Patrick F. Dunn, Measurement, Data Analysis, and Sensor Fundamentals for Engineering and Science, 2nd Edition
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Co ve r
Featured in the background on the cover are two photographs of instruments
that earmark measurement chronology. Leeuwenhoek’s microscope stands
at its beginning, ushering in a golden age of experimentation. A modern
temperature sensor symbolizes the present.
During the 17th century, Galileo Galilei’s (1564–1642) telescope and Antony
van Leeuwenhoek’s (1632–1723) microscope, both made of lenses, allowed
man to begin probing the intricacies of his macroscopic and microscopic
worlds. The microscope pictured on the front cover is an exact replica of van
Leeuwenhoek’s original microscope made before 1673. It was constructed
in 2006 by Mr. Leon Hluchota, tool and die maker, of the Department of
Aerospace and Mechanical Engineering at the University of Notre Dame.
One of Leeuwenhoek’s original microscopes is at the University Museum,
Utrecht, The Netherlands. That microscope’s magnication was calibrated
by Dr. J. van Zuylen in 1981 and found to be 266×, with a focal length of 0.94
mm and a resolution of 1.35 μm. This magnication was at least one order of
magnitude better than any other contemporary device and was not exceeded
until over a century later.
The temperature sensor shown on the front cover was developed by Eric
Matlis, Ph.D., in 2008 at the Institute for Flow Physics and Control at the
University of Notre Dame. This state-of-the-art sensor is part of a suite of
highbandwidth sensors based on the use of miniature, AC-driven, weakly
ionized plasmas. The sensors can be designed to measure surface pres-
sure, shear stress, gas temperature, and gas species, either singly or in
combination.
PATRICK F DUNN
University of Notre Dame
Indiana, USA
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Library of Congress Cataloging‑in‑Publication Data
Dunn, Patrick F.
Measurement and data analysis for engineering and science / author, Patrick F. Dunn.
-- 2nd ed.
p. cm.
“A CRC title.”
Includes bibliographical references and index.
ISBN 978-1-4398-2568-6 (hardcover : alk. paper)
1. Physical measurements--Textbooks. 2. Statistics--Textbooks. I. Title.
QC39.D86 2010
530.8--dc22 2009043222
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Contents
1 Experiments 1
1.1 Chapter Overview . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Role of Experiments . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 The Experiment . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.4 Experimental Approach . . . . . . . . . . . . . . . . . . . . . 7
1.5 Classification of Experiments . . . . . . . . . . . . . . . . . . 8
1.6 Problem Topic Summary . . . . . . . . . . . . . . . . . . . . 10
1.7 Review Problems . . . . . . . . . . . . . . . . . . . . . . . . 10
1.8 Homework Problems . . . . . . . . . . . . . . . . . . . . . . . 11
Bibliography 13
2 Electronics 15
2.1 Chapter Overview . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2 Concepts and Definitions . . . . . . . . . . . . . . . . . . . . 16
2.2.1 Charge . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2.2 Current . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2.3 Force . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2.4 Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2.5 Potential . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2.6 Resistance and Resistivity . . . . . . . . . . . . . . . . 18
2.2.7 Power . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.2.8 Capacitance . . . . . . . . . . . . . . . . . . . . . . . . 20
2.2.9 Inductance . . . . . . . . . . . . . . . . . . . . . . . . 20
2.3 Circuit Elements . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.3.1 Resistor . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.3.2 Capacitor . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.3.3 Inductor . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.3.4 Transistor . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.3.5 Voltage Source . . . . . . . . . . . . . . . . . . . . . . 24
2.3.6 Current Source . . . . . . . . . . . . . . . . . . . . . . 24
2.4 RLC Combinations . . . . . . . . . . . . . . . . . . . . . . . 24
2.5 Elementary DC Circuit Analysis . . . . . . . . . . . . . . . . 27
2.6 Elementary AC Circuit Analysis . . . . . . . . . . . . . . . . 33
2.7 *Equivalent Circuits . . . . . . . . . . . . . . . . . . . . . . . 36
2.8 *Meters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.9 *Impedance Matching and Loading Error . . . . . . . . . . . 39
v
vi
2.10 *Electrical Noise . . . . . . . . . . . . . . . . . . . . . . . . . 43
2.11 Problem Topic Summary . . . . . . . . . . . . . . . . . . . . 45
2.12 Review Problems . . . . . . . . . . . . . . . . . . . . . . . . 45
2.13 Homework Problems . . . . . . . . . . . . . . . . . . . . . . . 49
Bibliography 55
3 Measurement Systems 57
3.1 Chapter Overview . . . . . . . . . . . . . . . . . . . . . . . . 58
3.2 Measurement System Elements . . . . . . . . . . . . . . . . . 58
3.3 Sensors and Transducers . . . . . . . . . . . . . . . . . . . . 60
3.3.1 Sensor Principles . . . . . . . . . . . . . . . . . . . . . 61
3.3.2 Sensor Examples . . . . . . . . . . . . . . . . . . . . . 63
3.3.3 *Sensor Scaling . . . . . . . . . . . . . . . . . . . . . . 70
3.4 Amplifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
3.5 Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
3.6 Analog-to-Digital Converters . . . . . . . . . . . . . . . . . . 84
3.7 Example Measurement Systems . . . . . . . . . . . . . . . . 88
3.8 Problem Topic Summary . . . . . . . . . . . . . . . . . . . . 95
3.9 Review Problems . . . . . . . . . . . . . . . . . . . . . . . . 95
3.10 Homework Problems . . . . . . . . . . . . . . . . . . . . . . . 96
Bibliography 101
4 Calibration and Response 103
4.1 Chapter Overview . . . . . . . . . . . . . . . . . . . . . . . . 103
4.2 Static Response Characterization . . . . . . . . . . . . . . . 104
4.3 Dynamic Response Characterization . . . . . . . . . . . . . . 106
4.4 Zero-Order System Dynamic Response . . . . . . . . . . . . 108
4.5 First-Order System Dynamic Response . . . . . . . . . . . . 109
4.5.1 Response to Step-Input Forcing . . . . . . . . . . . . . 111
4.5.2 Response to Sinusoidal-Input Forcing . . . . . . . . . 112
4.6 Second-Order System Dynamic Response . . . . . . . . . . . 118
4.6.1 Response to Step-Input Forcing . . . . . . . . . . . . . 121
4.6.2 Response to Sinusoidal-Input Forcing . . . . . . . . . 123
4.7 Higher-Order System Dynamic Response . . . . . . . . . . . 125
4.8 *Numerical Solution Methods . . . . . . . . . . . . . . . . . 127
4.9 Problem Topic Summary . . . . . . . . . . . . . . . . . . . . 131
4.10 Review Problems . . . . . . . . . . . . . . . . . . . . . . . . 131
4.11 Homework Problems . . . . . . . . . . . . . . . . . . . . . . . 134
Bibliography 139
vii
5 Probability 141
5.1 Chapter Overview . . . . . . . . . . . . . . . . . . . . . . . . 142
5.2 Relation to Measurements . . . . . . . . . . . . . . . . . . . 142
5.3 Sample versus Population . . . . . . . . . . . . . . . . . . . . 143
5.4 Plotting Statistical Information . . . . . . . . . . . . . . . . 143
5.5 Probability Density Function . . . . . . . . . . . . . . . . . . 151
5.6 Various Probability Density Functions . . . . . . . . . . . . . 155
5.6.1 Binomial Distribution . . . . . . . . . . . . . . . . . . 157
5.6.2 Poisson Distribution . . . . . . . . . . . . . . . . . . . 158
5.7 Central Moments . . . . . . . . . . . . . . . . . . . . . . . . 160
5.8 Probability Distribution Function . . . . . . . . . . . . . . . 163
5.9 *Probability Concepts . . . . . . . . . . . . . . . . . . . . . . 165
5.9.1 *Union and Intersection of Sets . . . . . . . . . . . . . 165
5.9.2 *Conditional Probability . . . . . . . . . . . . . . . . . 166
5.9.3 *Coincidences . . . . . . . . . . . . . . . . . . . . . . . 171
5.9.4 *Permutations and Combinations . . . . . . . . . . . . 171
5.9.5 *Birthday Problems . . . . . . . . . . . . . . . . . . . 173
5.10 Problem Topic Summary . . . . . . . . . . . . . . . . . . . . 175
5.11 Review Problems . . . . . . . . . . . . . . . . . . . . . . . . 175
5.12 Homework Problems . . . . . . . . . . . . . . . . . . . . . . . 178
Bibliography 181
6 Statistics 183
6.1 Chapter Overview . . . . . . . . . . . . . . . . . . . . . . . . 183
6.2 Normal Distribution . . . . . . . . . . . . . . . . . . . . . . . 184
6.3 Normalized Variables . . . . . . . . . . . . . . . . . . . . . . 186
6.4 Student’s t Distribution . . . . . . . . . . . . . . . . . . . . . 190
6.5 Standard Deviation of the Means . . . . . . . . . . . . . . . 197
6.6 Chi-Square Distribution . . . . . . . . . . . . . . . . . . . . . 200
6.6.1 Estimating the True Variance . . . . . . . . . . . . . . 202
6.6.2 Establishing a Rejection Criterion . . . . . . . . . . . 205
6.6.3 Comparing Observed and Expected Distributions . . . 206
6.7 *Pooling Samples . . . . . . . . . . . . . . . . . . . . . . . . 207
6.8 *Hypothesis Testing . . . . . . . . . . . . . . . . . . . . . . . 209
6.9 *Design of Experiments . . . . . . . . . . . . . . . . . . . . . 213
6.10 *Factorial Design . . . . . . . . . . . . . . . . . . . . . . . . 215
6.11 Problem Topic Summary . . . . . . . . . . . . . . . . . . . . 219
6.12 Review Problems . . . . . . . . . . . . . . . . . . . . . . . . 219
6.13 Homework Problems . . . . . . . . . . . . . . . . . . . . . . . 222
Bibliography 227
viii
7 Uncertainty Analysis 229
7.1 Chapter Overview . . . . . . . . . . . . . . . . . . . . . . . . 230
7.2 Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230
7.3 Comparing Theory and Measurement . . . . . . . . . . . . . 232
7.4 Uncertainty as an Estimated Variance . . . . . . . . . . . . . 233
7.5 Systematic and Random Errors . . . . . . . . . . . . . . . . 235
7.6 Measurement Process Errors . . . . . . . . . . . . . . . . . . 237
7.7 Quantifying Uncertainties . . . . . . . . . . . . . . . . . . . . 239
7.8 Measurement Uncertainty Analysis . . . . . . . . . . . . . . 240
7.9 General Uncertainty Analysis . . . . . . . . . . . . . . . . . . 242
7.9.1 Single-Measurement Measurand Experiment . . . . . . 244
7.9.2 Single-Measurement Result Experiment . . . . . . . . 250
7.10 Detailed Uncertainty Analysis . . . . . . . . . . . . . . . . . 256
7.10.1 Multiple-Measurement Measurand Experiment . . . . 261
7.10.2 Multiple-Measurement Result Experiment . . . . . . . 262
7.11 Uncertainty Analysis Summary . . . . . . . . . . . . . . . . . 264
7.12 *Finite-Difference Uncertainties . . . . . . . . . . . . . . . . 267
7.12.1 *Derivative Approximation . . . . . . . . . . . . . . . 267
7.12.2 *Integral Approximation . . . . . . . . . . . . . . . . . 269
7.12.3 *Uncertainty Estimate Approximation . . . . . . . . . 274
7.13 *Uncertainty Based upon Interval Statistics . . . . . . . . . . 275
7.14 Problem Topic Summary . . . . . . . . . . . . . . . . . . . . 279
7.15 Review Problems . . . . . . . . . . . . . . . . . . . . . . . . 279
7.16 Homework Problems . . . . . . . . . . . . . . . . . . . . . . . 283
Bibliography 291
8 Regression and Correlation 295
8.1 Chapter Overview . . . . . . . . . . . . . . . . . . . . . . . . 296
8.2 Least-Squares Approach . . . . . . . . . . . . . . . . . . . . . 296
8.3 Least-Squares Regression Analysis . . . . . . . . . . . . . . . 297
8.4 Linear Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 299
8.5 Regression Parameters . . . . . . . . . . . . . . . . . . . . . 302
8.6 Confidence Intervals . . . . . . . . . . . . . . . . . . . . . . . 304
8.7 Linear Correlation Analysis . . . . . . . . . . . . . . . . . . . 311
8.8 Uncertainty from Measurement Error . . . . . . . . . . . . . 317
8.9 Determining the Appropriate Fit . . . . . . . . . . . . . . . . 319
8.10 *Signal Correlations in Time . . . . . . . . . . . . . . . . . . 325
8.10.1 *Autocorrelation . . . . . . . . . . . . . . . . . . . . . 325
8.10.2 *Cross-Correlation . . . . . . . . . . . . . . . . . . . . 328
8.11 *Higher-Order Analysis . . . . . . . . . . . . . . . . . . . . . 331
8.12 *Multi-Variable Linear Analysis . . . . . . . . . . . . . . . . 334
8.13 Problem Topic Summary . . . . . . . . . . . . . . . . . . . . 336
8.14 Review Problems . . . . . . . . . . . . . . . . . . . . . . . . 336
8.15 Homework Problems . . . . . . . . . . . . . . . . . . . . . . . 337
ix
Bibliography 341
9 Signal Characteristics 343
9.1 Chapter Overview . . . . . . . . . . . . . . . . . . . . . . . . 343
9.2 Signal Characterization . . . . . . . . . . . . . . . . . . . . . 344
9.3 Signal Variables . . . . . . . . . . . . . . . . . . . . . . . . . 347
9.4 Signal Statistical Parameters . . . . . . . . . . . . . . . . . . 349
9.5 Fourier Series of a Periodic Signal . . . . . . . . . . . . . . . 354
9.6 Complex Numbers and Waves . . . . . . . . . . . . . . . . . 361
9.7 Exponential Fourier Series . . . . . . . . . . . . . . . . . . . 363
9.8 Spectral Representations . . . . . . . . . . . . . . . . . . . . 365
9.9 Continuous Fourier Transform . . . . . . . . . . . . . . . . . 367
9.10 *Continuous Fourier Transform Properties . . . . . . . . . . 369
9.11 Problem Topic Summary . . . . . . . . . . . . . . . . . . . . 372
9.12 Review Problems . . . . . . . . . . . . . . . . . . . . . . . . 372
9.13 Homework Problems . . . . . . . . . . . . . . . . . . . . . . . 374
Bibliography 377
10 Signal Analysis 379
10.1 Chapter Overview . . . . . . . . . . . . . . . . . . . . . . . . 379
10.2 Digital Sampling . . . . . . . . . . . . . . . . . . . . . . . . . 380
10.3 Aliasing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382
10.4 Discrete Fourier Transform . . . . . . . . . . . . . . . . . . . 385
10.5 Fast Fourier Transform . . . . . . . . . . . . . . . . . . . . . 388
10.6 Amplitude Ambiguity . . . . . . . . . . . . . . . . . . . . . . 390
10.7 *Windowing . . . . . . . . . . . . . . . . . . . . . . . . . . . 399
10.8 Problem Topic Summary . . . . . . . . . . . . . . . . . . . . 403
10.9 Review Problems . . . . . . . . . . . . . . . . . . . . . . . . 403
10.10 Homework Problems . . . . . . . . . . . . . . . . . . . . . . 403
Bibliography 407
11 *Units and Significant Figures 409
11.1 Chapter Overview . . . . . . . . . . . . . . . . . . . . . . . . 410
11.2 English and Metric Systems . . . . . . . . . . . . . . . . . . 410
11.3 Systems of Units . . . . . . . . . . . . . . . . . . . . . . . . . 412
11.4 SI Standards . . . . . . . . . . . . . . . . . . . . . . . . . . . 417
11.5 Technical English and SI Conversion Factors . . . . . . . . . 418
11.5.1 Length . . . . . . . . . . . . . . . . . . . . . . . . . . . 419
11.5.2 Area and Volume . . . . . . . . . . . . . . . . . . . . . 419
11.5.3 Density . . . . . . . . . . . . . . . . . . . . . . . . . . 420
11.5.4 Mass and Weight . . . . . . . . . . . . . . . . . . . . . 420
11.5.5 Force . . . . . . . . . . . . . . . . . . . . . . . . . . . 422
11.5.6 Work and Energy . . . . . . . . . . . . . . . . . . . . . 422
11.5.7 Power . . . . . . . . . . . . . . . . . . . . . . . . . . . 423