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Reliability and uncertainty- Deterministic and probabilistic approaches -
Andreas KORTENHAUS
Ghent University, Department of Civil Engineering
Department of Civil Engineering - Ghent UniversitySymposium on ‘Update of the EurOtop Manual on wave overtopping’UNSESCO-IHE, Delft, 10 September 2014
Introduction Existing advice Background Updates Conclusions
Overview of presentation
Introduction
Existing EurOtop advice on uncertainties
Background calculations
Updates in the new EurOtop manual
Conclusions
Department of Civil Engineering - Ghent University 210 September 2014
INTRODUCTION
Department of Civil Engineering - Ghent University
Introduction Existing advice Background Updates Conclusions
Quotes on uncertainty
‘The only certainty is that nothing is certain.’ ... (Pliny the Elder)
‘There is nothing more certain and unchanging than uncertainty and change.’ ... (John F. Kennedy)
‘As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality.’ ... (Albert Einstein)
‘Only two things are certain: the universe and human stupidity; and I’m not certain about the universe.’ .... (Albert Einstein)
Department of Civil Engineering - Ghent University 410 September 2014
Introduction
Introduction Existing advice Background Updates Conclusions
What is the wave height?
Department of Civil Engineering - Ghent University 510 September 2014
Introduction
Introduction Existing advice Background Updates Conclusions
How high is the dike?
Department of Civil Engineering - Ghent University 610 September 2014
Introduction
Introduction Existing advice Background Updates Conclusions
What is uncertainty?
... the lack of certainty. A state of having limited knowledge where it is impossible to exactly describe the existing state, a future outcome, or more than one possible outcome (Wikipedia)
... parameter, associated with the result of a measurement, that characterizes the dispersion of the values that could reasonably be attributed to the measurand (ISO Guide on uncertainties in measurements)
... the relative variation in parameters or errors in the model description (EurOtop, 2007)
Department of Civil Engineering - Ghent University 710 September 2014
Introduction
Introduction Existing advice Background Updates Conclusions
Ok, what is reliability then?
Reliability is defined as the probability that a device will perform its intended function during a specified period of time under stated conditions (Wikipedia)
Some issues with this:‣ ... probability (of no failure) --> opposite to failure probability‣ ... intended function --> usually of the structure, not of a process‣ ... a specified period of time --> lifetime of the structure‣ ... under stated conditions --> data usually generated under
controlled and defined conditions
Department of Civil Engineering - Ghent University 810 September 2014
Introduction
Introduction Existing advice Background Updates Conclusions
Inherent (Basic) Uncertainties
Human & Organis. Errors
(HOE)Model
Uncertainties
Can be reduced by:- increased data- improved qualityof collected data
Can be reduced by:- increased knowledge- improved models
Can neither be- reduced nor- removed
Empirical and theoretical model
uncertainties
Statistical distribution
uncertainties
Can be reduced by:- improved knowledge- improved organisation
Environmental parameters, material properties of random nature (example: ex-pected wave height at certain site in 20 years)
Operators (desig-ners...), organisations, procedures, environ-ment, equipment and interfaces between these sources
Hypothesised / fitted statistical distributions of random quantities (fixed time parameters) and random processes (variable time parameters)
Empirical (based on data) and theoretical relationships used to describe physical processes, input variables and limit state equations (LSE)
How can we classify uncertainties?
Introduction
10 September 2014Department of Civil Engineering - Ghent University 9
Introduction Existing advice Background Updates Conclusions
Can we define a measure for uncertainty?
Usually errors are relative, i.e. errors increase with increasing mean values (e.g. wave height) Therefore, uncertainty is frequently defined as a relative error
(coefficient of variation):
where:‣ x = arithmetic mean ‣ σx = standard deviation
Department of Civil Engineering - Ghent University 1010 September 2014
'x
x
x
Introduction
Introduction Existing advice Background Updates Conclusions
68.3% of all values
95.5% of all values
99.7% of all values
= mean value = standard deviation
How does it look then?
Department of Civil Engineering - Ghent University 10 September 2014
Introduction
11
1.0 * --> 68.3%1.64 * --> 90%1.96 * --> 95%2.0 * --> 95.5%3.0 * --> 99.7%
Introduction Existing advice Background Updates Conclusions
Can we 'improve' uncertainty?
... by more and better data:
... by expert opinions:
... by taking it from the literature:
Department of Civil Engineering - Ghent University 1210 September 2014
Introduction
EXISTING EUROTOP ADVICE ON UNCERTAINTIES
Department of Civil Engineering - Ghent University
Introduction Existing advice Background Updates Conclusions
Uncertainties in EurOtop 1
General definitions:‣ Section 1.5.1 using the coefficient of variation‣ Section 1.5.2 provides some basic background on uncertainties‣ Section 1.5.3 on parameter uncertainty‣ Section 1.5.4 on model uncertainty
Parameter and model uncertainty:‣ Section 2.7 on water levels and wave heights‣ Section 4.8 on model and scale effects‣ Section 4.9 on prediction methods (empirical models, neural network,
CLASH database)
Department of Civil Engineering - Ghent University 1410 September 2014
Existing advice
Introduction Existing advice Background Updates Conclusions
Uncertainties in EurOtop 1 (cont.)
Predictions:‣ Section 5.6 and 5.7 on uncertainties of wave overtopping of coastal dikes‣ Section 6.7 on uncertainties of wave overtopping of armoured slopes‣ Section 7.3.7 on scale and model effects for vertical walls‣ Section 7.4.5 on scale effects of individual overtopping volumes‣ Section 7.6 on uncertainties of wave overtopping of vertical walls
Department of Civil Engineering - Ghent University 1510 September 2014
Existing advice
Introduction Existing advice Background Updates Conclusions
Design approach in EurOtop 1
'Probabilistic design':‣ for wave run-up: Equation 5.3 (average trend) with standard deviation of
key parameters provided‣ for wave overtopping: Equation 5.8 (average trend), again with standard
deviations of key parameters
'Deterministic design':‣ for run-up: Equation 5.4 (key parameters one standard deviation higher
than the probabilistic approach)‣ for overtopping: Equation 5.9 (key parameters one standard deviation
higher than the probabilistic approach)
Department of Civil Engineering - Ghent University 1610 September 2014
Existing advice
Introduction Existing advice Background Updates Conclusions
Design approach in EurOtop 1 (breaking waves)
Department of Civil Engineering - Ghent University 1710 September 2014
Existing advice
Deterministic design
Probabilistic design
BACKGROUND CALCULATIONS
Department of Civil Engineering - Ghent University
Introduction Existing advice Background Updates Conclusions
Example calculation for wave run-up
Department of Civil Engineering - Ghent University 10 September 2014
Hs
Wave length Lz
h
RcDesign water level DWL
Hs = significant wave height at toe [m]Tp = Peak period of waves [s]Rc = freeboard [m]z = wave run-up height [m]h = water level at dike toe [m] = seaward slope [°]
Background
19
Introduction Existing advice Background Updates Conclusions
Formula for wave run-up height
Department of Civil Engineering - Ghent University 10 September 2014
98 1 f b m0 pgz c H T tan
2 98 1 f b m0 pgz c H T tan
2
where:z98 = wave run-up height, being exceeded by 2% of the all the
waves [m]Hm0 = significant wave height at toe of dike [m]Tp = peak wave period at toe of dike [s]c1 = empirical factor [-]gf = roughness factor for the outer slope [-]gq = factor for oblique wave attack [-]gb = factor for berm at outer slope[-]g = gravitational constant [m/s2]a = angle of outer slope [°]
EAK 2002
Background
20
Introduction Existing advice Background Updates Conclusions
Uncertainties of parameters for run-up height
Department of Civil Engineering - Ghent University 10 September 2014
Description Dim. Mean Std. -dev. Distr.
Wave height Hs [m] 3.0 0.1 Normal
Wave period Tp [s] 6.0 0.1 Normal
Empirical factor c1 [-] 1.5 0.1 Normal
Slope n [-] 6.0 0.2 Normal
Angle of wave attack Q [°] 0.0 10.0 Normal
Roughness outer slope gf [-] 1.0 0.05 Normal
Factor for berm gb [-] 1.0 - -
Background
21
Introduction Existing advice Background Updates Conclusions
Run-up calculation with uncertainties
Deterministic calculation‣ z98 (deterministic) = 3.27 m
Consideration of uncertainties‣ Monte-Carlo-Simulation‣ 10000 calculations‣ z98 (mean) = 3.28 m‣ Std.-dev. = 0.32 m‣ CoV = 10%‣ 5%-percentile = 2.76 m‣ 95%-percentile = 3.82 m
Department of Civil Engineering - Ghent University 10 September 2014
Distribution for z98 p, VdM p/K33
0,000
0,200
0,400
0,600
0,800
1,000
1,200
1,400
Mean=3,280723
2 3 4 52 3 4 5
5% 90% 5% 2,7649 3,818
Mean=3,280723
Background
22
Introduction Existing advice Background Updates Conclusions
Calculations for EurOtop (vert. wall, impulsive)
Department of Civil Engineering - Ghent University 2310 September 2014
Background
Introduction Existing advice Background Updates Conclusions
Calculations for EurOtop (vert. wall, impulsive)
Department of Civil Engineering - Ghent University 2410 September 2014
Background
1,E-05
1,E-04
1,E-03
1,E-02
1,E-01
1,E+00
1,E+01
1,E+02
1,E+03
1,E-04 1,E-03 1,E-02 1,E-01 1,E+00 1,E+01 1,E+02 1,E+03
mea
sure
d di
men
sion
less
dis
char
ge Q
h
predicted dimensionless discharge Qh
28 224 225
351 502 802
UPDATES IN THE NEW EUROTOP MANUAL
Department of Civil Engineering - Ghent University
Introduction Existing advice Background Updates Conclusions
Updates in the new EurOtop manual (1)
What is kept?‣ Approach is as simple as it was before‣ Draw the 90% confidence bands as before
Provide different statistical values for wave run-up and overtopping predictions such as:‣ Mean‣ Standard deviation (with updates for the new formulae)‣ 90% and 95% confidence bands
Department of Civil Engineering - Ghent University 2610 September 2014
Updates
Introduction Existing advice Background Updates Conclusions
Updates in the new EurOtop manual (2)
Provide information on‣ mean value approach (previously 'probabilistic design')‣ design assessment approach (previously 'deterministic design')
New information‣ How to use the mean value approach for a full probabilistic analysis‣ Provide details on how to calculate the confidence bands from the
standard deviation
Department of Civil Engineering - Ghent University 2710 September 2014
Updates
CONCLUSIONS
Department of Civil Engineering - Ghent University
Introduction Existing advice Background Updates Conclusions
Conclusions
Uncertainties have to be considered, ignoring them makes things worse, not better! Approaches to uncertainties in EurOtop 2 should
remain simple and comparable to EurOtop 1!
EurOtop 2 will provide formulae for run-up and overtopping for:‣ a mean value approach (rather than 'probabilistic design')‣ a design assessment approach (rather than 'deterministic design')
AND ‣ EurOtop 2 will provide more information on how to use the mean value
approach for probabilistic modelling‣ the 90% confidence bands will still be consistently plotted in the manual,
but more values are also provided
Department of Civil Engineering - Ghent University 2910 September 2014
Conclusions
THANK YOU VERY MUCH FOR YOUR ATTENTION!
Department of Civil Engineering - Ghent University