RESEARCH ON STABILITY ANALYSIS OF INTERNATIONAL PROTOTYPE KILOGRAM

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1 Measuremen of Mass, Force and Torque (APMF 213) Inernaional Journal of Modern Physics: Conference Series Vol. 24 (213) 1364 (5 pages) The Auhors DOI: /S RESEARCH ON STABILITY ANALYSIS OF INTERNATIONAL PROTOTYPE KILOGRAM XIAOPING REN, YUE ZHANG, JIAN WANG Division of Mechanics and Acousics, Naional Insiue of Merology, Beijing, 113, P. R. China QINGXIONG REN Shanxi Province Insiue of Merology, Taiyuan, Shanxi Province, 32, P. R. China QINGMAO REN Boiler & Pressure Vessel Supervision and Inspecion Insiue of Shanxi Province Taiyuan, Shanxi Province, 312, P. R. China Today, he kilogram is he las of he seven base unis of he Inernaional Sysem of Unis (SI) which is based on a physical arifac. The demands of modern mass merology have led o an increasing focus on he surface sabiliy and analysis of mass sandard. Mehods for evaluaing he correlaion beween he measured mass values of he prooypes of he kilogram includes: collecion of hisorical calibraion daa for kilogram prooypes, seing up a model for deerminisic and random changes in he mass of a kilogram prooype (relaive o he IPK), adjusmen of parameers in a model using hisorical calibraion daa, and predicion of fuure mass values of a kilogram prooype using model and adjused parameers. Keywords: Inernaional prooype kilogram; model parameer idenificaion; sabiliy predicaion; kalman filer; leas-squares mehod. 1. Inroducion Of all he SI unis only he kilogram remains as he las one arifac sandard, and even hough his may no be he case for much longer, he sabiliy of ransfer sandards will be crucial for many years in he fuure. The sabiliy of reference masses has been a longsanding concern wihin he SI and researcher in he world. Tha s all due o he problems ha mass uni definiion are he lack of a value which is invarian in ime wih respec o This is an Open Access aricle published by World Scienific Publishing Company. I is disribued under he erms of he Creaive Commons Aribuion 3. (CC-BY) License. Furher disribuion of his work is permied, provided he original work is properly cied

2 X.-P. Ren e al. he fundamenal consans of physics, and he limied sabiliy of he mass of he sandards caused by amospheric conaminaion over ime. I has been known for many years ha he mass of prooype kilogram sandards increases over ime. Now analysis of he changes of he naional prooypes and BIPM working sandards wih respec o he inernaional prooype of he kilogram (IPK) is necessary, for he reason ha hese drifs were no aken ino accoun in he curren mass calibraion model of he BIPM. And mehods o evaluae he correlaion beween he measured mass values of he prooypes of he kilogram should be invesigaed. 2. Recen Research on Sabiliy Analysis of Mass Sandard In he repor of he 11h meeing o he Inernaional Commiee for Weighs and Measures by Consulaive Commiee for Mass and Relaed Quaniies (CCM, 28).Dr. Lars Nielsen from Denmark presened he issue ha wheher he sabiliy of he arifac and in paricular he lack of repeaabiliy of cleaning process should be aken ino accoun when assessing he uncerainy of Inernaional Prooype Kilogram (IPK) [1]. A plan for fuure work was decided in CCM11 ha o collec hisorical calibraion daa for kilogram prooypes, and se up a model for deerminisic and random changes in he mass of a kilogram prooype, hen make he adjusmen of parameers in a model using hisorical calibraion daa and predicion of fuure mass values of a kilogram prooype using model and adjused parameers. In he 21 CCM meeing, heir work group described hisorical daa which had been analyzed for 18 plainum-iridium kilograms (using he leas-squares mehod), including he IPK and he 6 official copies (during he period 1889 o 29) [2]. The daa showed ha mos kilogram sandards gained abou.5 µg per year wih respec o he IPK. Calculaed uncerainies for he modeled daa were 23.1 µg for he period and 7.7 µg for more recen daa. These agreed well wih he measuremen daa up o 23, when here appeared o be a sep change in he mass value of he weigh. Dr. Nielsen noed ha he had seen a similar change in he values of wo oher copies he had analyzed [3]. Table 1. Prooypes involved in sudy. Prooypes/working sandards period of use IPK Prooypes for winess: K1, K7, K8, K32, K43, K Prooype 25# for special use Prooype 9# and 31 #for rouine use Working sandard 42# Working sandard 65# Prooype 67# Prooype 77# Prooype 63# and 73# Prooype 88# and 91#

3 Research on Sabiliy Analysis of Inernaional Prooype Kilogram In 9 May 211, CCM13h meeing, Dr Nielsen presened he simple drif model ha had been assumed for he change in mass of a prooype wih ime [4]. This model includes a linear mass gain, a superimposed mass gain which varies wih ime afer cleaning and a componen for random mass changes. The parameers in he model were adjused by he mehod of leas squares. Mass sandard were analyzed are shown in able1. 3. Modeling of Inernaional Prooype Kilogram 3.1. Naional Physical Laboraory (NPL, UK) The mass sabiliy of kilogram No. 18, he Briish Naional Sandard made in 1884, has been closely moniored by NPL. Afer being cleaned and washed a BIPM in 1985, he mass increase of he prooype was moniored for more han 1 year. Afer 199, a bes-fi curve fied o he BIPM daa was obained ha expressed he mass change as a funcion of ime: M M = (1) where M : mass of he prooype a ime afer cleaning and washing M : mass of he prooype a he ime of cleaning and washing : elapsed ime in days. Using equaion (1), he mass value of kilogram No. 18 afer 6 years since he las cleaning was prediced o wihin 1.5 µg. Besides, a physical model was pu forward o explain he gradual increase in mass of prooype kilogram sandards, based on a diffusion-limied caalyic accreion of amospheric carbonaceous conaminaion [5]. Growh is limied by he rae of diffusion of new hydrocarbon maerial, and a quaniaive predicion of mass increase formula was given ou like his: ( ) ρσ 2 ( ) c m = D + c 1/2. (2) In his formula, where D is he diffusion consan for small molecules hrough he exising conaminaion of densiy ρ on a prooype of surface area σ, is he ime elapsed since he las cleaning procedure, and c is a consan describing quaniy of conaminaion ha builds up in he firs minues or hours afer cleaning, before he process becomes diffusion-limied. The diffusion limied carbonaceous growh model is in excellen agreemen wih he daa available for kilogram No Danish Fundamenal Merology (DFM, Denmark) The model presened by DMF was a drif model ha assumed for he change in mass of a prooype wih ime. This model (3) has an underlying linear mass gain, a superimposed

4 X.-P. Ren e al. mass gain which varies wih ime afer cleaning and a componen for random mass changes [6]: m( ) = m + α( ) + γ + δm( ) (3) C m( ) : Mass of weigh a ime m : Mass of weigh a reference ime α : Rae of change in mass of cleaned weigh γ : Removable dir collecion coefficien C : Time of las cleaning 2 δ m( ) : Random variable wih expecaion and varianceσ. The bes esimae of he random mass change δ m( ) is mg wih sandard uncerainy σ =.25 mg before 1946 and σ =.6 mg afer For he m = 1 kg, α = mg/year and σ =.1 mg. The slope of he Inernaional Prooype drif in mass of clean prooypes was mainly less han 1µg/year. The consan describing he accumulaion of conaminaion on clean prooypes in he firs year afer cleaning had a spread of values from (2 o 1) µg/year 1/ Naional Research Council (NRC, Canada) Claude Jacques makes he presenaion named Correlaions beween BIPM prooypes Preliminary resuls on he CCM 14h meeing. I poins ou ha leas-square is a way o curve he known calibraion values overime and o assess he rend of variance of mass. However, in his mehod, nohing is abou he rend of covariance, neiher correlaion beween weighs in any scheme of calibraion. So Kalman filer is a beer mehod o analyzing he rend of covariance, which can includes he facors of mass comparison: leas-squares, covariance and weighing design. A CCM13h meeing, BIPM said ha hey were also working owards resolving possible discrepancies beween he model and BIPM assigned values [7]. In heir repor noed ha during he period no direc mass measuremen agains IPK is available anymore. Therefore, he difficuly of exracing absolue mass values during his period will be paricularly challenging. 4. Conclusion Fuure work will include he analysis of daa o examine he qualiy of fi of he predicive model ha has been developed. Kalman filering may be a suiable mehod o analyze he hisorical daa and he suiabiliy of his analyical echnique for hese applicaions should be invesigaed. For many years several cleaning mehods have been used by he BIPM and a number of NMIs o reurn kilogram prooypes o heir original masses, noably he lavage/neoyage (cleaning/washing) procedure [8] applied by BIPM. However, In some cases deailed weighing have been performed of mass los during cleaning/washing and he re-growh of he mass in he monhs afer cleaning/washing, so he cleaning of

5 Research on Sabiliy Analysis of Inernaional Prooype Kilogram weighs should be reduced o a minimum; he mass will no be rese anyway. Because he modeling of he change in mass over ime is difficul and i reduces uncerainies and abrup mass changes. Besides, regular comparisons wih a primary realizaion are necessary in order o monior he change in he average mass of a group of weighs. Frequen comparisons are useful for monioring individual weighs in a group relaive o he average mass and for validaing he assumed mass change model. Acknowledgmens The auhor will also wish o hank for he gran of Naional Science and Technology Suppor Program (211BAK15B6); The gran of Special-Funded Program on Naional Key Scienific Insrumens and Equipmen Developmen (212YQ928). References 1. Consulaive Commiee for Mass and Relaed Quaniies. Repor of he 11h meeing o he Inernaional Commiee for Weighs and Measures April M. TANAKA. CCM 21 repor, Uncerainy componens due o raceabiliy o he Inernaional prooype of he kilogram, 22 March 21, hp:// 3. Consulaive Commiee for Mass and Relaed Quaniies. Repor of he 12h meeing o he Inernaional Commiee for Weighs and Measures, 26 March Consulaive Commiee for Mass and Relaed Quaniies. Repor of he 13h meeing o he Inernaional Commiee for Weighs and Measures May P. Cumpson, N. Sano. Sabiliy of reference masses V: UV/ozone reamen of gold and plainum surfaces. Merologia, 213, 5: L. Nielsen. Consideraions on mise en praique for he kilogram based on work of CCM WGM TG E. de Mirandés. A general mehod o reproduce he mass values assigned o BIPM working sa ndards from 1889 o 21. CCM Workshop on he mise en praique of he new definiion of he kilogram, November 212. hp:// 12/12b_6.2_BIPM_Hisorical_mass_values_EdeM.pdf 8. G. Girard. The Third Periodic Verificaion of Naional Prooypes of he Kilogram( ). Merologia, 1994:31,