## 1 Introduction
Their research demonstrated that this surrogate model could handle high-dimensional data and variable interactions, using permutation-based variable importance indices to quickly identify important inputs. [PERSON] et al. [22] proposed a new method combining model-dependent structure extraction with surrogate models to evaluate the individual, overall, and interactive contributions of related variables to the  
Figure 1: Manufacturing Process of Wind Turbine Blades. model output. Their study showed that this method could efficiently perform variance and derivative-based sensitivity analyses. [PERSON] et al. [23] introduced the matrix concept to improve the computational cost and accuracy of multi-objective reliability design for complex structures, developing a vector surrogate modeling (VSM) method. Numerical examples and engineering cases indicated that VSM is feasible for simultaneous modeling and integrated reliability design, offering superior computational efficiency and accuracy in high-dimensional, nonlinear problems. [PERSON] et al. [24] developed a new learning function, stopping criterion, and candidate selection method, proposing an optimized surrogate model method for sensitivity analysis. They introduced a hybrid candidate selection method and a stopping criterion based on the relative mean of the learning function. The results showed that the surrogate model has a high accuracy and efficiency in sensitivity analysis. [PERSON] et al. [25] proposed a system-reliability design optimization method based on surrogate models, using a new active learning function to predict the system-reliability gain after adding sample points, gradually updating the surrogate model and performing sensitivity analysis. Through three numerical examples and two engineering cases, they validated the efficiency and accuracy of the surrogate model-based method. The aforementioned studies offer critical methods for addressing the substantial data requirements in the sensitivity analysis of cracked carbon-fiber structures. However, when the sample size of the basic random input variables is small or the understanding of these variables is limited, the uncertainty in their distribution parameters can impact the accuracy of structural fatigue performance analysis [26]. Therefore, it is crucial to consider the impact of subjective uncertainty on structural fatigue performance. [PERSON] et al. [27] introduced distribution parameter uncertainty and proposed a novel method for efficiently evaluating the risk sensitivity of subjective uncertainty. This method is particularly effective in handling expensive models with numerous inputs and uncertain distribution parameters, demonstrating high accuracy and efficiency through two examples. [PERSON] et al. [28] proposed a framework based on a new finite mixture model (MM) to address the uncertainty of distribution parameters in systems. Their study showed that this framework excels in accurately and efficiently achieving uncertainty propagation under multimodal distribution random variables while avoiding the computation of higher-order moments through four examples. [PERSON] et al. [29] presented a method for modeling and assessing the uncertainty sensitivity for parameter distribution reliability problems. This method quantifies uncertainty sensitivity by using the Monte Carlo (MC) method to calculate the first-order derivative of the response function with respect to the distribution parameters. Their research indicated that considering the randomness of the distribution parameters allows for the accurate sensitivity analysis of each parameter. [PERSON] et al. [30] introduced distribution parameter uncertainty and proposed a method for estimating engineering systems' reliability that accounts for both frequency and epistemic uncertainties. The method's effectiveness and accuracy were validated through two engineering case studies. The above literature indicates that considering distribution parameter uncertainty can enhance the accuracy of structural fatigue reliability predictions.