AN ADAPTIVE ALGORITHM FOR THE MEASUREMENT DATA COMPRESSION

Transcription

1 XVI IMEKO Worl Cogress Measuremet - Supports Sciece - Improves Techology - Protects Eviromet... a Provies Employmet - Now a i the Future Viea, AUSTRIA,, September 5-8 AN ADAPTIVE ALGORITHM FOR THE MEASUREMENT DATA COMPRESSION W. Gawezki Departmet of Istrumetatio a Measuremet Uiversity of Miig a Metallurgy, al. Mickiewicza 3, 3-59 Krakow, Pola Abstract: A proposal a lossless aaptive compressio algorithm to be use i cotiuous measuremet ata recorig is presete i this paper. The operatio implemete by the algorithm ca be terme the sigal compressio bee uatizatio. Although the algorithm itself is iertialess, its efficiecy epes o the yamics of the measuremet sigal compressio. Thaks to the aaptatio of the compressio algorithm parameters to the variability characteristics (i.e. to the yamics) of the sigals recore, the compressio level ca be optimise. The algorithm, metho the aaptatio of the algorithm parameters a the compressio effect obtaie exemplary measuremet sigals are presete i this paper. Keywors: ata compressio, ata acuisitio, aaptive compressio algorithm DEFINITION OF THE PROBLEM Seekig the compressio algorithms to be applie the cotiuous measuremet ata recorig is coecte with the ee a solutio to the problem of the cotiuous log-term a simultaeous loggig of the measuremet sigal static (or low-variable) a yamic compoets with o loss of imatio essetial from the measuremet purpose poit of view. There are measure physical uatities of the prevailig static or a low-variable character of their variability a with yamic compoets occurrig at certai time istats or time perios. For example, the strai state of a rock mass i the mie is of a static or low-variable character uer ormal operatig coitios a of a yamic character urig rock bursts or blastig. I such cases, it is ecessary to register both compoets, the uasi-static a yamic oe, which is i geeral cotraictory to the relatio betwee a relatively short time of sigal samplig regarig the yamic compoet measuremet, a the reuiremet the registerig evice memory capacity, ecessary both cotiuous a log-term moitorig. The applicatio of a cotiuous, pipelie, ata loggig with samplig freuecy ajuste to the yamic compoet measuremet, a the simultaeous compressio of the measuremet ata ca be a solutio to the problem. The existig ata compressio algorithms are well recogise, aalyse a implemete the ees of the image a sou processig [,]. Regarig the coitios the compressio of the pipelie registere measuremet ata a the fact that the ature a properties of the measuremet sigals of the physical uatities as well as the sigal loggig uality reuiremets iffer from those the vieo a sou sigals, this results i the fact that ot all existig algorithms ca be irectly applie a a aalysis their metrological properties is ecessary. The measuremet sigal compressio of a physical uality ca result i a substatial reuctio of the amout of the imatio memorise; a the sigal compressio bee uatizatio ca be oe of the methos. The problem of sigal compressio bee uatizatio is kow i the fiel of sou sigal trasmissio, where the emphasisig of weak sigals with the simultaeous compressio of strog sigals eables a costat relative uatizatio error to be obtaie. The operatio of the above-metioe algorithms cosists i the oe-to-oe iertialess a oliear processig operatios where logarithmic fuctios are use. The applicatio of these algorithms to compressio i the cotiuous measuremet sigal loggig process oes ot prouces the expecte results. The authors have propose i the paper aother versio of the iertialess lossless aaptive algorithm the compressio bee uatizatio which leas to a reuctio i the absolute a relative uatizatio errors both weak a strog sigals at the uchage uatizator resolutio (the processig accuracy improvemet effect). I other wors, which - at the reuce uatizator resolutio - allows the preservatio of the assume iput uatizatio error (the effect of the registere measuremet ata lossless compressio). Although the algorithm itself is iertialess, its efficiecy epes o the yamics of the measuremet sigal uergoig compressio. Thaks to

2 XVI IMEKO Worl Cogress Measuremet - Supports Sciece - Improves Techology - Protects Eviromet... a Provies Employmet - Now a i the Future Viea, AUSTRIA,, September 5-8 the aaptatio of the compressio algorithm parameters to the variability characteristics (i.e. to the yamics) of the sigals recore, the compressio level ca be optimise. AN ADAPTIVE COMPRESSION ALGORITHM The propose compressio algorithm cosists i the iertialess, lossless a oliear coversio of the measure sigal u(t) bee the uatizatio. This coversio ca be carrie out i a aalogue or igital way to the measure sigal u() sample a uatize with much higher resolutio accorig to the followig coer fuctio: u ( ) ( u( ) u( ) ) m( ),K () a u () u() () where the multiplier m() is expresse as: M ( ) a M() is a iteger efie as: m( ),,K M ( ) log M () log U z u( ) u( ) U z u(),k a meetig a aitioal costrait: M ( ) N (5) where: U z measurig rage of the sigal u() recorig system. The umber N of bits results irectly from the assume limitig uatizatio error δ / N with which the measure sigal u() is recore. The compressio algorithm works as follows. For a specifie sample of the sigal u(), a ifferece is etermie betwee its value a the sample value just bee (relatioships () a ()). The ifferece is the multiplie by the coefficiet m() which is etermie accorig to euatios (3) through (5). It is easy to see that the value of m() epes o the sigal yamics: the larger the ifferece betwee the values of the successive samples, the smaller if the value of the multiplier m(). This results from the fact that the sigal u () obtaie from such a coversios has to be cotaie withi the give measurig rage U z. It shoul be ote that the multiplier M() etermie accorig to (4) a very small (eve almost zero) ifferece betwee the values of the successive samples will assume a large value exceeig cosierably N. The limitatio (5) is theree ecessary from the operatio correctess a compressio algorithm efficiecy poit of view. The m()-fol sigal ifferece amplificatio causes that the uatizatio error will be reuce m() times if the uatizator of uchage resolutio is applie i the further part of the chael (or, i other wors: a uatizator of resolutio smaller by M() bits may be applie, which will result i the ecrease by M() of the umber of bits ecessary recorig values of the sigal u() while the uchage uatizatio error of the compressig system compare to the o-compressig system). A block iagram the aaptive compressio algorithm uer cosieratio is presete i Fig.. After beig sample, the measure sigal u(t) is compresse followig the relatioships () through (5) a the resultig sigal u () is uatize i a (N-M())-bit uatizator. We get this way the compresse sigal u (). Base o (5), we ow see that the limit umber M()N - bits we get a -bit uatizator. Sigal reprouctio reuires usig a ecoig proceure accorig to the ecoer fuctio: u u u () () m() ( ) u u ( ) ( ) + m( ),K where: u () sigal u () uatize i a (N-M())-bit uatizator u () sigal obtaie after ecoig. The aitioal N-bit uatizator use i the coer chael a realisig the uatizatio of the referece sigal u(-) is ecessary because of the possibility of the correct ecoig of the sigal (3) (4) (6)

3 XVI IMEKO Worl Cogress Measuremet - Supports Sciece - Improves Techology - Protects Eviromet... a Provies Employmet - Now a i the Future Viea, AUSTRIA,, September 5-8 u (). The value of the u () is etermie base o the value of the ifferece sigal u () by aig the value of a N-bit-uatize sigal u (-) (6). u(t) S&H u() Acc. to () (5) u() (N-M()) - bit u() QUANTIZATOR MEMORY u(-) N - bit QUANTIZATOR u() Acc. to (6) u() MEMORY u(-) Figure. Block iagram the aaptive compressio algorithm As was metioe bee, the aaptatio of the compressio parameter M() to the variability characteristics of the recore sigals was use, which results i a automatic optimisatio of the compressio ratio. The iffereces betwee the successive samples are small costat or slowchagig values of the sigal u(); they icrease with sigal freuecy. As ca be see i (4), the optimum compressio parameter M() is selecte epeig o a value of the ifferece. Let us efie the compressio ratio G k the presete aaptive algorithm, referrig the umber Ψ of imatio uits of a registere o-compresse sigal, Ψ(u * ), to the umber of imatio uits of a registere compresse sigal, Ψ(u ): G k Ψ( u * ) Ψ( u ) + P Takig ito accout euatios () through (6), the compressio ratio ca be the expresse by the relatioship: G P N k P P N M ( ) + P where: P umber of registere samples of the sigal u(), N umber of bits results from the assume limitig uatizatio error δ / N The value of P i the eomiator of euatios (7) a (8) results from the ecessity of usig a -bit separator isolatig the successive values of the biary recore compresse ata u (). This is because the ata recorig fiel with is variable a euals to N-M(). Thaks to the use of the separator, both the value of the compresse ata ca be rea a the value of the assige multiplier M() ca be calculate. Aalysig the aopte criterio of the compressio ratio (8) it ca be otice e.g. that the accorig to (8) a M()N a the uasi-static sigal, the compressio gai will be the largest a will te to N/. The aalysis of the propose compressio algorithm sigals of other yamic properties shoul be carrie out by simulatio. (7) (8)

4 XVI IMEKO Worl Cogress Measuremet - Supports Sciece - Improves Techology - Protects Eviromet... a Provies Employmet - Now a i the Future Viea, AUSTRIA,, September u().5 u() u () u () M() M() u () u () u ()-u(). -. u ()-u() Figure. Illustrative iscrete-time courses Figure 3. Illustrative iscrete-time courses obtaie urig type a sigal compressio obtaie urig type b sigal compressio

5 3 EXAMPLE OF ALGORITHM OPERATION To illustrate the way the aaptive algorithm operates, the compressio of two selecte sigals of various yamic properties was mae. The sigals were escribe with the followig fuctios: sigal a : u() exp(- T) si( π f T) sigal b : u().75 si( π f T) where: T.s is a samplig perio, [, 5] The followig parameters of the simulatio experimet were assume: U z, N, P 5, f Hz, XVI IMEKO Worl Cogress Measuremet - Supports Sciece - Improves Techology - Protects Eviromet... a Provies Employmet - Now a i the Future Viea, AUSTRIA,, September 5-8 The research was carrie out with the Matlab simulatio software [5] accorig to the scheme presete i Fig. etermiig the compressio ratio i accorace with (8). Illustrative iscrete-time courses characterisig the compressio algorithm operatig way are presete i Figs. a 3. Deotatios i both figures are cosistet with those i Fig.. The values of the compressio ratio etermie accorig to (8) ivestigate sigals are respectively: G k 5.5 G k.48 sigal a, sigal b. Base o the obtaie illustrative values of the compressio ratio, it shoul be state that better effects are obtaie slower sigals a also that the preicte applicatio area the algorithm referre just to this type sigals. It shoul be stresse that i the paper a iea of a iertialess a lossless aaptive compressio algorithm was presete, which ca be of special importace i applicatios of cotiuous a accurate measuremet ata recorig. REFERENCES [] V. Bhaskara, K. Kostatiies, Image a Vieo Compressio Staars. Algorithms a Architectures. Kluwer Acaemic Publishers 997 [] N.S. Jayat, P. Noll, Digital Coig of Wavems. Priciples a Applicatios to Speech a Vieo. Pretice-Hall, Ic. Eglewoo Cliffs, New Jersey 984 [3] Gawêzki W.: New Compressio Algorithm Cotiuous Recorig of Measuremet Data. IX Sympozjum Moelowaie i Symulacja Systemów Pomiarowych, Kryica, Pola 999 (i polish). [4] W. Gawezki, J. Jurkiewicz, Ivestigatio o the Limit Quatizatio Error a Geeral Case of a Three-Voltage Measuremet Metho Ratiometric Output Sesors. IEEE Coferece IMTC 99, Veice, Italy, May 4-6, 999 [5] MATLAB & SIMULINK Wiows - User s Guie The MathWorks, Ic. AUTHOR: Waclaw GAWEDZKI, Uiversity of Miig a Metallurgy, Departmet of Istrumetatio a Measuremet, al. Mickiewicza 3, 3-59 Krakow, Pola, Phoe: , Fax: , waga@galaxy.uci.agh.eu.pl