Amercan Journal of Crcuts, Systems and Sgnal Processng Vol. 4, No. 2, 2018, pp. 23-37 http://www.ascence.org/journal/ajcssp ISSN: 2381-7194 (Prnt); ISSN: 2381-7208 (Onlne) Correctve Fltraton n the Processng of Electrcal Sgnals to Improve Measurement Accuracy Almaz Mehdyeva * Control and System Engneerng Department, Azerbajan State Ol and Industry Unversty, Baku, Azerbajan Abstract The research s devoted to the constructon of an nverse correcton flter, to solate a useful sgnal that has been exposed to a drect flter. The structure of the reverse flter for each drect flter s ndvdual and calculated based on the parameters of the drect flter. So, for a hgh-frequency fnte dfference flter, the flter of a fnte sum s nverse. The orders of the forward and reverse flters must be coordnated. Usng the software MATLAB, we assembled the crcut of the system, and nvestgated the effect of the reverse flter on the output sgnal of the system. The synthess of the most optmal low-frequency flter havng non-nteger coeffcents s carred out. In a cascade wth a fnte-dfference flter, t suppresses all components of the error n the entre frequency band of the measurng sgnal. Keywords Measurng System, Measurement Experment, Measurement Informaton, Dgtal Sgnal Processng, Correctng Fltraton, Reverse Flter, Flterng Algorthms, Adaptve Flters Receved: July 24, 2018 / Accepted: August 14, 2018 / Publshed onlne: August 31, 2018 @ 2018 The Authors. Publshed by Amercan Insttute of Scence. Ths Open Access artcle s under the CC BY lcense. http://creatvecommons.org/lcenses/by/4.0/ 1. Introducton The problem of nterference n a sgnal contanng also useful nformaton about the observed process s beng combated n varous ways, ncludng usng flterng algorthms. The use of measurng devces (for example, moton sensors) coexsts wth the problem of nterference n the sgnal. Analyss of real processes of movement of a well-known nature wth an accessble physcal model s accompaned by the need to receve ndcatons wthout nterference. They resort to sgnal flterng, whch mples that nformaton about sgnals and nterference, for example, ther statstcal models (lnearty of models, statonarty and normalty) s avalable to some extent. However, n practce, statstcal nformaton s not always known. A specal place among the algorthms ntended for the dentfcaton of a useful sgnal s occuped by "adaptve flters - systems whose parameters adapt to a sgnal wth a predetermned statstcal model". In other words, the flters transform the system, changng ts states dependng on the statstcal parameters. For example, the Kalman Flter s an adaptve flter that allows you to flter data usng nformaton about the physcs of the process [5-7]. The research topc s relevant n the scentfc feld. The subject of the study s to reduce the amount of nose and nose by adaptng the sensor readngs, applyng flters to mprove the accuracy of the readngs. Knowledge of the physcal law of the observed process helps when choosng a flterng algorthm. The latter fact and the undenable convenence of usng flters make researchers resort to the use of flters to solate a useful sgnal. There are also other approaches to solvng the problem of nterference n the sensor readngs. But, for example, by averagng the obtaned ndcatons, as proposed n the method of least squares, t wll not be possble to analyze and evaluate the state of dynamcal systems. Methods such as the least squares method can be appled when readngs are * Correspondng author E-mal address:
24 Almaz Mehdyeva: Correctve Fltraton n the Processng of Electrcal Sgnals to Improve Measurement Accuracy avalable from the start pont to the end of the readng. At the same tme, all the accumulated reports are processed at once, and ths can cause the processng tme to ncrease, whch s not always permssble. Of all the methods used for dgtal sgnal processng, the most mportant s dgtal flterng. In the past, nterest n t has been lmted to theoretcal research, but recently t has been used n many mportant practcal applcatons for processng the most complex sgnals, due to the avalablty of effectve and relatvely smple methods for constructng flters; success n the development of hardware and software for computers, especally wth the advent of mcroprocessors and mcro-computers, and the creaton of fast matrx processors that are used as perpherals of computng systems or as the man processng system [1-3,]. As a result, dgtal flterng has been used recently n a varety of areas, and the task of solatng a useful sgnal from a mxture s an urgent task. Therefore, wth respect to real measurng nstruments, t s not optmal, but quas-optmal (by some crtera) correctve flterng that s achevable. Wth ths approach to flterng, takng nto account the varety of structures, algorthms and practcal mplementaton of the components of the measurng channel, t s advsable to orent certan methods of correctng the flterng to the forms of representaton of the measurng sgnal (analog, dgtal, dgtal). Therefore, t s possble to dstngush three man varetes of correctve fltraton dependng on the subtract n whch t s realzed - contnuous, dscrete and dgtal. 2. Formulaton of the Problem Over the past decades, dgtal sgnal processng has become very mportant because now they not only replace classcal analog methods n many tradtonal areas of technology but are also used n many new areas. Of all the methods used for dgtal sgnal processng, the most mportant s dgtal flterng. In the past, nterest n t has been lmted to theoretcal research, but recently t has been used n many mportant practcal applcatons for processng the most complex sgnals. Ths fact can be explaned by the followng reasons: 1. the avalablty of effectve and relatvely smple methods for constructng flters; 2. huge achevements n the feld of hgh-ntegraton mcrocrcut technology for multplers, adders and memores wth ncreased maxmum operatng frequency and n the development of new elements; 3. success n the development of hardware and software of computers, especally wth the advent of mcroprocessors, and the creaton of fast matrx processors that are used as perpherals of computer systems or as the man processng system. As a result of these successes, dgtal flterng has recently been used n a wde varety of areas, such as rado communcaton, rado and sonar, physcal expermentaton, bomedcal research, aerospace systems, mneral exploraton usng satelltes, etc. Effcency Correctve flterng, characterzed by the degree of proxmty of the measurement result to the true value of the nformatve parameter of the measurng sgnal, determnes the achevable accuracy of the IR, whch most objectvely reflects the effectveness of the entre dgtal measurng nstrument. When settng and solvng problems, correctve flterng should take nto account the followng crcumstances: 1. the nput sgnal of each subtract can be represented as an addtve mxture of useful sgnal and nose, the latter ncludng systematc and random components; 2. a pror nformaton about the useful sgnal and nose components of the error s ncomplete because of ther probablstc-statstcal nature and varablty n the condtons of the functonng of the measurng channel; 3. due to the specfcs of the tasks of transformaton and processng of measurement nformaton, the components of the measurng channel contan components wth lmted nformaton, metrologcal, dynamc and operatonal characterstcs; 4. elements of correctve fltraton ntroduced nto separate sub-contracts have dfferent flterng propertes and consequences, whch can lead to the accumulaton and transformaton of error along the measurng channel; 5. most operators of dgtal processng of measurng nformaton are lnear, and therefore they are senstve to both components of the processed addtve mxture (sgnal + nose). 3. Resolvng the Problem The development of the theory of automatc control and the practce of creatng automatc systems over the past decades s nseparably lnked wth the dea of usng mcroprocessors n the processes of measurng and processng controlled parameters of objects [10-11]. The desre to desgn automatc systems that perform processng or measurement n the best way leads often to rather complex algorthms. It s clear that the result of these complex algorthms, as well as the mperfecton of the techncal means used, are the cause of the appearance of varous knds of errors and nose that can be represented as the dfference between the measurement result and the true value of the measured quantty:
Amercan Journal of Crcuts, Systems and Sgnal Processng Vol. 4, No. 2, 2018, pp. 23-27 25 where, [ xt ( )] и [ xt ( )] [ ] [ ] ε ( t) = θ xt ( ) θ xt ( ), (1) θ θ respectvely, the true and "nosy" values of the characterstc (parameter) of the process x (t), estmated under the measurement experment. Takng nto account that most of the real errors are descrbed by nonstatonary ones n mathematcal expectaton, but statonary by dsperson and autocorrelaton functon by random processes, we present the model of the basc error of the measurement system n the followng form: or: 0 ε( t) = ε ( t) + ε ( t), (2) 0 0 0 l h ε( t) = ε ( t) + ε ( t) + ε ( t) + ε, (3) where ε ( t) the systematc component of the error, whch s a non-statonary quantty (to t all the nonstatonary error s attrbuted); 0 0 l h ε ( t) и ε ( t) Low-frequency and hghfrequency components, whch are statonary centered random processes; 0 ε a random centered value to whch, for example, the analog-to-dgtal converter quantzaton nose, the computng nose of the computng devces. Expresson (1) defnes the total (resultng) error, whch conssts of the components that depend on the propertes of the measurement object, the sgnal x(t) and the measured characterstc, the measurement method, the algorthm mplementaton features, the measurement experment, the object nteracton, and the exchange of measurement nformaton. In the well-known scentfc works and normatve-techncal documents varous models of both the resultant error and ts characterstc components are gven. In the partal classfcatons of errors, two approaches are dstngushed. One approach s based on the choce as a classfcaton feature, the factor causng the appearance of errors. Ths, for example, methodologcal and nstrumental errors, errors due to the fnte sze of the sample, etc. Methodcal errors are nherent n the accepted method of measurement. These nclude, for example, the quantzaton error n the level, the error due to the power consumpton by the nstrument from the source of the measured parameter, etc. The quantzaton error (nose) s typcal for almost all dgtal measurng nstruments, automatc control systems, communcaton systems, etc. An enormous amount of work has been devoted to the study of the statstcal propertes and characterstcs of quantzaton nose, and also to ther nfluence on the measurement result. In these papers, the asymptotc propertes of the process of quantzaton of contnuous sgnals by level are determned and estmates of the parameters of the lmtng pulse (dgtal) system usng a quantzer wth a suffcently large number of quantzaton levels are obtaned. Under the second approach, the types of error, the nature of ther manfestaton n the measurement process, are taken for classfcaton characterstcs. Ths s a systematc and random error. The study of the components of error, correlated wth the factors that determne them, allows us to dentfy the domnant causes of errors and dentfy ways to suppress them. In the study of errors, we subsequently use the second method of ther classfcaton. In rough measurements, t s assumed that the random error s ndependent and centered, and the systematc error s a constant or regularly changng. For a random component, ths approach neglects that ts characterstcs can vary wth tme, and several error components can be stochastcally nterrelated. Wth more strngent requrements for the accuracy of estmates of error values, t s necessary to take nto account ts frequency spectrum or autocorrelaton functon. Among the methods for reducng the correlated (systematc) component of the measurement error, the most effectve are: 1. teratve methods; 2. method of exemplary measures; 3. test methods; 4. methods of auxlary measurements; 5. method of negatve feedback; 6. nvarance method. The measurement process s based on the followng algorthm. In the frst step, the measured value s connected to the nput of the uncorrected measurng devce by means of a dstrbutor (swtch). The nose present at the nput and output of the uncorrected sub-tract of the exchange of measurement nformaton s broadband, multcomponent and should be consdered as nonstatonary random processes (sequences). Therefore, the man requrement for correctve flters s the most complete suppresson of flterable nose sequences for both components: non-statonary and centered statonary. The correctve flter should be of a stoppng nature. Therefore, t must nclude two flters n seres: hghfrequency (for suppressng low-frequency nose) and lowfrequency (for suppressng hgh-frequency nose). Thus, wth respect to suppresson of all components of the resultng error of the measurng channel, the task of correctng flterng s sgnfcantly complcated. Ths dctates the need to develop unversal methods to mprove the accuracy of measurement results. The unversalty of the method of ncreasng accuracy
26 Almaz Mehdyeva: Correctve Fltraton n the Processng of Electrcal Sgnals to Improve Measurement Accuracy s understood as ts relevance to both the characters and the places of appearance and hstory of the components of the error of the measurement result. Combatng the accumulaton of a progressve component of the error leads to the need for ts localzaton and suppresson (as far as possble) wthn the framework of sngle measurements. In the case of the presence of only a centered statonary error n the results of sngle measurements, a powerful tool for suppressng t s the use of the averagng method. However, the combnaton of these two procedures for suppressng errors wthn the framework of one general method of ncreasng accuracy s very problematc. Therefore, t s necessary to dentfy or determne a balanced seres of procedures for localzaton and suppresson of all components of error, whch leads to the development of a unversal method for ncreasng the accuracy of the results of dgtal dynamc measurements: 1. localzaton and suppresson of progressve error wthn sngle measurements; 2. Suppresson of the resdual progressve error and the centered random statonary error at the stage of processng the results of sngle measurements. 3. The stage of processng the results of sngle measurements can be used: 4. when performng ndrect measurements, for example, n flow meterng; 5. wth secondary correctve flterng of measurement data; 6. for statstcal processng of useful and nose nformaton n the process of metrologcal testng and attestaton of the measurng devce; 7. durng the ntal processng of the measurng nformaton (lnearzaton, scalng, etc.). Proceedng from the above, we construct a measurng system wth correctve fltraton. At the nput of the system (Fgure 1), consstng of two flters - the fnte dfference flter and the nverse flter of the fnte sum, a nosy harmonc sgnal s appled [9]. As a useful sgnal, a snusod s taken, whte nose s the nterference, and the ampltude of the useful sgnal s several tmes greater than the nose ampltude. At the nput of the system, the useful sgnal and nterference are added together n order to gve a dstorted sgnal to the nput [4]. The dstorted sgnal s fed to the nput of the drect flter - the fnte dfference flter and to the nput of the graphc dsplay. Snce the snusod s a low-frequency sgnal and the nose s hgh-frequency, the fnte-dfference flter therefore suppresses the low-frequency components of the sgnal, at the output of the drect flter we obtan pure nose, whch s fed to the nput of the reverse flter and to the nput of the graphc dsplay. At the output of the reverse flter, whch restores the ntal useful sgnal, we get a few purfed harmonc sgnal, whch s fed to the nput of the graphc dsplay. To evaluate the effcency of the flter, t s necessary to calculate the flter suppresson coeffcent. For ths, the varances at the nput of the flter cascade and at ts output are calculated, and ther rato s found [8, 12-14]. The more ths rato, the more effectve the flter. Fgure 1. Measurng system wth correctve fltraton. 4. Concluson A revew s made of the exstng methods for ncreasng the accuracy of measurng dynamc quanttes. It s proved that most of them affect only a certan component of the errorthey suppress ether an accdental or systematc error. It s proved that a flter that suppresses both the random and systematc components of the error s a flter of fnte dfference. It s also the most optmal among hgh-frequency flters for the crteron of mnmum root-mean-square devaton of flter output nose. The synthess of the most optmal low-frequency flter havng non-nteger coeffcents s carred out. In a cascade wth a fnte-dfference flter, t
Amercan Journal of Crcuts, Systems and Sgnal Processng Vol. 4, No. 2, 2018, pp. 23-27 27 suppresses all components of the error n the entre frequency band of the measurng sgnal. References [1] Alyev Т. А. Robust Technology wth Analyss of Interference n Sgnal Processng. New-York: Kluwer, 2003. 199 p. [2] Alev T. A. Dgtal Nose Montorng of Defect Orgn/ Sprnger Scence + Busness Meda, New York, 2007, 224 p. [3] Abdullayev I. M., Goldberg O. D. Automaton of the control parameters and dagnostcs of electrcal machn. M. Energoatomzdat, 2007, 160 p. [4] Isayev M. M., Mehdyevа A. M. Combned test-algorthmc method for ncreasng the accuracy of measurements n fuelenergy facltes The 6th Internatonal Conference on Control and Optmzaton wth Industral Applcatons. July 11-13, 2018. Baku, Azerbajan. pp. 169-171. [5] Bollnger J. G., Duffe N. A. Computer Control of Machnes and Processes. Addson-Wesley, 2005. [6] Bolton W. Programmable Logc Controllers: An Introducton, Butterworth-Henemann, 2007. [7] Mamedov R. G., Isayev M. M., Agaev F. G., Mehdzade E. K. Structural-algorthmc methods for ncreasng the accuracy of measurements. "Problems of the ol and gas ndustry." 2010. pp. 229-242. [8] Mehdyev K. A., Mehdyeva A. M., Alyeva L. A. Means to mprove the accuracy of dgtal processng of measurement nformaton. Materals of the Internatonal scentfc and practcal conference. Proceedngs of academc scence- 2014. Sheffeld 2014, pp. 30-32. [9] Yusfov S. I., Mrzoyev O. M., Allahverdyev E. V. Modern automaton technologes for ol and gas resources masterng processes News of Azerbajan Hgher Techncal Schools of the Azerbajan State Ol Academy N 1, 2015. pp. 69-73. [10] Allahverdyeva N. R., Mehdyeva A. M., Mehdzadə E. K. Increase the accuracy of converson and dgtal processng of electrcal sgnals. "Informaton-measurng and control systems". Moscow, 2010, No. 9, vol. 8, pp. 69-74. [11] Isayev M. M. İncreasng accuracy of measurement usng the combned test algorthms. Transactons of Azerbajan Insttutes of Technology. Baku. 2018. 3 (113), pp. 77-84 [12] Mehdyeva A. M. Increase of accuracy of measurements at the ol and gas enterprses. Materal for the VIII Internatonal scentfc practcal conference. Modern nformaton technology. 17-25 February. T 34. Sofa. 2013. pp. 20-21. [13] Mehdyevа A. M. Cumulatve analyss of measurement processes and a correctng fltraton Internatonal Journal of Electronc Engneerng and Computer Scence. Vol. 1, No. 1, 2016, pp. 35-39. [14] Malov R. A., Mehdyevа A. M., Khanmamedova E. A. Correcton of electrc sgnals transmtted on damaged cable lnes «Kluczowe aspekty naukowej dzałalnośc - 2016». Volume 8, pp. 54-56.