satellite normal operating condition being carried out segmentation with argument catastrophe point for identifying, obtaining normal multidimensional time-series X={x ₁, x ₂..., x _j... x _n, wherein, Y is n _drow n _athe historical satellite telemetry matrix of row, n _dfor the dimension values of multidimensional time-series, n _afor the number of data points of all historical satellite telemetries, x _jfor n _drow n _lena jth sequence of column data matrix representation X, j=1,2 ..., n, n _lenfor length of time series, n is the number of members in X;

Step 2, the multidimensional time-series X={x will obtained after segmentation ₁, x ₂..., x _j... x _n, be that c carries out cluster operation to sequence by hierarchy clustering method setting cluster target class number, thus obtain the class label L={l of multidimensional time-series ₁, l ₂..., l _n; Wherein, c is greater than the positive integer that 1 is less than n, l _srepresent s element of L sequence, its value is determined by hierarchical clustering result, wherein s=1,2 ..., n;

Step 3: to extract in up-to-date satellite telemetering data test data within the corresponding time point of adjacent m+1 argument catastrophe point and multidimensional time-series to be sorted be X '=x ' ₁, x ' ₂..., x ' _m, wherein, m be greater than 0 positive integer;

Step 4, calculate multidimensional time-series X ' to be sorted=x ' ₁, x ' ₂..., x ' _mwith containing the multidimensional time-series X={x of class label ₁, x ₂..., x _j... x _nbetween DTW distance sequence

Wherein, d _ijaccount form as follows:

d _ij＝DTW _ma(x' _i,x _j)

X' _irepresent i-th sequence of X ', i=1,2 ..., m; DTW _marepresent the DTW distance algorithm based on mahalanobis distance; DTW, d _ijfor x' _iwith x _jbetween the DTW distance based on mahalanobis distance;

Step 5, adopt the KNN sorting technique of the DTW distance based on mahalanobis distance, according to the k nearest neighbor number of setting to multidimensional time-series X ' to be sorted=x ' ₁, x ' ₂..., x ' _mclassify, 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 certain number determined in 1,2, L, c; KNN is K arest neighbors sorting algorithm; Namely a kind of multidimensional time-series sorting technique based on mahalanobis distance DTW is completed.

Invention effect

Classifying to satellite telemetering data is critical function satellite telemetering data being carried out to data mining, can complete several data mining task, such as pattern-recognition, abnormality detection etc. on the basis of classification.And satellite telemetering data has himself feature, such as: parameter is many, dimension is high, there is drift etc., these features cause and adopt classical Time Series Similarity measure in the classification for satellite telemetering data, as Euclidean distance, Pearson correlation coefficients etc., embody inadaptability.Classical time series measure, the interdependence effects between multidimensional time-series can not be got rid of, meanwhile, there is minor shifts for time series and can not realize asynchronous tolerance and make measurement results not accurate enough, and then cause the classification results of satellite telemetering data not accurate enough.Therefore, the more rational Time Series Similarity measure of application is needed.For the satellite telemetering data that some complexity or feature are not quite similar, choose reasonable time sequence similarity measure, can guarantee that corresponding mode excavation obtains more good effect.The concrete invention effect of each several part is as follows:

The present invention is first for according to point of fixity to the undesirable situation of satellite telemetering data subsection efect as shown in Figure 3, proposing according to the argument catastrophe point in satellite telemetering data is the method that mark carries out segmentation, its subsection efect as shown in Figure 4, it is more compact with argument to be that mark carries out the segmentation result of segmentation, and the degree of coupling between each fragment sequence is higher, more reasonable.

Then, adopt dynamic time warping (the Dynamic Time Warping based on mahalanobis distance, DTW) distance is measured the distance between multidimensional satellite telemetering data time series, eliminate the interdependence effects between multidimensional time-series, realize asynchronous tolerance, solve the problem making measurement results true not because time series exists minor shifts.

Finally, in conjunction with K nearest-neighbors (K-Nearest Neighbor, KNN) sorting algorithm and satellite telemetering data history multidimensional time-series are classified to up-to-date remote measurement multidimensional time-series, achieve the differentiation to the current running status of satellite better.

Accompanying drawing explanation

Fig. 1 is the yaw-position angle sequence example schematic diagram that background technology proposes;

Fig. 2 is the yaw-position angle sequence details change example schematic diagram that background technology proposes;

Fig. 3 is that the employing point of fixity of embodiment one proposition is to the result of satellite telemetering data segmentation;

Fig. 4 be embodiment one propose with argument catastrophe point for the result of mark to satellite telemetering data segmentation;

Fig. 5 is Wafer parameter 1 example schematic diagram that embodiment proposes;

Fig. 6 is Wafer parameter 2 example schematic diagram that embodiment proposes;

Fig. 7 is Wafer parameter 3 example schematic diagram that embodiment proposes;

Fig. 8 is Wafer parameter 4 example schematic diagram that embodiment proposes;

Fig. 9 is Wafer parameter 5 example schematic diagram that embodiment proposes;

Figure 10 is Wafer parameter 6 example schematic diagram that embodiment proposes;

1st class schematic diagram data of the satellite telemetering data dimension 1 that Figure 11 (a) proposes for embodiment;

2nd class schematic diagram data of the satellite telemetering data dimension 1 that Figure 11 (b) proposes for embodiment;

3rd class schematic diagram data of the satellite telemetering data dimension 1 that Figure 11 (c) proposes for embodiment;

4th class schematic diagram data of the satellite telemetering data dimension 1 that Figure 11 (d) proposes for embodiment;

1st class schematic diagram data of the satellite telemetering data dimension 2 that Figure 12 (a) proposes for embodiment;

2nd class schematic diagram data of the satellite telemetering data dimension 2 that Figure 12 (b) proposes for embodiment;

3rd class schematic diagram data of the satellite telemetering data dimension 2 that Figure 12 (c) proposes for embodiment;

4th class schematic diagram data of the satellite telemetering data dimension 2 that Figure 12 (d) proposes for embodiment;

1st class schematic diagram data of the satellite telemetering data dimension 3 that Figure 13 (a) proposes for embodiment;

2nd class schematic diagram data of the satellite telemetering data dimension 3 that Figure 13 (b) proposes for embodiment;

3rd class schematic diagram data of the satellite telemetering data dimension 3 that Figure 13 (c) proposes for embodiment;

4th class schematic diagram data of the satellite telemetering data dimension 3 that Figure 13 (d) proposes for embodiment;

1st class result schematic diagram of the satellite telemetering data dimension 1 that Figure 14 (a) proposes for embodiment;

2nd class result schematic diagram of the satellite telemetering data dimension 1 that Figure 14 (b) proposes for embodiment;

3rd class result schematic diagram of the satellite telemetering data dimension 1 that Figure 14 (c) proposes for embodiment;

4th class result schematic diagram of the satellite telemetering data dimension 1 that Figure 14 (d) proposes for embodiment;

1st class result schematic diagram of the satellite telemetering data dimension 2 that Figure 15 (a) proposes for embodiment;

2nd class result schematic diagram of the satellite telemetering data dimension 2 that Figure 15 (b) proposes for embodiment;

3rd class result schematic diagram of the satellite telemetering data dimension 2 that Figure 15 (c) proposes for embodiment;

4th class result schematic diagram of the satellite telemetering data dimension 2 that Figure 15 (d) proposes for embodiment;

1st class result schematic diagram of the satellite telemetering data dimension 3 that Figure 16 (a) proposes for embodiment;

2nd class result schematic diagram of the satellite telemetering data dimension 3 that Figure 16 (b) proposes for embodiment;

3rd class result schematic diagram of the satellite telemetering data dimension 3 that Figure 16 (c) proposes for embodiment;

4th class result schematic diagram of the satellite telemetering data dimension 3 that Figure 16 (d) proposes for embodiment.

Embodiment

Embodiment one: a kind of multidimensional time-series sorting technique based on mahalanobis distance DTW of present embodiment, specifically prepare according to following steps:

Step one: the historical satellite telemetry Y under satellite normal operating condition being carried out segmentation with argument catastrophe point for identifying, obtaining normal multidimensional time-series X={x ₁, x ₂..., x _j... x _n, wherein, Y is n _drow n _athe historical satellite telemetry matrix of row, n _dfor the dimension values of multidimensional time-series, n _afor the number of data points of all historical satellite telemetries, x _jfor n _drow n _lena jth sequence of column data matrix representation X, j=1,2 ..., n, n _lenfor length of time series, n is the number of members in X;

Step 2, the multidimensional time-series X={x will obtained after segmentation ₁, x ₂..., x _j... x _n, be that c carries out cluster operation to sequence by hierarchy clustering method setting cluster target class number, thus obtain the class label L={l of multidimensional time-series ₁, l ₂..., l _n; Wherein, c is greater than the positive integer that 1 is less than n, l _srepresent s element of L sequence, its value is determined by hierarchical clustering result, wherein s=1,2 ..., n; Classification assigned work herein, its method is not fixed, can realize classification specify any existing method can, hierarchy clustering method to realize one of method that classification specifies;

Step 3: to extract in up-to-date satellite telemetering data test data within the corresponding time point of adjacent m+1 argument catastrophe point and multidimensional time-series to be sorted be X '=x ' ₁, x ' ₂..., x ' _m, wherein, m be greater than 0 positive integer;

Step 4, calculate multidimensional time-series X ' to be sorted=x ' ₁, x ' ₂..., x ' _mwith containing the multidimensional time-series X={x of class label ₁, x ₂..., x _j... x _nbetween DTW distance sequence

Wherein, d _ijaccount form as follows:

d _ij＝DTW _ma(x' _i,x _j)

X' _irepresent i-th sequence of X ', i=1,2 ..., m; DTW _marepresent the DTW distance algorithm based on mahalanobis distance; DTW (Dynamic Time Warping) is a kind of method for measuring similarity (existing theory) carrying out to carry out mating to time series form better mapping by bending time shaft, d _ijfor x' _iwith x _jbetween the DTW distance based on mahalanobis distance;

Step 5, adopt the KNN sorting technique of the DTW distance based on mahalanobis distance, according to the k nearest neighbor number of setting to multidimensional time-series X ' to be sorted=x ' ₁, x ' ₂..., x ' _mclassify, 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 certain number determined in 1,2, L, c; KNN (K-Nearest Neighbor) is K arest neighbors sorting algorithm; Namely a kind of multidimensional time-series sorting technique based on mahalanobis distance DTW is completed.

Present embodiment effect:

Classifying to satellite telemetering data is critical function satellite telemetering data being carried out to data mining, can complete several data mining task, such as pattern-recognition, abnormality detection etc. on the basis of classification.And satellite telemetering data has himself feature, such as: parameter is many, dimension is high, there is drift etc., these features cause and adopt classical Time Series Similarity measure in the classification for satellite telemetering data, as Euclidean distance, Pearson correlation coefficients etc., embody inadaptability.Classical time series measure, the interdependence effects between multidimensional time-series can not be got rid of, meanwhile, there is minor shifts for time series and can not realize asynchronous tolerance and make measurement results not accurate enough, and then cause the classification results of satellite telemetering data not accurate enough.Therefore, the more rational Time Series Similarity measure of application is needed.For the satellite telemetering data that some complexity or feature are not quite similar, choose reasonable time sequence similarity measure, can guarantee that corresponding mode excavation obtains more good effect.The concrete invention effect of each several part is as follows:

The present invention is first for according to point of fixity to the undesirable situation of satellite telemetering data subsection efect as shown in Figure 4, proposing according to the argument catastrophe point in satellite telemetering data is the method that mark carries out segmentation, its subsection efect as shown in Figure 5, it is more compact with argument to be that mark carries out the segmentation result of segmentation, and the degree of coupling between each fragment sequence is higher, more reasonable.

Then, adopt dynamic time warping (the Dynamic Time Warping based on mahalanobis distance, DTW) distance is measured the distance between multidimensional satellite telemetering data time series, eliminate the interdependence effects between multidimensional time-series, realize asynchronous tolerance, solve the problem making measurement results true not because time series exists minor shifts.

Finally, in conjunction with K nearest-neighbors (K-Nearest Neighbor, KNN) sorting algorithm and satellite telemetering data history multidimensional time-series are classified to up-to-date remote measurement multidimensional time-series, achieve the differentiation to the current running status of satellite better.

Embodiment two: present embodiment and embodiment one unlike: in step one, argument is one of test parameter of satellite telemetering data, argument Changing Pattern is for increase progressively successively from 0 ° ~ 360 °, have obvious periodicity, argument value becomes 0 ° for argument catastrophe point from 360 °.Other step and parameter identical with embodiment one.

Embodiment three: present embodiment and embodiment one or two unlike: in step one, the historical satellite telemetry Y under satellite normal operating condition being carried out segmentation with argument catastrophe point for identifying, obtaining normal multidimensional time-series X={x ₁, x ₂..., x _j... x _ndetailed process is:

(1) after argument reaches 360 °, then become 0 ° and restart to increase progressively, becoming 0 ° of this point from 360 ° is argument catastrophe point;

(2) the corresponding time of argument catastrophe point is recorded;

(3) corresponding according to the argument catastrophe point time, the test data extracted within adjacent two argument catastrophe points corresponding time is time series; Wherein multidimensional time-series is made up of many time serieses; Wherein, test data is yaw-position angle, Speed of Reaction Wheels and busbar voltage.Other step and parameter identical with embodiment one or two.

Embodiment four: one of present embodiment and embodiment one to three unlike: calculate d in step 4 _ijdetailed process be:

(1) the covariance matrix C between each dimension of multidimensional time-series to be sorted is calculated _cov, its account form is:

C _cov＝E{[Y-E(Y)][Y-E(Y)] ^T}

Wherein, Y is n _drow n _athe historical satellite telemetry matrix of row, E represents calculation expectation value;

(2) based on mahalanobis distance DTW distance namely two time serieses with between find optimum crooked route to obtain minimum mahalanobis distance metric DTW _ma(x' _i, x _j); Mahalanobis distance is adopted to carry out calculating d (p _k), account form is:

$d\left(p_k\right)=D_M({x^{\&prime;}}_{{\mathrm{ii}}^{\&prime;}k},x_{{\mathrm{jj}}^{\&prime;}k})=\sqrt{{x^{\&prime;}}_{{\mathrm{ii}}^{\&prime;}k}-x_{{\mathrm{jj}}^{\&prime;}k}{)}^T{C}_{\mathrm{cov}}^{-1}({x^{\&prime;}}_{{\mathrm{ii}}^{\&prime;}k},x_{{\mathrm{jj}}^{\&prime;}k})}$

In crooked route, there is bending total Least-cost that an optimal path makes it, that is:

${\mathrm{DTW}}_{ma}({x^{\&prime;}}_i,x_j)=\underset{p}{\min }\underset{k=1}{\overset{K^{\&prime;}}{\&Sigma;}}d\left(p_k\right)$

Wherein, P={p ₁, p ₂..., p _k'represent crooked route, p _krepresent a kth member of P, k=1,2 ..., K', and be used for representing x' _iin i-th ' individual element x ' _ii'kwith x _jin jth ' individual element x _jj'kbetween corresponding relation i'=1,2 ..., n _len, j'=1,2 ..., n _len, d (p _k) represent x' _ii'kwith x _jj'kbending cost;

(3) in order to solve a cost matrix R (i', j') is constructed, that is: by dynamic programming

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 (n _len, n _len) be exactly DTW measuring period sequence x' _iand x _jlowest distance value, namely obtain DTW _ma(x' _i, x _j)=R (n _len, n _len).Other step and parameter identical with one of embodiment one to three.

Embodiment five: one of present embodiment and embodiment one to four unlike the KNN sorting technique adopting the DTW distance based on mahalanobis distance in step 5, according to the k nearest neighbor number of setting to multidimensional time-series X ' to be sorted=x ' ₁, x ' ₂..., x ' _mclassify, determine multidimensional time-series X ' to be sorted=x ' ₁, x ' ₂..., x ' _mgeneric L '=l ' ₁, l ' ₂..., l ' _mprocess be:

(1) determine with multidimensional time-series X ' to be sorted=x ' ₁, x ' ₂..., x ' _min each member between based on the DTW of mahalanobis distance multidimensional time-series containing class label individual apart from minimum K, namely exist in, take out the individual minimum numerical value of K in every row element, determine the multidimensional time-series containing class label that the individual minimum numerical value of this K is corresponding, corresponding class label is

(2) classification often row class label is added up the classification that the middle frequency of occurrences is the highest, be the multidimensional time-series X ' of classification=x ' ₁, x ' ₂..., x ' _mgeneric be L '=l ' ₁, l ' ₂..., l ' _m.Other step and parameter identical with one of embodiment one to four.

Following examples are adopted to verify beneficial effect of the present invention:

Embodiment:

Carry out the KNN classification emulation experiment based on different time sequence similarity measure for Wafer data set, Wafer data set comprises 6 dimensions altogether, and each dimension data is as shown in Fig. 5 to Figure 10, and its classification results is as shown in table 1.

Table 1 adopts the classification results of different method for measuring similarity for Wafer data set

Result can find by experiment, the measurement results performance of tradition Euclidean distance is the poorest, and behave oneself best based on the DTW distance of mahalanobis distance, wherein when setting limited window length is 5, effect reaches best rate of accuracy reached to 98.10%, improves 10.85% relative to the accuracy rate of Euclidean distance.

Satellite telemetering data classification experiments:

The KNN classification experiments based on different time sequence similarity measure is carried out for satellite telemetering data, wherein number of training is 50, sample packages contains three its corresponding relations of dimension respectively: the corresponding dimension 1 in yaw-position angle, the corresponding dimension 2 of Speed of Reaction Wheels D, the corresponding dimension 3 of busbar voltage, it is always divided into 4 classification data of all categories such as Figure 11 (a) ~ (d) and shows to Figure 13 (a) ~ (d), test sample book is 50, its classification results is as shown in table 2, Figure 14 (a) ~ (d), be employing specifically to classify situation based on the KNN algorithm of the DTW distance of mahalanobis distance for Figure 15 (a) ~ (d) and Figure 16 (a) ~ (d), its classification results is as shown in table 2.

Table 2 adopts the classification results of different method for measuring similarity for satellite telemetering data

Result can find by experiment, and the measurement results still performance of traditional Euclidean distance is the poorest, and behaves oneself best based on the DTW distance of mahalanobis distance, and its rate of accuracy reached, to 98.00%, improves 4.35%. relative to the accuracy rate of Euclidean distance

The present invention also can have other various embodiments; when not deviating from the present invention's spirit and essence thereof; those skilled in the art are when making various corresponding change and distortion according to the present invention, but these change accordingly and are out of shape the protection domain that all should belong to the claim appended by the present invention.

Claims (5)

1., based on a multidimensional time-series sorting technique of mahalanobis distance DTW, it is characterized in that what a kind of multidimensional time-series sorting technique based on mahalanobis distance DTW was specifically carried out according to following steps:

Step one: the historical satellite telemetry Y under satellite normal operating condition being carried out segmentation with argument catastrophe point for identifying, obtaining normal multidimensional time-series X={x ₁, x ₂..., x _j... x _n, wherein, Y is n _drow n _athe historical satellite telemetry matrix of row, n _dfor the dimension values of multidimensional time-series, n _afor the number of data points of all historical satellite telemetries, x _jfor n _drow n _lena jth sequence of column data matrix representation X, j=1,2 ..., n, n _lenfor length of time series, n is the number of members in X;

Step 2, the multidimensional time-series X={x will obtained after segmentation ₁, x ₂..., x _j... x _n, be that c carries out cluster operation to sequence by hierarchy clustering method setting cluster target class number, thus obtain the class label L={l of multidimensional time-series ₁, l ₂..., l _n; Wherein, c is greater than the positive integer that 1 is less than n, l _srepresent s element of L sequence, its value is determined by hierarchical clustering result, wherein s=1,2 ..., n;

Step 3: to extract in up-to-date satellite telemetering data test data within the corresponding time point of adjacent m+1 argument catastrophe point and multidimensional time-series to be sorted be X '=x ' ₁, x ' ₂..., x ' _m, wherein, m be greater than 0 positive integer;

Step 4, calculate multidimensional time-series X ' to be sorted=x ' ₁, x ' ₂..., x ' _mwith containing the multidimensional time-series X={x of class label ₁, x ₂..., x _j... x _nbetween DTW distance sequence

Wherein, d _ijaccount form as follows:

d _ij＝DTW _ma(x' _i,x _j)

X' _irepresent i-th sequence of X ', i=1,2 ..., m; DTW _marepresent the DTW distance algorithm based on mahalanobis distance; DTW, d _ijfor x' _iwith x _jbetween the DTW distance based on mahalanobis distance;

Step 5, adopt the KNN sorting technique of the DTW distance based on mahalanobis distance, according to the k nearest neighbor number of setting to multidimensional time-series X ' to be sorted=x ' ₁, x ' ₂..., x ' _mclassify, 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 certain number determined in 1,2, L, c; KNN is K arest neighbors sorting algorithm; Namely a kind of multidimensional time-series sorting technique based on mahalanobis distance DTW is completed.

2. a kind of multidimensional time-series sorting technique based on mahalanobis distance DTW according to claim 1, it is characterized in that: in step one, argument is one of test parameter of satellite telemetering data, argument Changing Pattern is for increase progressively successively from 0 ° ~ 360 °, have obvious periodicity, argument value becomes 0 ° for argument catastrophe point from 360 °.

3. a kind of multidimensional time-series sorting technique based on mahalanobis distance DTW according to claim 1, it is characterized in that: in step one, the historical satellite telemetry Y under satellite normal operating condition being carried out segmentation with argument catastrophe point for identifying, obtaining normal multidimensional time-series X={x ₁, x ₂..., x _j... x _ndetailed process is:

(1) after argument reaches 360 °, then become 0 ° and restart to increase progressively, becoming 0 ° of this point from 360 ° is argument catastrophe point;

(2) the corresponding time of argument catastrophe point is recorded;

(3) corresponding according to the argument catastrophe point time, the test data extracted within adjacent two argument catastrophe points corresponding time is time series; Wherein multidimensional time-series is made up of many time serieses; Wherein, test data is yaw-position angle, Speed of Reaction Wheels and busbar voltage.

4. a kind of multidimensional time-series sorting technique based on mahalanobis distance DTW according to claim 1, is characterized in that: calculate d in step 4 _ijdetailed process be:

(1) the covariance matrix C between each dimension of multidimensional time-series to be sorted is calculated _cov, its account form is:

C _cov＝E{[Y-E(Y)][Y-E(Y)] ^T}

Wherein, Y is n _drow n _athe historical satellite telemetry matrix of row, E represents calculation expectation value;

(2) based on mahalanobis distance DTW distance namely two time serieses with between find optimum crooked route to obtain minimum mahalanobis distance metric DTW _ma(x' _i, x _j); Mahalanobis distance is adopted to carry out calculating d (p _k), account form is:

$d\left(p_k\right)=D_M\left({x^{\&prime;}}_{{\mathrm{ii}}^{\&prime;}k},x_{{\mathrm{jj}}^{\&prime;}k}\right)=\sqrt{{x^{\&prime;}}_{{\mathrm{ii}}^{\&prime;}k},x_{{\mathrm{jj}}^{\&prime;}k}{)}^T{C}_{\mathrm{cov}}^{-1}\left({x^{\&prime;}}_{{\mathrm{ii}}^{\&prime;}k},x_{{\mathrm{jj}}^{\&prime;}k}\right)}$

In crooked route, there is bending total Least-cost that an optimal path makes it, that is:

${\mathrm{DTW}}_{ma}\left({x^{\&prime;}}_i,x_i\right)=\underset{p}{\min }\underset{k=1}{\overset{K^{\&prime;}}{\&Sigma;}}d\left(p_k\right)$

Wherein, P={p ₁, p ₂..., p _k'represent crooked route, p _krepresent a kth member of P, k=1,2 ..., K', and be used for representing x' _iin i-th ' individual element x ' _ii'kwith x _jin jth ' individual element x _jj'kbetween corresponding relation i'=1,2 ..., n _len, j'=1,2 ..., n _len, d (p _k) represent x' _ii'kwith x _jj'kbending cost;

(3) in order to solve a cost matrix R (i', j') is constructed, that is: by dynamic programming

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 (n _len, n _len) be exactly DTW measuring period sequence x' _iand x _jlowest distance value, namely obtain DTW _ma(x' _i, x _j)=R (n _len, n _len).

5. a kind of multidimensional time-series sorting technique based on mahalanobis distance DTW according to claim 1, it is characterized in that: the KNN sorting technique adopting the DTW distance based on mahalanobis distance in step 5, according to setting k nearest neighbor number to multidimensional time-series X ' to be sorted=x ' ₁, x ' ₂..., x ' _mclassify, determine multidimensional time-series X ' to be sorted=x ' ₁, x ' ₂..., x ' _mgeneric L '=l ' ₁, l ' ₂..., l ' _mprocess be:

(1) determine with multidimensional time-series X ' to be sorted=x ' ₁, x ' ₂..., x ' _min each member between based on the DTW of mahalanobis distance multidimensional time-series containing class label individual apart from minimum K, namely exist in, take out the individual minimum numerical value of K in every row element, determine the multidimensional time-series containing class label that the individual minimum numerical value of this K is corresponding, corresponding class label is

(2) classification often row class label is added up the classification that the middle frequency of occurrences is the highest, be the multidimensional time-series X ' of classification=x ' ₁, x ' ₂..., x ' _mgeneric be L '=l ' ₁, l ' ₂..., l ' _m.