Measurement and Data Analvsis f or Engineering and Science Fourth Edition

Patrick F. Dunn Michael P. Davis

CRC Press is an imprint of the Taylor & Francis Group, an lnforma buslness

Contents

Preface

Authors

1 Introduction to Experimentation 1.1 A Farnous Experiment 1.2 Phases of an Experiment 1.3 Example Experiments

Bibliography

1 Planning an Experiment

2 Planning an Ezperi.ment - Overview

3 Experiments 3.1 Role of Experiments . . . . . 3.2 The Experiment . . . . . . . 3.3 Classification of Experiments 3.4 Plan for Successful Experimentation 3.5 Problems . . . . . . . . . . .

Bibliography

II Identifying Components

4 Identifying Components - Overview

5 Fundamental Electronics 5.1 Concepts and Definitions

5.2

5.1.1 Charge ... . 5.1.2 Current ... . 5.1.3 Electric Force . 5.1.4 Electric Field . 5.1.5 Electric Potential . 5.1.6 Resistance and Resistivity . 5;1.7 Power .... 5.1.8 Capacitance . 5.1.9 Inductance Circuit Elements 5.2.1 Resistor . 5.2.2 Capacitor 5.2.3 Inductor .

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5.2.4 Transistor . . . 5.2.5 Voltage Source 5.2.6 Current Source

5.3 RLC Combinations . 5.4 Elementary DC Circuit Analysis

Contents

5.4.1 Voltage Divider ..... . 5.4.2 Electric Motor with Battery . 5.4.3 Wheatstone Bridge . . . .

5.5 Elementary AC Circuit Analysis 5.6 Equivalent Circuits* . . . . . . . 5.7 Meters* ... . ......... . 5.8 Impedance Matching and Loading Error* 5.9 Electrical Noise* 5.10 Problems ... . ............. .

Bibliography

6 Measurement Systems: Sensorsand Transducers 6.1 The Measurement System 6.2 Sensor Domains .. .. .. . 6.3 Sensor Characteristics . . . . 6.4 Physical Principles of Sensors 6.5 Electric . . . . . .

6.5.1 Resistive .. 6.5.2 Capacitive . 6.5.3 Inductive

6.6 Piezoelectric . 6.7 Fluid Mechanic 6.8 Optic ..... 6.9 Photoelastic 6.10 Thermoelectric 6.11 Electrochemical 6.12 Sensor Scaling* 6.13 Problems

Bibliography

7 Measurement Systems: Other Components 7.1 Signal Conditioning, Processing, and Recording 7.2 Amplifiers . ... .... . . 7.3 Filters . . . . ........ . 7.4 Analog-to-Digital Converters 7.5 Smart Measurement Systems

7.5.1 Sensors and Microcontroller Platforms 7.5.2 Arduino Microcontrollers . . . . . . . 7.5.3 Wireless Transmission of Data .. . . 7.5.4 Using the MATLAB Programming Environment 7.5.5 Examples of Arduino Programming using Simulink .

7.6 Other Example Measurement Systems 7. 7 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Contents

Bibliography

III Assessing Performance

8 Assessing Perfonnance - Overview

9 Measurement Systems: Calibration and Response 9.1 Static Response Characterization by Calibration 9.2 Dynamic Response Characterization . . 9.3 Zero-Order System Dynamic Response 9.4 First-Order System Dynamic Response

9.4.1 Response to Step-lnput Forcing . 9.4.2 Response to Sinusoidal-Input Forcing

9.5 Second-Order System Dynamic Response . . 9.5.1 Response to Step-Input Forcing .... 9.5.2 Response to Sinusoidal-Input Forcing

9.6 Combined-System Dynamic Response 9.7 Problems ................... .

Bibliography

10 Measurement Systems: Design-Stage U ncertainty 10.1 Design-Stage Uncertainty Analysis . . . . . .. . . . 10.2 Design-Stage Uncertainty Estimate of a Measurand 10.3 Design-Stage Uncertainty Estimate of a Result 10.4 Problems . . . . . . . . . . . . . . . ... . . . . . .

Bibliography

IV Setting Sampling Conditions

11 Setting Sampling Conditions - Overview

12 Signal Characteristics 12.1 Signal Classification . .... 12.2 Signal Variables . . . . . 12.3 Signal Statistical Parameters 12.4 Problems ..... .. ... .

Bibliography

13 The Fourier Transform 13.1 Fourier Series of a Periodic Signal 13.2 Complex Numbers and Waves 13.3 Exponential Fourier Series 13.4 Spectral Representations 13.5 Continuous Fourier Transform 13.6 Continuous Fourier Transform Properties* 13.7 Discrete Fourier Transform 13.8 Fast Fourier Transform 13.9 Problems . . . . . . . . . .

Bibliography

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14 Digital Signal Analysis 283 14.1 Digital Sampling . . 283 14.2 Digital Sampling Errors 284

14.2.1 Aliasing . . . . . 285 14.2.2 Amplitude Ambiguity 289

14.3 Windowing* . . . . . . . . . 297 14.4 Determining a Sample Period 301 14.5 Problems . . . . . . . . 305

Bibliography 307

V Analyzing Data

15 Analyzing Results - Overview

16 Probability 16.1 Basic Probability Concepts ..... .

16.1.1 Union and Intersection of Sets 16.1.2 Conditional Probability ... . 16.1.3 Sample versus Population .. . 16.1.4 Plotting Statistical Information .

16.2 Probability Density Function ..... 16.3 Various Probability Density Functions

16.3.1 Binomial Distribution 16.3.2 Poisson Distribution . . . .

16.4 Central Moments ........ . 16.5 Probability Distribution Function 16.6 Problems . . . . . . . . . . . . . .

Bibliography

17 Statistics 17.1 Normal Distribution 17.2 Normalized Variables 17.3 Student's t Distribution 17.4 Rejection of Data

17.4.1 Single-Variable Outlier Determination 17.4.2 Paired-Variable Outlier Determination .

17.5 Standard Deviation of the Means 17.6 Chi-Square Distribution ......... .

17.6.1 Estimating the True Variance .. . 17.6.2 Establishing a Rejection Criterion 17.6.3 Comparing Observed and Expected Distributions .

17.7 Pooling Samples* 17.8 Hypothesis Testing* ...

17.8.1 One-Sample t-Test 17.8.2 Two-Sample t-Test

17.9 Design of Experiments* 17.10 Factorial Design* 17.11 Problems ....... .

Bibliography

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357 357 360 365 371 371 373 375 377 381 382 382 384 386 388 388 390 392 395

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Contents

18 U ncertainty Analysis 18.1 Modeling and Experimental Uncertainties 18.2 Probabilistic Basis of Uncertainty 18.3 Identifying Sources of Error . . . . . . . . 18.4 Systema.tic and R.8.ndom Errors . . . . . 18.5 Quantifying Systematic and Random Errors 18.6 Measurement Uncertainty Analysis ..... 18.7 Uncertainty Analysis of a Multiple-Measurement Result 18.8 Uncertainty Analysis for Other Measurement Situations 18.9 Uncertainty Analysis Summary ... 18.10 Finite-Difference Uncertainties* ..

18.10.1 Derivative Approximation* . 18.10.2 Integral Approximation* .. 18.10.3 Uncertainty Estimate Approximation*

18.11 Uncerta.inty Based upon Interval Statistics* 18.12 Problems ...... ...... ........ .

Bibliography

19 Regression and Correlation 19.1 Least-Squares Approach ..... . 19.2 Least-Squares Regression Analysis 19.3 Linear Analysis ........ . 19.4 Higher-Order Analysis* .... . 19.5 Multi-Variable Linear Analysis* 19.6 Determining the Appropriate Fit 19.7 Regression Confidence Intervals 19.8 Regression Parameters 19.9 Linear Correlation Analysis . 19.10 Signal Correlations in Time*

19.10.1 Autocorrelation* .. 19.10.2 Cross-Correlation* .

19.11 Problems ......... .

Bibliography

VI Reporting Results

20 Reporting Results - Overview

21 Units and Significant Figures 21.1 English and Metric Systems 21.2 Systems of Units ...... . 21.3 SI Standards . . . . . . . . . 21.4 Technical English and SI Conversion Factors

21.4.1 Length ...... . 21.4.2 Area and Volume . 21.4.3 Density . . . . . . 21.4.4 Mass and Weight . 21.4.5 Force . . . . . . . 21.4.6 Work and Energy . 21.4. 7 Power . . . . . . .

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21.4.8 Light Radiation . . 21.4.9 Temperature .. . 21.4.10 Other Properties .

21.5 Prefixes . . . . . . 21.6 Significa.nt Figures 21. 7 Problems . . . . .

Bibliography

22 Technical Communication

Contents

22.1 Guidelines for Writing ... . . . . . . 22.1.1 Writing in General ...... . 22.1.2 Writing Technical Memoranda 22.1.3 Number and Unit Formats 22.1.4 Graphical Presentation

22.2 Technical Memo ..... . 22.3 Technical Report ... .. . 22.4 Oral Technical Presentation 22.5 Problems .. . . . .... .

Bibliography

Glossary

Symbols

Review Problem Answers

Index

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