Experimentation, Validation, and Uncertainty Analysis for Engineers, 3rd Edition
1 Experimentation, Errors, and Uncertainty.
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.
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.