unit e.4 safety and security of buildings a matlab toolbox ... · a matlab toolbox for experimental...

1

The European Commission’s

science and knowledge service

Joint Research Centre

29 Maggio 2018

Milano

A MATLAB Toolbox

for Experimental

Modal Analysis of

Structures

Directorate E Space, Security and Migration

Unit E.4Safety and Security of Buildings

Daniel Tirelli

[email protected]

2

gaAccelerogram

dt...( ) ( ) ( ) gMa t Cv t R t MIa

Numerical Model

Servo-Hydraulic

Actuators

Displacement

Transducers

Reference

Frame

Measured

Restoring Force)(tR

Force

Transducers

Imposed

Displacement( )d t

The Pseudo Dynamic Method

ELSA Laboratory: The European Laboratory for Structural Assessment

Activity mainly for European Standards

in Civil Engineering

3

Dynamic Inputs

Wind RainSeism Traffic

Example of bi-directional test at real scale

Resonances

Storm on Volgograd Bridge (Russia 2010 ). Source: YouTube

For flexible structures, ex: Bridges, Cables etc…

Sometime resonances are visible to the naked eye.

4

s070108

10 12 14 16 18

-40

-30

-20

-10

0

10

20

30

40

s07: Cable 1 Fexi=100 N

X= 812

Y= 0Z= -150

time (sec)

Dis

plac

emen

t m

m

Measurement

on ELSA cable

Damping effect

ELSA Cable facility

Dangerous for structures

s094307

s094507

5 10 15 20 25

-15

-10

-5

0

5

10

s09:Snap back test:release of 700 N at 10 m

time (sec)

Dis

pla

ce

me

nt

[mm

]

Free Cable Dtime=18s

SSI Cable Dtime=4 s

Decay ratio at L/2 =0.22

Damping𝜻

Mode Shapes φi Amplitude at

different positions

What to understand from resonances?

From measurements at different positions of the structure the

toolbox calculates the three parameters which govern resonances

They depend from the structure only

(not from the input).

Frequency

5

Frequency~ (Ki/Mi)½

Damping

Mode Shapes φi

Amplitude at different

positions j

J positions

𝑀 𝑥′′ +

Inertial Forces

The three

parameters

calculated by the

toolbox from

experiments

Damping Forces

2. ζ. ω 𝑥′ +

Reaction Forces

[K]{x}=

- The mechanical state of the structure (damaged or not)

- Reference values to implement numerical models Could give:

Equation of motion of the structure

Dynamic Inputs

Fext

Source: Messaggero Veneto. Friuli Earthquake 1976

6

Practically

c030108

0 0.2 0.4 0.6 0.8 1-10

-8

-6

-4

-2

0

2

4

6

8

c03: Container with doors open:Cal:Impact no:1

X= 0

Y= 0Z= 130

time (sec)

Acc

ele

rati

on

m/s

/s

Real time history signals from a dynamic event

01

23

45

67

89

10

0

2

4

6

8

10

12

-30

-20

-10

0

10

20

30

1SE X042SE X05

3SE X061NE X10

2NE X113NE X12

1SE Y04

time [s]

2SE Y053SE Y06

1SW Y012SW Y02

3SW Y03

a09: Conf12: Snap-Back (run3): 150KN in X7

transducer

Acc

eler

atio

n m

/s/s

Fourier Transform

Aim of the Experimental Modal Analysis Toolbox:

extract parameters from “complex” signals

The “Genome” of the structural motion

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Instrumentation(Input)

Hammer

Impact

Piezo-Patch

(Embedded sensor)

Accelerometer

Wireless Acc.Displacement

transducers

(Output)

Load Y

c080113

Load Y

c080213

Load Y

c080313

0 0.05 0.1 0.15 0.2-200

0

200

400

600

800

1000

1200

1400

c08: Container + doors open 60d.:R.Panel.Imp.Po:1

X= 0

Y= 0Z= 0

time (sec)

Forc

e N

Ac.LP.Cen

c080101

Ac.LP.Cen

c080201

Ac.LP.Cen

c080301

0.05 0.1 0.15 0.2-6

-4

-2

0

2

4

6

8


X= 300

Y= 234Z= 132

time (sec)

Acc

ele

rati

on

m/s

/s

Output signals Y(t) in position jInput signals X(t) in position i

Truck Impact

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The toolbox is divided in two parts: in each of them

MATLAB eases and shortens the signal processing

1Process the data during the

acquisition

methods

Slide 9controls

Slide …interpolations

Slide 13

2After the acquisition extracts the

experimental modal parameters

displaying results in different forms

Extraction

Slide 14Mode shapes

Slide …Videos

Slide 20

9

Equality Limitations

( )

( )

i k

j k

A

F

Use of reciprocity property of the FRF (Transfer Function)

൯= 𝐻𝑗𝑖(𝜔𝑘𝐻𝑖𝑗(𝜔𝑘)

൯𝐴𝑗(𝜔𝑘

)𝐹𝑖(𝜔𝑘

The toolbox runs

with two types of

tests

Acquisition Methods

j Accelerometer positions

‘Classic’ Test or monitoring

Ref.

j limited by the number

of Output transducers

j is not limited ! More experimental data more accurate

results. It is possible to test additional positions etc…

Possible only with a fast check of the

coherence function (values near 1)MATLAB 1

Accelerometer Position

j Hammer Impact positions

Ham

Ham

Ham

Ham

Ham

Ham

Ham

Ham

Ham

Ham

Ham

Ham

Ham

Ham

Ham

Fast Impact Hammer Test (FIHT)

Ref.Accer Position

10

Control of the measurements

MATLAB: 1A first “Time Reduction” converting number

of curves in few histograms

Correct measurement

Represented by histogram of the coherence

with a

positive exponential fitting

FRF curves

After Noise filtering

Erroneous measurements ?(on displacement transducer)

Tenths or hundreds of coherence

curves to check

Coherence curves

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Spatial control of the measurements MATLAB: 2

A Typical Example Hammer tests on the first

composite bridge of a

motorway in Europe

(Asturia -Spain)

0

200

400

600

800

1000

1200

-100-50050100

0

50

100

150

200

250

0.94

Ac.Po.Z5 CarDi.8 Po.Z289

Di.11 Po.Z42

0.91

0.93

0.95

0.940.67

0.94

0.94

0.94

0.95

X

0.93

0.88

0.95

0.95

0.96

Map of the Filtered Mean Coherence for each position of impact:

FRF Output=Ac.Po.Z4

0.91

0.94

0.94

0.96

0.91

Ac.Po.Z5

0.96

Di.2 Po.Z0

0.93

0.95

Ac.Po.Z4 Ac.Po.Y4

Y

0.91

Ham.po.-Z1

Z

Output Transducer

Map of the coherence

Position to be

controlled !

Position and mean value of the Impact Load

Map of the Impacts

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Use of Macro for a fast 3D design of the structures MATLAB: 3

beam([-28 1385],[-126 126],[112 150],nf, [.6 .6 .6] );

Deck designed in grey color :

irsbeam([-28 1385],[60 -60 -90 90 60],[0 0 112 112 0],12,‘g‘)

Carbon Beam with irregular section designed in green

( [X], [Y], [Z], fig.Nb., color)

Design of a Building in ELSA (Duarem project)Examples:

Bridge element in ELSA (Prometeo project)

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Low frequencies distribution example : 0< f <10 Hz

Color grid in correspondence with the vibration amplitude levels

Ex: Prometeo Bridge Project

Interpolations of irregular mesh of measurement positions MATLAB: 4

1- Create a regular cartesian mesh:

[xi,yi] = meshgrid(mi1:step1:ma1,mi2:step2:ma2)

2-Interpolate the grid by the irregular distribution of

measurements.

High frequencies distribution example: 10 Hz < f

Produce an iso-surface with: ci = griddata(Xcap1,Ycap2,Vcou,xi,yi);

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Hammer Impacts (Input)

Allows to measure the

global mechanical properties

of the container or one of its

components.

Signals in time domain

3

x 25

x 5

x 3

= 1125

3 impacts at each position

25 positions for each panel

5 panels (each container)

3 transducers (Force+ 2 Acc)

Total: minimum time signals

Example of structure to illustrate the process of modal parameters extraction:

a smart composite container prototype

Vibrations

Induced by rain, wind,

transportation, damaging

etc..

Ac.EP.Cen

c080106

0.1 0.2 0.3 0.4

-3

-2

-1

0

1

2


X= 590

Y= 120Z= 132.5

time (sec)

Acce

lerati

on m

/s/s

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Signal processing to obtain modal parameters

250 Coherences functions

(“control” of the measurements)

Ac.LP.Cen

c051871

Piez.L.Cen.P

c051872

20 40 60 800

0.2

0.4

0.6

0.8

1

c05: Floor: Imp.Po:18

X= 300

Y= 234Z= 132

Frequency [Hz]

Coh

er.A

cce

[]

(125 positions*2 Outputs) =250 FRFs files

From Time domain (1125 signals) toFrequency domain (Fourier Transform)

Control of the data Physical interpretation of the data

Algorithm of automatic

identification of 3 parameters

of each peak in the

experimental and noisy 250

curves, and display of the

results in a few seconds

Matlab, step:5

250 vectors

of different

dimensions3 ×

Frequency

Amplitude

Damping

16

250

frequency

vectors0 50 100 150 200 250 300

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Point Nb.

|FR

F o

r F

FT|

cstruct:Position no:8 94.1 Hz

1.07 %

50.74 Hz

2.58 %

78.49 Hz

2.55 %

84.8 Hz

1.67 %

36.96 Hz

2.74 % 61.61 Hz

2.71 % 70.6 Hz

2.69 %

31.16 Hz

2.49 %28.24 Hz

2.92 %19.77 Hz

2.09 %

Sig.Processing: Danbox3

[email protected]

0 50 100 150 200 250 3000

0.01

0.02

0.03

0.04

0.05

0.06

0.07

Point Nb.

|FR

F o

r F

FT|

cstruct:Position no:17

90.83 Hz

1.09 %

51.05 Hz

2.31 %

78.99 Hz

2.1 %59.51 Hz

5.41 %96.7 Hz

0.617 %

83.51 Hz

1.37 %

39.69 Hz

2.38 %70.37 Hz

2.42 %29.4 Hz

2.39 %33.25 Hz

4.45 %25.81 Hz

4.26 %10.9 Hz

5.5 %


[email protected]

No:1

No:250

MATLAB, step:6 ( fastening with matrix)

Optimisation to obtain the final modal parameters

Which is the best clustering?

Solution in the set of frequency matrix

= Max(P/S)

Calculate for each Δfi , a Statistic S, and a Physical parameters P:

S=Mean Std. Deviation for all columns (modes)

P= Stability of the cluster (modes) when Δfi increases.

: Mf

1 column for each

frequencies cluster found

Δfi

Δfi

Clustering in

mi modes

For each window dispersion Δfi : 1 Frequency Matrix Mfi

250linesMf1

m1 col.

… Mfn

mn col.

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0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.050

0.05

0.1

0.15

0.2Conf11:1st Snap-Back:150KN in X7

Sum

of

Norm

alised S

TD

s

Max. Freq.dispersion [Hz]

0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.050

20

40

60

Max. Freq.dispersion [Hz]

Nb.o

f m

odes

*Stat.Solutions

P= cluster stability

S= std.[ Mfi ]

Δfi

Solution of the modal parameters extraction

Sig.Processing: Danbox3 [email protected]

CSTRUCT25 Highest modes/FRF.Minimum of. 8 values/modeFreq.Dispersion limits=0.3 to 1.3(Hz)Results from Output in: Acc4,

Solution Number:1Df<1.0470 Hz

Mode Freq. Damp. Fre.Disp.Nb. (Hz) (%) (%)--------------------------------------

01 8.3104 8.052 7.27402 22.764 1.089 1.42203 26.791 3.728 3.13904 29.280 1.766 3.14405 31.301 2.537 2.17906 35.294 2.548 2.25007 39.343 2.580 1.65508 42.393 1.480 1.31509 44.491 2.301 1.80310 63.185 1.554 1.62911 66.269 1.445 1.04712 90.515 1.329 0.713



01 8.3104 8.052 7.27402 22.764 1.089 1.42203 26.738 3.537 2.14704 29.297 1.717 1.32505 31.301 2.537 2.17906 42.393 1.480 1.31507 44.390 2.096 1.66408 66.257 1.433 0.801



01 22.764 1.089 1.42202 26.666 3.648 0.80103 29.297 1.717 1.32504 29.357 1.622 1.18505 31.268 2.470 1.12506 42.400 1.473 1.17507 66.397 1.447 0.63308 90.575 1.367 0.418

Mode shapes

Other Example: Duarem Frame in ELSA

2nd In-plane bending X2=7.42 Hz

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0 50 100 150 200 250 3000

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Point Nb.

|FR

F or

FFT

|

cstruct:Position no:19

80.25 Hz

1.46 %

40.49 Hz

1.87 %77.67 Hz

1.06 %22.97 Hz

1.44 %

30.17 Hz

0.846 %

74.95 Hz

1.2 % 85.18 Hz

2.06 %32.33 Hz

3.2 %42.85 Hz

1.51 %65.65 Hz

1.74 % 93.02 Hz

2.15 %

52.81 Hz

1.3 %60.21 Hz

1.56 %57.09 Hz

0.925 %5.866 Hz

4.52 %


[email protected]

Example of the main mode

shapes of the roof panel in

correspondence of the peaks

~23 Hz

Spline interpolation for a better shape interpretation

~64.7 Hz

~30 Hz

MATLAB, step:7

[xi,zi] =ndgrid([…],…

yi = interpn(X',Z',Y',xi',zi','spline');

Example of a mode shapes of

one of the vertical panel

19

Results recorded in video format without interpolation

20

Results recorded in video format with interpolation MATLAB, step:8

21

Use and Interpretation of the Results: examples

Right panel fr ~ 72,3 HzLeft Panel fl~77,2 Hz

Stiffness comparaison:

Left panel stiffer than the right

panel fl > fr

Mode ratio

Freq.ratioExp.

Freq.ratioTheo.

Y2/Z2 1.0661.077

Y3/Z3 1.08𝒇𝟑,𝟎~133 Hz

𝒇𝟎,𝟑~144 Hz

Theory of thin plates 𝒇𝒎,𝒏 =𝑐

2𝜋

𝑚𝜋

𝑎

2

+𝑛𝜋

𝑏

2Comparison with theory of thin plates:

in agreement with the theory

a=236

b=219

22

Conclusions

The methodology allows the experimental modal analysis based

only on measurements processing, with structured automated steps.

Automatisation of:

• Near Real-time Signal Processing during the tests for measurements control.

• Possibility to adopt Fast Hammer Testing method (faster method)

• Spatial control of the measurement to immediately detect the errors locations.

• Powerful Interpolation to control and for a great help in the interpretation of the

results.

• 3D Visual animated representation of the results.

23

Thank [email protected]

unit e.4 safety and security of buildings a matlab toolbox ... · a matlab toolbox for experimental...

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