Andreas KORTENHAUS Ghent University, Department · PDF fileAndreas KORTENHAUS Ghent University, Department of Civil Engineering ... Model Uncertainties Can be reduced by: ... 28 224

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


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)


Introduction


What is the wave height?


Introduction


How high is the dike?


Introduction


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)


Introduction


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


Introduction


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


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


'x

x

x

Introduction


68.3% of all values

95.5% of all values

99.7% of all values

= mean value = standard deviation

How does it look then?


Introduction

11

1.0 * --> 68.3%1.64 * --> 90%1.96 * --> 95%2.0 * --> 95.5%3.0 * --> 99.7%


Can we 'improve' uncertainty?

... by more and better data:

... by expert opinions:

... by taking it from the literature:


Introduction

EXISTING EUROTOP ADVICE ON UNCERTAINTIES



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)


Existing advice


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


Existing advice


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)


Existing advice


Design approach in EurOtop 1 (breaking waves)


Existing advice

Deterministic design

Probabilistic design

BACKGROUND CALCULATIONS



Example calculation for wave run-up


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


Formula for wave run-up height


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


Uncertainties of parameters for run-up height


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


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


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


Calculations for EurOtop (vert. wall, impulsive)


Background


Calculations for EurOtop (vert. wall, impulsive)


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



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


Updates


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


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


Conclusions

THANK YOU VERY MUCH FOR YOUR ATTENTION!


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Andreas KORTENHAUS Ghent University, Department · PDF fileAndreas KORTENHAUS Ghent University, Department of Civil Engineering ... Model Uncertainties Can be reduced by: ... 28 224