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Decentralize damage detection algorithm

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.

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Decentralize damage detection algorithm

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

  2. Outline • Motivation • Types of detection • 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 Wire sensors • 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

  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 iin the jth 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 5 3 4 4 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. 5 3 4 4 5 6 7 8 9 10 11 6 7 1 2 3 1 2 5 3 4 4 5 7 10 11 6 8 9 10 6 7 1 2 3 1 2 Two damage scenarios 1) 60% Reduction of Young's modulus at element 2. 2) 60% Reduction of Young's modulus at elements7 y 10.

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

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

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

  16. 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

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

  18. 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.  

  19. 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

  20. 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

  21. 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

  22. Decentralization

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

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

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

  26. Master nodes A B C D E F

  27. Master nodes A B C D E F

  28. Numerical example

  29. 27 28 29 30 31 32 33 25 26 23 24 16 17 18 19 20 21 22 14 15 12 13 11 5 9 10 7 6 8 4 1 2 3 Numerical example • A 20% reduction of stiffness is place at element between nodes 5, 12 and 16

  30. Excitation: white noise

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

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

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

  34. 27 28 29 30 31 32 33 25 26 23 24 16 17 18 19 20 21 22 14 15 12 13 11 5 6 7 8 9 10 4 1 2 3 R undamaged R damaged

  35. 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

  36. A B C Beam Beam Beam 16 5 C A B D E F 18 16 D E F 16 27 29 31 33 16 18 20 22 5 9 11 7

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

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

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

  40. Frame III

  41. 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.

  42. 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.

  43. 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.

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