Vibration Analysis using Time Domain Methods for the Detection of small Roller Bearing Defects

Transcription

1 SIRM 9-8th Internatonal Conference on Vbratons n Rotatng Machnes, Venna, Austra, 3-5 February 9 Vbraton Analyss usng Tme Doman Methods for the Detecton of small Roller Bearng Defects Tahsn Doguer Insttut für Mechank Otto-von-Guercke-Unverstät Magdeburg, Fakultät für Maschnenbau 316, Magdeburg, Germany tahsn.doguer@mb.un-magdeburg.de Jens Strackeljan Insttut für Mechank Otto-von-Guercke-Unverstät Magdeburg, Fakultät für Maschnenbau 316, Magdeburg, Germany jens.strackeljan@mb.un-magdeburg.de ABSTRACT The analyss of vbraton sgnals s a major technque for montorng the condton of machne components. A focus of ths paper s gven to the early detecton of very small bearng damages lke false brnellng faults, whch occur n the presence of a small relatve moton between the rollers and raceways durng non-rotaton tmes. Ths leads to a small damage whch s characterzed by ellptcal wear marks n the axal drecton at each roller poston. The paper shows that the vbraton structure generated by a small surface defect dffers from a normal state even f the sgnal energy s elmnated by normalsaton of the data. Sutable tme doman features are a mathematcal descrpton of the shape of selected tme doman peaks, whch could easly be calculated by the hgher dervatves of the tme acceleraton sgnal and some parameters characterzng the randomness of the peak postons. After the step of extractng 3 features from the tme sgnal a feature selecton process s executed automatcally. Ths enables the selecton of a feature subset whch s best suted to the present fault stuaton. Test rg results ndcate the hgh potental of the new tme doman features for both fault types. The last chapter gves a short ntroducton n an algorthm for bearng fault smulaton. 1 INTRODUCTION Condton montorng technques have the objectve of achevng the most effectve, safe and effcent operaton of mechancal plant, machnes or engnes. In recent years there has been an ncreasng nterest due to the requrement of reduced mantenance costs, mproved productvty and safety. Roller bearngs are used n a wde range n ndustral rotatng machnery and the robustness and relablty of roller bearngs are essental for the machne health. Damages can put human safety at rsk, cause long term machne down tmes, nterrupton of producton and result n hgh costs. Man steps n condton montorng are applyng measurement technques, sgnal processng and sgnal categorsaton combned wth classfcaton algorthms, see [13], [6], [1], [1] and [1]. The healthy sgnature can be measured on operatng machnes but data wth seeded faults are more dffcult to obtan. Ths paper presents an approach for detecton of roller bearng defects usng tme doman methods, wthout the necessty of specal nformaton about bearng type and other operatng parameters. The vbraton sgnals of a roller bearng delver a large content of nformaton about ts structural dynamcs and operatng condtons. Typcal representatves as measurement parameters are dsplacement, velocty and acceleraton. Dependng on bearng condton, sgnal can have varous forms: Structured sgnals due to rollng of a ball on a pttng, Nose sgnals wth stochastc exctaton due to rollng on a large-scale damage or on smooth surface of an ntact bearng. An automated condton montorng system works accordng to the man steps of measurng a sgnal, whch represents the vbratons of the bearng, analysng the sgnal accordng to features and assgnng the sgnal to a predefned damage category. 1 Paper ID-16

2 THEORY.1 Dervatve of tme sgnal The presence or absence of bearng faults can be determned form the raw acceleraton sgnal only n few cases. In general the sgnal contans a multtude of dfferent vbraton components. To get a better understandng of the random vbraton generated by rough surfaces we tred to solate all perodc, load dependent and external vbraton sources. Ths lead to a very smple test rg descrbng the pure vbraton generated by a rollng ball on an nclned level, where dfferent surface structures are acheved by usng two types of fles, see []. It s a hghly demandng problem of decdng whch features are to be formed from the tme sgnal n order to acheve the most error-free classfcaton between dfferent surface structures. The man dea s to perform a statstcal analyss of the tme sgnal or hgher dervatves of ths. Prevous work n hgher dervatves has been reported by J.D. Smth, Lahdelma and others, see [1], [11] and [14]. Specally Lahdelma has publshed a couple of papers descrbng the theoretcal background of hgher dervatves n combnaton wth condton montorng tasks, see [9]. The general sutablty of ths technque even n practcal real world applcatons s wthout any controversy. In general the dsplacement, velocty or acceleraton as a basc sgnal could be taken nto account. Ths data set (tme response), contanng the acceleraton values for dscrete tme steps can be seen as a functon of tme and hence dervable wth respect to tme. One possblty s to calculate the hgher dervatve for the complete tme sgnal and extracton of characterstc features from the new tme sgnal. RMS, Peak Value and statstcal parameters lke Kurtoss and Crest Factor are typcal features for the detecton of faults n roller bearngs. Applyng the Fast Fourer Transformaton (FFT) on a tme sgnal, performng the dervaton n frequency doman and reconstructng the tme sgnal va nverse FFT s an effcent method for calculatng dervatves of arbtrary order. An advantage of ths method s the ablty to obtan nteger, real or complex order dervatves, whch all can be used for machne dagnoss, see [1]. Hgh frequent vbratons are excted n roller bearng as the rollng element passes a damaged area. Fgure 1a shows the raw acceleraton tme sgnal x ganed by an accelerometer wth a length of.5 s, whch s n accordance to a number of dgtal data and a samplng rate of 1317 Hz. In orgnal and non-fltered tme sgnal, t s not possble to detect a hgh frequent vbraton n sgnal. But after zoomng n at.4 s, one can see how the sgnal structure changes at about.41 s. Another way to make ths change notceable s calculaton of the ampltude spectra of the sgnal wth data sets before and after the exctement. Two sets (each 14 data ponts) were taken out from x. Both have the same length. The frst data set ends at.4 s and the second one starts at.4 s. The comparson of ampltude spectra n Fgure 1e shows that the hgh frequent vbraton generated by the rollng contact between ball and the damaged surface s not present before the exctement. The spectrum on the rght shows the hgh frequent vbraton n 4 6 khz range shortly after the exctement. Hgh frequent vbraton can be shown also va flterng. In Fgure 1c and 1d fltered sgnal s shown by two dfferent band pass settngs (1-4 khz and 1-4kHz). The frst band pass fltered sgnal n Fgure 1c (1-4 khz) does not sgnfcantly dffer from the raw sgnal n Fgure 1a. A sgnfcant change can be seen n Fgure 1d, n whch the second band pass fltered sgnal (1-4kHz) s shown, at about.41 s. The smlar effect can be (4) obtaned va second dervatve x of the raw tme sgnal. The advantage s that t s not necessary to flter the raw sgnal (Fgure 1f). Ths method can be very helpful n searchng small faults n roller bearngs, hence hgh frequent vbratons are excted va small damages.. Feature extracton The dea suggested n ths paper s to use only parts of the tme sgnal whch stand n close relaton to possble bearng faults. For that purpose a peak n the tme sgnal s defned as a local extremum n the measured acceleraton sgnal x, where x s the dsplacement. All peaks n the tme sgnal whch fulfl the requrements of the peak defnton are detected and for each all sgnfcant nformaton lke peak poston, ampltude and adjacent data ponts are stored. Ths data are used as an nput for the calculaton of features. The calculaton of the fourth dervatve x (4) was carred out by usng a fourth-order centered dfference formula on unform grd. Therefore a set of adjacent data ponts on the left and rght sde of each peak have to be consdered. Now the calculaton of dfferent features on the bass of ths set of peak nformaton contanng ampltudes, poston and adjacent data ponts s possble. Paper ID-16

3 x (m/s ) x (m/s ) x (m/s ) x (m/s ) 1 x (t) raw sgnal zoom n x (t), from.3 to.5 s fltered sgnal, bandpass 1-4 khz fltered sgnal, bandpass 1-4 khz (a) (b) (c) (d) 14 ponts, left sde of t=.4 s 6 14 ponts, rght sde of t=.4 s 6 x (m/s ) 4 x (m/s ) 4 (e) x (4) (Gm/s 4 ) dervatve of raw sgnal 4 6 (f) Fgure 1: Example for demonstratng the usefulness of hgher dervatves for the detecton of bearng faults 3 Paper ID-16

4 A feature vector s defned as a set of parameters extracted from the consdered sgnal, whch gves ndcatons about the current state of the operatng system. In condton montorng statstcal methods have been wdely used for nvestgaton, where measured data are tme seres. Extensve lterature s avalable on dagnostc technques usng RMS, Kurtoss, Crest Factor and hstograms, see [13], [6], [11] and [9]. The method suggested here uses peaks as a source of nformaton correspondng to bearng faults. Possble (4) features may be calculated from the rato of local maxma of measured x and x. Also the dstance varaton between local maxma on adjacent or non-adjacent locatons over a predefned offset value can be consdered. Further features can be obtaned by the number of local maxma wth absolute values, whch are over some predefned threshold values. The hstogram of peak ampltude and peak dstance dstrbuton are addtonal features whch could be consdered. Takng the norm of sgnal values - for nstance wth root mean square - may be useful to elmnate the nfluence of sgnal energy of the measured mpact sound. A selecton of features from a total of 3 s lsted n Table 1. The feature extracton and analyss are performed n MATLAB 7.. For a fast, on-lne condton montorng, measurement equpment and the software routnes can be combned. 3 APPLICATIONS 3.1 Detecton of small bearng fault n smple demonstrator For the nvestgaton of the method descrbed n Secton a smple bearng test rg was used. In Fgure, on the left the very smple test assembly s shown. The components are the outer race of a roller bearng and a cage, n whch the outer rng s mounted. Only one ball drven by compressed ar s rotatng and the nner rng s replaced by a whole shaft wth eght nozzles around t. All nozzles are placed wth an offset angle of 45 to assure a contnuous load to the ball. The vbraton sgnal s measured by an accelerometer mounted at the outer rng. Ths assembly allows the measurement of the solated vbraton generated by the rotatng ball and all other sources of exctaton are omtted. The pathway from the source of vbraton and the sensor s well defned and the number of jon patches s mnmzed. Fgure, rght sde, shows the fault n the outer race, whch was nduced by creatng a small groove usng electrc spark eroson. 51 µm Fgure : (left) Test rg s ar drven and conssts of outer race of a deep groove ball bearng type 631, cage and accelerometer. (rght) Outer race of the ball bearng. A pont fault (dameter 51 µm) was ntroduced usng electrc spark eroson. The comparson of the sgnals n Fgures 3 (bearng wthout a fault) and 4 (faulty bearng) ndcates that a separaton of the sgnal from a bearng wthout a fault and the outer race groove s possble n the tme and frequency doman wthout any problems. The overall vbraton level dffers sgnfcantly. To elmnate the nfluence of the vbraton level sgnals are normalsed. The mpulse of the ball n contact wth the groove exctes natural frequences of the bearng and the surroundng elements (assembly parts). The ampltude spectra n Fgures 3 and 4 have ampltudes n a frequency range up to 3 khz, whch s typcal for a small damage sze but also for a random exctaton of an ntact bearng. One has to consder that the duraton of contact between the damage and the ball s very short n comparson to the complete measurement tme. In consequence the normalsed spectra n Fgure 3 (lower rght) and 4 (lower rght) do not show sgnfcant dfferences between the two states. 4 Paper ID-16

5 1 good bearng x (m/s ) x rms-normed x (m/s ) x rms-normed good bearng Fgure 3: Tme sgnals and the ampltude spectra of ntact outer race. Above measured sgnal, below sgnal was normalsed by ts rms value. 5 8 faulty bearng 6 x (m/s ) x (m/s ) x rms-normed x rms-normed faulty bearng Fgure 4: Tme sgnals and the spectra of faulty outer race. Above measured sgnal, below sgnal was normalsed by ts rms value. 5 Paper ID-16

6 All feature combnatons n Fgure 5 are calculated after the normalsaton of x, and are well suted to separate the both classes. The dstances between the class centres are much hgher then the varaton of the feature wthn a sngle class. In Table 1 a descrpton of the selected features used n the fgures and the correspondng dmensons are lsted. The numberng ndcates that these features are only a subset of the complete feature pool. All feature combnatons could be used to desgn an automatc classfcaton algorthm, but t s not the objectve of ths nvestgaton to test such a classfer. The two combnatons of features n Fgure 5 are selected to demonstrate the potental of the peak features. Comparng the scatter-plots of varous feature combnatons from dfferent surfaces, one can observe the separaton of data ponts whch belong to dfferent surfaces. Ths property can be used to montor bearng health state and to perform damage detecton. When usng the combnaton 5 8 and 9 1 an 1% classfcaton s possble. In general the selecton of feature combnatons could be executed by a software algorthm, see [3] and [4]. Strackeljan has developed dfferent tools for the task of automatc feature selecton consderng vbraton sgnals, see [16], [18] and [19]. In addton a couple of algorthms are avalable for a broad range of classfcaton tasks, see [17]. Table 1: Descrpton of features, whch are used for roller bearng tests. No. Descrpton 5 Mean value of the peak ampltudes from x at local maxma (peak) after normalsaton. x s the normalsed form of x. Dm: - (4) (4) 7 RMS of x. x was bult, usng local maxma (peak) n x. Dervaton method was (4) (4) named n Secton.. x s the normalsed form of x. x and x respectvely. Dm: (1/s ) (4) (4) 8 Mean ampltude value of x. x was bult as descrbed n Feature 7. Dm: (1/s ) (4) (4) 9 Standard devaton of x. x was bult as descrbed n Feature 7. Dm: (1/s ) 1 Mean value of the ratos, whch are obtaned usng the ampltude of the local maxma (peak) n ( ) x ( ) and x 4 at the correspondng poston. Dm: (1/s ) F 1 1 = n p n p x = 1 x ( 4 ) ( ) n p = Number of peaks 3 x 11 1 x 11 Feature 8 1 Feature Feature Feature 9 x 1 1 Fgure 5: Scatter-plots of good and faulty outer races n ar drven test rg. Each measured tme sgnal was normalsed by ts RMS value before feature extracton. Dm: -. 6 Paper ID-16

7 3. Detecton of small faults n the bearngs of vehcle wheels To nvestgate the potental of the features calculated from hgher dervatves we use a test rg for the dagnoss of a complete vehcle wheel bearng assembly. The test rg allows a radal of axal loadng of the bearng wth realstc forces, whch were obtaned from measurements n a car durng dfferent drve manoeuvres. Fgure 6 shows the damaged secton of the outer rng as a 3D surface measurement and a photograph of the damage n the outer rng of the demounted bearng. Objectve of the nvestgaton s the determnaton of detecton lmts of small faults by a measured acceleraton sgnal. The focus of the car manufacturers s orented to the problem whether the vbraton wll generate an acoustc emsson whch could be notced nsde the vehcle nteror. Fgure 6: Small fault at the outer rng of a roller bearng. In Fgure 7 good and damaged bearngs are compared. The acceleraton x was measured drectly on the housng of the outer race of the bearng. The data set conssts of equdstant data ponts by a samplng frequency of 1317 Hz. In a, b the raw sgnals and c, d fltered sgnals are compared. Notceable dfference n ampltude levels between good and damaged bearngs has occurred. Comparng the ampltude spectra n 7e wth 7f, one can see the ncreased ampltude level n the range 1 4 khz, whch s caused by the small fault on the (4) outer rng, shown n Fgure 6. On the other hand, the comparson of x n c and d shows also an ncreasng of the ampltude level but no sgnfcant change n the sgnal structure. 7 Paper ID-16

8 x (m/s ) x (m/s ) x (4) (Gm/s 4 ) x (4) (Gm/s 4 ) x (m/s ) x (t) raw sgnal, good bearng x (t) raw sgnal, damaged bearng nd dervatve of raw sgnal, good bearng nd dervatve of raw sgnal, damaged bearng FFT wth raw sgnal, good bearng (a) (b) (c) (d) (e) x (m/s ).4. FFT wth raw sgnal, damaged bearng Fgure 7: Comparson of good and damaged bearngs n the tme and frequency doman (f) 8 Paper ID-16

9 (4) Nevertheless the features calculated from the x and x, whch are descrbed n table 1 allows a 1% classfcaton of the complete data set for the states: bearng n good condton and bearng wth the small fault (Fgure 8). 5 x 11.5 x 11 Feature Feature Feature 5 Feature 7 x 1 1 Fgure 8: Scatter-plots of good and damaged bearngs descrbed n secton SIMULATION OF ROLLER BEARING FAULTS 4.1 Contact model Consderable attenton s beng carred out for the bearng faults and condton montorng. In ths area the man nterest lays on fault detecton and bearng lfe expectaton. However the ganng of data from the real machnery to study these subjects may be cost-ntensve and tme-consumng. Smulatons may supply a consderable help by gvng a better understandng n occurrence, shape and effects of faults n roller bearngs. Prevous work has been reported for fault smulaton, n whch roller bearngs and dfferent knds of faults are modelled as sprng-mass-dampng systems, see [13]. The smulaton model presented n ths paper consders the roller bearng as a mult body system, whch conssts of nner race, outer race, cage and balls, and takes nto consderaton the non-lnear forces between elements of the roller bearng, whch are calculated va Hertzan contact theory. Based on the dea of contact between two crcular elements, an approach for fault smulaton s presented, n whch the faulty regon s descrbed as a collecton of adjacent crcles wth varable sze, locaton and number (Fgure 9). Then as the rollng element moves on the outer race, the contact forces are calculated between two crcular elements (roller element and fault element). Each element s consdered as a rgd body. Three degrees of freedom are allowed, x, y translatonal and ϕ rotatonal about z -axs, whch descrbe the moton of a body on a plane. Each body s connected to orgn of nertal system. In the next step the contact condton between dfferent elements of the mult body system s defned n a way, that the algorthm defnes contact always between two bodes. In a system consstng of n elements, there are n ( n 1) / possble contacts between two bodes, whch must be determned for each tme step, see [5]. The algorthm takes the poston of each body as nput, calculates the dstance to other bodes and determnes whether, and between whch elements contact has occurred. In case of a penetraton between two bodes a contact force s calculated. The Contact force F r C contans the normal contact force ( F N ) and tangental contact force ( F T ). F N s the sum of the load n drecton of surface normal ( Q ) and the contact dampng force ( F D ). As shown n Eq. (1), Q s calculated accordng to the theory of Hertz for contact between elastc bodes, see [15]. sn s the depth of penetraton. µ s the Hertzan coeffcent, see []. For roller element and fault element, E b, E f are modulus of elastcty, ν b, ν f Posson s ratos, R b, R f rad and ρ total radus of curvature, see [8]. Fgure 9 shows the basc components of the bearng model. F D s the product of contact dampng coeffcent ( d ) and normal component of relatve velocty ( vn ) between contact partners at the contact pont. 3 f 3 E sn 1 1 ν 1 ν b 1 1 Q =, = +, ρ = +, FD = d vn ρ 3 µ E Eb E f Rb R f r r r r F = Q + F, F = F n, F = F n (1) N D N N N j N 9 Paper ID-16

10 After multplcaton of F N by the unt vector of surface normal ( n r ) the vector F r N for each contact partner s obtaned as shown n Eq. (1). FT s calculated va Coulomb frcton coeffcent ( µ R ), and µ R s a functon of relatve tangental velocty ( vt ) between contact partners. The vector F r T s obtaned va multplcaton by the unt vector of tangental component of relatve velocty ( t r ) as shown n Eq.. r r r r F = µ ( v ) F t, F = F T R T N The contact force ( F r C ) on each body s gven by addton of F r N and F r T. The momentum at the centre of mass due to F r C s calculated as shown n Eq. (3). r r r M = F (3) SZ C To smulate the ar drve mechansm (Fgure ) eght so called drve regons are defned n our program, where external load s ntroduced to rollng element each tme t passes by. In case of a frctonless rollng the rotatng frequency ncreases contnuously. If the frcton s consdered and the ntal rotatng frequency s gven zero, the value ncreases untl reachng a steady level. 4. Fault Smulaton The fault on a roller bearng race s smply thought to be consstng of a gap on the bearng race. At both ends of ths gap two crcles are attached tangentally to the outer race. As the bearng element moves, t enters the gap by rollng on the so called fault balls, as t leaves the faulty regon t contnues rollng on outer race. Fgure 9 shows the dea n an overstated way. In our smulaton the fault wdth ( f b ) s set to 5 µm, radus of the fault balls ( R b ) s mm, fault depth s 4 µm. Program requres only the angular poston of the fault centre ( ϕ f ) and f. The fault balls are then placed va smple trgonometrc constrans. b T j T Outer race y Rollng element ω φ f x R b + R a Fault element f b T T R f + + R f Fgure 9: Model for fault smulaton n a roller bearng. The depth of fault can be controlled by radus of crcular fault elements. It also gves an ndcaton about the steepness of fault regon. Raw surfaces can be smulated by ncreasng the number of balls n the fault regon. Hence the fault s body fxed, ths model can be appled not only to smulate outer race faults, but also to smulate faults on nner race and on rollng elements. 4.3 Results As smulaton results dsplacement, velocty, acceleraton and contact force can be plotted over tme or an FFT analyss can be performed. In Fgure 1 the x (t) and y (t) are shown. A small fault was ntroduced to the bearng model, wth a sze descrbed as n 4. at poston. The result s notceably smlar to the acceleraton sgnal, whch was measured on the real damaged outer rng n Fgure 4. After valdaton of the program wth the real test rg, the results may be used as a learnng set for further nvestgatons lke statstcal calculatons. 1 Paper ID-16

11 4 x (t) x (m/s ) y (t) y (m/s ) Fgure 1: x (t) and y (t) of the smulated roller bearng wth a small fault on the outer rng. 5 CONLUSION The results obtaned from two dfferent test rgs demonstrate that the proposed feature generaton s a promsng method for the detecton of faults n roller bearngs. The frst test rg represents the rollng contact between fles wth dfferent grades of cut and a roller ball. These test condtons are a smple model of an extended fault n roller bearngs, whch exceed the spacng between the balls and lead to a permanent contact between damaged surface and the ball. The second one consders a sngle small sze pttng fault on a bearng race. In both cases the separaton of dfferent surfaces and also faulty and non-faulty bearng condtons s possble. The method enables a new ntroducton of hgher dervatves because the algorthm s orented on sngle peaks and a complete tme sgnal. In the next steps the algorthm wll be tested n combnaton wth real world applcaton. Frst nvestgatons concernng vehcle wheel bearngs have been done and show that the method n general s a sutable tool n condton montorng. The results from the smulaton program ndcate clearly, that the smulaton of bearng faults n combnaton wth mult-body-system could help to mprove the understandng of fault nduced vbratons. Further work n progress s drected towards ganng the necessary mprovement of the smulaton programme and the mplementaton n standard MBS-Software lke ADAMS or SIMPACK. REFERENCES [1] Bolaers, F., Cousnard, O., Marconnet, P. and Rasolofondrabe, L. (4): Advanced detecton of rollng bearng spallng from de-nosng vbratory sgnals. Control Engneerng Practce, 1, pp [] Doguer, T. and Strackeljan, J. (8): New Tme Doman Method for the Detecton of Roller Bearng Defects. Accepted for publcaton, Internatonal Conference on Condton Montorng& Machnery Falure Preventon Technologes CM 8, Ednburgh. [3] Dy, J. G. and Brodley C. E. (4): Feature Selecton for Unsupervsed Learnng. Journal of Machne Learnng Research, 5, [4] Handl, J. and Knowles, J. (6): Feature Subset Selecton n Unsupervsed Learnng va 11 Paper ID-16

12 Multobjectve Optmzaton. Internatonal Journal of Computatonal Intellgence Research (IJCIR), (3), pp [5] Hppmann, G. (4): Modellerung von Kontakten Komplex geformter Körper n der Mehrkörperdynamk. Ph.D. Dssertaton, Technsche Unverstät Wen. [6] Jafarzadeh, M., Hassannejad, R., Ettefagh, M. and Chtsaz, S. (8): Asynchronous nput gear damage dagnoss usng tme averagng and wavelet flterng. Mechancal Systems and Sgnal Processng, (1), pp [7] Dy, J. G. and Brodley C. E. (4): Feature Selecton for Unsupervsed Learnng. Journal of Machne Learnng Research, 5, pp [8] Johnson, K. L. (199): Contact Mechancs. Cambrdge Unversty Press, Cambrdge. [9] Lahdelma, S. and Juuso, E. (6): Intellgent Condton Montorng for Lme Klns. Conference Akda, Aachen. [1] Lahdelma, S. and Kotla, V. (5): Complex Dervatve A New Sgnal ProcessngMethod. Kunnossapto, 19(4), pp [11] Lahdelma, S., Strackeljan, J. and Behr, D. (1999): Combnaton of hgher order dervatves and a fuzzy classfer as a new approach for montorng rotatng machnery. In Proc. of COMADEM, 1 th Internatonal Congress on Condton Montorng and Dagnostc Engneerng Management. Sunderland, Coxmoor Publshng, Oxford, pp [1] Mechefske, C. K. and Mathew, J. (199): Fault detecton and dagnoss n low speed rollng element bearngs Part I: The use of parametrc spectra. Mechancal Systems and Sgnal Processng, 6(4), pp [13] Sawalh, N. (7): Dagnostcs, prognostcs and fault smulaton for rollng element bearngs. Ph.D. Dssertaton, Unversty of New South Wales. [14] Smth, J. D. (198): Vbraton montorng of bearngs at low speeds. Trbology Internatonal, 15(3), pp [15] Stolarsk, T. A. and Tobe, S. : Rollng Contacts. (eds.: Neale, M. J., Polak, T. A. and Taylor, C. M.), Professonal Engneerng Publshng, Suffolk. [16] Strackeljan, J. (1): Feature selecton methods -an applcaton orented overvew. TOOLMET 1 Symposum. Oulu, Fnland, pp [17] Strackeljan, J. and Lahdelma, S. (5): Smart Adaptve Montorng and Dagnostc Systems. In Proceedngs of the nd Internatonal Semnar on Mantenance, Condton Montorng and Dagnostcs. 8 th -9 th September, Oulu, Fnland, POHTO Publcatons, pp [18] Strackeljan, J. and Schubert, A. (): Evolutonary Strategy to Select Input Features for a Neural Network Classfer. (eds.: Zmmerman, H. J., Tselents, G.), In Advances n Computatonal Intellgence and Learnng: Methods and Applcatons. [19] Strackeljan, J. (5): Montorng. In Do smart adaptve systems exst? (Studes n fuzzness and soft computng 173). Berln, Sprnger Verlag, pp [] Teutsch, R. (5): Kontaktmodelle und Strategen zur Smulaton von Wälzlagern und Wälzführungen. Ph.D. Dssertaton, Technsche Unverstät Kaserslautern. [1] Wang, B. and Cheng, D. (8): Modal analyss of mdof system by usng free vbraton response data only. Journal of Sound and Vbraton 311(3 5), pp Paper ID-16