Structural health monitoring of offshore jacket platforms by inverse - - PDF document

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Structural health monitoring of offshore jacket platforms by inverse - - PDF document

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/ / Sharif University of Technology Civil Engineering Department Structural health monitoring of offshore jacket platforms by inverse vibration problem M. T. Nikoukalam On behalf of Kiarash M. Dolatshahi 1 Sharif

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Civil Engineering Department Sharif University of Technology

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Structural health monitoring of offshore jacket platforms by inverse vibration problem

  • M. T. Nikoukalam

On behalf of Kiarash M. Dolatshahi Outline

1- Introduction 2- Motivation 3- Description of inverse problem 4- Health monitoring of: 2D shear building models 2D moment building models 3D shear building models 5- Conclusion

Sharif University of Technology

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Civil Engineering Department

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Offshore jacket platforms:

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Introduction Motivation Inverse Vibration Problem Conclusion Civil Engineering Department Sharif University of Technology

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Civil Engineering Department Introduction Motivation Inverse Vibration Problem Conclusion

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Civil Engineering Department Introduction Motivation Inverse Vibration Problem Conclusion Sharif University of Technology

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Civil Engineering Department Introduction Motivation Inverse Vibration Problem Conclusion

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Inspection:

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Civil Engineering Department Introduction Motivation Inverse Vibration Problem Conclusion

Structural Health Monitoring (SHM):

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1- Damage detection 2- Damage localization 3- Damage quantification 4- Damage diagnosis 5- Damage Prognosis

Introduction Motivation Inverse Vibration Problem Conclusion

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Experimental Modal Analysis (EMA)

Forced excitation

Operational Modal Analysis (OMA)

Ambient excitation

Motivation: (Damage detection methods)

Introduction Motivation Inverse Vibration Problem Conclusion

Inverse Vibration Problem:(IVP)

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,

:

,

M K Direct solution

ω ϕ →

,

:

,

M K

Inverse solution

ω ϕ →

,

:

,

n n

M K

IVP

ω ϕ →

Introduction Motivation Inverse Vibration Problem Conclusion

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Input

M u,w

Phase 1

u,w

Phase 2

IVP

K

Phase 1

K

Phase 2

Output

K

Phase 1

K

Phase 2

SHM

Damage estimation

Introduction Motivation Inverse Vibration Problem Conclusion

Formulation:

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Civil Engineering Department

[ ]

[ ]

( )

i i

K M λ φ − =

[

] [ ][ ]

T

M L L =

[ ] [ ] [ ]

1/2 1/2 1/2 1/2 1 2

, ,...,

T N

L L M diag m m m = = =

   

{ } [ ]{ } { } [ ] { }

1

u L L u φ φ

−

=  =

[ ] [ ][ ] { } [ ] [ ][ ] { }

1 1 1 1

L K L L L

u M u λ

− − − −

− =

[ ] [ ][ ] { } [ ] [ ][ ] { }

1/2 1/2 1/2 1/2

M M u M M u

K M

λ

− − − −

= (1) (2) (3) (4) (5) (6) [B] [I]

Introduction Motivation Inverse Vibration Problem Conclusion

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[ ] { } { }

1 ,..., n

U u u   =  

[ ][ ] [ ][ ]

B U U = Λ

(7) (8)

Introduction Motivation Inverse Vibration Problem Conclusion

Shear building:

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Inputs: [M], {u1}, w1 Output: [K] IVP

Introduction Motivation Inverse Vibration Problem Conclusion

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[ ][ ] [ ][ ]

B U

U

=

Λ

Introduction Motivation Inverse Vibration Problem Conclusion

SPD2 Platform:

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Civil Engineering Department Introduction Motivation Inverse Vibration Problem Conclusion

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Modeling:

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Civil Engineering Department Introduction Motivation Inverse Vibration Problem Conclusion

2-D platform: (Shear structural model)

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Civil Engineering Department m1,k1 m2,k2 m3,k3 m4,k4 u11 u21 u31 u41 w1

[ ]

1 2 3 4

m m M m m       =      

[ ]

1 1 1 1 2 2 2 2 3 3 3 3 4

k k k k k k K k k k k k k k −     − + −   =   − + −   − +  

Inputs: [M], {u1}, w1 Output: [K] IVP

Introduction Motivation Inverse Vibration Problem Conclusion

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٠٩/٠۴/١۴٣۶ ١٠ Damage detection of the 2-D platform: (Shear structural model)

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Civil Engineering Department Introduction Motivation Inverse Vibration Problem Conclusion

Inputs:

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Undamaged: Damaged:

Introduction Motivation Inverse Vibration Problem Conclusion

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٠٩/٠۴/١۴٣۶ ١١ Damage detection of the 2-D platform: (Shear structural model)

Sharif University of Technology Civil Engineering Department

29.5% in braces 21

Introduction Motivation Inverse Vibration Problem Conclusion

By considering rotational DoF: (Real case) 17% Estimated damage

  • f level 2

23.5% in braces

2-D platform: (flexural structural model)

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Civil Engineering Department Introduction Motivation Inverse Vibration Problem Conclusion

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[ ]

1 1 1 1 2 1 1 2 2 2 1 2 2 3 2 2 3 3 3 3 4 3 3 4 4 3 2 3 4

k k m m m k k k k m m m m m B k k k k m m m m m k k k m m m −         − + −     =   − + −       − +      

A1 B1 B1 A2 B2 A3 B2 B3 A4 B3 T T T

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Introduction Motivation Inverse Vibration Problem Conclusion Sharif University of Technology

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[ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ]

1 1 1 2 2 2 3 3 4 3 T T T

A B B A B B B A B B A       =        

Introduction Motivation Inverse Vibration Problem Conclusion

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2-D platform: (flexural structural model)

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Mode #1 Mode #2

Introduction Motivation Inverse Vibration Problem Conclusion

Lateral stiffness of undamaged 2-D platform: (flexural structural model) Damage detection of 2-D platform by two modes: (flexural structural model)

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Absolute error (%) Inverse solution (106 N/m) Direct solution (106 N/m)

stiffness symbol

Elevation number

1.0 594.2 600.4 kx1

1

  • 1.4

304.8 300.4 kx2

2

  • 1.5

266.8 262.9 kx3

3

0.2 766.0 767.2 kx4

4 Relative error (%) Estimated damage (%) Damaged (106 N/m) Undamaged (106 N/m)

stiffness symbol

Elevation number

3.1

  • 3.1

612.9 594.2 kx1

1

0.9 28.0 219.4 304.8 kx2

2

0.1 0.1 266.5 266.8 kx3

3

0.6

  • 0.6

771.0 766.0 kx4

4 31.1% in braces

Introduction Motivation Inverse Vibration Problem Conclusion

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3-D platform: (shear structural model)

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Civil Engineering Department Introduction Motivation Inverse Vibration Problem Conclusion Sharif University of Technology

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Civil Engineering Department

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A1 B1 B1 A2 B2 A3 B2 B3 A4 B3 T T T

Introduction Motivation Inverse Vibration Problem Conclusion

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Civil Engineering Department Introduction Motivation Inverse Vibration Problem Conclusion Sharif University of Technology

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Mode #2 Mode #3 Mode #1

Introduction Motivation Inverse Vibration Problem Conclusion

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٠٩/٠۴/١۴٣۶ ١۶ Damage detection of 3-D platform: (shear structural model)

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Civil Engineering Department Relative error (%) Estimated damage (%) ey (m) ex (m) Damaged (106 N/m) ey (m) ex (m) Undamaged (106 N/m) stiffness symbol Elevation number 0.3

  • 0.3
  • 0.57

1141.0

  • 0.57

1137.6 kx1 1 1061.9 1062.2 ky1 1.5 1.5 248472.9 252369.0 k1 0.1 14.8 2.37 471.4 0.74 553.0 kx2 2 730.3 730.5 ky2 1.4 7.8 148540.2 161158.1 k2 0.2 0.2

  • 0.43

480.9

  • 0.61

482.0 kx3 3 0.2 0.2 508.0 508.8 ky3 1.4 1.4 177094.5 179655.2 k3 0.7 0.7 1406.7 0.30 1416.4 kx4 4 0.2

  • 0.2

1048.8 1046.3 ky4 3.8

  • 3.8

484918.6 467053.0 k4

29.7% in braces

Introduction Motivation Inverse Vibration Problem Conclusion

Damage detection of 3-D platform:

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Civil Engineering Department Relative error (%) Estimated damage (%) ey (m) ex (m) Damaged (106 N/m) ey (m) ex (m) Undamaged (106 N/m) stiffness symbol Elevation number 0.3

  • 0.3
  • 0.76

308.8

  • 0.63

307.9 kx1 1 0.5 0.5 317.6 319.2 ky1 1.7 1.7 226881.2 230796.5 k1 2.6 8.3

  • 0.58

256.7

  • 2.40

280.0 kx2 2 0.2 0.2 333.2 333.9 ky2 1.4 4.7 145427.2 152646.5 k2 1.4 1.4 4.75 257.7 5.06 261.3 kx3 3 0.2

  • 0.2

379.8 379.2 ky3 4.9

  • 4.9

178217.1 169867.6 k3 1.3 1.3

  • 6.40

1436.6

  • 6.60

1455.9 kx4 4 0.2 0.2 1157.3 1159.6 ky4 1.1 1.1 472603.4 477693.5 k4

22.9% in braces

Introduction Motivation Inverse Vibration Problem Conclusion

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Uncertainty analysis:

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Civil Engineering Department Introduction Motivation Inverse Vibration Problem Conclusion

error range: 10%

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Civil Engineering Department

μ=28.1% σ=7.4%

20-38% 80%

Introduction Motivation Inverse Vibration Problem Conclusion

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٠٩/٠۴/١۴٣۶ ١٨ error range: 5%

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μ=28.3% σ=3.8%

80% 24-34%

Introduction Motivation Inverse Vibration Problem Conclusion

error range: 2%

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Civil Engineering Department Introduction Motivation Inverse Vibration Problem Conclusion

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٠٩/٠۴/١۴٣۶ ١٩ error range: 1%

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Civil Engineering Department Introduction Motivation Inverse Vibration Problem Conclusion

Probabilistic Sensitivity:

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2.25 . damage Sensitivity error of acc Δ = = Δ

Introduction Motivation Inverse Vibration Problem Conclusion

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Conclusion:

2-D platform: (shear structural model) 2-D platform: (flexural structural model) 3-D platform: (shear structural model) Uncertainty analysis

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1 mode 2 modes 3 modes

Introduction Motivation Inverse Vibration Problem Conclusion

Thanks for your attention

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Civil Engineering Department Introduction Motivation Inverse Vibration Problem Conclusion