Decentralize damage detection algorithm

Manuel Ruiz-Sandoval & Cesar Carpio

Outline

Motivation Types of detection

Modal energy deformation POD (Proper Orthogonal Decomposition).

Proposed method Numerical example Conclusions

Motivation

►The occurrence of The occurrence of structural damage can structural damage can originate threaten life originate threaten life situationssituations

►Damage detection at Damage detection at early stages could early stages could prevent the loss of prevent the loss of human lives, as well as human lives, as well as reduce maintenance reduce maintenance costcost

- Visual inspection- Optical sensing- Acoustic methods- Modal analysis- Damage Localization Vector- Among others

Damage detection methods

Damage detection methods based on signal processing

Modal parameters Frequency changes Mode shape changes

function of mass stiffness damping

Comparison between undamaged and damage stages

Traditional data acquisition systems use a centralized scheme.

This system is required to be capable of manage all channels

Cost could hinder the use a great number of sensors

Centralized data information

Wire sensors

►New technologies New technologies availableavailable►Smart sensors: on Smart sensors: on board processing and board processing and wireless communication.wireless communication.►New paradigm to be New paradigm to be exploreexplore

Decentralized data acquisition system

Wireless sensors

Damage detection methods

Modal energy deformation methodModal energy deformation method

jTjj KU

2

1

Where Where

is the jis the jthth the mode shape vector, the mode shape vector, and and

is the stiffness matrixis the stiffness matrix

Modal energy deformation methodModal energy deformation method

The total amount of deformation energy can be The total amount of deformation energy can be visualized as the sum of the energies of all visualized as the sum of the energies of all structural elements.structural elements.

N

iijj UU

1

Where U is the contribution of the energy deformation method of element i in the j th mode, and N is the number of structural elements.

The change if the energy between an undamaged (u) and damage (d) case can be calculated with the following expression ijijij UdUuU

2D Truss

6

1 27

3 4 5

1 2 3

4 5

6 7 8 9 10 11

DOF 1,2 DOF 3,4

DOF 5,6

DOF 7,8

DOF 9,10

Two damage scenariosTwo damage scenarios

1) 60% Reduction of Young's modulus at element 2.1) 60% Reduction of Young's modulus at element 2.

2) 2) 60% Reduction of Young's modulus at elements60% Reduction of Young's modulus at elements 7 y 10.7 y 10.

61 2

7

3 4 5

1 2 3

4 5

6 7 8 9 10 11

61 2

7

3 4 5

1 2 3

4 5

6 7 8 9 10 1110

UndamagedUndamaged

CASE 1)CASE 1)

Undamaged stiffness matrix for each element 1, 2, … 11Undamaged stiffness matrix for each element 1, 2, … 11

K

……

DamagedDamaged

PeriodsPeriods

j

jTjj KU

2

1

ijijij UdUuU

CASE 2)CASE 2)

K

……

UndamagedUndamaged DamagedDamaged

PeriodsPeriods

Undamaged stiffness matrix for each element 1, 2, … 11Undamaged stiffness matrix for each element 1, 2, … 11

ijijij UdUuU

Planar frame

Element 4 with a 70% reduction of stiffness

Mode 1 Mode 2 Mode 3 Mode 4 Mode 5 Mode 6 Mode 7 Mode 8 Mode 9 Mode 10 Mode 11 Mode 12

undamagedj

gdl 1gdl 2gdl 3gdl 4gdl 5gdl 6gdl 7gdl 8gdl 9gdl 10gdl 11gdl 12

damagejgdl 1gdl 2gdl 3gdl 4gdl 5gdl 6gdl 7gdl 8gdl 9gdl 10gdl 11gdl 12

j

Mode 1 Mode 2 Mode 3 Mode 4 Mode 5 Mode 6 Mode 7 Mode 8 Mode 9 Mode 10 Mode 11 Mode 12

ijU

123456

jTjj KU

2

1

Mode 1 Mode 2 Mode 3 Mode 4 Mode 5 Mode 6 Mode 7 Mode 8 Mode 9 Mode 10 Mode 11 Mode 12

 El POD is a tool  for the dynamics and vibration (also known as Karhunen-Loève) that provides with a base for the modal response during a experiment.   The POD based its results on sensor displacements over the structure.  It  compares  an  original  stated  with  an  unknown state. 

Also,  it  can  use  eigenvectors  and  eigenvalues  to  determine the  distribution  of  modal  energy,  as  well  as  the  energy participation of every mode.  

Proper Orthogonal Decomposition (POD)

_

iii dda

POD (Proper Orthogonal Decomposition)

di(t) = (di(t1), di(t2), di(t3),…. di(tM))T

Displacement history at different point over the structures are needed

These values are normalized by the mean value

 

 With matrix A, a correlation matrix R can be calculated 

 R matrix is real and symmetrical of N x N order

)t(a)t(a)t(a

)t(a)t(a)t(a

)t(a)t(a)t(a

A

MNMM

N

N

21

22221

11211

AAMR T/1

Matrix A is constructed of M x N (time Vs Number of sensor positions)

POD (Proper Orthogonal Decomposition)

The  correlation  matrix  represents  the  behavior  of  the structure at certain points. 

The second step for damage identification is to do a ratio between  R  undamaged  and  damage  for  every  corner sensor.  Those  point  with  a  great  difference  will  be indicative of presence of damage at that place 

POD Method

Decentralization

Sensors are collocated at joints and midsections

L

L

L L

L/2 L/2 L/2 L/2

L/2

L/2

Smart sensors

L/2L

Beam element

Column element

L/2L/2

L

Sensor placement

1 2 3

16

5

4

6 7 8 9 10 11

12 13 14 15

17 18 19 20 21 22

23

27 2928

24

30

25

31 3332

26

First level of sharing

Sensor used for damage detection

33312927

222018

11`975

16

Cluster head sharing

CBA

FED

Master nodes

CBA

FED

Master nodes

Numerical example

Numerical example

A 20% reduction of stiffness is place at element between nodes 5, 12 and 16

1 2 3

16

5

4

6 7 8 9 10 11

12 13 14 15

17 18 19 20 21 22

23

27 2928

24

30

25

31 3332

26

Ruido blanco

-15

-10

-5

0

5

10

15

0 5 10 15 20 25 30 35 40 45 50Tiempo (seg)

Ac

ele

rac

ión

(c

m/s

eg

2 )Excitation: white

noise

 Displacement matriz with/without damage is presented

(a) (b)

Tiempo (seg) Sensor 1 Sensor 5 Sensor 6 Sensor 121 0.01 -1.00E-04 -1.00E-04 -1.00E-04 -1.00E-042 0.02 -0.0002 -0.0003 -0.0003 -0.00043 0.03 -1.00E-04 -2.00E-04 -2.00E-04 -2.00E-044 0.04 0.00E+00 1.00E-04 1.00E-04 1.00E-045 0.05 1.00E-04 1.00E-04 1.00E-04 1.00E-046 0.06 1.00E-04 1.00E-04 1.00E-04 2.00E-047 0.07 1.00E-04 1.00E-04 1.00E-04 1.00E-048 0.08 0.00E+00 0.00E+00 0.00E+00 -1.00E-049 0.09 -0.0001 -0.0002 -0.0002 -0.000310 0.1 -1.00E-04 -2.00E-04 -2.00E-04 -2.00E-04: : : : : :: : : : : :

4991 49.91 0.00E+00 -1.00E-04 -1.00E-04 -1.00E-044992 49.92 -1.00E-04 -1.00E-04 -1.00E-04 -2.00E-044993 49.93 -1.00E-04 -1.00E-04 -1.00E-04 -2.00E-044994 49.94 0.00E+00 0.00E+00 0.00E+00 0.00E+004995 49.95 -1.00E-04 -1.00E-04 -1.00E-04 -1.00E-044996 49.96 -1.00E-04 -2.00E-04 -2.00E-04 -2.00E-044997 49.97 -1.00E-04 -1.00E-04 -1.00E-04 -1.00E-044998 49.98 0.00E+00 -1.00E-04 -1.00E-04 -1.00E-044999 49.99 -0.0001 -0.0002 -0.0002 -0.00035000 50 -0.0001 -0.0002 -0.0002 -0.0003

-1.61E-08 -3.22E-08 -3.22E-08 -3.95E-08

Sensor 5

M =

5000

d i sin daño

N = 4

d i promedio

Sensor 1 Sensor 5 Sensor 6 Sensor 12-1.00E-04 -1.00E-04 -1.00E-04 -1.00E-04-0.0002 -0.0003 -0.0003 -0.0004

-1.00E-04 -2.00E-04 -2.00E-04 -2.00E-040.00E+00 1.00E-04 1.00E-04 1.00E-041.00E-04 1.00E-04 1.00E-04 1.00E-041.00E-04 1.00E-04 1.00E-04 2.00E-041.00E-04 1.00E-04 1.00E-04 1.00E-040.00E+00 -1.00E-04 -1.00E-04 -1.00E-04-0.0001 -0.0002 -0.0002 -0.0003

-1.00E-04 -2.00E-04 -2.00E-04 -2.00E-04: : : :: : : :

0.00E+00 0.00E+00 0.00E+00 -1.00E-04-1.00E-04 -1.00E-04 -1.00E-04 -1.00E-04-1.00E-04 -1.00E-04 -1.00E-04 -2.00E-040.00E+00 -1.00E-04 -1.00E-04 -1.00E-04-1.00E-04 -1.00E-04 -1.00E-04 -2.00E-04-1.00E-04 -1.00E-04 -1.00E-04 -2.00E-040.00E+00 -1.00E-04 -1.00E-04 -1.00E-040.00E+00 -1.00E-04 -1.00E-04 -1.00E-04-0.0001 -0.0002 -0.0002 -0.0003-0.0001 -0.0002 -0.0003 -0.0003

-1.72E-08 -3.42E-08 -3.44E-08 -4.28E-08

d i promedio

Sensor 5

d i con daño

N = 4

Aplication of POD at sensor 5 (node 9).

Matrix A for sensor 5

(a) (b)

Sensor 1 Sensor 5 Sensor 6 Sensor 12

1 -1.00E-04 -1.00E-04 -1.00E-04 -1.00E-042 -2.00E-04 -3.00E-04 -3.00E-04 -4.00E-043 -1.00E-04 -2.00E-04 -2.00E-04 -2.00E-044 1.61E-08 1.00E-04 1.00E-04 1.00E-045 1.00E-04 1.00E-04 1.00E-04 1.00E-046 1.00E-04 1.00E-04 1.00E-04 2.00E-047 1.00E-04 1.00E-04 1.00E-04 1.00E-048 1.61E-08 3.22E-08 3.22E-08 -1.00E-049 -1.00E-04 -2.00E-04 -2.00E-04 -3.00E-0410 -1.00E-04 -2.00E-04 -2.00E-04 -2.00E-04: : : : :: : : : :

4991 1.61E-08 -1.00E-04 -1.00E-04 -1.00E-044992 -1.00E-04 -1.00E-04 -1.00E-04 -2.00E-044993 -1.00E-04 -1.00E-04 -1.00E-04 -2.00E-044994 1.61E-08 3.22E-08 3.22E-08 3.95E-084995 -1.00E-04 -1.00E-04 -1.00E-04 -1.00E-044996 -1.00E-04 -2.00E-04 -2.00E-04 -2.00E-044997 -1.00E-04 -1.00E-04 -1.00E-04 -1.00E-044998 1.61E-08 -1.00E-04 -1.00E-04 -1.00E-044999 -1.00E-04 -2.00E-04 -2.00E-04 -3.00E-045000 -1.00E-04 -2.00E-04 -2.00E-04 -3.00E-04

Sensor 5

Matriz A sin dañoM

=50

00

Sensor 1 Sensor 5 Sensor 6 Sensor 12

-1.00E-04 -1.00E-04 -1.00E-04 -1.00E-04-2.00E-04 -3.00E-04 -3.00E-04 -4.00E-04-1.00E-04 -2.00E-04 -2.00E-04 -2.00E-041.72E-08 1.00E-04 1.00E-04 1.00E-041.00E-04 1.00E-04 1.00E-04 1.00E-041.00E-04 1.00E-04 1.00E-04 2.00E-041.00E-04 1.00E-04 1.00E-04 1.00E-041.72E-08 -1.00E-04 -1.00E-04 -1.00E-04-1.00E-04 -2.00E-04 -2.00E-04 -3.00E-04-1.00E-04 -2.00E-04 -2.00E-04 -2.00E-04

: : : :: : : :

1.72E-08 3.42E-08 3.44E-08 -1.00E-04-1.00E-04 -1.00E-04 -1.00E-04 -1.00E-04-1.00E-04 -1.00E-04 -1.00E-04 -2.00E-041.72E-08 -1.00E-04 -1.00E-04 -1.00E-04-1.00E-04 -1.00E-04 -1.00E-04 -2.00E-04-1.00E-04 -1.00E-04 -1.00E-04 -2.00E-041.72E-08 -1.00E-04 -1.00E-04 -1.00E-041.72E-08 -1.00E-04 -1.00E-04 -1.00E-04-1.00E-04 -2.00E-04 -2.00E-04 -3.00E-04-1.00E-04 -2.00E-04 -3.00E-04 -3.00E-04

Matriz A con daño

Sensor 5

Undamaged Damaged

3.15E-08 6.28E-08 6.29E-08 7.75E-086.28E-08 1.25E-07 1.25E-07 1.54E-076.29E-08 1.25E-07 1.26E-07 1.55E-077.75E-08 1.54E-07 1.55E-07 1.90E-07

R Sensor 5 sin daño

3.07E-08 6.11E-08 6.13E-08 7.67E-086.11E-08 1.22E-07 1.22E-07 1.53E-076.13E-08 1.22E-07 1.23E-07 1.53E-077.67E-08 1.53E-07 1.53E-07 1.92E-07

R Sensor 5 con daño

1 2 3

16

5

4

6 7 8 9 10 11

12 13 14 15

17 18 19 20 21 22

23

27 2928

24

30

25

31 3332

26

R undamaged R damaged

3.16E-08 6.30E-08 6.30E-08 6.31E-08 7.77E-086.30E-08 1.26E-07 1.26E-07 1.26E-07 1.55E-076.30E-08 1.26E-07 1.25E-07 1.26E-07 1.55E-076.31E-08 1.26E-07 1.26E-07 1.26E-07 1.55E-077.77E-08 1.55E-07 1.55E-07 1.55E-07 1.91E-07

R Sensor 7 sin daño

3.11E-08 6.18E-08 6.20E-08 6.21E-08 7.72E-086.18E-08 1.23E-07 1.23E-07 1.23E-07 1.53E-076.20E-08 1.23E-07 1.23E-07 1.24E-07 1.54E-076.21E-08 1.23E-07 1.24E-07 1.24E-07 1.54E-077.72E-08 1.53E-07 1.54E-07 1.54E-07 1.92E-07

R Sensor 7 con daño

1 2 3

16

5

4

6 7 8 9 10 11

12 13 14 15

17 18 19 20 21 22

23

27 2928

24

30

25

31 3332

26

R undamaged R damaged

Sensor point i R undamged / R damage

5 0.98137 0.98649 0.99311 0.996116 0.979418 0.984322 0.986227 0.981329 0.984531 0.984733 0.9835

0.9794 16 0.9843 18 0.9835 33

0.9813 27 0.19 0.9845 29 0.02 0.9847 31 0.12

0.9843 18 0.31 0.9847 31 0.02 0.9862 22 0.15

0.9845 29 0.02 0.9863 20 0.16 0.9863 20 0.01

0.9794 16 0.9843 18 0.9862 22

0.9813 5 0.19 0.9863 20 0.20 0.9863 20 0.01

0.9843 18 0.31 0.9864 7 0.01 0.993 9 0.68

0.9864 7 0.21 0.993 9 0.67 0.9961 11 0.31

C

FE

BA

D

16

5 7 9 11

18 20 22

27 29 31 33

A B C

D E F

18

16

16

5

16

Beam

BeamBeam

0

0.2

0.4

0.6

0.8

1

30%40%50%60%70%80%90%100%

Porcentaje de daño

Ind

ice

Nodo 1,5,9

Nodo 2,6,11

Nodo 9,16,20

Nodo 13,18,24

Nodo 20,27,31

Nodo 26,30,37

Índice de daño estructural para cada barra del marco I.

Inde

x

Stiffness reduction

Frame II.

300 cm

300 cm

400 cm

400 cm600 cm400 cm

31 373635343332

26252423222120

27 302928

19181716

1514131211109

5 6 7 8

4321

1 2 3

16

5

4

6 7 8 9 10 11

12 13 14 15

17 18 19 20 21 22

23

27 2928

24

30

25

31 3332

26

37

43 4442

36

41

35

39 4038

34

39 40 4138

43 44 45 46 47 4842

300 cm

0

0.2

0.4

0.6

0.8

1

1.2

30%40%50%60%70%80%90%100%

Porcentaje de daño

Ind

ice

Nodo 1,5,9

Nodo 2,6,11

Nodo 9,16,20

Nodo 11,17,22

Nodo 20,27,31

Nodo 22,28,33

Nodo 31,38,42

Nodo 33,39,44

300 cm

300 cm

400 cm

400 cm600 cm400 cm

31 373635343332

26252423222120

27 302928

19181716

1514131211109

5 6 7 8

4321

1 2 3

16

5

4

6 7 8 9 10 11

12 13 14 15

17 18 19 20 21 22

23

27 2928

24

30

25

31 3332

26

37

43 4442

36

41

35

39 4038

3439 40 4138

43 44 45 46 47 4842

300 cm

Inde

x

Stiffness reduction

Frame III

32

39 4038

31

37

30

35 3634

29

262524232221

18171615

11109876

4

20

321

1 2 3 4

8765 10

11 12 13 14 15

20 21 22 23

35 36 3734

25 26 27 28 30 31

40 41 42 43 44 4539

500 cm 500 cm 500 cm

400 cm

300 cm

300 cm

500 cm

4746

3332

38

24

1716

5

5

13 14

19

27 28

4241

33

12

18 19

29 W18x35Vigas

ColumnasW24x55

0

0.2

0.4

0.6

0.8

1

1.2

30%40%50%60%70%80%90%100%

Porcentaje de daño

Ind

ice

Nodo 1,6,11

Nodo 2,7,13

Nodo 3,8,15

Nodo 11,20,25

Nodo 13,21,27

Nodo 15,22,29

Nodo 25,34,39

Nodo 27,35,41

Nodo 29,36,43

The use of smart sensor can allow implementing a decentralization of damage detection method.

Most the actual methods are use in a centralized fashion.

This works explore some of the existent methods and how to decentralize them.

CONCLUSIONS

Method is applied to planar shear deformation frame.

Modal Energy method was not able to detect damage for this specific case.

Proper Orthogonal Decomposition method was able to detect damage.

CONCLUSIONS

A proposal to decentralized POD methods is presented.

Only information of cluster head are required to determine damage.

This method detects damage for small stiffness changes at low level columns.

Damage detection for upper columns is achieve for relatively large change of stiffness.

CONCLUSIONS