MODELS AND TERMINOLOGY FOR THE

ANALYSIS OF GEODETIC MONITORING

OBSERVATIONS

- Official Report of the Ad-Hoc Committee

of FIG Working Group 6.1 -

Walter M. Welsch

Institute of Geodesy

Bundeswehr University

Munich

Otto Heunecke

Geodetic Institute

University of Hanover

10

th

FIG International Symposium

On Deformation Measurements

Orange, March 19 through 22 2001

Commission 6

Concern of Deformation

Measurements

Welsch, Heunecke: Models and

Terminology

2

Engineering Surveying
is
involved in all phases of
the lifetime of a
construction

With respect to this report
only deformation
measurements are of
special interest

3

c

o

n

s

tr

u

c

ti

v

e

a

tt

ri

b

u

te

s

s

u

rv

e

il

la

n

c

e

a

c

ti

v

it

y

c

o

n

c

e

p

ts

/

e

m

e

rg

e

n

c

y

c

o

n

c

e

p

t

Stability and operational

security of a construction

Stability and operational

security of a construction

c

o

-o

rd

in

a

ti

o

n

ir

re

g

u

la

ri

ti

e

s

?

qualitative,
e.g. visual
inspections

quantitati
ve
- direct
- non
direct

Meaning of
deformation
measurements in this
interdisciplinary
context ?

- 1 0

- 2 0

- 3 0

- 4 0

- 5 0

S e t z u n g in m m

Concern of Deformation

Measurements

Security

concept for

construction

s

History of FIG Com. 6, WG 6.1 Deformation

Measurements

Welsch, Heunecke: Models and

Terminology

4

• 1

st

Symposium

Krakow

1975

• identification of unstable reference points in geodetic
networks
• continuous measuring techniques were just at the
beginning

• 2

nd

Symposium

Bonn

1978

•

1

st

Ad-Hoc Committee with the tasks of comparing

different approaches for the geometrical analysis

• 3

th

Symposium

Budapest 1982

• report of the 1

st

Ad-Hoc Committee

• expansion of deformation analysis into the physical
interpretation
• increasing importance of automated measuring
techniques

• 4

th

Symposium

Kattowice 1985

• 5

th

Symposium

Frederiction 1988

History of FIG Com. 6, WG 6.1 Deformation

Measurements

Welsch, Heunecke: Models and

Terminology

5

• 6

th

Symposium

Hanover 1992

• (partly) confusing terminology of technical terms

• 2

nd

Ad-Hoc Committee was set to work

(members: Milev / Pfeufer / Proszynski / Steinberg /
Teskey / Welsch)

• 7

th

Symposium

Banff

1993

• 1

st

progress report of the Ad-Hoc Committee (prepared

by Pfeufer)

• 8

th

Symposium

Hong Kong

1996

• status report on the topic (prepared by Welsch)

• 9

th

Symposium

Olsztyn

1999

• final report of the committee (prepared by Welsch /
Heunecke)

• panel discussion and recommendations

• 10

th

Symposium

Orange

2001

• official report includes recommendations and concludes
the work!

Geodetic Modeling of Deformation

Processes

Welsch, Heunecke: Models and

Terminology

6

Real Object

Model of the

Object

Geometr

y

Domain

The object is a

continuum

The object is

dissected by

characteristic

points

Time

Domain

The object is

(more or less)

perma-nently in

motion

The object is

monitored in

certain time

intervals

Conventional Deformation Analysis

Welsch, Heunecke: Models and

Terminology

7

The classical deformation analysis consists in a
purely geometrical comparison of the state of a
geodetic network

Main problem: identification of unstable

reference points by congruence analysis

Conventional Deformation Analysis

Welsch, Heunecke: Models and

Terminology

8

 

 

.

Cov

,

H

,

E

1

2

0

2

0

0

:











P

Q

l

o

x

H

x

A

l





h

d

Q

d

dd

T

































1

0

1

2

0

2

H

|

F

s

P

,

f

,

h

global test of congruence:

The classical deformation analysis consists in a
purely geometrical comparison of the state of a
geodetic network

Main problem: identification of unstable

reference points by congruence analysis

null-hypothesis:

mean gap:

Kinemat

ic

Deform

ation

Analysis

Welsch, Heunecke: Models and

Terminology

9

Position x

Velocity x

Acceleration
x

= Finding of suitable

descriptions of point

movements by time functions,

especially by polynomial

approaches

...

²

2

1

...

²

)

(

²

²

2

1

)

(

1

1

2

1

2

1

2

























t

t

t

t

dt

d

t

t

dt

d

x

x

x

x

x

x

x





View from

the GOCA

web-side

System

equation

X

,

Y

,

H

[m]

[mm/d]

[mm/d

2]

Advanced Deformation Analysis

Welsch, Heunecke: Models and

Terminology

10

Object:

• object geometry

• material parameters

• material behavior

Object:

• object geometry

• material parameters

• material behavior

System reaction:

• rigid body movements

• distortions

System reaction:

• rigid body movements

• distortions

System input:

• internal forces

• external forces

System input:

• internal forces

• external forces

Causal chain of a dynamic system

Modeling

Welsch, Heunecke: Models and

Terminology

11

Theory

Object:

• object geometry

• material parameters

• material behavior

Object:

• object geometry

• material parameters

• material behavior

System reaction:

• rigid body movements

• distortions

System reaction:

• rigid body movements

• distortions

System input:

• internal forces

• external forces

System input:

• internal forces

• external forces

Measurement

s

Welsch, Heunecke: Models and

Terminology

12

Determination of deter-

ministic input quantities

Determination of deter-

ministic input quantities

Determination of

• strain / stress

• displacements

• other indicators

Determination of

• strain / stress

• displacements

• other indicators

Empirical

results

Modeling

Object:

• object geometry

• material parameters

• material behavior

Object:

• object geometry

• material parameters

• material behavior

System reaction:

• rigid body movements

• distortions

System reaction:

• rigid body movements

• distortions

System input:

• internal forces

• external forces

System input:

• internal forces

• external forces

Evaluation

methods

Welsch, Heunecke: Models and

Terminology

13

Deviation between

computed and measured

system reaction?

Deviation between

computed and measured

system reaction?

- parameter
matching

• adaptive

• probabilistic

Measurement

s

Determination of deter-

ministic input quantities

Determination of deter-

ministic input quantities

Modeling

Determination of

• strain / stress

• displacements

• other indicators

Determination of

• strain / stress

• displacements

• other indicators

System reaction:

• rigid body movements

• distortions

System reaction:

• rigid body movements

• distortions

Object:

• object geometry

• material parameters

• material behavior

Object:

• object geometry

• material parameters

• material behavior

System input:

• internal forces

• external forces

System input:

• internal forces

• external forces

Interpretati

on

Welsch, Heunecke: Models and

Terminology

14

-

conclusion on limiting

values of stresses
- prognosis of service
life

• verification of
results

• validation of
model

- model adaptation

Evaluation
methods

Deviation between

computed and measured

system reaction?

Deviation between

computed and measured

system reaction?

- parameter
matching

• adaptive

• probabilistic

Measurement

s

Determination of deter-

ministic input quantities

Determination of deter-

ministic input quantities

Modeling

System input:

• internal forces

• external forces

System input:

• internal forces

• external forces

Determination of

• strain / stress

• displacements

• other indicators

Determination of

• strain / stress

• displacements

• other indicators

Object:

• object geometry

• material parameters

• material behavior

Object:

• object geometry

• material parameters

• material behavior

System reaction:

• rigid body movements

• distortions

System reaction:

• rigid body movements

• distortions

Potentiality of Dynamic Models

Welsch, Heunecke: Models and

Terminology

15

u n k n o w n :

o u tp u t q u a n ti tie s

g iv e n :

in p u t q u a n titie s

tr a n s fe r fu n c tio n

D i r e c t p r o b le m

u n k n o w n :

in p u t q u a n titie s

g iv e n :

tr a n s f e r f u n c tio n

o u tp u t q u a n ti tie s

In v e r s e p r o b le m

u n k n o w n :

tr a n s fe r fu n c tio n

g iv e n :

in p u t q u a n titie s

o u tp u t q u a n titie s

Id e n tifi c a tio n p r o b l e m

X

G iv e n a n d u n k n o w n q u a n titie s o f d y n a m ic s y s te m s

X

„design

problem“

during the

planning of a

construction

„back analysis“

often used in

geotechniques

“system

identification”

regular case

Hierarchy of Models in Deformation

Analysis

Welsch, Heunecke: Models and

Terminology

16

C o n g r u e n c e M o d e l s

K i n e m a ti c M o d e l s

D e s c r i p ti v e M o d e l s

S ta ti c M o d e l s

D y n a m i c M o d e l s

C a u s e - R e p o n s e M o d e l s

X

D e f o r m a t i o n A n a l y s i s M o d e l s

X

Deformati

on

Models

Congruen

ce

Models

Kinematic

Models

Static

Models

Dynamic

Models

Time

no

modeling

movement

s as a

function of

time

no

modeling

movement

s as a

function of

time

Acting

Forces

no

modeling

no

modeling

displaceme

nts

as a

function of

loads

and

loads

Methods of System Identification

Welsch, Heunecke: Models and

Terminology

17

 
 

• White box modeling:

Some basic considerations of the

monitored

system to be verified by measurements are

demanded

(„model approach“)

• Black box modeling:

Knowledge about the transfer

function is achieved only by measurements

(„operational approach“)

Causal Chain of a Dynamic System

Welsch, Heunecke: Models and

Terminology

18

Input signal:

Causative forces

Transmission

through the object

Output signal:

Deformation

System equation

• determination of deter-
ministic input quantities

• formulation of transfer
behavior e.g. by FEM

Observation

equation

• determination of the geo-
metrical reaction

KALMAN-Filter

• innovation

• system identification

Theoretical results

Empirical results

Load Trials on a Shell Structure Made of Bricks

Welsch, Heunecke: Models and

Terminology

19

Project in cooperation with architectures at the
University of Hanover, see Hesse et al. 2000

• prototype made of bricks was built in 1996
• dimensions 10,0 x 2,0 m, height 2,50 m
• steel bands between abutments for clamped
support

(Parametric identification, integrated

evaluation)

steel bands

Load Trials

Welsch, Heunecke: Models and

Terminology

20

service load
1,0 kN/m

2

expected load for
break down approx.
1,9 kN/m

2

maximum load
brought
up: 4,0 kN/m

2

24 load

steps

(March 24 1999)

semi lateral surface
loading

FE grid

13

33

Comparison

of computed

and measured

settlements

of points

No. 13 and 33

Welsch, Heunecke: Models and

Terminology

21

Standard deviations:

ANSYS



0,05 mm/step

Levelling



0,05 mm

Extensometer



0,01 mm

1
3

3
3

0,2

mm

1,0

mm

Results

of the adaptive

KALMAN-filtering

process

Welsch, Heunecke: Models and

Terminology

22

1
3

levelling

extensomet

er

filtered

0,5

mm

prediction

Welsch, Heunecke: Models and

Terminology

23

1
3

3
3

0,5

mm

0,5

mm

Results

of the adaptive

KALMAN-filtering

process

Welsch, Heunecke: Models and

Terminology

24

1
3

3
3

0,5

mm

0,5

mm

Global test of innovation, 

= 5%

Results

of the adaptive

KALMAN-filtering

process

No. 33

No. 13

square sum

of residuals

Ground Subsidence at the Sparwood Coal

Fields

Welsch, Heunecke: Models and

Terminology

25

(Parametric identification, integrated

evaluation)

• movements caused by coal extraction, up to 2.5 m in
1980 / 1982
• suspicious discontinuity in the rock mass (fault), FE
modeling
• findings led to the closing of the mining operation

Project in British Columbia, details see

Chrzanowski et al.

faul
t

Non-Parametric Models

I

Welsch, Heunecke: Models and

Terminology

26

)

(

N

)

(

R

+

0

=

1

=

y

x

y

b

x

a

x

k

k

k-j

j

p

j

k-i

i

q

i

k











A

uto

R

egressive

M

oving

A

verage-

model:

recursive

part

non-

recursive

part

y

b

dt

dy

b

dt

y

d

b

dt

y

d

b

x

a

dt

dx

a

dt

x

d

a

dt

x

d

a

p

p

p

p

p

p

q

q

q

q

q

q

0

1

1

1

1

0

1

1

1

1

...

...































ordinary

differential

equation

most general description of a

S

ingle

I

nput -

S

ingle

O

utput

model:

• system identification means the estimation of
a

k

and b

k

• time series requested, no physical meaning

(‘behavior or black

box model’)

Welsch, Heunecke: Models and

Terminology

27

Non-Parametric Models II

y ( t )

y ( t )



g ( )



t -



t



x ( t )

x ( t )

t

E

in

fu

ß

gr

öß

e

D

ef

or

m

at

io

n

zurückliegende Werte einer

Gewichtsfunktion für zeitlich

Einfußgröße

t

t

single input y

single output
x

weight
function

non-

recursive

part

x

b y

y

k

j

k j

j

p

k











0

N ( )









0

)

(

)

(

)

(







d

t

y

g

t

x

SISO

approach based

on a convolution

integral:

Non-Parametric modeling of a turbine

plant

Welsch, Heunecke: Models and

Terminology

28

1 ,6 0

1 ,2 0

0 ,8 0

0 ,4 0

0 ,0 0

0

5

1 0

1 5

2 0

2 5

3 0

tim e [d a y s ]

d

e

fo

rm

a

tio

n

[

m

m

]

(

Project at the Bundeswehr University Munich, see

Ellmer 1987

)

• behavior of foundation pillars due to temperature
variations
• SISO identification, estimation of 30 significant
coefficients b

k

• diagnosis only symptom based, no physical
interpretation

measure
d

modeled

reaction caused by a unit impulse

of 1 K

Conclusion

Welsch, Heunecke: Models and

Terminology

29

We should make use of these

developments

!

• not all aspects of models and terminology are

treated in this presentation, more details can be

found in the paper
• orientation and classification on the basis of

system theory is recommended, system

identification is the tool for advanced analysis
• separation between models and methods is

important
• a commonly acknowledged terminology is a

requirement for an interdisciplinary approach to

problem solutions
• finally, during the last two decades, a significant

progress has been made from conventional

geometric descriptions of deformation processes

to highly sophisticated integrated models.