Signal Processing in Smart Sensor Systems 1

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1 Signal Procssing in Smart Snsor Systms Milan Miš, Ján Šturcl Abstract This rport is part on of a sris of articls that dscrib th xisting classic mthods and nw prspctiv mthods of snsor signal procssing. Th first part introducs smart snsor systms, spcially snsor arrays. It charactrizs in short smart snsor systms, dscribs thir basic proprtis and prsnts an ovrviw of thm as wll. Th articl also dals with classic mthods of snsor signal procssing that ar appropriat for scn or obct status idntification. Th articl is concrnd with th corrlation mthod in dtail and an xampl is givn for it. ywords: snsor array, smart snsor systm, snsor signal procssing, primary information procssing, pattrn rcognition, corrlation mthod Introduction Th prsnt stat of snsor tchnology in automation might b charactrizd as intrlaving of classic analogu masuring units and smart masuring units. Howvr, th trnd shows that smart masuring units ar coming into wid us bcaus of thir undoubtd advantags from a usr point of viw (procting, srvic, cost rduction of cabl distribution, rliability, maintnanc) and from a functionality point of viw (primary information procssing, autonomous opration, diagnostics, auto-calibration and communication with tchnical nvironmnt). Smart snsor systms [] ar mor powrful snsor masuring systms applicabl to nvironmntal masurmnts, automatic control systms, mchatronic dvics [] and many othr automation and control tchniqus. For xampl, th significant simplification of control algorithms in distributd control systms is achivd by using smart snsor systms built into th control structur, whr th smart snsor systms rprsnt th information subsystm. Bacaus a smart snsor systm alrady provids "clar" information about a masurand, th control systm can us this valu without any nd for furthr formatting dirctly in th algorithm. Thus, th dmands on control systm computational powr ar rducing, whil th rliability, accuracy and fficincy ar incrasing. Sinc th rang of us of smart snsor systms is still xpanding, th rquirmnts on th systm ar changing and nlarging. Th purpos of masurmnt is not only indicating th masurand valu, but also in most cass idntifying som scn or obct status. On of ky proprtis of th snsor systm is th ral-tim rspons. Snsor signal procssing is thrfor as important as its own construction. Improving and dvloping nw signal procssing mthods givs nw possibilitis for ralization of primary information procssing tasks implmntd in modrn smart snsor systms. Th chaptrs at th bgining of th articl ar ddicatd to radrs who hav nvr hard about signal procssing in a smart snsor systm as wll as for xprts in snsor tchniqus. In th last chaptrs, thr is prsntd in mor dtails th corrlation mthod as a rprsntativ of th classic mthods.. Snsor systm First of all, somthing about a snsor. Th trm of snsor has bn usd with ambiguous maning in svral publications. Many popl undrstand snsor as a snsitiv lmnt, th othr as a crtain masuring systm (a snsitiv lmnt togthr with a signal procssing unit). In this articl th trm of snsor will rprsnt only a snsitiv lmnt. Information obtaind from on snsor is in som cass (usualy for idntification) not nough and masurmnt is ambiguous. Thr is a nd to us mor than on snsor for th masurmnt. Anothr problm arising with this fatur - a lot of information should b procssd in ral tim (th most important of masuring systm). Fig. Snsor systm Th snsor systm (Fig.) is a masuring systm consisting of svral snsors, which togthr mak a function unit. Th

2 snsors ar non-slctiv (non-zro cross snsitivitis) with non-linar transfr charactristics and non-zro dynamics.a snsor systm is illustratd in Figur. On th snsors S i for i,..., ar dirctly or indirctly acting svral physical quantitis X for,...,n. Th numbr of snsors nd not b qual to th numbr of masurd quantitis N. Th snsors ar producing output signals E i that dpnd on th masurd quantitis. Th dpndncs ar givn by cross snsitivitis (f to f N ) and it gnrally holds E F f X f X,, f X () i x [ ( ) ( ) ( )] i, i for i,...,n. Th snsor signal procssing unit SSP provids th output signals Y k in dpndnc on th snsor signals E i Y k Fy[ E, E,, EN ] () for k,...,t. Thr ar ssntially two groups of snsor systms: procss quantity probs and snsor arrays. In th cas of procss quantity probs, th cross snsitivitis ar liminatd. Th tndncy is to choos snsors snsitiv only to on particular masurd quantity with proportional transfr charactristics. Thus, th numbr of snsors is usualy qual to th numbr of masurd physical quantitis ( N) and for snsitivitis f i it idally holds ki 0 for i, ls. f i (3) On snsor provids information about th main masurd (procss) quantity (.g. prssur, tmpratur, humidity, tc.) and information from othrs is usd for corrction of prturbation quantitis. Such snsor systms nowadays producd hav a rlativly high pric that is mainly givn by th computational powr of th control unit and th typ of snsors usd. To th scond group blong snsor arrays. Thy ar sparatd upon layout in th nvironmnt or snsor typ onto homognous or htrognous. Unlik in procss quantity probs, non-zro cross snsitivitis ar mployd. Th main considration is givn on ffctiv mthods of snsor signal procssing. Th principl is basd on th fact that a snsor with zro cross snsitivitis practicaly dos not xist and snsor transfr charactristics ar non-linar. Advantag of such a snsor systm against th first on is rsulting from th usag of common snsors. In addition, th numbr of snsors can b lss than th numbr of idntifiabl stats. Informations gnratd by ach snsor in th array hav th sam wight in signal procssing.. Smart snsor systm A smart snsor systm (SSS) is an autonomous digital masuring systm quippd with primary information procssing, diagnostic and auto-calibration functions and has th ability to communicat with its tchnical nvironmnt. In othr words, it is a snsor systm intgratd with digital blocks that provid digital procssing. Th block schm of a simpl smart snsor systm is dpictd in Figur. in N Fig. Simpl smart snsor systm A snsor S i rprsnts a filtr of typ and rang of th masurd physical quantity, which affcts dirctly or indirctly th snsor. Th snsor is continuously tracking th masurd quantity and gnrats information about it. Th output signal from th snsor is mostly a low nrgy analog signal. Modrn control systms ar almost allways working with information in lctronic form. Masuring systms ar dsignd to mt this rquirmnt, hnc a masurd physical quantity is oftn alrady transformd by th snsor into lctrical quantity (V, A, R, L, C, tc.). Th snsor S i provids primary information about th masurd quantity and thrfor can radically affct th ovrall quality of masurmnt. Th snsor signals ar consquntly handld by th masuring transmittr(s) MT. Th masuring transmittr has to nsur th unifid signal in th plac of masurd data procssing. Amplification of snsor's nativ signal and unification blong to th main tasks of th masuring transmittr. Th snsor togthr with masuring transmittr maks a transducr (i.. prob, transmittr). Th transducr is tratd as th basic function block of th snsor masuring systm and togthr with th incoming signal lin to th signal-procssing unit rprsnts a masuring channl. Snsor signal procssing is ralizd in digital form, hnc th analogu-digital convrtr ADC should b an insparabl part of SSS. Th multiplxr MUX controlld by th microcomputr µc switchs th signals from th masuring transmittrs to input of ADC. In this mannr, th microcomputr obtains digital information about chosn masurd quantity valu. Th digital communication btwn SSS and othr tchnical dvics, for xampl highr-lvl digital systm (.g. prsonal computr PC), is providd by th communication intrfac I. Spcial faturs of SSS ar auto-calibration and diagnostics A-CAL & DIAG [3] that incrasing accuracy and rliability. 3. Primary information procssing tasks Th primary information procssing (PIP) [4] is a charactristic fatur of smart snsor systms. It rprsnts primary convrsion of th signal obtaind from snsor(s) to nsur clar information about th masurd quantity. To th PIP tasks, xcpt for snsor signal amplification and analogudigital convrsion, spcially blong: masurd data rduction, filtration, transfr charactristics linarization, dynamic rror corrction, indirct masurmnt and calculations. Th intllignt function unit of SSS is usually a custommad monolithic microcomputr (MMC). MMC oftn prforms only som of PIP tasks listd abov. Whn choosing functions of primary information procssing that SSS should prform, many limitations aris. Th main limitation is th rquirmnt for ral-tim opration of SSS. This limitation rlats to th computational powr of MMC and mathmatical oprations ralizd in MMC. Svral mthods of signal procssing in SSS ar listd in [5].

3 3. Snsor transfr charactristics Snsors or transmittrs ar charactrizd by mtorological proprtis that dscrib thir static and dynamic paramtrs. On of th most important static paramtrs is th static transfr charactristic (TCH). It xprsss th rlation (dpndnc) btwn th input quantity x and output quantity y in a stady stat by th following quation ( x) y f (4) Almost all snsors hav non-linar transfr charactristics. Producrs of snsor prsnt thir snsor transfr charactristics in th catalogu sht in som of th following ways: polynomial functions on intrvals of masurd quantity, tabls of rfrnc points, tc. Th knowldg of TCH is mainly important for convrsion of th masurd signal valu to th masurd quantity valu. Thr ar svral mthods of approximation of snsor transfr charactristics [6,7]. Th important task of snsor producrs is to nsur high tim stability (larg rpatability) of snsors. Additional improvmnt of th mtrological paramtrs can b achivd in th digital sub-systm of SSS using appropriat mthods. 3. Scn or obct status idntification Somtims it is ndd to idntify th scn or obct status. It mans to valuat a coupl of physical quantitis that charactriz an idntifiabl status. For xampl, chmical transmittrs can idntify a gas mixtur xisting in nvironmnt. So a scn stat could b also th xistnc of a gas substanc in th nvironmnt, an obstacl location in th work ara of a robot tc. Th snsor array is vry appropriat for idntification purposss. On approach of signal procssing from th snsor array is to improv slctivity of th snsor by intllignt mthods. In this cas it would b idal to us on snsor only for on of ach of th masurd quantitis (as by procss quantity probs). Howvr, as it was said bfor, a snsor snsitiv to only on physical quantity practically dos not xist - th signal from th snsor is affctd by mor than on quantity (s th rlation ()). Sinc, th snsors hav non-zro cross snsitivitis, it is ncssary to raliz th disturbanc corrction. Th cross snsitivitis ar rducd by complicatd tchnological mans, which, howvr, nd not b nough. In addition, ral snsor transfr charactristics ar non-linar that usually rquirs mor complicatd mathmatical oprations to b applid, whrby dmands on th computational powr of intllignt unit ar incrasing. Anothr, mor ffctiv solution (typical for snsor arrays) is basd on xploitation of cross snsitivitis. Non-zro cross snsitivitis mak it possibil to idntify a lot of quantitis with a smallr numbr of snsors and using a classification mthod. Th non-linarity of snsor's transfr charaktristics nd not b a significant problm for idntification. If nonlinaritis wr almost idntical, thy would b omittd. Th principl of classification consists in comparision of actual pattrns A, A,, A t t t and thos from a group of rfrnc pattrns R, R,, R N. Pattrns ar virtual signal vctors mad from snsor signals obtaind from a snsor array. Th numbr of distinguishabl pattrns dpnds on th ability of th masuring transmittr to gnrat miscllanous output signal lvls. Now, th signal unification is not appropriat bcaus of pattrn count rduction. Nxt, th main considration will b takn of th idntification principl that rsids in comparison of th actually obtaind pattrn with svral pattrns that rprsnt known idntification targts. Such a way of idntification is known as pattrn rcognition (PARC) or classification. Pattrn rcognition algorithms hav bn dvlopd spcially for chmicals to idntify a substanc in a mixtur [8]. Fig.3 Various typs of classificators Th smll as a on of human snss is a good xampl of multidimnsional snsing and signal procssing. A paltt of smlls can b rcognizd by rcptors locatd at th nd of nrv clls in th nos. Enginrs hav dvlopd an "lctronic nos" as a tchnical analogy of th nos, whr th snsor array consists of X snsors and this snsor systm has th ability to distinguish Y gass (it holds Y > X). Figur 3 shows a tr diagram of svral classificators usd by PARC. Som classificator typs ar rprsntd by artifical intllignc mans, which ar boxd and bold markd in th diagram. In th nxt articl (part ), thr will b laboratd mthods using nural ntwork and fuzzy logic as a classificator in dtail. All othr mthods ar groupd in a spcial catgory. Lt th catgory b calld classic mthod, that can b xactly distinguishd from thos using artificial intllignc mans. Classic mthods will b discussd nxt. 4. Classic mthods Classic mthods [8] of signal procssing in snsor arrays ar applid spcially in chmical analysis snsor systms, whr on of th tasks is to idntify on or svral chmical 3

4 substancs and indicat thir concntrations. Th way of idntification is usually basd on th pattrn rcognition principl by comparing rfrnc and actual (ral) pattrns. Th mthods listd blow consist of two phass: calibration procss and valuation procss. Th bst known classic mthods: corrlation mthod (CM), vctor mthod (VM), partial last squars (PLS) mthod, transformd last squars (TLS) mthod. Th first two mthods srv th purpos of idntification only and valuation of th concntration has to b don sparatly. Th othr two mthods wr dvlopd for idntification and valuation of th concntration in on stp. Th way and procss of signal valuation using classic mthods is prsntd on a practical xampl in sction "Exampl for Idntification". Bcaus of availabl articl rang, thr is prsntd only on of thm. Th corrlation mthod was chosn as th rprsntativ. Th us of this mthod is prty wid but in th articl thr will b mainly discussd with th us of scn or obct status idntification. 4. Corrlation mthod Th corrlation mthod [8] is on of th bst known classic mthods usd for signal procssing from snsor arrays, whr th snsors hav non-zro cross snsitivitis. In gnral, lt snsor array (s Fig.) consist of snsor lmnts ddicatd to idntify N scn statuss and stands N>. Th mthod is basd on th pattrn rcognition principl and th matching of pattrns is valuatd through th corrlation cofficint. Th corrlation cofficint (CC) is valuatd in ach masuring cycl. If CC is around, thn th status is idntifid, ls th scn or obct is in an unknown status that was not considrd in th calibration procss. If mor than on pattrn is almost idntical, thn mor valus of th corrlation cofficint might b around. In such a cas idntifid status should b that with th CC valu closr to. Th mthod consist of two parts: calibration procss - prparation of rfrnc pattrns, valuation procss - ralization of th algorithm of th mthod. Calibration procss In th calibration procss th rfrnc pattrns ar gnratd and a spcific maning is assignd to ach pattrn. Th pattrns ar prprocssd signal vctors E obtaind from snsors usd in th snsor array. Signals dpnd on th masurands charactrizing an idntifiabl status. Each lmnt i of th signal vctor E can b, for xampl, prprocssd as an arithmtical avrag (5) of svral snsor output valus in crtain rang of masurd quantitis by quation m i ik m k for i,,;,,n whr (5) ik is th output of th i-th snsor whil scn is in th -th status during th k-th masurmnt, m is th numbr of masurmnts of i from th i-th snsor by -th scn status. Th rsult is *N valus dividd by th indx into N vctors E ach with lmnts. Mostly, all lmnts contain a bias unwantd for idntification, whrupon is liminatd. Th bias valu can b dtrmind as an avrag of valus of th lmnts of signal vctor E by i i whr i is th i-th lmnt of signal vctorfor -th mdium status. Aftr rmoving th bias from th valus of lmnts of signal vctor E, on obtains rfrnc pattrn R r r M r k M R (7) for,,n Evaluation procss In th valuation procss th actual pattrn A(t) is compard with rfrnc pattrn R for,,n. If th pattrns (th actual and any of th rfrncs) ar not idntical, thn th actual pattrn (status bing idntifid) might b markd as non-idntifid or a spcific maning can b assignd to it and th pattrn could b stord as a nw rfrnc pattrn. In ordr to compar pattrns, it is ncssary, that ral pattrns b prprocssd as th rfrnc pattrns. Hnc, th bias is rmovd from th actual signal vctor using th sam procdur as in th calibration procss by (6) and (7). Th corrlation cofficint is calculatd by [( a ] i i )( ri ) ( ai ) ( ri ) ρ (8) i i for,,n. Th corrlation cofficint valu lis in th intrval < -; >. Practically, ach masurmnt is affctd by som unknown rrors, which affct CC valu too. Hnc, valu ρ is not always, but it is only clos to. By this rason, it is ncssary to spcify an aprtur or intrval low boundary valu for ρ (.g. 0.85). If it stands ρ < 0.85; >, thn th status could b tratd as idntifid. 5. Exampl for idntification In th nxt xampl thr is dmonstratd an approach of corrlation mthod ralization for idntification of th scn status B for,,m using a transmittr with an array of snsors S i for i,,n. For simplicity, lt on scn status b charactrizd by ust on physical quantity. Lt snsors in th array hav non-zro cross snsitivitis and th numbr of th snsors b n 3, so that it holds n < m. Th snsor transfr charactristics ar nd ordr polynomial functions givn by y i ai + x + x (9) whr a i is y-axis shift, x is th masurd quantity [\%], so th non-linaritis ar idntical. (6) 4

5 Th graphical intrprtations of transfr charactristics of snsors S i in dpndnc on th scn statuss B ar dpictd in Figurs 4 to 6. a group of rfrnc pattrns that will b corrlatd with th actual pattrn. Th rfrnc pattrns (Tab.) ar achivd following th approach prsntd in sction "Corrlation mthod". For xampl, lt us tak a look at crating th rfrnc pattrn for status B in masurmnts: Snsor S : k k Snsor S : k k Snsor S 3 :, 8,6 Fig.4 Transfr charactristics of snsor S 3 3k k, Consquntly, it is ncssary to rmov th bias from th vctor lmnts calculatd abov. Th valu of th bias is calculatd following (6) and th rsult is 3 i 3 i 3,933 Such a signal vctor with lmnts without bias is th rfrnc pattrn ndd for idntifying status B. In this mannr, th othr pattrns ar cratd too. Tab. Th rfrnc pattrns for scn status B i S S S 3 R (B ) -,833 4,667 -,833 R (B ),500 -,000-0,500 R 3 (B 3 ) -4,667,833,833 R 4 (B 4 ),667 -,833-0,833 Fig.5 Transfr charactristics of snsor S Th graphical rprsntation of rfrnc pattrns is shown in Figur 7. Fig.6 Transfr charactristics of snsor S 3 Calibration procss At first, it is ncssary to choos all scn statuss that should b idntifid. All othr scn statuss will b valuatd as unidntifid. Th rsult of th calibration procss is Fig.7 Th rfrnc pattrns for th stats B i Evaluation procss For xampl, lt th scn b in status B and th quantity charactrizd this stat b in 0% of its rang. Lt signals from snsor array b masurd with prcision %. Ths signals rprsnt signal vctor 5

6 A [4,69,,67] Rfrncs Th lmnts of this vctor contain a bias that has to b rmovd by th known approach listd abov 3 a 3 i a i 3,6. Now, if all ndd paramtrs ar known, th corrlation cofficint can b valuatd for all rfrnc pattrns and th actual pattrn ρ 0,56888, ρ 0,999895, ρ3 0,94684, ρ 0, If th aprtur wr 0.99, idntification would b succssfuly don aftr valuation ρ. But according to th nxt valuatd cofficints, th rsult is fully ls. Also cofficint ρ 4 mts th givn critrion. Hnc, it should b dtrmind which cofficint valu is closr to. Th rsult is that scn is in status B 4. But that is a wrong rsult, bcaus th scn has bn in status B. Th similarity of pattrns R and R 4 is so clos that it causs wrong rsults. On of possibl solutions, in ordr to avoid such cass, is providing a mor prcis masurmnt. Conclusion Undoubtdly, smart snsor systms find thir wid rang of us in automation of many industry sctors. Thir qualitativ proprtis ar improvd thanks to nw mthods for tasks of information pr-procssing. Th articl on th prsntd xampl cannot, of cours, find out all solutions for all possibl problms that can aris hr. But it is a good xampl for any solutions of idntification purposs, whr most of th mthods can confirm thir bhaviours and b compard with ach othr. In this articl thr wr prsntd only th so-calld classic mthods using classic mathmatical oprations, which tak som advantags and disadvantags in snsor tchnology. Th main disadvantag ar larg computational powr dmands prohibiting th application of classic mthods in many of cass. Thus, limitation of ralization of primary information procssing tasks in smart snsor systms rsults from th intllignt unit computational powr. Computational tchnology and microlctronics dvlopmnt thrfor play an important rol hr. Rquirmnts on a largr numbr of snsors and highr rat of snsing caus a nd for much mor fficint mthods that hav ability to procss largr amount of data in ral tim. Som possibl solutions using artificial intllignc mans will b prsntd in th nxt part. [] Šturcl,J., Balogh,R.: Smart Snsors in Control Systms. In: Intrnational Carpathian Control Confrnc '000: Podbanské, Slovak Rpublic, , pp (in English) [] Šturcl,J., Toman,M.: Smart Snsors in Robotics. In: Cybrntics and Informatics, Slovak Acadmy of Scinc: Bratislava, Slovak Rpublic, 995, pp. -8. (In English) [3] Šturcl, J.: Diagnostics and Autocalibration in Smart Snsor Systms. In: 3rd Intrnational Symposium "Topical Qustions of Taching Mchatronics": očovc, Slovak Rpublic, pp (in Slovak) [4] Šturcl, J.: Information Procssing in Smart Snsor Systms. In: ŘÍP 96 Procss Control: Horní Bčva, Czch Rpublic, 996, pp (in English) [5] Šturcl,J., Balogh,R.: Mthods of Signal Procssing in Smart Snsor Systms. In: 3rd Scintific-Tchnical Confrnc with Intrnat. Participation Procss Control ŘÍP 98,V.: outy nad Dsnou, Czch Rpublic, , pp (in English) [6] Šturcl, J.: Mthod of Effctiv Ralisation of Approximation of Snsor Charactristics in µc. In: Procss Control 00: Štrbské Plso, Slovak Rpublic, CD-ROM. (in English) [7] Šturcl,J., Miš,M., Balogh,R.: Using Splin Polynominals for Approximation of Snsor Charactristics. In: 4th Intrnational Scintific-Tchnical Confrnc Procss Control 000: outy nad Dsnou, Czch Rpublic, CD-Rom. (in English) [8] Göpl,W., Hss,J., Zml,J.N.: Snsors; Fundamntals and Gnral Aspcts. VCH Publishrs, 989. (in English) Doc. Ing. Ján Šturcl, PhD. Slovak Univrsity of Tchnology Faculty of Elctrical Enginring and Information Tchnology Dpartmnt of Automation and Control Ilkovičova Bratislava Tl.: ( ) an.sturcl@stuba.sk 6

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Higher order derivatives Robrto s Nots on Diffrntial Calculus Chaptr 4: Basic diffrntiation ruls Sction 7 Highr ordr drivativs What you nd to know alrady: Basic diffrntiation ruls. What you can larn hr: How to rpat th procss of