## 6 Conclusions  
In practical conditions, the distribution parameters of structural system input variables cannot be accurately determined. During the laying and molding process of carbon-fiber composites, extensive manual operations and complex working environments lead to uncertainties in material parameters, initial cracks, and loads. These uncertainties significantly affect the operational safety of wind turbine blades. Therefore, it is necessary to consider the impact of distribution parameter uncertainty on their structural fatigue life. To overcome the high computational cost of directly solving sensitivity indices, an ALK-SS computational method based on surrogate models and Kriging models is proposed. The main conclusions are as follows:  
1. Finite element simulations were conducted on cracked carbon-fiber laminates with a \([0/90]_{4}\) ply sequence using simulation software and a UMAT subroutine. The results showed that stress concentration at the crack tip is the key reason for the failure of the carbon-fiber laminate. Comparative experiments indicated that the error in fatigue life prediction obtained from the simulation model is within 10%, demonstrating that the finite element simulation model can generate reliable response values for the training sample set, providing an accurate data foundation for subsequent sensitivity analysis. 2. By obtaining the true response values of the training samples from the simulation model, a fatigue life prediction model for cracked carbon-fiber structures based on the active learning Kriging (ALK) model was established. Combining surrogate sampling and the Kriging model to predict fatigue life data, the reliability function expression of cracked carbon-fiber structures was derived, and the reliability modeling and assessment of the fatigue life of cracked carbon-fiber structures were performed. 3. Compared with traditional experimental and simulation methods, the ALK model improves the computational efficiency by introducing an active learning function while ensuring accuracy, overcoming the high computational cost of directly solving indices. The ALK method can establish a Kriging surrogate model between the distribution parameters and the output statistical characteristics using a small number of distribution parameter sample points, reducing the number of function calls. Based on this framework, the ALK-SS method further introduces the SS-PDF, improving the utilization rate of inner-layer input variable samples and significantly reducing the computational load of parameter sensitivity analysis while ensuring computational accuracy. As discussed in Appendix A, the proposed method not only incorporates uncertainties in both parameters and distributions but also significantly reduces computational costs by using Kriging with proxy sampling, making it more suitable for large-scale applications compared to previous works. Despite the advantages of this study, incorporating a broader variety of comparison models to further enhance the robustness of the conclusions, improve the fitting accuracy, and reduce the computational workload is a direction for future research. **Author Contributions:** H.L. : data curation, formal analysis, investigation, visualization, writing--original draft. Z.L. : Management and coordination of the planning and execution of research activities, with supervisory and leadership responsibility for the planning and execution of research activities. L.T. : Provide experimental data, formal analysis, surveys, visualizations. J.L. : Provide experimental data, formal analysis, surveys, visualizations. Y.Z. : Provide experimental data, formal analysis, surveys, visualizations. All authors have read and agreed to the published version of the manuscript. **Funding:** This research was funded by the GuangDong Basic and Applied Basic Research Foundation (2022A1515240006), the National Natural Science Foundation of China (52175132), and National Natural Science Foundation of China (51905116). **Institutional Review Board Statement:** Not applicable.