research article radar emission sources...

Research ArticleRadar Emission Sources Identification Based on HierarchicalAgglomerative Clustering for Large Data Sets

Janusz Dudczyk

RampD Department WB Electronics SA Poznanska 129133 Street 05-850 Ozarow Mazowiecki Poland

Correspondence should be addressed to Janusz Dudczyk jdudczykwbcompl

Received 11 January 2016 Revised 22 March 2016 Accepted 27 April 2016

Academic Editor Fanli Meng

Copyright copy 2016 Janusz Dudczyk This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

More advanced recognition methods which may recognize particular copies of radars of the same type are called identificationThe identification process of radar devices is a more specialized task which requires methods based on the analysis of distinctivefeatures These features are distinguished from the signals coming from the identified devices Such a process is called SpecificEmitter Identification (SEI) The identification of radar emission sources with the use of classic techniques based on the statisticalanalysis of basic measurable parameters of a signal such as Radio Frequency Amplitude Pulse Width or Pulse Repetition Intervalis not sufficient for SEI problems This paper presents the method of hierarchical data clustering which is used in the process ofradar identification The Hierarchical Agglomerative Clustering Algorithm (HACA) based on Generalized Agglomerative Scheme(GAS) implemented and used in the research method is parameterized therefore it is possible to compare the results The resultsof clustering are presented in dendrograms in this paper The received results of grouping and identification based on HACA arecompared with other SEI methods in order to assess the degree of their usefulness and effectiveness for systems of ESMELINTclass

1 Introduction

In the EW aspect the way to increase the detail level of rec-ognition is the SEI method [1ndash3] It extracts distinctivefeatures in the process of signal processing which comes fromthe emission sourceThedistinctive features abovemay be theresult of transformations of received measurement data col-lections As a result of these transformations new collectionsshould have distinctive features by which it is possible toidentify precisely even a single copy of an emission sourceSome example features which may appear as a result ofspecific identification are fractal features especially used inimage transformation (Synthetic Aperture Radar SAR) [45] acoustic signal transformation and radar signal analysisand transformation [6 7] By the extraction of distinctivefeatures received as a result of radar signal transformationit is possible to identify radars of the same type In work[7] there is a method of identification which is based on theextraction of features by which it is possible to have acorrect identification with the probability 70 higher incomparison with classic methods (type identification) Also

measurement and analysis of out-of-band radiation are usedin the radar identification process The extraction of dis-tinctive features coming from the out-of-band radiationanalysis increases the precision of received results in the radaridentification process from 50 to 70 [7] Another waywhich is used in SEI methods is the analysis of inter-PulseRepetition Interval modulation and intrapulse analysis of aradar signal As it is presented in the work [8] the use ofLinear Discriminant Analysis (LDA) and Karhunen-LoeveTransform (K-LT) makes it possible to identify specificallyradars of the same type where the probability of correctidentification equals 98 and Correct Identification Coeffi-cient (CIC) value equals for the new features 098 and forthe old features 047 The results above present that radarsignal processing using intrapulse features and Karhunen-Loeve transform can be a useful tool for EW devices In thework [9] there is a method of SEI which can be used in ESMsystems The main idea is to analyze the radar pulses andcharacterize those by extracting features that should be dif-ferent for each radar The applicability of the feature extrac-tion procedure has been analyzed for different case studies

Hindawi Publishing CorporationJournal of SensorsVolume 2016 Article ID 1879327 9 pageshttpdxdoiorg10115520161879327

2 Journal of Sensors

to obtain a complete picture of the results achievable withthe different radar signals Also the Fourier Transform hasbeen widely used in radar signal and image processing Inthe work [10] it is presented that Joint Time-Frequency (JTF)domain analysis is a useful tool for improving radar signaland image processing for time- and frequency-varying casesAlso Vector Neural Network (VNN)with a supervised learn-ing algorithm suitable for signal classification is very usefulfor emitter identification process as shown in the work [11]Also the system for automatic recognizing of radar wave-forms was introduced in the work [12] where the interceptedradar signal is classified to eight classes based on the pulsecompression waveform linear frequency modulation (LFM)discrete frequency codes (Costas codes) binary phase andFrank P1 P2 P3 and P4 polyphase codes Simulation resultsshow that the classification system achieves overall correctclassification rate of 98 at signal-to-noise ratio (SNR) of6 dB on data similar to the training data

This paper deals with the problem of radar emissionsource identification with the use of the agglomerativemethod of hierarchical radar signal clustering The problemof object clustering is connected with diversity of definitionsresulting from no precise definition of a clusterThus cluster-ing is an issue which is not always solved explicitly Clusteringand classification are problems which are strictly connectedwith pattern recognition [13 14] Clustering concerns divid-ing a collection into groups (clusters)These clusters have theproperty owing to which elements in the same cluster aresimilar to each other while elements in different clusters aredifferent from each other Classification is assigning objectsto classes once defined As there are different criteria thereis also a different division of algorithms of clustering andclassification [15] These criteria are usually types of usedmeasures quality of solution or the way of getting algorithmto the solution

Methods of data clustering are also used in the processof radar recognition and identification The term of radarsource emission identification functions in radioelectronicidentification in the majority of cases in two senses that is ina broad sense and in a narrow sense The radar identificationin a broad sense consists of a quite accurate definition ofthe place the destination and options of this signal on thebasis of the results of detected parametersrsquo measurements andlocated signals from radar The identification in a narrowsense is the classification of these signals Depending onthe number of details the radar identification in a narrowsense might concern the classification of types and the iden-tification of copies where the classification of the emissionsources concerns the division of signal collections into groupscorresponding to particular types of emission sources whilethe identification of copies concerns the divisions of setsof signals into groups corresponding to particular copies ofelectromagnetic emission sources which are of the same type

It should be noticed that ldquomeasurement datardquo above arefrom radar devices which work physically on the battlefieldwhile basic measurement parameters of radar signal arereceived in the process of their analysis and initial processingThe second ones are described precisely in Section 32 (TheStructure of Data Sets) Basic measurement parameters of

radar signals are generated in a form of a signal sounding bya radar and are not enough to identify its emission sourcethat is to define its particular copy for the same type ofradarThis attitude to the process of radioelectronic emissionsource recognition is called Specific Emitter Identification Asa part of the advanced method of SEI analysis presented inthis paper it should be emphasized that there is a significantfact namely all measurement data in the form of recordedradar signals come from a dozen or so working radiolocationdevices of the same typeTheir structure in the form of PulseDescription World (PDW) is described in Section 32 Thestructure of PDW is not the main subject of this work andits detailed description is presented in works [7 16 17] Asuperheterodyne ELINT receiver is used in order to recorddata The description of the procedure is in Section 32

The aim of the authors is to emphasize the fact that thedescribed emission source identification process is a reallycomplex problem where a number of aspects such as Data-Base (DB) modelling [7 16] the method of creating thepattern the classification and identification process used cri-teria and methods estimating the CIC are currently a greatchallenge for researchers and have no optimal solutions Itis also good to point out the fact that their target is to beimplemented to ESMELINT systems and to be used in EWin an optimal way which causes no computational overloadto such a recognition system

2 Classic Model of Radar EmissionSources Recognition

The radar emission sources identification by the classificationof signals (images) which come from them can come downto the problem of object recognition through the recognitionof objectsrsquo images Techniques of object recognition are cur-rently developed fields of science however in many cases itis still not possible to formulate the optimal model of objectrecognition [1 18] Simultaneously in the process of identifi-cation the following problems appear

(i) The side conducting the identification has no suffi-cient information to describe the classes in a way thatwould fit with the reality

(ii) It is possible to define more or less accurate equiva-lents of particular classes in signal space through theirmodels

(iii) The decision about assigning a particular signal to aparticular class is arbitrary

(iv) Thepresence of random incidences causes the appear-ance of false classification

(v) There is a lack of possibility of identifying copies ofthe same type without using the method of SpecificEmitter Identification (SEI)

Disregarding the precise content of a recognized object(radar) what should be assumed is the fact that it can bedefined with the use of a set of features As a result of measureprocedure of a radar signal it is possible to present each of theanalyzed signal features 119873 in the form of a numerical value

Journal of Sensors 3

Thus a formal description of a radar is a set of119873numbers119909 =(1199091 1199092 119909

119873) called the object image In reality the object

image can be not only a set of numbers but also collectionsof logical expressions and collections describing its structureThe exact description of a source emission is significant as faras the proper construction register of a radar in DataBase isconcerned It is important as it eliminates redundancies fromDataBase and designs a DataBase increasing the probabilityof a proper radar identification [7] Methods based on unin-tentional emissions or distinctive features extraction withfractal properties [6] are often used in the process of radarrecognition These called also Specific Emitter Identification(SEI) increase probability of source emission identificationAs a result identification of each of the copies is possible

3 Hierarchical Clustering Dendrogram

Clustering is presented as a process of creating clusters ofelements similar to each other Clustering is based on thedivision of the finite set 119881 of elements on 119871 subsets 119881

119896of

similar elements This division can be written in the form ofa family 119876(119881) of subsets 119881

119896of the collection 119881 according to

119876 (119881) = 119881119896sub 119881 119896 isin [1 119871] (1)

The set of all possible (or all acceptable) divisions119876(119881) of set119881 on 119871 subsets is written as119876119871(119881) Division119876will be definedas an optimal division119876opt if the criterion function 119890(119876) fromthe criterion assumed is extremum for this division as shownin

119876 = 119876opt lArrrArr 119890 (119876) = min119876119897isin119876

119871

(119890 (119876119895)) (2)

The definition of similaritymeasure between objects is neces-sary to start the clustering processThis definition will be alsoused to provide classes A class in this case is considered to bea collection of objects whose similarity within the class is highwhereas that among classes is lowThe definition of similarityplays a key role in such amethod of clusteringThere are threecategories agglomeration category division category anddirect category in divisions based on the type of control usedwhile building clusters Agglomeration category is based onprogressive merging of clusters that is iteration connectionof separate small clusters in order to create bigger ones andmake a final one The process of such connection is usuallypresented in the form of a dendrogram By using thresholdwhich defines the minimum of similarity the process ofconnection may be broken before the clusters become thefinal oneThus there will be few clusters and for each of themthe value of similarity measure will be below the acceptablethreshold Division category is based on creating clustersby iteration division of the initial collection into smallerand smaller ones finally creating a situation in which everyelement will have its own clusterThe direct category is basedon finding a specific number of clusters What should bedone here is finding such division of existing data that willbe optimal in case of the measure defining the division intoclusters One of the first such methods is k-meansMacQueenalgorithm shown in work [19]

31 The Use of Threshold Criteria Methods and criteria ofelements clustering are significant in the process of clusteringDuring the completion of research procedure Euclidean andMahalanobis distances (119889

119864 119889119872) were used according to (3)

and (4) In this equation x and y are the elements of the setin space 119881 119899 is the number of elements in the set in space 119881and C is the covariance matrix according to (5) while V arethe average elements of the set according to (6)

1198892

119864(x y) 119889= (x minus y) (x minus y)119879 forall

xyisin119881 (3)

1198892

119872(x y) 119889= (x minus y)Cminus1 (x minus y)119879 forall

xyisin119881 (4)

C =1

119899

119899

sum

119895=1

(k119895minus V)119879

(k119895minus V) k

119895isin 119881 (5)

V =1

119899

119899

sum

119895=1

k119895 (6)

Two threshold criteria were used for the process of clusteringThese were the furthest neighbour criterion (FNC) and thenearest neighbour criterion (NNC) according to (7) and (8)where119881

119896are subsets of similar elements and 119889 is the distance

function according to (9) in which 1198771 is the real number

system

forall119881119896isin119876opt

forallxyisin119881119896

[119889 (x y) lt 119889max] (7)


forallxisin119881119896

existy =xVisin119881119896

[119889 (x y) le 119889max] (8)

119889 119881 times 119881 997888rarr 119903 isin 1198771 119903 ge 0 (9)

The advantage of these criteria is their simplicity and highagreement of optimal clustering results with those arbitraryrealized by a humanTheNNChighlights similarities of pairsThe FNC highlights the influence of the isolated elements ofspace 119881 This is some kind of disagreement as there is ele-ments deviation of the space 119881 resulting from defining theplace of elements in space119881 on the basis of quantities definedexperimentally

32 The Structure of Data Sets and Measurement ProcedureMeasurement data sets which are received as a result ofmeasurement procedure are treated as homogeneous datawhere interferences in PRI and RF measurement sequencesare removed The data selection and interferences removalmethods are described precisely in the work [20] All radarsignals measurements are done during warfare In total thereis a record of several thousand pulses coming from a dozen orso radar devices of the same type In order to provide repeti-tiveness of the received measurement results a measurementprocedure was introduced where radar signal measurementof every single radar is done in four measurement placeswith a constant distance from the radar emission sourceThe choice of three copies of the same type of radar todetailed verification is made in order to by their dislocation


provide comparable (in all three cases) landform features inthe area where the radar is dislocated For measurementthere are constant values of detection thresholds and constantvalues of superheterodyne receiver sensitivity which are setduringmeasurement on the Radio Frequency of the analyzedemission sourceThe received measurement (recording) dataset is described by the analyzed signal from the amplitudedemodulator (AM Lin) output and frequency demodulator[21] Recordings of radar signals in the forms of PDW werereceived during the measure procedure The vector receivedis a formalized structure of a record type according to (10)Specific PDW fields contain frequency parameters and timeparameters where PRI(119896) is the Pulse Repetition IntervalPW(119896) is the Pulse Width RF(119896) is the Radio Frequency 119899is the number of pulses in the recording which are qualifiedfor analysis and 119896 is the number of the pulses in recording

PDW =

[[[[[[[[[[[[[

[

PRI (1) PW (1) RF (1)PRI (2) PW (2) RF (2)

PRI (119896) PW (119896) RF (119896)

PRI (119899) PW (119899) RF (119899)

]]]]]]]]]]]]]

]

(10)

The holdout method (MH) was used in order to define thestructure of measure vectors This method divides the setof measurement data into two separate subsets that is thesubset used to teach the classificator and the subset used totest the classificator Usually the division is as follows 23available data is the teaching set and 13 is the testing set[22 23] With the use of PDW vector the vector of basicfeaturesVP was defined according to (11) inwhichRF

MH is theaverage value of Radio Frequency PWMH is the average valueof Pulse Width and PRIMH are average values of Pulse Rep-etition Interval

VP = [RFMHPWMH

PRIMH] (11)

Individual component features of VP vector were definedaccording to (12) divide (14) where 119899

119908is the number of pulses

in recording which were qualified for the analysis in order touse the holdout method

RFMH=

1

119899119908

119899119908

sum

119894=1

RF (119894) (12)

PWMH=

1

119899119908

119899119908

sum

119894=1

PW (119894) (13)

PRIMH=

1

119899119908

119899119908

sum

119894=1

PRI (119894) (14)

4 The Implementation of GAS andResults of Analysis

Thehierarchical clusteringmethodwas used in order to studyparticular features of VP vector This method uses hierar-chical clustering and grouping algorithm which is based onthe Generalized Agglomerative Scheme It is a special typeof hierarchical algorithms that are most appropriate for largedata sets [24ndash26] To divide a particular 119899 cluster of elementsinto 119871 groups what needs to be done first is dividing it into119899 groups This means that each of the groups consists ofonly one element Secondly two elements with the highestsimilarity should be connected into one group As a resultthere are (119899 minus 1) groups and later (119899 minus 2) groups until thereare an acceptable number of clusters The basic steps in theprocedure above are as follows

(1) 119898 = 119899 whereas the group119883119894= 119909[119894] 119894 = 1 2 119899

(2) If119898 le 119871 stop(3) Find the nearest pair of groups for example 119883

119894and

119883119895

(4) Combine 119883119894and 119883

119895 remove 119883

119895 and decrease 119898 by

one and jump to (2)

The procedure ends its activity after reaching the right num-ber of groups 119898 le 119871 The hierarchical clustering algorithmwhich was implemented for research purposes was two-element parameterized One of the parameters concerns theway of finding a similarity between features It uses Euclideandistance (119889

119864) and Mahalanobis distance (119889

119872) The second

parameter is connected with the clustering method by usingthe NNC and FNC criterionThe process of clustering in thisalgorithmmay be divided into three stages that is measuringthe distance dendrogram building (on the basis of specificparameters) and dendrogram cutting on the specific levelThemethod abovewas used in a research experiment in orderto group VP vectors in the process of radar identification VPvectors are basic measure parameters of radar signals Whatis important is that the measure vectors receivedVP are realradar signal recordings coming from few copies of radars ofthe same type Thus the process of identification is not easyIt is a special case of sources emissions identification Therewere three radars chosen of the same type for the analysisTheir basic measure parameters merged most The results ofclustering the PRIwere presented in the formof dendrogramsshown in Figures 1ndash9 The labels on the axis in the Figures1ndash9 present the initial value of these clusters and on the 119910-axis there is similarity between clusters As a result of thispresentation it is possible to estimate the number of clustersand it is also possible to have a PRI outlier vector

The process of cluster connection is carried out until thenumber of clusters received is sufficient Graphically shownin a dendrogram the condition of an alloy (ie a specificnumber of clusters) presents the horizontal line which cutsthe dendrogram The value bracket Δ119889

119909which is defined in

each of the dendrograms presents the ldquosafe areardquo for whichthere is a guaranteed correct result of data clustering Thereceived value Δ119889

119909 different for each of analyzed vectorsVP

means that these are vectors coming from different radars


19895

199

19905

1991

19915

1992

19925

1993

19935

1994

19945

1123 1 2 1422101519 3 21271625 4 13 8 29 51726 730 6 18122428 9 200

50

100

150

200

250

300

350

Copy of Radar Number 1 Copy of Radar Number 1

Clusters1123 1 21422101519 3 21271625 4 13 829 51726 730 6 18122428 9 20

Clusters

Dist

ance

Dist

ance

Δdx = 1994

Figure 1 The hierarchical clustering dendrogram of PRI (Euclidean distance NNC) for copy of Radar Number 1


1325 2122819 11118 72116 820 922 52910 6 262317 3 1530 4 2414270

50

100

150

200

250

300

350

Clusters1325 2122819 11118 72116 820 922 52910 6 262317 3 1530 4 241427

Clusters

19895

19896

19897

19898

19899

199

19901

19902

19903

19904

19905

Dist

ance

Dist

ance

Δdx = 199



728 324193021 1 9 261012221411231817 2 8202527 4 161315 5 6 290

50

100

150

200

250

300

350

Clusters728 324193021 1 9 261012221411231817 2 8202527 4 161315 5 6 29

Clusters

1979

19795

198

19805

1981

19815

1982

19825

1983

1984

19835

Dist

ance

Dist

ance

Δdx = 1982




1123 1 21422101519 3 21271625 4 13 829 5 1726 7 30 6 18122428 9200

02

04

06

08

1

12

14

16

18

Clusters1123 1 21422101519 3 21271625 4 13 829 5 1726 7 30 6 18122428 920

Clusters

0095

01

0105

011D

istan

ce

Dist

ance

Δdx = 0104

Figure 4 The hierarchical clustering dendrogram of PRI (Mahalanobis distance NNC) for copy of Radar Number 1


1325 2122819 11118 72116 820 922 52910 6 262317 3 1530 4 241427

Clusters1325 2122819 1 1118 72116 820 922 52910 6 262317 3 1530 4 241427

Clusters

0

02

04

06

08

1

12

14

16

18

0095

01

0105

011

Dist

ance

Dist

ance

Δdx = 0099


copies of the same type As a result of the use of agglomerativemethod (bottom-up) initially each PRI measurement vectoris a separate cluster (class) in further iterations clusters arejoined to bigger clusters until all PRI values belong to onecluster In this way clusterization is presented in the form ofdendrograms

Figures 1ndash3 present dendrograms for Euclidean distanceand NNC in which the distance between the first pair ofclusters is quantified The dendrograms which appeared hereare cut at the level of the first pairThe functionwhich cuts thestructure of dendrogram restores the results as follows 1994199 and 1982

Figures 4ndash6 present dendrograms for Mahalanobis dis-tances and NNC in which the distance in the first pair ofclusters is quantified and the rest of the dendrograms are cut

at the level of the first pair The results of clusterization Δ119889119909

are as follows 0104 0099 and 0101Similarly Figures 7ndash9 present dendrograms for Euclidean

distances and FNC where the results of clusterization Δ119889119909

are as follows 2008 2026 and 2024 As a result of such anattitude there is information about distinctive features of thevector of radar signal basic measurement parameters VP inthe aspect of PRI

The use of clusterization result Δ119889119909makes it possible to

expand features of the vector VP into the received clusteri-zation values Thus there is a measurement vector for everycopy of a radar of the same type The Hierarchical Agglom-erative Clustering Algorithm used in the SEI process basedon GAS makes it possible to receive hierarchical clusteringfor Pulse Repetition Intervals In the process of clustering



7 28 324193021 1 9 261012221411231817 2 8202527 4 161315 5 6 29

Clusters728 324193021 1 9 261012221411231817 2 8202527 4 161315 5 6 29

Clusters

0

02

04

06

08

1

12

14

16

18

0095

01

0105

011D

istan

ce

Dist

ance

Δdx = 0101



1123 1 21422101519 32521 1627 413 829 51726 730 618122428 920

Clusters1123 1 21422101519 32521 1627 413 829 51726 730 618122428 920

Clusters

0

100

200

300

400

500

600

700

198

199

20

201

202

203

204

205D

istan

ce

Dist

ance

Δdx = 2008

Figure 7 The hierarchical clustering dendrogram of PRI (Euclidean distance FNC) for copy of Radar Number 1

Euclidean and Mahalanobis distance measures are used aswell as the nearest neighbour criterion (NNC) and the fur-thest neighbour criterion (FNC) for three different types ofradar copies of the same type that is Number 1 Number 2and Number 3

5 Conclusion

Thecharacteristic feature of the algorithm implemented is thepossibility of presenting clustering structure in the form of adendrogram Such presentation of clustering results providesa wide range of options for example estimating the numberof clusters (if it is not known before) and the possibility ofanalyzing appearing diverge vectors

Using Euclidean distance andNNCcriterion the receivedvalues Δ119889

119909for particular radar copies are as follows 1994

199 and 1982 Using Mahalanobis distance and NNC crite-rion the received values Δ119889

119909for particular radar copies are

as follows 0104 0099 and 0101 Using Euclidean distanceand FNC criterion the received values Δ119889

119909for particular

radar copies are as follows 2008 2026 and 2024The deter-minant which influences the Δ119889

119909quantity is the type of mea-

sure distance used Similarity between clusters was definedby quantities thus the dendrograms received will have par-ticular proportions of similarity As a result it is possible touse the change of the distance to assess if the connectionwas natural or forced This method makes it possible todifferentiate particular radar copies of the same type on thebasis of the dendrograms received



1423 1 7 2519 2131724 8 122021 9 5 62910112622 3152730 4 1618280

100

200

300

400

500

600

700

Clusters1423 1 7 2519 2131724 8 122021 9 5 62910112622 3152730 4 161828

Clusters

198

199

20

201

202

203

204

205D

istan

ce

Dist

ance

Δdx = 2026



22 612231015112421 1 91428 2 82026 3 730192725 41618 51713290

100

200

300

400

500

600

700

Clusters22 612231015112421 1 91428 2 82026 3 730192725 41618 5171329

Clusters

198

199

20

201

202

203

204

205D

istan

ce

Dist

ance

Δdx = 2024


The received measurement results have a significantinfluence on the radar emission sources specific identificationof radar copies of the same type Other methods mentionedin Section 1 of this paper such as the use of the out-of-bandradiation [7] fractal features extraction [6] and methodsbased on the intrapulses analysis [8] increase the probabilityof identification to 50ndash70 In the work [6] there was anincrease of the Correct Identification Coefficient level fromthe value CIC = 0169 to the value CIC = 0916 while in work[16] the value of decision function for the same radar typesidentification equals 63 As it is presented in the work [8]radar signal processing using intrapulse features Karhunen-Loeve Transform (K-LT) and Linear Discriminant Analysiscan be a useful tool for ElectronicWarfare devices Both LDAand K-LT gave very similar results and the received Correct

Identification Coefficient (CIC) value equals 098 for thenew features and 047 for the old features The measurementresults present that the new transformed features includeabout 90 of the recognized information needed to resolvethe complicated problem of radar signal classification Theresults of the speed and numerical stability of algorithmsseem to be enough to put them into practice in the ESMdevices Simulation results presented in the work [12] showclassification rate of 98 at signal-to-noise ratio (SNR) of6 dB on data similar to the training data

It must be admitted that it is an extremely high increasehowever the level of complexity of these methods and theused algorithms are complicated computationally whichcauses the identification time to increase as well The hierar-chical PRI clustering method presented in this paper based


on HACA is realized on the basis of the use of MATLABsoftware and the received vectors VP are recorded in thededicated DB for EWELINT system Further works on theuse of HACA in SEI process work out the matrix of mutualsimilarity by which it is possible to estimate automaticallythe similarity among PRI vectors for different radars of thesame type Also the automatic defining mechanism of Δ119889

119909

value should be applied and an additionalΔ119889119909and a feature to

VP measure vector should be added The feature mentionedhere is a good separation measure in the process of radarsidentification This problem will be still examined in thepresented SEI area

Competing Interests

The author declares that he has no competing interests

References

[1] R G Willey Electronic Intelligence The Analysis of Radar Sig-nals Artech House London UK 1993

[2] M-W Liu and J F Doherty ldquoSpecific emitter identificationusing nonlinear device estimationrdquo in Proceedings of the IEEESarnoff Symposium (SARNOFF rsquo08) pp 1ndash5 Princeton NJUSA April 2008

[3] K I Talbot P R Duley andMH Hyatt ldquoSpecific emitter iden-tification and verificationrdquoTechnology Review Journal vol 1 pp113ndash133 2003

[4] F Berizzi G Bertini M Martorella and M Bertacca ldquoTwo-dimensional variation algorithm for fractal analysis of sea SARimagesrdquo IEEE Transactions on Geoscience and Remote Sensingvol 44 no 9 pp 2361ndash2373 2006

[5] M Germain G B BEnie J-M Boucher S Foucher K Fungand K Goıta ldquoContribution of the fractal dimension to multi-scale adaptive filtering of SAR imageryrdquo IEEE Transactions onGeoscience and Remote Sensing vol 41 no 8 pp 1765ndash17722003

[6] J Dudczyk and A Kawalec ldquoIdentification of emitter sourcesin the aspect of their fractal featuresrdquo Bulletin of the PolishAcademy of Sciences Technical Sciences vol 61 no 3 pp 623ndash628 2013

[7] J DudczykApplying the radiated emission to the radio-electronicdevices identification [dissertation thesis] Department of Elec-trical Military University of Technology 2004 (Polish)

[8] A Kawalec R Owczarek and J Dudczyk ldquoData modeling andsimulation applied to radar signal recognitionrdquo Molecular andQuantum Acoustics vol 26 pp 165ndash173 2005

[9] S DrsquoAgostino G Foglia and D Pistoia ldquoSpecific emitter iden-tification analysis on real radar signal datardquo inProceedings of theEuropean Radar Conference (EURAD rsquo09) pp 242ndash245 RomaItaly 2009

[10] V Chen and H Ling ldquoJoint time-frequency analysis for radarsignal and image processingrdquo IEEE Signal Processing Magazinevol 16 no 2 pp 81ndash93 2002

[11] C-S Shich and C-T Lin ldquoA vector neural network for emitteridentificationrdquo IEEETransactions onAntennas and Propagationvol 50 no 8 pp 1120ndash1127 2002

[12] J Lunden and V Koivunen ldquoAutomatic radar waveform recog-nitionrdquo IEEE Journal on Selected Topics in Signal Processing vol1 no 1 pp 124ndash136 2007

[13] S Theodoridis and K Koutroumbas Pattern Recognition Aca-demic Press Boston Mass USA 2009

[14] J T Tou and R C Gonzalez Pattern Recognition PrinciplesAddison-Wesley Reading Mass USA 1974

[15] W Sobczak and W MalinaTheMethods of Selection and Infor-mation Reduction Scientific Press WNT Warsaw Poland 1985(Polish)

[16] J Dudczyk and A Kawalec ldquoFast-decision identification algo-rithm of emission source pattern in databaserdquo Bulletin of thePolish Academy of Sciences Technical Sciences vol 63 no 2 pp385ndash389 2015

[17] J Dudczyk and A Kawalec ldquoSpecific emitter identificationbased on graphical representation of the distribution of radarsignal parametersrdquo Bulletin of the Polish Academy of SciencesTechnical Sciences vol 63 no 2 pp 391ndash396 2015

[18] R Tadeusiewicz and P Korohoda Computer Analysis andImage Processing Progress of Telecommunication FoundationPublishing House Krakow Poland 1997

[19] D J C Mackay ldquoProbable networks and plausible predictions-a review of practical bayesian methods for supervised neuralnetworksrdquo Network Computation in Neural Systems vol 6 no3 pp 469ndash505 1995

[20] SWnuczek Radar type classification with secondary parametersof signalsrsquo visional structure [dissertation thesis] Department ofElectronics Military University of Technology 1993 (Polish)

[21] J B Y TsuiMicrowave Receivers with Electronic Warfare Appli-cations John Wiley amp Sons New York NY USA 1986

[22] R O Duda P E Hart and D G Stork Pattern ClassificationJohn Wiley amp Sons New York NY USA 2nd edition 2000

[23] K Fukunaga Introduction to Statistical Pattern RecognitionAcademic Press New York NY USA 2nd edition 1990

[24] T Zhang R Ramakrishnan andM Livny ldquoBIRCH an efficientdata clustering method for very large databasesrdquo in Proceedingsof the 1996 ACM SIGMOD international conference on Man-agement of data (SIGMOD rsquo96) pp 103ndash114 Montreal Canada1996

[25] E M Rasmussen and P Willett ldquoEfficiency of hierarchicagglomerative clustering using the ICL distributed array pro-cessorrdquo Journal of Documentation vol 45 no 1 pp 1ndash24 1989

[26] C F Olson ldquoParallel algorithms for hierarchical clusteringrdquoTech Rep University of California Oakland Calif USA 1993

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



to obtain a complete picture of the results achievable withthe different radar signals Also the Fourier Transform hasbeen widely used in radar signal and image processing Inthe work [10] it is presented that Joint Time-Frequency (JTF)domain analysis is a useful tool for improving radar signaland image processing for time- and frequency-varying casesAlso Vector Neural Network (VNN)with a supervised learn-ing algorithm suitable for signal classification is very usefulfor emitter identification process as shown in the work [11]Also the system for automatic recognizing of radar wave-forms was introduced in the work [12] where the interceptedradar signal is classified to eight classes based on the pulsecompression waveform linear frequency modulation (LFM)discrete frequency codes (Costas codes) binary phase andFrank P1 P2 P3 and P4 polyphase codes Simulation resultsshow that the classification system achieves overall correctclassification rate of 98 at signal-to-noise ratio (SNR) of6 dB on data similar to the training data

This paper deals with the problem of radar emissionsource identification with the use of the agglomerativemethod of hierarchical radar signal clustering The problemof object clustering is connected with diversity of definitionsresulting from no precise definition of a clusterThus cluster-ing is an issue which is not always solved explicitly Clusteringand classification are problems which are strictly connectedwith pattern recognition [13 14] Clustering concerns divid-ing a collection into groups (clusters)These clusters have theproperty owing to which elements in the same cluster aresimilar to each other while elements in different clusters aredifferent from each other Classification is assigning objectsto classes once defined As there are different criteria thereis also a different division of algorithms of clustering andclassification [15] These criteria are usually types of usedmeasures quality of solution or the way of getting algorithmto the solution

Methods of data clustering are also used in the processof radar recognition and identification The term of radarsource emission identification functions in radioelectronicidentification in the majority of cases in two senses that is ina broad sense and in a narrow sense The radar identificationin a broad sense consists of a quite accurate definition ofthe place the destination and options of this signal on thebasis of the results of detected parametersrsquo measurements andlocated signals from radar The identification in a narrowsense is the classification of these signals Depending onthe number of details the radar identification in a narrowsense might concern the classification of types and the iden-tification of copies where the classification of the emissionsources concerns the division of signal collections into groupscorresponding to particular types of emission sources whilethe identification of copies concerns the divisions of setsof signals into groups corresponding to particular copies ofelectromagnetic emission sources which are of the same type

It should be noticed that ldquomeasurement datardquo above arefrom radar devices which work physically on the battlefieldwhile basic measurement parameters of radar signal arereceived in the process of their analysis and initial processingThe second ones are described precisely in Section 32 (TheStructure of Data Sets) Basic measurement parameters of

radar signals are generated in a form of a signal sounding bya radar and are not enough to identify its emission sourcethat is to define its particular copy for the same type ofradarThis attitude to the process of radioelectronic emissionsource recognition is called Specific Emitter Identification Asa part of the advanced method of SEI analysis presented inthis paper it should be emphasized that there is a significantfact namely all measurement data in the form of recordedradar signals come from a dozen or so working radiolocationdevices of the same typeTheir structure in the form of PulseDescription World (PDW) is described in Section 32 Thestructure of PDW is not the main subject of this work andits detailed description is presented in works [7 16 17] Asuperheterodyne ELINT receiver is used in order to recorddata The description of the procedure is in Section 32

The aim of the authors is to emphasize the fact that thedescribed emission source identification process is a reallycomplex problem where a number of aspects such as Data-Base (DB) modelling [7 16] the method of creating thepattern the classification and identification process used cri-teria and methods estimating the CIC are currently a greatchallenge for researchers and have no optimal solutions Itis also good to point out the fact that their target is to beimplemented to ESMELINT systems and to be used in EWin an optimal way which causes no computational overloadto such a recognition system

2 Classic Model of Radar EmissionSources Recognition

The radar emission sources identification by the classificationof signals (images) which come from them can come downto the problem of object recognition through the recognitionof objectsrsquo images Techniques of object recognition are cur-rently developed fields of science however in many cases itis still not possible to formulate the optimal model of objectrecognition [1 18] Simultaneously in the process of identifi-cation the following problems appear

(i) The side conducting the identification has no suffi-cient information to describe the classes in a way thatwould fit with the reality

(ii) It is possible to define more or less accurate equiva-lents of particular classes in signal space through theirmodels

(iii) The decision about assigning a particular signal to aparticular class is arbitrary

(iv) Thepresence of random incidences causes the appear-ance of false classification

(v) There is a lack of possibility of identifying copies ofthe same type without using the method of SpecificEmitter Identification (SEI)

Disregarding the precise content of a recognized object(radar) what should be assumed is the fact that it can bedefined with the use of a set of features As a result of measureprocedure of a radar signal it is possible to present each of theanalyzed signal features 119873 in the form of a numerical value







119896of



119876 (119881) = 119881119896sub 119881 119896 isin [1 119871] (1)



119871

(119890 (119876119895)) (2)





1198892


xyisin119881 (3)

1198892


xyisin119881 (4)

C =1

119899

119899

sum

119895=1

(k119895minus V)119879

(k119895minus V) k

119895isin 119881 (5)

V =1

119899

119899

sum

119895=1

k119895 (6)




system



[119889 (x y) lt 119889max] (7)




[119889 (x y) le 119889max] (8)






PDW =

[[[[[[[[[[[[[

[

PRI (1) PW (1) RF (1)PRI (2) PW (2) RF (2)

PRI (119896) PW (119896) RF (119896)

PRI (119899) PW (119899) RF (119899)

]]]]]]]]]]]]]

]

(10)



VP = [RFMHPWMH

PRIMH] (11)




RFMH=

1

119899119908

119899119908

sum

119894=1

RF (119894) (12)

PWMH=

1

119899119908

119899119908

sum

119894=1

PW (119894) (13)

PRIMH=

1

119899119908

119899119908

sum

119894=1

PRI (119894) (14)





119894and

119883119895

(4) Combine 119883119894and 119883

119895 remove 119883


one and jump to (2)



119872) The second








19895

199

19905

1991

19915

1992

19925

1993

19935

1994

19945

1123 1 2 1422101519 3 21271625 4 13 8 29 51726 730 6 18122428 9 200

50

100

150

200

250

300

350


Clusters1123 1 21422101519 3 21271625 4 13 829 51726 730 6 18122428 9 20

Clusters

Dist

ance

Dist

ance

Δdx = 1994



1325 2122819 11118 72116 820 922 52910 6 262317 3 1530 4 2414270

50

100

150

200

250

300

350

Clusters1325 2122819 11118 72116 820 922 52910 6 262317 3 1530 4 241427

Clusters

19895

19896

19897

19898

19899

199

19901

19902

19903

19904

19905

Dist

ance

Dist

ance

Δdx = 199



728 324193021 1 9 261012221411231817 2 8202527 4 161315 5 6 290

50

100

150

200

250

300

350

Clusters728 324193021 1 9 261012221411231817 2 8202527 4 161315 5 6 29

Clusters

1979

19795

198

19805

1981

19815

1982

19825

1983

1984

19835

Dist

ance

Dist

ance

Δdx = 1982




1123 1 21422101519 3 21271625 4 13 829 5 1726 7 30 6 18122428 9200

02

04

06

08

1

12

14

16

18

Clusters1123 1 21422101519 3 21271625 4 13 829 5 1726 7 30 6 18122428 920

Clusters

0095

01

0105

011D

istan

ce

Dist

ance

Δdx = 0104



1325 2122819 11118 72116 820 922 52910 6 262317 3 1530 4 241427

Clusters1325 2122819 1 1118 72116 820 922 52910 6 262317 3 1530 4 241427

Clusters

0

02

04

06

08

1

12

14

16

18

0095

01

0105

011

Dist

ance

Dist

ance

Δdx = 0099













7 28 324193021 1 9 261012221411231817 2 8202527 4 161315 5 6 29

Clusters728 324193021 1 9 261012221411231817 2 8202527 4 161315 5 6 29

Clusters

0

02

04

06

08

1

12

14

16

18

0095

01

0105

011D

istan

ce

Dist

ance

Δdx = 0101



1123 1 21422101519 32521 1627 413 829 51726 730 618122428 920

Clusters1123 1 21422101519 32521 1627 413 829 51726 730 618122428 920

Clusters

0

100

200

300

400

500

600

700

198

199

20

201

202

203

204

205D

istan

ce

Dist

ance

Δdx = 2008



5 Conclusion













1423 1 7 2519 2131724 8 122021 9 5 62910112622 3152730 4 1618280

100

200

300

400

500

600

700

Clusters1423 1 7 2519 2131724 8 122021 9 5 62910112622 3152730 4 161828

Clusters

198

199

20

201

202

203

204

205D

istan

ce

Dist

ance

Δdx = 2026



22 612231015112421 1 91428 2 82026 3 730192725 41618 51713290

100

200

300

400

500

600

700

Clusters22 612231015112421 1 91428 2 82026 3 730192725 41618 5171329

Clusters

198

199

20

201

202

203

204

205D

istan

ce

Dist

ance

Δdx = 2024







119909



Competing Interests


References





























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation















119896of



119876 (119881) = 119881119896sub 119881 119896 isin [1 119871] (1)



119871

(119890 (119876119895)) (2)





1198892


xyisin119881 (3)

1198892


xyisin119881 (4)

C =1

119899

119899

sum

119895=1

(k119895minus V)119879

(k119895minus V) k

119895isin 119881 (5)

V =1

119899

119899

sum

119895=1

k119895 (6)




system



[119889 (x y) lt 119889max] (7)




[119889 (x y) le 119889max] (8)






PDW =

[[[[[[[[[[[[[

[

PRI (1) PW (1) RF (1)PRI (2) PW (2) RF (2)

PRI (119896) PW (119896) RF (119896)

PRI (119899) PW (119899) RF (119899)

]]]]]]]]]]]]]

]

(10)



VP = [RFMHPWMH

PRIMH] (11)




RFMH=

1

119899119908

119899119908

sum

119894=1

RF (119894) (12)

PWMH=

1

119899119908

119899119908

sum

119894=1

PW (119894) (13)

PRIMH=

1

119899119908

119899119908

sum

119894=1

PRI (119894) (14)





119894and

119883119895

(4) Combine 119883119894and 119883

119895 remove 119883


one and jump to (2)



119872) The second








19895

199

19905

1991

19915

1992

19925

1993

19935

1994

19945

1123 1 2 1422101519 3 21271625 4 13 8 29 51726 730 6 18122428 9 200

50

100

150

200

250

300

350


Clusters1123 1 21422101519 3 21271625 4 13 829 51726 730 6 18122428 9 20

Clusters

Dist

ance

Dist

ance

Δdx = 1994



1325 2122819 11118 72116 820 922 52910 6 262317 3 1530 4 2414270

50

100

150

200

250

300

350

Clusters1325 2122819 11118 72116 820 922 52910 6 262317 3 1530 4 241427

Clusters

19895

19896

19897

19898

19899

199

19901

19902

19903

19904

19905

Dist

ance

Dist

ance

Δdx = 199



728 324193021 1 9 261012221411231817 2 8202527 4 161315 5 6 290

50

100

150

200

250

300

350

Clusters728 324193021 1 9 261012221411231817 2 8202527 4 161315 5 6 29

Clusters

1979

19795

198

19805

1981

19815

1982

19825

1983

1984

19835

Dist

ance

Dist

ance

Δdx = 1982




1123 1 21422101519 3 21271625 4 13 829 5 1726 7 30 6 18122428 9200

02

04

06

08

1

12

14

16

18

Clusters1123 1 21422101519 3 21271625 4 13 829 5 1726 7 30 6 18122428 920

Clusters

0095

01

0105

011D

istan

ce

Dist

ance

Δdx = 0104



1325 2122819 11118 72116 820 922 52910 6 262317 3 1530 4 241427

Clusters1325 2122819 1 1118 72116 820 922 52910 6 262317 3 1530 4 241427

Clusters

0

02

04

06

08

1

12

14

16

18

0095

01

0105

011

Dist

ance

Dist

ance

Δdx = 0099













7 28 324193021 1 9 261012221411231817 2 8202527 4 161315 5 6 29

Clusters728 324193021 1 9 261012221411231817 2 8202527 4 161315 5 6 29

Clusters

0

02

04

06

08

1

12

14

16

18

0095

01

0105

011D

istan

ce

Dist

ance

Δdx = 0101



1123 1 21422101519 32521 1627 413 829 51726 730 618122428 920

Clusters1123 1 21422101519 32521 1627 413 829 51726 730 618122428 920

Clusters

0

100

200

300

400

500

600

700

198

199

20

201

202

203

204

205D

istan

ce

Dist

ance

Δdx = 2008



5 Conclusion













1423 1 7 2519 2131724 8 122021 9 5 62910112622 3152730 4 1618280

100

200

300

400

500

600

700

Clusters1423 1 7 2519 2131724 8 122021 9 5 62910112622 3152730 4 161828

Clusters

198

199

20

201

202

203

204

205D

istan

ce

Dist

ance

Δdx = 2026



22 612231015112421 1 91428 2 82026 3 730192725 41618 51713290

100

200

300

400

500

600

700

Clusters22 612231015112421 1 91428 2 82026 3 730192725 41618 5171329

Clusters

198

199

20

201

202

203

204

205D

istan

ce

Dist

ance

Δdx = 2024







119909



Competing Interests


References





























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











PDW =

[[[[[[[[[[[[[

[

PRI (1) PW (1) RF (1)PRI (2) PW (2) RF (2)

PRI (119896) PW (119896) RF (119896)

PRI (119899) PW (119899) RF (119899)

]]]]]]]]]]]]]

]

(10)



VP = [RFMHPWMH

PRIMH] (11)




RFMH=

1

119899119908

119899119908

sum

119894=1

RF (119894) (12)

PWMH=

1

119899119908

119899119908

sum

119894=1

PW (119894) (13)

PRIMH=

1

119899119908

119899119908

sum

119894=1

PRI (119894) (14)





119894and

119883119895

(4) Combine 119883119894and 119883

119895 remove 119883


one and jump to (2)



119872) The second








19895

199

19905

1991

19915

1992

19925

1993

19935

1994

19945

1123 1 2 1422101519 3 21271625 4 13 8 29 51726 730 6 18122428 9 200

50

100

150

200

250

300

350


Clusters1123 1 21422101519 3 21271625 4 13 829 51726 730 6 18122428 9 20

Clusters

Dist

ance

Dist

ance

Δdx = 1994



1325 2122819 11118 72116 820 922 52910 6 262317 3 1530 4 2414270

50

100

150

200

250

300

350

Clusters1325 2122819 11118 72116 820 922 52910 6 262317 3 1530 4 241427

Clusters

19895

19896

19897

19898

19899

199

19901

19902

19903

19904

19905

Dist

ance

Dist

ance

Δdx = 199



728 324193021 1 9 261012221411231817 2 8202527 4 161315 5 6 290

50

100

150

200

250

300

350

Clusters728 324193021 1 9 261012221411231817 2 8202527 4 161315 5 6 29

Clusters

1979

19795

198

19805

1981

19815

1982

19825

1983

1984

19835

Dist

ance

Dist

ance

Δdx = 1982




1123 1 21422101519 3 21271625 4 13 829 5 1726 7 30 6 18122428 9200

02

04

06

08

1

12

14

16

18

Clusters1123 1 21422101519 3 21271625 4 13 829 5 1726 7 30 6 18122428 920

Clusters

0095

01

0105

011D

istan

ce

Dist

ance

Δdx = 0104



1325 2122819 11118 72116 820 922 52910 6 262317 3 1530 4 241427

Clusters1325 2122819 1 1118 72116 820 922 52910 6 262317 3 1530 4 241427

Clusters

0

02

04

06

08

1

12

14

16

18

0095

01

0105

011

Dist

ance

Dist

ance

Δdx = 0099













7 28 324193021 1 9 261012221411231817 2 8202527 4 161315 5 6 29

Clusters728 324193021 1 9 261012221411231817 2 8202527 4 161315 5 6 29

Clusters

0

02

04

06

08

1

12

14

16

18

0095

01

0105

011D

istan

ce

Dist

ance

Δdx = 0101



1123 1 21422101519 32521 1627 413 829 51726 730 618122428 920

Clusters1123 1 21422101519 32521 1627 413 829 51726 730 618122428 920

Clusters

0

100

200

300

400

500

600

700

198

199

20

201

202

203

204

205D

istan

ce

Dist

ance

Δdx = 2008



5 Conclusion













1423 1 7 2519 2131724 8 122021 9 5 62910112622 3152730 4 1618280

100

200

300

400

500

600

700

Clusters1423 1 7 2519 2131724 8 122021 9 5 62910112622 3152730 4 161828

Clusters

198

199

20

201

202

203

204

205D

istan

ce

Dist

ance

Δdx = 2026



22 612231015112421 1 91428 2 82026 3 730192725 41618 51713290

100

200

300

400

500

600

700

Clusters22 612231015112421 1 91428 2 82026 3 730192725 41618 5171329

Clusters

198

199

20

201

202

203

204

205D

istan

ce

Dist

ance

Δdx = 2024







119909



Competing Interests


References





























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










19895

199

19905

1991

19915

1992

19925

1993

19935

1994

19945

1123 1 2 1422101519 3 21271625 4 13 8 29 51726 730 6 18122428 9 200

50

100

150

200

250

300

350


Clusters1123 1 21422101519 3 21271625 4 13 829 51726 730 6 18122428 9 20

Clusters

Dist

ance

Dist

ance

Δdx = 1994



1325 2122819 11118 72116 820 922 52910 6 262317 3 1530 4 2414270

50

100

150

200

250

300

350

Clusters1325 2122819 11118 72116 820 922 52910 6 262317 3 1530 4 241427

Clusters

19895

19896

19897

19898

19899

199

19901

19902

19903

19904

19905

Dist

ance

Dist

ance

Δdx = 199



728 324193021 1 9 261012221411231817 2 8202527 4 161315 5 6 290

50

100

150

200

250

300

350

Clusters728 324193021 1 9 261012221411231817 2 8202527 4 161315 5 6 29

Clusters

1979

19795

198

19805

1981

19815

1982

19825

1983

1984

19835

Dist

ance

Dist

ance

Δdx = 1982




1123 1 21422101519 3 21271625 4 13 829 5 1726 7 30 6 18122428 9200

02

04

06

08

1

12

14

16

18

Clusters1123 1 21422101519 3 21271625 4 13 829 5 1726 7 30 6 18122428 920

Clusters

0095

01

0105

011D

istan

ce

Dist

ance

Δdx = 0104



1325 2122819 11118 72116 820 922 52910 6 262317 3 1530 4 241427

Clusters1325 2122819 1 1118 72116 820 922 52910 6 262317 3 1530 4 241427

Clusters

0

02

04

06

08

1

12

14

16

18

0095

01

0105

011

Dist

ance

Dist

ance

Δdx = 0099













7 28 324193021 1 9 261012221411231817 2 8202527 4 161315 5 6 29

Clusters728 324193021 1 9 261012221411231817 2 8202527 4 161315 5 6 29

Clusters

0

02

04

06

08

1

12

14

16

18

0095

01

0105

011D

istan

ce

Dist

ance

Δdx = 0101



1123 1 21422101519 32521 1627 413 829 51726 730 618122428 920

Clusters1123 1 21422101519 32521 1627 413 829 51726 730 618122428 920

Clusters

0

100

200

300

400

500

600

700

198

199

20

201

202

203

204

205D

istan

ce

Dist

ance

Δdx = 2008



5 Conclusion













1423 1 7 2519 2131724 8 122021 9 5 62910112622 3152730 4 1618280

100

200

300

400

500

600

700

Clusters1423 1 7 2519 2131724 8 122021 9 5 62910112622 3152730 4 161828

Clusters

198

199

20

201

202

203

204

205D

istan

ce

Dist

ance

Δdx = 2026



22 612231015112421 1 91428 2 82026 3 730192725 41618 51713290

100

200

300

400

500

600

700

Clusters22 612231015112421 1 91428 2 82026 3 730192725 41618 5171329

Clusters

198

199

20

201

202

203

204

205D

istan

ce

Dist

ance

Δdx = 2024







119909



Competing Interests


References





























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











1123 1 21422101519 3 21271625 4 13 829 5 1726 7 30 6 18122428 9200

02

04

06

08

1

12

14

16

18

Clusters1123 1 21422101519 3 21271625 4 13 829 5 1726 7 30 6 18122428 920

Clusters

0095

01

0105

011D

istan

ce

Dist

ance

Δdx = 0104



1325 2122819 11118 72116 820 922 52910 6 262317 3 1530 4 241427

Clusters1325 2122819 1 1118 72116 820 922 52910 6 262317 3 1530 4 241427

Clusters

0

02

04

06

08

1

12

14

16

18

0095

01

0105

011

Dist

ance

Dist

ance

Δdx = 0099













7 28 324193021 1 9 261012221411231817 2 8202527 4 161315 5 6 29

Clusters728 324193021 1 9 261012221411231817 2 8202527 4 161315 5 6 29

Clusters

0

02

04

06

08

1

12

14

16

18

0095

01

0105

011D

istan

ce

Dist

ance

Δdx = 0101



1123 1 21422101519 32521 1627 413 829 51726 730 618122428 920

Clusters1123 1 21422101519 32521 1627 413 829 51726 730 618122428 920

Clusters

0

100

200

300

400

500

600

700

198

199

20

201

202

203

204

205D

istan

ce

Dist

ance

Δdx = 2008



5 Conclusion













1423 1 7 2519 2131724 8 122021 9 5 62910112622 3152730 4 1618280

100

200

300

400

500

600

700

Clusters1423 1 7 2519 2131724 8 122021 9 5 62910112622 3152730 4 161828

Clusters

198

199

20

201

202

203

204

205D

istan

ce

Dist

ance

Δdx = 2026



22 612231015112421 1 91428 2 82026 3 730192725 41618 51713290

100

200

300

400

500

600

700

Clusters22 612231015112421 1 91428 2 82026 3 730192725 41618 5171329

Clusters

198

199

20

201

202

203

204

205D

istan

ce

Dist

ance

Δdx = 2024







119909



Competing Interests


References





























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











7 28 324193021 1 9 261012221411231817 2 8202527 4 161315 5 6 29

Clusters728 324193021 1 9 261012221411231817 2 8202527 4 161315 5 6 29

Clusters

0

02

04

06

08

1

12

14

16

18

0095

01

0105

011D

istan

ce

Dist

ance

Δdx = 0101



1123 1 21422101519 32521 1627 413 829 51726 730 618122428 920

Clusters1123 1 21422101519 32521 1627 413 829 51726 730 618122428 920

Clusters

0

100

200

300

400

500

600

700

198

199

20

201

202

203

204

205D

istan

ce

Dist

ance

Δdx = 2008



5 Conclusion













1423 1 7 2519 2131724 8 122021 9 5 62910112622 3152730 4 1618280

100

200

300

400

500

600

700

Clusters1423 1 7 2519 2131724 8 122021 9 5 62910112622 3152730 4 161828

Clusters

198

199

20

201

202

203

204

205D

istan

ce

Dist

ance

Δdx = 2026



22 612231015112421 1 91428 2 82026 3 730192725 41618 51713290

100

200

300

400

500

600

700

Clusters22 612231015112421 1 91428 2 82026 3 730192725 41618 5171329

Clusters

198

199

20

201

202

203

204

205D

istan

ce

Dist

ance

Δdx = 2024







119909



Competing Interests


References





























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











1423 1 7 2519 2131724 8 122021 9 5 62910112622 3152730 4 1618280

100

200

300

400

500

600

700

Clusters1423 1 7 2519 2131724 8 122021 9 5 62910112622 3152730 4 161828

Clusters

198

199

20

201

202

203

204

205D

istan

ce

Dist

ance

Δdx = 2026



22 612231015112421 1 91428 2 82026 3 730192725 41618 51713290

100

200

300

400

500

600

700

Clusters22 612231015112421 1 91428 2 82026 3 730192725 41618 5171329

Clusters

198

199

20

201

202

203

204

205D

istan

ce

Dist

ance

Δdx = 2024







119909



Competing Interests


References





























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











119909



Competing Interests


References





























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









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