Structural health monitoring of offshore jacket platforms by inverse vibration problem. M. T. Nikoukalam On behalf of Kiarash M.

Transcription

1 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

2 Offshore jacket platforms: 3 4 ٢

3 5 6 ٣

4 Inspection: 7 Structural Health Monitoring (SHM): 1- Damage detection 2- Damage localization 3- Damage quantification 4- Damage diagnosis 5- Damage Prognosis 8 ۴

5 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

6 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

7 [ U] { u} { u } =,..., 1 n (7) [ B][ U] = [ U][ Λ] (8) 13 Shear building: Inputs: [M], {u1}, w1 IVP Output: [K] 14 ٧

8 [ B][ U] = [ U][ Λ] 15 SPD2 Platform: 16 ٨

9 Modeling: 17 2-D platform: (Shear structural model) m1,k1 m2,k2 [ M ] m m = 0 0 m m4 w1 u11 u21 m3,k3 K m4,k4 [ ] k1 k1 0 0 k k + k k = 0 k2 k2 + k3 k3 0 0 k3 k3 + k4 u31 u41 Inputs: [M], {u1}, w1 IVP Output: [K] 18 ٩

10 Damage detection of the 2-D platform: (Shear structural model) 19 Inputs: Undamaged: Damaged: 20 ١٠

11 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 % in braces 21 2-D platform: (flexural structural model) 22 ١١

12 A1 B1 T B1 [ B] k1 k1 0 0 m1 mm 1 2 k1 k1+ k2 k 2 B2 0 mm m mm 2 3 = k2 k2 + k3 k 3 0 T mm m mm 3 4 k3 k3 k A3 mm m 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 ] = ١٢

13 2-D platform: (flexural structural model) Mode #1 Mode #2 25 Lateral stiffness of undamaged 2-D platform: (flexural structural model) Elevation number stiffness symbol kx 1 kx 2 kx 3 kx 4 Direct solution (10 6 N/m) Inverse solution (10 6 N/m) Absolute error (%) 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 kx % in kx braces kx ١٣

14 3-D platform: (shear structural model) 27 A1 B1 B1 T A2 T B2 B2 A3 B3T B3 A ١۴

15 29 Mode #1 Mode #2 Mode #3 30 ١۵

16 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 k kx % 0.1 in braces 0 k kx k kx k 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 k kx % 2.6 in braces 0.2 k kx k kx k ١۶

17 Uncertainty analysis: 33 error range: 10% μ=28.1% σ=7.4% 80% 20-38% 34 ١٧

18 error range: 5% μ=28.3% σ=3.8% 80% 24-34% 35 error range: 2% 36 ١٨

19 error range: 1% 37 Probabilistic Sensitivity: Sensitivity Δdamage = = 2.25 Δerror of acc. 38 ١٩

20 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