Stability Analysis of Dual-Lifting Vessels under Collaborative Lifting Operation

The current market for the assembly and disassembly of offshore platforms exceeds $100 billion. However, existing methods face limitations that reduce their efficiency. To address these limitations, we propose a dual-vessel collaborative assembly and disassembly system with multiple motion-compensated lifting arms. The compensation system enables the lifting arms to isolate the topside module from the wave-induced loads, and specifically the torque, transmitted from the lifting vessel. Through theoretical derivations based on hydrostatics principles, a mathematical model of the topside module is established. We consider the effects of lifting load, tidal changes and the ballast water system on stability, and develop a stability analysis model for the dual-vessel system. The intact stability and loss-of-load stability under dual-vessel collaborative lifting conditions are analysed to verify compliance with stability requirements for lifting a 30,000 ton topside module. The results conclusively demonstrate that the proposed system with multiple motion-compensated lifting arms meets the stability performance needs for dual-vessel collaborative offshore assembly and disassembly operations.

The trend towards larger, more integrated marine equipment is driving the offshore construction industry towards collaborative installation practices as the primary operational model [1][2][3][4].Taking platform deployment as an example, we note that the structure is generally divided into two key components: the lower jacket foundation and the topside module.These are typically fabricated separately, and the docking and installation of the topside unit atop the substructure is a crucial but challenging undertaking.The size, weight and functional requirements of offshore platforms lead to varied designs for support structures and modules, each with their own considerations related to installation/ removal.
In the early years, the industry's main focus in regard to the installation and dismantling of a platform was to find a lifting ship that could meet the weight and scale requirements of the topside module.The integrated lifting of the upper deck blocks with relatively small scale and weight was completed by lifting equipment positioned on the ship.The capabilities of vessels have been continually increased to accommodate the growing infrastructure.Shanghai Zhenhua's 240 m Blue Whale [5,6] (Fig. 1(a)) entered service in 2008, offering 7,500-ton lifting, whereas their 2016-delivered Zhenhua 30 [7] (Fig. 1(b)) lifted 12,000 tons, with a length of 320 m.Heerema and Sembcorp launched the semi-submersible crane vessel Sleipnir [8] (Fig. 1(c)) in 2019, which was equipped with dual revolving cranes providing 20,000-ton lifting via a dual-lift configuration.(a) Blue Whale (COOEC) [7,8]; (b)Zhenhua 30 (ZPMC) [7]; (c) semisubmersible Sleipnir(HMC) [8]; (d) bridge installation method of John Du Bois (US Patent 36606) [9] As demand for deep-water oil and gas development has increased, the scale and dimensions of offshore platform topside modules have likewise expanded significantly.In parallel with further developments in the specifications of heavy lift vessels, alternative integrated installation methods that are not wholly reliant on a single vessel's maximum lifting capacity have also drawn attention.One early inspiration was an 1862 patent for a process of installing bridge structures, which foreshadowed later developments in the float-over technique that is now common in marine engineering projects [9].As depicted conceptually in Fig. 1(d), this approach involved floating key structural elements into position rather than hoisting them via crane.This pioneering work highlighted the potential for collaborative, multi-unit solutions to tackle the challenges of infrastructure installation posed by the ever-growing specifications for topside modules.
Aker, a US firm, developed a movable rod lifting system known as the VERSATRUSS technique.Using tension rods, hoists and support rods positioned across two construction barges, this system enables the lifting of modules of up to 10,000 tons in shallow waters with small air gaps between the surface and load [10,11].However, this method is subject to environmental and dimensional constraints.Another solution, the VB10000 Versabar lifting crane, consists of a heavyduty double gantry catamaran design with two 91 m truss frame barges, each capable of 7,500-ton lifting [12].Dynamic positioning systems maintain the positioning of the barges during operations.Although this offers expanded capabilities compared to single-vessel options, limitations remain in terms of block dimensions and weight, due to the intrinsic configuration of these multibarge collaborative systems.
Both of these innovative approaches rely on the concept of distributed lifting forces across two or more purpose-built units.
A mainstream solution based on a 10,000-ton floating installation emerged in the late 1970s.In 1979, its first offshore application involved installing the 6,500-ton topside module onto the Zakum jacket platform in Abu Dhabi [13].Then, in 1980, Abbot developed the HIDECK float-over methodology [14], as illustrated in Figs.2(c) and (d) [15].Although first applied to Maureen's gravity platform, its principles apply similarly to fixed jacket structures.Related patents proliferated between 1980 and 1981 [16,17].Subsequently, Technip developed the UNIDECK float-over technique, in which hydraulic lifting was used to rapidly transfer the module mass to the foundations between wave periods, thereby avoiding collisions from excessive heave [18][19][20].A detailed comparison of UNIDECK and HIDECK was conducted by Liu and Li [21].Today, the world's most advanced installation/removal vessel, Pioneering Spirit, uses a double-sided bow lifting arm configuration based on UNIDECK principles [22,23], as depicted in Fig. 2(f).The docking time has been reduced from hours with HIDECK/ UNIDECK to just seconds through the use of collaborative dual-arm operations.
POLISH MARITIME RESEARCH, No 2/2024 2 the topside module.The integrated lifting of the upper deck blocks with relatively small scale and weight was completed by lifting equipment positioned on the ship.The capabilities of vessels have been continually increased to accommodate the growing infrastructure.Shanghai Zhenhua's 240 m Blue Whale [5,6] (Fig. 1(a)) entered service in 2008, offering 7,500ton lifting, whereas their 2016-delivered Zhenhua 30 [7] (Fig. 1(b)) lifted 12,000 tons, with a length of 320 m.Heerema and Sembcorp launched the semi-submersible crane vessel Sleipnir [8] (Fig. 1(c)) in 2019, which was equipped with dual revolving cranes providing 20,000-ton lifting via a dual-lift configuration.(a) Blue Whale (COOEC) [7,8]; (b)Zhenhua 30 (ZPMC) [7]; (c) semisubmersible Sleipnir(HMC) [8]; (d) bridge installation method of John Du Bois (US Patent 36606) [9] As demand for deep-water oil and gas development has increased, the scale and dimensions of offshore platform topside modules have likewise expanded significantly.In parallel with further developments in the specifications of heavy lift vessels, alternative integrated installation methods that are not wholly reliant on a single vessel's maximum lifting capacity have also drawn attention.One early inspiration was an 1862 patent for a process of installing bridge structures, which foreshadowed later developments in the float-over technique that is now common in marine engineering projects [9].As depicted conceptually in Fig. 1(d), this approach involved floating key structural elements into position rather than hoisting them via crane.This pioneering work highlighted the potential for collaborative, multi-unit solutions to tackle the challenges of infrastructure installation posed by the ever-growing specifications for topside modules.
Aker, a US firm, developed a movable rod lifting system known as the VERSATRUSS technique.Using tension rods, hoists and support rods positioned across two construction barges, this system enables the lifting of modules of up to 10,000 tons in shallow waters with small air gaps between the surface and load [10,11].However, this method is subject to environmental and dimensional constraints.Another solution, the VB10000 Versabar lifting crane, consists of a heavy-duty double gantry catamaran design with two 91 m truss frame barges, each capable of 7,500-ton lifting [12].Dynamic positioning systems maintain the positioning of the barges during operations.Although this offers expanded capabilities compared to single-vessel options, limitations remain in terms of block dimensions and weight, due to the intrinsic configuration of these multi-barge collaborative systems.Both of these innovative approaches rely on the concept of distributed lifting forces across two or more purpose-built units.
A mainstream solution based on a 10,000-ton floating installation emerged in the late 1970s.In 1979, its first offshore application involved installing the 6,500-ton topside module onto the Zakum jacket platform in Abu Dhabi [13].Then, in 1980, Abbot developed the HIDECK float-over methodology [14], as illustrated in Figs.2(c) and (d) [15].Although first applied to Maureen's gravity platform, its principles apply similarly to fixed jacket structures.Related patents proliferated between 1980 and 1981 [16,17].Subsequently, Technip developed the UNIDECK float-over technique, in which hydraulic lifting was used to rapidly transfer the module mass to the foundations between wave periods, thereby avoiding collisions from excessive heave [18][19][20].A detailed comparison of UNIDECK and HIDECK was conducted by Liu and Li [21].Today, the world's most advanced installation/removal vessel, Pioneering Spirit, uses a double-sided bow lifting arm configuration based on Fig. 2. (a) VERSATRUSS hoist system [10,11]; (b) VB10000 hoist system [12]; (c) HIDECK floating installation concept (OTC3978) [15]; (d) HIDECK floating installation concept [15];(e) Pioneering Spirit (Allseas) [23]; (f) ACG Caspian floating installation of a topside module jacket platform in a sea area [24]; (g Catamaran collaborative operation [25] Fig. 2. (a) VERSATRUSS hoist system [10,11]; (b) VB10000 hoist system [12]; (c) HIDECK floating installation concept (OTC3978) [15]; (d) HIDECK floating installation concept [15];(e) Pioneering Spirit (Allseas) [23]; (f) ACG Caspian floating installation of a topside module jacket platform in a sea area [24]; (g)Catamaran collaborative operation [25] Although extremely heavy lifting vessels can conduct floatover installations independently, multi-vessel cooperative operations have emerged as a novel methodology.These typically involve three barges, with one acting as a transport unit and two collaborating in float-over activities.As distinguished from fixed-jacket foundations, where docking is carried out solely by ballast manoeuvres of the support unit/structure, multi-vessel cooperation involves synchronised control challenges during offshore execution.If the topside module is transferred from the transport to two float-over installation barges in a rigidly connected configuration, the entire structural system resembles the bow U-notch configuration of Pioneering Spirit, and is known as a catamaran due to its two-hull form, as illustrated in Fig. 2(g) [25].The catamaran mode allows for active distance adjustments between vessels to accommodate modules of varying dimensions.However, rigidly connecting these modules introduces structural loading complexities, as loads are directly transmitted to potentially fragile, aging modules that are not designed to withstand such dynamic offshore stresses, and this is a significant design consideration.
There are several limitations on current offshore installation and disassembly equipment, for example: (i) existing lifting ships have low lifting capacity, and large modules need to be divided into many segments for disassembly operations, resulting in long operation times and high risk; (ii) when the barge floating mode is used, operation is greatly affected by the tide; (iii) topside modules with large air gap heights impose requirements for the selection of barge dimensions; (iv) the U-groove mode of operation is limited by the size of the block, the equipment cost is very high, and the operational flexibility is insufficient; and (v) the use of the catamaran mode of operation presents a huge challenge in terms of the strengthening of old oilfield facilities.
To address these existing challenges, this study proposes a novel dual-vessel cooperative assembly/disassembly system that involves multiple motion-compensated lifting arms.Through theoretical modelling based on static principles, a mathematical representation is derived to characterise the model of the lifted topside module.A distinguishing feature is the implementation of a compensation mechanism that isolates the bending moments at the module-lifting interface.This mitigates the transmission of wave loads, and particularly wave-induced torques, from the lifting vessel to the lifting arms and topside module.Variations in lifting load, tidal fluctuations, and ballast conditions are considered, and rigorous stability analyses are conducted to assess the intact and loss-of-load stability under collaborative heavy lifting operations.The compliance of our system with the relevant standards is numerically validated.

TYPES OF COnnECTiOn AnD SiMuLATiOn OF A MuLTi-FLOATinG BODY OPErATiOn SYSTEM
The operation of the dual-vessel lifting arm process is as follows.Multiple sets of lifting arm systems are installed on each of the two lifting vessels, positioned on opposing sides of the target object.Hydraulically actuated bearing components are located at the distal ends of the arms to enable lifting and lowering of the target through precise adjustments that are coordinated with ballast water trim.Long-distance transport is facilitated via a dedicated third barge.In addition to dismantling aging platforms, the system is equally capable of installing new modules by directing lifting/offloading to alternate docking positions as required.Fig. 3 provides an analytical schematic depicting sample configurations during dismantling operations, and illustrates the spatial layout of the HLV1 (Heavy Lifting Vessel 1), the HLV2, the target object (e.g.topside, jacket), and the CV3 (Carrier Vessel 3).Dual-vessel cooperative lifting operations differ in a fundamental way from single-ship heavy lifting by virtue of their increased complexity.For single-vessel lifts, we only consider the stability of the vessel and crane load capacity, whereas collaborative lifts necessitate an analysis of the loads on the lifted topside module along with the intact stability of both the lifting vessels and the integrated system as a whole.
In general, there are two types of connection between the topside module and lifting vessels.One is a rigid connection, in which all components are structurally welded to form a unified whole, while the other relies on a motion compensation system that provides a degree of freedom, approximating a hinge-like connection.
Table 1 compares the hydrostatic parameters of the stability models for the two connection modes.It can be seen that the stability parameters differ noticeably between the rigid and hinged configurations.
Fig. 4 shows the hydrostatic table corresponding to the rigid connection model, and Fig. 5 presents the coordinate system for the hydrostatic models.Fig. 6 illustrates the hydrostatic models for a 16 m draft.As illustrated in Fig. 6(a), with a rigid connection, the lifting arm binds the topside module to both lifting vessels, forming a unified whole where the parts are incapable of independent motion.This integrated system resembles a semi-submersible platform with a double-hull form, and in a stability modelling analysis, it can be treated as a catamaran and assessed in the same manner.Table 1 provides the key hydrostatic parameters for evaluation, of which the transverse and longitudinal stability centre heights are particularly important metrics.With a rigid arm connection, the longitudinal stability centre height is 292 m as compared to a transverse height of 227 m, with both being on the same order of magnitude.This connection approach thus confers strong longitudinal and transverse stability for heights that are well above the waterline.
With the rigid connection method, the wave load acting on the two lifting ships is completely transferred to the lifting system and the topside module via the rigid connection between the lifting system and the topside module, which imposes high requirements for the structural strength of the topside module.In practice, the initial design of the topside module does not consider the need to bear the part of the load generated by the movement of the lower floating body.
In contrast, a hinged connection allows the lifting arm, topside module and vessels to behave as three independent bodies with relative movement, although this is somewhat constrained.Consequently, the bending moments induced by ship motions are released at hinge points.For stability analysis, the system can thus be decomposed into the individual floating bodies (the two vessels and the lifted module) for evaluation of the intact stability.As shown in Fig. 6(b) and Table 1, when modelling a single vessel, the height of the lateral system stability centre is a mere 32 m when hinged, much lower than the longitudinal height of 292 m, meaning that lateral stability across the entire cooperative system is relatively weak.
Hence, after comparing and analysing the characteristics of the two connection forms, it is found that although a rigid connection has very high stability and safety, it is very difficult to realise in actual marine engineering, especially for the dismantling of old platforms, due to stiffness and strength problems.An approach based on a lifting arm motion  As illustrated in Fig. 6(a), with a rigid connection, the lifting arm binds the topside module to both lifting vessels, forming a unified whole where the parts are incapable of independent motion.This integrated system resembles a semi-submersible platform with a double-hull form, and in a stability modelling analysis, it can be treated as a catamaran and assessed in the same manner.Table 1 provides the key hydrostatic parameters for evaluation, of which the transverse and longitudinal stability centre heights are particularly important metrics.With a rigid arm connection, the longitudinal stability centre height is 292 m as compared to a transverse height of 227 m, with both being on the same order of magnitude.This connection approach thus confers strong longitudinal and transverse stability for heights that are well above the waterline.
With the rigid connection method, the wave load acting on the two lifting ships is completely transferred to the lifting system and the topside module via the rigid connection between the lifting system and the topside module, which imposes high requirements for the structural strength of the topside module.In practice, the initial design of the topside module does not consider the need to bear the part of the load generated by the movement of the lower floating body.
In contrast, a hinged connection allows the lifting arm, topside module and vessels to behave as three independent bodies with relative movement, although this is somewhat constrained.Consequently, the bending moments induced by ship motions are released at hinge points.For stability analysis, the system can thus be decomposed into the individual floating bodies (the two vessels and the lifted module) for evaluation of the intact stability.As shown in Fig. 6(b) and Table 1, when modelling a single vessel, the height of the lateral system stability centre is a mere 32 m when hinged, much lower than the longitudinal height of 292 m, meaning that lateral stability across the entire cooperative system is relatively weak.
Hence, after comparing and analysing the characteristics of the two connection forms, it is found that although a rigid connection has very high stability and safety, it is very difficult to realise in actual marine engineering, especially for the dismantling of old platforms, due to stiffness and strength problems.An approach based on a lifting arm motion compensation system is therefore proposed.Through the compensation system is therefore proposed.Through the action of the compensation system, the bending moment at the connection between the lifting system and the topside module is released, and load from waves acting on the lifting ship (and especially the torque) is avoided, as it is transmitted to the lifting arm and the topside module, thus ensuring the structural integrity of the topside module.However, the way in which the resulting multi-body system provides sufficient stability and safety, its evaluation and the method used for analysis need further study.

PrinCiPLE OF AnALYSiS OF COLLABOrATiVE LiFTinG OPErATiOn
For the hinged configuration shown in Fig. 7, preliminary evaluations suggest that without corrective measures, the lifting of a topside module would induce an overturning moment in a single lift vessel, causing a static heel angle exceeding 15º.This inclination would prevent the targeted lift height from being achieved, while also potentially damaging the lifting equipment.To balance this substantial rolling moment produced by the weight-arm lifting, precise ballast transfers are required within the lift vessel during its operation.The internal repositioning of ballast is done with the aim of maintaining safe intact stability in the vessel, as it interacts dynamically with the lifted module as an integrated multibody system.Without real-time compensation of the heeling forces via the ballast system, safe collaborative offshore lifts would not be feasible, given the excessive motions and stresses on equipment and infrastructure that would otherwise result.Hence, in order to provide sufficient lifting capacity, there is a need for real-time monitoring and adjustments to the internal ballast distribution network as a critical active control method for counteracting rolling incidents induced at the unique motion-constrained connection points between the floating bodies under the hinged configuration.Reliable and efficient ballast management is paramount to achieving both the lifting function and overall system stability under dynamic offshore conditions.In the following section, we use static equilibrium principles to analyse the moment variations that occur throughout the lifting process.

LiFTinG LOAD STOWAGE
Prior to initiating the lift, it is imperative to maintain positive stability.At this pre-engagement stage, minor ballast water adjustments suffice to counteract any deviations in the lifting arm's centre of gravity from its ideal aligned position, thereby minimising incipient rolling moments.However, as the arm extends outward, its centre of gravity shifts correspondingly, inducing an increasing heeling torque upon the vessel.Precise ballast redistribution is thus necessitated to prevent undesirable heel and retain upright equilibrium.Through analytical modelling of the load balance preservation process arising from ballast regulation at each phase of the arm's movement, from retraction to full extension, the overturning moment directly correlating with arm lengthening can be derived.
It is assumed that the centre of gravity of the lifting arm is in position y 1 before it is extended.When the lifting arm extends outboard, it reaches a position y 2 .This process of overhanging will cause the ship to heel.
The overhang of the lifting arm on the ship is equivalent to the movement of a heavy object on the ship.From statics, we know that the moment causing the ship to tilt is: Reliable and efficient ballast management is paramount to achieving both t and overall system stability under dynamic offshore conditions.In the followin static equilibrium principles to analyse the moment variations that occur thro process.

LIFTING LOAD STOWAGE
Prior to initiating the lift, it is imperative to maintain positive stabi engagement stage, minor ballast water adjustments suffice to counteract any lifting arm's centre of gravity from its ideal aligned position, thereby minimisin moments.However, as the arm extends outward, its centre of gravity shifts inducing an increasing heeling torque upon the vessel.Precise ballast redi necessitated to prevent undesirable heel and retain upright equilibrium.Th modelling of the load balance preservation process arising from ballast regulat of the arm's movement, from retraction to full extension, the overturning correlating with arm lengthening can be derived.
It is assumed that the centre of gravity of the lifting arm is in position  1 bef When the lifting arm extends outboard, it reaches a position  2 .This process of cause the ship to heel.
The overhang of the lifting arm on the ship is equivalent to the movement on the ship.From statics, we know that the moment causing the ship to tilt is: where  is the displacement of the ship and can be obtained from the weight o hydrostatic curve; and  is the heeling angle of the ship caused by the load, initial stability of the ship, and is obtained by the following formula: where Δ is the displacement of the ship and can be obtained from the weight of the ship and the hydrostatic curve; and ϕ is the heeling angle of the ship caused by the load, which is the high initial stability of the ship, and is obtained by the following formula 6

Fig. 7. Diagram of the lifting arm overhang
Reliable and efficient ballast management is paramount to achieving both th and overall system stability under dynamic offshore conditions.In the followin static equilibrium principles to analyse the moment variations that occur throu process.

LIFTING LOAD STOWAGE
Prior to initiating the lift, it is imperative to maintain positive stabil engagement stage, minor ballast water adjustments suffice to counteract any lifting arm's centre of gravity from its ideal aligned position, thereby minimising moments.However, as the arm extends outward, its centre of gravity shifts inducing an increasing heeling torque upon the vessel.Precise ballast redis necessitated to prevent undesirable heel and retain upright equilibrium.Th modelling of the load balance preservation process arising from ballast regulat of the arm's movement, from retraction to full extension, the overturning correlating with arm lengthening can be derived.
It is assumed that the centre of gravity of the lifting arm is in position  1 bef When the lifting arm extends outboard, it reaches a position  2 .This process of cause the ship to heel.
The overhang of the lifting arm on the ship is equivalent to the movement on the ship.From statics, we know that the moment causing the ship to tilt is: where  is the displacement of the ship and can be obtained from the weight o hydrostatic curve; and  is the heeling angle of the ship caused by the load, w initial stability of the ship, and is obtained by the following formula: where ( 2 −  1 ) is the vertical distance moved by the centre of gravity of the the ship's width, and  0 is the weight of the lifting arm.Using the formula abov moment generated when the lifting arm of the ship is extended can be  =    at small angles, GZ does not appear in the equations pres overturning moment generated by the lifting arm will be balanced by the transfe By redistributing ballast water, the overturning moment induced by exten arm is counteracted, establishing a new positive metacentric height for the cr sufficient for the subsequent lift stages.An evaluation of the minimum duration must account for the individual tank volumes, centroid locations, and position gravity of loads, in conjunction with each tank's hold capacity.The overall sy including the maximum shifting rate and total shift volume, must also be chara analytical modelling incorporating these constraints and considerations, an opt approach can be developed to precisely manage the stability challenges with demanded by heavy lifting operations.
Maintaining a state of positive equilibrium for the crane vessel throughout process is imperative to ensure the safety of operations.As expressed in the the provided above, the change in rolling moment caused by incremental load necessarily equal the rolling moment generated by the regulation of ballast wate where ( 2 −  1 ) is the vertical distance moved by the centre of gravity of the the ship's width, and  0 is the weight of the lifting arm.Using the formula abov moment generated when the lifting arm of the ship is extended can be  =    at small angles, GZ does not appear in the equations pre overturning moment generated by the lifting arm will be balanced by the transfe By redistributing ballast water, the overturning moment induced by exten arm is counteracted, establishing a new positive metacentric height for the cr sufficient for the subsequent lift stages.An evaluation of the minimum duration must account for the individual tank volumes, centroid locations, and position gravity of loads, in conjunction with each tank's hold capacity.The overall sy including the maximum shifting rate and total shift volume, must also be chara analytical modelling incorporating these constraints and considerations, an opt approach can be developed to precisely manage the stability challenges with demanded by heavy lifting operations.
Maintaining a state of positive equilibrium for the crane vessel throughou process is imperative to ensure the safety of operations.As expressed in the the provided above, the change in rolling moment caused by incremental loa where ( 2 −  1 ) is the vertical distance moved by the centre of gravity of the the ship's width, and  0 is the weight of the lifting arm.Using the formula abov moment generated when the lifting arm of the ship is extended can be  =    at small angles, GZ does not appear in the equations pre overturning moment generated by the lifting arm will be balanced by the transfe By redistributing ballast water, the overturning moment induced by exten arm is counteracted, establishing a new positive metacentric height for the cr sufficient for the subsequent lift stages.An evaluation of the minimum duration must account for the individual tank volumes, centroid locations, and position gravity of loads, in conjunction with each tank's hold capacity.The overall sy including the maximum shifting rate and total shift volume, must also be chara analytical modelling incorporating these constraints and considerations, an op approach can be developed to precisely manage the stability challenges with demanded by heavy lifting operations.
Maintaining a state of positive equilibrium for the crane vessel throughou process is imperative to ensure the safety of operations.As expressed in the th where (y 2 − y 1 ) is the vertical distance moved by the centre of gravity of the lifting arm along the ship's width, and p 0 is the weight of the lifting arm.Using the formula above, the overturning moment generated when the lifting arm of the ship is extended can be calculated.Since GZ = GM tan ϕ at small angles, GZ does not appear in the equations presented here.The overturning moment generated by the lifting arm will be balanced by the transfer of ballast water.
By redistributing ballast water, the overturning moment induced by extension of the lifting arm is counteracted, establishing a new positive metacentric height for the crane vessel that is sufficient for the subsequent lift stages.An evaluation of the minimum duration of ballast shifting must account for the individual tank volumes, centroid locations, and positions of the centre of gravity of loads, in conjunction with each tank's hold capacity.The overall system capabilities, including the maximum shifting rate and total shift volume, must also be characterised.Through analytical modelling incorporating these constraints and considerations, an optimised ballasting approach can be developed to precisely manage the stability challenges within the timescales demanded by heavy lifting operations.
Maintaining a state of positive equilibrium for the crane vessel throughout the load transfer process is imperative to ensure the safety of operations.As expressed in the theoretical equation provided above, the change in rolling moment caused by incremental load additions must necessarily equal the rolling moment generated by the regulation of ballast water, as follows: =       (5) 1 ) is the vertical distance moved by the centre of gravity of the lifting arm along th, and  0 is the weight of the lifting arm.Using the formula above, the overturning rated when the lifting arm of the ship is extended can be calculated.Since  at small angles, GZ does not appear in the equations presented here.The oment generated by the lifting arm will be balanced by the transfer of ballast water.ributing ballast water, the overturning moment induced by extension of the lifting racted, establishing a new positive metacentric height for the crane vessel that is he subsequent lift stages.An evaluation of the minimum duration of ballast shifting for the individual tank volumes, centroid locations, and positions of the centre of ds, in conjunction with each tank's hold capacity.The overall system capabilities, maximum shifting rate and total shift volume, must also be characterised.Through delling incorporating these constraints and considerations, an optimised ballasting be developed to precisely manage the stability challenges within the timescales heavy lifting operations.ing a state of positive equilibrium for the crane vessel throughout the load transfer erative to ensure the safety of operations.As expressed in the theoretical equation ve, the change in rolling moment caused by incremental load additions must ual the rolling moment generated by the regulation of ballast water, as follows: med that the position of the lifting head during the lifting process is y m from the p, and that the overturning moment increases with the lifting load .The torque   he lifting load can be expressed as: ue generated by an increase in the lifting load will be balanced by the ballast water the ballast water system.The transverse distance between the port and starboard participating in the load adjustment is   , and the transverse ballast water allocation ained by the following formula: g that the flow rate of the ballast pump is  and the amount of water to be adjusted adjustment time  of the ballast water is shown in Eq. ( 9): imum ballast water transfer volume Q (transferred from the port ballast tanks to the ast tanks) is approximately 10,900 m 3 .A single vessel is equipped with seven groups tanks and a total of 14 anti-heeling pumps.The flow rate of each pump q is 1,500

OF THE TIDE ON HULL BALLAST WATER ADJUSTMENT
odelling the lifting process, tidal influences on hull loads must be considered in module weight.For dismantled topside assemblies that are initially fixed to jackets, It is assumed that the position of the lifting head during the lifting process is y m from the mid of the ship, and that the overturning moment increases with the lifting load w.The torque M y generated by the lifting load can be expressed as: =       (5) 1 ) is the vertical distance moved by the centre of gravity of the lifting arm along h, and  0 is the weight of the lifting arm.Using the formula above, the overturning rated when the lifting arm of the ship is extended can be calculated.Since  at small angles, GZ does not appear in the equations presented here.The oment generated by the lifting arm will be balanced by the transfer of ballast water.ributing ballast water, the overturning moment induced by extension of the lifting acted, establishing a new positive metacentric height for the crane vessel that is he subsequent lift stages.An evaluation of the minimum duration of ballast shifting for the individual tank volumes, centroid locations, and positions of the centre of s, in conjunction with each tank's hold capacity.The overall system capabilities, aximum shifting rate and total shift volume, must also be characterised.Through elling incorporating these constraints and considerations, an optimised ballasting be developed to precisely manage the stability challenges within the timescales eavy lifting operations.ng a state of positive equilibrium for the crane vessel throughout the load transfer erative to ensure the safety of operations.As expressed in the theoretical equation e, the change in rolling moment caused by incremental load additions must ual the rolling moment generated by the regulation of ballast water, as follows: ed that the position of the lifting head during the lifting process is y m from the , and that the overturning moment increases with the lifting load .The torque   he lifting load can be expressed as: e generated by an increase in the lifting load will be balanced by the ballast water he ballast water system.The transverse distance between the port and starboard articipating in the load adjustment is   , and the transverse ballast water allocation ined by the following formula: that the flow rate of the ballast pump is  and the amount of water to be adjusted adjustment time  of the ballast water is shown in Eq. ( 9): mum ballast water transfer volume Q (transferred from the port ballast tanks to the st tanks) is approximately 10,900 m 3 .A single vessel is equipped with seven groups tanks and a total of 14 anti-heeling pumps.The flow rate of each pump q is 1,500

OF THE TIDE ON HULL BALLAST WATER ADJUSTMENT
delling the lifting process, tidal influences on hull loads must be considered in module weight.For dismantled topside assemblies that are initially fixed to jackets, The torque generated by an increase in the lifting load will be balanced by the ballast water allocation of the ballast water system.The transverse distance between the port and starboard heeling tanks participating in the load adjustment is L y , and the transverse ballast water allocation Q y can be obtained by the following formula: =       (5) 1 ) is the vertical distance moved by the centre of gravity of the lifting arm along h, and  0 is the weight of the lifting arm.Using the formula above, the overturning rated when the lifting arm of the ship is extended can be calculated.Since  at small angles, GZ does not appear in the equations presented here.The oment generated by the lifting arm will be balanced by the transfer of ballast water.ributing ballast water, the overturning moment induced by extension of the lifting acted, establishing a new positive metacentric height for the crane vessel that is he subsequent lift stages.An evaluation of the minimum duration of ballast shifting for the individual tank volumes, centroid locations, and positions of the centre of s, in conjunction with each tank's hold capacity.The overall system capabilities, aximum shifting rate and total shift volume, must also be characterised.Through elling incorporating these constraints and considerations, an optimised ballasting be developed to precisely manage the stability challenges within the timescales eavy lifting operations.ng a state of positive equilibrium for the crane vessel throughout the load transfer erative to ensure the safety of operations.As expressed in the theoretical equation e, the change in rolling moment caused by incremental load additions must ual the rolling moment generated by the regulation of ballast water, as follows: ed that the position of the lifting head during the lifting process is y m from the , and that the overturning moment increases with the lifting load .The torque   he lifting load can be expressed as: e generated by an increase in the lifting load will be balanced by the ballast water he ballast water system.The transverse distance between the port and starboard articipating in the load adjustment is   , and the transverse ballast water allocation ined by the following formula: that the flow rate of the ballast pump is  and the amount of water to be adjusted adjustment time  of the ballast water is shown in Eq. ( 9): mum ballast water transfer volume Q (transferred from the port ballast tanks to the st tanks) is approximately 10,900 m 3 .A single vessel is equipped with seven groups tanks and a total of 14 anti-heeling pumps.The flow rate of each pump q is 1,500

OF THE TIDE ON HULL BALLAST WATER ADJUSTMENT
delling the lifting process, tidal influences on hull loads must be considered in module weight.For dismantled topside assemblies that are initially fixed to jackets, Assuming that the flow rate of the ballast pump is q and the amount of water to be adjusted is Q , the load adjustment time t of the ballast water is shown in Eq. ( 9): =       (5) 1 ) is the vertical distance moved by the centre of gravity of the lifting arm along h, and  0 is the weight of the lifting arm.Using the formula above, the overturning rated when the lifting arm of the ship is extended can be calculated.Since  at small angles, GZ does not appear in the equations presented here.The oment generated by the lifting arm will be balanced by the transfer of ballast water.ributing ballast water, the overturning moment induced by extension of the lifting acted, establishing a new positive metacentric height for the crane vessel that is he subsequent lift stages.An evaluation of the minimum duration of ballast shifting for the individual tank volumes, centroid locations, and positions of the centre of s, in conjunction with each tank's hold capacity.The overall system capabilities, aximum shifting rate and total shift volume, must also be characterised.Through elling incorporating these constraints and considerations, an optimised ballasting be developed to precisely manage the stability challenges within the timescales eavy lifting operations.ng a state of positive equilibrium for the crane vessel throughout the load transfer erative to ensure the safety of operations.As expressed in the theoretical equation e, the change in rolling moment caused by incremental load additions must ual the rolling moment generated by the regulation of ballast water, as follows: ed that the position of the lifting head during the lifting process is y m from the , and that the overturning moment increases with the lifting load .The torque   he lifting load can be expressed as: e generated by an increase in the lifting load will be balanced by the ballast water he ballast water system.The transverse distance between the port and starboard articipating in the load adjustment is   , and the transverse ballast water allocation ined by the following formula: that the flow rate of the ballast pump is  and the amount of water to be adjusted adjustment time  of the ballast water is shown in Eq. ( 9): mum ballast water transfer volume Q (transferred from the port ballast tanks to the st tanks) is approximately 10,900 m 3 .A single vessel is equipped with seven groups tanks and a total of 14 anti-heeling pumps.The flow rate of each pump q is 1,500

OF THE TIDE ON HULL BALLAST WATER ADJUSTMENT
delling the lifting process, tidal influences on hull loads must be considered in module weight.For dismantled topside assemblies that are initially fixed to jackets, The maximum ballast water transfer volume Q (transferred from the port ballast tanks to the starboard ballast tanks) is approximately 10,900 m 3 .A single vessel is equipped with seven groups of anti-heeling tanks and a total of 14 antiheeling pumps.The flow rate of each pump q is 1,500 m 3 / h.

inFLuEnCE OF THE TiDE On HuLL BALLAST WATEr ADJuSTMEnT
When modelling the lifting process, tidal influences on hull loads must be considered in addition to the module weight.For dismantled topside assemblies that are initially fixed to jackets, the seabed interface height remains fixed, while the sea level fluctuates with the tide.We adopt conservative assumptions, and hypothesise that load transfers during lifts require maintenance of elevation relative to the seabed rather than the sea surface, absent tidal assistance.Thus, the ballast water system capacity must accommodate tidal variances.Precise adjustments to ballast volumes can mitigate tidal impacts, whereby ballast is increased during flood tides and decreased during ebb tides.This stabilises the unchanging differential in elevation between the vessel and seabed throughout lifts.Ensuring this constant relative positioning facilitates a smooth load transfer sequence between the lifting arms and payloads.
The regulation of ballast water can be determined according to the tidal information of the sea area of operation and the variation of the unit cm drainage tonnage of the lifting vessel.It is assumed that the tidal change is ℎ m, and for variation TPC of the drainage tonnage per cm of a single ship, the ballast water required to be discharged or loaded during the adjustment process is: the seabed interface height remains fixed, while the sea level fluctuates with the tide.conservative assumptions, and hypothesise that load transfers during lifts require maint elevation relative to the seabed rather than the sea surface, absent tidal assistance.Thus, water system capacity must accommodate tidal variances.Precise adjustments to ballas can mitigate tidal impacts, whereby ballast is increased during flood tides and decreas ebb tides.This stabilises the unchanging differential in elevation between the vessel a throughout lifts.Ensuring this constant relative positioning facilitates a smooth loa sequence between the lifting arms and payloads.
The regulation of ballast water can be determined according to the tidal informat sea area of operation and the variation of the unit cm drainage tonnage of the lifting v assumed that the tidal change is ℎ m, and for variation  of the drainage tonnage pe single ship, the ballast water required to be discharged or loaded during the adjustme is:

BALLAST WATER SYSTEM MATCHING
Based on prior research into load stowage optimisation and the assessment of tidal dual-vessel cooperative heavy lifts require consideration of both the load transfer seque tidal impacts to adequately prepare for variance between sea areas.When we factor in th induced by increasing payloads, we see that vessel heeling tends to develop.To co inclination, a transverse load equalisation system is installed to enable coordinated bal reallocation in reverse, thereby achieving the object of load transfer while preserving equilibrium.Lifting vessels are thus outfitted with ballast plants capable of both asse disassembly operations.Through precise control, the ballast system ensures that th elevation between the lifting vessel and topside module remains essentially unchanged th the entire load transfer process.
In order to achieve the above functions, we set up seven pairs of side cabins on vessel, as shown in the ballast tank layout diagram in Fig. 8: the heeling cabin, the p heeling cabin (represented as 2P), and the starboard heeling cabin (represented as 2S) used for the ballast transfer of load transfer during lifting.These heeling tanks are dist both sides of the hull.The regulating water can be transferred from the heeling tank o to the tank on the other through the heeling pump, to realise the internal transfer of the water, thus increasing the regulating force arm and the restoring moment to the greates the limited space on board the ship.The transverse tilting tanks are deep tanks extendin bottom of the ship to the top of the main deck, to increase the amount of water and th of reloading.The lifting ship is equipped with ballast tanks, which are represented as 1 C (indicating the port, starboard and intermediate ballast tanks, respectively).During load transfer process, these ballast tanks are loaded and discharged with external seawat the ballast system in order to adapt to tidal changes.

BALLAST WATEr SYSTEM MATCHinG
Based on prior research into load stowage optimisation and the assessment of tidal influence, dual-vessel cooperative heavy lifts require consideration of both the load transfer sequencing and tidal impacts to adequately prepare for variance between sea areas.When we factor in the moment induced by increasing payloads, we see that vessel heeling tends to develop.To control this inclination, a transverse load equalisation system is installed to enable coordinated ballast water reallocation in reverse, thereby achieving the object of load transfer while preserving a positive equilibrium.Lifting vessels are thus outfitted with ballast plants capable of both assembly and disassembly operations.Through precise control, the ballast system ensures that the relative elevation between the lifting vessel and topside module remains essentially unchanged throughout the entire load transfer process.
In order to achieve the above functions, we set up seven pairs of side cabins on the lifting vessel, as shown in the ballast tank layout diagram in Fig. 8: the heeling cabin, the port layout heeling cabin (represented as 2P), and the starboard heeling cabin (represented as 2S), which is used for the ballast transfer of load transfer during lifting.These heeling tanks are distributed on both sides of the hull.The regulating water can be transferred from the heeling tank on one side to the tank on the other through the heeling pump, to realise the internal transfer of the regulating water, thus increasing the regulating force arm and the restoring moment to the greatest extent in the limited space on board the ship.The transverse tilting tanks are deep tanks extending from the bottom of the ship to the top of the main deck, to increase the amount of water and the moment of reloading.The lifting ship is equipped with ballast tanks, which are represented as 1P, 1S and C (indicating the port, starboard and intermediate ballast tanks, respectively).During the lifting load transfer process, these ballast tanks are loaded and discharged with external seawater through the ballast system in order to adapt to tidal changes.In order to more clearly describe the relationship between the load transfer and the change in the ballast water during the lifting operation, Fig. 10 shows the ballast water changes of 5%, 95%, 100% of in the transverse ballest warehouse during the lifting and lowering processes.The process of ballast water in the left and right two transverse ballest warehouse to achieve load transfer, and the operational draught remains unchanged.
Fig. 11 provides schematic representations of the variations in ballast tank volumes over the high and low tidal stages.Calculations are conducted based on the tidal datum specific to the project area to quantify the ballast demand for an entire tidal cycle.This ensures sufficient ballast reserves and tankage when establishing the starting load conditions.At high tide, pumps convey seawater into tanks, causing a concurrent rise in draught.Conversely, low tides necessitate tank deballasting to lower the draught via controlled discharge overboard.Through analytical modelling of the overturning moment induced by the lifting arm and lifted payload, and accounting for the tidal influences integral to the disassembly activities, an optimised design solution was obtained.The ballast compartment layout and system capacity were matched to stabilise the lifting vessel configuration for varying operational load cases.

STABiLiTY AnALYSiS OF THE TOPSiDE MODuLE
Through a comparative assessment of the rigid and hinged interfacing between the topside module and dual lifting vessels, a motion-compensated lifting arm configuration mimicking a hinged connection was selected for the integrated operational system.The overall stability of the multi-body collaborative approach is markedly influenced by the intactness or loss-of-load stability states of the lifted module.Further analytical investigation is therefore required to resolve how the motion of the module affects the equilibrium of the lifting vessel for all potential load cases.
The stability state diagram in Fig. 12 shows the ultimate tilt state of the topside module.At this time, the two lifting vessels are in a synchronous right roll tilt state.The lifting head of the left lifting vessel is downward, and that of the right lifting vessel is upward, so that the topside module produces the maximum left roll tilt state.Conversely, when the two lifting vessels are in reverse roll tilt, the lateral tilt state of the block is relatively small.The limiting tilt state is therefore selected as an example to study the stability analysis method of the topside module.
For the topside module, the two lifting vessels are equivalent to two springs that provide stiffness support, and this system can be simplified as shown in Fig. 13.In the multi-body system, the topside module, as an independent entity, has its own instability.Even in still water, the topside module will have a tendency to tilt, and a small disturbance from the outside will cause it to tilt.When this inclination occurs, the centre of gravity G of the topside module is shifted from its original position to G', producing an inclination angle θ 2 .In order to maintain balance, the two spring support points will produce a pair of couples M(F, F').The force F reversely acts on the HLV 1 and increases the lateral overturning moment.For the HLV 2 , this is equivalent to reducing the lateral overturning moment.If the stiffness provided by the lifting vessel to the topside module is insufficient, the topside module will become unstable; in order to ensure the stability of the topside module, the crane must provide sufficient stiffness, as determined by the GM value for the ship that determines the draught.Hence, the stability of the topside module can be quantified by the GM value of the lifting vessel The increased force F of the topside module tilted to the lifting vessel  In the multi-body system, the topside module, as an independent entity, instability.Even in still water, the topside module will have a tendency to tilt, disturbance from the outside will cause it to tilt.When this inclination occurs, the cen  of the topside module is shifted from its original position to  ′ , producing an incl  2 .In order to maintain balance, the two spring support points will produce a pa (,  ′ ) .The force F reversely acts on the HLV1 and increases the lateral overturn For the HLV2, this is equivalent to reducing the lateral overturning moment.If provided by the lifting vessel to the topside module is insufficient, the topside module unstable; in order to ensure the stability of the topside module, the crane must prov stiffness, as determined by the GM value for the ship that determines the draught stability of the topside module can be quantified by the GM value of the lifting vesse The increased force F of the topside module tilted to the lifting vessel  =  ⋅   2 ⋅   The overturning moment from the topside module on the lifting vessel is The overturning moment from the topside module on the lifting vessel is The relationship between the ship inclination  1 and block inclination  2 is 1  Hence, the overturning moment generated by the block is or The restoring force moment can then be expressed as： In the formulae above,   is the overturning moment,   is the restoring force is the ship tilt angle,  2 is the inclination angle of the topside module,  is the total topside module,  is the vertical center of gravity of the topside module,  is the spacing,  is the breadth of the ship,  is the overhanging outboard distance of the lif the displacement, and  is the initial stability is high.
The term + ) 2 in Eq. ( 16) is an important parameter tha restoring moment of the system.It can be regarded as the minimum requirement fo module for the lifting vessel, and is called the stability of the topside module.This m requirement can also be understood as the correction of the stability of the lifting topside module in the stability analysis of the multi-body system, that is, the stabili term for the lifting vessel .
From the above derivation, the influence of the topside module on the stability of the whole lifting operation in the multi-body system can be decomposed into tw static load of the topside module borne by the lifting vessel, and the overturning mo by the dynamic inclination of the topside module.The static load of the topside mod the lifting vessel is balanced by the transfer of ballast water from the left and right tanks, while the overturning moment caused by the dynamic inclination of the top requires the displacement of the lifting vessel and high initial stability to provide The relationship between the ship inclination θ 1 and block inclination θ 2 is The relationship between the ship inclination  1 and block inclination  2 is 1  Hence, the overturning moment generated by the block is or The restoring force moment can then be expressed as： In the formulae above,   is the overturning moment,   is the restoring force is the ship tilt angle,  2 is the inclination angle of the topside module,  is the total w topside module,  is the vertical center of gravity of the topside module,  is the spacing,  is the breadth of the ship,  is the overhanging outboard distance of the lif the displacement, and  is the initial stability is high.
The term + ) 2 in Eq. ( 16) is an important parameter tha restoring moment of the system.It can be regarded as the minimum requirement fo module for the lifting vessel, and is called the stability of the topside module.This m requirement can also be understood as the correction of the stability of the lifting v topside module in the stability analysis of the multi-body system, that is, the stabili term for the lifting vessel .
From the above derivation, the influence of the topside module on the stability of the whole lifting operation in the multi-body system can be decomposed into tw static load of the topside module borne by the lifting vessel, and the overturning mo by the dynamic inclination of the topside module.The static load of the topside mod the lifting vessel is balanced by the transfer of ballast water from the left and right Hence, the overturning moment generated by the block is The relationship between the ship inclination  1 and block inclination  2 is 1  Hence, the overturning moment generated by the block is or The restoring force moment can then be expressed as： In the formulae above,   is the overturning moment,   is the restoring force is the ship tilt angle,  2 is the inclination angle of the topside module,  is the total topside module,  is the vertical center of gravity of the topside module,  is the spacing,  is the breadth of the ship,  is the overhanging outboard distance of the lif the displacement, and  is the initial stability is high.
The term + ) 2 in Eq. ( 16) is an important parameter tha restoring moment of the system.It can be regarded as the minimum requirement fo module for the lifting vessel, and is called the stability of the topside module.This m requirement can also be understood as the correction of the stability of the lifting topside module in the stability analysis of the multi-body system, that is, the stabili term for the lifting vessel .
From the above derivation, the influence of the topside module on the stability of the whole lifting operation in the multi-body system can be decomposed into t static load of the topside module borne by the lifting vessel, and the overturning mo by the dynamic inclination of the topside module.The static load of the topside mod or The relationship between the ship inclination  1 and block inclination  2 is 1  Hence, the overturning moment generated by the block is or The restoring force moment can then be expressed as： In the formulae above,   is the overturning moment,   is the restoring force is the ship tilt angle,  2 is the inclination angle of the topside module,  is the total topside module,  is the vertical center of gravity of the topside module,  is the spacing,  is the breadth of the ship,  is the overhanging outboard distance of the lif the displacement, and  is the initial stability is high.
The term + ) 2 in Eq. ( 16) is an important parameter tha restoring moment of the system.It can be regarded as the minimum requirement fo module for the lifting vessel, and is called the stability of the topside module.This m requirement can also be understood as the correction of the stability of the lifting topside module in the stability analysis of the multi-body system, that is, the stabili term for the lifting vessel .
From the above derivation, the influence of the topside module on the stability of the whole lifting operation in the multi-body system can be decomposed into tw static load of the topside module borne by the lifting vessel, and the overturning mo The restoring force moment can then be expressed as： The relationship between the ship inclination  1 and block inclination  2 is Hence, the overturning moment generated by the block is or The restoring force moment can then be expressed as： (1 In the formulae above,   is the overturning moment,   is the restoring force moment, is the ship tilt angle,  2 is the inclination angle of the topside module,  is the total weight of t topside module,  is the vertical center of gravity of the topside module,  is the lifting poi spacing,  is the breadth of the ship,  is the overhanging outboard distance of the lifting arm,  the displacement, and  is the initial stability is high. The term  ⋅  ⋅ 1 ⋅ 2 ⋅ 2(  2 + ) 2 in Eq. ( 16) is an important parameter that affects t restoring moment of the system.It can be regarded as the minimum requirement for the topsi module for the lifting vessel, and is called the stability of the topside module.This minimum  requirement can also be understood as the correction of the stability of the lifting vessel by t topside module in the stability analysis of the multi-body system, that is, the stability correctio term for the lifting vessel .
From the above derivation, the influence of the topside module on the stability performan of the whole lifting operation in the multi-body system can be decomposed into two parts: t static load of the topside module borne by the lifting vessel, and the overturning moment caus by the dynamic inclination of the topside module.The static load of the topside module borne b the lifting vessel is balanced by the transfer of ballast water from the left and right side heelin tanks, while the overturning moment caused by the dynamic inclination of the topside modu In the formulae above, M H is the overturning moment, M R is the restoring force moment, θ 1 is the ship tilt angle, θ 2 is the inclination angle of the topside module, W is the total weight of the topside module, VCG is the vertical center of gravity of the topside module, D is the lifting point spacing, B is the breadth of the ship, L is the overhanging outboard distance of the lifting arm, Δ is the displacement, and GM is the initial stability is high.
The term The relationship between the ship inclination  1 and block inclination  2 is Hence, the overturning moment generated by the block is or The restoring force moment can then be expressed as： In the formulae above,   is the overturning moment,   is the restoring force moment,  1 is the ship tilt angle,  2 is the inclination angle of the topside module,  is the total weight of the topside module,  is the vertical center of gravity of the topside module,  is the lifting point spacing,  is the breadth of the ship,  is the overhanging outboard distance of the lifting arm, is the displacement, and  is the initial stability is high.
The term  ⋅  ⋅ 1 ⋅ 2 ⋅ 2(  2 + ) 2 in Eq. ( 16) is an important parameter that affects the restoring moment of the system.It can be regarded as the minimum requirement for the topside module for the lifting vessel, and is called the stability of the topside module.This minimum  requirement can also be understood as the correction of the stability of the lifting vessel by the topside module in the stability analysis of the multi-body system, that is, the stability correction term for the lifting vessel .
From the above derivation, the influence of the topside module on the stability performance of the whole lifting operation in the multi-body system can be decomposed into two parts: the static load of the topside module borne by the lifting vessel, and the overturning moment caused by the dynamic inclination of the topside module.The static load of the topside module borne by the lifting vessel is balanced by the transfer of ballast water from the left and right side heeling tanks, while the overturning moment caused by the dynamic inclination of the topside module requires the displacement of the lifting vessel and high initial stability to provide the restoring moment to reach a balance.

STABILITY ANALYSIS OF THE MULTI-BODY COLLABORATIVE
in Eq. ( 16) is an important parameter that affects the restoring moment of the system.It can be regarded as the minimum requirement for the topside module for the lifting vessel, and is called the stability of the topside module.This minimum GM requirement can also be understood as the correction of the stability of the lifting vessel by the topside module in the stability analysis of the multi-body system, that is, the stability correction term for the lifting vessel δGM.
e formulae above,   is the overturning moment,   is the restoring force moment,  1 tilt angle,  2 is the inclination angle of the topside module,  is the total weight of the odule,  is the vertical center of gravity of the topside module,  is the lifting point is the breadth of the ship,  is the overhanging outboard distance of the lifting arm, is cement, and  is the initial stability is high.term  ⋅  ⋅ 1 ⋅ 2 ⋅ 2(  2 + ) 2 in Eq. ( 16) is an important parameter that affects the moment of the system.It can be regarded as the minimum requirement for the topside r the lifting vessel, and is called the stability of the topside module.This minimum  nt can also be understood as the correction of the stability of the lifting vessel by the odule in the stability analysis of the multi-body system, that is, the stability correction he lifting vessel .
the above derivation, the influence of the topside module on the stability performance ole lifting operation in the multi-body system can be decomposed into two parts: the of the topside module borne by the lifting vessel, and the overturning moment caused namic inclination of the topside module.The static load of the topside module borne by vessel is balanced by the transfer of ballast water from the left and right side heeling ile the overturning moment caused by the dynamic inclination of the topside module he displacement of the lifting vessel and high initial stability to provide the restoring o reach a balance.

BILITY ANALYSIS OF THE MULTI-BODY COLLABORATIVE OPERATION SYSTEM
n conducting a stability analysis of the multi-body floating system, the load from the odule acting on the lifting system, the self-weight of the lifting system, and the load n of the lifting system are considered and transformed into a point load on the hull, and n is carried out by establishing a stability model of the hull and analysing the relevant ndexes for the hull.overturning moment generated by the inclination of the topside module is reflected in ty analysis.There are two possible approaches: one is to convert the overturning moment G of the topside module, which is reflected by increasing the VCG of the topside From the above derivation, the influence of the topside module on the stability performance of the whole lifting operation in the multi-body system can be decomposed into two parts: the static load of the topside module borne by the lifting vessel, and the overturning moment caused by the dynamic inclination of the topside module.The static load of the topside module borne by the lifting vessel is balanced by the transfer of ballast water from the left and right side heeling tanks, while the overturning moment caused by the dynamic inclination of the topside module requires the displacement of the lifting vessel and high initial stability to provide the restoring moment to reach a balance.

STABiLiTY AnALYSiS OF THE MuLTi-BODY COLLABOrATiVE OPErATiOn SYSTEM
When conducting a stability analysis of the multi-body floating system, the load from the topside module acting on the lifting system, the self-weight of the lifting system, and the load distribution of the lifting system are considered and transformed into a point load on the hull, and calibration is carried out by establishing a stability model of the hull and analysing the relevant stability indexes for the hull.
The overturning moment generated by the inclination of the topside module is reflected in the stability analysis.There are two possible approaches: one is to convert the overturning moment to the VCG of the topside module, which is reflected by increasing the VCG of the topside module; the other is that overturning moment be added to the loading calculation in the form of a free surface inertia moment.In this study, a stability analysis of the multi-body system is carried out based on the free surface inertia moment.The free surface inertia moment can be expressed as: the other is that overturning moment be added to the loading calculation in the form of a ce inertia moment.In this study, a stability analysis of the multi-body system is carried d on the free surface inertia moment.The free surface inertia moment  can be d as: odelling the lifting vessel, the contours of the wind area and the design water inlet point lished, and the stability performance of the multi-body system is analysed based on the e stability evaluation criteria.Table 2 shows the main dimensions of the lifting vessel e multi-body collaborative operation system.By modelling the lifting vessel, the contours of the wind area and the design water inlet point are established, and the stability performance of the multi-body system is analysed based on the applicable stability evaluation criteria.Table 2 shows the main dimensions of the lifting vessel used in the multi-body collaborative operation system.

Main scale parameters
Parameter value (m)

Moulded depth 21
Designed draft 12.5 Maximum draught for lifting operation 16.5 Table 3 provides the empty ship weight for the lifting vessel and centre of gravity position.The origin of the coordinate system applied here is at the intersection of the base plane, midship vertical plane, and stern bulkhead.In addition, each vessel design incorporates multiple lifting arms to enable diverse dual-vessel lifting schemes.A 5,000-ton sternmounted offshore crane is included to independent heavy marine capabilities and to support dual-vessel operations.The weight of the offshore crane is calculated as part of the weight of the empty vessel, while the weight of the lifting system is calculated together with the weight of the block as the load weight.The typical topside module information is selected as the target analysis block.Information on a typical topside module is given in Table 4.The environmental conditions are selected based on a previous sea state information survey and window period analysis in the Beihai area.Environmental information is shown in Table 5.  17), the moment of inertia of the free surface can be calculated as 1,123,776 ton•m.The stability analysis model is established as shown in Fig. 14, and the wind profile is established to determine the wind surface area as shown in Fig. 15.(1) The specific requirements for the integrity and stability of lifting operations are as follows, and are illustrated in Fig. 16: (i) The freeboard deck cannot be submerged.(ii) A RL ≥ 1.4A HL (iii) The minimum area under the curve of the restoring force arm from the equilibrium angle φ 1 to φ 2 the water inlet angle φ f or 20° is at least equal to 0.03mrad.

Tab. 4. Typical topside module data
Here, A RL is the area under the curve of the restoring force arm from the equilibrium angle φ 1 to φ 2 ; A HL is the area under wind tilt arm curve from the equilibrium angle φ 1 to φ 2 .φ 2 is the minimum value of the second intersection of the water inlet angle, the stability disappearance angle, and two curves.
(2) The specific requirements for sudden loss of stability of the hook load are as follows: Ships engaged in lifting operations and with reverse ballast should be able to withstand the sudden loss of hook load.Since the hook load may be applied to the most unfavourable point of the ship (i.e. with the maximum overturning moment), the area under the restoring arm curve on the opposite side of the crane is larger than the area on the side of the crane.For non-shielded waters, the following conditions need to be met, as shown in Fig. 17: Area 2 >1.4Area 1.

Fig. 16. Intact stability criteria under environmental and operational constraints
Fig. 17.Stability criterion in the case of heavy object loss GZ 1 is the resilience arm curve considering the influence of heavy moudle and ballast water before the loss of hook ; GZ 2 is the resilience arm curve considering the influence of ballast water after the loss of hook ; φ e2 is the static balance angle after loss of hook, the water inlet angle φ f is the small value of the second intersection point of the restoring force arm curve and the heeling force arm curve.
Fig. 18 shows the loading conditions for the two-ship lifting operation, and the results of an intact stability analysis under these conditions are shown in Fig. 19.It can be seen from Fig. 19(a) that the statistical angle is 0.1º and the dynamic angle is 28.5º.MOM denotes the heeling moment.Because the environmental is mild, so the overturning moment is small.Tables 6 and 7 present the results of an intact stability analysis and uncoupling stability analysis, respectively.
The deck immersion angle is found to be 7.619º and the static angle is 0.1º, meaning that the deck will not be submerged.7 also give a value of A1/A2 = a/b = 1.585 > 1.4.The angle of static equilibrium after loss of the crane load is zero and the position of opening immersion is 0.425º, so the openings will not be immersed when the ship is in the equilibrium position after losing the hook.The verification results demonstrate that the proposed dual-vessel cooperative approach to assembly and disassembly operations, in which we use multi-arm connections with motion compensation, meets the stability performance requirements for lifting a 30,000 ton topside module.The stability analysis method presented in this paper enables a stability evaluation of the multi-body cooperative operation system.Comprehensive stability checks were conducted on the vessels, lifting system, and topside module.

COnCLuSiOn
The aim of this paper was to address the limitations associated with current offshore assembly and disassembly equipment by proposing a new approach based on multi-arm lifting connections with integrated motion compensation capabilities.From hydrostatic considerations, we develop an equivalent simplified overall stability analysis method for a multi-body system, which enables checks of the intact and loss-of-load stability of the dual-vessel collaborative operation system.In this system, multiple lifting arms connect the lifting vessels to the topside module, and integrated motion compensation is applied between components.The main conclusions of the study are as follows： (1) Although rigid connections can offer excellent stability and safety, realising these in practical offshore engineering scenarios poses considerable challenges, especially when decommissioning aged platforms, due to issues with stiffness and resistance.This paper has put forth a lifting arm motion compensation system to help resolve such difficulties.The proposed mechanism aims to relieve the bending moments at the connection point between the lifting apparatus and topside module, and to prevent the transfer of wave loads impacting the lifting vessel, particularly via torque stresses on the lifting arms and topside assembly.By offsetting the relative motion, this approach endeavours to guarantee the structural soundness of the topside module.Our solution seeks to overcome the technical barriers hampering renewal and disassembly operations involving outdated fixed offshore structures.
(2) A formula is derived to allow us to calculate the transverse ballast water allocation required to balance the torque generated by the increase in the lifting load.The variation in the ballast water needed to cope with the tidal changes in the working sea area is also calculated.Through an analysis of the tilting moments imparted on the lifting arms and the lifting loads exerted on the vessel, and considering the effects of the tide on the disassembly operation, the design of the cabin layout and ballast water system was optimised.The results showed that equipping the single vessel with seven groups of anti-heeling tanks and 14 anti-heeling pumps was an effective approach.The maximum volume of ballast water transfer was determined to be approximately 10,900 m 3 , where each pump had a flow rate of 1,500 m 3 /h.This optimised ballast water system design will help ensure safe and stable heavy lifting operations in variable tidal environments.
(3) Intact and loss-of-hook stability analyses were conducted for a dual-vessel heavy lifting configuration, where the overturning moment imparted by inclination of the module was incorporated into the loading calculations as an inertial moment from free surface effects.The results demonstrated that lifting a 30,000-ton topside module using this approach would satisfy all stability criteria under both intact and loss of hook stability conditions.The results for the intact stability exceeded the calibration thresholds by a wide margin, and the loss of hook stability was also above the required levels.This confirms that the proposed lifting configuration and methodology can safely perform heavy lifting operations for very large modules, while effectively achieving both intact and loss-of-hook stability throughout the operation.Our approach was therefore validated in this analysis, and provides an efficient solution for offshore disassembly of mega-scale oil and gas infrastructure modules.
In summary, this paper has presented a dual-vessel lifting approach with motion compensation, which was validated using stability analysis.Our scheme addresses the shortcomings of current systems and enables the optimisation of collaborative offshore module disassembly operations.

Fig. 6 .
Fig. 6.Stability models for rigid and hinged connections: (a) hydrostatic model for a rigid connection; (b) hydrostatic model for a hinged connection

Fig. 8 .
Fig. 8. Layout of the ballast tanks of the lifting ship

Fig. 9
Fig.9shows a schematic diagram of the lateral section of the ballast tank.The initial ballast water condition, the ballast water adjustment between the 2S and 2P heeling tanks, the tidal adjustment of the ballast water condition of the ballast tank, and the real-time changes are used to reflect the changes in the ballast water volume of each cabin during the operation.

Fig. 9 .
Fig. 9. Horizontal section diagram of the ballast tank

Fig. 11 .
Fig. 11.Schematic diagrams showing the change in ballast tank water volume at: (a) high tide; (b) ebb tide

Fig. 12 .
Fig. 12. Stability state diagram for the multi-body system

Fig. 12 .
Fig. 12. Stability state diagram for the multi-body system Fig. 13.Force diagram of the top

Tab. 3 .
Empty ship weight for the lifting vessel and centre of gravity position

Table 2 .
Main dimensions of the lifting vessel 4 Tab.7. Results of a loss of hook stability analysis POLISH MARITIME RESEARCH, No 2/2024 57