The Diagnosis of Tool Wear Based on EMD and GA-B-Spline Network

Transcription

1 Sensors & Transducers, Vol. 56, Issue 9, September 03, pp Sensors & Transducers 03 by IFSA The Dagnoss of Tool Wear Based on EMD and GA-B-Splne Network * Weqng Cao, Pan Fu, Xaohu L School of Mechancal Engneerng, Southwest Jaotong Unversty, Chengdu, 6003, Chna * Tel.: , * E-mal: caoweqng@swtu.cn Receved: 5 June 03 /Accepted: 5 August 03 /Publshed: 30 September 03 Abstract: In vew of the strong background nose nvolved n vbraton sgnal of tool wear and the dffculty to obtan fault frequences, ths paper proposed a tool wear fault feature etracton method based on morphologcal flters-sngularty value decomposton (SVD) wth emprcal mode decomposton (EMD). Frstly, an eperment system of the cuttng tool wear montorng was set up and a varety of data comng from vbratory sensor were collected, then, the pulse components from the orgnal sgnal were nhbted by morphologcal flters and the sgnal sequences removed outler were reconstructed, the attractor track matr was decomposed usng SVD for further nose reducton, and then we got weak sgnal falure frequency after the de-nose sgnals were decomposed wth EMD. Fnally, tool wear was dentfed by GA-B-splne neural network. B-splne networks were traned usng genetc algorthms to search for global optmzaton. The epermental results shown that the dagnoss approach put forward n ths paper could dentfy tool wear fault patterns effectvely n nose background. Copyrght 03 IFSA. Keywords: Emprcal mode decomposton; Morphologcal flterng; Sngularty value decomposton; Genetc algorthm; B-splne Neural Networks.. Introducton Onlne montorng of the tool wear condton s very crucal n order to mprove the qualty of the unmanned manufacturng systems. In tool wear montorng process, t s very mportant for tool wear early fault dagnoss how to etract the weak sgnal characterstcs. Tool wear s a very comple phenomenon and the vbraton sgnal s nonstatonary sgnal wth strong nose, so FFT and Wavelet analyss s not sutable for t. Emprcal mode decomposton (EMD) s emprcal, ntutve, drect, adaptve and s used wdely n many areas [, ]. EMD s a good sgnal processng technque capable of decomposng a sgnal nto several sngle stable components at dfferent tme scales by sftng process. In vew of the vbraton sgnal from the sensors contans a lot of nterference nose, whch can affect the result of EMD, so, the sgnals must be denosng before mplementng the EMD. Hao Ruang [3] appled morphology flters to remove the nose n the sgnal and got obvous perodc fault mpact characterstcs. Wang Tayong [4], Shn [5] proposed that the sgnal was pretreated by SVD before EMD decomposton and obtaned better effect. Tang Baopng [6], appled sngular value decomposton-morphology flter to reduce nose and got better fault characterstcs. Morphologcal flterng can nhbt mpulse nose sgnal and SVD can restran random nose obvously. So, we can construct a confederatve flter by Artcle number P_347 95

2 Sensors & Transducers, Vol. 56, Issue 9, September 03, pp combnng the morphologcal flterng and SVD as the sgnal pre-processng unt before mplementng the EMD and acheve weak sgnal fault frequency well. In order to realze the ntellgent dentfcaton based on the weak sgnal feature etracton, ths paper puts forward that ntellgent dagnoss of the tool fault based on GA-B-splne network. B-splne network s a three-layer system, and s tradtonally traned by usng gradent-based methods [7], ths may fall nto local mnmum durng the learnng process. Genetc algorthms (GAs) have drawn sgnfcant attentons n varous felds due to ther capabltes of drected random search for global optmzaton [8-9]. So, n ths paper, the weghtng factors and the knot ponts are searched by usng a genetc algorthm. The epermental results show that the dagnoss approach put forward n ths paper can effectvely dentfy tool wear fault patterns n nose background.. Emprcal Mode Decomposton Emprcal mode decomposton (EMD) can decompose a sgnal nto several sngle stable components at dfferent tme scales by sftng process and t s emprcal, ntutve, drect and adaptve wth the a posteror defned bass derved from the data. The components are referred to as Intrnsc Mode Functons (IMFs), subect to the followng condtons: ) In the whole data set of IMFs, the number of etremes and the number of zero crossng must ether be equal or dffer at most by one. ) At any pont, the mean value of the envelope defned by the local mama and the envelope defned by the local mnma must be zero. At the end of the algorthm, the sgnal (t) can be epressed as: n ( t) c r n, () where c, c,, c n s the ntrnsc mode functon from hgh frequency to low frequency and r n s the resdue of the decomposton. Because of the fault nformaton manly n the hgh frequency regon, therefore, we can calculate energy percentage of the pre-n IMF component to show sgn fault nformaton [0]. The total energy E, E c,,, n; dt () We can structure vector characterstcs usng the percentage of energy to represent the characterstcs of sgnal E n E, (3) T E E E E,, E E (4), 3. Sgnal Nose Reducton Analyss In tool wear montorng process, the vbraton sgnal from the sensors contans a lot of nterference nose. It wll ncrease the number of splne nterpolaton and EMD layers whch can ncrease cumulatve error []. At the same tme, because of the nose, IMF component can not be decomposed effectvely and even ncrease alasng modal. So, the sgnals must be de-nosng before mplementng the EMD. 3.. Morphologcal Flterng Morphologcal flterng s a nonlnear flterng technology based on mathematcal morphology. Its advantage s fast and smple, generally contanng only Boolean operatons, ncludng subtracton but not multplcaton. Based on the geometrc characterstcs of the sgnal, morphologcal flterng uses pre-defned structure elements (SEs) to match the sgnal n order to etract t, mantanng the detals and reducng the nose, t s used wdely n the mechancal fault dagnoss []. Mathematcal morphology s basc operatons are: dlaton, eroson, openng operaton and closng operaton. To get a good flterng result, n the process of fault dagnoss, the average value of the openng-closng (OC) and closng-openng (CO) flters s appled, whch can restran both postve and negatve mpulse nose. It can be defned as: f n F f n y ( n ) F (5) OC In morphologcal flterng, the results of the operatons depend on not only the form of morphologcal transformaton but also the sze and shape of the SE. There are varous knds of SEs, such as flat SE, trangular SE and semcrcular SE etc. The attrbutes of the SE are controlled by ts shape and the selected SE should be as close as possble to the sgnal that beng analyzed. In theory, a more comple SE wll have a much stronger de-nosng ablty. Through the processng vbraton sgnal usng of dfferent SE, the sne SE should frst be consderaton n the treatment of the vbraton sgnal and the best flter effect can be got whle the SE wdth s samplng ponts / and the SE hgh s selected tmes of the sgnal ampltude [3]. n CO 96

3 Sensors & Transducers, Vol. 56, Issue 9, September 03, pp Method of Sgnal Processng Based on Sngularty Value Decomposton Though morphologcal flterng can nhbt mpulse nose sgnal well, t s not better than Sngularty Value Decomposton (SVD) to flterng random nose. SVD de-nosng s a method to ncreasng the sgnal-to-nose rato based on the reconstructed attractor track matr. Supposng there s a sampled tme seres from a sensor:,, N, an m n dmenson matr can be reconstructed based on t: where n(t) s a whte nose wth effectve value equal to, t s an mpulse nose sgnal. The samplng frequency of the sgnal (t) s 000 Hz, the length of the tme seres s 04 ponts. The tme doman wave form of the sgnal (t) s shown as Fg., Fg. s the results of EMD mplementng on (t) drectly. H m 3 m n n N (6) Fg.. Smulaton sgnal. In the formula, N=m+n-, T H UDV S W, (7) r, and r 0 s called sngularty value of matr H. S s the track matr of attractor correspondng to the smooth sgnal n reconstructed vector space; W s the track matr correspondng to the nose or the abrupt nformaton from abrupt fault [4]. SVD s a new and effectve way to reduce nose. The order of sngular spectrum wll nfluence the effectveness of de-nosng drectly. If the order s too small, the nformaton n orgnal sgnals s short of lose and even to cause the waveform dstorton. If the order s too hgh, one part nose n orgnal sgnals has been retaned. The effect of de-nosng s not very deal. So, we wll defne the concept of sngular energy dfference spectrum whch s normalzed for easy of comparng [5]: where D dag,,,, r mnm, n ma mn,,,, r (8) It shows that there must be a peak n the partng between sgnal and nose. Behnd the peak, spectrum peaks caused by nose are smaller. So, k - non-zero sngular values can be acheved by t Smulaton To llustrate the effects of nose on EMD decomposton, we smulated sgnal (t) added nose defned as follows: ( t) ( cos(0t ))sn(30t ) sn(70t ), (9) n( t) ( t) Fg.. The EMD of Smulaton sgnal. It s clear that the frst three orders of IMFs are hgh frequency nose and the useful components are decomposton out on IMF4, IMF5 and IMF6, but the dstnct frequency alasng happened because of the nose nterference. In order to mprove the qualty of EMD decomposton, the orgnal sgnal contaned nose has to be sutably pre-processed. The results of pre-processng by morphologcal flterng, SVD and confederatve flter of them are shown as Fg. 3 - Fg. 5. It can be seen, morphologcal flterng can nhbt mpulse nose sgnal well and SVD can restran random nose obvously. So, we can construct a confederatve flter by combnng the morphologcal flterng and SVD as the sgnal-pre-processng unt before mplementng the EMD. From the Fg. 6, t can be seen that IMF has no frequency alasng because the pulse sgnal and random sgnal are effectvely controlled and the qualty of EMD decomposton can be mproved. 97

4 Sensors & Transducers, Vol. 56, Issue 9, September 03, pp Fg. 3. Sgnal based on morphologcal flterng. hardness 0 HB), the tool s PVD TAlN coatng blade (KC500), man parameters: K r =90, the speed of the tool s V c =95 m/mn, the feed rate of tool s f=0. mm/r, the depth of cut s a p =mm. The samplng frequency of AD board s MHz, the samplng pont s 8. We adopt the low temperature cold wnd coolng n the eperments, as shown n Fg. 8. Fg. 4. De-nosed sgnal based on SVD. Fg. 7. Sensor nstallaton. Fg. 5. De-nosed sgnal based on confederatve flter. Fg. 8. Low temperature ar coolng cuttng. In the eperment process, the tool wear status was dvded nto 3 patterns (shown n Table ). Table. The classfcaton of tool wear. Fg. 6. EMD result of De-nosed sgnal based on morphologcal flters and SVD. Tool wear value (mm) Tool state >0.3 Mld wear Moderate wear Severe wear 4. Weak Feature Etracton n Tool Wear Process The eperments were carred out on a CK643/00 CNC machne tool made n Wuhan Hankou Machnng Centre, the spndle speed: rpm, spndle motor power: 5.5 kw, a Kstler 870B5OMI vbraton sensor nstallaton s shown n Fg. 7. The materal of the workpece: 45# (average 300 samples were selected wear n the eperment and 0 samples were pcked as testng samples. Fg. 9 shows the recognzed results of tool mld wear and severe wear. It can be seen that the sgnals were decomposed wth EMD after the de-nosng and the fault characterstc lay n the frst fve orders of IMFs. So, we calculate the energy percentage of them. Part test samples are shown n Table. 98

5 Sensors & Transducers Journal, Vol.0, Issue 0, Month 008, pp. (a) The vbraton sgnal of tool mld wear. (a) The vbraton sgnal of tool severe wear. (b) De-nosed mld wear vbraton sgnal based on morphologcal flterng and SVD. (b) De-nosed severe wear vbraton sgnal based on morphologcal flterng and SVD. (c) The EMD of mld wear vbraton sgnal based on morphologcal flters and SVD and combnng. (c) The EMD of severe wear vbraton sgnal based on morphologcal flters and SVD and combnng. Fg. 9. Sgnal analyss of Tool wear. Samples (N) Table. Part test samples of networks. Status of tool The energy percentage of IMFs wear E/E E/E E3/E E4/E E5/E Mld wear Mld wear Mld wear Moderate wear Moderate wear Moderate wear Severe wear Severe wear Severe wear

6 Sensors & Transducers, Vol. 56, Issue 9, September 03, pp GA-B-Splne Neural Network In tool wear montorng process, n order to realze the ntellgent dentfcaton based on the weak sgnal feature etracton, ths paper puts forward that ntellgent dagnoss of the tool fault based on GA-B-splne network. B-splne network s a member of the class of lattce Assocatve Memory Networks (AMN). It can be represented as a three-layer system: a normalzed nput space layer, a bass functons layer and a lnear weght layer. The structure llustrated n Fg. 0. Fg. 0. B-splne network. B-splne functons are composed of a lnear combnaton of bass functons. The th B-splne bass functon of order k and the nternal knot pont number r s defned as follows: B k I, f I B ( ) 0, otherwse (0),, k,,, r r k k B k B k () () When the B-splne fuzzy neural network s used for a modelng, there are some problems, such as how to select the approprate weghtng factors w, and how to choose the knot ponts r optmally, these problems are very mportant n achevng good appromaton. B-splne neural networks are tradtonally traned by usng gradent-based methods [7], and may fall nto local mnmum durng the learnng process. Genetc algorthms (GAs) have drawn sgnfcant attentons n varous felds due to ther capabltes of drected random search for global optmzaton. So, n ths paper, the weghtng factors and the knot ponts are searched by usng a genetc algorthm. GA s powerful search optmzaton algorthm, whch mantans a populaton of ndvduals (chromosomes) for teraton [6]. Each chromosome represents a potental to the problem. It forms a new populaton by selectng the more ft ndvduals wth ts ftness. After some numbers of generatons, t s hoped that the system converges wth a near-optmal soluton. Here, the ntal chromosomes are randomly generated wthn the feasble ranges. A chromosome s defned as follows: Z p =(w,,w n,r, r m ), (3) where Z p s the p th chromosome for p=,,,k. k s the fed number of populaton sze and s used to prevent the unlmted growth of populaton. A set of the weghtng factors w range from wthn the nterval: [ mn, ma ] R, and r range from wthn the nterval rmn, rma R. The performance of each chromosome s evaluated accordng to ts ftness. After generatons of evoluton, t s epected that the genetc algorthm converges and a best chromosome wth largest ftness representng the optmal soluton to the problem s obtaned. The ftness functon s defned as follows: ftness E, (4) where E s an estmaton error functon of th sample defned as follows: E ' y y, (5) where y s the current outputs of th sample, y s the desred outputs of th sample. Two prmary groups of genetc operators are crossover and mutaton. Crossover combnes the features of two parent chromosomes to form two smlar offsprng by swappng correspondng segments of the parents. Mutaton, on the other hand, arbtrarly alters one or more genes of a selected chromosome, by a random change wth a probablty equal to the mutaton rate. When the number of teratons s the mamum or the ftness s smaller than settng accuracy, the optmzaton s termnated. 6. Tool Wear Intellgent Dagnoss In ths secton, the better characters from the vbraton sgnal (got n Secton 4) are put nto GA-Bsplne neural network (got n Secton 5). The network wth 5 nputs and one output was adopted and the output of network s the dagnoss value of the tool 00

7 Sensors & Transducers, Vol. 56, Issue 9, September 03, pp wear. Each nput of network has 7 knot ponts and each order of B-splne bass functons s. The network s traned wth GA, and the classfcaton accuracy s 0.00, the largest number of teratons s 600, the crossover rate p c =0.8, the varaton rate p m =0.. Part of the dentfcaton results are shown n Table 3. It can be seen that the recognton rate acheves 98 % wthn the scope of the error s 0.0. Table 3. The dentfcaton results of networks. Sample (N) Actual wear value (mm) Dagnoss result (mm) Sample (N) Actual wear value (mm) Dagnoss result (mm) The same datasets of the tool wear are traned wth the dfferent learnng algorthms, the error curves of tranng usng the gradent-based methods and GA are llustrated n Fg. and the results are compared each other, the average result can be shown n Table 4. It can be seen that the GA-Bsplne s the best choce to dentfy tool wear wth a lower average error and the hgher dagnoss rate. 7. Conclusons An ntellgent tool wear montorng system has been establshed. On the bass of the study, the followng conclusons can be made.. In the tool wear montorng process, t s dffcult to etract tool wear feature nformaton because of nose nterference. The paper proposed a confederatve flter by combnng the morphologcal flterng and SVD as the sgnal-pre-processng unt before mplementng the EMD. Ths can effectvely remove the nose and reduce modal alasng of the EMD. At last, the weak sgnal fault frequency was acheved.. The fault characterstc lay n the frst fve orders of IMFs. So, we calculate the energy percentage of them and put them nto GA-B-splne networks. It smplfes the structure of the network and does not affect tool fault dagnoss. 3. The advanced GA-B-splne networks are appled n the tool wear montorng process. Because the B-splne network wth tradtonally traned by usng gradent-based methods may fall nto local mnmum durng the learnng process, ths paper appled Genetc algorthms (GAs) to search the weghtng factors and the knot ponts and got better results. It can mprove the accuracy of tool wear and adapt to onlne montorng. Acknowledgment GA Gradent-based Ths work s supported by the Fundamental Research Funds for the Central Unverstes (SWJTUCX039). References error epoches Fg.. Error curves of tranng the B-splne neural network usng the dfferent algorthms. Table 4. The results for tool wear wth dfferent methods. Learnng algorthms Average Error Average Dagnoss rate Gradent-based % GA % []. Sun Bn, Huang Shengquan, et al., Identfcaton method of gas lqud two phase flow regme based on emprcal mode decomposton, Chnese Journal of Scentfc Instrument, 9, 5, 008, pp []. Xng Hongyan, Xu Ruqng, Wang Changsong, Pulse sgnal feature research based on emprcal mode decomposton, Chnese Journal of Scentfc Instrument, 30, 3, 009, pp [3]. Hao Ruang, Lu Wenu, Chu Fule, Morphology flters for analyzng roller bearng fault usng acoustc emsson sgnal processng, Journal of Tnghua Unversty, 48, 5, 008, pp [4]. Wang Tayong, Wang Zhengyng, Xu Yonggang, et al., Emprcal mode decomposton and ts engneerng applcatons based on SVD de-nosng, Journal of Vbraton and Shock, 4, 4, 005, pp [5]. Shn K., Hammond J. K., Whte P. R., Iteratve SVD method for nose reducton of low-dmenson chaotc tme seres, Mechancal Systems and Sgnal Processng, 3,, 999, pp [6]. Tang Baopng, Jang Yonghua, Zhang Xngchun, Feature etracton method of rollng bearng fault based on sngular value decomposton- morphology 0

8 Sensors & Transducers, Vol. 56, Issue 9, September 03, pp [7]. [8]. [9]. [0]. []. flter and emprcal mode de-composton, Journal of Mechancal Engneerng, 46, 5, 00, pp. 37-4, 48. Fan Junbo, Hao Jsheng, An Adaptve Learnng Algorthm for B-splne Networks, Acta Electronca Snca, 7, 8, August 999, pp Sang Hafeng, He Dakuo, Zhang Dapeng, Softsensng modelng of a fermentaton process through support vector machnes and genetc algorthms, Journal of North Eastern Unversty (Natural Scence), 8, 6, 007, pp L Shchao, Sh Xuhua, Fault Dagnoss Based on Genetc Algorthms Wavelet Neural Network n Dual-Redundancy Brushless DC Motor, Journal of Vbraton, Measurement & Dagnoss, 9,, June 009, pp Ln Ruln, Zhou Png, Fault dagnoss of valve tran based on EMD and neural network, Journal of Naval Unversty of Engneerng, 0,, 008, pp Hu Aun, An Lansuo, Tang Gu, New Process Method for End Effects of Hlbert-Huang Transform, Journal of Mechancal Engneerng, 44, 4, 008, pp []. Du Bqng, Wang Songlng, Tang Gu, Applcaton of Morphologcal De-nosng n Rotor Fault State Identfyng by Fractal Method, n Proceedngs of the CSEE, 8, 6, 008, pp [3]. Du Bqng, Wang Songlng, Tang Gu, Morphologcal flter desgn for vbraton sgnals from rotor system, Chnese Journal of Constructon Machnery, 6,, 008, pp [4]. Sanlturk Y., Cakay O., Nose elmnaton from measured frequency response functons, Mechancal Systems and Sgnal Processng, 5, 3, 005, pp [5]. Xu Feng, Lu Yunfe, Song Jun, Feature etracton of acoustc emsson sgnals based on medan fltersngular value decomposton and emprcal mode decomposton, Chnese Journal of Scentfc Instrument,, 3, 0, pp [6]. W. Y. Wang, Y. H. L, Evolutonary Learnng of BMF Fuzzy-Neural Networks Usng a ReducedForm Genetc Algorthm, IEEE Trans. Syst., Man, Cybern. B, 33, 003, pp Copyrght, Internatonal Frequency Sensor Assocaton (IFSA). All rghts reserved. ( 0