hans neuner th. october 2018

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Hans Neuner

30th. October 2018

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Introduction• Generation and processing of geometrical information from the perspective

of model building in engineering geodesy

Measurement model

Refers the raw measurements to the geodetic model by applying

corrections,

reductions,

quality assessment methods.

Geodetic model

Relates the measured variable to the measures of interest by

mathematical-physical equations

quality propagation.

Knowledge gain from observations

Based on Brunner, 1991 and Kutterer, 2002

analysis, interpretation, decisions

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Traditionally defined influence due to the incidence angle (IA)

Alternative perspective: combined influence of IA and roughness

Space-continuous measurement model

(Zámečníková and Neuner, 2017)

• Aim of the research: Determination of the joint influence of the incidence angle and of the surface roughness on the resulting distance measurement

• TLS: The beam reflected on the object surface obtaining distance measurement results are influenced by measurement configuration and surface properties

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• Object of investigation:Granite ledges with three roughness-levels (smooth, rough, very rough)


• Realisation of the traditional IA :Object rotation with respect to its vertical axis

• Scanning parameters: distance 10 m, frequency 62 Hz, Point spacing 1 cm

• Key feature of the principle: analysis of single distances

∆D = Dref – DTLS


• Scanning total station (TLS+TS)

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• Determination of the reference distance:1. Determination of a common reference frame: high-accuracy network2. Starting point: resection based on angular measurements to the network points3. End points: reference scan of the measuring object with close range scanner


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• Determination of the scanned distance: Transformation of the TLS-point cloud into polar coordinates


• Allocation of reference and scanned distances by corresponding and commonly referenced Hz- and V-angles.

• Repeated determination of the reference distance’s endpoints and scanned distances for every plate position (traditional IA) and roughness level


• Quantification of the uncertainty of the reference distance according to GUM

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- Obtained results:



• DD: mean values

• Reproducibility: Second campaign with completely new set-up.

• Max. discrepancy between curves 0.09 mm

• Effect of traditional IA: smooth curve 0.8 mm

• Joint effect of IA and roughness: differences between curves < 1.0 mm

• Statistical significance of the joint effect

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• Consideration of the measurement model: extending the geodetic model (approximation of the geometric form) with correction terms or formulation of an appropriate covariance matrix of the measurements

Space-continuous geodetic model

• Determination of the approximating B-Spline-surface in an adjustment model:

0 0

n m

ip jp iji j

S u,v S u,v e u,v N u N v P

where: Ŝ(u, v) - point on the surface

S(u, v) - measured pointe(u, v) - error term

Nip(u), Njp(v) - B-Splines basis functions of order p in the direction of the parameter axis u and v

Pij - control points

0 ≤ u, v ≤ 1 - surface parameters

Solution obtained by solving the Gauß-Markov model if:- the parameters u, v are known,- the number of control points m and n are fixed.

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Deer pass

• 53 x 48.2 x 8.4 m

• Over a two railway track

Info Pavillon

• 26.5 x 19.1 x 4.2 m

• Deer pass model 1:2

• Applied to a concrete freeform shell structure built by the ÖBB – Koralm railway section, Austria


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Space-continuous geodetic model• Pneumatic Forming of Hardened Concrete:

Flat hardened concrete plate raised by a air cushion

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• Finite Elemente Modeling:

Automatic mesh generation on the continuous surface

Linear elastic

Actual geometry modelled as a B-Spline surface used to:

Generate the mesh on the continuous surface to analyse the load-bearing behavior of the actual structure

Calculate expected deformations during the various construction steps

Calculate occurred deformations


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Accuracy level 1σ ~2cm

Continuous freeform surface

Levelled geometric model

Clear support connections

Interface compatible

• Requirements for the modelling

Space-continuous geodetic model• Bottom edge artefacts

Connection of the two parameter edge lines

Introduction of bottom edge restriction of the approximation

• Creation of an *.igs, *.iges file

• Challenge: Interface max. 100 control points

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Summary and Outlook

- Representative for measurement models: joint influence of the angle of incidence and of the roughness on the distances measured by terrestrial laser scanners.

Ongoing research: instrumental error models, establishing synthetic covariance matrices...

- Representative for geodetic models: flexible representation of surfaces with B-Splines functions

Ongoing research: mesh-based and parametric representation of geometry and retrieval of deformations;

- The development of comprehensive and merged measurement and geodetic models covering the full chain from data acquisition to the estimation results is prerequisite for the establishment of space-continuous measurement and processing techniques in engineering geodesy tasks.

- Development in the right direction: customers and research partners ask for and need solutions for the space-continuous representation of geometry.

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Thank you

for your attention!

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Structure

Introduction


Summary and outlook


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Introduction

Framework of the activity – Definition of Engineering geodesy:

Engineering geodesy is the discipline of

reality capture,

setting-out and

monitoring

of local and regional geometry-related phenomena paying particular attention to

quality assessment,

sensor systems and

reference frames.

Kuhlmann, Schwieger, Niemeier and Wieser 2014

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Introduction

Methodological elements of Engineering Geodesy

1: Discretisation

2: Coordinate and observations domain

3: Reference systems

4: Specification of unknown parameters and aimed precisions

5: Geodetic network and observation design

6: Quality control of equipment

7: Quality control of measurements

8: Establishment of measurement models

9: Establishment of parameter estimation models

10: Quality control of resultsBased on Brunner, 2007

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Space-continuous measurement model• Discretisation in space domain high-resolution:

technology-driven

TLS

(Alba et al., 2008)

GbSAR

(Wagner et al., 2014)

Image assisted total station

Laser tracker +close range scanner

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Raumkontinuierliche AnsätzeTLS (polare Punktbestimmung): etabliertes Messverfahren in der IG

Interaktion Laser / Oberfläche variiert im Zuge des Scanvorganges Qualität der Messpunkte variiert entlang der Oberfläche

OberflächeneigenschaftenFarbeRauheitMaterial – Struktur

GeometrieEntfernungOrientierung (Auftreffwinkel)

Direkt von der Oberfläche reflektierter Messstrahl Distanzauswertung Ergebnisse beeinflusst durch:

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TLS: interaction laser / surface varies during the scanning the quality of the measurements varies along the scanned surface

Surface propertiescolourroughnessmaterial – structure

Geometrydistanceangle of incidence

The beam reflected on the object surface obtaining distance measurement results are influenced by:

Aim of the research: Determination of the joint influence of the angle of incidence and of the surface roughness on the quality of point determination


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Abgrenzung zu bisherigen Untersuchungen:

- unmittelbare Untersuchung der Distanzen- Im Nahbereich 3,5 – 5,2 m und

für 10 m, 20 m, 30 m

Messpunkte :nicht signalisiert auf der Oberfläche nicht reproduzierbar

Raumkontinuierliche Ansätze

Instrumentarium: Leica MS50

smartnet-eu.com

Ziel der Untersuchung:Einfluss des Auftreffwinkels einschl. Rauheit und Distanzauf die Qualität der Punktbestimmung

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Raumkontinuierliche Ansätze- Messkonfiguration 1:

Netz

- Absteckung von Einzelpunkten

- Zeitlich aufwändig

- Genauigkeit der Referenzdistanzen

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• Quality assessment:


- Quantification of the uncertainty of the reference distance according to GUM

- Periodic measurements to check:- stability of TLS-specimen- stability of the laser tracker- stability of the reference frame

- Measuring configurations that reduce other influences causing similar effects,e.g. eccentricity between collimation and distance axis.


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23.11.2016Molas

1.Results

Smooth – max. impact between epochs of 0,09 mm

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Space-continuous measuring model- Influences due to the angle of incidence: obtained from both measuring

configurations and for distinct roughness levels.Each point represents the mean of the deviations DRef - DTLS obtained from at least 5 corresponding points.

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1. a slight shift of approx. 0.1 mm between curves is visible (at IA 0 gon)

23.11.2016

Results – Distance

differences [mm] 10-20 m 20-30 m 10-30 m

smooth -0,13 -0,13 -0,26

rough -0,14 -0,14 -0,28

very rough -0,12 -0,22 -0,34

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Sensoreigenschaften - Ergebnisse- Qualitativer Vergleich der Kurvenverläufe für die Distanzabweichung (links) und

die Signalstärke (rechts)

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Raumkontinuierliche Ansätze• Parametrisierung der Fläche:

0 0

n m

ip jp iji j


• Problemstellung:

Parametrisierung entlang der ursprünglichen Koordinatenachsen Datenlücken Singularität des Gleichungssystems

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Raumkontinuierliche Ansätze• Standardverfahren (Coons Patch) zur Parametrisierung der Fläche

führen bei der iterativen Ausgleichung zur Divergenz

neue Basisfläche: besserangepasst an die Punktwolke

• Entwickelter Ansatz: weicher Zwang der Flächenausdehnung auf vorab berechnete Randkurven (Formulierung geeigneter Restriktionen in der Ausgleichungsaufgabe)

• Konvergenz, Verbesserte Schätzung (s02 sinkt; Spur(QPP) – nimmt ab)

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Space-continuous geodetic model• Estimation of the number of control points

model selection task

• Developed approach is based on the concept of model complexity:Complexity measure: VC-dimension h – basis of statistical learning theory

ln 1 0 5 ln

1

emp

obs.obs.

obs.

ˆRˆR

n. n

hn

h

PP with:

4min 1

obs.

,n

– empirical risk(mean squared error) of the estimation

emp

ˆR P

• Use the estimated VC-dimension h to select from a set of model candidatesthe model that leads to the lowest upper boundary for the true risk ,when the following upper bound holds with probability 1- :

ˆR P

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• Estimation of the number of control points model selection task

• Influence of the number of control points on the B-spline’s curve form:- n + 1 chosen to small large bias, underfitting- n + 1 chosen to large approximation of noise, large variance, overfitting

bias-variance trade-off to identify the optimal model.

(Harmening and Neuner, 2016)

• Similar estimation of B-Spline-curves: 0

n

ip ii

C u C u e u N u P

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Raumkontinuierliche Ansätze• Festlegung der Anzahl von Kontrollpunkten

0 0

n m

ip jp iji j


→ Aufgabe der Modellselektion

0

n

ip ii

C u C u e u N u P

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Raumkontinuierliche Ansätze• Hier: Bestimmung der Anzahl der Kontrollpunkte

Aufgabe der Modellselektion

• Alternatives Komplexitätsmaß: VC-Dimension h– Grundlage der statistischen Lerntheorie

• Entwickelter Ansatz beruht auf dem Konzept der Modellkomplexität:- Anzahl der Parameter ist für die Beschreibung nicht geeignet: f (x)=sin(a x)

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Raumkontinuierliche Ansätze• VC-Dimension: Maximale Stichprobengröße, die durch eine Familie von Modellen

(Indikatorfunktionen) in allen möglichen Kombinationen klassifiziert werden kann

• Eine 2-D Gerade klassifiziert fehlerfrei jede möglicheKombination von drei Punkten

• Vier Punkte können nicht fehlerfrei klassifiziert werden

• Schätzung der VC-Dimension h mit einem probabilistischen Ansatz,in dem die Variation der Fehlerrate einer zufälligen Klassifizierung der Daten mit der Stichprobenlänge betrachtet wird.

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Raumkontinuierliche Ansätze• Klassifizierung mit einer Struktur von Freiformfunktionen nicht unmittelbar

• Transformation der Daten in einen hochdimensionalen Raumunter Nutzung struktureller Elemente der untersuchten Modellfamilieermöglicht die Klassifizierung.

• Bestimmung der VC-Dimension durch die Klassifizierung im hochdimensionalen Raum mit dem genannten probabilistischen Ansatz.

• Entwickelter Kernel für die Transformation im Falle der B-Spline Kurven:

1

n

s t i ,p s i ,p ti

K u ,u N u N u

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Space-continuous geodetic model• Development of a B-Spline classifier (for curves and surfaces)

• Basic ideas:

Dimensionality increases because of the mapping efficient computation using the Kernel trick

T T

feature space feature space feature space feature spaceK , ,x x x x x x

2

2

1

obs .n

i feature spacei

ˆL e P

1Tα XX Ι y Adopting the dual solution of the optimization problem:

Input vector has to appear solely in form of the inner product Ridge regression:

0 0

n m

s s t t i ,p s j ,q s i ,p t j ,q ti j

K u ,v ,u ,v N u N v N u N v

Development of the B-spline-kernel:

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Raumkontinuierliche Ansätze

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Space-continuous geodetic model• Validation based on measurements performed on a test specimen

with (9, 7) control points

• Six data sets obtained at different distances and orientation between TLS and test objectas well as with different point spacing:

Data set Result of model selection

1 10,10

2 9, 7

3 9,8

4 9,7

5 9,7

6 9,7

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Raumkontinuierliche Ansätze• Vollständige Darstellung der Starrkörperbewegung auf Ebene der Kontrollpunkte

100; 250; 50;

7 ; 15 ; 45

x y z

x y z

t t t

r r r

• Transformation der Punktwolke mit den Parametern:

• Transformationsparameter geschätzt aus Kontrollpunkten :

99 9999908 249 999979 50 000011

7 0000034 15 0000042 44 9999

; ; ;

; ; 974

x y z

x y z

. . .

. .

t t

.

t

r r r

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Space-continuous geodetic model• Integrating space-continuous geometrical model in numerical models for structural

analysis

1. Cause

2. Measuring

4. Analysis

3. Modelling

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• Solution of the model selection task on the basis of statistical learning theory

• Introduce the concept of model complexity; Complexity measure: VC-dimension h

ln 1 0 5 ln

1

emp

obs.obs.

obs.

ˆRˆR

n. n

hn

h

PP with:

4min 1

obs.

,n

– empirical risk(mean squared error) of the estimation

emp

ˆR P

• Use the estimated VC-dimension h to select from a set of model candidatesthe model that leads to the lowest upper bound for the true risk ,when the following upper bound holds with probability 1- :

ˆR P

• Estimation of the number of control points model selection task

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Space-continuous geodetic model• The VC-dimension h of a set of indicator functions is defined by the maximum

number of samples which can be error-free separated in all possible ways by the set of functions.

x2

x1

x2

x1

x2

x1

x2

x1?• In the 2D-space a line can separate a set of three points in all possible ways.

• In the 2D-space a line cannot separate a set of four points in all possible ways.

h = 3

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Space-continuous geodetic model• Development of a B-Spline classifier (for curves and surfaces)

• Basic ideas:

Linear decision boundaries (! linear optimization problem)

Mapping of the input space in a high dimensional feature space

(Harmening and Neuner, 2017)

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Space-continuous geodetic model• Development of a B-Spline-classifier (for curves and surfaces)

• Basic ideas:

Dimensionality increases because of the mapping efficient computation using the Kernel trick

T T

feature space feature space feature space feature spaceK , ,x x x x x x

0 0

n m

s s t t i ,p s j ,q s i ,p t j ,q ti j

K u ,v ,u ,v N u N v N u N v

Development of the B-spline-kernel:

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Space-continuous geodetic model• Validation based on measurements performed on a test specimen

with (9, 7) control points

• Six data sets obtained at different distances and orientation between TLS and test object as well as with different point spacing:

Data set Sample size

Distance[m]

Orientation [°]

Result of modelselection

1 16 612 8.3 0 10,10

2 4 086 8.3 0 9, 7

3 15 648 8.3 20 9,8

4 3 883 8.3 20 9,7

5 4 671 6.8 30 9,7

6 4 805 7.1 30 9,7

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Time-continuous geodetic model• Trajectory estimation of kinematic multi-sensor-systems

• Methodological background: Filtering in state-space-domain. Here: Kalman-filtering

• Focus on system descriptions leading to improved filter performances

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Time-continuous geodetic model• Undisturbed equations of motion: uniform circular movement

D

D

1 1

11

1

1 1

1

1

1

sincos -sin

sin cos 1 cos

;

k k ,kk k k k

k

k k k k k k ,k

l ,k r ,k

k k

k k

k

r ,k r ,k l ,k l ,k

k

v v v

tx xR

y y t

v

v v

R

angular velocity = Da/Dtk,k+1

vl – velocity of the left wheel-pair

vr – velocity of the right wheel-pair

Rk+1 – radius

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Time-continuous geodetic model• Retain the same movement model but with changed parameterisation of the state:

use of mean velocity vm and differential velocity Dv

1 1

1

1 1 1

;2

l ,k r ,k

m,k

k l ,k r ,k

v vv

v v vD

• Introduction of transmission coefficients as a ratio between target-velocity vmeasured at the drive shaft and the actual velocity v‘ of the effective movement of the robot

• These coefficients include effects due to the slip, to the different tyre pressure and to different rolling resistance:

1

1

1

1

1

1

;

;

l ,k

l ,k

l ,k

r ,k

r ,k

r ,k

v'sl

v

v'sl

v

use of relative transmissioncoefficients:

1

1 1 1

1;

1 ;

r

l ,k

r

r ,k l ,k r ,k

sl

sl sl sl

• Calibration of the coefficients in an initialisation phase with direct line of sight to a total station

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Time-continuous geodetic model

Metrology basementMetrology roof

• Maximum trajectory deviations in trajectory parts unsupported by total station

• Maximum deviations of the “odometry only”-trajectory could be reducedto ~20 cm after 3 minutes

(Thalmann, 2017)

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Time-continuous geodetic model• State-space estimation of the orientation components for a PDR-based positioning

approach, based on acceleration, gyro and magnetometer data

(Ettlinger et al., 2017)

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Time-continuous geodetic model• Observation equations – allow no expression in the typical Gauss-Markov model

of the Kalman-Filter

Development of the Kalman-Filter solution in Gauß-Helmert model (here: Innovation d and corresponding Covariance matrix D):

• This approach allows for the estimation of the partial redundancies of each measurement type assessment of internal reliability

1 1

1

tan ; tansin cos

sin costan

cos sin sin sin cos

y x

z y z

z y

x y z

a a

a a a

m m

m m m

k k

* * T T

k k ll ,k k k ,k kxx

d w

D B Σ B A A

k k k k

T

k ,k k ,k kll xx

d l A x

D Σ A Σ A

GHM: GMM:

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Time-continuous geodetic model• Assessment of the estimation quality: internal reliability

• Partial redundancies of gyro and magnetometer measurements using nominal weights (left) and adapted weights (right)

(Ettlinger et al., 2017)

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Time-continuous geodetic model• Results obtained for a linear movement of the robot

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Time-continuous geodetic model• Result:

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Time-continuous geodetic model• State-space estimation of the orientation components for a PDR-based positioning

approach, based on acceleration, gyro and magnetometer data

• System equations

State vector contains φ, θ and ψ

Control inputs: gyro measurements ωy and ωz

Disturbance: wφ, wθ and wψ

User walks straight

User is turning

2 1 1,k k kf w 1 1 1,k k kf w

3 1 1,k k kf w

3 1 1 , 1 , 1,

1

sin coscos

k k k y k k z k k

k

tf w

D

Random walkmodel

hans neuner th. october 2018

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