[eBook Code] Experimentation, Validation, and Uncertainty Analysis for Engineers (eBook Code, 4th)

· 제목 : [eBook Code] Experimentation, Validation, and Uncertainty Analysis for Engineers (eBook Code, 4th) 
· 분류 : 외국도서 > 기술공학 > 기술공학 > 기계공학
· ISBN : 9781119417668
· 쪽수 : 384쪽
· 출판일 : 2018-03-29

Preface xv

1 Experimentation, Errors, and Uncertainty 1

1-1 Experimentation, 2

1-1.1 Why Is Experimentation Necessary?, 2

1-1.2 Degree of Goodness and Uncertainty Analysis, 3

1-1.3 Experimentation and Validation of Simulations, 5

1-2 Experimental Approach, 6

1-2.1 Questions to Be Considered, 7

1-2.2 Phases of Experimental Program, 8

1-3 Basic Concepts and Definitions, 8

1-3.1 Errors and Uncertainties, 9

1-3.2 Categorizing and Naming Errors and Uncertainties, 13

1-3.3 Estimating Standard Uncertainties, 15

1-3.4 Determining Combined Standard Uncertainties, 16

1-3.5 Elemental Systematic Errors and Effects of Calibration, 18

1-3.6 Expansion of Concept from “Measurement Uncertainty” to “Experimental Uncertainty”, 20

1-3.7 Repetition and Replication, 22

1-3.8 Associating a Percentage Coverage or Confidence with Uncertainty Estimates, 24

1-4 Experimental Results Determined from a Data Reduction Equation Combining Multiple Measured Variables, 25

1-5 Guides and Standards, 27

1-5.1 Experimental Uncertainty Analysis, 27

1-5.2 Validation of Simulations, 29

1-6 A Note on Nomenclature, 31

References, 31

Problems, 32

2 Coverage and Confidence Intervals for an Individual Measured Variable 33

2-1 Coverage Intervals from the Monte Carlo Method for a Single Measured Variable, 34

2-2 Confidence Intervals from the Taylor Series Method for a Single Measured Variable, Only Random Errors Considered, 35

2-2.1 Statistical Distributions, 35

2-2.2 The Gaussian Distribution, 36

2-2.3 Confidence Intervals in Gaussian Parent Populations, 42

2-2.4 Confidence Intervals in Samples from Gaussian Parent Populations, 43

2-2.5 Tolerance and Prediction Intervals in Samples from Gaussian Parent Populations, 48

2-2.6 Statistical Rejection of Outliers from a Sample Assumed from a Gaussian Parent Population, 51

2-3 Confidence Intervals from the Taylor Series Method for a Single Measured Variable: Random and Systematic Errors Considered, 55

2-3.1 The Central Limit Theorem, 55

2-3.2 Systematic Standard Uncertainty Estimation, 56

2-3.3 The TSM Expanded Uncertainty of a Measured Variable, 58

2-3.4 The TSM Large-Sample Expanded Uncertainty of a Measured Variable, 61

2-4 Uncertainty of Uncertainty Estimates and Confidence Interval Limits for a Measured Variable, 63

2-4.1 Uncertainty of Uncertainty Estimates, 63

2-4.2 Implications of the Uncertainty in Limits of High Confidence Uncertainty Intervals Used in Analysis and Design, 65

References, 67

Problems, 68

3 Uncertainty in a Result Determined from Multiple Variables 71

3-1 General Uncertainty Analysis vs. Detailed Uncertainty Analysis, 72

3-2 Monte Carlo Method for Propagation of Uncertainties, 73

3-2.1 Using the MCM in General Uncertainty Analysis, 73

3-2.2 Using the MCM in Detailed Uncertainty Analysis, 75

3-3 Taylor Series Method for Propagation of Uncertainties, 78

3-3.1 General Uncertainty Analysis Using the Taylor Series Method (TSM), 79

3-3.2 Detailed Uncertainty Analysis Using the Taylor Series Method (TSM), 80

3-4 Determining MCM Coverage Intervals and TSM Expanded Uncertainty, 82

3-4.1 MCM Coverage Intervals for a Result, 82

3-4.2 TSM Expanded Uncertainty of a Result, 85

3-5 General Uncertainty Analysis Using the TSM and MSM Approaches for a Rough-walled Pipe Flow Experiment, 87

3-5.1 TSM General Uncertainty Analysis, 88

3-5.2 MCM General Uncertainty Analysis, 89

3-5.3 Implementation Using a Spreadsheet, 89

3-5.4 Results of the Analysis, 92

3-6 Comments on Implementing Detailed Uncertainty Analysis Using a Spreadsheet, 95

References, 96

Problems, 97

4 General Uncertainty Analysis Using the Taylor Series Method (TSM) 99

4-1 TSM Application to Experiment Planning, 100

4-2 TSM Application to Experiment Planning: Special Functional Form, 103

4-3 Using TSM Uncertainty Analysis in Planning an Experiment, 107

4-4 Example: Analysis of Proposed Particulate Measuring System, 109

4-4.1 The Problem, 109

4-4.2 Proposed Measurement Technique and System, 109

4-4.3 Analysis of Proposed Experiment, 110

4-4.4 Implications of Uncertainty Analysis Results, 112

4-4.5 Design Changes Indicated by Uncertainty Analysis, 113

4-5 Example: Analysis of Proposed Heat Transfer Experiment, 114

4-5.1 The Problem, 114

4-5.2 Two Proposed Experimental Techniques, 115

4-5.3 General Uncertainty Analysis: Steady-State Technique, 117

4-5.4 General Uncertainty Analysis: Transient Technique, 121

4-5.5 Implications of Uncertainty Analysis Results, 123

4-6 Examples of Presentation of Results from Actual Applications, 124

4-6.1 Results from Analysis of a Turbine Test, 124

4-6.2 Results from Analysis of a Solar Thermal Absorber/Thruster Test, 125

References, 126

Problems, 127

5 Detailed Uncertainty Analysis: Overview and Determining Random Uncertainties in Results 131

5-1 Using Detailed Uncertainty Analysis, 131

5-2 Detailed Uncertainty Analysis: Overview of Complete Methodology, 134

5-3 Determining Random Uncertainty of Experimental Result, 137

5-3.1 Example: Random Uncertainty Determination in Compressible Flow Venturi Meter Calibration Facility, 139

5-3.2 Example: Random Uncertainty Determination in Laboratory-Scale Ambient Temperature Flow Test Facility, 141

5-3.3 Example: Random Uncertainty Determination in Full-Scale Rocket Engine Ground Test Facility, 143

5-3.4 Summary, 146

References, 146

6 Detailed Uncertainty Analysis: Determining Systematic Uncertainties in Results 147

6-1 Estimating Systematic Uncertainties, 149

6-1.1 Example: Estimating Uncertainty in Property Values, 152

6-1.2 Example: Estimating Systematic Uncertainties in the Turbulent Heat Transfer Test Facility (THTTF), 153

6-1.3 Example: An “Optimum” Calibration Approach Used in a Test to Determine Turbine Efficiency, 163

6-2 Determining Systematic Uncertainty of Experimental Result Including Correlated Systematic Error Effects, 165

6-2.1 Example: Correlated Systematic Error Effects with “% of Full Scale” (%FS) Systematic Uncertainties, 168

6-2.2 Example: Correlated Systematic Error Effects with “% of Reading” Systematic Uncertainties, 170

6-2.3 Example: Correlated Systematic Error Effects with Systematic Uncertainties that Vary with Set Point, 171

6-2.4 Example: Correlated Systematic Error Effects When Only Some Elemental Sources Are Correlated, 172

6-2.5 Example: Correlated Systematic Error Effects When Determining Average Velocity of a Fluid Flow, 176

6-3 Comparative Testing, 177

6-3.1 Result Is a Difference of Test Results, 178

6-3.2 Result Is a Ratio of Test Results, 181

6-4 Some Additional Considerations in Experiment Execution, 183

6-4.1 Choice of Test Points: Rectification, 183

6-4.2 Choice of Test Sequence, 188

6-4.3 Relationship to Statistical Design of Experiments, 189

6-4.4 Use of a Jitter Program, 191

6-4.5 Comments on Transient Testing, 193

6-4.6 Comments on Digital Data Acquisition Errors, 193

References, 194

Problems, 195

7 Detailed Uncertainty Analysis: Comprehensive Examples 199

7-1 TSM Comprehensive Example: Sample-to-Sample Experiment, 199

7-1.1 The Problem, 199

7-1.2 Measurement System, 200

7-1.3 Zeroth-Order Replication-Level Analysis, 201

7-1.4 First-Order Replication-Level Analysis, 205

7-1.5 Nth-Order Replication-Level Analysis, 206

7-2 TSM Comprehensive Example: Use of Balance Checks, 207

7-3 Comprehensive Example: Debugging and Qualification of a Timewise Experiment, 210

7-3.1 Orders of Replication Level in Timewise Experiments, 211

7-3.2 Example, 212

7-4 Comprehensive Example: Heat Exchanger Test Facility for Single and Comparative Tests, 216

7-4.1 Determination of the Uncertainty in q for a Single Core Design, 219

7-4.2 Determination of the Uncertainty in Δq for Two Core Designs Tested Sequentially Using the Same Facility and Instrumentation, 224

7-5 Case Study: Examples of Single and Comparative Tests of Nuclear Power Plant Residual Heat Removal Heat Exchanger, 230

7-5.1 Single Test Results for an RHR Heat Exchanger (HX1), 231

7-5.2 Comparative Test Approach for the Decrease in Fouling Resistance and Its Uncertainty, 234

References, 235

Problems, 235

8 The Uncertainty Associated with the Use of Regressions 239

8-1 Overview of Linear Regression Analysis and Its Uncertainty, 240

8-1.1 Uncertainty in Coefficients, 241

8-1.2 Uncertainty in Y from Regression Model, 241

8-1.3 (X_i, Y_i) Variables Are Functions, 243

8-2 Determining and Reporting Regression Uncertainty, 243

8-2.1 MCM Regression Uncertainty Determination, 244

8-2.2 TSM Regression Uncertainty Determination, 244

8-2.3 Reporting Regression Uncertainties, 244

8-3 Method of Least Squares Regression, 246

8-4 First-Order Regression Example: MCM Approach to Determine Regression Uncertainty, 249

8-5 Regression Examples: TSM Approach to Determine Regression Uncertainty, 252

8-5.1 Uncertainty in First-Order Coefficients, 252

8-5.2 Uncertainty in Y from First-Order Regression, 253

8-5.3 Uncertainty in Y from Higher-Order Regressions, 255

8-5.4 Uncertainty in Y from Regressions in Which X and Y Are Functional Relations, 255

8-5.5 Uncertainty Associated with Multivariate Linear Regression, 257

8-6 Comprehensive TSM Example: Regressions and Their Uncertainties in a Flow Test, 259

8-6.1 Experimental Apparatus, 261

8-6.2 Pressure Transducer Calibration and Uncertainty, 261

8-6.3 Venturi Discharge Coefficient and Its Uncertainty, 265

8-6.4 Flow Rate and Its Uncertainty in a Test, 269

References, 273

Problems, 273

9 Validation of Simulations 277

9-1 Introduction to Validation Methodology, 277

9-2 Errors and Uncertainties, 278

9-3 Validation Nomenclature, 279

9-4 Validation Approach, 280

9-5 Code and Solution Verification, 284

9-6 Interpretation of Validation Results Using E and u_val, 284

9-6.1 Interpretation with No Assumptions Made about Error Distributions, 285

9-6.2 Interpretation with Assumptions Made about Error Distributions, 285

9-7 Estimation of Validation Uncertainty u_val, 286

9-7.1 Case 1: Estimating u_val When Experimental Value D of Validation Variable Is Directly Measured, 287

9-7.2 Cases 2 and 3: Estimating u_val When Experimental Value D of Validation Variable Is Determined from Data Reduction Equation, 290

9-7.3 Case 4: Estimating u_val When Experimental Value D of Validation Variable Is Determined from Data Reduction Equation That Itself Is a Model, 295

9-8 Some Practical Points, 297

References, 299

Answers to Selected Problems 301

Appendix A Useful Statistics 305

Appendix B Taylor Series Method (TSM) for Uncertainty Propagation 311

B-1 Derivation of Uncertainty Propagation Equation, 312

B-2 Comparison with Previous Approaches, 316

B-2.1 Abernethy et al. Approach, 316

B-2.2 Coleman and Steele Approach, 317

B-2.3 ISO Guide 1993 GUM Approach, 318

B-2.4 AIAA Standard, AGARD, and ANSI/ASME Approach, 319

B-2.5 NIST Approach, 319

B-3 Additional Assumptions for Engineering Applications, 319

B-3.1 Approximating the Coverage Factor, 320

References, 322

Appendix C Comparison of Models for Calculation of Uncertainty 325

C-1 Monte Carlo Simulations, 325

C-2 Simulation Results, 328

References, 336

Appendix D Shortest Coverage Interval for Monte Carlo Method 337

Reference, 338

Appendix E Asymmetric Systematic Uncertainties 339

E-1 Procedure for Asymmetric Systematic Uncertainties Using TSM Propagation, 340

E-2 Procedure for Asymmetric Systematic Uncertainties Using MCM Propagation, 344

E-3 Example: Biases in a Gas Temperature Measurement System, 344

References, 351

Appendix F Dynamic Response of Instrument Systems 353

F-1 General Instrument Response, 353

F-2 Response of Zero-Order Instruments, 355

F-3 Response of First-Order Instruments, 356

F-4 Response of Second-Order Instruments, 359

F-5 Summary, 362

References, 362

Index 363