Risk Analysis in
Environmental Systems
Understanding Uncertainty, Risk and Reliability
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Instructor: M. Reza Najafi
Learning Objectives
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Describe
uncertainty, risk
and reliability
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Describe measures
of reliability and
uncertainty
quantification
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Describe ways to
handle the
reliability
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Describe
challenges related
to decision making
under uncertainty
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Understanding and
motivation
• The most important responsibility of an engineer is to make
decision, or aid in the process of decision making, on matters that
relate to technology and industry.
• The decision process is particularly complicated because of the
prevailing uncertainties and lack of complete information.
• Whereas a scientist is in pursuit of a deeper understanding of a
phenomena, an engineer is entrusted with making decision under
uncertainty, often with severe constraints on time and budget.
Example: A seismologist is interested in understanding the nature of earthquake,
but an earthquake engineer is interested in designing structures to withstand
earthquakes, even when limited knowledge may exist regarding the frequency and
severity of future earthquakes in the region.
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Engineering systems
Engineering systems can be classified loosely into two types:
Manufactured Systems: Equipment and assemblies, such as
pumping stations, computers, airplanes, bulldozers, and tractors,
that are designed, fabricated, operated, and moved around
totally by humans.
Infrastructural Systems: Structures or facilities, such as
bridges, buildings, dams, roads, levees, sewers, pipelines, power
plants, and coastal and offshore structures, that are built on,
attached to, or associated with the ground or earth.
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Failure of systems
• Failure of Infrastructures: usually caused by
natural processes, such as earthquakes,
tornadoes, hurricanes, heavy rain or snow,
and floods, that are beyond human control.
✓ Classified as structural and functional failures
• Failure of Manufactured Systems: wear and
tear, deterioration, and improper operation,
which could be dealt with by human abilities
but may not be economically desirable.
✓ Classified into repairable and nonrepairable
types
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Reliability Engineering is a field developed
in recent decades to deal with safety and
performance issues.
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The reliability of an engineering system may be considered:
• Casually (through the use of a subjectively decided factor of
safety)
• In a more comprehensive and systematic manner through
the aid of probability theory.
Ways to
handle the
reliability
Factors that contribute to the slow development and application
of reliability in hydrosystem engineering:
1.
Those who understand the engineering processes well
often are not trained adequately and are uncomfortable
with probability.
2.
Those who are good in probability theory and statistics
seldom have sufficient knowledge of the details of the
engineering process involve.
3.
Some of the factors are still beyond the firm grasp of
engineers and statisticians.
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• Engineers have a tendency to focus on components
affecting their problem most, while ignoring other
contributing elements.
Ways to handle
the reliability
(cont’d)
• The factors affecting the reliability of a system usually
require the work of experts in different disciplines,
whereas interdisciplinary communication and
cooperation often are a problem.
• Engineers’ devotion and accomplishment hinder the
vision to see beyond a broader view of uncertainty and
reliability analyses.
• It is far better to have an approximate model of the
whole problem than an exact model of only1 a portion
of it.
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What is risk?
“The expected losses (of lives, persons injured, property
damaged and economic activity disrupted) due to a particular
hazard for a given area and reference period.”
The United Nations Department of Humanitarian Affairs (1992)
Risk: the actual exposure of something of human value to a
hazard:
𝑅𝑖𝑠𝑘 = 𝐻𝑎𝑧𝑎𝑟𝑑 × 𝑉𝑢𝑙𝑛𝑒𝑟𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑜𝑓 𝐸𝑙𝑒𝑚𝑒𝑛𝑡𝑠 𝑎𝑡 𝑅𝑖𝑠𝑘
Hazard: a threatening event or the probability of occurrence of a
potentially damaging phenomenon within a given time period and
area.
Vulnerability: degree of loss resulting from a potentially
damaging phenomenon.
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Example of flood hazard parameters for a
coastal zone
Salinity
Volume
Volumetric flow rate
Debris and contaminants
Velocity
Density
Depth
Wave height, length, and frequency
Rise of water
Temperature
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Confusion on risk and risk analysis
Inconsistent definitions of risk and risk analysis cause considerable confusion and doubt about the subject.
Example: in flood protection engineering
✓ Hydraulic Engineers: risk analysis is the analysis of the probability of failure to achieve the intended
objectives.
✓ Hydrologists: often consider risk in terms of the return period
✓ Water Resources Planners and Decision Makers: regard risk analysis as the analysis of risk costs,
assessment of the economic and social consequence of a failure, and risk management.
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What is
consequence?
• Loss of life
• Stress
• Material damage
• Environmental degradation and so on.
 It is possible to measure consequence
qualitatively (such as “an area of high
flood risk”), and quantitatively (such as
“value of a damaged house”)
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• Loads, stresses, and
demands tend to cause
failure of the system.
• Failure occurs when the
demand exceeds the
supply or the load
exceeds the resistance.
Fault (logic) tree for culvert
design
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The basic idea of reliability
engineering is to determine
the failure probability of
an engineering system,
from which the safety of
the system can be
assessed or a rational
decision can be made on
the design, operation, or
forecasting of the system.
Reliability Engineering
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Various types of uncertainty
exist in the contributing
components of:
• The performance of a
hydrosystem engineering
infrastructure
• Function of an engineering
project
• Completion of an operation
Uncertainty
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Decision making
under uncertainty
• Engineers always face the dilemma of decision
making or design with imperfect information.
• It is the engineer’s responsibility to obtain a
solution with limited information
✓ Guided by experience and judgment
✓ Considering the uncertainties and
probable ranges of variability of the
pertinent factors
✓ Considering economic, social, and
environmental implications
✓ Assessing a reasonable level of safety
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Uncertainty,
definition
and
importance
• Uncertainty is attributed to the lack
of perfect information concerning
the phenomena, processes, and
data
• Uncertainty reflects the lack of
sureness about something
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• Uncertainty could simply be defined as the occurrence
of events that are beyond one’s control
• It is a very recent development in the modelling
community.
• Most papers in the beginning of the last century did
acknowledge the existence of Uncertainty, but did not
deal with it in an explicit way.
• Uncertainty analysis aims to quantify the overall
uncertainty associated with the response as a result of
uncertainties in the model, input, parameters,
structure, etc.
Uncertainty, definition and
importance
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Types of uncertainty
Yen and Ang (1971), Halder and Mahgavan (2000) and
NRC (2000) classified uncertainties into two types:
▪ Epistemic/Subjective/Cognitive Uncertainty
• Due to ignorance/imperfect knowledge
• No quantitative factual information is available
• Can be minimized with additional data
▪ Aleatory/Objective/Noncognitive/Stochastic Uncertainty
(Natural/Inherent Variability)
• Associated with any random process or deducible
from statistical samples
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Sources of
uncertainty
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Inherent randomness of different
geophysical variables encountered in civil
engineering infrastructural systems design
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Uncertainties in hydrosystem
infrastructures
• Geophysical
• Structural
▪ Refers to failure from structural weaknesses.
▪ Caused by water saturation and loss of soil stability, erosion or
hydraulic soil failure, wave action, overloading, and structural
collapse.
• Operational
• Economic
▪ Uncertainties in construction costs, damage costs, projected
revenue, operation and maintenance cost, inflation, project life, and
other intangible benefit and cost items.
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• Uncertainties about model, model structure or
formulation
Beck (1987) noted that
uncertainties affect
primarily four problem
areas that must be
addressed to improve
the accuracy and
usefulness of models:
• Uncertainty in the model parameters, i.e., parameter
identification and calibration problems.
• Uncertainty associated with estimates of the future
behavior of the system
• Reduction of critical modelling uncertainties through
carefully designed experiments and monitoring
programs.
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Model is only an abstraction of reality, which
generally involves certain degrees of simplifications
and idealizations.
What is a
model and
model
uncertainty?
Model formulation ranges from simple empirical
equations to sophisticated partial differential
equations with computer simulations.
Model formulation uncertainty reflects the inability of
the model or design procedure to represent
precisely the system’s true physical behavior.
Examples in Hydrologic Modelling?
▪ Unit Hydrograph model
▪ Flood frequency analysis
What is a parameter uncertainty?
Parameter uncertainties result from the inability to
accurately quantify model inputs and parameters.
Examples:
• Statistical parameters, such as mean and standard
deviation, in a probability distribution model that cannot
be estimated accurately due to limited amounts of
sample data
• Physical parameters, such a channel slope, roughness
coefficient, and bed material properties that can vary
both in space and time
• Coefficients in Empirical Equations that are developed
on the basis of a limited amount of sample data
through calibration or fitting of the model to the data.
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What is data uncertainty?
 Measurement errors
Inconsistency and
nonhomogeneity of data
Data handling and transcription
(recording) errors
Inadequate representation of
data samples due to time and
space limitations.
https://www.pinterest.ca/pin/414964553147336543/
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What is operational uncertainty?
• Uncertainties associated with
construction, manufacture,
procedure, deterioration,
maintenance, and human
activities.
• Construction and manufacturing
tolerances may result in a
difference between the “nominal”
and actual values.
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Sources of prediction errors
 Systematic Errors: arise from factors
not accounted for in the model.
▪ Model prediction tends to produce
biased results that consistently
overpredict or underpredict the
outcomes of the process.
▪ Can be removed by multiplying by
bias correction factor or
subtracting the bias from the
prediction.
 Random Errors: are associated with
the range of possible errors primarily
due to sampling error.
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Types of prediction error
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Uncertainty analysis
 The task of uncertainty analysis is to determine the uncertainty features of the
system responses as a function of uncertainties associated with the system model
itself and the stochastic basic parameters involved.
 Uncertainty analysis provides a formal and systematic framework to quantify the
uncertainty associated with system outputs.
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A practical way to quantify the level of uncertainty for
a parameter is to use the statistical moments
associated with a quantity subject to uncertainty.
Measures of
uncertainty
• The second-order moment called Variance or
Standard Deviation.
• Coefficient of variation: Ratio of Standard
Deviation to Mean
• Confidence Interval: a numerical interval that
would capture the true value of a variable
subject to uncertainty, with a specified
probabilistic confidence.
• The most complete and ideal description of the
uncertainty features of a quantity can be given
by the Probability Density Function (PDF)
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Drawbacks of confidence
interval analysis
• The parameter population may not be normally
distributed as required in the conventional
procedures (particularly when the sample size is
small)
• No means are available to directly combine the
confidence intervals of individual contributing
random components to give the overall confidence
interval of the entire system.
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 The existence of various uncertainties
(including the inherent randomness of natural
processes) is the main contributor to the
potential failure of many infrastructural
systems.
 knowledge about the uncertainty features of
an engineering system is essential for its
reliability analysis.
Implications of
uncertainty
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• Fundamentally, STATISTICS is concerned with
UNCERTAINTY.
What is
statistics?
• Evaluating and quantifying uncertainty, as well as
making inferences and forecasts in the face of
uncertainty, are all parts of statistics.
• It should not be surprising, then, that statistics has
many roles to play in the Water Resources
Engineering and Environmental Science
Example: Weather forecasting
Descriptive
and
inferential
statistics
 Descriptive Statistics relates to the
organization and summarization of
data.
 Inferential Statistics is traditionally
understood as consisting of
methods and procedures used to
draw conclusions regarding
underlying processes that generate
the data.
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Statistical inference
Statistical inference is used to learn from incomplete or imperfect data. There are two standard
paradigms for inference:
▪ In the Sampling Model, we are interested in learning some characteristics of a population
▪ In the measurement Error Model, we are interested in learning aspects of some underlying
pattern or law (for example, the parameters “𝑎” and “𝑏” in the regression model 𝑌 = 𝑎 + 𝑏𝑋
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Learning Objectives
1
Describe
uncertainty, risk
and reliability
2
Describe measures
of reliability and
uncertainty
quantification
3
Describe ways to
handle the
reliability
4
Describe
challenges related
to decision making
under uncertainty
38
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