A Novel Simplified Algorithm for Calculating the Mooring Line Based on Lumped-Mass Method
As an important component in Anchor Handling Simulator(AHS), the mooring system’s modeling and simulation have great impact on the AHS’s physical realism, behavioural realism and operating environment. We built the mooring line’s dynamics model based on L
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Navigation College, Dalian Maritime University, Dalian 116026, China {zzx19861018,bushyin}@163.com, [email protected]
Abstract. As an important component in Anchor Handling Simulator(AHS), the mooring system’s modeling and simulation have great impact on the AHS’s physical realism, behavioural realism and operating environment. We built the mooring line’s dynamics model based on Lumped-Mass Method (LMM) and used 4th order Runge-Kutta to solve it; However, the huge amounts of calculation in the model’s solving seriously hindered its application in AHS. To speed up the model’s solving process and realize the real-time simulation, we analysed the variables’ variation rates in the governing equation, identified the invariants, fast variables and slow variables, then proposed a novel simplified algorithm by adopting different time steps for their calculation. Experimental results show that, our simplified algorithm can reduce more than 64.5 % of the calculating time on the premise of assuring the accuracy and numerical stability. Keywords: Anchor handling simulator · Mooring system · Lumped mass method · Dynamics model · Simplified algorithm
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Introduction
There are various methods in dynamically analysising of the mooring system, including Lumped-Mass Method, Finite Element Method (FEM), Finite Difference Method (FDM), and etc. Among which, LMM [1–4] is a simple and easy to understand method, with definitely physical meaning and was extensively applied in the mooring line’s modeling and simulation. Chai [5] established a three-dimensional lumped-mass formulation of a catenary riser, capable of handling line-seabed interaction, bending and torsional stiffness. Wang Fei [6–8] and Zhu Ke-qiang [9, 10] established the underwater cable’s dynamics model based on LMM and investigated the current’s drag force, bending and cable-seabed interaction, and also simulated the cable’s deployment and retrieval. Hall [11] indicated that the quasi-static model would significantly under-predict the mooring loads and introduced a lumped-mass line model, and validated it against the scale-model test data of the floating offshore wind turbine. In the lumped-mass model, the mooring line need to be fully discreted in space, and the time step size is usually very limited (within 10 ms) for assuring the accuracy and the numerical stability. This leads into huge amounts of calculation, and brings the severe challenge to real-time simulation. © Springer Science+Business Media Singapore 2016 L. Zhang et al. (Eds.): AsiaSim 2016/SCS AutumnSim 2016, Part III, CCIS 645, pp. 89–97, 2016. DOI: 10.1007/978-981-10-2669-0_10
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The quest for real-time solving and simulation promoted the development of fast algorithms to accelerate the model’s solving process. Generally, if an improved algo‐ rithm is 20 %~50 % faster than the original, it can be considered as a significant contri‐ bution and can be published in academic journals. Obviously, this improvement is not easy. It requires thorough understanding on the algorithm’s connotation, very deep
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