Increasing Measurement Accuracy via Corrective Filtering in Digital Signal Processing

Transcription

1 ISSN(Online): ISSN (Prin): Engineering and echnology (An ISO 397: 7 Cerified Organizaion) Vol. 6, Issue 5, ay 7 Increasing easuremen Accuracy via Correcive Filering in Digial Signal Processing ehdiyeva A *, Guliyeva SV Azerbaijan Sae Oil and Indusry Universiy, Azerbaijan Absrac: his paper considers he problem of einaing he errors ha arise in he phase of processing, aking ino accoun he increased demand for digial signal processing of he measuremen resuls in he oil and gas indusry. Invesigaed he issues around correcive filering and discree averaging in digial signal processing. Keywords: Non-sinusoidal signal, Specrum of signal, ahemaical epressions, Noise and inerference, Digial measuremen, Average value. I. INRODUCION Any measured value, for eample, he mains volage is a sine wave signal. As a par of his signal has only one harmonic. As a resul, he analog measuremen value we ge a non-sinusoidal signal. I is a sinusoid having a composiion furher odd harmonics. he causes of hese harmonics are noise and inerference imposed on he main signal. herefore, he measured signals, in mos cases (8%) are non-sinusoidal [,]. Curves Insan coninuous signal values are mos useful, bu no always foreseeable. herefore, for conrol and analysis of conrolled processes and faciliies is of grea imporance in he deerminaion of real-ime inegral signal parameers (ISP). Recen characerize he oal amoun of maer and energy o be made and received in he producion for a cerain period of ime, regime performance and feaures, is he average of he measured values, ec. Specificiy deerminaion ISP digial mehods and ools are o perform discree averaging (DA) or discree inegraion (DI) values, coninually changing over ime. Among digial echniques ISP measuremens are widely used so-called mehod of digial processing of he resuls of direc measuremens of insananeous values of he signal during averaging (inegraion). In recen years, ineres in his mehod has increased significanly, due o he possibiliy of he inroducion of compuing power in he measuremen channels in dealing wih his kind of measuremen asks. his problem becomes even more complicaed when IRS digial measuremens of elecrical signals of comple shape (non-sinusoidal signals). Neverheless, he wellknown advanages of elecrical conrol and measuremen mehods of physical quaniies conribue o more widespread primary daa converers wih he oupus in he form of fied and variable currens and volages. AC signals are more informaive, and in some cases are he only possible form of obaining measuremen daa, paricularly in he objecs of producion and conversion of elecrical energy. In he able shows he mahemaical epressions o define commonly used in pracice, measuremens of heir own and muual ISP [3-]. In he ransiion from he coninuous inegraion of he numerical algorihms using he able, i is necessary o draw aenion o he fac ha almos all he algorihms used by he remoe operaor. Copyrigh o IJIRSE

2 ISSN(Online): ISSN (Prin): Engineering and echnology (An ISO 397: 7 Cerified Organizaion) Vol. 6, Issue 5, ay 7 IRS he curren average value Average value Average recified value ean square value Fourier coefficien Shape facor able. Characerisic own IPS. Non-random signals he formula for deermining he IRS cp / / () () CB / () C ck n ф / / K ck / R a n d o m s i g n a l s () () ()e CB jn edian value (firs-order momen) () he mean square value (second-order momen) / /,, 5 () () Average square value ( 5, D (, 5 ck ) D () Dispersion Specral funcion S ( ) / ()e j {() ) Auocorrelaion funcion R ( ) / ()( ) Power specrum densiy G ( ) R ( )e j d [()]} o perform he conrol class of coninuous funcions С,] uses quadraure formula of he form: i ~ (m) [ I y(i ), () Copyrigh o IJIRSE

3 ISSN(Online): ISSN (Prin): Engineering and echnology Where, ime sampling sep. (An ISO 397: 7 Cerified Organizaion) Vol. 6, Issue 5, ay 7 Consider he case where a non-sinusoidal signal ineracs wih a random signal cenered; in paricular, find ou how he specrum of he produc of hese signals [-5]. As a non-sinusoidal signal source acceps a sine wave superimposed on i 3 odd harmonics of he form: N y( ik ) sin( kn ), N 6, n Where - he carrier frequency of he signal, Т - sampling frequency ( = /3), к - discree sample numbers, n - harmonic number. As a random signal cenered considered uniformly disribued on he inerval [, ] signal generaed by he buil-in alab rand. he specrum of he original signal is calculaed in alab sofware environmen using a fas Fourier ransform-funcion ff. Fig. (a, b) shows he original signals in Fig. (v, q) - specrum of he original signals. Fig.. Specrum of inpu signal a) random signal (inerference); b) a non-sinusoidal signal; v) non-sinusoidal signal specrum; q) specrum of a random signal. Furher, he resuling produc signal is non-sinusoidal and random signals received resuling signal whose specrum is shown in Fig. a. As seen in Fig. a, he resulan specrum conains in is srucure a cerain number of harmonics (3). o suppress hese harmonics we used a mehod of discree averaging he resuling signal a regular inervals. he calculaions shown in Fig. b show ha in he specrum significanly reduced he impac of addiional harmonics. heir ampliude was he order of, ha is, he suppression of he specrum was almos, imes. And i shows he possibiliies of correcing discree averaging operaor wih respec o he non-sinusoidal signals. Fig.. Specrum significanly reduced he impac of addiional harmonics a) a non-sinusoidal signal specrum; b) he discree signal specrum afer averaging. Copyrigh o IJIRSE

4 ISSN(Online): ISSN (Prin): Engineering and echnology (An ISO 397: 7 Cerified Organizaion) Vol. 6, Issue 5, ay 7 A similar calculaion was made by us in relaion o he non-sinusoidal signal of he form () and sysemaic error of abou described funcion of he form: j ( k ) a jk, () j where k - discree samples bias а j - polynomial coefficiens describing his slowly changing error. Figs. 3 (a, b) and 3 (c, d) shows he original signals and heir specra - range of bias and non-sinusoidal signal. Fig. 4a shows he specrum of he resuling signal is equal o he produc of a non-sinusoidal signal, and sysemaic errors. he resul of he conrol in relaion o he resuling signal is shown in Fig. 4b. Fig. 3. Iniial specrum of signals and heir specra-range of bias and non-sinusoidal signal. a) sysemaic error; b) a non-sinusoidal signal; v) nonsinusoidal signal specrum; q) range of sysemaic errors. Fig. 4. a) he specrum of he inpu signal; b) specrum afer digial averaging. As can be seen from his figure, he specrum as a resul signal of he discree averaging significanly decreased. Comparaive analysis of he resuls of he eperimen wih he random and sysemaic errors shows ha i is beer suppressed bias. Consequenly, discree averaging operaor, applied o boh ypes of error is a correcion wih respec o all ypes of errors. hus, one can say ha he digial averaging operaor applied o boh ypes of error correcion is o all kinds of errors. his has been proven wih simulaions in alab program. REFERENCES []. Beralmio, G. Sapiro, V. Caselles, and C. Balleser, Image inpaining, in Proc. SIGGRAPH, pp ,. [] A. Criminisi, P. Perez, and K. oyama, Region filling and objec removal by eemplar-based image inpaining., IEEE ransacions on Image Processing, vol. 3, no.9, pp., 4. [3] arcelo Beralmio, Luminia Vese, Guillermo Sapiro, Sanley Osher, Simulaneous Srucure and eure Image Inpaining, IEEE ransacions On Image Processing, vol., No. 8, 3. [4] ТА. Aliyev, Robus echnology wih Analysis of Inerference in Signal Processing. New-York, pp.99, 3. [5] PA. Aruyunov, heory and Applicaion of algorihmic measuremens..: Energoaomizda, pp. 56, 99. Copyrigh o IJIRSE

5 ISSN(Online): ISSN (Prin): Engineering and echnology (An ISO 397: 7 Cerified Organizaion) Vol. 6, Issue 5, ay 7 [6] OD. Goldberg, I. Abdullayev, AN. Abiyev, Auomaion of he conrol parameers and diagnosics of inducion moors,. Energoaomizda, pp. 6, 999. [7] I. Abdullayev, NR. Allahverdiyeva, Correcion filer in he means of measuremen, Baku: Chashiogli, pp.84, 5. [8] AB. Sergienko, Digial signal processing. SPb.: Peer,, pp. 64, 5. [9] LA. Rams, Level quanizaion and sampling ime in digial conrol sysems, Energoaomizda, pp. 34, 99. [] VA. Bruchanov, ehods of improving he accuracy of measuremens in indusry, Publishing House of Sandards,. pp.8, 99. [] J. Pbenley, Principles of easuremens Sysems. NewYork. s, pp. 4p, 983. [] A. ehdiyevа Esablishmen of informaion-measuring sysems o improve he accuracy of digial processing of he measuring informaion, he modern scienific bullein. Series: Engineering. Vol. 5, no 89, Belgorod. pp. 6-63, 3. [3] A. ehdiyeva Conversion and iniial processing errors of measuremen resuls, American Journal of Circuis, Sysems and Signal Processing. No3, pp.56-59, 5. [4] A. ehdiyeva, Increase of accuracy of measuremens a he oil and gas enerprises, aerial for he VIII Inernaional scienific pracical conference. odern informaion echnology. pp. 7-5, 3. [5] A.. ehdiyeva, E.K. ehdizadə Informaion-measuremen sysem developmen for conrolling of parameers of measuremen, Global Sandard Journal., Vol, no., рр. 3-33, 4. Copyrigh o IJIRSE