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, 25-27 March 2014 2 1
Introduction! Calibration! adjustment Adjustments @ EuroLoop 5% Linear 25% 25% 45% Polynomial Piecewise linear None 2nd European Flow Measurement Workshop, Lisbon, 25-27 March 2014 3 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, 25-27 March 2014 4 2
Introduction 3 1.00 24 G16000 Meter Turbine curve gasmeter 0.90 0.80 0.70 deviation e (%) 0.60 0.50 0.40 Calibration data 0.40 0.50 0.60 0.70 0.80 0.90 1.00 2nd European Flow Measurement Workshop, Lisbon, 25-27 March 2014 5 Introduction 4 0.50 16 Ultrasonic Meter flowmeter curve 0.40 Calibration data deviation e (%) - - - -0.40-0.50 0.40 0.50 0.60 0.70 0.80 0.90 1.00 2nd European Flow Measurement Workshop, Lisbon, 25-27 March 2014 6 3
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, 25-27 March 2014 7 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, 25-27 March 2014 8 4
Adjustment procedures 2 Polynomial adjustment! Least square curve fit p q r s e = a + a x + a x + a x + a x + p 0 1 2 3 4, 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, 25-27 March 2014 9 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, 25-27 March 2014 10 5
Adjustment procedures 4 1.00 24 G16000 Meter Turbine curve gasmeter 0.90 0.80 0.70 deviation e (%) 0.60 0.50 0.40 Calibration data Straatsma 3rd order polynomial 4th order polynomial WME 0.40 0.50 0.60 0.70 0.80 0.90 1.00 2nd European Flow Measurement Workshop, Lisbon, 25-27 March 2014 11 Adjustment procedures 5 0.50 16 Ultrasonic Meter flowmeter curve deviation e (%) 0.40 - Calibration data Straatsma 3rd order polynomial Series4 WME - - -0.40-0.50 0.40 0.50 0.60 0.70 0.80 0.90 1.00 2nd European Flow Measurement Workshop, Lisbon, 25-27 March 2014 12 6
Residuals 24 G16000 Residuals Turbine gasmeter fit - deviation e (%) - - Straatsma 3rd order polynomial 4th order polynomial WME Piecewise - 0.40 0.50 0.60 0.70 0.80 0.90 1.00 2nd European Flow Measurement Workshop, Lisbon, 25-27 March 2014 13 Residuals 2 Residuals 16 Ultrasonic flowmeter fit - deviation e (%) - - Straatsma 3rd order polynomial 4th order polynomial WME Piecewise - 0.40 0.50 0.60 0.70 0.80 0.90 1.00 2nd European Flow Measurement Workshop, Lisbon, 25-27 March 2014 14 7
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, 25-27 March 2014 15 Uncertainty 2 24" G16000 turbine Residuals Calibration Total U res [%] U cal [%] U tot [%] WME 0.43 0.48 Straatsma polynomial 0.23 3rd order polynomial 0.15 0.25 4th order polynomial 0.12 0.24 Piecewise linear 0 16" ultrasonic Residuals Calibration Total U res [%] U cal [%] U tot [%] WME 0.22 0.26 0.34 Straatsma polynomial 0.22 0.35 0.42 3rd order polynomial 0.28 0.35 0.45 4th order polynomial 0.35 0.35 0.49 Piecewise linear 0 0.35 0.35 2nd European Flow Measurement Workshop, Lisbon, 25-27 March 2014 17 8
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, 25-27 March 2014 18 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, 25-27 March 2014 19 9
Thank you! uestions???? Linear Polynomial Piecewise linear? None 2nd European Flow Measurement Workshop, Lisbon, 25-27 March 2014 20 10