IRREGULARITY DETECTION IN ARTIFICIAL SIGNAL USING TIME-FREQUENCY ANALYSIS

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1 IRREGULARITY DETECTION IN ARTIFICIAL SIGNAL USING TIME-FREQUENCY ANALYSIS A. Mlik Hmt 1, M. Firushm Ghzli 2, Mkeen Amin 2 nd Ftihh Adnn 2 1 Fculty of Mechnicl Engineering, Universiti Teknikl Mlysi Melk, Hng Tuh Jy, Durin Tunggl, Melk, Mlysi 2 Fculty of Mechnicl Engineering, Universiti Mlysi Phng, Pekn, Phng, Mlysi E-Mil: firushm@ump.edu.my ABSTRACT A typicl time signl contin overwhelming mounts of dt nd some of the signl components represent for irregulrity such s crck nd lek which gretly importnt to e identified precisely insted of using trditionl method. The strtegy cn e done using signl processing method through high-qulity time-frequency representtion (TFR) for nlysing such time dependent signls to ccurtely discover these superposition signl components. A few populr TFR methods such s wvelet trnsform nlysis nd reltively new, synchrosqueezed wvelet trnsform were pplied in current study using rtificil signl. From the result, oth methods successfully discover n irregulrity in the signl with different degree of ccurcy nd it is shown tht synchrosqueezed wvelet trnsform provide the est nd detiled timefrequency representtion. Keywords: irregulrity, time-frequency nlysis, synchrosqueezed wvelet trnsform. INTRODUCTION For frmeworks of enthusism to reserchers nd engineers, exmining the chnging properties of frmework is normlly performed y investigting signl informtion from the frmework, insted of direct investigtion of every prt. Propelled time-frequency nlysis give n rrngement of explortory pproches for investigting chnging frequency content in signl, which cn then e connected with nomlies forms in frmework. Methods of signl trnsforming re mjor in comprehension signls from wide mixed g of fields. Rw time-mplitude signl tht ws trnsformed into frequency domin distinguishes the frequency sustnce of the signl, which is regulrly more helpful thn time spce dt for exmintion of dynmic properties. A fourier trnsform of time period rrngement, for exmple dt signl of tremor record, contins dt in regrds to the frequency sustnce, however it cn't resolve the ccurte onset of chnges in nturl frequency, s time of trnsient dt is crried just in the phse of the chnge. Time-frequency nlysis is technique for chnging from time rrngement into two-dimensionl representtion of frequency sustnce s for time. A TF nlysis, y communicting frequency content t distinctive segments of record, tkes into considertion exmintion of developing signs. Numerous ppliction or specilized works were directed utilizing TFR device for instnce s prt of mechnicl shortcoming nlysis (Li et l., 2013) nd (Dong nd Chen, 2012), speech (Tntiundhit et l., 2010), iomedicl (Adull nd Wong, 2011) nd (Musselmn nd Djurdjnovic, 2012), electronic frmework (Cstillejos et l., 2012), seismic (Zho et l., 2014) nd (Zheng et l., 2013), geotechnicl (Sudh et l., 2009), etc., in which different TFR techniques hve een employed to extrct significnt physicl prmeters from the rw signls. In this pper we show the proility of the time frequency representtion to identify inconsistency in rtificil signl. First nd foremost, utilizing couple of TFR strtegies, we extrct the instntneous frequency to mke comprison then determine the est representtion in time-frequency plne. At tht point we pply tht TFR strtegy to identify irregulrity in rtificil signl. TIME-FREQUENCY ANALYSIS STRATEGY Introduction of time-frequency nlysis Time-frequency representtions re more generlly utilized for non sttionry signl exmintion which roust strtegy to trnsform one-dimensionl signl x(t) into two-dimensionl function of time nd frequency, TFR (x;t, ω) to concentrte pertinent dt. There exist numerous sorts of TFR lgorithms which most of these instruments fll into two clssifictions: liner nd qudrtic techniques (Flndrin, 1999), ech of which hs its own prticulr qulities nd shortcomings. In the first method known s liner methods, the signl to e investigted is portryed y its inner products with pressigned group of lyouts, creted from one (or couple of) essentil formt y sic opertions. Cses re the windowed fourier trnsform, where the group of formts is produced y trnslting nd modulting n essentil window cpcity. Another exmple is wvelet trnsform, where the lyouts re gotten y trnslting nd dilting the sic or so clled mother wvelet. The second strtegy of TFR ws qudrtic method, which the signl is directly compred nd evluted without preceding fmily of templtes. Susequently, few components cn hve crisper, 3593

2 giving etter concentrtion in the time-frequency plne. Even so, the representtion of multi-segment signl is rendered more muddled y the vicinity of interference etween the TF representtions of the individul segments; these impcts dditionlly cuse the time-frequency density to e negtive in few sections of the TF plne. These negtive sections however cn e uprooted y some dditionl opertion. In summry, the liner methods re normlly effective nd simple to remke, however give lcking resolution. While the qudrtic methods give comprtively etter resolution yet need higher computtionl expense due to extr works for signl reconstruction. Among the methodologies proposed to tret this issue, the relloction (or ressignment) methods (Auger nd Flndrin, 1995), (Chssnde-Mottin et l., 2003), (Chssnde-Mottin et l., 1997) nd (Duechies nd Mes, 1996) cn e seen s liner strtegies, ccompnied y ressigning estimtions of the TFR. Exmple of such methods is the synchrosqueezed wvelet trnsform, which ws introduced in (Duechies nd Mes 1996) nd given thorough legitimiztion for criticl clss of signls (Duechies et l., 2011). Synchrosqueezed wvelet trnsform (SWT), initilly presented in the speech signls (Duechies nd Mes, 1996) hs demonstrted to e distinct option for the EMD method (Duechies et l., 2011), giving contriution of enhncing spectrl resolution. This method is siclly comintion of wvelet nlysis nd timefrequency relloction method tht reltively new pproch to enhnce the nture of time-frequency representtion. SWT hs well cpility to decompose non-sttionry nd noisy signls into its components nd gives n ppeling distinct option for EMD. Its fundmentl focl points re: vigor in the vicinity of noise nd no prerequisites of nd pss filtering or discontinuity mesure. Numericl exmple As discussed ove regrding to TFR of sign x(t), TFR(t, ω ), the ojective is to figure out the intensity of the frequency ω t time t. As the vulnerility guideline locks n immculte concurrent portryl of time nd frequency, ll TF representtions re y need close estimtions to instntneous frequency. These estimtions vry in exctness, nd there exist dditionl ostructions to trnslting generl TFR s vitlity dispersion in the TF plne. As smple of clcultion, let us consider lend of one sinusoid nd one AM-FM type signls. This cn e outlined y n illustrtion s demonstrted in Figure 1 where signl x(t) is chrcterized y cos + sin, 5 = { cos +.5, 5 (1) The synthetic signl x(t) hs 15 Hz component modulted y 1 Hz sinusoid from 0 to 5s nd constnt hrmonics of 15 Hz from time 5 to 10s. Figure-1 shows the instntneous frequencies for oth components. Figure-1. Numericl signl. ) Synthetic signl with four sinusoidl components, ) Instntneous frequencies otined s the derivtive of ech one of the independent components. As such, wvelet nlysis is one of the est pproprite nd fvourite types of TFR y most reserchers for nlysing non sttionry nd non liner signl dt. The ump wvelet type nlysis s plotted in the Figure-2 le to identify oth locl frequency components efore nd fter the switch point s well s the position of the frequency switch t 5s. The frequency resolution however is not ll tht gret prticulrly for the high frequency rnge nd there is extr verticl line t the switching point t 5s. Second type of wvelet known s lognorm (Figure-2), demonstrtes superior frequency resolution contrsted with ump type in which more shrpened. In generl oservtion of wvelet nlysis, it cn e seen tht there is lekge energy to neighouring modes. In this wy, the selection of wvelet type ssumes criticl prt with specific end gol to get helpful nd exct results from the nlysis. Accordingly from this figure, we cn see tht the wvelet-sed TFR is excessively miguous for us, mking it insufficient to perceive the TF informtion of the signl. To get clerer TF mpping, the synchrosqueezed wvelet trnsform lgorithm is utilized s demonstrted in Figure-2c. The synchrosqueezed hs the cpcity impeccly depict every individul segment nd to determine the instntneous frequencies ner to the theoreticl vlue, including modulted mplitude signl. The overlpping point dditionlly gives superior representtion contrst with wvelet nlysis. Compring etween of oth strtegy, its shows tht the wvelet trnsform technique produces widespred resolution in frequency lines s opposed to 3594

3 synchrosqueezed which is more concentrte nd enhncing fundmentlly the frequency resolution to show signs of improvement result s demonstrted in Figure-2c. c Figure-2. Time-frequency representtion; ) Bump wvelet type. ) Lognorm wvelet type. d) Synchrosqueezed wvelet trnsform. IRREGULARITY DETECTION In numerous resonle pplictions, in n extensive vriety of fields for exmple mnufcturing nd seismology, one is confronted with signl tht hve few components, ll sensily very much confined in timefrequency spce, t distinctive positions. The components which frequently non-sttionry, s in they cn present jumps or chnges in conduct, might e vitl to extrct s precisely s could resonly e expected. In engineering ppliction, for instnce in mnufcturing industril, there constntly mechnicl filure hppen tht t lst impct the production or profit of the compny. The more regrettle cse perhps hppen if the filure will give more prominent hrm to individuls encompssing furthermore wful impct to environment, for exmple, contmintion. It ws hppened more often thn not egin from the minor hrm tht cn e forestlled in cse if it ws identified t right on time stge. Tht ws solid motivtion ehind why ll the mechnicl prt ought to e checked nd services frequently. One of the strtegies is y doing normlity discovery t right on time phse of filure nd this cn e done using signl nlysis pproch. For preliminry study, this work will perform signl nlysis to detect irregulrity using rtificil signl. Employing time-frequency representtion, wvelet trnsform nd synchrosqueezed wvelet trnsform nlysis will e utilized in this work. Consider simple sine wve with one frequency ll of sudden chnging to nother frequency with the vicinity of dirc type impulse t certin time. This impulse represents the irregulrity in the signl which cn e considered for exmple s the reflection of the mechnicl filure in the system. This signl v(t) which 3595

4 hs two different frequencies f 1 nd f 2 is chrcterized y the Eqution = {,.5 + =. 5,.5. (2) synschrosqueezed hs the cpcity delinete smooth nd shrp chnges in the frequency lines, which is enhncing fundmentlly the frequency resolution. where f 1 nd f 2 hve the vlue of 7Hz nd 14Hz individully. This signl hs een chosen so s to demonstrte the cpcity of the time frequency nlysis strtegy to isolte the distinctive frequency components nd lso to recognize the normlities exhiit in the signl. Figure-3 demonstrtes the time domin of the signl longside its Fourier spectrum. As we cn see from Figure-3, the two frequencies components re very much displyed in the fourier spectrum nywy it neglects to recognize the spike of the nomly in the signl. Figure-3. Representtion of signl v(t). ) Time domin, ) frequency spectrum. Figure 4 nd 4 demonstrte the lognorm type wvelet trnsform nlysis nd synschrosqueezed wvelet trnsform nlysis seprtely. As should e ovious in the first strtegy, wvelet trnsform redy to distinguish the two segments signl including the impulse which correspond to normlity in the signl however reltively give poor resolution with spred norml frequency rnge. On the other hnd, the synschrosqueezed wvelet (Figure-4) hs the cpcity consummtely portry every individul segment nd dditionlly the normlity ner to the theoreticl vlue. Contrsted with wvelet, the Figure-4. Irregulrity detection using rtificil signl. ) Lognorm type wvelet trnsform nlysis. ) Synschrosqueeze wvelet trnsform nlysis. CONCLUSIONS A numer of different time frequency pproches hve een developed to trnsform time series into twodimensionl representtion of frequency content with respect to time. This pper riefly utilised two different methods sed on wvelet trnsform nd reltively new pproch derived from wvelet known s synchrosqueezed wvelet trnsform. Both methods hve een compred to clculte instntneous frequency s well s to detect impulse or irregulrity in the signl using rtificil signl. 3596

5 From this study, it cn e summrised tht the irregulrity in the signl is successfully identified using time frequency nlysis. An pproched introduced y Duechies et l., (2011) (Duechies et l. 2011) known s synchrosqueezed wvelet trnsform give the est representtion compre to wvelet trnsform nlysis. Using this method, it s le to perfectly delinete ech individul component s well s the irregulrity in the signl close to the theoreticl vlue. The time frequency components shrper nd more condensed long the time nd frequency lines in which overlly improving significntly the mping resolution. Therefore, synchrosqueezed wvelet trnsform nlyses hve een shown to provide etter identifiction of the irregulrity in the signl compre to currently well-known wvelet trnsform. ACKNOWLEDGMENTS The support from the Ministry of Higher Eduction Mlysi vi FRGS grnt RDU is grtefully cknowledged. The uthors would like to thnk the tem memers of Advnced Structurl Integrity nd Virtion Reserch (ASIVR) group under Fculty of Mechnicl Engineering, Universiti Mlysi Phng for their support nd eneficil ide to improve the content of the pper. REFERENCES Adull, W. nd Wong, L Neontl EEG signl chrcteristics using time frequency nlysis. Physic A: Sttisticl Mechnics nd its Applictions. 390(6), pp Auger, F. nd Flndrin, P Improving the redility of time-frequency nd time-scle representtions y the ressignment method. IEEE Trnsctions on Signl Processing. 43(5), pp Cstillejos, H., Ponomryov, V., Nino-De-River, L. nd Golikov, V Wvelet trnsform fuzzy lgorithms for dermoscopic imge segmenttion. Computtionl nd Mthemticl Methods in Medicine, Chssnde-Mottin, E., Duechies, I., Auger, F. nd Flndrin, P Differentil ressignment. IEEE Signl Processing Letters. 4(10), pp Duechies I. nd Mes S A nonliner squeezing of the continuous wvelet trnsform sed on uditory nerve models. In Wvelets in Medicine nd Biology. CRC Press. pp Dong G. nd Chen J Noise resistnt time frequency nlysis nd ppliction in fult dignosis of rolling element erings. Mechnicl Systems nd Signl Processing. 33, pp Flndrin P Time-Frequency/Time-Scle Anlysis, Wvelet Anlysis nd Its Applictions. In Sn Diego, CA, Acdemic Press Inc. Li B., Mi S.S., Liu P.Y. nd Wng Z.J Clssifiction of time-frequency representtions using improved morphologicl pttern spectrum for engine fult dignosis. Journl of Sound nd Virtion. 332(13): Musselmn M. nd Djurdjnovic D Time frequency distriutions in the clssifiction of epilepsy from EEG signls. Expert Systems with Applictions. 39(13): Sudh K., Isril M., Mittl S. nd Ri J Soil chrcteriztion using electricl resistivity tomogrphy nd geotechnicl investigtions. Journl of Applied Geophysics. 67(1): Tntiundhit C., Pernkopf F. nd Kuin G Joint time-frequency segmenttion lgorithm for trnsient speech decomposition nd speech enhncement. IEEE Trnsctions on Audio, Speech nd Lnguge Processing. 18(6): Zho Y., Liu Y., Li X. nd Jing N Time-frequency domin SNR estimtion nd its ppliction in seismic dt processing. Journl of Applied Geophysics. 107, pp Zheng J., Peng S., Liu M. nd Ling Z A novel seismic wvelet estimtion method. Journl of Applied Geophysics. 90, pp Chssnde-Mottin, E., Auger, F. nd Flndrin, P Time-frequency/time-scle ressignment. In Wvelets nd signl processing. Birkhà user, Boston, MA, pp Duechies I., Lu J. nd Wu H.T Synchrosqueezed wvelet trnsforms: An empiricl mode decompositionlike tool. Applied nd Computtionl Hrmonic Anlysis. 30(2):