Comparison of K-means and GMM methods for contextual clustering in HSM

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Comparison of K-means and GMM methods for

contextual clustering in HSM

Zhiqiang Wang, Catherine da Cunha, Mathieu Ritou, Benoît Furet

To cite this version:

Zhiqiang Wang, Catherine da Cunha, Mathieu Ritou, Benoît Furet. Comparison of K-means

and GMM methods for contextual clustering in HSM. International Conference on

Change-able, Agile, Reconfigurable and Virtual Productio, Oct 2018, Nantes, France. pp.154-159,

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ScienceDirect

Available online at www.sciencedirect.com

ScienceDirect

www.elsevier.com/locate/procedia

Procedia Manufacturing 28 (2019) 154–159

This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/)

Peer-review under responsibility of the scientific committee of the International Conference on Changeable, Agile, Reconfigurable and Virtual Production.

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This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/)

Peer-review under responsibility of the scientific committee of the International Conference on Changeable, Agile, Reconfigurable and Virtual Production.

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ect

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acturing. [5] U tool wear pre that uses a su There are som -means [8]. A els GMM [9]. g system for th . It collects the , every 0.1s. fferent time sc ool breakage; data collection. d in [12], data calculated in d aterials; while ta is better fo machine-tool is must be rotatin ns. Therefore, ool can be sto ata. A criterio

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ediction meth upport vector m me other algor Also, there ar Next chapter he machine-to e data from th This project cales [10]. Th and collision a clustering is different clust e criterion of r a more relev s not stopped ng. Eventually classifying th opped or mov on for classif anufacturing, s, and to avoi nd chatter), a s hods employe re extraction, turn the mach data analytic machine tool rder to tackle et up the ada d to exploit ning to improv hod based on machine (SVM rithms in mac re some Stat r will introduc ool. he CNC (Com finally led to hen, Godreau n. s very importa ters. For exam f tool breaka vant calculatio

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156 Zhiqiang Wang et al. / Procedia Manufacturing 28 (2019) 154–159 symm (∆ mach the d Whi (mac not n spee mov 3. K T nam each three an a selec mov of th error is la Mac are p mach whil man foun that the d popu clust metric ΔVf. I � hine-tool mov data whose V ich means, fir chine-tool stop null’, the data ed’. Also in th ves at varying K-means To classify th med K-means m h observation e clusters: ma aircraft compa ction. And th ving at constan his classificati rs of classifica abeled with d chine-tool mov presented by b hine-tool mov le the K-mean ny other classi nd by K-mean it deals with distribution of ulation. Whic ter machine-to It is equal to . And the ving at constan Vf are less tha

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any was taken he K-means w nt or varying s ion can be te ation. Fig.3 il different color ving at consta blue plus. It is ving at consta ns suppose tha fication errors ns TΔVf = 1 (m spherical clus f ΔVf is not sp h means K-m ool moving at the half of th e objective is nt speed and w an the thresho a whose spind n, the data who

ess than thresh f not null’, th he Fig.2. Fig. 2. Process o ol context in ful. K-means he cluster with ops; machine-n for example was applied f speed locates sted by manu llustrates the r rs according t ant speed are s found manua ant speed) in t at these points

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el the true dat with our true d scissa Y is the r true data. Ne d the threshold d by drawing Fig. 4. D errors Vf-T according to (GMM) [9] a to the multiv advantage is s probabilities. I oo, and the sa ool moves at c

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Zhiqiang Wang et al. / Procedia Manufacturing 28 (2019) 154–159 157 symm (∆ mach the d Whi (mac not n spee mov 3. K T nam each three an a selec mov of th error is la Mac are p mach whil man foun that the d popu clust metric ΔVf. I � hine-tool mov data whose V ich means, fir chine-tool stop null’, the data ed’. Also in th ves at varying K-means To classify th med K-means m h observation e clusters: ma aircraft compa ction. And th ving at constan his classificati rs of classifica abeled with d chine-tool mov presented by b hine-tool mov le the K-mean ny other classi nd by K-mean it deals with distribution of ulation. Whic ter machine-to It is equal to . And the ving at constan Vf are less tha

rstly, the data ps). And then whose ΔVf le he cluster ‘Vf speed’. See th e machine-to may be helpf belongs to th achine-tool sto

any was taken he K-means w nt or varying s ion can be te ation. Fig.3 il different color ving at consta blue plus. It is ving at consta ns suppose tha fication errors ns TΔVf = 1 (m spherical clus f ΔVf is not sp h means K-m ool moving at the half of th e objective is nt speed and w an the thresho a whose spind n, the data who

ess than thresh f not null’, th he Fig.2. Fig. 2. Process o ol context in ful. K-means he cluster with ops; machine-n for example was applied f speed locates sted by manu llustrates the r rs according t ant speed are s found manua ant speed) in t at these points

s in the machi m/s²) is too hig sters and that pherical. And means will pa t constant spee he difference b s to find the which data be old TΔVf will b

dle feed rate V ose Vf bigger hold TΔVf is to e data whose of classification ac nformation int clustering aim h the nearest m tool moves at e. Firstly, the for the ΔVf ( on the bounda ual mining of results of cont to their cluste presented by ally that, durin this accelerati are in the clu ine-tool movin gh. In fact, the

each cluster there are muc artition the da ed. So other d between the V threshold TΔV elongs to mach be considered Vf less than T r than TΔVf, is o be found, an ΔVf bigger t

ccording the Feed

to 3 clusters, ms at partition mean, serving t constant or v e data with V (m/s²) for this ary between t f feed rate Vf textual classif ers. red asterisk w ng the Vf acc ion period. W uster machine-ing at constan ere is a limita has roughly e ch more popu ata where mac data clustering Vf the time a Vf which can hine-tool mov d as Vf null (m TΔVf is to be f labelled ‘Vf n nd is labelled ‘ than threshold d rate Vf and ΔV an unsuperv ning n observ g as a prototy varying speed Vf equal to 0 s given day. two clusters: T f classification fication of Vf, -tool stops are

while machin celeration, ther Which means t -tool moving t speed (cycle ation when usi equal numbers ulation of ΔVf

chine-tool mo methods will

fter and the V define which ing at varying machine-tool found, and is not null’. And ‘machine-tool d TΔVf is label

f

vised machine vations into k ype of the clu d. The data du m/min were r The threshold TΔVf =1 (m/s²) n in 3 clusters , during a peri e presented b ne-tool moving re are many re the machine-to at constant sp e purple). It m ing K-means. s of observati f around zero, oving at varyi be tested. Vf the time b ch data belon g speed. More stops) in indu labelled ‘Vf d in the cluste l moves at con elled ‘machine e learning me k clusters in w uster [8]. Ther

uring one day removed from d of machine ). The perform s, by detectin iod of 30s. Th by green diam g at varying s ed asterisk (cl tool is acceler peed. And ther means the thre

K-means assu ions. For this

compared to ing speed int

3 efore gs to eover, ustry. null’ er ‘Vf nstant e-tool ethod which re are from m the e-tool mance g the he Vf mond; speed luster rating re are shold umes case, other o the 4. G G assig prob estim Vf=0 ΔVf of pr fine are s to be X is mod Gau 4 σ w GMM classific Gaussian mixt gning query bability given mate compone 0 m/min was f into 2 cluster robability of Δ and high; ΔV set up to mode e compared w ΔVf, the abs deled well our ssian. To find will be tested Fig. 3. V cation ture models ( data points the data. Its a ent posterior p

taken away to rs: machine-to ΔVf during th Vf distributed a

el the true dat with our true d scissa Y is the r true data. Ne d the threshold d by drawing Fig. 4. D errors Vf-T according to (GMM) [9] a to the multiv advantage is s probabilities. I oo, and the sa ool moves at c

is day is draw along the who ta. The sum o density of prob

e density of p ext step, the p d of the mach

the Vf along

Density of probab

o K-means classif

are often use variate norma showing how In this case, th ame column Δ constant speed wn. There are 2

ole day (Y2) w f the probabil bability of ΔV probability in population of ine-tool movi with the time bility of ΔVf for errors fication during on ed for data c al componen w to fit a GMM he same data a ΔVf is created d, machine-to 2 great popula which is wide lity of these 2 Vf (Histogram scale linear. I f Y1 (fine and ing at constan e, and zoom a

one day modeled

ne day (zoom 30 lustering. Usu nts that maxim M to data, clu as in chapter 3 d also. Then G ool moves at v ations of ΔVf: e and low. The Gaussians alo m of ΔVf). The It is found tha d high) is supp nt speed or var a period of 3� d by GMM (2 Gau err seconds) ually, fitted G mize the com uster using the

3 is to be used GMM was to b

varying speed ΔVf around z erefore, 2 Gau

ong with the Δ e result is in F at the sum of posed to follo rying speed, th � seconds to a ussians). ors GMMs cluste mponent post e fitted model d for example be used to cla d. Here, the de zero (Y1) wh ussian distribu ΔVf (Y3) is d Fig. 4: the abs these 2 Gaus ow the distrib the σ, 2 σ, 3 σ analyze. 4 er by terior l, and . The assify ensity ich is utions drawn scissa ssians bution σ and

(6)

158 Zhiqiang Wang et al. / Procedia Manufacturing 28 (2019) 154–159 5. R A or 4 [-2σ thres the m perio The meth beca befo class the F ΔVf thres mach Fig 6. C T class resu a c e Results and di As the ΔVf wit σ_{. (While th} σ_{, 2σ] repres} shold TΔVf =2 most suitable od 30s is alwa result is in th hod. However ause the 1σis ore and during

sification by t Fig.5 (d): the f=0.0059<4σ shold. Therefo hine-tool stop . 5. (a) Vf-T acco Vf-T accordin onclusion Two methods sification, bas lts are as belo  K-me large) error iscussion thin Y1 follow he mean of no sents the 95.45 σ_{= 0.0033 m} for this case, t ays taken to b he Fig.5 (a): t r, just at the b s too small. A g acceleration threshold 3σ ere is a classi , 4σsuppose fore, the thresh ps and machin ording to 1σ class ng to 3σ classific of unsuperv sed on the ma ow:

ans is not suit ). However, G 1 ws a normal d ormal distribut 5%, and [-3σ m/s² and 3σ

the feed rate V be analyzed. F there is no wr beginning of t And then the t

n which is be is not better t fication error that this poin hold T∆�=2σ ne-tool moving sification of ΔVf ation of ΔVf duri vised machin achine-tool fee table because GMM can class 1 istribution, th tion � � �, an , 3σ] repres = 0.005 m/s² Vf can be clas Firstly, the cla rong classifica the acceleratio threshold 2σ etter than 1σ than that of 2 r at the end o nt belongs to =0.0033 m/s² g at constant o during 30 second ing 30 seconds; ( ne learning, edrate, into 3 the data is no sify the raw d

he threshold TΔ nd σ is the sta sents the 99.73 as well as 4σ ssified into 3 c assification by ation during a on, there is a b is tested in th σ_{. And then} σ_{. To confirm} of this 30s, du machine-tool ² can be set a or varying spe ds; (b) Vf-T accor (d) Vf-T accordin K-means and clusters: mac ot spherical da data well. b d ΔVf can be def andard deviati 3% of all the d σ_{= 0.0067 m/} clusters by usi y threshold T∆ acceleration w blue plus poin he Fig.5 (b):

the threshold m this thresho uring the vary moving at co as the threshol eed. See the Fi

rding to 2σ classi ng to 4σ classifica

d GMM, hav chine stopped;

ata (the popul

fined to be equ ion of ΔVf wi data within Y /s². To verify ing these 3 thr ∆�=1σ= 0.00 which is better nt while it sho there is no w d 3σis tested old, the thresh ying speed V onstant speed. ld for this day ig.5. fication of ΔVf d ation of ΔVf durin ve been test ; constant or v lation of ΔVf ual to σ, 2σ ithin Y1). Be Y1. For this da which thresh resholds. The 0167 m/s² is te r than the K-m ould be green wrong classific d in the Fig.5 hold 4σis test Vf. It is becau

. 4σ is too b y’s data to cla

during 30 seconds ng 30 seconds;

ted for conte varying move around zero i error 5 , 3σ cause y, the old is same ested. means n. It is cation 5 (c): ted in use its ig for assify s; (c) extual e. The is too 6

 According to GMM classification and statistical analyzes, the distribution of ΔVf in the Y1 population follows a normal distribution, the threshold can be defined as TΔVf = 2σ=0.0033m/s².

 The data whose Vf is less than TΔVf is labeled as ‘machine-tool stopes’; the data whose Vf is greater than

2σ and its ΔVf is less than 2σ is labeled as ‘machine-tool moves at constant speed’; the data whose Vf and ΔVf are greter than 2σ is labeled as ‘machine-tool moves at varying speed’.

 The threshold was chosen at 2σ by manual mining, through the verification of classification results.  As the raw data has been classified into 3 clusters, the new KPIs can be calculated in each cluster in the

future. Such as, the tool will cut materials linear in the cluster ‘machine-tool moves at constant speed’ while the tool will cut materials in bending surface in the cluster ‘machine-tool moves at varying speed’.

Acknowledgements

This research was funded by the French National Research Agency (ANR). We gratefully acknowledge for the financial support within the ANR SmarEmma project (ANR-16-CE10-0005).

References

[1] Godreau, V. (2017). Extraction des connaissances à partir des données de la surveillance de l'usinage.

[2] Zhou, Y., & Xue, W. (2018). Review of tool condition monitoring methods in milling processes. The International Journal of Advanced Manufacturing Technology, 1-15.

[3] Emeric O., Alexandre D., Le Julien D., Christophe D. Un Système à Base de Connaissances pour la gestion de données d’usinage dans une perspective de fouille de données. In : MUGV2018 et Manufacturing’21 Conf. Bordeaux, France ; 2018.

[4] Lenz, J., Wuest, T., & Westkämper, E. (2018). Holistic approach to machine tool data analytics. Journal of Manufacturing Systems.

[5] Da Cunha, C., Agard, B., & Kusiak, A. (2006). Data mining for improvement of product quality. International journal of production research, 44(18-19), 4027-4041.

[6] Martínez-Arellano, G., Terrazas, G., Benardos, P., & Ratchev, S., (2018). In-process Tool Wear Prediction System Based on Machine Learning Techniques and Force Analysis. In: 8th CIRP Conference on High Performance Cutting (HPC 2018). Budapest, Hungary; 2018. [7] Denkena, B., Dittrich, M. A., & Uhlich, F. (2016). Self-optimizing cutting process using learning process models. Procedia Technology, 26,

221-226.

[8] Julien JACQUES. Fouille de données / Data mining Université Lumière Lyon 2, 2001. 12. [9] Reynolds, D. (2015). Gaussian mixture models. Encyclopedia of biometrics, 827-832.

[10] De Castelbajac, C., Ritou, M., Laporte, S., & Furet, B. (2014). Monitoring of distributed defects on HSM spindle bearings. Applied Acoustics, 77, 159-168. 16.

[11] Godreau, V., Ritou, M., Chové, E., Furet, B., & Dumur, D. (2018). Continuous improvement of HSM process by data mining. Journal of Intelligent Manufacturing, 1-8.

(7)

Zhiqiang Wang et al. / Procedia Manufacturing 28 (2019) 154–159 159 5. R A or 4 [-2σ thres the m perio The meth beca befo class the F ΔVf thres mach Fig 6. C T class resu a c e Results and di As the ΔVf wit σ_{. (While th} σ_{, 2σ] repres} shold TΔVf =2 most suitable od 30s is alwa result is in th hod. However ause the 1σis ore and during

sification by t Fig.5 (d): the f=0.0059<4σ shold. Therefo hine-tool stop . 5. (a) Vf-T acco Vf-T accordin onclusion Two methods sification, bas lts are as belo  K-me large) error iscussion thin Y1 follow he mean of no sents the 95.45 σ_{= 0.0033 m} for this case, t ays taken to b he Fig.5 (a): t r, just at the b s too small. A g acceleration threshold 3σ ere is a classi , 4σsuppose fore, the thresh ps and machin ording to 1σ class ng to 3σ classific of unsuperv sed on the ma ow:

ans is not suit ). However, G 1 ws a normal d ormal distribut 5%, and [-3σ m/s² and 3σ

the feed rate V be analyzed. F there is no wr beginning of t And then the t

n which is be is not better t fication error that this poin hold T∆�=2σ ne-tool moving sification of ΔVf ation of ΔVf duri vised machin achine-tool fee table because GMM can class 1 istribution, th tion � � �, an , 3σ] repres = 0.005 m/s² Vf can be clas Firstly, the cla rong classifica the acceleratio threshold 2σ etter than 1σ than that of 2 r at the end o nt belongs to =0.0033 m/s² g at constant o during 30 second ing 30 seconds; ( ne learning, edrate, into 3 the data is no sify the raw d

he threshold TΔ nd σ is the sta sents the 99.73 as well as 4σ ssified into 3 c assification by ation during a on, there is a b is tested in th σ_{. And then} σ_{. To confirm} of this 30s, du machine-tool ² can be set a or varying spe ds; (b) Vf-T accor (d) Vf-T accordin K-means and clusters: mac ot spherical da data well. b d ΔVf can be def andard deviati 3% of all the d σ_{= 0.0067 m/} clusters by usi y threshold T∆ acceleration w blue plus poin he Fig.5 (b):

the threshold m this thresho uring the vary moving at co as the threshol eed. See the Fi

rding to 2σ classi ng to 4σ classifica

d GMM, hav chine stopped;

ata (the popul

fined to be equ ion of ΔVf wi data within Y /s². To verify ing these 3 thr ∆�=1σ= 0.00 which is better nt while it sho there is no w d 3σis tested old, the thresh ying speed V onstant speed. ld for this day ig.5. fication of ΔVf d ation of ΔVf durin ve been test ; constant or v lation of ΔVf ual to σ, 2σ ithin Y1). Be Y1. For this da which thresh resholds. The 0167 m/s² is te r than the K-m ould be green wrong classific d in the Fig.5 hold 4σis test Vf. It is becau

. 4σ is too b y’s data to cla

during 30 seconds ng 30 seconds;

ted for conte varying move around zero i error 5 , 3σ cause y, the old is same ested. means n. It is cation 5 (c): ted in use its ig for assify s; (c) extual e. The is too 6

 According to GMM classification and statistical analyzes, the distribution of ΔVf in the Y1 population follows a normal distribution, the threshold can be defined as TΔVf = 2σ=0.0033m/s².

 The data whose Vf is less than TΔVf is labeled as ‘machine-tool stopes’; the data whose Vf is greater than

2σ and its ΔVf is less than 2σ is labeled as ‘machine-tool moves at constant speed’; the data whose Vf and ΔVf are greter than 2σ is labeled as ‘machine-tool moves at varying speed’.

 The threshold was chosen at 2σ by manual mining, through the verification of classification results.  As the raw data has been classified into 3 clusters, the new KPIs can be calculated in each cluster in the

future. Such as, the tool will cut materials linear in the cluster ‘machine-tool moves at constant speed’ while the tool will cut materials in bending surface in the cluster ‘machine-tool moves at varying speed’.

Acknowledgements

This research was funded by the French National Research Agency (ANR). We gratefully acknowledge for the financial support within the ANR SmarEmma project (ANR-16-CE10-0005).

References

[1] Godreau, V. (2017). Extraction des connaissances à partir des données de la surveillance de l'usinage.

[2] Zhou, Y., & Xue, W. (2018). Review of tool condition monitoring methods in milling processes. The International Journal of Advanced Manufacturing Technology, 1-15.

[3] Emeric O., Alexandre D., Le Julien D., Christophe D. Un Système à Base de Connaissances pour la gestion de données d’usinage dans une perspective de fouille de données. In : MUGV2018 et Manufacturing’21 Conf. Bordeaux, France ; 2018.

[4] Lenz, J., Wuest, T., & Westkämper, E. (2018). Holistic approach to machine tool data analytics. Journal of Manufacturing Systems.

[5] Da Cunha, C., Agard, B., & Kusiak, A. (2006). Data mining for improvement of product quality. International journal of production research, 44(18-19), 4027-4041.

[6] Martínez-Arellano, G., Terrazas, G., Benardos, P., & Ratchev, S., (2018). In-process Tool Wear Prediction System Based on Machine Learning Techniques and Force Analysis. In: 8th CIRP Conference on High Performance Cutting (HPC 2018). Budapest, Hungary; 2018. [7] Denkena, B., Dittrich, M. A., & Uhlich, F. (2016). Self-optimizing cutting process using learning process models. Procedia Technology, 26,

221-226.

[8] Julien JACQUES. Fouille de données / Data mining Université Lumière Lyon 2, 2001. 12. [9] Reynolds, D. (2015). Gaussian mixture models. Encyclopedia of biometrics, 827-832.

[10] De Castelbajac, C., Ritou, M., Laporte, S., & Furet, B. (2014). Monitoring of distributed defects on HSM spindle bearings. Applied Acoustics, 77, 159-168. 16.

[11] Godreau, V., Ritou, M., Chové, E., Furet, B., & Dumur, D. (2018). Continuous improvement of HSM process by data mining. Journal of Intelligent Manufacturing, 1-8.