Adjustment procedures and their corresponding uncertainties

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1 Adjustment procedures and their corresponding uncertainties Jos van der Grinten Chief Metrologist, NMi EuroLoop Contents! Introduction! Currently applied adjustment procedures! Residuals! Uncertainties! Discussion! Conclusion & recommendations 2nd European Flow Measurement Workshop, Lisbon, March

2 Introduction! Calibration! adjustment EuroLoop 5% Linear 25% 25% 45% Polynomial Piecewise linear None 2nd European Flow Measurement Workshop, Lisbon, March Introduction 2! Deviation and correction ind 1 e = " 1! ref = 1+ e ref! Adjustment methods (correction)! Linear adjustment! Polynomial adjustment! Piecewise linear or multipoint adjustment Ultrasonic meters allow methods in combination! uestion: most accurate procedure?! Residues! Uncertainties ind 2nd European Flow Measurement Workshop, Lisbon, March

3 Introduction G16000 Meter Turbine curve gasmeter deviation e (%) Calibration data nd European Flow Measurement Workshop, Lisbon, March Introduction Ultrasonic Meter flowmeter curve 0.40 Calibration data deviation e (%) nd European Flow Measurement Workshop, Lisbon, March

4 Calibration! Meters arrive with programmed corrections! Factory settings! Adjustments from previous calibrations! Pre-calibration with existing parameters! Reset programmed polynomials or adjustment tables! Calibration! Adjustment! Verification points 2nd European Flow Measurement Workshop, Lisbon, March Adjustment procedures Linear adjustment! WME " wi ei WME =, " w i i wi = max!! w i OIML R32 (1989), OIML R137-1 (2006), R137-1,2 (2012), AGA-9! Adjusted deviation d = e WME i i! c new cold = 1+ WME 2nd European Flow Measurement Workshop, Lisbon, March

5 Adjustment procedures 2 Polynomial adjustment! Least square curve fit p q r s e = a + a x + a x + a x + a x + p , x =! Specify powers and calculate coefficients a i! Straatsma p = -0.2, q = -0.33, r = -2! 3 rd order p = 1, q = 2, r = 3! 4 th order p = 1, q = 2, r = 3, s = 4! Interpolation! Adjusted deviation = e! e d i i p, i max 2nd European Flow Measurement Workshop, Lisbon, March Adjustment procedures 3! Piecewise linear or multipoint adjustment! Adjusted deviation d e! e = 0! Linear interpolation between two adjacent calibration points! When in [ i, i+1 ] i = i i ei + 1! ei e = ei + (! i )! i+ 1 i e ( 1,e 1 ) ( 2,e 2 ) ( 3,e 3 ) ( 4,e 4 ) 2nd European Flow Measurement Workshop, Lisbon, March

6 Adjustment procedures G16000 Meter Turbine curve gasmeter deviation e (%) Calibration data Straatsma 3rd order polynomial 4th order polynomial WME nd European Flow Measurement Workshop, Lisbon, March Adjustment procedures Ultrasonic Meter flowmeter curve deviation e (%) Calibration data Straatsma 3rd order polynomial Series4 WME nd European Flow Measurement Workshop, Lisbon, March

7 Residuals 24 G16000 Residuals Turbine gasmeter fit - deviation e (%) - - Straatsma 3rd order polynomial 4th order polynomial WME Piecewise nd European Flow Measurement Workshop, Lisbon, March Residuals 2 Residuals 16 Ultrasonic flowmeter fit - deviation e (%) - - Straatsma 3rd order polynomial 4th order polynomial WME Piecewise nd European Flow Measurement Workshop, Lisbon, March

8 Uncertainty Two uncertainty sources 1.! Not correcting for a known deviation or residual d u d! Uk 2d = = = 2 2.! Uncertainty of calibration points! Piecewise linear (d i = 0) ( 2,e 2 ) e ( 1,e 1 ) ( 3,e 3 ) ( 4,e 4 ) 2nd European Flow Measurement Workshop, Lisbon, March Uncertainty 2 24" G16000 turbine Residuals Calibration Total U res [%] U cal [%] U tot [%] WME Straatsma polynomial rd order polynomial th order polynomial Piecewise linear 0 16" ultrasonic Residuals Calibration Total U res [%] U cal [%] U tot [%] WME Straatsma polynomial rd order polynomial th order polynomial Piecewise linear nd European Flow Measurement Workshop, Lisbon, March

9 Discussion All science is either physics or stamp collecting! For polynomial adjustment Ernest Rutherford! Physics model! uncertainty reduction! 3 rd or 4 th order polynomials are not smooth, curve bends and goes wild at both ends of interval! try negative powers for smooth curve! Observe degree of freedom > 6! take sufficient calibration points, otherwise poor fit and high uncertainty! Observe the standard deviation of y estimate 2nd European Flow Measurement Workshop, Lisbon, March Conclusion & recommendations! Adjustment helps, verified procedure! Residuals! piecewise adjustment! zero residual! Uncertainty! Piecewise linear adjustment best overall uncertainty! Ultrasonic meters! Physics inside the meter! rest are stamps! Turbine! Linear adjustment +! correction by physics based polynomial or piecewise 2nd European Flow Measurement Workshop, Lisbon, March

10 Thank you! uestions???? Linear Polynomial Piecewise linear? None 2nd European Flow Measurement Workshop, Lisbon, March

Urban Legends in Gasmetering

Urban Legends in Gasmetering Jos van der Grinten Scientist High Pressure Gas Department Enquiry three statements A national standards institute can disseminate the m³ accurately without re-calibration.