SAE AIR 1678B-2011 Uncertainty of In-Flight Thrust Determination《飞行中推力测定的不确定性》.pdf

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2、QVLELOLWRIWKHXVHU SAE reviews each technical report at least every five years at which time it may be revised, reaffirmed, stabilized, or cancelled. SAE invites your written comments and suggestions. Copyright 2016 SAE International All rights reserved. No part of this publication may be reproduced,

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4、0790 Email: CustomerServicesae.org SAE WEB ADDRESS: http:/www.sae.org SAE values your input. To provide feedback on this Technical Report, please visit http:/www.sae.org/technical/standards/AIR1678B AEROSPACE INFORMATION REPORT AIR1678 REV. B Issued 1985-08 Revised 2011-05 Reaffirmed 2016-10 Superse

5、ding AIR1678A Uncertainty of In-Flight Thrust Determination RATIONALE AIR1678B has been reaffirmed to comply with the SAE five-year review policy. FOREWORD In 1972, the Safety Standardization Advisory Committees of the SAE Aerospace Council, working with the SAE Propulsion Division suggested the nee

6、d for improved knowledge of aircraft propulsion system in-flight thrust. Later, the U.S. Air Force Aeronautical Systems Division independently made a similar suggestion. The Propulsion Division and the Aerospace Council concluded that the real need was to establish a forum where this subject could b

7、e discussed by knowledgeable experts on a technical basis. SAE undertook to do so. Dr. Robert Abernethy was commissioned by George Townsend, Propulsion Division Chairman, to organize the In-Flight Propulsion Measurement Committee E-33. Mr. Gary Adams, representing the Air Force, was also involved in

8、 organizing the E-33 Committee at this early stage. The first meeting took place in December 1978. The E-33 Committee endeavored to gather industry-wide expertise in in-flight thrust measurement and uncertainty analysis. The committee was organized into Subcommittees A/B which concentrated on thrust

9、-drag bookkeeping and thrust determination methodology and Subcommittee C which addressed the subject of thrust determination uncertainty. After reviewing the industry state-of-the-art, Committee E-33 determined that it would be appropriate to assemble and publish two companion Aerospace Information

10、 Reports. Subcommittee E-33A/B was organized under Chairman John Roberts to produce AIR1703, “In-Flight Thrust Determination.“ Subcommittee E-33C, under Chairman Gary Adams, produced AIR1678, “Uncertainty of In-Flight Thrust Determination.“ Together these reports provided a comprehensive survey of i

11、n-flight thrust determination, beginning with definitions and concluding with guidelines for planning a total program and estimating the measurement errors. The original version of AIR1678 was published in 1985 and later reaffirmed in December 1992. In 1996, Subcommittee E-33C under the chairmanship

12、 of Mike McGonigle undertook a revision to the document to bring it into compliance with other national and international standards, primarily ANSI/ASME PTC 19.1-1998 and the ISO Guide to the Expression of Uncertainty in Measurement. This work was completed by the committee under the leadership of G

13、lenn Steele and published in 2002. Revision B continued this development and was completed in 2011. SAE INTERNATIONAL AIR1678B Page 2 of 77 INTRODUCTION Estimating the measurement error or uncertainty is an essential element in the complex process of evaluating in-flight thrust. During the pre-fligh

14、t planning phase, it is necessary to assess the accuracy of the candidate methodologies for determining in-flight thrust and to select those which best satisfy program requirements and resources. Estimation of measurement error defines parameter accuracy, data acquisition, and data reduction require

15、ments for the ground and flight test phases; and post-flight is used to examine the consistency of the test results with pretest predictions and with vehicle performance estimates. The purpose of this document is to provide information covering methods for estimating the effects of the measurement e

16、rror or uncertainty of in-flight thrust determination in aircraft employing conventional turbofan/turbojet engines. Methodologies beyond those presented are required in order to evaluate configurations such as vectored thrust or V/STOL. This document is intended to be used as a technical guide. It i

17、s not intended to be used as a standard or legal document. A companion document, Reference 2.1.1.1, presents information and guidance on the selection and use of methodologies to predict and assess propulsion system in-flight thrust. Both documents describe comprehensive procedures and tasks for imp

18、lementing the methodologies. Each program would select those tasks that are appropriate to meet its particular objectives. The term “in-flight thrust determination“ is used synonymously with “in-flight thrust measurement“ although in-flight thrust is not directly measured but is determined or calcul

19、ated using mathematical modeling relationships between in-flight thrust and various direct measurements of physical quantities. The in-flight thrust determination process includes both Ground Testing and Flight Testing, Figure 1. The mathematical modeling relationships between the in-flight thrust a

20、nd the measurements of the physical quantities are calibrated in Ground Tests. Error effect estimates for each item shown in Figure 1 are required to calculate the uncertainty of the “in-flight thrust measurement.“ FIGURE 1 - THE IN-FLIGHT THRUST MEASUREMENT PROCESS Ground Test Facility Measured Thr

21、ust (gt) Math Model(s) Calculated Thrust (gi) Flight TestBasic Measurement Parameters Calculated In-Flight Thrust (fi), (t) Calculated In-Flight Thrust Corrected to Desired Flight Condition (c) Calibrated Lapse Rate Model (cm) Basic Measurement Parameters Calibrated Math Model(s) (mm) SAE INTERNATIO

22、NAL AIR1678B Page 3 of 77 The text is organized into the following major topics: Measurement Uncertainty Methodology (Section 4): This section describes the concepts involved in estimating the uncertainty of in-flight thrust. Its purpose is to provide a common basis for understanding. The methodolog

23、y includes the use of statistical and engineering concepts to meet the need for an easily interpreted estimate of uncertainty (References 2.1.2.1, 2.1.4.1). In-Flight Thrust Measurement Processes (Section 5): This section describes the ground test and flight test phases of the in-flight thrust deter

24、mination process. The five sets of fundamental error components which must be evaluated to determine the uncertainty of in-flight thrust are identified. Application of Uncertainty Methodology to the In-Flight Thrust Program (Section 6): The uncertainty methodology described in Section 4 is applied t

25、o the In-Flight Thrust Measurement Process described in Section 5. Four representative test program phases are defined, i.e., Program Definition Planning, Ground Test, Flight Test, and Results Analysis. The tasks to be accomplished in each phase are described in Reference 2.1.4.5 and shown in Table

26、8. Seven Appendices are also included: x Appendix A - Small Sample Statistical Methods Special, small sample, statistical methods are required to determine the value for the Students “t95“ distribution when the degrees of freedom of the result is less than 10 (Reference 2.1.4.2). This appendix discu

27、sses the t value, degrees of freedom, and the propagation of degrees of freedom. A table of “t95“ values is presented for degrees of freedom from one to thirty. x Appendix B - Impact of Measurement Process on Error Classification and Estimation This appendix discusses the decision logic for the clas

28、sification of error based on the actual measurement process. Reclassification is discussed and the concept of fossilized error is introduced. x Appendix C - Example Influence Coefficient Calculations x Appendix D - Initial Performance Survey of Thrust Measurement Options This appendix uses the publi

29、shed results of the Air Launched Cruise Missile Program to illustrate the approach for conducting an initial performance survey of thrust options. x Appendix E - Calibrated Mathematical Model and the Associated Uncertainty Components for Flight Test The term “calibrated mathematical model“ is discus

30、sed and simplified examples of two common approaches are provided. x Appendix F Nonsymmetric Uncertainties x Appendix G Background of Uncertainty Methodology SAE INTERNATIONAL AIR1678B Page 4 of 77 TABLE OF CONTENTS 1.SCOPE 6 2.REFERENCES 6 2.1Applicable Documents 62.1.1SAE Publications . 62.1.2ANSI

31、 Publications . 72.1.3ASME Publications 72.1.4Applicable References 72.2Symbols 92.3Subscripts . 102.4Superscripts 11 3.GLOSSARY 11 4.MEASUREMENT UNCERTAINTY METHODOLOGY 13 4.1Measurement Error . 144.1.1Error Classification 144.1.2Sources of Measurement Errors . 184.1.3Estimating Measurement Uncerta

32、inty . 214.1.4Combining Measurement Uncertainties 244.1.5Propagation of Basic Measurement Uncertainties to Thrust Parameters 254.2Measurement Uncertainty . 264.2.1Uncertainty Interval Coverage 264.2.2Propagation of Uncertainty Components 264.2.3Pretest and Posttest Analyses 274.3Reporting Measuremen

33、t Uncertainty 27 5.IN-FLIGHT THRUST MEASUREMENT PROCESSES 29 5.1Ground Test Measurement Process . 305.2Flight Test Measurement Process 32 6.APPLICATION OF UNCERTAINTY METHODOLOGY TO THE IN-FLIGHT THRUST PROGRAM . 32 6.1Program Definition and Planning 346.1.1In-Flight Thrust Measurement Options . 356

34、.1.2Initial Survey of Thrust Measurement Options 356.2Ground Test 376.2.1Ground Pretest Uncertainty Analysis 376.2.2Ground Posttest Analysis 406.3Flight Test . 456.3.1Flight Pretest Uncertainty Analysis . 476.3.2Flight Posttest Analysis . 476.4Results Analyses. 476.4.1Review of Ground and Flight Tes

35、t Results . 476.4.2Test Data Averaging . 486.4.3Program Data Uncertainty Reporting 48 SAE INTERNATIONAL AIR1678B Page 5 of 77 FIGURE 1 THE IN-FLIGHT THRUST MEASUREMENT PROCESS . 2FIGURE 2 MEASUREMENT ERROR, G 14FIGURE 3 ERROR CLASSIFICATION 15FIGURE 4 MEASUREMENT ERROR COMPONENTS (SYSTEMATIC AND RAN

36、DOM) . 15FIGURE 5 NORMAL DISTRIBUTION CURVE RESULTING FROM TYPICAL STEADY-STATE DATA MEASUREMENT . 16FIGURE 6 SYSTEMATIC ERROR . 17FIGURE 7 MEASUREMENT CALIBRATION HIERARCHY . 18 FIGURE 8 EXAMPLE DATA ACQUISITION SYSTEM 20 FIGURE 9 DISTRIBUTION OF iX AND iX 22FIGURE 10 SYSTEMATIC STANDARD UNCERTAINT

37、Y ESTIMATION (WITH A NORMAL DISTRIBUTION OF ) . 23FIGURE 11 GROUND TEST THRUST MEASUREMENT PROCESS INCLUDING DEFINITION/CALIBRATION OF MATHEMATICAL MODEL(S) 31 FIGURE 12 GENERAL FLIGHT TEST THRUST MEASUREMENT PROCESS . 338FIGURE 13 GROUND TEST MEASUREMENT PROCESS EVALUATION CYCLE . 38FIGURE 14 IN-FL

38、IGHT THRUST MEASUREMENT PROCESS UNCERTAINTY PROPAGATION 42FIGURE 15 ILLUSTRATION OF MATHEMATICAL MODEL SYSTEMATIC ERROR . 43FIGURE 16 ILLUSTRATION OF MATHEMATICAL MODEL (CORRECTED FOR rE ) STANDARD DEVIATION 44FIGURE 17 FLIGHT TEST MEASUREMENT PROCESS EVALUATION CYCLES 46TABLE 1 CALIBRATION HIERARCH

39、Y ERROR SOURCES . 19TABLE 2 TEST ARTICLE AND / OR INSTRUMENTATION INSTALLATION ERROR SOURCES 19TABLE 3 TYPICAL DATA ACQUISITION ERROR SOURCES . 20TABLE 4 TYPICAL DATA REDUCTION ERROR SOURCES . 21TABLE 5 TYPICAL ERRORS OF METHOD SOURCES . 21TABLE 6 RECOMMENDED TABLE FORMAT FOR REPORTING ELEMENTAL UNC

40、ERTAINTIES FOR ONE BASIC MEASUREMENT . 28TABLE 7 RECOMMENDED TABLE FORMAT FOR PERFORMANCE PARAMETER UNCERTAINTY SUMMARY . 29TABLE 8 IN-FLIGHT THRUST MEASUREMENT UNCERTAINTY ACTIVITIES 34TABLE 9 EXAMPLE PRELIMINARY PERFORMANCE SURVEY FOR NET THRUST OPTION 1 36TABLE 10 EXAMPLE ELEMENTAL UNCERTAINTIES

41、FOR ONE BASIC MEASUREMENT REPORT 39TABLE 11 EXAMPLE PERFORMANCE PARAMETER UNCERTAINTY SUMMARY 40APPENDIX A SMALL SAMPLE STATISTICAL METHODS 49APPENDIX B IMPACT OF MEASUREMENT PROCESS ON ERROR CLASSIFICATION AND ESTIMATION . 54 APPENDIX C EXAMPLE INFLUENCE COEFFICIENT CALCULATIONS 56APPENDIX D INITIA

42、L PERFORMANCE SURVEY OF THRUST MEASUREMENT OPTIONS . 59 APPENDIX E CALIBRATED MATHEMATICAL MODEL AND THE ASSOCIATED UNCERTAINTY COMPONENTS FOR FLIGHT TESTS 62APPENDIX F NONSYMMETRIC UNCERTAINTIES 71 APPENDIX G BACKGROUND OF UNCERTAINTY METHODOLOGY 76 SAE INTERNATIONAL AIR1678B Page 6 of 77 1. SCOPE

43、This document defines and illustrates the process for determination of uncertainty of turbofan and turbojet engine in-flight thrust and other measured in-flight performance parameters. The reasons for requiring this information, as specified in the E-33 Charter, are: x determination of high confiden

44、ce aircraft drag; x problem rectification if performance is low; x interpolation of measured thrust and aircraft drag over a range of flight conditions by validation and development of high confidence analytical methods; x establishment of a baseline for future engine modifications. This document de

45、scribes systematic and random measurement uncertainties and methods for propagating the uncertainties to the more complicated parameter, in-flight thrust. Methods for combining the uncertainties to obtain given confidence levels are also addressed. Although the primary focus of the document is in-fl

46、ight thrust, the statistical methods described are applicable to any measurement process. The E-33 Committee has endeavoured to gather industry-wide expertise in in-flight measurement and uncertainty analysis to collect and promulgate recommended practices in the subject disciplines. The Committee i

47、s organized into subcommittees to address both the analytical and test methodology for determination of in-flight thrust and also the uncertainty of the determination. This document; Uncertainty of In-flight Thrust Determination, AIR1678, addresses the process for determining the uncertainty of in-f

48、light thrust. A companion document, In-Flight Thrust Determination, AIR1703, addresses the basic methodology for determining in-flight thrust. The Committee, after reviewing recommended changes and clarification in definitions and application of statistical uncertainty items, made small revisions to the original documen