## 1 Introduction  
Compared with the fixed-type Offshore Wind Turbines (OWTs), the advantages of the floating OWTs are more suitable for mass production and easy to install offshore. They can be roughly divided into three primary concepts, spar buoy, TLP, and barge, in terms of how they achieve the basic stability [1]. The spar buoy maintains the stability of the platform from a deep draft. The original spar buoy, developed by Statoil of Norway [2], is called Hywind, and the bottom is connected by three catenary mooring lines. The stability of Hywind can be enhanced by adding the ballast water. The TLP maintains its stability basically by way of a mooring system and buoyancy [3]. The requirement of ballast for TLP is relatively low compared with the other concepts, but the design of the mooring system is the most complex. Since the vertical direction of the mooring lines corresponding to TLP needs to be subjected to large force, the requirement of the mooring system for stability is the most high. [PERSON] and [PERSON] [4] indicated that the performance of TLP can be improved in different environmental conditions and water depths by using several design parameters like ballast, pretension, and pontoon radius. On the other hand, the barge maintains stability by using a large water plane and shallow draft. The concept of the barge is a flat-bottom platform, which has a large waterline area and a high restoring stiffness [5]. Another hybrid concept is semi-submersible [6; 7], which is mainly composed of structural columns connected with the pontoons and the operating deck. The operating deck is located high above the sea level due to the good stability of the design, and thus is kept away from the waves. [PERSON] and [PERSON] [8] suggested that the stability of floating OWTs be increased with help of mooring system, ballast and floating platform. There are three common mooring configurations, including taut-leg, catenary, and semi-taut mooring systems [9]. The taut-leg mooring system is usually used with the TLP, whereas the catenary mooring system is used with the spar buoy, the semi-submersible, and the barge floating platforms. The other concept of the mooring system is the semi-taut mooring system, which is a mix between the characteristics mentioned above, though this configuration is less common. [PERSON] and [PERSON] [10] indicated that the catenary mooring lines hanging horizontally at the seabed are capable of sharing the external forces over their lengths. [PERSON] and [PERSON] [11] explained that the taut-leg mooring line does not contact the seabed and is taut due to the pretension caused by the platform excess buoyancy. The restoring forces are generated mostly by line elasticity. For the same size and weight of the platform, the mooring radius of the taut-leg system is smaller than that of the catenary mooring system. Semi-taut moorings are also used on some semi-submersibles, consisting of synthetic fibers, chains, or wire moorings. More specifically, the mooring system consists of three parts: an anchor system, a mooring line and a specific mooring layout. The mooring layout depends on the local environmental conditions and the purpose of the offshore unit. Since it is quite complicated to calculate the mooring load, the mooring system is usually defined as a rigid body fixed on the seabed. In addition, the whole system is assumed to be a homogeneous material, so it can be regarded as the product of the linearized restoring matrix and motion responses of the floating unit. In case of neglecting inertia and damping forces in the mathematical model, the computing speed can be enhanced by considering elastic stiffness and effective stiffness in the stiffness matrix [12]. The quasi-static approach like DeepC [13] used for solving the quasi-static mooring system considers the relationship between displacement and force regardless of heave motion, inertia and damping effect of mooring lines.