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# Practical Uncertainty Estimation in Load Cell Calibration

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By LaVar Clegg - Interface, Inc.
Presented at the NCLSI - Northwestern US Region
Measurement Training Summit - May 21, 2014

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### Practical Uncertainty Estimation in Load Cell Calibration

1. 1. by LaVar Clegg Interface, Inc. Presented at the NCLSI Northwestern US Region Measurement Training Summit May 21, 2014 1
2. 2. 2
3. 3. Measurement An established process performed to determine a physical property of an object quantitatively True Value The correct value of a measurand 3
4. 4. Poor accuracy due to inconsistency 4 Poor accuracy due to lack of trueness Accuracy Closeness of a measured value to the true value
5. 5. Reading (RDG) The direct measurand output Full Scale (FS) The measurand output corresponding to the Maximum or Rated input in a specific calibration or application 5
6. 6. Error The difference between the measured value and the true value Measurement Uncertainty An estimate of the range of measured values within which the true value lies or, alternatively, the degree of doubt about a measured value 6
7. 7. The GUM Evaluation of measurement data — Guide to the expression of uncertainty in measurement This Guide establishes general rules for evaluating and expressing uncertainty in measurement that are intended to be applicable to a broad spectrum of measurements 7 Responsibility is shared jointly by the JCGM (BIPM, IEC, IFCC, ILAC, ISO, IUPAC, IUPAP and OIML) and comparable to NIST Technical Note 1297
8. 8. Calibration A documented procedure that compares the measurements performed by an instrument to those made by a more accurate instrument or standard In the case of Load Cell Calibration, the procedure establishes a relationship between the input and the output of the load cell 8
9. 9. 9 Methods of Load Cell Calibration Approximate feasible expanded uncertainty Direct Dead Weight ( best for accuracy but slow and space inefficient) 0.005% Leveraged Dead Weight (medium for accuracy but slow and space inefficient) 0.01% Hydraulic Force Generation Comparison (fast and space efficient with reasonable accuracy) 0.04%
10. 10. Self-contained for minimum floor space Automated to reduce human error Fast Tension and Compression 10 Interface 10Klbf Calibration Machine Exemplifies advantages of Comparison Method
11. 11. Inside view of Calibration Machine 11 Hydraulic Pump Fluid Reservoir Cylinder Control Feedback Amplifier Servo Amplifier for driving Servo Valve
12. 12. Calibration Machine Load String 12 Load Cell Under Test Standard Load Cell Servo System Feedback Load Cell
13. 13. 13
14. 14. A. Determine what parameter is to be measured and the units of measure. B. Identify the components of the calibration process and the accompanying sources of error. C. Write an expression for the uncertainty of each source of error. D. Determine the probability distribution for each source of error. E. Calculate a standard uncertainty for each source of error for the range or value of interest. F. Construct an uncertainty budget that lists all of the components and their standard uncertainty calculations G. Combine the standard uncertainty calculations and apply a coverage factor to obtain the final expanded uncertainty. 14
15. 15. Block Diagram: 15 Load Frame Test Transducer Standard Transducer Feedback Transducer Hydraulic Force Generator Servo Valve Servo Amplifier & Controller Data Archive Computer Gold Standard Software HRBSC HRBSC Printer Monitor
16. 16. 1. Interface servo-controlled hydraulic load frame 2. Interface model 1600 Standard Transducer 3. Industrial computer 4. HRBSC mV/V signal conditioning instruments 5. 8-wire Interconnect cables 6. Gold Standard software for automation and data handling 16
17. 17. A. (Cont’d) What we are actually measuring is the mV/V signal from two load cells. The association of these signals to units of force is done by mathematics in software. We will express uncertainty in units of %RDG. 17
18. 18. The overall expression for Vtest as a function of uncertainty contributors: Vtest = f (CS, DS, PS, TS, RF, CH, DH, TH, LH, NH, RH CH, DH, TH, LH, NH, RH) Where CS = Calibration of a Standard Transducer. DS = Drift in Standard Transducer since last Calibration. PS = Creep in the Standard Transducer. TS = Temperature Effect On Output of the Standard Transducer. RF = Nonreproducibility of the hydraulic load frame due to errors in alignment, thread concentricity, parallelism, and flatness of the load string components. CH = Calibration of HRBSC Indicating instrument. DH = Drift in HRBSC Indicating instrument since last calibration. TH = Temperature effect on HRBSC Indicating instrument. LH = Nonlinearity of HRBSC Indicating instrument. NH = Noise of HRBSC Indicating instrument. RH = Digital resolution of HRBSC Indicating instrument. 18
19. 19. For example, for the parameter LH = Nonlinearity of HRBSC Indicating instrument. Nonlinearity was measured on several instruments over many calibration intervals over several years making 720 data points. The result: Maximum Nonlinearity = 0.00007 mV/V Standard Deviation = 0.00002 mV/V 19
20. 20. For illustration, consider a scenario where both the test and the Standard transducers have rated sensitivity of 4 mV/V at the same capacity. We desire to evaluate uncertainty at 20% of capacity. (0.8mV/V) We must express the uncertainty in units of %RDG. Then LH = 0.00007 mV/V = 0.00007 / 0.8 = 0.0088 %RDG 20
21. 21. We generally choose among 3 distribution types Factor Normal – fits many natural 1 phenomena Rectangular or Uniform – fits 0.557 parameters with limits Triangular – fits parameters 0.408 with a central tendency 21
22. 22. For the LH example, a central tendency was observed in the data being analyzed. This is consistent with the large difference between the Std Dev and the Peak Error and therefore suggests a triangular distribution. Selecting the probability distribution is often a judgment call. 22
23. 23. Multiply the uncertainty expression by the distribution factor. For the LH example, Standard uncertainty ui = 0.0088 (0.408) = 0.0036 %RDG 23
24. 24. In similar manner, derive the standard uncertainty for all other error sources by determining the expression of uncertainty and the probability distribution, and then calculating the standard uncertainty. Express each component in units of %RDG. Sources are usually evaluated by actual data and/or established specifications. The following slide shows a summary for typical values. 24
25. 25. Example for 4 mV/V load cells at 20% of capacity: 25 Interval Interval Probability Uncertainty Source of Uncertainty Type Expression (%RDG) Distribution Factor ui (%RDG) CS NIST Cal of Standard A 0.00160%Cal Range 0.0128 Std Dev 1 0.0128 DS Drift in Standard B 0.012% RDG 0.0120 Triangular 0.408 0.0049 PS Creep in Standard B 0.0055% RDG 0.0055 Rectangular 0.577 0.0032 TS Temperature Effect on Std B 0.0029% RDG 0.0029 Rectangular 0.577 0.0017 RF Nonreproducibility , load frame B 0.0130% RDG 0.0130 Std Dev 1 0.0130 CH Cal of HRBSC, Std B 0.0056% RDG 0.0056 Rectangular 0.577 0.0032 DH Drift in HRBSC, Std A 0.0009% RDG 0.0009 Std Dev 1 0.0009 TH Temperature Effect HRBSC, Std B 0.0020% RDG 0.0020 Rectangular 0.577 0.0012 LH Nonlinearity of HRBSC, Std B 0.00007 mV/V 0.0088 Triangular 0.408 0.0036 NH Noise of HRBSC, Std B 0.00004 mV/V 0.0050 Rectangular 0.577 0.0029 RH Digital Resolution HRBSC, Std B 0.00001 mV/V 0.0013 Rectangular 0.577 0.0008 CH Cal of HRBSC, Test B 0.0056% RDG 0.0056 Rectangular 0.577 0.0032 DH Drift in HRBSC, Test A 0.0009% RDG 0.0009 Std Dev 1 0.0009 TH Temperature Effect HRBSC,Test B 0.0020% RDG 0.0020 Rectangular 0.577 0.0012 LH Nonlinearity of HRBSC, Test B 0.00007 mV/V 0.0088 Triangular 0.408 0.0036 NH Noise of HRBSC, Test B 0.00004 mV/V 0.0050 Rectangular 0.577 0.0029 RH Digital Resolution HRBSC, Test B 0.00001 mV/V 0.0013 Rectangular 0.577 0.0008
26. 26.  Per the GUM, we combine the component standard uncertainty numbers using the root-sum-of-squares method.  The combined RSS result will have a confidence level of only one standard deviation or about 68%. It is more practical to have higher confidence. Therefore we apply a coverage factor of 2 meaning the confidence of all results being within 2 standard deviations which confidence is 95%. The following budget chart includes the RSS combination and the Expanded Uncertainty with coverage factor = 2. 26
27. 27. Expanded uncertainty U estimation example complete 27 Interval Interval Probability Uncertainty Source of Uncertainty Type Expression (%RDG) Distribution Factor ui (%RDG) CS NIST Cal of Standard A 0.00160%Cal Range 0.0128 Std Dev 1 0.0128 DS Drift in Standard B 0.012% RDG 0.0120 Triangular 0.408 0.0049 PS Creep in Standard B 0.0055% RDG 0.0055 Rectangular 0.577 0.0032 TS Temperature Effect on Std B 0.0029% RDG 0.0029 Rectangular 0.577 0.0017 RF Nonreproducibility , load frame B 0.0130% RDG 0.0130 Std Dev 1 0.0130 CH Cal of HRBSC, Std B 0.0056% RDG 0.0056 Rectangular 0.577 0.0032 DH Drift in HRBSC, Std A 0.0009% RDG 0.0009 Std Dev 1 0.0009 TH Temperature Effect HRBSC, Std B 0.0020% RDG 0.0020 Rectangular 0.577 0.0012 LH Nonlinearity of HRBSC, Std B 0.00007 mV/V 0.0088 Triangular 0.408 0.0036 NH Noise of HRBSC, Std B 0.00004 mV/V 0.0050 Rectangular 0.577 0.0029 RH Digital Resolution HRBSC, Std B 0.00001 mV/V 0.0013 Rectangular 0.577 0.0008 CH Cal of HRBSC, Test B 0.0056% RDG 0.0056 Rectangular 0.577 0.0032 DH Drift in HRBSC, Test A 0.0009% RDG 0.0009 Std Dev 1 0.0009 TH Temperature Effect HRBSC,Test B 0.0020% RDG 0.0020 Rectangular 0.577 0.0012 LH Nonlinearity of HRBSC, Test B 0.00007 mV/V 0.0088 Triangular 0.408 0.0036 NH Noise of HRBSC, Test B 0.00004 mV/V 0.0050 Rectangular 0.577 0.0029 RH Digital Resolution HRBSC, Test B 0.00001 mV/V 0.0013 Rectangular 0.577 0.0008 uc Combined Uncertainty Root Sum of Squares Method 0.0207 U Expanded Uncertainty U = k uc where k = 2 for confidence level of 95% 0.041
28. 28. A. We determined that we were measuring mV/V output of load cells in a comparison method. B. We identified the components of the calibration process that contribute error. C. We wrote an expression for the uncertainty for an example source of error. D. We determined the probability distribution for the example source of error. E. We calculated a standard uncertainty for the example source of error for a range of interest. F. We constructed an uncertainty budget using typical values for all of the sources and their standard uncertainty calculations G. Combine the standard uncertainty calculations by the RSS method and applied a coverage factor of 2 for 95% confidence in U. 28
29. 29. These parameters are typically stated on transducer data sheets and are often confused with “accuracy”: Nonlinearity Hysteresis Static Error Band They are “relative” because they are only ratios and are stated in units of “% Full Scale” rather than in force units or mV/V units. 29
30. 30. One could ask, “Can a calibration process that has an expanded uncertainty of approximately 0.04% produce a valid test for a nonlinearity specification of 0.02%FS, for example”? The answer is yes. The reasoning lies in these facts: 1. The 0.04% is the uncertainty of a measurement of physical units, say mV/V or lbf or kN. The measurement has scale. 2. Whereas nonlinearity is a relative quantity that ratios measurements at 2 different input values, all other conditions remaining constant. The quantity has no scale. 3. Most of the uncertainty sources are errors that are constant as %RDG over a wide range of inputs. 4. The readings for the relative ratio are taken at nearly the same time and in the same setup under similar conditions. 30
31. 31. 31 Source of Uncertainty Comment CS NIST Cal of Standard Fitted Curve minimizes nonlinearity over wide range DS Drift in Standard Linear as %RDG PS Creep in Standard Linear as %RDG TS Temperature Effect on Std Linear as %RDG RF Nonreproducibility , load frame Near linear as % RDG CH Cal of HRBSC Linear as %RDG DH Drift in HRBSC Linear as %RDG TH Temperature Effect HRBSC Linear as %RDG LH Nonlinearity of HRBSC Nonlinear but small contributor NH Noise of HRBSC Nonlinear but small contributor RH Digital Resolution HRBSC, Std Nonlinear but small contributor
32. 32. Measurement uncertainty for relative errors is not normally reported or stated. To show that relative errors can be tested with the process for absolute uncertainty herein discussed, 3 demonstrations are presented. a. Use of fitted curves for standard transfer function b. Linearity of load cell drift over time c. Interface tests of nonlinearity and hysteresis compared to NIST 32
33. 33. The above plot shows an extreme case of high nonlinearity that contributes small error due to the 5th degree polynomial fit 33
34. 34. -0.040 -0.020 0.000 0.020 0.040 0.060 0.080 0.100 0.120 0.140 1980 1984 1988 1992 1996 2000 2004 2008 2012 2016 OutputDeviationfromNominal(%RDG) History of NIST Calibration, STD-18 4K T 10K T 4K C 10K C 34
35. 35. 35 -0.200 -0.180 -0.160 -0.140 -0.120 -0.100 -0.080 -0.060 -0.040 -0.020 0.000 0.020 0.040 0.060 0.080 0.100 1986 1990 1994 1998 2002 2006 2010 2014 OutputDeviationfromNominal (%RDG) History of NIST Calibration, STD-16 100K Ten 200K Ten 100K Comp 200K Comp
36. 36. 36 Standard 10, FS=75Klbf 6/28/2013 2/10/2009 4/11/2005 Average LAB TENSION (%FS) (%FS) (%FS) (%FS) NIST Nonlinearity -0.027 -0.026 -0.026 Interface Nonlinearity -0.027 -0.028 -0.029 Difference 0.001 0.002 0.003 0.002 NIST Hysteresis 0.033 0.036 0.035 Interface Hysteresis 0.033 0.035 0.032 Difference 0.000 0.001 0.003 0.001 COMPRESSION NIST Nonlinearity -0.026 -0.026 -0.026 Interface Nonlinearity -0.028 -0.023 -0.023 Difference 0.003 -0.004 -0.004 -0.001 NIST Hysteresis 0.033 0.035 0.032 Interface Hysteresis 0.031 0.031 0.034 Difference 0.002 0.004 -0.002 0.001
37. 37. 37 Standard 13, FS=25Klbf 11/17/2011 10/23/2007 6/22/2005 Average LAB TENSION (%FS) (%FS) (%FS) (%FS) NIST Nonlinearity -0.012 -0.012 -0.012 Interface Nonlinearity -0.012 -0.009 -0.010 Difference 0.001 -0.003 -0.002 -0.002 NIST Hysteresis 0.022 0.023 0.023 Interface Hysteresis 0.024 0.027 0.022 Difference -0.002 -0.004 0.001 -0.002 COMPRESSION NIST Nonlinearity -0.015 -0.015 -0.017 Interface Nonlinearity -0.015 -0.013 -0.012 Difference 0.000 -0.002 -0.005 -0.002 NIST Hysteresis 0.025 0.027 0.029 Interface Hysteresis 0.024 0.024 0.024 Difference 0.001 0.003 0.005 0.003 Interface and NIST tests have minimal difference in NL & H (25 Klbf example)
38. 38. The preceding charts of actual data show that it is very feasible to test relative parameters (in units of %FS) for tolerances tighter than the uncertainty of the absolute measurements (in units of force). 38
39. 39. Answer: In many applications the gain or scale of the system is set on site, a separate operation from the load cell calibration and usually at a different place and time. This is where the load cell mV/V output is converted to other physical units. Often this gain setting or conversion process has no capability for nonlinearity and hysteresis correction. Therefore it is desirable for these parameters to be minimal. 39
40. 40. 40