Lateral vibration behavior analysis and TLD vibration absorption design of the soft yoke single-point mooring system

Mooring system is the key equipment of FPSO safe operation. The soft yoke mooring system is regarded as one of the best shallow water mooring strategies and widely applied to the oil exploitation in the Bohai Bay in China and the Gulf of Mexico. Based on the analysis of numerous monitoring data obtained by the prototype monitoring system of one FPSO in the Bohai Bay, the on-site lateral vibration behaviors found on the site of the soft yoke subject to wave load were analyzed. ADAMS simulation and model experiment were utilized to analyze the soft yoke lateral vibration and it was determined that lateral vibration was resonance behaviors caused by wave excitation. On the basis of the soft yoke longitudinal restoring force being guaranteed, a TLD-based vibration damper system was constructed and the vibration reduction experiments with multi-tank space and multi-load conditions were developed. The experimental results demonstrated that the proposed TLD vibration reduction system can effectively reduce lateral vibration of soft yoke structures.


Introduction
FPSO has been widely applied to the world marine petroleum exploitation. Without its own dynamical system, it usually relies on the mooring system as a positioning device to guarantee the safety of operation in a fixed area. Soft yoke mooring system realizes FPSO weather vane effects by the multiple hinge points connection mode and it has been widely applied to oil and gas exploitation in the Bohai Bay in China and the Gulf of Mexico .
Compared with traditional internal and external turrets and other single point mooring systems, the soft yoke singlepoint mooring system owns obvious technological advantages. It can realize vessel (floater)-mooring (mooring system) separation, satisfying a set of the mooring system applicable to multiple ship-type structures. It can realize repeated applications of the mooring system in multiple sea areas, which makes it easy to disassemble the whole mooring and its local components by hinge points. Meanwhile, the above water mooring mode of the soft yoke system avoids the direct contact between components and sea water and the impacts of sea ice in ice regions, reduces the influences of environmental corrosion and lengthens the service life. Thus, the soft yoke mooring system has drawn wide con-cern from domestic and overseas oil and gas companies. Multi-hinge soft yoke mooring system is considered as the currently best single-point mooring form and has been applied to oil and gas exploitation in China's Bohai Bay.
Many colleges and scientific research institutions have conducted researches on the soft yoke mooring system from the point of the design of the mooring system, dynamic response of the soft yoke mooring system and capacity of mooring. Fan (1992) discussed the design flow of the working principle, the system performance and basic parameters of the soft yoke mooring system. Naciri et al. (2005) carried out hydrodynamic analysis on the transport process of FLNG in extreme sea environment, and the soft yoke mooring system developed by SBM Company. Clauss et al. (2009) studied the mutually mechanical response among floating bodies 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 3 FPSOs equipped with the soft yoke mooring system in the Bohai Bay and established dynamic model of the fixed points of offshore jacket. Xiao et al. (2007Xiao et al. ( , 2008 established the system dynamic equation for the soft yoke mooring system in shallow water of the Bohai Bay with the 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) developed the fullscale monitoring system of the soft yoke mooring system, and started field monitoring of the response, position and posture change of the soft yoke, and environmental load in the Bohai Bay on the mooring system of an FPSO from 2010, and they further developed the computing method of dynamic mooring force based on the Kane dynamic method on the basis of the full-scale monitoring information (Sun, 2014).
Based on information analysis of the prototype monitoring system of one FPSO soft yoke mooring system in China's Bohai Bay, this paper focuses on the study of abnormal lateral vibration behaviors of SYMs (Soft Yoke Mooring System) on combination with on-site monitoring information. By studies on the ADAMS simulation and model experiment, it was determined that the lateral vibration was due to resonance behaviors caused by wave frequency. A large-scale model experiment system is constructed with a 6-DOF motion simulator which simulates FPSO ship motion responses. Lateral vibration cycle and amplitude variations of SYMs were obtained under different floater motions. Furthermore, a TLD vibration reduction system was designed under the condition that mooring restoring force was guaranteed to be unchanged, and the experimental results show that it greatly reduced the soft yoke lateral vibration behaviors.

FPSO prototype monitoring system
The global dynamic response of SYMs is uncertain un-der the coupling actions of wind, wave and current load. Neither the hydrodynamics numerical analysis nor the model test can effectively obtain the true design criteria. The above problem brings risks to the mooring system and FPSO safe operation, therefore it is necessary to develop the on-site monitoring of ocean environmental load, FPSO motion responses, and mooring system restoring force. Since 2011, Dalian University of Technology has established the on-site FPSO prototype monitoring project in the Bohai Bay, including ocean environmental load information, FPSO floating body response information, soft yoke attitude, restoring force information, and mooring leg hotspot stress information. Long-term stable information monitoring is made on the platform. Table 1 provides each monitoring subsystem, monitoring information and sensor list. Fig. 2 shows the measuring points distribution of FPSO monitoring system sensor.
After the analysis of the monitoring information, the lateral vibration behaviors are found in the YOKE structure of the soft yoke system (shown in Fig. 3) and the significant lateral vibration might lead to the collision between the vessel and ballast tank of SYMs.
By a comprehensive analysis of the monitoring FPSO rolling data and lateral vibration data of SYMs, it is found that the amplitude of the soft yoke lateral vibration increases rapidly when the input excitation of FPSO is within the specific frequency range. When it goes beyond this range, the amplitude of the soft yoke lateral vibration becomes small. Fig. 4 shows the time-history curve of FPSO   rolling and the soft yoke yawing rate (Among them, the measured rolling angle by FPSO was small, so it was amplified by 20 times). It can be observed from Fig. 4 that even FPSO roll value was small (smaller than 0.5°), the lateral response amplitude of the mooring leg was still larger than 15°. It can be seen that within 200 s, both FPSO rolling and the soft yoke mooring system yawing moved for about 29 cycles, with approximate constant phase difference. Fig. 5 shows the time-history curve and spectrum analysis curve of the FPSO roll in 2012. It can be seen that the FPSO rolling response is concentrated near 0.14 Hz. It was the common behavior of the significant lateral vibration behaviors of SYMs. It can be seen from Table 2 that all significant lateral vibration behaviors were monitored within three time periods a day.
In Table 2, T YOKE is the YOKE lateral vibration spectrum peak period, and T FPSO is the FPSO roll spectrum peak period.
The significant lateral vibration amplitude may not only cause the collision between the vessel and the ballast tank but also influence the stability of the joint and thrust bearing at the upper part of the mooring leg. Owing to the increasing mooring leg tension, the upper hinge node friction increases, which brings a great danger to the hinge structural strength, fatigue and wear and may have influences on the platform security (Wu et al., 2015). Therefore, further studies should be performed on the mechanism of the soft yoke lateral amplitude vibration to avoid the destruction of the lateral vibration on the soft yoke and vessel structure, which is of great significance to improving the FPSO security and structural stability of the mooring system.

Simulation analysis of ADAMS-based soft yoke lateral vibration
The soft yoke mooring system is a complex multi-body dynamic system constituting of multiple hinged structures. ADAMS model was established and the lateral vibration behavior analysis was conducted on SYMs by considering multi-body dynamics characteristics.
In order to study the stress bearing situation of the upper hinge point, frequency sweeping experiments were made under different excitation driving frequencies ranging from 0.05 Hz to 0.30 Hz (increment equal to 0.05 Hz) with the angle amplitude of 1° step. The simulated period of each working case was 60 s. The curves in Fig. 7 respectively represent the stresses of the upper hinge points in x, y, and z axes. The coordinate axis is selected as the local coordinate    It can be seen that when the input excitation lateral load of FPSO is 0.15 Hz, a great lateral vibration is observed in the mooring system and the stress of the mooring legs increases significantly. The simulated results are consistent with the monitoring data analysis results.

Lateral frequency sweeping experiment of a large-scale
FPSO soft yoke mooring system To verify the numerical calculation results and analyze the lateral vibration mechanism of the soft yoke mooring system, the model experiments were developed on SYMs. 6-DOF motion simulator was utilized to establish the oneway excitation and multi-DOF coupling excitations of the FPSO vessel excitation including roll, pitch, yaw, sway, surge and heave.
The geometric similarity ratio between the model and its prototype is 1:16. As shown in Fig. 8, the ratio shrinking of the actual size of the soft yoke mooring system was conducted to guarantee that its center-of-gravity position was consistent with the original structure. Rolling frequency sweeping experiment was made on the model to verify the vibration mechanism of the mooring system. The vibration frequency was about 1/4 to that of the actual one due to the scaling of the mooring leg length is 1/16 actual size. On this basis, the experimental scheme was established and the frequency sweep parameter settings in the soft yoke model experiment are shown in Table 3.
In the experiment, the tilt sensors were installed at both sides of the ballast tank and angle variations represented the mooring legs vibration amplitude. Fig. 9 provides the inclination angle time-history curves under different frequencies.
It can be known that lateral vibration amplitude changed with the increase of load frequency. The vibration amplitude of the scaling model suddenly changed (as shown in Fig. 10) and reached the maximum under the frequency excitation of 0.52 Hz (the corresponding actual structure frequency was 0.13 Hz). The amplitude of the inclination angle was far larger than the amplitude of the input excitation.
Combined with the monitoring data, ADAMS simulation analysis and model experiment results, it can be found that SYMs at specific frequency excitation had a significant lateral vibration. This frequency fell at near 0.14 Hz. As  LYU Bai-cheng et al. China Ocean Eng., 2017, Vol. 31, No. 3, P. 284-290 287 shown in Table 4, the results of three analysis methods were approximated. It can be determined through the analysis that the significant lateral vibration of SYMs is due to the resonance behaviors caused by the FPSO rolling motion. The vessel rolling response is induced by wave load. Thus, it can be indirectly regarded that the lateral vibration of the soft yoke mooring structure is of resonance phenomena caused by wave load. The resonance phenomena may generate risks to the structure, so they should be avoided in constructional engineering, ocean engineering, etc. The vibration control design of resonance behaviors should comprehensively consider the characteristics of ocean engineering structures and the limitations of the soft yoke configurations.

Conceptual design of TLD control system
In general, a TLD (Tune Liquid Damper) is a certain shaped tank with liquid inside (Li and Ma, 1996). TLD is a type of effective device for the structural vibration reduction and has been widely applied in the design of marine structures (Roy and Ghosh, 2013;Li and Ma, 1997). According to various forms, it is the liquid in the container that has damping effects. The installation site of a TLD usually selects the one with large displacement. When the structure drives TLD to move, the liquid in the TLD has damping effects due to retardation (Dong et al., 2001). The inherent frequency of the liquid motion is determined by the liquid depth and height in the motion direction. By adjusting the consistency between the inherent frequencies of the liquid and the structure, best damping effects can be realized (Li et al., 1995). Soft yoke mooring system provides the restore force by a ballast tank. In the anti-vibration design, the transverse space between the ballast tank and tank water can be fully considered. When part of the ballast liquid is transferred to TLD, the position of the center-of-gravity of the whole mooring system is kept unchanged to guarantee the unchanged longitudinal mooring stiffness of the mooring structure.
The space distance between two-yoke ballast tanks is 18 m, so the lateral dimension of the TLD is preliminarily set 18 m. According to the expression of the TLD system's natural frequency at different water depths, deep water theory can be adopted (Eq. (3)) as the ratio of the liquid depth to the length in the motion direction is larger than 1/8, and the shallow water theory (Eq. (4)) can be utilized to calculate the natural frequency when the ratio is smaller than 1/8 (Won et al., 1997;Li et al., 2002).
The TLD liquid tank model is selected as a rectangular and the TLD model can be simplified into a two-dimensional problem. The natural frequency is correlated to the liquid     depth, h, and the length in the motion direction, L. According to the natural frequency value from the on-site monitoring and the model test, the preliminarily dimension of the ideal liquid depth is chosen to be 3 m. The ratio of the liquid depth to the lateral dimension is 1:6, which suits the deep water theory. However, the fully sloshing depth of the liquid should be defined below 1/3 tank height, so the designed height of the tank is at least 9 m, which is higher than the designed height of the soft yoke ballast tank (7.27 m). The overly high tank design brings potential risks to the whole structure of the mooring system. There are several methodologies, such as reducing the liquid depth, h, changing the lateral dimension, L, adding clapboards in the tank, can be applied to decrease the designed water depth of the TLD tank. For example, clapboards are set in the middle of the TLD and the lateral dimension is reduced to half of the original size. The liquid depth is about 0.7 m and the TLD liquid tank height is set to be 2 m, which can be satisfied by the soft yoke mooring structure. In consideration of that the larger the reserved space of the TLD tank is, the better the free motion of the liquid inside will be. By comprehensively considering the above indexes, the final height of the TLD vibration control tank, H, is designed as 4 m. (as shown in Fig. 11).

Experimental results and analysis
5.1 Single-tank TLD vibration control experiment Single-tank TLD vibration reduction experiment was performed to simulate the lateral vibration reduction effect. Ratio shrinking was made on the TLD which was then placed between two ballast tanks. To ensure the constant of the longitudinal stiffness, partial liquid in the ballast tank was injected into the TLD tank. The rolling experiment was made as the TLD with the sweeping frequency range falls 0.3-0.7 Hz. The results are as follows.
By comparing the vibration control effects of the model test with and without TLD system, it can be found that the vibration amplitude with the TLD system decreases under different excitation amplitudes. The decrease near the resonance frequency is obvious. The experiment proved that the TLD system had significant damping effects on the SYMs.
However, the experiment also indicated that with the lateral vibration of the mooring system, the damping liquid had strong slamming against the TLD upper cover plate. The liquid could overflow from it, showing that the longitudinal height of the single-tank TLD vibration control system was not enough and failed to satisfy the safety requirement of the structural vibration reduction.

Verification experiment of FPSO lateral two-tank vibration reduction
Owing to the allowable height limits of the TLD structure, single-tank could not be satisfied with the requirements of good vibration control. A clapboard was added in the middle of the water tank to achieve the two-tank design of the TLD system. A series of two-tank TLD damping experiments were performed and verified to compare with single-tank TLD results.  It is found through data comparison that under the same load frequency, the two-tank TLD vibration control system could achieve good damping effects in the resonance interval. Meanwhile, in the experimental procedure, the two-tank TLD vibration control system could effectively avoid the slamming effects of the damping fluid and satisfy the safety requirement. Thus, the two-tank TLD vibration control system can be effectively applied to the lateral vibration reduction design of the SYMs.

Conclusions
(1) When the SYMs is subjected to complex ocean environmental load, the reason for the dangerous severe lateral vibration behaviors is the resonance behaviors caused by the FPSO vessel rolling motions, with the resonance frequency of 0.14 Hz. The monitoring data, ADAMS simulation analysis, and model experiment results show that the SYMs at a specific frequency excitation exhibit significant lateral vibration.
(2) The TLD passive vibration control system is presented with single-tank and two-tank subdivisions. Experimental results show that single-tank TLD system can have better damping effects on the SYMs. However, the experiments also indicated that with the lateral vibration of the mooring system, the damping liquid exhibited the strong slamming behavior to the TLD upper cover plate.
(3) Two-tank rectangle TLD vibration control experiment could also achieve good damping effects in the resonance interval. Meanwhile, it reduced the slamming effects of the TLD damping liquid, which greatly increases the safety and owns high applicability.