Structural health monitoring of offshore jacket platforms by inverse vibration problem M. T. Nikoukalam On behalf of Kiarash M. Dolatshahi 1 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 2 ١
Offshore jacket platforms: 3 4 ٢
5 6 ٣
Inspection: 7 Structural Health Monitoring (SHM): 1- Damage detection 2- Damage localization 3- Damage quantification 4- Damage diagnosis 5- Damage Prognosis 8 ۴
Motivation: (Damage detection methods) Experimental Modal Analysis (EMA) Forced excitation Operational Modal Analysis (OMA) Ambient excitation 9 Inverse Vibration Problem:(IVP) Direct solution : M, K, ω ϕ ω ϕ Inverse solution :, M, K IVP : M, ω, ϕ n n K 10 ۵
M Input u,w Phase 1 Phase 2 IVP K u,w Output Phase 1 Phase 2 K Phase 1 K Phase 2 K SHM Damage estimation 11 Formulation: [ K] λ [ M] ( ) φ = 0 [ M ] = [ L][ L] T i i T [ ] [ ] [ ] 1/2 1/2 1/2 1/2,,..., L L M diag m m m 1 2 N = = = 1 {} u = [ L]{ φ} {} φ = [ L] {} u [ ] 1 [ ][ ] 1 { } [ ] 1 L K L u λ L [ M][ L] 1 { u} = 0 [ ] 1/2 [ ][ ] 1/2 {} [ ] 1/2 M K M u = λ M [ M][ M] 1/2 {} u [B] [I] (1) (2) (3) (4) (5) (6) 12 ۶
[ U] { u} { u } =,..., 1 n (7) [ B][ U] = [ U][ Λ] (8) 13 Shear building: Inputs: [M], {u1}, w1 IVP Output: [K] 14 ٧
[ B][ U] = [ U][ Λ] 15 SPD2 Platform: 16 ٨
Modeling: 17 2-D platform: (Shear structural model) m1,k1 m2,k2 [ M ] m1 0 0 0 0 m 0 0 2 = 0 0 m3 0 0 0 0 m4 w1 u11 u21 m3,k3 K m4,k4 [ ] k1 k1 0 0 k k + k k 0 1 1 2 2 = 0 k2 k2 + k3 k3 0 0 k3 k3 + k4 u31 u41 Inputs: [M], {u1}, w1 IVP Output: [K] 18 ٩
Damage detection of the 2-D platform: (Shear structural model) 19 Inputs: Undamaged: Damaged: 20 ١٠
Damage detection of the 2-D platform: (Shear structural model) 29.5% in braces By considering rotational DoF: (Real case) 17% Estimated damage of level 2 23.5% in braces 21 2-D platform: (flexural structural model) 22 ١١
A1 B1 T B1 [ B] k1 k1 0 0 m1 mm 1 2 k1 k1+ k2 k 2 B2 0 mm m 1 2 2 mm 2 3 = k2 k2 + k3 k 3 0 T mm m 2 3 3 mm 3 4 k3 k3 k + 4 0 0 A3 mm m 3 4 4 A2 B2 B3T B3 A4 23 [ B] [ A1] [ B1] [ 0] [ 0] T [ B1] [ A2] [ B2] [ 0] T [ 0] [ B2] [ A3] [ B3] T [ 0] [ 0] [ B ] [ A ] = 3 4 24 ١٢
2-D platform: (flexural structural model) Mode #1 Mode #2 25 Lateral stiffness of undamaged 2-D platform: (flexural structural model) Elevation number 1 2 3 4 stiffness symbol kx 1 kx 2 kx 3 kx 4 Direct solution (10 6 N/m) 600.4 300.4 262.9 767.2 Inverse solution (10 6 N/m) 594.2 304.8 266.8 766.0 Absolute error (%) 1.0-1.4-1.5 0.2 Damage detection of 2-D platform by two modes: (flexural structural model) Elevation stiffness Undamaged Damaged Estimated damage Relative error number symbol (10 6 N/m) (10 6 N/m) (%) (%) 1 kx 1 594.2 612.9-3.1 3.1 2 kx 2 304.8 219.4 28.0 31.1% in 0.9 3 kx 3 266.8 266.5 0.1 braces 0.1 4 kx 4 766.0 771.0-0.6 0.6 26 ١٣
3-D platform: (shear structural model) 27 A1 B1 B1 T A2 T B2 B2 A3 B3T B3 A4 28 28 ١۴
29 Mode #1 Mode #2 Mode #3 30 ١۵
Damage detection of 3-D platform: (shear structural model) ky 1 ky 2 ky 3 ky 4 Estimated Relative Elevation stiffness Undamaged ex ey Damaged ex ey damage error number symbol (10 6 N/m) (m) (m) (10 6 N/m) (m) (m) (%) (%) kx 1 1137.6 1141.0-0.3 0.3 1 1062.2 0-0.57 1061.9 0-0.57 0 0 k 1 252369.0 248472.9 1.5 1.5 kx 2 553.0 471.4 14.8 29.7% 0.1 in 2 730.5 0 0.74 730.3 0 2.37 0 braces 0 k 2 161158.1 148540.2 7.8 1.4 kx 3 482.0 480.9 0.2 0.2 3 508.8 0-0.61 508.0 0-0.43 0.2 0.2 k 3 179655.2 177094.5 1.4 1.4 kx 4 1416.4 1406.7 0.7 0.7 4 1046.3 0 0.30 1048.8 0 0-0.2 0.2 k 4 467053.0 484918.6-3.8 3.8 31 Damage detection of 3-D platform: ky 1 ky 2 ky 3 ky 4 Estimated Relative Elevation stiffness Undamaged ex ey Damaged ex ey damage error number symbol (10 6 N/m) (m) (m) (10 6 N/m) (m) (m) (%) (%) kx 1 307.9 308.8-0.3 0.3 1 319.2 0-0.63 317.6 0-0.76 0.5 0.5 k 1 230796.5 226881.2 1.7 1.7 kx 2 280.0 256.7 8.3 22.9% 2.6 in 2 333.9 0-2.40 333.2 0-0.58 0.2 braces 0.2 k 2 152646.5 145427.2 4.7 1.4 kx 3 261.3 257.7 1.4 1.4 3 379.2 0 5.06 379.8 0 4.75-0.2 0.2 k 3 169867.6 178217.1-4.9 4.9 kx 4 1455.9 1436.6 1.3 1.3 4 1159.6 0-6.60 1157.3 0-6.40 0.2 0.2 k 4 477693.5 472603.4 1.1 1.1 32 ١۶
Uncertainty analysis: 33 error range: 10% μ=28.1% σ=7.4% 80% 20-38% 34 ١٧
error range: 5% μ=28.3% σ=3.8% 80% 24-34% 35 error range: 2% 36 ١٨
error range: 1% 37 Probabilistic Sensitivity: Sensitivity Δdamage = = 2.25 Δerror of acc. 38 ١٩
Conclusion: 2-D platform: (shear structural model) 1 mode 2-D platform: (flexural structural model) 2 modes 3-D platform: (shear structural model) 3 modes Uncertainty analysis 39 Thanks for your attention 40 ٢٠