Ground-based Radar Interferometry

C.I. di Tecniche Diagnostiche e Materiali per l’Architettura Modulo di Diagnostica Fisica delle Costruzioni

A.A. 2014-2015

Dott. Sergio Vincenzo Calcina Contatti: sergiocalcina@unica.it - 3318582016

The IBIS-S sensor detects the position and the displacement of target points placed at different distances from the equipment using two well-known radar techniques:

1. the Stepped-Frequency Continuous Waves (SF-CW) technique, adopted to resolve the scenario in the range direction, i.e. to detect the position in range of different targets placed along the radar line of sight LOS;

2. the Interferometric technique, implemented to compute the displacement of each target comparing the phase information of the back-scattered electromagnetic waves collected at different times.

Theoretical Background of the radar technique

GBR Interferometry

SFCW technique is based on the transmission of sweep consisting of a series N monochromatic electromagnetic pulses of Ttone duration (Continuous Waves) at different frequencies (Stepped Frequency).

Δf= frequency step

f0

f1=f0+ Δf

f2= f1+ Δf = f0 + 2Δf

fn=f0 + n Δf

Stepped-Frequency Continuous Waves (SF-CW) technique

GBR Interferometry

The transmitted SFCW signal:

At the end of a sweep IBIS-S system has acquired a vector of complex numbers that corresponds to a frequency sampling of the observed scenario.

Sweep duration

Ttone

f0 f0+Df f0+2Df f0+(N-1)Df

Next sweep

t

I0+jQ0 I1+jQ1 I2+jQ2 IN-1+jQN-1

f(t)

GBR Interferometry

Virtual B f [Hz]

n-th frequency

The SFCW technique allows IBIS to obtain the same performance of a synthetic pulse of

duration to which corresponds a range resolution of B

1

F(f)

B

ccR

22D

GBR Interferometry

Range direction: straight direction from IBIS to the target;

Range resolution: capability to distinguish two targets in the range direction;

Range bin: range resolution area.

One-dimensional radar profile

The Stepped Frequency - Continuous Wave technique allows the resolution of

the scenario along range direction independently from the distance.

IBIS Range Resolution up to 0.75 m

GBR Interferometry

The interferometric analysis provides data on object displacement by comparing phase information, collected in different time periods, of reflected waves from the object.

The IBIS sensor is able to evaluate the displacement for each range-bin resolved by mean of SFCW technique.

Time-Frequency Duality

GBR Interferometry

The phase ambiguity bounds the maximum displacement measurable between two consecutive acquisition to ± λ/4 ≈ 4.38 mm

?

GBR Interferometry

• Maximum distance: 1Km (static surveys), 500 m (dynamic – sampling frequency of 40Hz)

• Maximum sampling frequency: 200 Hz

• One Dimensional radar imaging

• Range resolution: 0.75 m independent from the range

• Measurement of the displacement of the entire scenario at the same time

• Displacement accuracy: up to 0.01mm

IBIS-S radar sensor: capabilities

Ku band system Band of 200 MHz, between 17.1GHz and 17.3 GHz

GBR Interferometry

IBIS-S radar sensor: capabilities

The Ku band IBIS-S system is provided with two identical IBIS-ANT3 antennas operating in vertical polarisation and characterised by a maximum gain of 19dBi.

GBR Interferometry

The displacement is measured in LOS direction (Line Of Sight) target-sensor. To calculate the true displacements: -acquisition geometry; -identification of natural reflectors.

β=LOS angle

GBR Interferometry

Church of San Giacomo e Filippo (1771-1774) - San Giacomo Roncole

This structure was damaged by the earthquakes of 20th and 29th May 2012. The damage consists in a collapse of the top and in many cracks at the base.

GBR Interferometry

Morphology of the southern side. The dashed lines are fractures directly observed by visual inspection and along which the maps show a clear color discontinuity.

By Pesci et al. (2012).

Study of the base where there is a crack extended to the whole horizontal section. The deformation maps show slippage of the body of the bell tower fractured area and to identify clearly the contours.

GBR Interferometry

GBR Interferometry

The IBIS system was configured with the following acquisition parameters:

Antenna type 3 (Gain max = 19 dB);

Survey duration: 10 - 15 min;

Max distance Rmax: 75 - 100 m;

Distance resolution ΔR: 0.75 m;

Sampling frequency: 56.09 Hz.

GBR Interferometry

Scenario - Location St02

Scenario -Location St01

Scenario - Location St03

GBR Interferometry

Interometric Data Processing:

1) Radar pixel selection: selection of the echoes characterized by better signal to noise ratio, attributable to reflections from structural and decorative details of the building, such as eaves, arches and balustrades and other natural back-scatterers.

The identification of the different back-scatterers points on the structure was performed taking account of the range bin in which is included the peak selected (i.e. the distance between the point and the sensor) and the position and inclination of the radar antenna respect to the base of the tower.

GBR Interferometry

Step 1: interpretetation of the echos

Reflection point on the structure

Radar configuration St2 Horizontal distance 23 m

Central LOS angle 30°

GBR Interferometry

Step 2: Frequency Domain Decomposition method (Brincker et al. 2001)

The FDD shows a frequency response recognizable to about 0.96 Hz, obtained by integrating over 15 minutes of acquisition

Top

Base

Frequency analysis of the natural oscillations induced by the wind and the other sources of random vibrations

GBR Interferometry

Comparison between the time-series at the several floors of the building

ttf 96.02sin15.0)(

GBR Interferometry

Vibration time history and frequency analysis of the tower (55th range bin)

Fourier Domain (f0=0.96 Hz)

Time Domain

f=0.96 Hz

f=0.96 Hz

GBR Interferometry

IBIS-S configuration St01

52nd range bin shows further frequency peaks, probably related to the asymmetrical distribution of the loads within the structure or in the top of the building.

GBR Interferometry

IBIS-S configuiration St03

Effect produced by the vibrations of the cable – 22nd range bin

GBR Interferometry

First experimental mode shape (eigen-frequency 0.96 Hz)

Displacement projected in the horizontal direction

GBR Interferometry

Several empirical relationships available to estimate the

fundamental frequency of masonry structures provide

results in the range between 1.4 and 1.5 Hz.

Italian Code (NTC-08):

Spanish Code (NSCE-02):

Linear relationship proposed by Faccio et al. (2010):

Rainieri et al. (2012):

The significant difference (31-36%) between the

experimental value and the estimated values could be

imputed to the damage caused by the earthquake. It is

generally recognised that the period of vibration grows

while increasing the mass of the vibrating system and while

reducing the stiffness.

GBR Interferometry

Finite Element Model: comparison between the period of vibration of the tower before the earthquake (not damaged condition) and obtained experimentally on the structure damaged.

Finite Element Model Subdomain Setting

Young modulus 2800 MPa

Density 1800 Kg/m3

Poisson ratio 0.2

GBR Interferometry

GBR Interferometry

Mode 1: 1.22 Hz – simple bending (X direction)

GBR Interferometry

Mode 2: 1.23 Hz – simple bending (Y direction)

GBR Interferometry

Mode 3: 5.64 Hz – bending (XY direction)

GBR Interferometry

Mode 4: 5.64 Hz – bending (YX direction)

GBR Interferometry

Mode 5: 6.22 Hz – first torsional

GBR Interferometry

Mode 5: 6.22 Hz – first torsional

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Mode 6: 9.89 Hz

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Mode 7: 11.99 Hz

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Mode 8: 12.09 Hz - bending

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Mode 9: 12.12 Hz - bending

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Mode 10: 15.23 Hz - torsional

6. GBR Interferometry – Principi e applicazioni

Image by Interferometric Survey

Characterisation of natural and compulsory vibrations

Monitoring of Pisa Tower

6. GBR Interferometry – Principi e applicazioni

ACQUISITION : GEOMETRY and PARAMETRES

Plan view of the area with the four positions of measure

A B C D

DISTANCE TOWER [m] 30.3 25.3 26.3 27.3

RADAR ELEVATION FORM

THE GROUND [m] 0.60 0.60 0.62 0.61

WIND Weak,

from N-E

Weak,

from N-E

Weak,

from N-E

Weak,

from N-E

ENFORCEMENT ACTION YES NO NO NO

FREQUENCY OF

SAMPLING [Hz] 30 30 30 30

RESOLUTION IN RANGE

[m] 0.5 0.5 0.5 0.5

MAXIMUM RANGE [m] 200 200 200 200

Operative conditions and configuration of IBIS-S for the four acquisitions

GBR Interferometry

ANALYSIS OF THE RESULTS - POSITION A

Power profile – selection of measuring points

A

TOWER

DISTANCE [m] 30.3

HEIGHT RADAR

TO GROUND [m] 0.60

WIND Weak,

from N-E

ENFORCEMENT

ACTION YES

FREQUENCY OF

SAMPLING [Hz] 30

RESOLUTION IN

RANGE [m] 0.5

MAXIMUM

RANGE [m] 200

It’s important to distinguish between peak power on metal scaffolding and those really belonging to the structure

GBR Interferometry

ANALYSIS OF THE RESULTS - POSITION A, POINTS 5, 11

Natural vibration induced by the wind and the random movement of people – Results obtained in the time and frequency domain

PUNTO 5 PUNTO 11

6. GBR Interferometry – Principi e applicazioni

ANALYSIS OF THE RESULTS - POSITION A, POINT 11

Vibration induced by the coordinated movement of twenty people placed on top of the tower (results obtained in time and frequency domain)

During stress forced the displacement component orthogonal structure takes a sinusoidal with fundamental frequency f0 = 1Hz and maximum amplitude peak-peak equal to 0.60 mm

1 Hz1 Hz1 Hz1 Hz

GBR Interferometry

45

ANALYSIS OF THE RESULTS - POSITION A, POINT 5

Vibration induced by the coordinated movement of twenty people placed on top of the tower – Results obtained in time and frequency domain

During stress forced the displacement component orthogonal structure takes a sinusoidal with fundamental frequency f0 = 1Hz and maximum amplitude peak-peak equal to 0.34 mm

GBR Interferometry

ANALYSIS of RESULTS - POSITION D

D

TOWER

DISTANCE [m] 27.3

HEIGHT RADAR

TO GROUND [m] 0.61

WIND Weak,

from N-E

ENFORCEMENT

ACTION NO

FREQUENCY OF

SAMPLING [Hz] 30

RESOLUTION IN

RANGE [m] 0.5

MAXIMUM

RANGE [m] 200

Frequency analysis of natural vibrations induced by the wind and the random movement of people

GBR Interferometry

ANALYSIS of RESULTS - POSITION D

Frequency analysis of natural vibrations induced by the wind and the random movement of people: first modal shape.

0.1 0.15 0.2 0.25 0.325

30

35

40

45

50

55

Horizontal displacement [mm]

Str

uct

ure

ran

ge

[m]

2 4 6 8 10 12 14 16

x 10-3

25

30

35

40

45

50

55

Horizontal displacement [mm]

Str

uct

ure

ran

ge

[m]

Passive survey Forced survey

11 11

7 7

6 6

5 5

4 4

GBR Interferometry