Vibrodiagnostics Faults Classification for the Safety Enhancement of Industrial Machinery

machines A icle Vib odiagnos ics Faul s Classi ica ion o he Sa e y Enhancemen o Indus ial Machine y Daniel Zu h 1,* , Pe Blecha 1, Tomas Ma ada 1, Ros isla Huzlik 1, Ji i Tuma 1, Ka la Ma ado a 1 and Voj ech F kal 2   Ci a ion: Zu h, D.; Blecha, P.; Ma ada, T.; Tuma, J.; Huzlik, R.; Ma ado a, K.; F kal, V. Vib odiagnos ics Faul s Classi ica ion o he Sa e y Enhancemen o Indus ial Machine y. Machines 2021, 9, 222. h ps://doi.o g/10.3390/ machines9100222 Academic Edi o : An onio J. Ma ques Ca doso Recei ed: 3 Sep embe 2021 Accep ed: 23 Sep embe 2021 Published: 30 Sep embe 2021 Publishe ’s No e: MDPI s ays neu al wi h ega d o ju isdic ional claims in published maps and ins i u ional a il- ia ions. Copy igh : © 2021 by he au ho s. Licensee MDPI, Basel, Swi ze land. This a icle is an open access a icle dis ibu ed unde he e ms and condi ions o he C ea i e Commons A ibu ion (CC BY) license (h ps:// c ea i ecommons.o g/licenses/by/ 4.0/). 1Facul y o Mechanical Enginee ing, B no Uni e si y o Technology, 616 69 B no, Czech Republic; [email p o ec ed].cz (P.B.); [email p o ec ed].cz (T.M.); huzlik@ u b .cz (R.H.); [email p o ec ed].cz (J.T.); [email p o ec ed].cz (K.M.) 2TOSHULIN, a.s., Wolke o a 845, 768 24 Hulin, Czech Republic; [email p o ec ed] *Co espondence: [email p o ec ed].cz Abs ac : The cu en digi iza ion o indus ial p ocesses is leading o he de elopmen o sma machines and sma applica ions in he ield o enginee ing echnologies. The basis is an ad anced senso sys em ha moni o s selec ed cha ac e is ic alues o he machine. The ob ained da a need o be u he analysed, co ec ly in e p e ed, and isualized by he machine ope a o . Thus he machine ope a o can gain a six h sense o keeping he machine and he p oduc ion p ocess in a sui able condi ion. This has a posi i e e ec on educing he s ess load on he ope a o in he p oduc ion o expensi e componen s and in moni o ing he sa e condi ion o he machine. The key elemen he e is he use o a sui able classi ica ion model o da a e alua ion o he moni o ed machine pa ame e s. The a icle deals wi h he compa ison o he success a e o classi ica ion models om he MATLAB Classi ica ion Lea ne App. Classi ica ion models will compa e da a om he equency and ime domain, he da a sou ce is he same. Bo h da a samples a e om eal measu emen s on he CNC e ical machining cen e (CNC-Compu e Nume ical Con ol). Th ee basic s a es ep esen ing machine ool damage a e ecognized. The da a a e hen p ocessed and educed o he use o he MATLAB Classi ica ion Lea ne app, which c ea es a model o ecognizing aul s. The a icle aims o compa e he success a e o classi ica ion models when he da a sou ce is a da ase in ime o equency domain and combina ion. Keywo ds: ib odiagnos ics; classi ica ion lea ne app; machine lea ning; MATLAB; Py hon; classi i- ca ion model; unbalance 1. In oduc ion The cu en de elopmen o Indus y 4.0 b ings, in addi ion o he digi iza ion o p oduc ion, he collec ion o la ge amoun s o da a, which a e sui able o he use o a - i icial in elligence me hods. Pa icula ly in he ield o echnical diagnos ics, his opens possibili ies o he ea ly de ec ion s a e o an objec (machine) based on he measu ed da a, which a e ob ained om di e en s anda d diagnos ic me hods (e.g., ib odiagnos ics, he modiagnos ics o elec odiagnos ics) and i is possible o use special me hods o ech- nical diagnos ics such as measu ing he magne ic ield o he machine [ 1 ]. I is he e o e a mul i-pa ame e diagnos ic ha can mo e accu a ely de ec , iden i y, and localize he eme ging aul , hanks o a combina ion o inpu da a om di e en a eas o diagnos ics. Vib a ions a e an impo an ca ie o in o ma ion abou he condi ion o o a ing equipmen and his ac is commonly used in he ield o ib odiagnos ics. This a icle ocuses on he machining cen e and he e i is possible o use he ib odiagnos ic sys em o de ec o he in o ma ion such as machining quali y o ool damage. Thus, unexpec ed s a es can be de ec ed by a ib odiagnos ic signal, which may indica e a aul o a sa e y isk. Howe e , hese signals a e unexpec ed and a simple e alua ion mechanism canno be designed, o example, wi h he de ec ion o equen ailu es o o a y machines such Machines 2021,9, 222. h ps://doi.o g/10.3390/machines9100222 h ps://www.mdpi.com/jou nal/machines Machines 2021,9, 222 2 o 19 as misalignmen , unbalance, o bea ing damage. In hese cases, i is app op ia e o use sel -lea ning a i icial in elligence me hods, i.e., hey can lea n o ecognize a aul condi ion om his o ical da a o a speci ic machine o speci ic machining ope a ions. In he de elopmen p ocess o sma machine ools capable o ope a ing wi hin he amewo k o indus y 4.0, i is necessa y o implemen isk analysis al eady du ing he machine design s age no only in e ms o po en ial damage o he heal h o he machine ope a o (acco ding o ISO 12100 [ 2 ]), bu also in e ms o quali y managemen and moni o ing o he capabili y o he manu ac u ing p ocess on he machine ool (acco ding o ISO 9001 [ 3 ]). We can apply he good echnical p ac ice as desc ibed in IEC 31010 [ 4 ] and hen implemen he necessa y diagnos ic ools in o he machine design o modi y his machine design so ha he measu emen unce ain y o he senso sys em (acco ding o ISO 3534-1 [ 5 ]) would no a ec he in e p e a ion o he measu ed da a and he subsequen decision-making p ocesses in a nega i e way. A ypical example could be ea ly de ec ion o ool damage and subsequen b inging he machine o a sa e s a e. B eaking and ejec ing he ca bide inse om a ool holde can cause damage o he anspa en gua d o he machine’s wo king a ea, and hus lead o a subsequen loss o i s sa e y unc ion, o i may cause i e e sible damage o he machined su ace. The e o e, by ea ly de ec ion o a machine aul , we can p o ec he heal h o he ope a o as well as educe he inancial losses caused by poo p oduc ion o inc eased wea o he sma machine’s spindle. This a icle will, he e o e, compa e classi ica ion me hods ha can de ec a speci ic aul om eal da a, namely a missing inse on a machining ool, he absence o which could ha e occu ed due o ool damage. A me hod will be used whe e p edic o s o machine lea ning will be e alua ed in ad ance and hei choice is he e o e up o he expe . The co ec choice o p edic o s has a majo impac on he classi ica ion success a e. The au ho s o he wo k ha e al eady deal wi h he issue o e alua ing ib odiagnos ic signals in [ 6 – 8 ]. The idea o using a i icial in elligence me hods in diagnos ics is desc ibed in o he publica ions such as in [ 9 – 12 ] , whe e a i icial in elligence me hods a e used o he ecogni ion o gea box aul s. Also, in he pape [ 13 ] au ho s ocus on he classi ica ion using neu al ne wo ks in he plane a y gea . The a icle [ 14 ] uses a i icial in elligence me hods o ecognize he shape o a o a y machine sha ’s o bi ; i is a pic u e classi ica ion acco ding o he shape o sha o bi . The aim o his esea ch is o de e mine a as me hod ( eal- ime e alua ion) o he imely e alua ion o a ailu e ha would educe he sa e y o he machine. Thus, he p ima y goal is no o diagnose he condi ion o he machine, such as a bea ing o gea box ailu e, and o p edic esidual li e, bu o de ec ailu es ela ed o machine sa e y and o wa n he ope a o immedia ely. This a icle has se e al goals and hey a e: • Ve i y ha he missing inse on he ool is de ec able on he ib odiagnos ic signal measu ed on he machine spindle. • Selec and compa e p edic o s om ime and equency domains. • E ec spindle speeds on he classi ica ion success a e. • Selec and compa e he mos success ul classi ica ion me hods • E alua e de ec ion success a e o aul - ee s a e I is assumed ha he p ocess o da a collec ion and e alua ion akes place on an IPC (Indus ial PC) compu e nea he machine ( o example IPC SIMATIC PC-based, whe e one IPC will be p epa ed o each CNC machine), and he lea ning and model gene a ed p ocess will ake place on a se e con aining comme cial so wa e such as MATLAB (se e will be used o many CNC machines). Lea ning and expo ing he model is an impo an ope a ion and will ake place unde s ic supe ision. The c ea ed MATLAB model will be expo ed o he use o indi idual IPCs wi hou MATLAB. The Py hon en i onmen also includes Machine Lea ning ools such as sciki [ 15 ] o A ap used in [ 16 ], howe e in his case he ambi ions a e o be used in a sa e y en i onmen and he au ho s he e ely on he p o essional Ma lab en i onmen . In he u u e, he abo e- men ioned oolboxes will be used and es ed o e alua e he condi ion o he machine. Machines 2021,9, 222 3 o 19 Py hon en i onmen is used o signal p ocessing, he MATLAB and Classi ica ion Lea ne App [17] a e used o da a classi ica ion. 2. Expe imen al P ocedu e The da a we e ob ained om he machine MCV 754 QUICK (Figu e 1), i is a h ee-axis CNC (Compu e Nume ical Con ol) machining cen e, mo e in o ma ion can be ob ained on he manu ac u e ’s websi e [ 18 ]. The ob ained da a a e om he measu ing ins umen Mic olog CMXA48 and he measu emen pa ame e s a e in he Table 1. Table 1. Measu emen pa ame e s o Mic olog CMXA48. Measu emen Pa ame e s: Analysis ype: Accele a ion ime domain Uni s: g F equency ange: 1000 Hz Y-Axis uni s: g WAV (Wa e o m Audio File Fo ma ) File Pa ame e s: Bi s pe sample: 16 Samples pe second: 2560 A e age by es pe second: 10,240 Fo ma : PCM (Pulse Code Modula ion) Figu e 1. CNC e ical machining cen e MCV 754. The ins umen Mic olog uses a CMSS 2111 accele ome e senso ha has been a - ached o he spindle wi h a magne . The posi ion o he senso on he machine is shown in Figu e 2. Used ool H490 F90AX D040-4-16-12 has he possibili y o changing he ee h (inse s), which a e ixed wi h a sc ew, as shown in Figu e 3. Th ee s a es/classes we e chosen o he expe imen , namely: •Class 0—Tool in he aul - ee s a e (Figu e 3-le ) •Class 1 —Tool wi hou inse (ca bide inse ), bu wi h sc ew-simula ion o damage and b eakage o an inse (Figu e 3-middle) •Class 2 —Tool wi hou inse and sc ew (Figu e 3- igh ) Machines 2021,9, 222 4 o 19 CMSS 2111 accele ome e Figu e 2. Placemen o he CMSS 2111 accele ome e o he machine MCV 754. Expec ed measu able changes a e caused by he unbalance o he ool when his ib a ion is ansmi ed o he spindle. The ailu e o unbalance is cha ac e ized by an inc ease in ib a ions in he egion o he i s ha monic equency. The unbalance is desc ibed in he [19–21] and is di ided in o a s a ic unbalance and a dynamic unbalance. The i s expe imen e i ied ha he missing inse was e lec ed in spindle ib a ions a 700, 1050, and 1400 RPM. The esul s a e shown in Figu e 4, which shows he a ea a ound he i s ha monic equency. The aim o his expe imen was o de e mine a which spindle speeds he mani es a ions a e isible in he equency spec um and which speeds a e sui able o da a collec ion in a machine lea ning da ase . F om he esul , i is e iden ha a he speed 700 RPM he e ec o he unbalances in he equency domain is insigni ican , and he e o e unde ec able. Fo his eason, speeds we e selec ed o ob ain a da ase om 1000 o 1500 RPM. Figu e 3. The ool H490 F90AX D040-4-16-12 in aul - ee s a e- Class 0 ( le ), wi hou he inse Class 1 (middle) and wi hou he inse and wi hou he sc ew Class 2 ( igh ). 2.1. Da ase Ob ain Fo each s a e/class, a se ies o da a was measu ed o di e en ope a ing speeds ha a e wi hin he ecommended speed ange o he ool. Speci ically, he speed was om 1000 RPM o 1500 RPM a e he s ep o 50 RPM in wo epe i ions and 20 s is main ained a each speed le el. The o al ime is he e o e 20 × 11 × 2 = app ox. 440 s o one s a e (class). The speed se ing was p og ammed and s a ed o each s a e in he same way, Figu e 5 shows he ime eco d o he speed change o e ime. The aim is o ob ain da a a a wide ange o ope a ing speeds. The da a we e cap u ed in a eco de mode, i.e., one long ime eco d was ob ained, which was la e p ocessed in o indi idual samples, which o med a da ase o machine lea ning. Machines 2021,9, 222 5 o 19 10 15 20 0 2 4 Accele a ion (g) 10-4 C0 700RPM FFT 1H max(1H) 10 15 20 0 2 4 Accele a ion (g) 10-4 C1 700RPM FFT 1H max(1H) 10 15 20 F equency Hz 0 2 4 Accele a ion (g) 10-4 C2 700RPM FFT 1H max(1H) 15 20 25 30 0 2 4 10-4 C0 1050RPM FFT 1H max(1H) 15 20 25 30 0 2 4 10-4 C1 1050RPM FFT 1H max(1H) 15 20 25 30 F equency Hz 0 2 4 10-4 C2 1050RPM FFT 1H max(1H) 20 25 30 35 40 0 2 4 10-4 C0 1400RPM FFT 1H max(1H) 20 25 30 35 40 0 2 4 10-4 C1 1400RPM FFT 1H max(1H) 20 25 30 35 40 F equency Hz 0 2 4 10-4 C2 1400RPM FFT 1H max(1H) Figu e 4. The i s es o he e ec o he aul in equency domain (C0 − C2 a e Class 0 − Class 2, 1H— i s ha monic equency, max(1H)—maximum o he i s ha monic equency). 0 50 100 150 200 250 300 350 400 Time (s) 900 1000 1100 1200 1300 1400 1500 1600 Re olu ion pe Minu e (RPM) RPM Measu emen o Da aSe Figu e 5. The a ia ion o he spindle speed o e ime du ing he da ase ob ain. 2.2. P edic o s P edic o s a e a bi a y pa ame e s, and hei alues (o combina ions he eo ) de e - mine he p ope ies o he class being sea ched. I hese pa ame e s did no adequa ely e lec he p ope ies o he class, he da a classi ica ion would no be success ul. An ex- ample o he use o a p edic o is he known a ea o image da a p ocessing. The inpu is in o ma ion abou indi idual pixels and a ull HD esolu ion (1920 × 1080) i is mo e han 2 × 10 6 pixels and each pixel con ains in o ma ion abou h ee colou s (RGB). This amoun o da a is disp opo iona ely la ge and con ains a lo o useless in o ma ion, so he e is a need o educe da a such as educing he numbe o colou s, edge de ec ion, and mo e. The ou pu s o his educ ion a e p edic o s, which a e he inpu o a i icial in elligence, and based on hei alues (and hei combina ions) i is possible o classi y indi idual classes. The p ope ies o p edic o s should be: • Clea ly desc ibe he class p ope ies (s a e)-imp o ed achie emen classi ica ion Machines 2021,9, 222 6 o 19 • Low compu a ional complexi y-speeds up he p edic o calcula ion • Low numbe o p edic o s-speeds up he lea ning and e alua ion p ocess The inpu da a in ib odiagnos ics a e ime domain signals. In his pa icula case, he sampling equency is 2560 Hz (sampling pe iod is app oxima ely 0.4 ms), which means 2560 alues e e y second o eco ding o one axis. I is, he e o e, necessa y o educe his da a low and e alua e sui able p edic o s om i , which will be he inpu o a i icial in elligence. The aim is o selec app op ia e p edic o s and compa e hei impac on he success o da a classi ica ion. 2.3. Da a P ocessing and Selec ion o P edic o s In his a icle, a me hod is chosen ha classi ies da a in o indi idual classes based on p edic o s. The selec ion and calcula ion o p edic o s a e pe o med be o e he classi i- ca ion o da a and he co ec choice o hese p edic o s has a signi ican impac on he esul s o he classi ica ion and i is necessa y o know he issue and ha e expe ience wi h simila expe imen s. The au ho o he a icle has al eady deal wi h his issue in [ 7 , 8 ] and e i ied which p edic o s a e applicable o a simila ype o p oblem. This a icle will compa e he classi ica ion successes o ime and equency domain p edic o s and hei combina ions. I was also necessa y o choose he leng h o he ime signal and di ide he esul ing samples. The imes o 0.25 s and 0.5 s we e chosen and again he ad an ages and disad an ages o hese leng hs we e compa ed. The ollowing p edic o s we e used. P edic o s om he ime domain: •Speed-Cu en RPM du ing one sample •RMS-Roo Mean Squa e o accele a ion ampli udes om one sample •STD-The s anda d de ia ion o he accele a ion ampli udes om a single sample •PCA -P incipal Componen Analysis ealized wi h sciki lea n lib a y R2 (wi h pa am- e e s n_componen s = 1 and explained_ a iance_ = 0) [22] The esul is a ec o ha con ains 4 p edic o s o each sample (RPM, RMS, STD and PCA); he alues in his ec o a e u he labelled as “T p edic o s”. F equency domain p edic o s a e based on FFT (Fas Fou ie T ans o m) equency analysis pe o med using he NumPy lib a y “S anda d FFTs” [ 23 ] and a ange o 4 o 100 Hz is used. The minimum alue o 4 Hz is de e mined by he minimum measu ing ange o he senso used. The maximum alue o 100 Hz is he maximum alue o he occu ence o he i s ha monic in all ope a ing speeds o he ool and any oo h equency. The maximum ope a ing speed is 1432 RPM, he maximum oo h equency is he e o e (1432 ×4)/60 = 95.47 Hz, he e o e he maximum equency o 100 Hz was chosen. •Speed-Cu en RPM du ing one sample •Spec um ene gy (eF) -calcula ed as ∑A (i)2 o he 4–100 Hz ange, whe e A (i) a e ampli udes o spec al lines. •A (i) - he sequence o ampli udes o indi idual spec al lines o equencies 4–100 Hz The esul is a ec o whose size a ies acco ding o he leng h o he signals used, i.e., di ision in o indi idual samples. Fo example, i he signal is 0.25 s long and has a sampling equency o 2560 Hz, he si ua ion is as ollows: N= s· =2560 ·0.25 =640 Bin(∆ ) = s N=2560 640 =4 Fo ange 4–100 Hz: NBin = max − min Bin =100 −4 4=24 Machines 2021,9, 222 7 o 19 Fo a 0.25 s signal ( 1), he ou pu will be a ec o con aining 26 (24 + 1 + 1) p edic o s o each da a sample. The disad an age o such a sho signal is he equency esolu ion ( Bin ) o 4 Hz, whe e his alue may be insu icien . Fu he mo e, signals wi h a leng h o 0.5 s will be compa ed. The e is he ollowing si ua ion N= s· =2560 ·0.5 =1280 Bin(∆ ) = s N=2560 1280 =2 Fo ange 4–100 Hz: NBin = max − min Bin =100 −4 2=48 Fo a 0.5 s signal ( 2), he ou pu will be a ec o con aining 50 (48 + 1 + 1) p edic o s o each da a sample. Wi h his signal dis ibu ion, we ge a equency esolu ion ∆ ( Bin ) o 2 Hz, which is mo e sui able han he p e ious case, bu we ge only hal o he samples o machine lea ning om he limi ed eco ding. The esul ing ec o o equency domain p edic o s con ains he measu ed RPM alue, he calcula ed Spec um ene gy alue (labeled as eF) and he sequence o ampli udes o indi idual spec al lines (A 1 o A 24 o 1 and A 1 o A 48 o 2), calcula ed using he FFT unc ion, see Figu e 6. The alues in his ec o a e u he labelled as “F p edic o s”. Bo h a ian s will be compa ed wi h each o he . The de ailed da a p ocessing p ocedu e is as ollows: Da a p ocessing (ou side MATLAB) • Combina ion o ib a ion channel and acho channel da a • Spli ing he signal acco ding o he selec ed ime ( 1 = 0.25 s o 2 = 0.5 s) • Checking whe he he change is no g ea e han 10 RPM du ing he du a ion ( 1 o 2) (elimina ion o ansien s) • So ing he signal in o indi idual classes • P edic o calcula ion, o each sample (T- ime domain, F-F equency domain o FT-all p edic o s) • Sa ing p edic o s o a ile acco ding o indi idual classes (p epa a ion o MATLAB) P ocessed in MATLAB: • Random mixing and me ging o da a o indi idual classes in o one da ase • E alua ing in he en i onmen “Classi ica ion lea ne app” • Gene a ing and sa ing he mos success ul model Ve i ica ion o he gene a ed model: • Randomly selec ed n samples om each class (selec ed n = 100 pe class) • Accu acy and TPR (T ue posi i e a e) and FNR (False nega i e a e) e alua ed • Resul s displayed and sa ed as he Con usion ma ix Figu e 6. Scheme o p edic o s calcula ion using IPC (“eF”—Spec um ene gy, “A 1” o “A n”— he sequence o ampli udes o indi idual spec al lines). Machines 2021,9, 222 8 o 19 3. Classi ica ion Me hods Classi ica ion Lea ne App (CL) compa ed di e en classi ica ion me hods o de e - mine which me hods a e app op ia e o he p oblem. This applica ion allows you o compa e di e en me hods and hen selec and c ea e a model con aining he selec ed me hod (chosen we e he mos success ul). The indi idual me hods a e desc ibed in mo e de ail in [ 24 ]. Da ase s we e es ed on all me hods ha CL allows and hei success is in a Tables 2–4. The numbe o epe i ions o he lea ning p ocess was 10 o each model, and he in e al es ima e was calcula ed using “The Con idence in e al” [ 25 ] wi h alpha = 0.05 . Fu he mo e, he hype pa ame ic op imiza ion p o ided by Ma lab was e i ied. Each winning model was subjec ed o hype pa ame ic op imiza ion wi h he same da ase , and hese esul s a e shown in Table 5. Due o he ime consuming, only one epe i ion was pe o med, he a e age imp o emen o he p edic ion accu acy wi h hype pa ame ic op imiza ion is only 0.55%. Models wi hou hype pa ame ic op imiza ion we e used o u he alida ion. B ie ly, hese a e he ollowing classi ica ion me hods: Table 2. Resul ing success a e o classi ica ion o indi idual me hods o expe imen s wi h sample ime 1 (0.25 s). The bes esul s a e ma ked in bold. 1R1T 1R1F 1R2T 1R2F 1R3T 1R3F 1R4T 1R4F Fine ee 79.9 ± 0.55 69.9 ± 1.66 67.9 ± 1.14 80.1 ± 1.23 63.9 ± 0.95 94.1 ± 0.32 59.4 ± 0.60 73.2 ± 0.37 Medium ee 77.2 ± 0.89 59.4 ± 1.29 62.3 ± 0.89 79.2 ± 1.29 55.6 ± 1.15 94.1 ± 0.32 54.9 ± 0.40 67.1 ± 0.24 Coa se ee 76.8 ± 0.54 47.2 ± 1.08 57.6 ± 0.89 72.4 ± 0.97 51.6 ± 0.98 94.5 ± 0.46 52.9 ± 0.29 58.1 ± 0.42 Linea disc iminan 74.1 ± 0.30 60.1 ± 0.95 56.8 ± 0.30 74.1 ± 0.80 51.8 ± 0.62 95.0 ± 0.30 51.3 ± 0.18 64.3 ± 0.19 Quad a ic disc iminan 74.2 ± 0.52 69.1 ± 1.41 59.9 ± 0.20 81.4 ± 0.86 44.7 ± 0.93 95.6 ± 0.58 52.3 ± 0.07 69.5 ± 0.18 Gaussian Nai e Bayes 69.6 ± 0.68 57.5 ± 1.13 56.7 ± 0.38 73.7 ± 0.61 42.0 ± 0.65 91.1 ± 0.61 48.8 ± 0.12 59.2 ± 0.37 Ke nel Nai e Bayes 68.1 ± 0.51 60.3 ± 0.88 60.8 ± 0.61 77.0 ± 0.82 48.1 ± 0.82 94.0 ± 0.31 53.6 ± 0.16 64.1 ± 0.19 Linea SVM 73.0 ± 0.50 60.3 ± 0.80 57.1 ± 0.56 75.4 ± 0.93 51.9 ± 0.62 94.9 ± 0.51 52.1 ± 0.13 65.1 ± 0.23 Quad a ic SVM 73.5 ± 0.31 73.8 ± 1.06 59.9 ± 0.49 83.5 ± 0.50 48.9 ± 0.69 96.9 ± 0.28 51.2 ± 0.80 74.6 ± 0.26 Cubic SVM 73.0 ± 0.73 78.6 ± 1.11 60.2 ± 1.08 85.2 ± 0.59 34.9 ± 1.15 96.6 ± 0.31 35.5 ± 0.80 83.4 ± 0.35 Fine Gaussian SVM 73.8 ± 0.93 71.0 ± 1.20 65.3 ± 1.13 67.4 ± 1.07 55.9 ± 0.87 70.2 ± 1.80 61.7 ± 0.19 79.0 ± 0.65 Medium Gaussian SVM 71.7 ± 0.45 73.9 ± 0.64 60.5 ± 0.60 83.1 ± 0.71 50.7 ± 0.97 96.7 ± 0.48 57.6 ± 0.24 75.6 ± 0.27 Coa se Gaussian SVM 73.0 ± 0.44 57.2 ± 0.84 57.2 ± 0.54 71.4 ± 0.96 49.8 ± 0.87 93.5 ± 0.23 52.8 ± 0.13 65.4 ± 0.17 Fine KNN 82.2 ± 0.63 75.0 ± 1.24 78.7 ± 1.12 80.2 ± 0.94 74.5 ± 0.66 89.6 ± 0.59 77.5 ± 0.21 81.7 ± 0.29 Medium KNN 72.1 ± 0.72 53.5 ± 0.69 59.7 ± 0.78 64.8 ± 0.79 51.6 ± 0.86 81.4 ± 0.74 60.9 ± 0.32 67.7 ± 0.37 Coa se KNN 68.4 ± 0.30 44.9 ± 1.00 56.2 ± 0.59 65.5 ± 0.92 47.8 ± 0.83 75.2 ± 1.11 59.3 ± 0.18 64.5 ± 0.11 Cosine KNN 68.2 ± 0.98 55.7 ± 0.94 57.4 ± 1.06 63.0 ± 0.61 51.4 ± 1.57 81.2 ± 1.13 59.4 ± 0.30 66.6 ± 0.17 Cubic KNN 72.1 ± 0.73 55.4 ± 1.26 59.2 ± 0.94 64.0 ± 1.07 51.3 ± 1.10 78.1 ± 2.12 60.9 ± 0.23 66.8 ± 0.27 Weigh ed KNN 82.8 ± 0.40 76.1 ± 1.01 80.6 ± 1.24 81.8 ± 0.70 75.3 ± 0.84 89.4 ± 0.77 78.5 ± 0.31 82.6 ± 0.34 Boos ed T ees 79.0 ± 0.95 72.9 ± 1.12 65.2 ± 1.05 84.3 ± 0.90 61.5 ± 1.04 35.4 ± 0.00 57.0 ± 0.39 71.5 ± 0.31 Bagged T ees 84.1 ± 0.58 76.9 ± 1.13 78.8 ± 1.19 77.0 ± 1.00 75.7 ± 0.94 96.1 ± 0.39 78.4 ± 0.27 84.4 ± 0.33 Subspace Disc iminan 73.4 ± 0.42 59.6 ± 0.83 55.6 ± 0.61 73.0 ± 0.64 52.3 ± 0.44 95.3 ± 0.32 51.1 ± 0.11 63.2 ± 0.29 Subspace KNN 82.1 ± 0.67 72.6 ± 1.18 76.3 ± 1.16 74.8 ± 0.71 74.7 ± 0.98 84.3 ± 1.64 75.5 ± 0.25 77.4 ± 0.51 RUSBoos ed T ees 76.9 ± 0.58 64.1 ± 1.34 63.4 ± 0.97 82.4 ± 1.03 61.5 ± 1.57 66.6 ± 9.85 55.8 ± 0.41 68.4 ± 0.28 Machines 2021,9, 222 9 o 19 Table 3. Resul ing success a e o classi ica ion o indi idual me hods o expe imen s wi h sample ime 2 (0.5 s). The bes esul s a e ma ked in bold. No e: F-model ailed (one o mo e o he classes ha e singula co a iance ma ices). 2R1T 2R1F 2R2T 2R2F 2R3T 2R3F 2R4T 2R4F Fine ee 81.8 ± 1.70 72.9 ± 1.79 65.5 ± 1.58 85.1 ± 1.39 63.3 ± 2.23 94.2 ± 0.60 62.6 ± 0.48 82.9 ± 0.81 Medium ee 81.6 ± 1.61 72.8 ± 1.67 62.4 ± 1.86 85.1 ± 1.39 60.3 ± 2.21 94.2 ± 0.60 58.1 ± 0.52 73.9 ± 0.74 Coa se ee 75.7 ± 0.78 55.2 ± 1.02 58.0 ± 1.12 79.4 ± 1.60 59.5 ± 1.69 94.1 ± 0.95 53.9 ± 2.25 60.9 ± 0.39 Linea disc iminan 76.9 ± 0.90 70.6 ± 2.28 55.1 ± 0.83 84.4 ± 1.46 59.0 ± 0.86 97.7 ± 0.31 54.5 ± 0.24 72.0 ± 0.17 Quad a ic disc iminan 72.3 ± 0.86 F 53.3 ± 0.75 F 50.5 ± 1.05 F 54.3 ± 0.31 83.2 ± 0.28 Gaussian Nai e Bayes 68.2 ± 0.67 67.2 ± 1.68 52.6 ± 1.17 74.2 ± 1.60 41.0 ± 0.59 85.4 ± 0.50 51.8 ± 0.31 64.5 ± 0.51 Ke nel Nai e Bayes 69.3 ± 0.99 77.8 ± 1.46 50.7 ± 0.77 84.6 ± 1.92 48.0 ± 1.22 98.4 ± 0.72 55.0 ± 0.27 74.4 ± 0.27 Linea SVM 74.2 ± 0.76 71.7 ± 0.78 55.7 ± 1.30 83.1 ± 1.35 59.9 ± 0.78 95.7 ± 0.43 55.7 ± 0.27 72.7 ± 0.28 Quad a ic SVM 77.4 ± 0.72 84.0 ± 1.87 55.4 ± 1.40 89.5 ± 0.84 61.6 ± 0.99 98.0 ± 0.50 56.6 ± 0.31 87.4 ± 0.33 Cubic SVM 76.8 ± 1.25 84.9 ± 1.76 54.0 ± 1.54 88.2 ± 0.83 54.8 ± 1.85 97.9 ± 0.67 39.3 ± 1.35 89.6 ± 0.31 Fine Gaussian SVM 78.6 ± 1.38 73.9 ± 1.65 64.9 ± 1.81 75.4 ± 2.42 64.0 ± 1.07 72.9 ± 1.47 63.9 ± 0.34 71.7 ± 0.34 Medium Gaussian SVM 76.7 ± 1.85 84.9 ± 1.95 56.2 ± 1.17 87.8 ± 1.30 62.1 ± 1.07 97.9 ± 0.49 60.9 ± 0.30 84.7 ± 0.30 Coa se Gaussian SVM 71.8 ± 1.07 58.1 ± 0.64 54.3 ± 0.91 72.0 ± 1.29 50.8 ± 1.18 81.7 ± 0.59 55.4 ± 0.21 70.0 ± 0.22 Fine KNN 86.2 ± 1.61 82.0 ± 2.13 78.4 ± 1.44 83.2 ± 1.52 74.7 ± 1.77 91.7 ± 1.19 78.3 ± 0.46 85.1 ± 0.40 Medium KNN 69.9 ± 1.28 59.3 ± 1.82 54.5 ± 1.62 70.8 ± 1.39 59.5 ± 2.03 85.1 ± 1.19 64.2 ± 0.21 73.6 ± 0.45 Coa se KNN 49.9 ± 1.05 53.9 ± 1.09 52.0 ± 1.21 54.9 ± 1.37 58.5 ± 0.95 72.0 ± 0.68 61.8 ± 0.24 68.3 ± 0.20 Cosine KNN 64.0 ± 0.91 62.5 ± 1.53 57.9 ± 1.09 67.6 ± 1.26 57.7 ± 1.73 84.2 ± 1.12 61.7 ± 0.33 73.5 ± 0.61 Cubic KNN 71.5 ± 1.23 59.1 ± 1.32 55.7 ± 1.14 69.4 ± 1.36 60.8 ± 1.43 79.9 ± 0.75 64.0 ± 0.39 72.5 ± 0.32 Weigh ed KNN 87.6 ± 1.61 81.7 ± 1.69 78.7 ± 1.41 84.3 ± 0.87 77.7 ± 1.68 91.5 ± 1.46 79.6 ± 0.40 86.2 ± 0.43 Boos ed T ees 87.1 ± 1.19 79.6 ± 1.29 70.6 ± 1.80 37.3 ± 0.00 70.3 ± 2.40 36.7 ± 0.00 60.3 ± 0.37 81.3 ± 0.38 Bagged T ees 88.4 ± 1.18 79.9 ± 1.18 77.2 ± 1.38 87.8 ± 1.22 77.4 ± 1.30 94.3 ± 1.21 79.8 ± 0.39 86.0 ± 0.41 Subspace Disc iminan 75.5 ± 0.86 71.6 ± 1.59 51.7 ± 0.80 84.1 ± 1.34 58.6 ± 1.13 96.9 ± 0.41 53.7 ± 0.20 71.1 ± 0.12 Subspace KNN 85.0 ± 1.59 73.4 ± 1.41 72.5 ± 2.22 78.3 ± 2.00 73.7 ± 1.97 85.5 ± 1.93 76.7 ± 0.36 79.7 ± 0.49 RUSBoos ed T ees 86.2 ± 1.44 77.7 ± 1.53 67.1 ± 1.56 47.9 ± 3.86 62.6 ± 2.08 76.0 ± 9.04 59.4 ± 0.34 77.6 ± 0.46 3.1. Classi ica ion T ees Bina y decision ees o mul iclass lea ning [ 26 ]. This me hod is easy o in e p e and as o da a p edic ion, has low memo y equi emen s, bu may no achie e su icien p edic ion accu acy. Decision making akes place h ough a ee s uc u e om he begin- ning ( oo ) o he inal class (lea es). The me hod was p obably i s published by J. Ross Quinlan in 1975. The es ed a ian s a e: • Fine ee • Medium ee • Coa se ee 3.2. Disc iminan Analysis Regula ized linea and quad a ic disc iminan analysis [ 27 ]. This me hod is easy o in e p e and as o da a p edic ion o la ge da ase s. Using “Quad a ic Disc iminan ” inc eases memo y equi emen s. I is one o he me hods o N-dimensional s a is ical analysis (mul i a ia e s a is ical analysis), whe e, based on he decision ule, objec s a e di ided in o g oups acco ding o p obabili y densi ies. The me hod was p obably i s published by Ronald Fishe in 1936. The es ed a ian s a e: • Linea disc iminan • Quad a ic disc iminan Machines 2021,9, 222 16 o 19 Time Consump ion o P edic ion The ime consump ion o he p edic ion is highly dependen on he pe o mance o he compu ing uni ha will pe o m he p edic ion. In gene al, he ime-consuming p ocess is he lea ning o he model, bu his ope a ion is only pe o med once when he sys ems a e deployed o when a new da ase is a ailable o lea ning. Thus, he lea ning p ocess can be e icien ly scheduled and is no c i ical o he unning o he sys em. Mo e impo an is he p edic ion ime and he possible eac ion o he sys em o a possible p oblem. The p edic ion ime consis s o wo s eps, namely da a p ep ocessing, i.e., ex ac ion o p edic o s, and hen he p edic ion i sel . These imes we e es ed on a pe sonal compu e wi h In el(R) Co e(TM) i7-2600 CPU @ 3.40 GHz, 16 GB RAM and a simila con igu a ion is possible o he cu en IPC. Time was measu ed o 100 epe i ions each ime o elimina e andom a ia ions in pe o mance. Measu ed ime includes only compu a ion ime wi hou loading o sa ing da a om eco ding media. Winning models o he mos challenging a ian s con aining all p edic o s ( ime and equency domain) we e used. Fo expe imen T1R4, he winning model was “Bagged T ees” and he esul s a e as ollows. The da a p ocessing ime o 100 epe i ions is 1.13 s and he p edic ion ime o 100 epe i ions is 5.12 s, ha is, he a e age o al ime is (1.13 + 5.12)/100 = 0.0625 s i.e., 62.5 ms. Fo T2R4 expe imen , he winning model was “Cubic SVM” and he esul s a e as ollows. The da a p ocessing ime o 100 epe i ions is 2.04 s and he p edic ion ime o 100 epe i ions is 1.43 s, ha is, he a e age o al ime is (2.04 + 1.43)/100 = 0.0347 s i.e., 34.7 ms. The measu ed imes a e only app oxima e and depend on many ci cums ances, also he e is a possibili y o op imizing he classi ie selec ion acco ding o i s p edic ion ime. Fo ou pu poses, he achie ed imes a e su icien . 6. Implemen a ion o he T ained Model The p ocedu e o implemen ing a ained model is as ollows. The model can be gene a ed as a unc ion o MATLAB, o as sou ce code in C language, hen i is easy o compile i o any pla o m. I s unc ion (abili y o classi y) does no change o e ime because he e is no lea ning p ocess. Howe e , p o ided he condi ions ha e changed o a new da ase is a ailable, i is possible o s a he lea ning p ocess again and ain he model o he new da a. Figu e 12 schema ically shows he possible connec ion o he se e wi h indi idual clien s. Each IPC pe o ms da a collec ion and especially imely e alua ion based on a ained model ha was lea ned in he MATLAB en i onmen on he se e and hen expo ed. The p ocess is as ollows: (a) Da a acquisi ion and lea ning p ocess • The se e eques s da a om indi idual IPCs and c ea es a da ase o c ea ing a clas- si ica ion model (Da a is p edic o s-i e alua es IPCs, only p edic o s a e ansmi ed). • I he e is a su icien amoun o da a (o condi ions ha e changed, e c.), hen MATLAB pe o ms lea ning and c ea es a ained classi ica ion model o a speci ic IPC and expo s i o he C language ( his MATLAB allows). • The ained model is sen o a speci ic IPC. Indi idual machines and hei IPCs can be dis ibu ed anywhe e in di e en places and he e will be only one se e wi h MATLAB, which will gene a e a model o a speci ic machine and send i o a speci ic IPC. I necessa y, he MATLAB SW can be eplaced by ano he sys em, howe e , he unc ionali y will be main ained and he change will be made on only one se e . (b) E alua ion p ocess • IPC pe o ms da a collec ion and p edic o calcula ion- his is a simple ope a ion and can be pe o med in any p og amming language, o simplici y and a ailabili y Py hon was chosen, which pe o ms s a is ical ope a ions and equency analysis. • Pe o ms classi ica ion using MATLAB c ea ed and ained model, which was ex- po ed o C language (Py hon allows o un code in C language). Machines 2021,9, 222 17 o 19 Such a opology and pa i ioning allows o easy changes on bo h he IPC and se e - side, including changing he p og amming en i onmen . As o he speci ic deploymen o moni o ing he machine, i is impo an o no e ha nowadays i is no easy o implemen elemen s o a i icial in elligence in he sa e y segmen , whe e i is necessa y o ce i y he so wa e and e i y i s unc ions. Howe e , i is possible o deploy a simila sys em only as an in o ma i e elemen ha would ale he ope a o , bu no in e e e wi h he ope a ion o he machine. The use o a i icial in elligence me hods is pa icula ly ad an ageous in he ield o echnical diagnos ics o he e alua ion o mul iple c i e ia and ope a o ale s. Figu e 12. IPC and se e loca ion opology. 7. Resul s and Discussions Figu e 9summa izes he esul s in g aphical o m and exp esses he dependence o he p edic o s on he spindle speed. Fo p edic o s om he equency domain, an inc ease in success wi h inc easing speed is e iden due o a mo e p onounced mani es a ion o an unbalance aul in he equency spec um (inc easing he i s ha monic). In con as , ime domain p edic o s achie e a highe success a e a lowe speeds han equency domain p edic o s. Thus, using all p edic o s ( ime and equency) inc eases he success a e a lowe speeds and does no dec ease a highe speeds. The igu e also ocuses on he de ec ion o a aul - ee s a e, i.e., assuming ha we modi y he classes only o he aul - ee s a e (class0) and any aul s a e (class 1 o 2), hen i is ob ious ha he success o aul - ee de ec ion will inc ease because we do no include misclassi ica ion be ween class 1 and class 2, which a e simila . This is impo an i we only wan o de ec a aul - ee condi ion and in any o he case, an ope a o wa ning is issued. Impo an esul s a e shown in he Tables 2–4, which compa e he successes o indi- idual classi ica ion me hods. Fu he mo e, Figu es 10 and 11 compa e he successes o he classi ica ion o indi idual classes and he mos impo an is he compa ison in Figu e 9, which shows he success o he classi ica ion and he success o aul - ee s a e de ec ion, whe ewi h a ian R4 (TF mix- he combina ion o all speeds), 97% o 1 and 98% o 2 success a e is achie ed. Machines 2021,9, 222 18 o 19 8. Conclusions The a icle aimed o e i y he possibili ies o a i icial in elligence o he classi ica ion o machine ool ailu e based on an expe imen om a eal machine. Ea ly de ec ion o he diso de is an impo an ac o in p o ec ing he heal h and elimina ing damage. The use o a i icial in elligence me hods b ings he possibili y o c ea ing uni e sal algo i hms, which, hanks o he abili y o lea n, adap o a speci ic machine, and a speci ic phase o machining. The desc ibed me hod app oaches he possibili y o using a i icial in elligence o da a classi ica ion, in his case o he classi ica ion o a ious machine s a es. A simila me hod can be used o classi y any classes, whe e only a change o p edic o s ha desc ibe he p oblem sough is needed. The choice o p edic o s used is an impo an ac o which, oge he wi h he ope a ing condi ions, in luences he success o he classi ica ion. Fu u e expe imen s will ocus on he possibili y o de ec ing a aul condi ion o a ool du ing machining and will ocus on ob aining a la ge da ase wi h di e en machining condi ions. Au ho Con ibu ions: Resou ces, So wa e, W i ing—o iginal d a , D.Z.; W i ing—o iginal d a , P.B.; Valida ion, Visualiza ion, T.M.; Resou ces, J.T.; W i ing— e iew and edi ing, R.H.; Valida ion, K.M.; Resou ces, V.F. All au ho s ha e ead and ag eed o he published e sion o he manusc ip . Funding: This esea ch was suppo ed by he Minis y o Educa ion, You h and Spo s o he Czech Republic and The Eu opean Union-Eu opean S uc u al and In es men s Funds in he ame o Ope a ional P og amme Resea ch De elopmen and Educa ion-P ojec : Machine Tools and P ecision Enginee ing (P ojec No. CZ.02.1.01/0.0/0.0/16_026/0008404). Con lic s o In e es : The au ho s decla e no con lic o in e es . Re e ences 1. O a ec, M.; Pacaio a, H.; Iza iko a, G.; Ho anec, M. Magne ic Field Image-Sou ce o In o ma ion o Ac ion Causali y. 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