Damage Detection in Offshore Platform Structures under Environmental Loads Using Modal Strain Energy

Damage Detection in Offshore Platform Structures under Environmental Loads Using Modal Strain Energy Method Guijie Liu1, Jianbo Jiao*2, Ruilin Jiang3 Shandong Provincial Key Laboratory of Ocean Engineering, Ocean University of China, Qingdao 266100, China China Ocean Oilfield Services Limited, Beijing 101149, China

1,2 3

liuguijie039@163.com; *2jianbojiao@live.com; 3jiangruilin@126.com

1

Abstract A damage detection and severity estimation method for jacket offshore platform under environmental loads using modal strain energy method is presented in this paper. This method is different from former localization ones which need complete modal parameters after the damage occurring. It is remarkable because of its ability to diagnose platform health conditions within only a few amounts of identified natural frequencies and limited modal shapes from the damaged structure. First of all, a study of environmental conditions and environmental loads is introduced to expound how the wind, wave and current effect on the structure. After the theoretical derivation of modal strain energy method and the algorithm analysis, a Bohai Bay offshore platform model is demonstrated in the numerical examples, and the final results indicate that an excellent updating is achievable by applying the new method. Keywords Jacket Offshore Platform; Damage Detection; Healthy Diagnose; Environmental Loads; Modal Strain Energy Method

measurable dynamic parameters in turn could be used for damage localization and quantification. Natural frequencies are the most accessible among these parameters which could be obtained accurately from the time response record of a single sensor arranged any location in the structure. However, in some occasion only the information from frequencies is not sufficient, particularly when the structures are geometrically symmetry. Mode shapes are helpful to solve the issue, but still some considerations should be noted. One problem is the dimensional structure mode shapes are incomplete; the other rub is matching between natural frequencies and mode shapes. This paper’s objective is an improved damage localization method for offshore platforms under environmental loads during the damage develops from micro fracture to macro broken crackle using the modal strain energy method (A.G. Madhavarao et al., 2004.) The approach is expected to detect damage to specific element in 3D platform model. Environmental Conditions and Loads

Introduction Offshore platforms accumulate damage during their service life on account of the influence of various environmental loads. Obviously the techniques for damage detection and localization are very considerable to avoiding the occurrence of a fatal accident caused by the structural failure of platform structural. In the past few decades, several approaches to damage detection methods have been studied to damage detection methods based on vibration techniques. Since the structures weakeness will lead to the variety of system mass and/or stiffness distribution, the modal properties of platform system (such as natural frequencies, damping ratios, and mode shapes) will alter as well. Meantime these

Wind loads on offshore platform structures can be evaluated using the model approaches adopted for land‐based structures but still a distinction here is that an open sea presents a lower category of roughness to the free‐stream wind, which leads to a more slowly varying mean wind profile with height and to lower levels of turbulence intensity than encountered on land. As a consequence, wind speed values at the same height above still water level (for offshore conditions) as those above ground level (for land‐ based structures) for nominal storm conditions, tend to be stronger and lead to higher wind loads. The wind drag force exerted on a bluff body (e.g. such as the exposed frontal deck area of an offshore oil rig),

28 Guijie Liu, Jianbo Jiao, Ruilin Jiang

by turbulent wind pressure effects can be evaluated from: ·

· ·

·

drag coefficients for the individual cylinder may be used.

(1)

Where is the density of air (1.2 kg/m3), is the is the shape exposed area of the bluff body, coefficient associated with the body geometry, is the height coefficient associated with the height from sea surface and is the design wind speed at the location of the bluff body (Zhang Zenghai et al., 2011.) The wave loads experienced by offshore structural elements depend upon their geometry, (the sizes of these elements are relative to the wavelength and their orientation to the wave propagation), the hydrodynamic conditions and whether the structural system is compliant or rigid. Structural elements that are large enough to deflect the impinging wave (diameter to wavelength ratio, D/L>0.2) undergo loading in the diffraction regime, whereas smaller, much slender, structural elements are subject to loading in the Morison regime (Nakatsuji et al., 2003.) The along wave or in‐line force per unit length acting on the submerged section of a rigid vertical surface‐ piercing cylinder,fromthe interaction of the wave kinematics at a certain position from sea floor, isgiven by Morison’s equation, via: ·

·

· | | · (2)

·

· (3)

Where and represent the inertia and drag force contributions respectively, and are the inertia and drag force coefficients respectively, is the density of sea water and is the cylinder diameter, and are the velocity and acceleration of water particle normal to the member. When using Morisonʹs equation to calculate the hydrodynamic loads on a structure, one should preferably take into account the variation of as function of Reynoldʹs number, the Keulegan‐Carpenter number ( ) and the roughness number in addition to the variation of cross‐sectional geometry. For split tube chords (Jack‐up leg chords) the hydrodynamic coefficients may, in lieu of more detailed information be taken in accordance with Figure 1 and corresponding formulae, as appropriate. For several cylinders close together, group effects may be taken into account. If no adequate documentation of group effects for the specific case is available, the

FIGURE 1. TYPICAL

VALUES FOR SPLIT TUBE CHORD.

Ocean current is generally simplified as steady stationary flow in construction practice and only drag force is exerted on the platform structures, therefore the force of current could be calculated as a resistance which is directly proportional to the kinetic energy. ·

·

(4)

Where is the velocity of ocean current, and other parameters are same as Eq. 2, for the wave and current are simultaneous occasion, the total fluid drag force could be given: ·

·

(5)

The drag coefficient for steady current is equal to the asymptotic value for is equal to infinity. For combined wave and current action, the increase of due to the current may be taken into account. A number of regular wave & current coupling theories have been developed to describe the water particle kinematics associated with ocean waves of varying degrees of complexity and levels of acceptance by the offshore engineering community. These would include linear or Airy wave theory, Stokes second and other higher order theories. The rather confused irregular sea state associated with storm conditions in an ocean environment is often modeled as a superposition of a number of Airy wavelets of varying amplitude, wavelength, phase and direction, consistent with the conditions at the site of interest. The current induced drag forces are to be determined in combination with the wave forces. This may be done by vector addition of wave and current induced particle velocities. If available, computations of the total particle velocities and accelerations based on more exact theories of wave/current will be preferred. For frame structures, the current may be reduced due to interference from the structure on the flow field of

Damage Detection in Offshore Platform Structures under Environmental Loads Using Modal Strain Energy Method 29

the current.

∑

Modal Strain Method In the certain numerical model, a differential vibration equation could be utilized to describe the undamaged system with theoretical information as:

When m modes are available for the healthy structure and damaged structure, then m equations could be formed from Equation 12. Written in a matrix form, one has: α

(6) Where K and M are the stiffness and the mass matrix, and are ith eigenvalue and eigenvector(Z. Y. Shi. et al., 1998). A mark “*” is added to the equation above to denote damaged system with measured values as:

. In order to associate them and eliminate the and matrix M, two matrixes multiplied by these two equations:

should be pre‐

(9) Combined with equations 6 and 7 and considered the symmetry of mass and stiffness matrices which would be obtained is: (10) For finite element analysis, the damage locations are supposed already known, K could be written as an accumulation of continuous decreases as: ∑

(11)

Where is the amount of the damaged members, and and are damaged extent and stiffness matrix of nth element. The value of is from 0 to ‐1 which indicates the structure state from healthy to totally damaged (Wang Shuqing et al., 2013.) Introduce Equation 11 into Equation 10, one obtains: ∑

α

1

(12)

Define the structural modal strain energy between the baseline structure and the damaged structure for ith mode, as , and the corresponding elemental strain energy for the stiffness matrix , as . Then / for short, , equation 12 could be simplified as:

(15)

The damage severity can be estimated iteratively as follows. Step 1: Assume the damage severity to be zeros 0 . Then compute the damaged initially, i.e. mode shapes yields

(8)

(14)

matrix, and α and are column In which E is a vectors of size and m, respectively. When m is greater than or equal to , a least‐squares approach can be taken to solve for α. The estimate of α, denoted asα, is written as:

(7) It is assumed the individual initial local damage would bring about stiffness matrix loss within little change for mess matrix (Ahmed A. et al., 2009), that is

(13)

,

.

Step 2: Solve Equation 15 for the estimated damage using the computed mode shapes . severity The first iteration for estimating the damage severity is finished. by Step 3: Compute the damaged mode shapes , and using the estimated damage severity via Equation 15 by estimate the damage severity using

for k=2,3,..., sequentially.

Step 4: Set the condition of iteration termination. Repeat step 3 until max where tol is a pre‐determinate threshold (S. A. HSU et al., 2008.).For example, one can set tol to be 0.001, 0.005, or 0.01, it is up to the precision of the severity estimation. Numerical Analysis of Structure Model In this numerical study, the new proposed damage assessment method will be illustrated and verified on an offshore platform structure, as shown in Figure 2 in finite element analysis software ANSYS. This structure consists of 44 steel tubular members (without two decks) that comprise 24 vertical pile members, 16 horizontal beam members and 20 slanted brace members. The finite element model is taken as the undamaged baseline model. For facilitating the following presentation, each structural member of the offshore platform is distinguished by assigning a unique number from L1 to L44. Two layers of decks concern the building of steel I‐Beam frameworks and

30 Guijie Liu, Jianbo Jiao, Ruilin Jiang

separately. It is obvious that wind is not the only factor who acts on the platform so the current remote force acting on the jacket platform legs are is 1351.4N; the current force is from NW direction and is same all around the year because of steady current phenomena, on other hand wave remote force is 122081.5N; the wave force is from NW direction but keeps changing position all around the year. Remote forces are considered to be acting on the platform because some parts of the platform are complex and complicated to determine forces reaction.

plate iron.

FIGURE 2. FINITE ELEMENT WIRE FRAME MODAL. TABLE. 1 ENVIRONMENTAL CONDITIONS OF BOHAI BAY

Mean wind velocity all year [m/sec]

6.5

Wind direction (average)

NNW

Depth of water [m]

32

Wave height [m]

7.8

Time period of wave [sec]

3.8

Wave direction (average)

NW

Current velocity (surface) [m/sec]

2.35

Current velocity (medium depth) [m/sec]

1.96

Current velocity (sea floor) [m/sec]

1.6

Current direction(average)

NW

This is a simplified model of a real existed platform in Bohai Bay, the environmental condition is given by Table 1 (OuJinping et al., 2011.).Through the early analysis about loading, cases have been found if the incident angel of acting waves accedes 52 degrees. The wind force acting on the deck area is 1289.6N and atmospheric pressure is 23.884MPa, at the wind direction NNW. Vice versa wind force acting on the legs of the platforms jacket are 39.5N excluding shield factor (η) because the direction of the wind makes a certain angel so the forces strike on each leg

FIGURE 3. NODAL FATIGUE DAMAGE RESULT.

The fatigue damage result of different loads combination in Figure 3 shows that the most severely damaged part is the slanted member L33. With the stiffness loss of this member, the results of damage localizationare shown in Figure 4 when the first and / or second modal parameters are considered in algorithm respectively. The top panel of Figure 4 is the damage indicator when only the first mode shape is utilized, which shows that damage is correctly located. When only the second mode shape is taken, the damage indicator in the middle panel of Figure 4 illustrates that the second mode shapehas no help for the damage localization. The reason is the structure is symmetric geometric and the damaged member (L33) is located in the short span direction and the damage only has effects on the first mode. As the bottom panel of Figure 4 shows, the damage indicator obtains a correct result when both the first and second mode

Damagge Detection in Offshore Platfoorm Structures under Environ nmental Loads U Using Modal S Strain Energy M Method 31

mo odes) are hellpful as the result in Fiigure 5, on the con ntrary, modees that vibratte in the long g‐span directtion (2n nd modes in n this case) have little association, as sho own in Figurre 6. This is aattributed to the fact that the dam mage of a short‐span member cau uses negligiible cha ange for th he modes v vibrating in the long‐sp pan direction.

shaapes are takeen into accou unt.

FIG GURE 4. DAMA AGE LOCALIZATION USING G MODAL SHAP PES

FIGURE 6. DAM MAGE LOCALIZATION USIN NG 2ED MODAL L APES. SHA

onclusion Co

FIGURE 5. DA AMAGE LOCAL LIZATION USIN NG 1STMODAL L SHA APES

In this numeriical study, th his new metthod can cleaarly obtain the dam mage locatio on at memb ber L33. At the sam me time, th he damage severities of o member L33 asssociated with h each casee are estimatted and perrfect damage extentt (about 0.255 stiffness lo oss on mem mber L33) is achiev ved by usin ng the pressent procedu ure, wh hich could be b a wearing g sign beforre the comp plete breeakdown. On ne more thin ng which co ould not be ignored is that t both the firstt two modees should be b utilized for avo oiding falsse damage localizatio on when the oriientations of o damaged d members are unknown. Reesults from presented above indiccate that when w damaged mem mber (L33) is oriented d in short‐span dirrection,modees note thee short‐span n direction (1st

Thiis paper intrroduces a neew access to detect damage location and esstimate severrity of 3D offfshore platfo orm stru ucture under environmeental loads by b applying the mo odal strain energy. e Enviironmental loads l (staticc or dyn namic) are simplified as mean forces and momeents practice. Lo in engineering e oads caused by wind, wave and d current arre exerted o on finite elem ment modell in AN NSYS, and then t fatiguee damage result could be obttained, which h would hellp find dang gerous memb ber. Decreasing stifffness caused d by member damage would lead to divergeent structuree response, and a this mo odal stra ain energy method usees natural frrequencies and a onlly few minim mal modal sshapes from m measuremeent. Thee efficiency and robusttness have been b numerical inv vestigated by y 1st and/o or 2nd mod del shapes are utillized with th he offshore platform. Results R indiccate tha at the present modal straain energy m method is ablee to find d the exact location and d severity of o the damag ged elem ments. ACKNOWLEDGM MENT

32 Guijie Liu, Jianbo Jiao, Ruilin Jiang

This work was financially supported by the Natural Science Foundation of China 1600‐911221610 (51175485). REFERENCES

A.G. Madhava, “Handbook of Fatigue Crack Propagation in Metallic Structures.” In Structural Engineering Research Centre,edited by Madras D.S. Ramchandra Murthy and S. Seetharaman, IndiaAPI, 2004. Ahmed A. Elshafey, Mahmoud R. Haddara, H. Marzouk. “Dynamic Response of Offshore Jacket Structures under Random Loads.” Marine Structures 22(2009) : 504–521. Nakatsuji, K.Yamanaka, R.Liang, “Seasonal Change of BaroclinicCirculation and Water Exchange in the Bohai Sea.” 8th International Conference on Estuarine and Coastal Modeling, Singapore, 2003. OuJinping, DuanZhongdong, Xiao Yiqing,”Theory and Application of Safety Assessment for Offshore Platform Structures.” Science Press, Beijing, China, 2007. S. A. HSU, “Modals for Estimating Offshore Winds from Meteorological Measurements.” Marine Boundery Layer Meteorology, (2008) 20: 341‐351. Sun Dongchang, “Design and Research of Self‐elevating Offshore Platform.”Shanghai Jiao Tong University press, China, 2011. Wang Shuqing, Li Huajun, “Damage Detection in Offshore Platform Structures from Limited Modal Data.” Applied Ocean Research 41(2013): 48–56. Z. Y. Shi, S. S. Law, L. M. Zhang, “Structural Damage Localization from Modal Strain Energy Change.” Journal of Sound and Vibration(2008)218(5): 825–844. Zhang Zenghai, Zhao Wei, Cao Yuenan, “Wind Condition

Property in Bohai Bay Compared with Land Wind.”Marine forecast, vol.06 (2011): 8‐13. Guijie. Liu Professor in Ocean Unversity of China, born in Shandong China in August 1968.Northeastern University Ph.D. in mechanical engineering and automation (2003), Hefei University of TechnologyM.s. in mechanical design and theory (1993), Shandong Polytechnic UniversityB.s. in mechanical engineering (1990). His expertise is about autonomous underwater vehical technology and on‐line monitoring and diagnosis technology of the mechanical equipment and Ocean engineering structur damage. He workd in teaching Shandong Polytechnic University as assistant/lecturer/associate professor from 1993 to 2004. Then did post doctor work in water conservancy project and postdoctoral research station of Ocean University of China. Since 2004 he worked as associate professor/professor(2005) of Ocean University of China. “Study on the detecting data acquisition system for sea bed oil & gas pipe‐line”, Chinese Journal of Scientific Instrument, 2006, Vol.27 (nS):421(EI included). Prof. Liu is the committee member of Abrasive Technology Committee of Chinese Mechanical Engineering Society, Important member of the Chinese Mechanical Engineering Society and the chief expert of Qingdao underwater oil spill detection robot experts workstations. Won Third Award of Natural Science Outstanding Achievements Prize, Shandong Province in 2003 and Second Award of Natural Science Outstanding Achievements Prize, Shandong Province in 2008. Jianbo. Jiao postgraduate in Ocean Unversity of China, major in mechanical engineering. Jiao Acquired B.s. in Shandong University of Technology inmechanical design and its automation in 2012. Ruilin. Jiang senior engineer in technical department of China Ocean Oilfield Services Limited and senior expert in marine engineering.

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