## 1 Introduction  
As traditional energy sources have been increasingly exhausted over the past decades, renewable energy, especially wind energy, has received more attention than ever before. Wind energy has less environmental pollution and can reduce greenhouse gas emissions such as carbon dioxide. Because wind energy has such good properties and meets the expectations of improving the global climate, it has been promoted and developed over the past few decades, and the technology is becoming more mature. According to relevant reports, the annual share of wind energy used to generate electricity in the world is increasing, and has reached \(2.74\times 10^{9}\) MW [1]. On the other hand, in wind energy production, due to factors such as the environment, for example, the open space on the sea is rarely obstructed, and it is significantly different from the land, so that the average speed of the wind is 90% higher than that on the land [2]. At present, the fixed bottom offshore wind turbines that are favored worldwide mainly include the following forms: single piles, tripods, and jackets. These structures are mostly used in shallow-water offshore wind facilities. However, with the increase of water depth, the construction cost of fixed-bottom offshore wind turbines with fixed foundations such as pile-supported foundations significantly increases, especially when the water depth exceeds50 m. The floating foundation anchors the floating structure to the seabed using an anchoring system and serves as a base platform for installing wind turbines. Compared with the fixed foundation of the offshore wind turbines, the floating foundations of wind turbines have the advantage that the installation position of the floating foundation can be moved easily. It can be installed in deeper waters with more abundant wind energy, not necessarily limited to shallow water shelves with limited area. In comparison, the floating base applicable in the sea area is much larger than that in the shallow sea area; it is installed in the waters far away from the coastline, eliminating the visual impact and greatly reducing the influence of noise and electromagnetic waves [3]. Since floating offshore wind turbines have many of the advantages described above, in the field of wind turbines, researchers have conducted extensive research work on them in order to install wind turbines on floating devices [4; 5; 6; 7]. At the same time, on the technical level, since offshore oil rigs have been operating safely for decades, a large amount of empirical data has been accumulated to ensure the long-term use of floating structures in the marine environment. This provides sufficient conditions for the design and construction of a floating wind turbine. Floating offshore wind turbines (FOWT) [8] are particularly suitable for use in waters with a depth of more than 50 m [4], so it is a more worthwhile option for offshore wind farms that meet this condition and can achieve more economic benefits. According to relevant information, in June 2009, the 2.3 MW Hywind facility, the world's first large-scale floating wind turbine, was towed to a Norwegian North Sea location with a water depth of about 220 m (722 feet) and began operation. The Hywind Floating Wind Turbine is the first large-scale wind turbine supported by an underwater floating structure similar to ones used by off-shore oil rigs. The project is running successfully and the turbine has produced over 80 GWh of energy to date [9]. Inspired by the success of the Hywind Demo, the Scottish government has approved Statoil plans for the 30 MW Hywind 2 floating offshore wind project some 25 km off Peterhead. The Norwegian company was issued with a marine license to build five Siemens 6 MW turbines on spar foundations [10; 11]. It is expected that the farm could power up to 19,900 homes. Even though the concept of a FOWT was proposed by [PERSON] [12] in 1972, due to the immature technology at that time, the concept of FOWT was not widely known until the mid 1990s.