Experimentation, Validation, and Uncertainty Analysis for Engineers

Experimentation, Validation, and Uncertainty Analysis for Engineers, Third Edition provides a thorough description of techniques for greater sophistication and verifiability to engineering experiments from early stages through debugging, execution, data analysis, and reporting phases. New material includes direct Monte Carlo (MC) simulation, incorporation of the new approach to determining the random uncertainty of a result in steady state testing, plus a new chapter on "Verification and Validation of Simulation Results." Practicing engineers (Mechanical, Chemical, Electrical, Materials, Industrial), as well as engineering students in upper-level undergraduate and graduate curriculums, will benefit greatly from this valuable source.

Table of Contents:
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.