7. THE MODELLING AND REPRESENTATION OF UNCERTAINTY.pdf

7/28/2019 7. THE MODELLING AND REPRESENTATION OF UNCERTAINTY.pdf

1/19

THE MODELLING AND

REPRESENTATION OF

UNCERTAINTY


2/19

THE CONCEPT OF UNCERTAINTY

In a general sense, uncertainty can be interpreted as lack of

precise knowledge by the engineer at a time when he/she

needs to make a decision. This can include:

Lack of knowledge about something that is fixed but

unknown

(e.g. mechanical properties of a particular piece of steel)

Uncertainty in the magnitude of a future event

(e.g. maximum height of a wave impacting a particular

offshore structure in 2012)

In general, uncertainty can be reduced by increased

information.


3/19

TYPES OF UNCERTAINTY

At least three basic types:

Physical uncertainty (e.g. natural variability)

Statistical uncertainty (e.g. in parameters of probability

distributions)

Model uncertainty (e.g.in the mathematical models for

engineering calculations)

All these uncertainties must be included in reliability analyses.


4/19

PHYSICAL UNCERTAINTY SOME EXAMPLES

Random time to failure of a sub-sea valve

Extreme pressures/loads on structures (e.g. wave)

Peak combinations of time-varying loads (e.g.wind,

wave, current)

Material properties (e.g. yield strength, fracture

toughness)

Physical dimensions (esp. in imperfection sensitive

structures)

Corrosion rates

Fatigue crack growth rates


5/19

PHYSICAL UNCERTAINTY SOME EXAMPLES


6/19

Piper Bravo, 1990


7/19

Initial surface breaking crack

Crack starting from weld toe

Crack growth with time t

t

a

no initial crack

Initial crack depth

Fatigue crack growth with time showing

dependence on initial defect size


8/19Data from the Hutton Tension leg platform during fabrication, 1984


9/19

Monitoring fatigue crack growth in the laboratory


10/19

0

10

20

30

40

50

0 50,000 100,000 150,000 200,000 250,000 300,000 350,000Number of cycles

Cracklength(mm)

Variation in crack length with number of cycles of applied stress for

68 nominally identical specimens

[plotted from Virkler et al(1978) data set]


11/19

1 E-02

1 E-03

1 E-04

1 E-05

1 E-06

200 500 1000 2000 3000K (Nmm-3/2)

da

/dN

(mm/cycle)

Variable fatigue crack growth rate data from a single piece of

Grade 50 D steel


12/19

Failure by Fatigue and Fracture

Pf

Time (years)


13/19

Damage following hurricane Rita in the Gulf of Mexico - 2005


14/19

Variation of concrete slab thickness - for a 150 mm nominal slab


15/19

Data from steel samples taken during the re-construction of steel bridges

between Kings Cross and Edinburgh in the 1970s


16/19

TIME-VARYING QUANTITIES

(e.g. wind speed, significant wave height)


17/19

Mean daily wind speed from M.V. Famita in early days of

North Sea oil and gas development


18/19

Distributions of parent and annual extreme wind speeds for Lerwick


19/19

Synthesis of Availability and Reliability for multiple variables

RESPONSE

MODEL

Y = h(X)

x1

x2

x3

x4

yy*

INPUTS

DETERMINISTIC

CALCULATION

MODEL

OUTPUT

Illustration

of

random

input

7. THE MODELLING AND REPRESENTATION OF UNCERTAINTY.pdf

Documents