A New Data Processing Algorithm for the Standard Meter

Transcription

1 Sensors & Transduers, ol. 162, Issue 1, January 2014, pp Sensors & Transduers 2014 by IFSA Publishing, S. L. hp:// A New Daa Proessing Algorihm for he Sandard Meer Faquan ZHANG, Pingdong GAO, Guofu WANG, Jinai YE Shool of Informaion and Communiaion, Guilin Universiy of Eleroni Tehnology, Guilin , China Tel.: , fax: zhangfq@gue.edu.n Reeived: 9 Oober 2013 /Aeped: 9 January 2014 /Published: 31 January 2014 Absra: A new daa proessing algorihm was proposed agains shoromings in ompensaing algorihm for daa of he sandard meer. Aording o fluid oninuiy, volume daa of flow for he sandard meer were normalized so ha differene values beween alulaing volume and sandard volume were omparable. Using spline inerpolaing algorihm flow differene value of arbirary flow poin was obained. Then his value was hanged ino orresponding value of presen flow poin. Approximae daa o sandard volume was obained by modifying alulaing volume. The algorihm hanged hree-dimensional inerpolaing operaion ino wodimensional inerpolaing operaion and improved auray of inerpolaing operaion and preision of he whole alibraing failiy. Resuls show ha he algorihm is of fully operaional, easy o implemen and effeive. Copyrigh 2014 IFSA Publishing, S. L. Keywords: Sandard meer, Daa proessing, Daa normalizaion, Spline inerpolaion, Dimension. 1. Inroduion The flow meers mus be alibraed by he sandard alibraing failiy before hey leave he manufauring faory, and heir meer parameers were reahed. There are wo ypes of he alibraing failiy inluding he primiive sandard failiy and he ransfer sandard failiy. The former is of he highes preision in all of flow meer devies and i is implemened by he sandard vessel. The laer is omposed of he sandard flow meer whih has exellen repeaabiliy and sabiliy and is alibraed by he primiive sandard failiy. An example of he laer is he flow sandard failiy of sandard meer mehod. Sine he alibraing failiy of sandard vessel need big disposable invesmen and long onsruion period, he flow sandard failiy of sandard meer mehod is uilized by many flow meer manufauring enerprises [1-3]. The sandard meer in he flow sandard failiy mus be alibraed by he sandard vessel alibraing failiy before i is used in he alibraing failiy of sandard meer mehod. Then he sandard meer an be used as ransfer sandard o alibrae he oher heked meer [4, 5]. Sine here is erain deviaion beween he sandard meer and he sandard vessel, alibraing error is ineviable and i degrades auray of he alibraing failiy [6-7]. In order o narrow error inrodued from deviaion beween he sandard meer and he sandard vessel, ompensaing algorihm is adoped o make daa of he sandard meer lose daa of he sandard vessel. In he oher hand, alibraed daa of he sandard meer is only from some finie flow poins, so some inerpolaing algorihms should be used in praial appliaion. Therefore, daa proessing of he sandard meer is inerpolaing operaion among hree parameers inluding flow rae, deviaion value and ime inerval. The inerpolaing operaion aually belongs o hree 184 Arile number P_1768

2 Sensors & Transduers, ol. 162, Issue 1, January 2014, pp dimension inerpolaion. Effeive daa is so less ha error resuled from inerpolaion is larger [8-10]. A new daa proessing algorihm based on flow oninuiy is proposed in he paper. Daa for he sandard meer alibraed by he sandard vessel alibraing failiy is normalized and is of omparabiliy. Thereby hree dimension inerpolaing operaion is hanged ino wo dimension inerpolaing operaion and inerpolaion preision is inreased. This algorihm an effeively derease unerainy from daa of he sandard meer and improve alibraing auray of he whole alibraing failiy. 2. Shoromings of he Exising Daa Compensaing Algorihm for he Sandard Meer When he sandard meer is alibraed by he sandard vessel, only some finie flow poins an be alibraed. Fig. 1 show ha an example ha hree axes are respeively ime, flow rae and flow differene value. Differene value/(m/s) Flow rae/(m/s) Saer plo of original daa Time/s Fig. 1. Calibraed daa of a erain sandard meer. Calibraed daa are some disree poins in hree dimension spae. In praial appliaion inerpolaing operaion whih belongs o hree dimension inerpolaing operaion mus be implemened. In he ondiion of oo lile effeive daa, auray of inerpolaing resul is no enough. The exising mehod is ha alulaing volume and sandard volume are hanged ino flow hrough divided by ime inerval, and flow differene value is reahed. Then inerpolaing operaion is implemened o flow and flow differene value [11, 12]. By means of inerpolaing resul, flow differene value of he urren flow poin is obained. Afer he las value is muliplied by ime inerval, volume differene value of he urren flow poin is alulaed and alulaing volume an be modified by volume differene value. Typial esimaion algorihms inlude inerpolaing algorihm and urve-fiing algorihm [13]. The former is omprised by linear inerpolaion and hree spline inerpolaion. The laer is usually implemened by leas-square polynomial urve-fiing algorihm. Afer inerpolaing operaion is implemened, flow differene value E v is muliplied by ime inerval and volume differene value is obained. Aording o error heory, oal error is given by ( Ev v v v ) E ( ) ( E ) ( E ), (1) where ( E v ) is he oal error, () is he error of ime inerval, and ( Ev ) is he error of flow differene value E v. 6 Preision of ime inerval is up o 10 and flow differene value E is very lile so ha he firs par v E v () an be ignored. Time inerval may be very large, suh as ime inerval of he eighh flow poin s in Fig. 1. Even hough preision of 4 inerpolaing operaion is up o 10, ombined error may be also very large. The alulaing resul is 4 ( ) (2) E v 3. New Daa Proessing Algorihm for he Sandard Meer Preondiion of he new daa proessing algorihm is ha flow of alibraing media keeps onsan in ime inerval a one alibraing poin. Aording o flow oninuiy, his ondiion is saisfied when hydrauli pressure remains onsan. Calibraed daa for he sandard meer is from he primiive sandard failiy. Relaive o he sandard vessel, he flow-meer aed as he sandard meer is heked meer in he siuaion. Therefore, he heked meer menioned in he following daa proessing algorihm is jus he sandard meer alibraed by he primiive sandard failiy. Three ses of original daa are obained in alibraing proedure by he primiive sandard failiy inluding sandard ime inerval, alulaing volume whih is measured by he heked meer in he sandard ime inerval and sandard volume s whih is measured by he sandard vessel in he same ime inerval. The algorihm is inrodued as follows. 185

3 Sensors & Transduers, ol. 162, Issue 1, January 2014, pp Normalizing Daa In daa of alulaing volume obained by measured from several flow poins, differene values beween sandard volume and alulaing volume are inomparable. Only when one of hem keeps onsan differene values of hem have omparable. So we sele alulaing volume o make normalizing operaion. The seps are as follows. 1) Wih seleing a erain fixed volume value, all alulaing volumes of heked daa for he sandard meer are adjus o. Priniple of hoosing he fixed volume is median mehod. All alulaing volumes are rearranged in order from larges o smalles suh as i1 i2 in, where n is he number of alulaing volumes. When n is odd, median is given by n1 i( 1) 2 When n is even, median. (3) is given by n / 2. n (4) i i( 1) 2 2 2) To modify ime inervals Aording o priniple ha flow rae remains onsan, we ge Hene. (5). (6) 3) To modify sandard volumes Aording he same priniple, we ge Thus, s s. (7) s s. (8) should be smooh and oninuous. Three-order spline funion omprises segmen hree-order urves and is seond derivaive is oninuous in onseuive poins. Therefore, we sele hree-order spline inerpolaing algorihm o implemen inerpolaing operaion. In inerpolaing operaion we sele flow F as horizonal axis parameer, differene value beween alulaing volume and sandard volume s as verial axis parameer Modifying Calulaing olume In praial alibraing proedure, we an ge sandard ime inerval and alulaing volume for he sandard meer in every flow poin. Then we arry ou flow in every flow poin F In aordane wih inerpolaing resul in seion 3.2, we ge orresponden volume differene value of flow F of every flow poin and we modify alulaing volume of he sandard meer. Sep 1: To alulae sandard ime inerval orresponding o he fixed volume urren flow in he. (9) F Sep 2: To alulae praial volume differene value in he flow poin afer normalized. In he same flow, volume differene value is aumulaed and i is proporional o ime inerval, ha is, Therefore,. (10). (11) Sep 3: To modify alulaing volume., (12) where is he alulaing volume for he sandard meer afer proessed Inerpolaing Algorihm We design inerpolaing operaion by using hreeorder spline inerpolaing algorihm. Sine a fluid behaves as oninuiy, parameers reeived from fluid 4. Algorihm erifiaion We arry ou algorihm verifiaion by he below daa from a praial alibraing proess. Daa proessing resuls are lis in he Table

4 Sensors & Transduers, ol. 162, Issue 1, January 2014, pp Flow poin Table 1. Praial alibraing daa for he sandard meer. Sandard ime Calulaing Sandard Flow F (s) volume (m 3 ) volume s (m 3 ) (m 3 /s) Fundamenal error From Table 1 alulaing volumes and sandard volumes measured from several flow poins are no exaly he same and differene values beween sandard volumes and alulaing volumes are no omparable. Therefore, we are no able o handle wih direly differene value of he volume. Fig. 2 is he resul of hree-order spline inerpolaing operaion orresponding o daa of Table 1. Sandard volume daa of he forh olumn in Table 1 is modified aording o equaion (8). Fig. 2. Resul of hree-order spline inerpolaing operaion. Linear inerpolaing operaion is simple and easy o implemen, bu operaion resul is no smooh. Three-order spline funion is made by segmen hree-order urves and is seond derivaive is oninuous in onseuive poins. Sine a fluid behaves as oninuiy, parameers reeived from fluid should be smooh and oninuous. Therefore, resul of hree-order spline inerpolaion is more in line wih haraerisi of fluid. Daa of he hird olumn in Table 1 are sored aording o he smalles order. The soring algorihm is bubble sor. Flow har of sor algorihm is shown in Fig. 3. Resuls of sor are shown in Table 2. The number of alulaing volume n is even, so he median is given by equaion (4) and is value is = Time inerval daa of he seond olumn in Table 1 is modified aording o equaion (6). Fig. 3. Flow har of bubble sor algorihm Table 2. Resuls of sor for daa of alulaing volume. No. Resul of sor

5 Sensors & Transduers, ol. 162, Issue 1, January 2014, pp Differene values of volume are alulaed by equaion (11). Calulaing volumes are modified aording o equaion (12). Aording o he above algorihm, we proess all daa in Table 1 and arrive a daa in Table 3. We normalize alulaing volumes in Fig. 1 aording o he priniple in seion 3.1 ino Meanwhile, we modify aordingly sandard volumes and sandard ime inervals and ge volume differene values whih are omparable. Then we arry ou inerpolaing operaion by using spline inerpolaion algorihm and arrive a flow differene value orresponding o flow of he urren flow poin. Hene, we an modify direly alulaing volume of he urren flow poin. By now we hange hree dimension inerpolaing operaion ino ow dimension inerpolaing operaion so ha we solve he problem ha o muliply ime inerval an bring error in hree dimension inerpolaing operaion. I an be shown from Table 3 ha flow of he every flow poin and fundamenal error are he same as he daa in Table 1. Flow poin Table 3. Proessed resuls by using he new algorihm. Differene of Sandard ime Calulaing Sandard Flow F (s) volume ( m³) volume s (m 3 volume ) (m 3 /s) E v (m 3 ) Fundamenal error Calibraed daa in Table 4 is obained from a erain heked meer using old algorihm. Daa in Table 5 is obained from he same heked meer using new algorihm. Daa in Table 6 is obained from he same heked meer using sandard failiy. Table 4. Calibraed daa of a heked meer by old algorihm using sandard meer mehod. Serial No. Frequeny Flow(l/s) Meer Consan Table 5. Calibraed daa of he same heked meer by new algorihm using sandard meer mehod. Serial No. Frequeny Flow(l/s) Meer Consan Table 6. Calibraed daa of he same heked meer using sandard failiy. Serial No. Frequeny Flow(l/s) Meer Consan From he above hree ables we an draw a onlusion ha meer onsan obained by he new algorihm using sandard meer mehod is lose o he daa from sandard failiy. Three group daa of meer onsan are drawn in Fig. 4.We an see ha he new algorihm improves preision of he alibraing sysem using sandard meer mehod. meer onsan serial number 5. Conlusions Fig. 4. Daa omparison diagram. old algorihm new algorihm sandard failiy Aording o oninuiy of fluid, when waer pressure is invariable, flow rae of alibraing media remain unhanged in he ime inerval a he same flow poin. Under his ondiion, we normalize daa 188

6 Sensors & Transduers, ol. 162, Issue 1, January 2014, pp for he sandard meer o make differene values beween alulaing volumes and sandard volumes omparable. Then we sele spline inerpolaing algorihm and obain flow deviaion orresponding o any flow. Daa whih is inerpolaed is daa when he sandard meer is alibraed, so we need hange flow deviaion obained in he above ino flow deviaion of he urren flow poin. Finally, we modify alulaing volume and arrive a daa whih is lose o he sandard volume. The algorihm hange hree dimension inerpolaing operaion ino wo dimension inerpolaing operaion by using oninuiy of fluid and improve preision of inerpolaing resul. By he new algorihm we an derease effeively unerainy from daa of he sandard meer and improve he auray of he overall alibraing failiy. Aknowledgemens The auhors wish o hank he helpful ommens and suggesions from my eahers and olleagues in Guangxi Key Lab of Wireless Wideband Communiaion & Signal Proessing a Guilin. This work was suppored in par by NSFC under Gran No , Guangxi Naural Siene Foundaion (2013GXNSFAA019327), Guangxi Key Lab of Wireless Wideband Communiaion & Signal Proessing under Gran No , Researh Proje of Universiies of Guangxi (201204LX144) and Innovaion Proje of Guangxi Graduae Eduaion (YCSZ ). Referenes [1]. R. Doihara, T. Shimada, Y. Terao, M. Takamoo, Developmen of he naional sandard failiy for hydroarbon flow a 0.1 o 15 m3/h, in Proeedings of he 14 h Inernaional Flow Measuremen Conferene, Sandon, Gaueng, Souh Afria, 2007, pp [2]. R. Engel, K. Beyer, H.-J. Baade, Design and realizaion of he high-preision weighing sysems as he gravimeri referenes in PTBs naional waer flow sandard, Measuremen Siene and Tehnology, ol. 23, Issue 7, 2012, pp [3]. A. Fonsea, I. M. Raimundo, J. J. R. Rohwedder, R. S. Lima, M. C. U. Araújo, A mirofluidi devie wih inegraed fluorimeri deeion for flow injeion analysis, Analyial and Bioanalyial Chemisry, ol. 396, Issue 2, 2009, pp [4]. G. Li, Q.-Z. Li, H.-P. Zhang, Design of pressureadjusable gas flow experimenal failiy, in Proeedings of he Inernaional Conferene on Eleronis and Opoeleronis, Dalian, China, ol. 3, 2011, pp [5]. C.-K. Liu, T.-B. Li, H.-G. Zhang, W. Yu, H.-Q. Qu, Z.-C. Bu, Developmen of gas flow sandard failiies, Aa Merologia Sinia, ol. 29, No. 5, 2008, pp [6]. Y. Liu, L. Sun, L. Qi, S. Li, Y. Wei, Developmen of a gas flow and veloiy alibraion failiy, in Proeedings of he 2 nd Inernaional Conferene on Consumer Eleronis, Communiaions and Neworks, Three Gorges, China, 2012, pp [7]. J.-L. Meng, Z.-Q. Yin, Numerial simulaion on he parallel ombined nozzles of mini/miro gas flow sandard devie, Advaned Maerials Researh, ol , 2012, pp [8]. H. Sao, Y. Terao, N. Furuihi, M. Takamoo, Unerainy examinaion of new waer flow alibraion failiy for nulear power appliaion, in Proeedings of he ASME Join U.S.-European Fluids Engineering Summer Meeing, Miami, FL, USA, 2006, pp [9]. L. Tymeki, K. Srzelak, R. Konki, A single sandard alibraion module for flow analysis sysems based on solenoid mirodevies, Talana, ol. 79, Issue 2, 2009, pp [10]. C. Wang, H. Ding, Q. Liu, Design of he gas soure sysem for soni nozzle gas flow sandard devie based on posiive pressure mehod, Chinese Journal of Sienifi Insrumen, ol. 33, No. 6, 2012, pp [11]. C. Wang, Y. Wang, Design and realizaion of gassolid wo-phase flow sandard failiy, in Proeedings of he 2 nd Inernaional Conferene on Mehani Auomaion and Conrol Engineering, Inner Mongolia, China, 2011, pp [12]. Y. Wei, L. Sun, Z. He, T. Zhang, Analysis and seleion of he flow sabiliy parameer of flow sandard failiy, in Proeedings of he Inernaional Conferene on Elerial and Conrol Engineering, Yihang, China, 2011, pp [13]. K. Zanker, D. Goodson, Qualifiaion of a flow ondiioning devie aording o he new API 14.3 proedure, Flow Measuremen and Insrumenaion, ol. 11, Issue 2, 2000, pp Copyrigh, Inernaional Frequeny Sensor Assoiaion (IFSA) Publishing, S. L. All righs reserved. (hp:// 189