efdua - SUMMARY OF EXPERIMENTAL UNCERTAINTY ASSESSMENT...

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SUMMARY OF EXPERIMENTAL UNCERTAINTY ASSESSMENT METHODOLOGY WITH EXAMPLE by Fred Stern, Marian Muste, Maria-Laura Beninati, and William E. Eichinger IIHR Technical Report No. 406 Iowa Institute of Hydraulic Research College of Engineering The University of Iowa Iowa City, Iowa 52242 July 1999
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i TABLE OF CONTENTS Abstract. ............................................................................................................................... iii Acknowledgments . .............................................................................................................. 1. Introduction. .................................................................................................................... 1 2. Test Design Philosophy. ................................................................................................. 2 3. Accuracy, Errors, and Uncertainty. ................................................................................ 4 4. Measurement Systems, Data-Reduction Equations, and Error Sources . ........................ 6 5. Derivation of Uncertainty Propagation Equation. .......................................................... 8 6. Uncertainty Equations for Single and Multiple Tests. .................................................. 12 6.1 Bias Limits. ...................................................................................................... 12 6.2 Precision Limits for Single Tests. .................................................................... 13 6.3 Precision Limits for Multiple Tests . .................... ……………………………14 7. Implementation. ............................................................................................................ 15 8. Example for Measurement of Density and Kinematic Viscosity. ................................ 16 8.1 Test Design . ..................................................................................................... 17 8.2 Measurement Systems and Procedures. ........................................................... 18 8 . 3 Test Results. ..................................................................................................... 20 8.4 Uncertainty Assessment. .................................................................................. 20 8.4.1 Multiple Tests . .................................................................................. 21 8.4.2 Single Test . ....................................................................................... 25 8.5 Discussion of Results. ...................................................................................... 27 8.6 Comparison with Benchmark Data. ................................................................. 28 9. Conclusions and Recommendations . ............................................................................ 32 References. ......................................................................................................................... 34 Appendix A. Individual Variable Precision Limit. ........................................................... 35
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ii LIST OF FIGURES Figure Page 1. Integration of uncertainty assessment in test process (AIAA, 1995) . ........................... 3 2. Errors in the measurement of a variable X (Coleman and Steele, 1995). ...................... 5 3. Propagation of errors into experimental results (AIAA, 1995) . .................................... 7 4. Sources of errors (adapted AIAA, 1995). ...................................................................... 7 5. Schematic of error propagation from a measured variable into the result. .................... 8 6. Propagation of bias and precision errors into a two variable result (Coleman and Steele, 1995). ........................................................................................ 10 7. Experimental arrangement . .......................................................................................... 17 8. Block diagram of experiment . ..................................................................................... 19 9. Density of 99.7% aqueous glycerin solution test results and comparison with benchmark data. ................................................................................................................. 31 10. Kinematic viscosity of 99.7% aqueous glycerin solution test results and comparison with benchmark data . ............................................................................... 32 LIST OF TABLES Table 1. Gravity and sphere density constants . ......................................................................... 20 2. Typical test results . ...................................................................................................... 20 3. Bias limits for individual variables D and t ................................................................. 22 4. Uncertainty estimates for density using multiple test method. .................................... 23 5. Uncertainty estimates for kinematic viscosity (teflon spheres) using multiple test method . ................................................................................................... 25 6. Uncertainty estimates for density using single test method. ........................................ 27 7. Uncertainty estimates for kinematic viscosity (teflon spheres) using single test method . ....................................................................................................... 27 8. Total uncertainty estimates for density and kinematic viscosity of glycerin (values in parenthesis include consideration of correlated bias errors). ...................... 28
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iii Abstract A summary is provided of the AIAA Standard (1995) for experimental uncertainty assessment methodology that is accessible and suitable for student and faculty use both in classroom and research laboratories. To aid in application of the methodology for academic purposes, also provided are a test design philosophy; an example for measurement of density and kinematic viscosity; and recommendations for application/integration of uncertainty assessment methodology into the test process and for documentation of results. Additionally, recommendations laboratory administrators are included.
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This note was uploaded on 12/08/2011 for the course MECHANICS 57:020 taught by Professor Fredrickstern during the Fall '10 term at University of Iowa.

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efdua - SUMMARY OF EXPERIMENTAL UNCERTAINTY ASSESSMENT...

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