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Experimentation, Validation, and Uncertainty Analysis for Engineers, 3rd Edition



Experimentation, Validation, and Uncertainty Analysis for Engineers, 3rd Edition

Hugh W. Coleman, W. Glenn Steele

ISBN: 978-0-470-16888-2 July 2009 336 Pages

Editions Previous


This Third Edition helps you assess and manage uncertainty at all stages of experimentation and validation of simulations

In 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.


1 Experimentation, Errors, and Uncertainty.

1-1 Experimentation.

1-2 Experimental Approach.

1-3 Basic Concepts and Definitions.

1-4 Experimental Results Determined from Multiple Measured Variables.

1-5 Guides and Standards.

1-6 A Note on Nomenclature.



2 Errors and Uncertainties in a Measured Variable.

2-1 Statistical Distributions.

2-2 Gaussian Distribution.

2-3 Samples from Gaussian Parent Population.

2-4 Statistical Rejection of Outliers from a Sample.

2-5 Uncertainty of a Measured Variable.

2-6 Summary.



3 Uncertainty in a Result Determined from Multiple Variables.

3-1 Taylor Series Method for Propagation of Uncertainties.

3-2 Monte Carlo Method for Propagation of Uncertainties.



4 General Uncertainty Analysis: Planning an Experiment and Application in Validation.

4-1 Overview: Using Uncertainty Propagation in Experiments and Validation.

4-2 General Uncertainty Analysis Using the Taylor Series Method.

4-3 Application to Experiment Planning (TSM).

4-4 Using TSM Uncertainty Analysis in Planning an Experiment.

4-5 Example: Analysis of Proposed Particulate Measuring System.

4-6 Example: Analysis of Proposed Heat Transfer Experiment.

4-7 Examples of Presentation of Results from Actual Applications.

4-8 Application in Validation: Estimating Uncertainty in Simulation Result Due to Uncertainties in Inputs.



5 Detailed Uncertainty Analysis: Designing, Debugging, and Executing an Experiment.

5-1 Using Detailed Uncertainty Analysis.

5-2 Detailed Uncertainty Analysis: Overview of Complete Methodology.

5-3 Determining Random Uncertainty of Experimental Result.

5-4 Determining Systematic Uncertainty of Experimental Result.

5-5 Comprehensive Example: Sample-to-Sample Experiment.

5-6 Comprehensive Example: Debugging and Qualification of a Timewise Experiment.

5-7 Some Additional Considerations in Experiment Execution.



6 Validation Of Simulations.

6-1 Introduction to Validation Methodology.

6-2 Errors and Uncertainties.

6-3 Validation Nomenclature.

6-4 Validation Approach.

6-5 Code and Solution Verification.

6-6 Estimation of Validation Uncertainty uval.

6-7 Interpretation of Validation Results Using E and uval.

6-8 Some Practical Points.


7 Data Analysis, Regression, and Reporting of Results.

7-1 Overview of Regression Analysis and Its Uncertainty.

7-2 Least-Squares Estimation.

7-3 Classical Linear Regression Uncertainty: Random Uncertainty.

7-4 Comprehensive Approach to Linear Regression Uncertainty.

7-5 Reporting Regression Uncertainties.

7-6 Regressions in Which X and Y Are Functional Relations.

7-7 Examples of Determining Regressions and Their Uncertainties.

7-8 Multiple Linear Regression.



Appendix A Useful Statistics.

Appendix B Taylor Series Method (TSM) for Uncertainty Propagation.

B-1 Derivation of Uncertainty Propagation Equation.

B-2 Comparison with Previous Approaches.

B-3 Additional Assumptions for Engineering Applications.


Appendix C Comparison of Models for Calculation of Uncertainty.

C-1 Monte Carlo Simulations.

C-2 Simulation Results.


Appendix D Shortest Coverage Interval for Monte Carlo Method.


Appendix E Asymmetric Systematic Uncertainties.

E-1 Procedure for Asymmetric Systematic Uncertainties Using TSM Propagation.

E-2 Procedure for Asymmetric Systematic Uncertainties Using MCM Propagation.

E-3 Example: Biases in a Gas Temperature Measurement System.


Appendix F Dynamic Response of Instrument Systems.

F-1 General Instrument Response.

F-2 Response of Zero-Order Instruments.

F-3 Response of First-Order Instruments.

F-4 Response of Second-Order Instruments.

F-5 Summary.



"…present a logical approach to experimentation and validation through the application of uncertainty analysis in the planning, design, construction, and reporting phases of experimental and validation programs." (Book News, August 2009)