Trade study to select best alternative for cable and pulley simulation for cranes on offshore vessels

Funding information NorwegianResearchCouncil,Grant/Award Number: 237896 Abstract Cranes onoffshore vessels are subjected to crane dynamics, structural couplings to the vessel, and environmental influence bywaves and currents. The recent trend has been to use larger cranes on smaller vessels, which makes the lifting operation more complex and potentially dangerous. The use of digital twins (DTs) is emerging as one way to enable safer operations, real-time simulation, andmaintenance prediction. On offshore vessels, a DT canmonitor the lifting operation to create a saferwork environment. The SPADEmodel has beenused as a framework toward the creation of a DT of cranes on offshore vessels. Several cases involving simulation of cranes revealed the lack of an adequate simulation of cable and pulleys suitable for use in aDT. The simulation is important for accurate results and for implementation in control systems. A trade study was performed to determine a numerical method adequate for cable and pulley simulation. The trade study identified the absolute nodal coordinate formulation in the framework of arbitrary Lagrangian–Eulerian as a promising numerical formulation.


INTRODUCTION
Offshore vessels with cranes are used for operations, such as installation of subsea templates, offshore wind turbine installation, and loading and unloading of equipment. Wind, waves, and currents complicate these operations. The recent trend has been to use smaller vessels, with larger cranes, as a means for saving costs. This makes the lifting operation more subject to instability due to the environmental excitations. A digital twin (DT) of an offshore crane supports a wide range of applications. It would allow for safer lifting operations with less downtime based on anticipated failure modes, such as buckling in bars and actuators, material yielding and fatigue predictions, as well as an improved control system. The DT simulations improve payload control allowing for lifting operations in demanding weather conditions, and better maintenance schemes based on fatigue predictions. If the control system detects irregularities, the operator is notified. In dangerous situations, the control system could restrict continuation of the operation. A DT could be used to estimate the weight of the payload, instead of using a scale, and the project manager could use data from the DT as basis for risk analysis when planning lifting operations.
This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. c 2019 The Authors. Systems Engineering published by Wiley Periodicals, Inc.
A step toward creating a DT of a crane on offshore vessels is to improve the simulations. The Norwegian oil and gas industry relies heavily on offshore vessels with cranes, and the Research Council of Norway is currently funding this research through an innovation grant (SFI). This paper investigates the requirements for improved simulations as part of this research. The structure of this paper is as follows: first, the paper presents a context diagram of crane dynamics for a better understanding of physics and dynamics, with the theoretical background for simulation. Then, stakeholders are identified to investigate different interests in the research. The main body of the paper then reports on requests for crane simulation according to cases and previous research. Here, it is observed that cable and pulley simulation lacks sufficient accuracy, and a better simulation of cable and pulleys is needed for a DT. Based on design requirements, a trade study is performed to investigate alternatives for different numerical methods for dynamic simulations of cable and pulleys to embed in a DT, where the real-time aspect is important. The paper concludes with a suggested cable and pulley simulation and further work. The paper follows the SPADE methodology as proposed by Haskins. 1 Systems Engineering. 2019; 1-12. wileyonlinelibrary.com/journal/sys 2 FOTLAND ET AL.

BACKGROUND
Schluse and Rossmann 2 list several domains where the term "digital twin" is used differently for industrial practices: manufacturing flexibility, product design, maintenance, increased lifetime, testing, structural monitoring, performance efficiency, quality, and automation.
A DT can be used, not only for engineering and manufacturing, but also operations and service. According to Boschert and Rosen,3 this implies that the DT could become a part of the real system, with actionable interactions. For the remainder of this paper, DT is defined as a digital copy of a physical asset, collecting real-time data from the asset and deriving information not being measured directly in the hardware.
The context diagram is a helpful tool to examine the systemic picture of what must be included to create a DT of an offshore crane, see Figure 1. The goal of a DT is to be able to simulate the whole crane system. The primary context for the DT is crane dynamics, which is an attribute of the crane, both the physical asset and its maintenance and operation. These in turn are mounted on a vessel that operates in maritime environments, including both open water and harbor operations. The way these elements interact during a lifting operation is described here.
The winch on the crane is an essential part of the lifting mechanism.
The crane operator is responsible for safe lifting operations, and therefore could be willing to work in harsher environments with a better control system. Likewise, maintenance is a critical factor for the crane to be operational and is important when planning, to minimize downtime.
A functioning DT requires the physical crane to be equipped with weather-resistant sensors, placed where they are shielded from the environment.
A multibody system (MBS) consists of several submodels, which make up the system being simulated, see Figure 2. The different parts have a computer aided design (CAD) model, which could be used as a rigid body, or meshed with finite elements for elastic behavior. Mechanism modeling uses joints to connect the parts for interaction. Control system modeling is used for actuators, such as the hydraulic cylinders F I G U R E 2 A CAD model of the crane system with different submodeling elements indicated and the virtual sensors. The 1D flow chart presents an example of a control system, where real or virtual sensors can be the position input.
The applied force will be set according to deviation in measurement and reference value. Cable and pulley modeling is usually simplified to an axial spring. A simple example of a DT is found in Figure 3. In this illustration, the physical sensor data (PSD) from the physical crane are stored in a state vector, which contains stroke length of actuators, turn angle, reference strain for verification and calibration, and applied load from the payload at the crane tip.  what sensors to use, where to install them, and how to process and filter the data from the sensors will not be addressed in this paper.

RESEARCH METHOD
When exploring new complex systems, it is useful to structure the relevant information. This increases the possibility of making good decisions, exposing gaps, problem solving, and making progress with confidence. Systems engineering (SE) provides tools to handle this. Creating a reliable and robust DT of an offshore crane is new technology. This makes SE tools highly relevant and useful for such a development project.
The SPADE methodology was introduced by Haskins, 1 see Industry Partners: Partners meet regularly, and industry partners make themselves available to academic researchers. Figure 6 summarizes the needs of the stakeholders for this research.
• SFI crane producer partners are interested in making safe and reliable products. Improved simulations of cranes as well as real-time feedback would help them to understand how forces acts on the

Measures of effectiveness
When the problem has been formulated, then criteria are put in correct term as measures of effectiveness (MOE). MOE represent the viewpoint of stakeholders and Sproles 11 argues that it assists in making the right choices based on the stakeholders' needs. This establishes the success criteria to recognize when the end goal is reached. MOE for this project: • A cable and pulley simulation that improves the overall real-time simulation of a crane on an offshore vessel.
• A cable and pulley simulation that can be integrated with DT of a crane on an offshore vessel.

Technical performance measures
Technical performance measures (TPMs) are key goals to be met, where the actual progress of technical achievement is monitored using periodic measures or tests. As noted by Garvey and Chien-Ching, 12 this will indicate how well a system is approaching its performance requirements. The TPMs for this project include: • Less unplanned downtime: Due to better prediction of equipment failure, the crane can be maintained prior to breakdown.
• Less downtime: Maintenance is performed when required, instead of on a predetermined schedule.
• Less maintenance cost: Only the worn-out parts are replaced, leading to a longer lifetime of crane and parts.
• Less waste: As the crane and the parts are in service for a longer period, there will be less waste.
• Fewer incidents: The number of industrial injuries concerning work with cranes on offshore vessels is reduced when using a DT. The DT has alarm systems for dangerous situations and has improved payload control.
• Faster operations: With better payload control, the lifting operations will be carried out more efficiently.
• Increased operational time: Due to a better control system, work can be done in harsher environments.
Most of these measures have a temporal quality, which means that the researcher must rely on historical data and data collected after the DT is implemented to assess the actual benefits of the DT, and then the simulation. However, some practical assertions regarding increased operational time and maintenance can be estimated.

PROBLEM FORMULATION
Over simulation. The cases exposed the need for an improved cable and pulley simulation and will function as benchmarks for further research.

Laboratory crane 1 -knuckle boom crane
A knuckle boom crane for testing is built in a laboratory at NTNU, see Figure 7. The crane is accessible for running experiments and benchmarking. It is instrumented with strain gauges for data collection when running experiments, as well as a detailed FEM model. The Insight gained here could be used for condition-based maintenance.

Laboratory crane 2 -knuckle boom crane
A knuckle boom crane for testing in a wave pool is located in a laboratory at NTNU, see

Johan Sverdrup -tower crane
Structural vibrations in the tower cranes on the recently deployed oil rig Johan Sverdrup have been investigated, see Figure 9. The FEM model of the oil rig is very detailed. FEM accounts for internal deformations in the crane, which is a reason to use it for analysis of structural flexibility. The crane is a complicated system with delays related to boom flex, hydraulics, and tension in the cable. Since the frequency in the cable changes with varying length, mass, and stiffness in the cable, an improved cable and pulley simulation could make the overall results more accurate for this case.

ALTERNATIVES FROM TRADE STUDY
To identify the best alternative feasible as a numerical formulation for cable and pulley simulation, a trade-off analysis based on Blanchard and Fabrycky 7 has been performed, see Figure 5. 6. The simulation method should result in reliable numerical formulation with documentation as evidence of extensive testing.

Alternatives for cable and pulley simulation
Based on the MOE, stakeholders, and design requirements, alternatives for cable and pulley simulation are identified and briefly described in the following sections.

Spring
In FEA, a cable has commonly been represented as an axial spring. 14,17 This is derived from Hooke's law, F = −kx, where F is the force, k is the spring characteristic, and x is the axial displacement. For more advanced behavior, the spring characteristic can be tabulated dependent on the cable length. This formulation neglects mass and inertia forces, only axial stiffness is included in the cable dynamics. The normal forces on the pulleys are not considered. The approach results in fast calculations, and can provide sufficient results for certain simulations. The formulation is reliable, as it is simple and has been extensively tested.

Isogeometric analysis
Raknes et al 18  still suffers from some numerical challenges, and the major drawback is that it struggles to handle contact analysis. 21 The use of IGA would involve a risk, as the numerical formulation is less mature than FEM, and possess possible complications when combining it with FEA.

The bar finite element for cable
The bar finite element 22 is based on a principle to split the bar element into perfectly straight and homogeneous elements. The elements have elastic properties without rotational degrees of freedom (DOF).
Through a coupling between consecutive bar elements, bending stiffness is included. This leads to forces on the extremities of these two elements when a curvature occurs on the modelled cable. A large number of elements are required for an exact representation of the cable. The formulation includes drag forces from water, and has been tested for simulation of fish cages and fishing gear.

A parametric super element
Ju and Choo 23 present a super element numerical formulation for a cable passing through several pulleys. The method can represent complex geometric paths for a long cable. A tower crane has been analyzed by this formulation. Static simulations are the primary target for this formulation; therefore, it neglects the dynamic behavior of the pulley.

The floating frame of reference formulation
Floating frame of reference formulation (FFRF) was the most widely used formulation for simulation of flexible MBS. 24 In FFRF, there are two sets of coordinates used to describe the configuration of the deformable bodies; the rigid is described in the global coordinate system, while the local deformation is described in a local coordinate system. To compensate for the distance between the global and local coordinate system, centrifugal and Coriolis terms must be considered. variant of the FFRF, as presented in, for example, Horie et al, 26 is good for MBS. 27 The VFE cannot account for large deformations and large overall motion with variable-length bodies due to the inherent nature of FFRF. it is more accurate and less computationally demanding. Romero 30 points out that a geometrically exact formulation requires a special time stepping method. This makes the geometrically exact formulation more complicated to implement than ANCF.

The absolute nodal coordinate formulation
For the last two decades, the ANCF has gained attention for modeling of large-deformations and large-rotations in multibody dynamics, with simulation of tires and belt drives as examples. 33 44 Both studies used a master-slave technique.

Arbitrary Lagrangian-Eulerian -ANCF
The  Figure 10. The advantage being that fewer elements are needed to represent the cable. The reason for this is that contact is numerically difficult to simulate, especially for the timesteps when contact between elements occur during a simulation.
When any random cable element can happen to be in contact with the pulley at some point of time, all the cable elements must be small. With ALE, free cable elements can be larger, allowing for fewer elements and faster simulations. Another advantage is that for the simulation of reeling, it is possible to add or remove excessive cable.
Based on Hong and Ren, 45 Peng et al 46

Coupling motion between cable and pulley
Qi et al 49

Evaluation of alternatives
It is not straightforward to decide upon the best alternative for a numerical formulation to use for cable and pulley simulation. There are many aspects to take into consideration, such as calculation time, dynamics, and contact formulations. An analysis based on the subjective value method according to Kossiakoff et al 8 is presented in Figure 11. This was used for cross-referencing design requirements and options for evaluation of the different formulation candidates.
Based on the alternatives of numerical formulations for cable and pulley simulation evaluated in this paper, the spring element is commonly used, but is lacking both a good dynamic representation and contact formulation. IGA is premature, as it is not FEM compatible, and the formulation is not extensively tested, although it might be relevant in the future. ANCF converges faster than FFRF. 35  SE has proven to be a useful approach for the creation of a DT, because it provides a ready-made framework with tools to expose deficiencies, establish design requirements, and find alternatives. For structuring complex systems, this is invaluable. Since the creation of DT of offshore cranes has never been done before, SE is highly relevant.

FURTHER WORK
This paper documents the process of choosing a numerical formulation method. It remains now to move to the next phases as follows: • To verify the selected formulation for cable and pulley simulation, a DT of the laboratory knuckle boom crane should be made for benchmarking. This will verify if the selected alternative is feasible. Testing will also reveal further requirements for having a fully functioning DT of an offshore crane.