## 1 Introduction  
Wind energy, as a renewable and clean energy source, has the advantages of abundant reserves, no need for transportation, and wide distribution [1, 2]. The stable and efficient development and utilization of wind energy is one of the most important development directions for achieving the goals of carbon peak and carbon neutrality [3, 4, 5]. The frequent movement of yaw results in long-term and unbalanced force loads on wind turbine blades, leading to fatigue accumulation [6], which may potentially cause structural damage to the blades, resulting in cracks and damages that may shorten its expected service life. Research on large wind turbines has shown that the accurate failure location of blades is generally at the stress concentration location [7]. Therefore, the study of blade stress under yaw conditions has a direct and important impact on the reliability and lifespan of wind turbine blades. The load on the wind turbine blades changes with azimuthal changes; the trailing and shed wake vortices increase indistinctly; and the wake velocity distribution is asymmetrical, according to aeroelasticity studies of wind turbines [8, 9, 10]. Numerous numerical techniques have been utilized to determine the effects of the yaw coefficient on wind turbines' power,power coefficients, and rotor torque. Experimental investigations have demonstrated a substantial link between the power coefficient and the yaw angle [11; 12]. Yaw inputs lead the axial velocity to decrease, which significantly lowers the output power and thrust [13; 14; 15]. [PERSON] et al. [16; 17; 18] examined the power and thrust coefficients of wind turbines under various steady and transient yaws while taking into account the dynamic yaw process. For each of the spanwise portions, the aerodynamic performance and angle of attack distribution were calculated. They discovered that dynamic yawing resulted in larger fluctuations than static yawing, and analyzed the causes of this. The angle of attack (AOA) of a blade on a horizontal offshore floating wind turbine was studied by [PERSON] et al. [19] using the free vortex method under both static and dynamic yaw conditions. They discovered that in the dynamic yawed condition, upwind and downwind yawing effects occurred and contributed to AOA fluctuations. [PERSON] et al. [20; 21] investigated the structural responses, buckling stability, and ultimate bearing capacity of a large-scale wind turbine system under various wind and wind-rain conditions, taking into account the effect of the yaw angle. This was accomplished in the study of stress-strain on wind turbine blades combined with yaw. The results demonstrated that the yaw angle may significantly affect a wind turbine system's aerodynamic efficiency and overall stress performance, and that fatigue brought on by the yaw circumstances can significantly reduce the system's lifespan. [PERSON] et al. [22] studied the influence of the interaction between a flange diffuser and the yaw angle of a blade, and found that the influence of the wind-lens on the dynamic strain in the blade root was substantial, and that large yaw angles led to low strains. [PERSON] et al. [23] analyzed the aeroelastic performance of wind turbines under various fixed yaw angles, and concluded that the blade strain had a fairly asymmetrical distribution during one rotation of the rotor. Studies have shown that the measured fatigue spectrum of a free-yaw small wind turbine consists mostly of many low-mean-stress and low-stress ratio cycles. By decreasing unsteady yaw behavior and lowering the maximum yaw rate, the mean stresses of these loads can be decreased [24]. Wind turbine blade stress causes blade fatigue, and fatigue failure is the main cause of wind turbine blade failure. The influence of bend-twist coupling (BTC) on fatigue loads under various wake situations has been examined using a stress-based methodology, and the BTC method was found to reduce those loads [25; 26]. [PERSON] et al.