Experimentation, Validation, and Uncertainty Analysis for Engineers

Abstract

Preface. 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. References. Problems. 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. References. Problems. 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. References. Problems. 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. References. Problems. 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. References. Problems. 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 u val . 6-7 Interpretation of Validation Results Using E and u val . 6-8 Some Practical Points. References. 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. References. Problems. 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. References. Appendix C Comparison of Models for Calculation of Uncertainty. C-1 Monte Carlo Simulations. C-2 Simulation Results. References. Appendix D Shortest Coverage Interval for Monte Carlo Method. Reference. 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. References. 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. References. Index.