CEE 3030 ● Uncertainty in
Engineering Analysis
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Instructor
Lectures
Classroom
Textbook
Notes
Gilberto E. Urroz
MW 3:30-4:20 pm
ENGR ...
Spiegel et. al. “PROBABILITY
AND STATISTICS, Schaum,
McGraw-Hill”
See course web site
ABET Outcomes for CEE 3030 (1)
Upon successful completion of undergraduate
program for CE at USU, students will have:
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http://www.engineering.usu.edu/cee/faculty/gurro
Click on Classes, then on CEE 3030
ABET Outcomes for CEE 3030 (2)
Upon successful completion of undergraduate
program for CE at USU, students will have:
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Outcome 3 – Shown a capacity for investigation
and experimentation into physical (engineering)
phenomena along with the ability to analyze and
interpret engineering data ...
Outcome 1 – Proven themselves proficient in
mathematics, the sciences, ...
Outcome 2 – Demonstrated the ability to solve
engineering problems, utilizing fundamental
engineering principles as well as the latest
technologies and engineering tools, in the process
of engineering analysis and design. ....
Class Contents (1)
1 – Introduction
2 – Probability
3 – Random variables
4 – Probability distributions
5 – Samples, frequency distributions, graphs
6 – Sampling distributions
7 – Interval estimation
8 – Regression techniques
Assignments, exams, grading
Tools
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Assignments: 60% of grade
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Exams: 40% of grade
MAPLE 10
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Two tests (50 minutes, each): 10% of grade, each
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Final exam (110 minutes):
20% of grade
Calculators
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Mathematics software with statistics package
Point-and-click mathematics
Relatively easy to use
Hp 49g+
TI 89 Titanium
Spreadsheets
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Excel (MS Office)
Calc (Open Office)
Uncertainty in Engineering
Analysis – An Introduction (1)
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Probability and statistics for engineers
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Knowledge needed:
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Algebra
Univariate calculus
Multivariate calculus
Types of systems
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Systems – e.g., pipe flow
Well-defined input and well-known system
response →DETERMINISTIC
 p 8 LQ 2  4Q
⋅f  ,

=
  g D5 D  D
Examples from Civil Engineering 1
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If uncertainty exists in input or response
→STOCASTIC
Examples from Civil Engineering 2
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Water engineering
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Transportation engineering
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Statistics of transportation systems
Modeling of transportation systems
Examples from Environmental
Engineering
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Turbulence – time uncertainty
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Hydrology
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Statistics of soil samples
Earthquakes (probability of liquefaction)
Uncertainties in water quality in rivers and lakes
Hydraulics and fluid mechanics
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Earthquakes (accelerations, structural responses)
Samples of concrete quality
Geotechnical engineering
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Structural engineering
Statistics of weather quantities (precipitation)
Prediction of runoff
Probability of flooding/period of return
Groundwater
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Uncertainties in groundwater supply
Variations in aquifer properties
Statistics of groundwater contamination
Uncertainties in location of contamination sources
(non-point source pollution)
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Statistical analysis of water and air quality
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Modeling of environmental contamination
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Statistics of animal and fish habitat
Random variables
Statistics
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Variables associated with uncertainties
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Examples:
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Precipitation in a basin
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Number of cars per unit time in highway ramp
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Strength of concrete cylinders
Science and technology of data analysis (rough
definition)
Statistical techniques:
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Processing large amounts of data
Reducing data to measures and graphs
Reduced data can be used for decision making
Statistical techniques originated from
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City government needs
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Probability
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What is probability?
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Intensity of earthquakes
Number between 0 and 1
Provides estimate of how likely an event is to occur
Probability theory: science of prediction of
random systems (rough definition)
Probability theory originated to understand the
outcome of games of chance
Population, samples, inference
Taxation
Health Services
Napoleonic wars
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Casualties
Statistical inference (1)
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Population: all possible values of measurement or
collection of all individuals of interest in a study
Sample: sub-set of a population used to obtain
statistical measures
Statistical inference: use samples to make
inferences on population
Techniques of statistical inference:
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Estimation
Hypothesis testing
Regression
Random samples
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Each element selected with the same probability or
likelihood
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Is representative of a population
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Biased sample: not representative of population
Sample space and events
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Sample space (Ω): set of all possible outcomes of
an experiment
Events (A, B, ...): subsets of the sample space.
Example: casting a die
Ω = {1, 2, 3, 4, 5, 6}, A = {2, 4, 6}, B = {1, 3, 5}
Events are also sets:
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Venn diagrams
2 ∈ A, 3 ∉ A
A ⊂ Ω, B ⊂ Ω, A ⊄ B
Sets and set operations
Ω = universal set , ∅ = empty set = {}
A ⊂ Ω, B ⊂ Ω, ...
∅ ⊂ A, ∅ ⊂ A, ...
Operations:
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Complement: A' = {elements not in A}
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Union:
A ∪ B = {elements in A or B}
Intersection: A ∩ B = {elements in A and B}
A∪Ω=Ω,
A∩Ω= A,
A∪∅ = A
A∩∅=∅,
A∪A'= Ω,
A∩A'=∅
By definition: ∅ ' = Ω, Ω' = ∅
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(A∪ B)' = A' ∩ B'