1. Decentralize damage detection algorithm
Manuel Ruiz-Sandoval
& Cesar Carpio

2. Outline Motivation Types of detection Proposed method
Modal energy deformation
POD (Proper Orthogonal Decomposition).
Proposed method
Numerical example
Conclusions

3. Motivation
The occurrence of structural damage can originate threaten life situations
Damage detection at early stages could prevent the loss of human lives, as well as reduce maintenance cost

4. Damage detection methods
Visual inspection
Optical sensing
Acoustic methods
Modal analysis
Damage Localization Vector
Among others

5. 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

6. Centralized data information
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
Wire sensors

7. Decentralized data acquisition system
Wireless sensors
New technologies available
Smart sensors: on board processing and wireless communication.
New paradigm to be explore

8. Damage detection methods

9. Modal energy deformation method
Where
is the jth the mode shape vector, and
is the stiffness matrix

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

11. 2D Truss
DOF 7,8 3 4 4 5 5
DOF 5,6
DOF 9,10 6 7 8 9 10 11 6 7 1 2 3 1 2
DOF 1,2
DOF 3,4

12. Two damage scenarios
1) 60% Reduction of Young's modulus at element 2. 6 1 2 7 3 4 5 8 9 10 11
2) 60% Reduction of Young's modulus at elements 7 y 10. 6 1 2 7 3 4 5 8 9 10 11

13. CASE 1) Periods Undamaged Damaged
Undamaged stiffness matrix for each element 1, 2, … 11 …

17. CASE 2) Periods Undamaged Damaged
Undamaged stiffness matrix for each element 1, 2, … 11 …

19. Planar frame
Element 4 with a 70% reduction of stiffness

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

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

22. Proper Orthogonal Decomposition (POD)
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.  

23. POD (Proper Orthogonal Decomposition)
Displacement history at different point over the structures are needed
di(t) = (di(t1), di(t2), di(t3),…. di(tM))T
These values are normalized by the mean value

24. POD (Proper Orthogonal Decomposition)
Matrix A is constructed of M x N (time Vs Number of sensor positions)
With matrix A, a correlation matrix R can be calculated
R matrix is real and symmetrical of N x N order

25. POD Method
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

26. Decentralization

27. Sensors are collocated at joints and midsections
Sensor placement
Smart sensors
Beam element
Column element L
L/2 L
L/2 L
L/2
L/2
L/2
L/2
L/2
L/2
L/2 L L L
Sensors are collocated at joints and midsections

28. First level of sharing 27 28 29 30 31 32 33 23 24 25 26 16 17 18 19 20 21 22 12 13 14 15 5 7 9 10 11 6 8 1 2 3 4

29. Sensor used for damage detection
Cluster head sharing 27 29 31 33 16 18 20 22 5 7 9
11`
Sensor used for damage detection

30. Master nodes A B C D E F

31. Master nodes A B C D E F

32. Numerical example

33. 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 29 28 24 30 25 31 33 32 26

34. Excitation: white noise

35. Aplication of POD at sensor 5 (node 9).
Displacement matriz with/without damage is presented
(a)
(b)

36. Matrix A for sensor 5
Undamaged Damaged
(a)
(b)

37. R undamaged
R damaged 1 2 3 16 5 4 6 7 8 9 10 11 12 13 14 15 17 18 19 20 21 22 23 27 29 28 24 30 25 31 33 32 26

38. R undamaged
R damaged 1 2 3 16 5 4 6 7 8 9 10 11 12 13 14 15 17 18 19 20 21 22 23 27 29 28 24 30 25 31 33 32 26

39. Sensor point i R
undamged
/ R
damage 5
0.9813 7
0.9864 9
0.993 11
0.9961 16
0.9794 18
0.9843 22
0.9862 27
0.9813 29
0.9845 31
0.9847 33
0.9835

40. A B C Beam 18 5 16 16 D E F Beam Beam 16 C F E B A D 27 29 31 33 16 18
0.9794 16
0.9843 18
0.9835 33
0.9813 27
0.19
0.9845 29
0.02
0.9847 31
0.12
0.31
0.9862 22
0.15
0.9863 20
0.16
0.01 5
0.20
0.9864 7
0.993 9
0.68
0.21
0.67
0.9961 11
Beam 18 5 16 16 D E F
Beam
Beam 16 C F E B A D 27 29 31 33 16 18 20 22 5 7 9 11

41. Índice de daño estructural para cada barra del marco I.
Index
Índice de daño estructural para cada barra del marco I.
Stiffness reduction

42. Frame II.
300 cm
400 cm
600 cm 31 37 36 35 34 33 32 26 25 24 23 22 21 20 27 30 29 28 19 18 17 16 15 14 13 12 11 10 9 5 6 7 8 4 3 2 1 43 44 42 41 39 40 38 45 46 47 48

43. Index Stiffness reduction 300 cm 400 cm 600 cm 31 37 36 35 34 33 32 2625 24 23 22 21 20 27 30 29 28 19 18 17 16 15 14 13 12 11 10 9 5 6 7 8 4 3 2 1 43 44 42 41 39 40 38 45 46 47 48

44. Frame III

46. CONCLUSIONS
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.

47. 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.

48. 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.