# Fatigue Characteristics Analysis of Carbon Fiber Laminates with Multiple Initial Cracks
Later, [PERSON] et al. [13], focusing on issues related to low failure probabilities, proposed a reliability analysis method for time-variant systems that integrates MRGP with Subset Simulation (SS). By using a new single-loop decoupling strategy to avoid inner-loop extremum optimization, they utilized MRGPs to build a proxy model of the extremum response surface and combined it with the Kriging model to identify new sample points. Finally, the SS method was applied to address low failure probabilities, and the effective  
Figure 1: Schematic diagram of the basic structure of wind turbine blades. ness of this method was confirmed through case studies. [PERSON] et al. [14] developed a reliability evaluation technique combining transfer learning and the Direct Probability Integral method to gauge offshore wind turbine blade dependability amidst complex physical interactions. By using adaptive sampling strategies and surrogate models, they were able to efficiently predict the performance of the blades, offering valuable insights for blade design and safety considerations. Besides contemplating the effects of multiple initial cracks on the fatigue characteristics of carbon fiber-reinforced plastics, the interplay of various uncertainties during manufacturing and assembly processes cannot be overlooked; since they significantly affect the accuracy of fatigue life forecasting and trustworthiness evaluation, the examination of uncertainties deserves consideration. [PERSON] et al. [15] observed that the majority of research on the simultaneous optimization of composite material layout and fiber direction is carried out under fixed conditions, neglecting the effect of variable factors on the structural dependability of fiber-reinforced composites. [PERSON] et al. [16] utilized experimental data on effective stiffness and strength to identify critical random parameters and updated their probabilistic models through Bayesian inference, markedly enhancing the accuracy of uncertainty in the micro-parameters of carbon fiber unidirectional composites. [PERSON] et al. [17], through the analysis of T700 carbon fiber single-fiber test data, discovered that the influence of sampling randomness on the uncertainty of fiber strength exceeds that of measurement-induced uncertainty. The research highlights the significance of employing stochastic uncertainty in the reliability of fiber composite material strength models. Incorporating parameters associated with material properties, sampling variability, measurement uncertainties, and stochastic elements into the analysis of fatigue life and reliability is important. Considering this, the present study selects carbon fiber composite laminates with multiple initial cracks as the research subject, taking into account the impact of cracks in different combinations and the uncertainty of physical parameters on the fatigue performance of carbon fiber composite laminates. A new method for assessing their fatigue characteristics and fatigue reliability under conditions of physical parameter uncertainty is proposed in this study. By combining static and fatigue tests, a simulation method has been developed to predict the fatigue life of the laminates. In response to the challenges of data requirements and time consumption associated with single fatigue life simulations of carbon fiber laminates, this study utilizes a Particle Swarm Optimization-Backpropagation (PSO-BP) neural network as a surrogate model for predicting fatigue life. This model is then applied for the modeling and assessment of fatigue reliability of carbon fiber laminates with multiple cracks, as shown in Figure 2.  
Figure 2: Research framework diagram.