Experimentation, Validation, and Uncertainty Analysis for Engineers

Hugh W. Coleman, W. Glenn Steele

• Publisher: Wiley
• Year: 2018
• Print ISBN: 9781119417514
• eBook ISBN: 9781119417705
• Edition: 4
• Topic: Technology & Engineering
• Subtopic: Mechanical Engineering
• Index: Technology & Engineering

Helps engineers and scientists assess and manage uncertainty at all stages of experimentation and validation of simulations

Fully updated from its previous edition, Experimentation, Validation, and Uncertainty Analysis for Engineers, Fourth Edition includes expanded coverage and new examples of applying the Monte Carlo Method (MCM) in performing uncertainty analyses. Presenting the current, internationally accepted methodology from ISO, ANSI, and ASME standards for propagating uncertainties using both the MCM and the Taylor Series Method (TSM), it provides a logical approach to experimentation and validation through the application of uncertainty analysis in the planning, design, construction, debugging, execution, data analysis, and reporting phases of experimental and validation programs. It also illustrates how to use a spreadsheet approach to apply the MCM and the TSM, based on the authors' experience in applying uncertainty analysis in complex, large-scale testing of real engineering systems.

Experimentation, Validation, and Uncertainty Analysis for Engineers, Fourth Edition includes examples throughout, contains end of chapter problems, and is accompanied by the authors' website www.uncertainty-analysis.com.

• Guides readers through all aspects of experimentation, validation, and uncertainty analysis
• Emphasizes the use of the Monte Carlo Method in performing uncertainty analysis
• Includes complete new examples throughout
• Features workable problems at the end of chapters

Experimentation, Validation, and Uncertainty Analysis for Engineers, Fourth Edition is an ideal text and guide for researchers, engineers, and graduate and senior undergraduate students in engineering and science disciplines. Knowledge of the material in this Fourth Edition is a must for those involved in executing or managing experimental programs or validating models and simulations.

1
EXPERIMENTATION, ERRORS, AND UNCERTAINTY

When the word experimentation is encountered, most of us immediately envision someone in a laboratory “taking data.” This idea has been fostered over many decades by portrayals in periodicals, television shows, and movies of an engineer or scientist in a white lab coat writing on a clipboard while surrounded by the piping and gauges in a refinery or by an impressive complexity of laboratory glassware. In recent years, the location is often a control room filled with computerized data acquisition equipment with lights blinking on the racks and panels. To some extent, the manner in which laboratory classes are typically implemented in university curricula also reinforces this idea. Students often encounter most instruction in experimentation as demonstration experiments that are already set up when the students walk into the laboratory. Data are often taken under the pressure of time, and much of the interpretation of the data and the reporting of results is spent on trying to rationalize what went wrong and what the results “would have shown if…”

Experimentation is not just data taking. Any engineer or scientist who subscribes to the widely held but erroneous belief that experimentation is making measurements in the laboratory will be a failure as an experimentalist. The actual data-taking portion of a well-run experimental program generally constitutes a small percentage of the total time and effort expended. In this book we examine and discuss the steps and techniques involved in a logical, thorough approach to the subject of experimentation.

1-1 EXPERIMENTATION

1-1.1 Why Is Experimentation Necessary?

Why are experiments necessary? Why do we need to study the subject of experimentation? The experiments run in science and engineering courses demonstrate physical principles and processes, but once these demonstrations are made and their lessons taken to heart, why bother with experiments? With the laws of physics we know, with the sophisticated analytical solution methods we study, with the increasing knowledge of numerical solution techniques, and with the awesome computing power available, is there any longer a need for experimentation in the real world?

These are fair questions to ask. To address them, it is instructive to consider Figure 1.1, which illustrates a typical analytical approach to finding a solution to a physical problem. Experimental information is almost always required at one or more stages of the solution process, even when an analytical approach is used. Sometimes experimental results are necessary before realistic assumptions and idealizations can be made so that a mathematical model of the real-world process can be formulated using the basic laws of physics. In addition, experimentally determined information is generally present in the form of physical property values and the auxiliary equations (e.g., equations of state) necessary for obtaining a solution. So we see that even in situations in which the solution approach is analytical (or numerical), information from experiments is included in the solution process.

Figure 1.1 Analytical approach to solution of a problem.

From a more general perspective, experimentation lies at the very foundations of science and engineering. Webster's [1] defines science as “systematized knowledge derived from observation, study, and experimentation carried on in order to determine the nature or principles of what is being studied.” In discussing the scientific method, Shortley and Williams [2] state: “The scientific method is the systematic attempt to construct theories that correlate wide groups of observed facts and are capable of predicting the results of future observations. Such theories are tested by controlled experimentation and are accepted only so long as they are consistent with all observed facts.”

In many systems and processes of scientific and engineering interest, the geometry, boundary conditions, and physical phenomena are so complex that it is beyond our present technical capability to formulate satisfactory analytical or numerical models and approaches. In these cases, experimentation is necessary to define the behavior of the systems and/or processes (i.e., to find a solution to the problem).

1-1.2 Degree of Goodness and Uncertainty Analysis

If we are using property data or other experimentally determined information in an analytical solution, we should certainly consider how “good” the experimental information is. Similarly, anyone comparing results of a mathematical model with experimental data (and perhaps also with the results of other mathematical models) should certainly consider the degree of goodness of the data when drawing conclusions based on the comparisons. This situation is illustrated in Figure 1.2. In Figure 1.2a the results of two different mathematical models are compared with each other and with a set of experimental data. The authors of the two models might have a fine time arguing over which model compares better with the data. In Figure 1.2b, the same information is presented, but a range representing the uncertainty (likely amount of error) in the experimental value of Y has been plotted for each data point. It is immediately obvious that once the degree of goodness of the ...

Table of contents

• COVER
• TITLE PAGE
• TABLE OF CONTENTS
• PREFACE
• 1 EXPERIMENTATION, ERRORS, AND UNCERTAINTY
• 2 COVERAGE AND CONFIDENCE INTERVALS FOR AN INDIVIDUAL MEASURED VARIABLE
• 3 UNCERTAINTY IN A RESULT DETERMINED FROM MULTIPLE VARIABLES
• 4 GENERAL UNCERTAINTY ANALYSIS USING THE TAYLOR SERIES METHOD (TSM)
• 5 DETAILED UNCERTAINTY ANALYSIS: OVERVIEW AND DETERMINING RANDOM UNCERTAINTIES IN RESULTS
• 6 DETAILED UNCERTAINTY ANALYSIS: DETERMINING SYSTEMATIC UNCERTAINTIES IN RESULTS
• 7 DETAILED UNCERTAINTY ANALYSIS: COMPREHENSIVE EXAMPLES
• 8 THE UNCERTAINTY ASSOCIATED WITH THE USE OF REGRESSIONS
• 9 VALIDATION OF SIMULATIONS
• ANSWERS TO SELECTED PROBLEMS
• APPENDIX A: USEFUL STATISTICS
• APPENDIX B: TAYLOR SERIES METHOD (TSM) FOR UNCERTAINTY PROPAGATION
• APPENDIX C: COMPARISON OF MODELS FOR CALCULATION OF UNCERTAINTY
• APPENDIX D: SHORTEST COVERAGE INTERVAL FOR MONTE CARLO METHOD
• APPENDIX E: ASYMMETRIC SYSTEMATIC UNCERTAINTIES
• APPENDIX F: DYNAMIC RESPONSE OF INSTRUMENT SYSTEMS
• INDEX
• END USER LICENSE AGREEMENT