Experimentation, Validation, and Uncertainty Analysis for Engineers, Third Edition

✍ Scribed by Hugh W. Coleman, W. Glenn Steele

• Publisher: Wiley
• Year: 2009
• Tongue: English
• Leaves: 334
• Edition: 3
• Category: Library

✦ Synopsis

This Third Edition helps you assess and manage uncertainty at all stages of experimentation and validation of simulationsIn this greatly expanded Third Edition, the acclaimed Experimentation, Validation, and Uncertainty Analysis for Engineers guides readers through the concepts of experimental uncertainty analysis and the applications in validating models and simulations, solving problems experimentally, and characterizing the behavior of systems. This Third Edition presents the current, internationally accepted methodology from ISO, ANSI, and ASME standards to cover the planning, design, debugging, and execution phases of experiments. Cases in which the experimental result is determined only once or when the result is determined multiple times in a test are addressed and illustrated with examples from the authors' experience. The important practical cases in which multiple measured variables share correlated errors are discussed in detail, and strategies to take advantage of such effects in calibrations and comparative testing situations are presented. The methodology for determining uncertainty by Monte Carlo analysis is described in detail.Knowledge of the material in this Third Edition is a must for those involved in executing or managing experimental programs or validating models, codes, and simulations. Professionals and students in disciplines spanning the full range of engineering and science will find this book an essential guide.

✦ Table of Contents

Cover
......Page 1
EXPERIMENTATION, VALIDATION, AND UNCERTAINTY ANALYSIS FOR ENGINEERS, 3rd ed.......Page 4
ISBN 9780470168882......Page 5
CONTENTS......Page 8
PREFACE......Page 16
1 EXPERIMENTATION, ERRORS, AND UNCERTAINTY......Page 18
1-1.1 Why Is Experimentation Necessary?......Page 19
1-1.2 Degree of Goodness and Uncertainty Analysis......Page 20
1-1.3 Experimentation and Validation of Simulations......Page 22
1-2.1 Questions to Be Considered......Page 23
1-2.2 Phases of Experimental Program......Page 24
1-3.1 Errors and Uncertainties......Page 25
1-3.2 Degree of Confidenc and Uncertainty Intervals......Page 31
1-3.3 Expansion of Concept from “Measurement Uncertainty” to “Experimental Uncertainty”......Page 32
1-3.4 Elemental Systematic Errors and Effects of Calibration......Page 34
1-3.5 Repetition and Replication......Page 36
1-4 EXPERIMENTAL RESULTS DETERMINED FROM MULTIPLE MEASURED VARIABLES......Page 38
1-5.1 Experimental Uncertainty Analysis......Page 41
1-6 A NOTE ON NOMENCLATURE......Page 42
2-1 STATISTICAL DISTRIBUTIONS......Page 46
2-2.1 Mathematical Description......Page 50
2-2.2 Confidence Intervals in Gaussian Distribution......Page 55
2-3.1 Statistical Parameters of Sample Population......Page 57
2-3.2 Confidence Intervals in Sample Populations......Page 58
2-3.3 Tolerance and Prediction Intervals in Sample Populations......Page 61
2-4 STATISTICAL REJECTION OF OUTLIERS FROM A SAMPLE......Page 64
2-5.1 Systematic Standard Uncertainty Estimation......Page 68
2-5.2 Overall Uncertainty of a Measured Variable......Page 70
2-5.3 Large-Sample Uncertainty of a Measured Variable......Page 72
2-5.4 Uncertainty of Measured Variable by Monte Carlo Method......Page 74
2-6 SUMMARY......Page 75
3 UNCERTAINTY IN A RESULT DETERMINED FROM MULTIPLE VARIABLES......Page 78
3-1.1 TSM for Function of Multiple Variables......Page 79
3-1.3 Large-Sample Approximation for Uncertainty of a Result......Page 82
3-1.4 Example of TSM Uncertainty Propagation......Page 85
3-1.5 Numerical Approximation for TSM Propagation of Uncertainties......Page 87
3-2.1 General Approach for MCM......Page 88
3-2.2 Example of MCM Uncertainty Propagation......Page 91
3-2.3 Coverage Intervals for MCM Simulations......Page 95
3-2.4 Example of Determination of MCM Coverage Interval......Page 97
4-1 OVERVIEW: USING UNCERTAINTY PROPAGATION IN EXPERIMENTS AND VALIDATION......Page 102
4-2 GENERAL UNCERTAINTY ANALYSIS USING THE TAYLOR SERIES METHOD (TSM)......Page 103
4-3.1 Simple Case......Page 105
4-3.2 Special Functional Form......Page 109
4-4 USING TSM UNCERTAINTY ANALYSIS IN PLANNING AN EXPERIMENT......Page 113
4-5.2 Proposed Measurement Technique and System......Page 115
4-5.3 Analysis of Proposed Experiment......Page 116
4-5.4 Implications of Uncertainty Analysis Results......Page 118
4-5.5 Design Changes Indicated by Uncertainty Analysis......Page 119
4-6.1 The Problem......Page 120
4-6.2 Two Proposed Experimental Techniques......Page 121
4-6.3 General Uncertainty Analysis: Steady-State Technique......Page 123
4-6.4 General Uncertainty Analysis: Transient Technique......Page 127
4-6.5 Implications of Uncertainty Analysis Results......Page 129
4-7.1 Results from Analysis of a Turbine Test......Page 130
4-7.2 Results from Analysis of a Solar Thermal Absorber/Thruster Test......Page 131
4-8 APPLICATION IN VALIDATION: ESTIMATING UNCERTAINTY IN SIMULATION RESULT DUE TO UNCERTAINTIES IN INPUTS......Page 132
5-1 USING DETAILED UNCERTAINTY ANALYSIS......Page 138
5-2 DETAILED UNCERTAINTY ANALYSIS: OVERVIEW OF COMPLETE METHODOLOGY......Page 141
5-3 DETERMINING RANDOM UNCERTAINTY OF EXPERIMENTAL RESULT......Page 145
5-3.1 Example: Random Uncertainty Determination in Compressible Flow Venturi Meter Calibration Facility......Page 147
5-3.2 Example: Random Uncertainty Determination in Laboratory-Scale Ambient Temperature Flow Test Facility......Page 149
5-3.3 Example: Random Uncertainty Determination in Full-Scale Rocket Engine Ground Test Facility......Page 152
5-3.4 Summary......Page 154
5-4.1 Systematic Uncertainty for Single Variable......Page 155
5-4.2 Systematic Uncertainty of a Result Including Correlated Systematic Error Effects......Page 162
5-4.3 Comparative Testing and Correlated Systematic Error Effects......Page 168
5-5.1 Problem......Page 174
5-5.2 Measurement System......Page 175
5-5.3 Zeroth-Order Replication-Level Analysis......Page 176
5-5.4 First-Order Replication-Level Analysis......Page 180
5-6.1 Basic Ideas......Page 182
5-6.2 Example......Page 183
5-7.1 Choice of Test Points: Rectification......Page 189
5-7.2 Choice of Test Sequence......Page 194
5-7.3 Relationship to Statistical Design of Experiments......Page 196
5-7.4 Use of Balance Checks......Page 197
5-7.5 Use of a Jitter Program......Page 200
5-7.6 Comments on Transient Testing......Page 201
6-1 INTRODUCTION TO VALIDATION METHODOLOGY......Page 210
6-2 ERRORS AND UNCERTAINTIES......Page 211
6-3 VALIDATION NOMENCLATURE......Page 212
6-4 VALIDATION APPROACH......Page 214
6-6 ESTIMATION OF VALIDATION UNCERTAINTY......Page 217
6-6.1 Estimating uval When Experimental Value D of Validation VariableIs Directly Measured (Case 1)......Page 218
6-6.2 Estimating uval When Experimental Value D of Validation VariableIs Determined from Data Reduction Equation (Cases 2 and 3)......Page 221
6-6.3 Estimating uval When Experimental Value D of Validation VariableIs Determined from Data Reduction Equation That Itself Is a Model (Case 4)......Page 226
6-7.1 Interpretation with No Assumptions Made about Error Distributions......Page 230
6-7.2 Interpretation with Assumptions Made about Error Distributions......Page 231
6-8 SOME PRACTICAL POINTS......Page 232
7 DATA ANALYSIS, REGRESSION, AND REPORTING OF RESULTS......Page 234
7-1.1 Categories of Regression Uncertainty......Page 235
7-1.3 Uncertainty in Y from Regression Model......Page 236
7-2 LEAST-SQUARES ESTIMATION......Page 238
7-3 CLASSICAL LINEAR REGRESSION UNCERTAINTY: RANDOM UNCERTAINTY......Page 240
7-4.1 Uncertainty in Coefficiets: First-Order Regression......Page 242
7-4.2 Uncertainty in Y from Regression Model: First-Order Regression......Page 244
7-5 REPORTING REGRESSION UNCERTAINTIES......Page 246
7-6 REGRESSIONS IN WHICH X AND Y ARE FUNCTIONALRELATIONS......Page 248
7-7 EXAMPLES OF DETERMINING REGRESSIONS AND THEIR UNCERTAINTIES......Page 250
7-7.1 Experimental Apparatus......Page 251
7-7.2 Pressure Transducer Calibration and Uncertainty......Page 252
7-7.3 Venturi Discharge Coefficien and Its Uncertainty......Page 255
7-7.4 Flow Rate and Its Uncertainty in a Test......Page 259
7-8 MULTIPLE LINEAR REGRESSION......Page 263
APPENDIX A USEFUL STATISTICS......Page 268
APPENDIX B TAYLOR SERIES METHOD (TSM) FOR UNCERTAINTY PROPAGATION......Page 274
B-1 DERIVATION OF UNCERTAINTY PROPAGATION EQUATION......Page 275
B-2 COMPARISON WITH PREVIOUS APPROACHES......Page 279
B-3 ADDITIONAL ASSUMPTIONS FOR ENGINEERING APPLICATIONS......Page 282
C-1 MONTE CARLO SIMULATIONS......Page 288
C-2 SIMULATION RESULTS......Page 291
APPENDIX D SHORTEST COVERAGE INTERVAL FOR MONTE CARLO METHOD......Page 300
APPENDIX E ASYMMETRIC SYSTEMATIC UNCERTAINTIES......Page 302
E-1 PROCEDURE FOR ASYMMETRIC SYSTEMATIC UNCERTAINTIES USING TSM PROPAGATION......Page 303
E-3 EXAMPLE: BIASES IN A GAS TEMPERATURE MEASUREMENT SYSTEM......Page 307
F-1 GENERAL INSTRUMENT RESPONSE......Page 316
F-2 RESPONSE OF ZERO-ORDER INSTRUMENTS......Page 318
F-3 RESPONSE OF FIRST-ORDER INSTRUMENTS......Page 319
F-4 RESPONSE OF SECOND-ORDER INSTRUMENTS......Page 321
F-5 SUMMARY......Page 325
C......Page 326
D......Page 327
F......Page 328
M......Page 329
R......Page 330
S......Page 331
T......Page 332
V......Page 333
Z......Page 334