## 1 Introduction  
With the economic and social development and the increasing global population, the demand for high-quality protein is constantly rising. Demand for marine-raised fish, as one of the primary sources of protein, is also increasing. The development of offshore cage aquaculture is becoming critical as one of the global fishing powers due to the diminishing space for nearshore aquaculture [1]. In China, the main types of cage aquaculture facilities include nearshore raft-mounted cages, gravity-type deep-water cages, and large truss-type cages. However, due to the limitation of the simple structure, poor wind and wave resistance, and potential pollution issues, the scale of nearshore raft-mounted cage aquaculture has gradually decreased in recent years. Large truss-type cages, while offering robust support for aquaculture operations, are expensive and mainly adopted as management and support platforms for fishing farms, rather than for widespread deployment in a single fishing ground. In contrast, gravity-type deep-water cages offer significant advantages in terms of ease of daily operation. And they are also cost-effective, which makes them the leading choice for offshore cage aquaculture. Over 95% of deep-sea fish production in China comes from high-density polyethylene (HDPE) gravity-type deep-water cages. The cages are required to possess sufficient natural risk resistance for cultivating in deep and remote offshore areas, especially under extreme conditions such as typhoons, which is crucial for achieving economic benefits from aquaculture. Therefore, it is required to develop reliable cage facilities and accurately assess their dynamic response characteristics under wave and current. This work focuses on studying the dynamic response of a novel single-point mooring gravity-type deep-water cage (Figure 1). Numerical simulation methods are employed to investigate its dynamic response characteristics under irregular wave and current interactions, which consider actual service conditions. The findings of this research will provide valuable insights for the optimized design and analysis of gravity-type deep-water cages, contributing to the sustainable development of offshore aquaculture. The gravity-type deep-water cage system comprises three integral components, i.e., the mooring system, the net system, and the floating collar system. Prior research efforts have centered on these three aspects. As one of the most important elements of the deep-water cage, through connecting to the cage's main frame and constraining its movement within a safe limit, the mooring system effectively resists wave and current impacts. Mooring systems usually include mooring lines and anchors. The materials of mooring lines are usually divided into ropes, steel chains, or a combination of ropes and steel chains. The mooring rope is generally used in GDW net cages, and for large fish farming platforms (cages), steel mooring chains are generally used. Anchor types can be selected as needed, such as ordinary iron anchors, high-holding power anchors, etc. To reduce the mooring cost of multiple facilities in sea areas, some shared anchors were also used [2]. Depending on the number of mooring lines, mooring systems can be broadly classified  
Figure 1: The new type of single-point mooring gravity-type deep-water (SPM-GDW) net cage. (**a**) The real net cage in the sea; (**b**) The diagram of the net cage. into two categories, i.e., multi-point mooring (MPM) and single-point mooring (SPM). Multi-point mooring cages, being a traditional type of cage, offer the distinct advantage of maintaining a relatively stable position under wave and current impacts. The research on cage mooring usually focuses on the evaluation of mooring bearing capacity and mooring optimization.