Structural health monitoring of offshore jacket platforms...
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٠٩/٠۴/١۴٣۶ ١ Civil Engineering Department Sharif University of Technology 1 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 2 Civil Engineering Department
Transcript of Structural health monitoring of offshore jacket platforms...
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Civil Engineering DepartmentSharif University of Technology
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Structural health monitoring of offshore jacket platforms by inverse vibration problem
M. T. NikoukalamOn 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
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Offshore jacket platforms:
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Inspection:
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Structural Health Monitoring (SHM):
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1- Damage detection
2- Damage localization
3- Damage quantification
4- Damage diagnosis
5- Damage Prognosis
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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 KDirect solution ω ϕ→
,: , M KInverse solution ω ϕ →
,: , n nM KIVP ω ϕ →
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Input
M u,wPhase 1
u,wPhase 2
IVP KPhase 1
KPhase 2
Output
KPhase 1
KPhase 2
SHM Damageestimation
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Formulation:
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[ ] [ ]( ) 0i iK Mλ φ− =
[ ] [ ][ ]T
M L L=
[ ] [ ] [ ]1/2 1/2 1/2 1/21 2, ,...,T
NL L M diag m m m= = =
{ } [ ]{ } { } [ ] { }1u L L uφ φ −= =
[ ] [ ][ ] { } [ ] [ ][ ] { }1 1 1 1 0L K L L Lu M uλ− − − −− =
[ ] [ ][ ] { } [ ] [ ][ ] { }1/2 1/2 1/2 1/2M M u M M uK Mλ− − − −=
(1)
(2)
(3)
(4)
(5)
(6)
[B] [I]
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[ ] { } { }1 ,..., nU u u =
[ ][ ] [ ][ ]B U U= Λ
(7)
(8)
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Shear building:
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Inputs: [M], {u1}, w1 Output: [K]IVP
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[ ][ ] [ ][ ]B U U= Λ
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SPD2 Platform:
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Modeling:
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2-D platform: (Shear structural model)
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m1,k1
m2,k2
m3,k3
m4,k4
u11
u21
u31
u41
w1
[ ]1
2
3
4
0 0 00 0 00 0 00 0 0
m
mM
m
m
=
[ ]1 1
1 1 2 2
2 2 3 3
3 3 4
0 00
00 0
k k
k k k kK
k k k k
k k k
− − + − = − + − − +
Inputs: [M], {u1}, w1 Output: [K]IVP
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Damage detection of the 2-D platform: (Shear structural model)
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Inputs:
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Undamaged:
Damaged:
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Damage detection of the 2-D platform: (Shear structural model)
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29.5% in braces
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By considering rotational DoF:(Real case)
17%Estimated damage
of level 2
23.5% in braces
2-D platform: (flexural structural model)
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[ ]
1 1
1 1 2
1 1 2 2
21 2 2 3
2 2 3
3
3
3 4
3 3 4
43
2 3
4
0 0
0
0
0 0
k k
m m m
k k k k
mm m m mB
k k k k
mm m m m
k k k
mm m
− − + − = − + − − +
A1 B1
B1 A2
B2 A3
B2
B3
A4B3
TT
T23
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[ ]
[ ] [ ] [ ] [ ][ ] [ ] [ ] [ ][ ] [ ] [ ] [ ][ ] [ ] [ ] [ ]
1 1
1 2 2
2 3 3
43
0 0
0
0
0 0
T
T
T
A B
B A BB
B A B
B A
=
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2-D platform: (flexural structural model)
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Mode #1 Mode #2
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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
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3-D platform: (shear structural model)
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A1 B1
B1 A2
B2 A3
B2
B3
A4B3
TT
T
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Mode #2 Mode #3Mode #1
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Damage detection of 3-D platform: (shear structural model)
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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 -0.570
1141.0 -0.570
1137.6 kx1
1 0 0 1061.9 1062.2 ky1 1.5 1.5 248472.9252369.0k�1 0.1 14.8
2.370471.4
0.740 553.0 kx2
2 0 0 730.3 730.5 ky2 1.4 7.8 148540.2161158.1k�2 0.2 0.2
-0.430480.9
-0.610 482.0 kx3
3 0.2 0.2 508.0 508.8 ky3 1.4 1.4 177094.5179655.2k�3 0.7 0.7
0 01406.7
0.300 1416.4 kx4
4 0.2 -0.2 1048.8 1046.3 ky4 3.8 -3.8 484918.6467053.0k�4
29.7% in braces
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Damage detection of 3-D platform:
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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 -0.760
308.8 -0.630
307.9 kx1
1 0.5 0.5 317.6 319.2 ky1 1.7 1.7 226881.2230796.5k�1 2.6 8.3
-0.580256.7
-2.400280.0 kx2
2 0.2 0.2 333.2 333.9 ky2 1.4 4.7 145427.2152646.5k�2 1.4 1.4
4.750257.7
5.060261.3 kx3
3 0.2 -0.2 379.8 379.2 ky3 4.9 -4.9 178217.1169867.6k�3 1.3 1.3
-6.4001436.6
-6.6001455.9 kx4
4 0.2 0.2 1157.3 1159.6 ky4 1.1 1.1 472603.4477693.5k�4
22.9% in braces
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Uncertainty analysis:
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error range: 10%
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μ=28.1%σ=7.4%
20-38%
80%
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error range: 5%
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μ=28.3%σ=3.8%
80%
24-34%
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error range: 2%
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error range: 1%
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Probabilistic Sensitivity:
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2.25 .
damageSensitivity
error of acc
Δ= =Δ
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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
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Thanks for your attention
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