Experimentation and Uncertainty Analysis for Engineers, 2nd Edition

by Hugh W. Coleman (Univ. of Alabama ); W. Glenn Steele (Mississippi State Univ.)

• ISBN13: 9780471121466
• ISBN10: 0471121460
• Edition: 2nd
• Format: Hardcover
• Copyright: 1999-01-01
• Publisher: Wiley-Interscience

Summary

The dramatic developments in the field of experimental uncertainty analysis over the last ten years have led to sweeping changes in applications, resulting in a new international experimental uncertainty standard. Now, in the only manual available with direct applications to the design and analysis of engineering experiments, respected authors Hugh Coleman and Glenn Steele have thoroughly updated their bestselling title to include the new methodologies being used by the United States and international standards committee groups. Along with several new examples, this latest edition includes new material on: The utilization of Uncertainty Magnification Factors (UMFs) and Uncertainty Percentage Contributions (UPCs) in the planning and early design phases of experiments Refined procedures for accounting for the effects of correlated bias errors Improved methods for accounting for the effects of asymmetric systematic uncertainties The importance of (previously ignored) correlated random errors with an example illustrating how to account for them Uncertainties in comparative testing Uncertainties in the comparison of data and predictions (code validation) Uncertainty analysis by direct Monte Carlo simulation A new method to determine regression uncertainties that properly accounts for both random and systematic uncertainties With a step-by-step approach, engineering students as well as practicing professional engineers who analyze or design experiments will find Experimentation and Uncertainty Analysis for Engineers, Second Edition to be an invaluable reference tool.

Author Biography

HUGH W. COLEMAN, PhD, PE, holds the Eminent Scholar Chair in Propulsion and is a professor of mechanical engineering at the University of Alabama in Huntsville. Dr. Coleman holds advanced degrees in mechanical engineering from Stanford University and is a fellow of the American Society of Mechanical Engineers and an associate fellow of the American Institute of Aeronautics and Astronautics (AIAA). He has served on uncertainty standards writing committees for the NATO Advisory Group for Aerospace Research and Development and the AIAA. W. GLENN STEELE, PhD, PE, is a William L. Giles Distinguished Professor and head of the Department of Mechanical Engineering at Mississippi State University. Dr. Steele holds advanced degrees in mechanical engineering from North Carolina State University and is a fellow of the American Society of Mechanical Engineers and an associate fellow of the American Institute of Aeronautics and Astronautics. He has served on uncertainty standards writing committees for the ISO, the Society of Automotive Engineers-Aerospace, and the ASME.

Table of Contents

PREFACE	xiii	(2)
PREFACE TO THE FIRST EDITION	xv
1 Experimentation, Errors, and Uncertainty	1	(15)
1-1 Experimentation	1	(3)
1-1.1 Why Is Experimentation Necessary?	1	(2)
1-1.2 Degree of Goodness and Uncertainty Analysis	3	(1)
1-2 Experimental Approach	4	(2)
1-2.1 Questions to Be Considered	4	(1)
1-2.2 Phases of an Experimental Program	5	(1)
1-3 Basic Concepts and Definitions	6	(8)
1-3.1 Systematic and Random Errors: Uncertainty	6	(4)
1-3.2 Systematic Errors and Calibration	10	(2)
1-3.3 Repetition and Replication	12	(2)
1-4 Recent Developments in Uncertainty Analysis	14	(2)
2 Statistical Considerations in Measurement Uncertainties	16	(31)
2-1 Statistical Distributions	16	(2)
2-2 Gaussian Distribution	18	(6)
2-2.1 Mathematical Description	18	(5)
2-2.2 Confidence Intervals in a Guassian Distribution	23	(1)
2-3 Samples from a Gaussian Parent Population	24	(10)
2-3.1 Statistical Parameters of a Sample Population	24	(1)
2-3.2 Confidence Intervals in Sample Populations	25	(3)
2-3.3 Effect of Sample Size	28	(3)
2-3.4 Tolerance and Prediction Intervals in Sample Populations	31	(3)
2-4 Statistical Rejection of Outliers from a Sample	34	(4)
2-5 Uncertainty of a Measured Variable	38	(5)
2-5.1 Systematic Uncertainty Estimation	38	(1)
2-5.2 Overall Uncertainty of a Measured Variable	39	(2)
2-5.3 Large-Sample Uncertainty of a Measured Variable	41	(1)
2-5.4 Comparison with Previous Uncertainty Models	42	(1)
2-6 Summary	43	(4)
3 Planning an Experiment: General Uncertainty Analysis	47	(36)
3-1 Propagation of Uncertainties	48	(1)
3-2 General Uncertainty Analysis	49	(1)
3-3 Application of General Uncertainty Analysis	50	(9)
3-3.1 Simple Case	50	(4)
3-3.2 Special Functional Form	54	(5)
3-4 Using Uncertainty Analysis in Planning an Experiment	59	(1)
3-5 Analysis of a Proposed Particulate Measuring System	60	(6)
3-5.1 Problem	60	(1)
3-5.2 Proposed Measurement Technique and System	61	(1)
3-5.3 Analysis of the Proposed Experiment	62	(2)
3-5.4 Implications of the Uncertainty Analysis Results	64	(1)
3-5.5 Design Changes Indicated by the Uncertainty Analysis	65	(1)
3-6 Analysis of a Proposed Heat Transfer Experiment	66	(10)
3-6.1 Problem	66	(1)
3-6.2 Two Proposed Experimental Techniques	67	(2)
3-6.3 General Uncertainty Analysis: Steady-State Technique	69	(3)
3-6.4 General Uncertainty Analysis: Transient Technique	72	(2)
3-6.5 Implications of the Uncertainty Analysis Results	74	(2)
3-7 Examples of Uncertainty Analysis Applications	76	(2)
3-7.1 Results from Analysis of a Turbine Test	76	(1)
3-7.2 Results from Analysis of a Solar Thermal Absorber/Thruster Test	77	(1)
3-8 Numerical Approximation to General Uncertainty Analysis	78	(1)
3-9 Summary	79	(4)
4 Designing an Experiment: Detailed Uncertainty Analysis	83	(49)
4-1 Detailed Uncertainty Analysis: Overview	83	(2)
4-2 Determining the Systematic Uncertainty of an Experimental Result	85	(13)
4-2.1 Systematic Uncertainty of a Measured Variable	86	(1)
4-2.2 Propagation of Systematic Uncertainties into the Experimental Result	87	(1)
4-2.3 Procedures for Correlated Systematic Uncertainties	88	(6)
4-2.4 Determining Systematic Uncertainties	94	(4)
4-3 Determining the Random Uncertainty of an Experimental Result	98	(11)
4-3.1 Random Uncertainty of a Measured Variable	100	(2)
4-3.2 Propagation of Random Uncertainties into the Experimental Result	102	(2)
4-3.3 Direct Determination of the Random Uncertainty of an Experimental Result: Multiple Tests	104	(4)
4-3.4 Determining Random Uncertainties	108	(1)
4-4 Small-Sample-Size Determination of the Uncertainty of an Experimental Result	109	(4)
4-5 Using Detailed Uncertainty Analysis	113	(2)
4-6 Using Detailed Uncertainty Analysis in a Sample-to-Sample Experiment	115	(8)
4-6.1 Problem	115	(1)
4-6.2 Measurement System	115	(2)
4-6.3 Zeroth-Order Replication-Level Analysis	117	(4)
4-6.4 First-Order Replication-Level Analysis	121	(1)
4-6.5 Nth-Order Replication-Level Analysis	122	(1)
4-7 Using Detailed Uncertainty Analysis in a Timewise, Steady-State Experiment	123	(5)
4-7.1 Measurement System	124	(1)
4-7.2 Consideration of Error Sources	124	(2)
4-7.3 Calculation of Random and Systematic Uncertainties in the Result	126	(2)
4-8 Using Detailed Uncertainty Analysis in a Timewise, Transient Experiment	128	(4)
5 Additional Considerations in Experimental Design	132	(45)
5-1 Asymmetric Systematic Uncertainties	133	(17)
5-1.1 Procedures for Asymmetric Systematic Uncertainties	133	(3)
5-1.2 Example: Biases in a Gas Temperature Measurement System	136	(7)
5-1.3 Example: Determination of the Velocity Profile in a Pipe	143	(7)
5-2 Comparative Testing	150	(6)
5-2.1 Difference of Results of Two Tests	151	(3)
5-2.2 Ratio of Results of Two Tests	154	(2)
5-3 Comparing Data and Predictions: Code Validation	156	(6)
5-3.1 Strategy for Validation	157	(3)
5-3.2 Validation of a Single Code	160	(1)
5-3.3 Comparison of Multiple Codes and/or Models in a Validation Effort	161	(1)
5-3.4 Validation of Predictions of Trends	162	(1)
5-4 Uncertainty Analysis by Direct Monte Carlo Simulation	162	(2)
5-5 Digital Data Acquisition	164	(1)
5-6 Dynamic Response of Instrument Systems	165	(12)
5-6.1 General Instrument Response	165	(1)
5-6.2 Response of Zero-Order Instruments	166	(1)
5-6.3 Response of First-Order Instruments	167	(3)
5-6.4 Response of Second-Order Instruments	170	(2)
5-6.5 Summary	172	(5)
6 Debugging and Execution of Experiments	177	(25)
6-1 Debugging and Qualification Checks	178	(8)
6-1.1 Basic Ideas	178	(1)
6-1.2 Example	178	(8)
6-2 Use of Balance Checks	186	(3)
6-2.1 Basic Ideas	186	(1)
6-2.2 Application to a Flow System	186	(3)
6-3 Use of a Jitter Program	189	(2)
6-4 Experiment Execution	191	(11)
6-4.1 Choice of Test Points: Rectification	191	(3)
6-4.2 Example of Use of Rectification	194	(2)
6-4.3 Test Sequence	196	(6)
7 Data Analysis, Regression, and Reporting of Results	202	(33)
7-1 Overview of Regression Analysis and Its Uncertainty	203	(3)
7-1.1 Categories of Regression Uncertainty	204	(1)
7-1.2 Uncertainty in Coefficients	204	(1)
7-1.3 Uncertainty in Y from Regression Model	204	(2)
7-1.4 (X(i), Y(i)) Variables Are Functions	206	(1)
7-2 Least-Squares Estimation	206	(2)
7-3 Classical Linear Regression Uncertainty: Random Uncertainty	208	(2)
7-4 Comprehensive Approach to Linear Regression Uncertainty	210	(3)
7-4.1 Uncertainty in Coefficients: First-Order Regression	210	(2)
7-4.2 Uncertainty in Y from Regression Model: First-Order Regression	212	(1)
7-4.3 Higher-Order Regressions	213	(1)
7-5 Reporting Regression Uncertainties	213	(2)
7-6 Regressions in which X and Y Are Functional Relations	215	(2)
7-7 Examples of Determining Regressions and Their Uncertainties	217	(12)
7-7.1 Experimental Apparatus	218	(1)
7-7.2 Pressure Transducer Calibration and Uncertainty	219	(3)
7-7.3 Venturi Discharge Coefficient and Its Uncertainty	222	(4)
7-7.4 Flow Rate and Its Uncertainty in a Test	226	(3)
7-8 Multiple Linear Regression	229	(6)
Appendix A Useful Statistics	235	(7)
Appendix B Methods for Uncertainty Propagation	242	(16)
B-1 Derivation of the Uncertainty Propagation Equation	243	(4)
B-2 Comparison with Previous Approaches	247	(4)
B-2.1 Abernethy et al. Approach	247	(1)
B-2.2 Coleman and Steele Approach	248	(1)
B-2.3 ISO Guide Approach	249	(1)
B-2.4 AIAA, AGARD, and ANSI/ASME Approach	250	(1)
B-2.5 NIST Approach	250	(1)
B-3 Additional Assumptions for Engineering Applications	251	(7)
B-3.1 Approximating the Coverage Factor	251	(2)
B-3.2 Estimating Random Uncertainties	253	(5)
Appendix C Comparison of Models for Calculation of Uncertainty	258	(13)
C-1 Monte Carlo Simulations	258	(3)
C-2 Simulation Results	261	(10)
Index	271