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

٠٩ / ٠۴ / ١۴٣۶ 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 University of Technology Civil Engineering Department 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

٠٩ / ٠۴ / ١۴٣۶ Sharif University of Technology Civil Engineering Department Introduction Motivation Inverse Vibration Problem Conclusion Offshore jacket platforms: 3 Sharif University of Technology Civil Engineering Department Introduction Motivation Inverse Vibration Problem Conclusion 4 ٢

٠٩ / ٠۴ / ١۴٣۶ Sharif University of Technology Civil Engineering Department Introduction Motivation Inverse Vibration Problem Conclusion 5 Sharif University of Technology Civil Engineering Department Introduction Motivation Inverse Vibration Problem Conclusion 6 ٣

٠٩ / ٠۴ / ١۴٣۶ Sharif University of Technology Civil Engineering Department Introduction Motivation Inverse Vibration Problem Conclusion Inspection: 7 Sharif University of Technology Civil Engineering Department Introduction Motivation Inverse Vibration Problem Conclusion Structural Health Monitoring (SHM): 1- Damage detection 2- Damage localization 3- Damage quantification 4- Damage diagnosis 5- Damage Prognosis 8 ۴

٠٩ / ٠۴ / ١۴٣۶ Sharif University of Technology Civil Engineering Department Introduction Motivation Inverse Vibration Problem Conclusion Motivation: (Damage detection methods) Experimental Modal Analysis (EMA) Forced excitation Operational Modal Analysis (OMA) Ambient excitation 9 Sharif University of Technology Civil Engineering Department Introduction Motivation Inverse Vibration Problem Conclusion Inverse Vibration Problem:(IVP) , M K : → ω ϕ , Direct solution , : ω ϕ → , Inverse solution M K , : ω ϕ → , IVP M K n n 10 ۵

٠٩ / ٠۴ / ١۴٣۶ Sharif University of Technology Civil Engineering Department Introduction Motivation Inverse Vibration Problem Conclusion Input Output Phase 1 Phase 1 u,w K IVP M Phase 2 Phase 2 u,w K Phase 1 K SHM Damage estimation Phase 2 K 11 Sharif University of Technology Civil Engineering Department Introduction Motivation Inverse Vibration Problem Conclusion Formulation: [ ] [ ] ( ) 0 − λ φ = (1) K M i i [ ] [ ][ ] T (2) M = L L 1/2   [ ] [ ] T [ ] 1/2 , 1/2 ,..., 1/2 = = =   (3) L L M diag m m m 1 2 N 1 { } [ ] { }  { } [ ] { } − = φ φ = (4) u L L u 1 1 1 1 [ ] [ ][ ] { } − − [ ] [ − ] [ ] { } − 0 − λ = (5) L K L u L M L u 1/2 1/2 1/2 1/2 − [ ] [ − − [ ] [ − [ ] ] { } [ ] ] { } K = λ M M M u M M u (6) [ I ] [B] 12 ۶

٠٩ / ٠۴ / ١۴٣۶ Sharif University of Technology Civil Engineering Department Introduction Motivation Inverse Vibration Problem Conclusion [ ] =   { } { }  1 ,..., (7) U u u  n [ ][ ] [ ][ ] = Λ B U U (8) 13 Sharif University of Technology Civil Engineering Department Introduction Motivation Inverse Vibration Problem Conclusion Shear building: IVP Inputs: [M], {u1}, w1 Output: [K] 14 ٧

٠٩ / ٠۴ / ١۴٣۶ Sharif University of Technology Civil Engineering Department Introduction Motivation Inverse Vibration Problem Conclusion [ ] [ ] [ ][ ] Λ B U = U 15 Sharif University of Technology Civil Engineering Department Introduction Motivation Inverse Vibration Problem Conclusion SPD2 Platform: 16 ٨

٠٩ / ٠۴ / ١۴٣۶ Sharif University of Technology Civil Engineering Department Introduction Motivation Inverse Vibration Problem Conclusion Modeling: 17 Sharif University of Technology Civil Engineering Department Introduction Motivation Inverse Vibration Problem Conclusion 2-D platform: (Shear structural model)  0 0 0  m w1 1   u11 0 0 0 m m1,k1   =  2 [ ] M  0 0 0 m 3   0 0 0  m  u21 m2,k2 4  0 0  − k k 1 1   u31 m3,k3 0 − + − k k k k   =  [ ] 1 1 2 2 K  0 − + − k k k k 2 2 3 3   0 0  − +  k k k u41 3 3 4 m4,k4 IVP Inputs: [M], {u1}, w1 Output: [K] 18 ٩

٠٩ / ٠۴ / ١۴٣۶ Sharif University of Technology Civil Engineering Department Introduction Motivation Inverse Vibration Problem Conclusion Damage detection of the 2-D platform: (Shear structural model) 19 Sharif University of Technology Civil Engineering Department Introduction Motivation Inverse Vibration Problem Conclusion Inputs: Undamaged: Damaged: 20 ١٠

٠٩ / ٠۴ / ١۴٣۶ Sharif University of Technology Civil Engineering Department Introduction Motivation Inverse Vibration Problem Conclusion Damage detection of the 2-D platform: (Shear structural model) 29.5% in braces By considering rotational DoF: 17% 23.5% in braces (Real case) Estimated damage of level 2 21 Sharif University of Technology Civil Engineering Department Introduction Motivation Inverse Vibration Problem Conclusion 2-D platform: (flexural structural model) 22 ١١

٠٩ / ٠۴ / ١۴٣۶ Sharif University of Technology Civil Engineering Department Introduction Motivation Inverse Vibration Problem Conclusion A1 B1   − k k T 1 1 0 0   m m m   B1 B2 A2 1 1 2   − + − k k k k 1 1 2 2 0   m  m m m m  2 1 2 2 3 [ ] =  B  T − + − k k k k   0 2 2 3 3   m m m m m B3 B2 A3 3 2 3 3 4   − + k k k   0 0 3 3 4   m  m m  4 3 4 T B3 A4 23 Sharif University of Technology Civil Engineering Department Introduction Motivation Inverse Vibration Problem Conclusion   [ ] [ ] [ ] [ ] 0 0 A B 1 1   [ ] T [ ] [ ] [ ]  0  B A B 1 2 2 =  [ ]  B [ ] [ ] T [ ] [ ] 0   B A B 2 3 3   [ ] [ ] [ ] T [ ] 0 0  B A  3 4 24 ١٢

٠٩ / ٠۴ / ١۴٣۶ Sharif University of Technology Civil Engineering Department Introduction Motivation Inverse Vibration Problem Conclusion 2-D platform: (flexural structural model) Mode #1 Mode #2 25 Sharif University of Technology Civil Engineering Department Introduction Motivation Inverse Vibration Problem Conclusion Lateral stiffness of undamaged 2-D platform: (flexural structural model) stiffness Elevation Direct solution Inverse solution Absolute error (10 6 N/m) (10 6 N/m) number symbol (%) 1 kx 1 600.4 594.2 1.0 2 kx 2 300.4 304.8 -1.4 kx 3 262.9 266.8 -1.5 3 4 kx 4 767.2 766.0 0.2 Damage detection of 2-D platform by two modes: (flexural structural model) stiffness Elevation Undamaged Damaged Estimated damage Relative error (10 6 N/m) (10 6 N/m) number symbol (%) (%) 1 kx 1 594.2 612.9 -3.1 3.1 kx 2 304.8 219.4 28.0 0.9 2 31.1% in braces 3 kx 3 266.8 266.5 0.1 0.1 kx 4 766.0 771.0 -0.6 0.6 4 26 ١٣

٠٩ / ٠۴ / ١۴٣۶ Sharif University of Technology Civil Engineering Department Introduction Motivation Inverse Vibration Problem Conclusion 3-D platform: (shear structural model) 27 Sharif University of Technology Civil Engineering Department Introduction Motivation Inverse Vibration Problem Conclusion B1 A1 T B2 A2 B1 T B2 B3 A3 T B3 A4 28 28 ١۴

٠٩ / ٠۴ / ١۴٣۶ Sharif University of Technology Civil Engineering Department Introduction Motivation Inverse Vibration Problem Conclusion 29 Sharif University of Technology Civil Engineering Department Introduction Motivation Inverse Vibration Problem Conclusion Mode #1 Mode #2 Mode #3 30 ١۵