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E-raamat: Engineering Modelling and Analysis

(University of Adelaide, Australia), (University of Adelaide, Australia), (University of Adelaide, Australia), (University of Adelaide, Australia)
  • Formaat: 440 pages
  • Ilmumisaeg: 03-Sep-2018
  • Kirjastus: CRC Press
  • Keel: eng
  • ISBN-13: 9781482266405
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Engineering Modelling and AnalysisSuurem pilt
  • Formaat: 440 pages
  • Ilmumisaeg: 03-Sep-2018
  • Kirjastus: CRC Press
  • Keel: eng
  • ISBN-13: 9781482266405
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Introducing engineering students to numerical analysis and computing, this book covers a range of topics suitable for the first three years of a four year undergraduate engineering degree. The teaching of computing to engineers is hampered by the lack of suitable problems for the students to tackle, so much effort has gone into making the problems in this book realistic and relevant, while at the same time solvable for undergraduates.

Taking a balanced approach to teaching computing and computer methods at the same time, this book satisfies the need to be able to use computers (using both formal languages such as Fortran and other applications such as Matlab and Microsoft Excel), and the need to be able to solve realistic engineering problems.

Preface xv
1 Introduction (Engineering Modelling and Analysis)
1
1.1 Introduction
1
1.2 Engineering models
5
1.3 Engineering modelling
6
1.4 Physical models
7
1.5 Modern engineering computing
8
1.6 A word of warning
9
Problems
10
2 Introduction (Accuracy, Speed and Algorithms)
11
2.1 Introduction
11
2.2 A brief history of computers and computing
12
2.3 Topics and their focus
14
2.4 Topics and their connections
15
2.5 Developing computing skills
17
2.6 Numerical recipes
18
Problems
18
3 Roots of Equations (Introduction)
19
3.1 Introduction
19
3.2 What are roots?
20
3.3 Engineering problems requiring root finding
21
3.4 Worked example
23
3.5 Goal Seek in Excel
24
Problems
25
4 Roots of Equations (Bracket Methods)
27
4.1 Introduction
27
4.2 Bracket methods in general
27
4.3 Bisection method
28
4.4 Method of false position (regula falsi)
30
4.5 Convergence criteria
32
4.6 Application of bisection method in Excel
32
4.7 Determining start values for bracket methods
33
Problems
35
5 Roots of Equations (Open Methods)
37
5.1 Introduction
37
5.2 Simple one-point iteration
37
5.3 Newton-Raphson method
38
5.4 Secant method
39
5.5 Multiple roots
40
5.6 Other problems and general considerations
41
5.7 Case study: pollutant transport in a river
42
5.8 Case study: wet detention treatment basins
42
Problems
43
6 Numerical Integration (Trapezoidal Rule)
45
6.1 Introduction
45
6.2 Trapezoidal rule
48
6.3 Worked example: cumulative normal probability
49
6.4 Sources of error with the trapezoidal rule
50
Problems
51
7 Numerical Integration (Simpson's Rule)
53
7.1 Introduction
53
7.2 Simpson's 3/8 rule
55
7.3 An efficient Simpson's rule
55
7.4 Integration in Matlab
56
Problems
58
8 Numerical Interpolation (Newton's Method)
61
8.1 Introduction
61
8.2 Polynomial equations
62
8.3 Newton's linear interpolation
63
8.4 Newton's quadratic interpolation
64
8.5 General form of Newton's polynomials
65
8.6 Lagrange's interpolating polynomials
67
8.7 Polynomial interpolation in practice
68
8.8 Polynomial interpolation in Excel
69
8.9 Polynomial interpolation in Matlab
70
Problems
70
9 Numerical Interpolation (Cubic Splines and Other Methods)
73
9.1 Introduction
73
9.2 Cubic splines
73
9.3 Trigonometric interpolation
77
9.4 Other methods of interpolation
79
9.5 Extrapolation
80
Problems
80
10 Systems of Linear Equations (Introduction) 83
10.1 Introduction
83
10.2 The basic equations
84
10.3 Graphical methods
85
10.4 Cramer's rule
85
10.5 Elimination of unknowns
86
10.6 Gauss elimination
87
10.7 Problems and their solution for Gauss elimination
89
Problems
90
11 Systems of Equations (Gauss-Seidel Method) 93
11.1 Gauss-Seidel method
93
11.2 Convergence
96
11.3 Relaxation
97
Problems
97
12 Systems of Equations (LU Decomposition and Thomas Algorithm) 99
12.1 LU decomposition
99
12.2 Crout decomposition
100
12.3 Banded matrices and the Thomas algorithm
103
12.4 Example of a banded matrix
104
Problems
105
13 Ordinary Differential Equations (Euler's Method) 107
13.1 Introduction
107
13.2 Ordinary differential equations in engineering
108
13.3 Pre-computer methods of solving ODEs
111
13.4 One-step methods
112
13.5 Euler's method
112
13.6 Chaotic behaviour in solutions
114
13.7 Modified Euler method
115
Problems
115
14 Ordinary Differential Equations (Henn and Runge-Kutta Methods) 117
14.1 Introduction
117
14.2 Heun's method
117
14.3 Runge-Kutta methods
119
14.4 Computational effort
120
14.5 Adaptive step methods
120
14.6 Integration using ODE techniques
122
Problems
122
15 Finite Difference Modelling (Introduction) 123
15.1 Introduction
123
15.2 First-order finite difference approximations
125
15.3 Higher-order finite difference approximations
126
15.4 Second derivative approximations
128
15.5 Application of finite difference method
128
15.6 Selecting the space step
129
15.7 Selecting the time step
129
Problems
130
16 Finite Difference Modelling (Laplace's Hot Plate) 133
16.1 Introduction
133
16.2 Elliptic finite difference techniques
134
16.3 Worked example
136
16.4 Coding Liebmann's method in Fortran
138
Problems
139
17 Finite Difference Modelling (Solution of Pure Convection Equation) 141
17.1 Introduction
141
17.2 Selecting the space step size
141
17.3 Deriving the finite difference approximation
142
17.4 Worked example in Excel
143
17.5 Stability, accuracy and other issues
145
Problems
148
18 Finite Difference Modelling (Solution of Pure Diffusion Equation) 149
18.1 Introduction
149
18.2 Selecting the space step size
149
18.3 Deriving the finite difference approximation
150
18.4 Boundary conditions
152
18.5 Coding the heat equation in Fortran
154
18.6 Heated bar simulation
154
Problems
156
19 Finite Difference Modelling (Solution of Full Transport Equation) 159
19.1 Introduction
159
19.2 Deriving the finite difference approximation
159
19.3 Verification of finite difference approximation
160
19.4 Case study: thermal river pollution
162
Problems
162
20 Finite Difference Modelling (Alternate Schemes) 163
20.1 Introduction
163
20.2 Advanced explicit methods
163
20.3 implicit schemes
164
20.4 Solving implicit methods
164
20.5 Accuracy and the finite difference
166
20.6 Lewis Fry Richardson
168
Problems
168
21 Probability and Statistics (Descriptive Statistics) 169
21.1 Introduction
169
21.2 Data exploration
169
21.3 Summary statistics
173
Problems
176
22 Probability and Statistics (Population and Sample) 177
22.1 Introduction
177
22.2 Probability
177
22.3 Estimation
180
22.4 Bayes' rule and total probability
181
Problems
183
23 Probability and Statistics (Linear Combination of Random Variables) 185
23.1 Introduction
185
23.2 Mathematical model
185
23.3 Distribution of the sample mean
187
Problems
188
24 Probability and Statistics (Correlation and Regression) 189
24.1 Introduction
189
24.2 Correlation
189
24.3 Correlation and time series
192
24.4 Testing a random number generator
193
24.5 Simple linear regression
195
24.6 Regression towards the mean
198
Problems
199
25 Probability and Statistics (Multiple Regression) 201
25.1 Introduction
201
25.2 Multiple regression model
201
25.3 Worked example
203
25.4 Regression in Excel
205
25.5 Fitting quadratic surfaces
208
25.6 Indicator variables
210
Problems
212
26 Probability and Statistics (Non-Linear Regression) 215
26.1 Introduction
215
26.2 Non-linear regression example
215
Problems
217
27 Probability Distributions (Introduction) 219
27.1 Introduction
219
27.2 Discrete variables
219
27.3 Continuous variables
220
27.4 Probability mass and probability density functions
222
27.5 Cumulative probability distributions
224
27.6 Common distributions in engineering
224
27.7 Uniform distribution
225
Problems
226
28 Probability Distributions (Bernoulli, Binomial, Geometric) 227
28.1 Introduction
227
28.2 Properties of the Bernoulli distribution
228
28.3 Geometric distribution
230
28.4 Return period
230
28.5 Negative binomial distribution
231
Problems
231
29 Probability Distributions (Poisson, Exponential, Gamma) 233
29.1 Introduction
233
29.2 Poisson process and Poisson distribution
234
29.3 Prussian army horses
235
29.4 Return periods and probability
236
29.5 Exponential distribution
237
29.6 Gamma distribution
237
29.7 Worked example
238
Problems
239
30 Probability Distributions (Normal and Log-Normal) 241
30.1 Introduction
241
30.2 Normal distribution
242
30.3 Excel example
244
30.4 Application of normal distribution to diffusion
244
30.5 Log-normal distribution
245
30.6 A word of warning
246
Problems
247
31 Probability Distributions (Extreme Values) 249
31.1 Introduction
249
31.2 Genesis of an extreme value distribution
249
31.3 The Gumbel distribution
250
31.4 Modelling cyclones
251
31.5 Pareto distribution
252
31.6 Generalised Pareto distribution
254
Problems
256
32 Probability Distributions (Chi-Square and Rayleigh) 257
32.1 Introduction
257
32.2 Chi-square distribution
257
32.3 Rayleigh distribution
258
Problems
258
33 Probability Distributions (Multivariate) 259
33.1 Introduction
259
33.2 Discrete bivariate distributions
259
33.3 Bivariate normal distribution
260
33.4 Multivariate normal distribution
263
33.5 Continuous multivariate distributions
266
Problems
268
34 Monte Carlo Method (Introduction) 269
34.1 Introduction
269
34.2 Illustrative example of Monte Carlo simulation
270
34.3 Basic procedure for Monte Carlo simulation
272
Problems
275
35 Monte Carlo Method (Generation of Random Numbers) 277
35.1 Introduction
277
35.2 Distributions of random numbers
278
35.3 Uniform distribution
279
35.4 Exponential distribution
280
35.5 Normal distribution
281
35.6 Log-Normal distribution
281
35.7 Central limit theorem
282
35.8 Solution of pollutant dispersion
283
Problems
285
36 Monte Carlo Method (Acceptance/Rejection) 287
36.1 Introduction
287
36.2 The Metropolis algorithm
288
Problems
290
37 Monte Carlo Method (Metropolis Applications) 291
37.1 Introduction
291
37.2 The Ising model
291
37.3 The Strauss model
294
37.4 Parameter uncertainty
296
37.5 Conclusion
299
Problems
299
38 Stochastic Modelling (Goodness of Fit and Model Calibration) 301
38.1 Introduction
301
38.2 The method of moments
301
38.3 Probability plots
302
38.4 Statistical tests
306
38.5 Least squares
306
Problems
308
39 Stochastic Modelling (Likelihood and Uncertainty) 309
39.1 Introduction
309
39.2 Bayes' rule
309
39.3 Maximum likelihood
311
39.4 Uncertainty
314
Problems
317
40 Stochastic Modelling (Markov Chains) 319
40.1 Introduction
319
40.2 Regular Markov chains
319
40.3 Absorbing Markov chains
322
40.4 Regular Markov processes
323
Problems
325
41 Stochastic Modelling (Time Series) 327
41.1 Introduction
327
41.2 Environmental time series applications
328
41.3 Concepts of time series
330
41.4 Modelling trends and seasonal effects
331
41.5 Autoregressive processes
334
41.6 Simulation
335
41.7 Forecasting
336
41.8 Summary
337
Problems
338
42 Optimisation (Local Optimisation) 339
42.1 Introduction
339
42.2 The Simplex method
340
Problems
344
43 Optimisation (Global Optimisation) 345
43.1 Introduction
345
43.2 Combinatorial optimisation
345
43.3 Simulated annealing
348
Problems
352
44 Linear Systems and Resonance 353
44.1 Introduction
353
44.2 Mathematical description of linear systems
356
44.3 Resonance in the coastal environment
359
44.4 Resonance in structural engineering
360
Problems
361
45 Spectral Analysis (Introduction) 363
45.1 Introduction
363
45.2 Frequency and time domains
364
45.3 History – Fourier
365
45.4 The Fourier transform
366
45.5 Case study #1: earthquake analysis
368
45.6 Case study #2: pink noise
368
45.7 Case study #3: red noise
369
45.8 Worked example
370
Problems
371
46 Spectral Analysis (Discrete Fourier Transform) 373
46.1 Introduction
373
46.2 The Fourier transform of discrete data
374
46.3 Worked example
375
46.4 The fast Fourier transform in Matlab
377
46.5 The fast Fourier transform and Excel
378
46.6 Discrete Fourier transform summary
379
46.7 The sampling theorem
379
46.8 Examples from data collection studies
381
Problems
382
47 Spectral Analysis (Practical Aspects I) 383
47.1 Introduction
383
47.2 Data pre-processing
383
47.3 Worked example: water temperature series
386
47.4 Spectral energy
387
47.5 Frequency resolution
388
47.6 Spectral confidence
388
Problems
390
48 Spectral Analysis (Practical Aspects II) 391
48.1 Introduction
391
48.2 Excel example
392
48.3 Practical aspects of spectral analysis
394
48.4 Data collection for spectral analysis
395
Problems
396
Appendix A: Taylor Series 399
A.1 Introduction
399
A.2 Fundamental Taylor (Maclaurin) series
401
A.3 Geometric series and convergence
401
A.4 Coding in Fortran
403
A.5 Coding in Excel
403
A.6 Finite difference approximation
404
A.7 Matrix exponential
404
Appendix B: Error Function and Gamma Function 407
B.1 Error function
407
B.2 Gamma function
408
Appendix C: Complex Sinusoid 409
C.1 Complex exponential
409
C.2 Coding in Excel and Matlab
409
C.3 Single mode of vibration
410
Appendix D: Open-Source Software 411
D.1 Introduction
411
D.2 Open-source numerical software
411
D.3 Freely available compilers
412
References 413
Index 421
David Walker, Michael Leonard and Martin Lambert are in the School of Civil, Environmental and Mining Engineering, and Andrew Metcalfe is in the School of Mathematical Sciences, all at the University of Adelaide, Australia. They are all active in teaching and research and the content of the book reflects a strong belief that the one should complement the other.
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