Decentralize damage detection algorithm Manuel Ruiz-Sandoval & Cesar Carpio

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

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

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

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

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

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

Damage detection methods

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

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

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

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

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

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

Planar frame Element 4 with a 70% reduction of stiffness

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

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.  

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

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

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

Decentralization

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

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

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

Master nodes A B C D E F

Master nodes A B C D E F

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 29 28 24 30 25 31 33 32 26

Excitation: white noise

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

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

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

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

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

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

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

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

Index Stiffness reduction 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

Frame III

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.

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.