Steady-State Configuration and Tension Calculations of Marine Cables Under Complex Currents via Separated Particle Swarm Optimization？

Under complex currents, the motion governing equations of marine cables are complex and nonlinear, and the calculations of cable configuration and tension become difficult compared with those under the uniform or simple currents. To obtain the numerical results, the usual Newton-Raphson iteration is often adopted, but its stability depends on the initial guessed solution to the governing equations. To improve the stability of numerical calculation, this paper proposed separated the particle swarm optimization, in which the variables are separated into several groups, and the dimension of search space is reduced to facilitate the particle swarm optimization. Via the separated particle swarm optimization, these governing nonlinear equations can be solved successfully with any initial solution, and the process of numerical calculation is very stable. For the calculations of cable configuration and tension of marine cables under complex currents, the proposed separated swarm particle optimization is more effective than the other particle swarm optimizations.     

Dynamic motion and tension of marine cables being laid during velocity change of mother vessels

Flexible segment model （FSM） is adopted for the dynamics calculation of marine cable being laid. In FSM, the cable is divided into a number of flexible segments, and nonlinear governing equations are listed according to the moment equilibriums of the segments. Linearization iteration scheme is employed to obtain the numerical solution for the governing equations. For the cable being laid, the payout rate is calculated from the velocities of all segments. The numerical results are shown of the dynamic motion and tension of marine cables being laid during velocity change of the mother vessels.     

Nonlinear dynamics of an elastic cable during laying operations in rough sea

A numerical approach for predicting motion and tension of extensible marine cables during laying operations in a rough sea is presented here. The solution methodology consists of dividing the cable into straight elements, which must satisfy an equilibrium equation and compatibility relations. The system of nonlinear differential equations is solved by the Runge–Kutta method, taking the effect of regular and/or irregular waves into account explicitly.

Illustrative applications of the method are given for a typical cable laying ship. The results are presented as rms values of the cable dynamic tension and corresponding dynamic factor for two different types of cable and several values of cable stiffness. The effect of axial deformation on the maximum tension at the shipboard pulley location is highlighted.     

A flexible-segment-model-based dynamics calculation method for free hanging marine risers in re-entry

In re-entry,the drilling riser hanging to the holding vessel takes on a free hanging state,waiting to be moved from the initial random position to the wellhead.For the re-entry,dynamics calculation is often done to predict the riser motion or evaluate the structural safety.A dynamics calculation method based on Flexible Segment Model(FSM) is proposed for free hanging marine risers.In FSM,a riser is discretized into a series of flexible segments.For each flexible segment,its deflection feature and external forces are analyzed independently.For the whole riser,the nonlinear governing equations are listed according to the moment equilibrium at nodes.For the solution of the nonlinear equations,a linearization iteration scheme is provided in the paper.Owing to its flexibility,each segment can match a long part of the riser body,which enables that good results can be obtained even with a small number of segments.Moreover,the linearization iteration scheme can avoid widely used Newton-Rapson iteration scheme in which the calculation stability is influenced by the initial points.The FSM-based dynamics calculation is timesaving and stable,so suitable for the shape prediction or real-time control of free hanging marine risers.     

水下非均匀拖缆稳态动力学分析

水下拖缆物理参数不均匀会影响拖缆的动力特性,研究非均匀拖缆的参数变化对拖缆动力特性的影响有一定的工程实际意义。建立了拖曳系统运动的三维数学模型,推导出了水下非均匀拖缆的稳态运动控制方程,在首尾两端加上相应的定解条件,直接求得或使用嵌套二分法求得非均匀拖缆在端点的初始值,进而求解稳态动力学方程。借助文献中的拖缆—海底拖车系统算例,通过计算结果的对比,验证了数学模型及计算方法的正确性。通过四阶龙格库塔法进行数值仿真计算,得到了稳态解,分析了非均匀拖缆自身物理参数变化对缆绳系统稳态运动的影响。结果表明,非均匀拖缆的切向阻力系数、法向阻力系数、直径和密度变化会影响稳态缆形和张力分布,影响的程度各不相同。最后给出了两个尾拖船系统非均匀拖缆的稳态运动算例。     

Time-domain numerical simulation of ocean cable structures

This paper describes the numerical features of WHOI Cable, a computer program for analyzing the statics and dynamics of oceanographic cable structures. The governing equations include the effects of geometric and material nonlinearities, bending stiffness for seamless modeling of slack cables, and a model for the interaction of cable segments with the sea floor. The program uses the generalized-α time integration algorithm, adaptive time stepping, and adaptive spatial gridding to produce accurate, stable solutions for dynamic problems. The nonlinear solver uses adaptive relaxation to improve robustness for both static and dynamic problems. The program solves surface and subsurface single-point mooring problems, multi-leg and branched array systems, and towing and drifting problems. User specified forcing can include waves, currents, wind, and ship speed.     

Free vibrations of three-dimensional extensible marine cables with specified top tension via a variational method

This paper presents a model formulation that can be used for analyzing the three-dimensional vibration behaviours of an inclined extensible marine cable. The virtual work-energy functional, which involves strain energy due to axial stretching of the cable and virtual work done by external hydrostatic forces is formulated. The coupled equations of motion in the Cartesian coordinates of global systems are obtained by taking into account the difference between Euler’s equations and equilibrium equations. The method of Galerkin finite element is used to obtain the mass and stiffness matrices which are transformed into the local coordinate systems. Then the eigenvalue problem is solved to determine its natural frequencies and corresponding mode shapes. The model formulation developed herein is conveniently applied for the cases of specified top tension. The numerical investigations are carried out to demonstrate the validity of the model and to explore in details the influence of various parameters on the behaviours of marine cables. Results for the frequency avoidance phenomenon, maximum dynamic tension and coupled transverse mode shapes are presented and discussed.     

Simulation of unsteady oceanic cable deployment by direct integration with suppression

An improved algorithm is developed for predicting the transient response of a system of serially connected cables and bodies during unsteady deployment from a surface vessel. The governing equations of a cable-body system are derived with dependent variables of cable velocities, direction cosines and tension magnitude to form a nonlinear combined initial-value and boundary-value problem. The problem is then solved by introducing a stable Newmark-like implicit integration scheme in time and by a direct integration method with suppression of extraneous erroneous solutions. Special boundary conditions simulating actively controlled payout and slack-cable/ocean-bottom contact boundary conditions are included in the present model.     

Nonlinear Finite Element Analysis of Ocean Cables

This study has focused on developing numerical procedures for the dynamic nonlinear analysis of cable structures subjected to wave forces and ground motions in the ocean. A geometrically nonlinear finite element procedure using the isoparamnetrie curved cable element based on the Lagrangian folmulation is briefly summarized. A simple and accurate method to determine the initial equilibrium state of cable systems associated with self-weights, buoyancy and the motion of end points is presented using the load incremental method combined with penalty method. Also the Newmark method is used for dynamic nonlinear analysis of ocean cables. Numerical examples are presented to validate the present numerical method.     

A Geometrically Exact Formulation for Three-Dimensional Numerical Simulation of the Umbilical Cable in A Deep-Sea ROV System

This paper proposes a geometrically exact formulation for three-dimensional static and dynamic analyses of the umbilical cable in a deep-sea remotely operated vehicle(ROV) system. The presented formulation takes account of the geometric nonlinearities of large displacement, effects of axial load and bending stiffness for modeling of slack cables. The resulting nonlinear second-order governing equations are discretized spatially by the finite element method and solved temporally by the generalized-a implicit time integration algorithm, which is adapted to the case of varying coefficient matrices. The ability to consider three-dimensional union action of ocean current and ship heave motion upon the umbilical cable is the key feature of this analysis. The presented formulation is firstly validated, and then three numerical examples for the umbilical cable in a deep-sea ROV system are demonstrated and discussed, including the steady configurations only under the action of depth-dependent ocean current, the dynamic responses in the case of the only ship heave motion, and in the case of the combined action of the ship heave motion and ocean current.     

Stability analysis of TLP tethers

Compliant offshore TLPs are essentially meant for deep oil/gas exploration and are usually constructed on the seashore and then towed down to the particular location for anchorage. They are connected to the sea bed by means of pretension cables. The increased use of TLPs in deep waters and necessity of reduction of usually high value of pretension make the effect of variable tension in the tether dynamics more significant. This work presents the dynamic analysis of tethers and TLPs considering the linearly varying tension along the tether length. The modal analysis considers a linear cable equation for tether modeling subjected to tension which varies along its length. A Mathieu stability analysis is then performed for TLPs of different shapes and different water depth vis-à-vis of 527.8, 872, and 1200 m respectively to obtain the amplitudes of tether vibrations. The unstable modes of vibration are also verified. The resultant modal forms for the tether's dynamic model are then obtained in form of Bessel's function. From the numerical studies conducted it is seen that increased tether tension not only leads to a stable platform but also improves the stability due to increased hydrodynamic loading contributing to added mass. From the studies conducted it is also seen that the triangular configuration TLPs with increased initial pretension are more stable compared to four leg TLP in the first mode of vibration.     

A Geometrically Exact Formulation for Three-Dimensional Numerical Simulation of the Umbilical Cable in A Deep-Sea ROV System

This paper proposes a geometrically exact formulation for three-dimensional static and dynamic analyses of the umbilical cable in a deep-sea remotely operated vehicle (ROV) system. The presented formulation takes account of the geometric nonlinearities of large displacement, effects of axial load and bending stiffness for modeling of slack cables. The resulting nonlinear second-order governing equations are discretized spatially by the finite element method and solved temporally by the generalized- implicit time integration algorithm, which is adapted to the case of varying coefficient matrices. The ability to consider three-dimensional union action of ocean current and ship heave motion upon the umbilical cable is the key feature of this analysis. The presented formulation is firstly validated, and then three numerical examples for the umbilical cable in a deep-sea ROV system are demonstrated and discussed, including the steady configurations only under the action of depth-dependent ocean current, the dynamic responses in the case of the only ship heave motion, and in the case of the combined action of the ship heave motion and ocean current.     

A tension measurement method of a towing cable or a buoy cable

An indirect tension measurement method of a towing cable in midwater or a buoy cable is proposed using underwater acoustic positioning systems, etc., to give the in-water cable tension. The most simple and traditional cable tension measurement method is to apply a mechanical tension meter at the one end of the cable, but the method has limits in the aspects of continuous monitoring and manual operation. However, the technique in this study is to apply the Pode's analysis of the equilibrium configuration and tension of a flexible twine, in which the cable tension is given as a function of the geometric positions of both ends of the cable. A set of nonlinear integral equations is formulated and solved numerically by the Newton-Raphson method. Then the inclination angles and the tensions at the lower and the upper ends of the cable could be obtained. The derived method enables us to track a towed object, to measure the tension of a towing cable or a buoy cable and is also applicable to the remotely operated vehicle (ROV) tethered to a mother ship.     

铯光泵磁力仪(G880)在海洋工程勘探方面的应用

为准确测出光、电缆的位置,利用G880铯光泵磁力仪,在芦潮港和大小洋山之间进行了磁力探测。经过探测,海底通信光缆能引起8~20 nT磁异常,海底动力电缆能引起约2 000 nT的强磁异常,根据磁异常形态曲线可定出光缆的位置。依据光缆的结构原理图,分析探讨光、电缆产生磁异常的原因。     

Numerical simulation of towed cables

A numerical method for the dynamic simulation of towed cables is presented. The cable is loaded by fluid drag, tension, gravity and buoyancy, including the effects of weights and floats. The development of a cable can be simulated as well as the separation of a cable under excessive load and the subsequent behavior of the broken parts. The system is constructed from a set of generic elements representing such items as cable or rope strands, knots (reference points on rope sections), kinks (sliding reference points on cable sections that change length), cable ends and winches. A mathematical graph organizes these elements in a general and flexible fashion: it allows construction of complex systems and permits structural redefinition during the simulation. The nodes of the graph coincide with the various reference points of the problem, at which physical parameters are lumped and to which sets of ordinary differential equations are associated that define the motions of the points. The links of the graph describe the physical connections between the nodes. Application of new methods for solving stiff, sparse systems of coupled ordinary differential equations enables efficient simulation of snap-loads and other severe events. Results are presented that compare quantitatively with laboratory measurements. A further example shows the behavior of a breaking cable that is qualitatively reasonable.     

深海平台系缆形状和张力分析

考虑海底地形的变化、系缆的拉伸形变及海流力等因素,研究了深海平台系缆形状和张力分析方法采用集中质量法,得到系缆方程组,采用牛顿法求解该非线性系缆方程组,建立系缆形状和张力的计算方法。计算了平坦海底和海底地形凹凸变化时水深1 018 m情况下的系缆形状、系泊张力和浮体平衡位置。计算结果表明,海底地形对于深海系泊系统张力影响较大,而计算系缆形状和张力、系泊浮体的运动时,需要考虑海底地形的影响。     

Numerical modeling of nonlinear water waves over heterogeneous porous beds

The transformation of nonlinear water waves over porous beds is studied by applying a numerical model based on Chen's [2006. Fully nonlinear Boussinesq-type equations for waves and currents over porous beds. Journal of Engineering Mechanics, 132:2, 220–230] Boussinesq-type equations for highly nonlinear waves on permeable beds. The numerical model uses a high-order time-marching solution and fourth-order finite-difference schemes for discretization of first-order spatial derivatives to obtain a computational accuracy consistent with the model equations. By forcing the wave celerity and spatial porous-damping rate of the linearized model to match the exact linear theory for horizontal porous bed over a prescribed range of relative depths, the values of the model parameters are optimally determined. Numerical simulations of the damped wave propagation over finite-thickness porous layer demonstrate the accuracy of both the numerical model and governing equations, which have been shown by prior theoretical analyses to be accurate for both nominal and thick porous layers. These simulations also elucidate on the significance of the higher-order porous-damping terms and the influence of the hydraulic parameters. Application of the model to the simulation of the wave field around a laboratory-scale submerged porous mound provides a measure of its capability, as well as useful insight into the scaling of the porous-resistance coefficients. For application to heterogeneous porous beds, the assumption of weak spatial variation of the porous resistance is examined using truncated forms of the governing equations. The results indicate that the complete set of Boussinesq-type equations is applicable to porous beds of nonhomogeneous makeup.     

A finite element cable model and its applications based on the cubic spline curve

For accurate prediction of the deformation of cable in the towed system, a new finite element model is presented that provides a representation of both the bending and torsional effects. In this paper, the cubic spline interpolation function is applied as the trial solution. By using a weighted residual approach, the discretized motion equations for the new finite element model are developed. The model is calculated with the computation program complier by Matlab. Several numerical examples are presented to illustrate the numerical schemes. The results of numerical simulation are stable and valid, and consistent with the mechanical properties of the cable. The model can be applied to kinematics analysis and the design of ocean cable, such as mooring lines, towing, and ROV umbilical cables.     

Quasi-static three-dimensional analysis of suction anchor mooring system

The suction anchor has been widely used in taut or semi-taut mooring systems as an effective and economical solution to anchoring problems. To ensure high reliability, the profile of the mooring cable connecting the fairlead and the pad-eye must be accurately designed. However, previous studies have rarely considered the effect of cable slippage in soil on the mooring behavior, or embedded cables have been studied with an assumed tension at the seabed. This paper, by treating the cable suspended in water and the cable embedded in soil as a single cable, presents a two-dimensional (2D) static model and a three-dimensional (3D) quasi-static model for the cable during pretensioning and in service, respectively. The two models take into account the comprehensive effects of ocean currents, soil resistance and cable elasticity, all of which are critical for the design of a mooring system. Three examples are analyzed using the models and some useful conclusions are drawn.