Research on analytical method of fatigue characteristics of Soft Yoke Mooring System based on full-scale measurement

By focusing on the vulnerability of the structure of marine equipments, together with considering the randomness of meta-ocean load in statistics, a kind of analytical method of fatigue characteristics of marine structure based on full-scale and actual measurement of prototype is proposed. On the basis of short-term field measurement results of structural response, research is carried out on the fatigue analysis of hinge joints at the upper part of the Soft Yoke single point Mooring System (SYMS) by simultaneously monitoring the environmental load and considering the design criteria of offshore structure. Through analysis of finite element modeling, the time-histories of typical stress response are obtained, and then the assessment of fatigue damage at key hinge joints is conducted. The simulation results indicate that the proposed method can accurately analyze the fatigue damage of offshore engineering structure caused by the effect of wave load. The present analytical method of fatigue characteristics can be extended on other offshore engineering structures subjected to meta-ocean load.


Introductions
FPSO has been widely used in the world's marine petroleum exploitation. It has no power system itself, and generally uses mooring system as its position-keeping device to ensure its operation in a certain area. The Soft Yoke single point Mooring System (SYMS) guarantees the effect of weathervane of FPSO by the above water multi-hinge joint connection mode.
Compared with other single point mooring systems like internal turret and external turret (Subrata, 2005), the SYMS has significant technical advantages as below. It can realize the separation between the hull (floater) and moored structure, and the multi-purpose mooring system can be applied in other FPSO by adjusting the ballista. It achieves convenient disassembly of the overall and local components of the mooring system through the way of hinging, and thus the SYMS can be used for many times in different sea areas. It breaks through the limitation of combinational design of the moored structure and floater, and improves universality in shallow water. Hence, the soft yoke mooring system has received great attention from the international petroleum com-panies. Multiple hinge mode soft yoke mooring system has been regarded as the best single point mooring system in shallow zone, and applied in the oil and gas exploitation in Bohai Bay of China.
Many scientific research institutions and universities have conducted researches on SYMS from the point of design of mooring system, dynamic response of soft yoke mooring system and capacity of mooring. Fan (1992) discussed the design procedure of the mechanical principle, system performance and key parameters of the soft yoke mooring system. Mamoun and Walter (2005) carried out hydrodynamic analysis of SYMS which developed by SBM company on the transport process of FLNG under extreme sea state. Günther et al. (2009) studied the mutually mechanical response between floater of LNG during serial docking by using newly defined soft yoke mooring system. Liu et al. (1994) studied the force analysis of the single point platform with opposite turret of three FPSOs equipped with soft yoke mooring system in Bohai Bay and established dynamic model of the fixed points of offshore jacket. Xiao et al. (2008Xiao et al. ( , 2014 established the system dynamic equation for the soft yoke mooring system in shallow water of the Bohai Bay by using analytical method of rigid multi-body dynamics. They calculated the mooring force under environmental loads including wind and wave, and conducted contrastive analysis with the model test. Fan et al. (2014) and Wu et al. (2016) have developed the full-scale monitoring system of soft yoke mooring system, and started field monitoring of the response, position and posture of soft yoke, and environmental load from 2010. They further developed the numerical method of dynamic restore force based on Kane dynamic method on the basis of the full-scale monitoring information.
This article mainly analyzes the abnormal transverse swing behavior of the moored leg observed during the monitoring, and proposes that the transverse swing will cause fatigue of hinge joints at the upper part of moored leg. It further puts forward an analytical method of fatigue of upper hinge joints of soft yoke based on the full-scale monitoring information and designed sea conditions. By using finite element simulation of local hinge joints, the fatigue life of the hinge joints at the upper part is studied. The analysis results indicate that the fatigue life of the hinge joint does not meet the design notes and regular maintenance is needed for the hinge joints, to pay closely attention to the damage inside.

Full-scale monitoring of FPSO and analysis on transverse swing of moored leg
During the full-scale monitoring of FPSO, SYMS has performed well in a whole, but under certain sea conditions, transverse swing in a large angle happens at the moored legs, 20° at most. As shown in Fig. 2, ellipse curve between the left picture and right picture shows two moments of moored legs. It can be seen that the structure has obvious swing. Owing to the large transverse swing of the mooring system, the dynamic effect will increase the contact force on the hinge joints, and the alternating stress causes fatigue rupture of the whole moored structure so as to reduce its working life; secondly, the transverse swing of the soft yoke mooring system is coupled with the ship hull, and complicated motions of the massive structure will be caused, so as to result in the failure of movement functionality of the moored structure.
It has been concluded through the analysis on the characteristics of SYMS that the posture of the soft yoke mooring system depends on the amplitude of angle between the moored leg and soft yoke, and meanwhile, the restoring force of the mooring system is also directly related to the posture. In the full-scale measuring system on site, inclinometers are respectively arranged between the left and right moored leg and "A"-frame of soft yoke to measure variations of angle. The layout of instruments is indicated as in Fig. 3. Fig. 4 illustrates the time period curve of monitoring data of the transverse swing process of two moored legs. It can be seen that multi-frequency transverse swings exist between the two moored legs within the monitoring for one day, and the maximum amplitude is close to 19°.

Statistics of measured time of transverse swing of soft yoke
The full-scale measuring system was installed in the end of 2011, and has been operated for over 2 years so far. Statistics are conducted on the transverse swing behavior of the soft yoke system by selecting data of the whole 2012. The quantitative statistics of the transverse swing of SYMS have been conducted under different constant wave heights. Together by considering environmental conditions provided by  WU Wen-hua et al. China Ocean Eng., 2017, Vol. 31, No. 2, P. 230-237 231 numerical simulation and model test of SYMS, the wave scatter diagram in design for reference is indicated in Table 1.
The monitoring system of SYMS carries out real-time monitoring on the information of wave at the place where FPSO is located. A significant wave height is recorded every hour to obtain the wave scatter diagram within the year of 2012, as shown in Table 2.
Under different constant wave heights, the number of times of transverse swing of soft yoke system is shown in Tables 3 and 4. For the soft yoke mooring system studied in this article, the design working life is 15 years. According to the number of times of transverse swing within a year of statistics in Tables 3 and 4, wave scatter diagram in Table 1 and the measured wave scatter diagram in Table 2, the time of transverse swing of soft yoke within a cycle of 15 years can be Table 1 Wave scatter diagram   Tables 5 and 6. According to the statistic wave scatter diagram in design and monitoring period (Tables 1 and 2), we can obtain continuous distribution function f M (H s ) and f D (H s ) with the curing fitting toolbox (CFTOOL) in MATLAB, as shown in Fig. 5.
During monitoring period, the global transverse swing number n α under certain swing angle α is written as the summation form according to different wave height H s .
in which H max is the maximum wave height. Eq. (1) can be rewritten as: where t α (H s ) is the time period with α, the swing angle un-der certain wave height H s .
is the swing number with α in unit time.

Considering
, we can obtain the relation of n α in the integral form of the wave height as follows: n α Then, the global transverse swing number within the design period (15 years) with the swing angle α can be written as the similar form according to different wave height H s .
in which, t D is the design period, and t M is the monitoring period.
It can be concluded from Tables 3-6 that the transverse swing of soft yoke belongs to the high-frequency vibration. The number of times of transverse swing in the designed life exceeds 0.28 million times, and the swing in high frequency accounts for a larger proportion. Hence, the research on fatigue behavior of the key hinge joints caused by transverse swing is crucial and necessary.  soft yoke mooring system circles the hinge joint marked as "Eye" at the upper part.
Because of the interaction between the hinge and axle, finite element modeling is conducted on the global mooring leg system. During the simulation process, the balance weight of ballast is treated as the concentrated mass; since the distribution of internal stress of hinge joints is specially considered, the deformation of moored leg is neglected, and the central part of the moored leg is assumed as a rigid body. Fig. 7 shows the finite element model of the moored leg, and Fig. 8 indicates the model of the detail part of the upper hinge joints.
About the defined material properties, elasticity modulus E is 210 GPa, Poisson's ratio μ is 0.3, and density ρ is 7.8×10 3 kg/m 3 . Friction exists between the hinge and axle in the middle, and the friction coefficient is defined as 0.15 according to the design documents. As for the mesh division, since we mainly focus on the influence of transverse swing   WU Wen-hua et al. China Ocean Eng., 2017, Vol. 31, No. 2, P. 230-237 235 on the upper hinge joints, the mesh refinement shall be conducted on the upper hinge joints. Hinge and the axle in the middle are the key objects for us to watch out. Divided into 91792 units by using C3D8R unit simulation, the model of the joint part between the hinge and the moored leg is complicated, and it is hard to divide the mesh into C3D8R unit, and it is also not the key part to care about, so C3D4 is to be divided into 95840 units (SIMULIA, 2013). Fig. 9 indicates the finite element mesh distribution of the upper hinge joints. Boundary conditions: Define the boundary conditions for the fixed bearing at interfaces at both ends of the axle.
Loading definition: Gravity is added at first; after adding gravity on the whole model, impose the specified revolving on the whole hinge joint to simulate the transverse swing of the soft yoke mooring system. Time-history of the movement is a cycle, and the swing starts from the lowest point. According to the measured statistic analysis of data, the degree of transverse is from 1° to 19°. Carry out dynamic simulation respectively for different degrees of the transverse swing. The stress nephogram of the hinge with the degree of transverse 19° is shown in Fig. 10.

Fatigue analysis of hinge joint
Analyze the time-history of stress of the hinge joint under different tilt angles to achieve stress amplitude and mean stress. According to the computational formula of equivalent stress, in which σ m is the mean stress, σ b is the yield stress, and σ a is the stress amplitude. Then the equivalent stress σ e of the hinge joint can be obtained, as indicated in Table 7.     According to the relevant design information, S-N curve of the hinge is indicated in Fig. 11. By comparing Table 7 and Fig. 11, and the time of transverse swing of hinge joints within 15 years through statistics, the results of fatigue damage of the hinge can be obtained, as shown in Table 8.
It can be known from the data analysis in Table 8 that the overall damage ratio of the upper hinge joint within the designed 15 years reaches 0.57. Design specifications point out that the design safety factor of the hinge is 2, so it can be regarded that the design of the hinge is dangerous to some extent during the design process of soft yoke system for not fully considering the influence of the transverse swing.

Conclusion
Aiming at the transverse swing of the soft yoke single point mooring system, a new-type analytical method for fatigue damage is proposed in this article. By establishing full-scale monitoring system of the upper hinge joint of the moored leg and ocean-environmental parameters, the periodic monitoring parameter and marine environmental parameters of the full-scale structural response are obtained. By considering the marine environment design guides, the overall structural response of the concerned joint within the designed life is simulated. Finite element modeling is carried out on the upper hinge joints of the concerned moored leg, and the time-history of equivalent stress within a single cycle is obtained. Based on the corresponding fatigue theory and fatigue life analysis method, the fatigue life and degree of structural damage of the upper joint connection are calculated. Through the analysis by the proposed method, it has been found that the fatigue design of the concerned hinge joint is dangerous to some extent, and the maintenance of soft yoke mooring system and vibration absorption designing should be the key content of further research.