1、GuideAssessing Experimental Uncertainty Supplement to AIAA S-071A-1999AIAA standards are copyrighted by the American Institute of Aeronautics andAstronautics (AIAA), 1801 Alexander Bell Drive, Reston, VA 20191-4344 USA. All rightsreserved.AIAA grants you a license as follows: The right to download a
2、n electronic file of this AIAAstandard for temporary storage on one computer for purposes of viewing, and/or printingone copy of the AIAA standard for individual use. Neither the electronic file nor the hardcopy print may be reproduced in any way. In addition, the electronic file may not bedistribut
3、ed elsewhere over computer networks or otherwise. The hard copy print may onlybe distributed to other employees for their internal use within your organization.AIAAG-045-2003AIAAG-045-2003GuideAssessing Experimental Uncertainty Supplement to AIAA S-071A-1999Sponsored byAmerican Institute of Aeronaut
4、ics and AstronauticsAbstractThis AIAA Guide supplements the methodology for assessment of experimental uncertainties andtechniques for evaluating experimental error sources provided in AIAA Standard S-071A-1999,“Assessment of Experimental Uncertainty with Application to Wind Tunnel Testing.“ This do
5、cumentprovides additional information and examples to assist the experimentalist in performing an uncertaintyanalysis. Its focus is on helping the experimenter begin to apply uncertainty analysis techniques. Theinformation contained in the standard and this guide is not limited to wind tunnel testin
6、git can be appliedto a wide range of experiments.AIAA G-045-2003iiLibrary of Congress Cataloging-in-Publication DataGuide : assessing experimental uncertainty : supplement to AIAAS-071A-1999 / sponsored by American Institute of Aeronautics andAstronautics.p. cm.Includes bibliographical references.IS
7、BN 1-56347-663-0 (hardcopy) - ISBN 1-56347-664-9 (electronic)1. Wind tunnels. 2. Airplanes-Models-Testing-Standards. 3.Uncertainty (Information theory) I. Title: Assessing experimentaluncertainty. II. American Institute of Aeronautics and Astronautics.III. Assessment of experimental uncertainty with
8、 application to windtunnel testing.TL567.W5A87 1999 Suppl.629.13452-dc222003024006Published byAmerican Institute of Aeronautics and Astronautics1801 Alexander Bell Drive, Suite 500, Reston, VA 20191-4344Copyright 2003 American Institute of Aeronautics andAstronauticsAll rights reserved.No part of th
9、is publication may be reproduced in any form, in an electronic retrievalsystem or otherwise, without prior written permission of the publisher.Printed in the United State of AmericaAIAA G-045-2003iiiCONTENTSForeword.vDedication viPart I Basic Topics. 11 Introduction 12 Uncertainty Methodology and Ap
10、plication 22.1 Methodology Primer . 22.1.1 Single Test 42.1.2 Multiple Tests 42.1.3 Relative Sensitivity Factors 52.2 Application Primer. 52.2.1 Experiment Definition . 52.2.2 Uncertainties of the Experimental Results. 62.2.2.1 Multiple Tests 62.2.2.2 Single Test 93 General Uncertainty Analysis Exam
11、pleEvaluating Measurement Methods. 113.1 Introduction . 113.2 Mach Number Equations 113.3 Uncertainty Analysis. 123.3.1 Partial Derivative Terms . 133.3.2 Transducer Uncertainty 143.3.3 Mach Number Uncertainty 143.3.4 Relative Sensitivity Factors 164 General Uncertainty Analysis ExampleEvaluating Da
12、ta Reduction Equations . 184.1 Turbine Efficiency Equations 194.2 Procedure . 194.3 Results 204.3.1 Overall Uncertainty . 204.3.2 UMF. 204.3.3 UPC. 214.3.4 Summary. 225 Systematic Uncertainties and Correlation. 305.1 Systematic Uncertainties 305.2 Correlated Systematic Uncertainties 325.2.1 Bath Uni
13、formity . 335.2.2 Standard Uncertainty 34AIAA G-045-2003iv5.3 Correlated Systematic Uncertainties Example 34Part II Advanced Topics 386 Random Uncertainties and Correlation. 386.1 Random Uncertainties 386.2 Correlated Random Uncertainty Example . 386.2.1 Background. 386.2.2 Calibration Approach and
14、Results . 396.2.3 Uncertainty Analysis. 406.3 Discharge Coefficient and Mass Flow Rate Equations . 447 Regression Uncertainty . 477.1 Categories of Regression Uncertainty . 477.1.1 Uncertainty in Coefficients 487.1.2 Uncertainty in Y from Regression Model . 487.1.3 (Xi, Yi) Variables are Functions 4
15、97.2 Linear Regression Uncertainty. 497.2.1 General Approach. 497.2.2 Reporting Regression Uncertainties 517.2.3 Differential Pressure Transducer Calibration Example . 527.2.4 X and Y as Functional Relations 547.2.5 1stOrder Regressions. 567.2.5.1 Uncertainty in Coefficients 567.2.5.2 Classical Regr
16、ession Random Uncertainty . 587.2.5.3 Lift Slope and Lift Coefficient Example 598 Automated Uncertainty Analysis for Production Experiments . 648.1 Introduction . 648.2 Error Propagation . 648.3 Estimation of Input Uncertainties . 658.3.1 Systematic Uncertainty Estimation 668.3.2 Random Uncertainty
17、Estimation. 678.3.3 Specific Uncertainty Estimates. 678.4 Results 688.5 Summary. 689 Useful References . 79AIAA G-045-2003vForewordExperimental uncertainty is a complex subject involving both statistical techniques and engineeringjudgment. In 1995 the AIAA Standards Technical Council approved an AIA
18、A Standard on experimentaluncertainty that was revised in 1999 (AIAA S-071A-1999, “Assessment of Experimental Uncertainty withApplication to Wind Tunnel Testing“). The AIAA adopted the contents of an Advisory Report (AR-304) setforth by the Advisory Group for Aerospace Research and Development (AGAR
19、D). The AIAA Standarddefines a rational and practical framework for quantifying and reporting experimental uncertainty andpresents the application of the methodology to wind tunnel testing. This AIAA Guide supplements thestandard. It provides additional information and examples to assist the experim
20、entalist in performing anuncertainty analysis. Its focus is on helping the experimenter begin to apply uncertainty analysistechniques.The AIAA Standards Procedures provide that all approved Standards, Recommended Practices, andGuides are advisory only. Their use by anyone engaged in industry or trad
21、e is entirely voluntary. Thereis no agreement to adhere to any AIAA standards publication and no commitment to conform to or beguided by a standards report. In formulating, revising, and approving standards publications, theCommittees on Standards will not consider patents that may apply to the subj
22、ect matter. Prospectiveusers of the publications are responsible for protecting themselves against liability for infringement ofpatents or copyrights, or both.The Standards Subcommittee of the AIAA Ground Test Technical Committee (Mr. E.A. Arrington,Chairperson) had many members who contributed to t
23、his document over the course of its preparation.The following individuals should be recognized for their contributions:Gregory Addington, Chairperson Air Force Research LabDavid M. Cahill Sverdrup Tech., AEDCJulie Carlile Air Force Research LabDaniel Cresci GASLSusan T. Hudson, Technical Editor-in-C
24、hiefMississippi State UniversityWayne Kalliomaa Air Force Research LabJerry Kegelman NASA Langley Research CenterDaniel E. Marren AEDC/White OakLaura J. McGill RaytheonThomas McLaughlin U.S. Air Force AcademyJulie Morrow U.S. Air Force AcademyMathew L. Rueger BoeingWilliam A. Straka Applied Research
25、 Lab., Penn State UniversityJames C. Yu NASA Langley Research CenterAIAA G-045-2003viThe committee members would like to acknowledge the following individuals for their valuablecontributions and reviews of this document:Kendall Brown NASA Marshall Spaceflight CenterMark Kammeyer BoeingHugh Coleman U
26、niv. of Alabama in HuntsvilleGlenn Steele Mississippi State UniversityStephen McClain University of Alabama in BirminghamThe principal authors and reviewers of this document were: Susan Hudson, Kendall Brown, MarkKammeyer, David Cahill, Hugh Coleman, Glenn Steele, and Stephen McClain.The AIAA Ground
27、 Test Technical Committee (Mr. Allen Arrington, Chairman) approved the document forpublication in January 2003The AIAA Standards Executive Council (Mr. Phil Cheney, Chairman) accepted the document forpublication in September 2003.The AIAA Standards Procedures provide that all approved Standards, Rec
28、ommended Practices, andGuides are advisory only. Their use by anyone engaged in industry or trade is entirely voluntary. There isno agreement to adhere to any AIAA standards publication and no commitment to conform to or beguided by a standards report. In formulating, revising, and approving standar
29、ds publications, theCommittees on Standards will not consider patents which may apply to the subject matter. Prospectiveusers of the publications are responsible for protecting themselves against liability for infringement ofpatents or copyrights, or both.DedicationThis document is dedicated to the
30、late Frank Wright of Boeing Commercial Airplane Company. Frankserved as an outstanding role model for those practicing experimental uncertainty analysis and itsapplications to data quality assurance in ground testing. He was a world-wide crusader for experimentaluncertainty analysis. Most of us on t
31、he Standards Subcommittee had the privilege of working with Frank.It was his inspiration and dedication to excellence in wind tunnel testing in general and data quality inparticular that started this project. Frank developed the first draft of the guide in 1996 when he was theChair of the Standards
32、Subcommittee. Much of Franks vision is incorporated in this Guide. Our hope isthat, through this Guide, more engineers will be inspired as we were inspired by Frank.AIAA G-045-20031Part I Basic Topics1 IntroductionExperimental uncertainty has long been a topic of discussion and controversy in the ae
33、rospacecommunity. The problem is not the lack of good methodology in this area; references on the subject existand are readily available. The difficulty has been in the application of the methodology with consistencyand regularity. For the novice, or even the experienced researcher, the mass of equa
34、tions presented inthe references can be intimidating. Further, although some examples illustrating the application of theuncertainty analysis methodology are presented in the references, it is sometimes difficult for the readerto grasp how the examples apply to their particular testing requirements.
35、 This document providessupplemental information and examples to assist the experimentalist in performing an uncertaintyanalysis. Its focus is on helping one get started. This document assumes that the reader has reviewedthe Standard to become familiar with the principles and terminology. The example
36、s given are simplymeant to guide one through the uncertainty analysis process for particular cases so that the process canbe more easily understood. They are not meant to define techniques for conducting similar experiments,though sound engineering principles are applied throughout the document.Unce
37、rtainty analysis is a useful and essential part of an experimental program. Data quality assessmentis a key part of the entire testing process, and should, therefore, be applied in all phases of anexperiment. A general analysis performed in the planning phase allows a comprehensive examination ofthe
38、 experimental process. This type of analysis can inform one beforehand, during the design of theexperiment, when the experiment cannot meet the desired uncertainty limits. It can also show whenimproved instruments and/or improved processes must be found to obtain a given output uncertainty.Similarly
39、, it can identify instrumentation and/or processes that control uncertainty and allow changes to bemade to meet test goals. Additionally, a general uncertainty analysis can provide a check againstunknowingly taking data under test conditions where uncertainties become intolerably large.Once the test
40、 data is collected, a detailed uncertainty analysis should be performed. The detailedanalysis uses the actual experimental data and the uncertainties associated with this data. This analysisprovides an assessment of the quality of the experimental data and provides a basis for comparing thetest resu
41、lts with analyses or results from other test facilities.Any uncertainty analysis requires “engineering judgment.” A lack of explicit information for uncertaintyestimates does not prohibit performing an uncertainty analysis. The use of some appropriate uncertaintyanalysis is indispensable in experime
42、ntation and any appropriate or approximate analysis is far betterthan no analysis, as long as the process is explained for the user.This document will provide examples to help with the application of uncertainty analyses. It will begin witha brief overview of the methodology. (Details of the methodo
43、logy are contained in the Standard.) Thiswill be followed by a detailed example of applying uncertainty analysis to a simple situation to illustratethe basics of the methodology. Increasingly complex examples will then address various uncertaintyanalysis aspects. Details of the calculations will be
44、shown in the early chapters to aid in understanding.As the examples become more complex and the reader becomes more familiar with the methodology,fewer calculations will be shown. A comprehensive example for an experimental system is given as thelast example to further demonstrate the potential of u
45、ncertainty analysis. The document will end with amodern list of useful references. Since the field of uncertainty analysis is constantly evolving, one mustbe particularly careful to use up-to-date references.AIAA G-045-200322 Uncertainty Methodology and Application2.1 Methodology PrimerThis section
46、will give a brief overview of uncertainty analysis methods and how errors propagate througha given data reduction equation. A comprehensive discussion of uncertainty analysis techniques iscontained in the AIAA Uncertainty Standard (Ref. 2.1). The reader is directed to the Standard andreference 2.2 t
47、o get in-depth information on experimental uncertainty and its application to anexperimental process.The word accuracy is generally used to indicate the relative closeness of agreement between anexperimentally-determined value of a quantity and its true value. Error is the difference between theexpe
48、rimentally-determined value and its true value; therefore, as error decreases, accuracy is said toincrease. Since the true value is not known, it is necessary to estimate error, and that estimate is calledan uncertainty, U. Uncertainty estimates are made at some confidence levela 95% confidenceestim
49、ate, for example, means that the true value of the quantity is expected to be within the U intervalabout the experimentally-determined value 95 times out of 100.Total error can be considered to be composed of two components: a random (precision) component, ,and a systematic (bias) component, . The terms precision and random as well as bias and systematicwill be used interchangeably in this document. The classification of errors as random or systematic isdefined in the Standard and maintained in this Guide. An error is classified as random if it contributes tothe scatter of th
