## 6 Conclusions  
This research work has significant simulation and experimental cost advantages. Based on this, a mapping path from the key structural elements of a large aviation planetary system to the system reliability indexes is established as well as a bi-objective optimization design based on an NSGA-II genetic algorithm, using ring gear rim thickness as a key structural element for system reliability and lightweight design. The mechanism of the coupling effect of its dimensional variation on the stiffness condition and fatigue reliability level of the planetary wheel system is revealed. Then, a new method of reliability-driven multi-objective optimization design for planetary mechanism structural dimensions is formed, and the specific conclusions are as follows:  
1. In the face of advanced simulation and analysis tasks for a large aviation planetary system, only considering the convenience of modeling and boundary condition settings, the computational efficiency of the hierarchical finite element method will be much higher than that of the general finite element method. Moreover, the stress results without considering system elastic deformation are 11.9-17.3% higher than those considering this factor, which indicates that ignoring the flexible behavior characteristics of the large aviation planetary system may directly lead to an over conservative design scheme for corresponding structural strength. Additionally, the use of a group method for testing under four stress levels, and the probability life relationship between the gear and tooth, is established based on the concept of minimum order statistics. The linear correlation of the P-S-N curves obtained by the statistical method in this paper is more than 96%, which ensures the effectiveness of strength input variables for the reliability model. 2. With the increase in the ring gear rim thickness of the large thin-walled internal gear ring, its elastic deformation under the rated working condition gradually decreases, and the maximum node resultant displacement almost stops decreasing when the rim thickness reaches 25.02 mm, indicating that the rigidity reserve of the ring gear raised by increasing the rim size can no longer be effectively utilized at this limit value. 3. Within a certain size range, the increase in the ring gear rim thickness will improve the stiffness conditions of the planetary gear system and optimize the gear meshing performance, thus improving the fatigue reliability level of the planetary gear system. Within the range of static strength requirements of the ring gear rim, the bending fatigue reliability index of the planetary gear system increases with the increase in the ring gear rim thickness, and when the value of the rim thickness reaches 22.5 mm, the reliability growth starts to become weak, and this sluggish trend becomes increasingly more obvious with the increase in the planet carrier base plate thickness. In the end, while ensuring reliability based on the premise of lightweight, the dimension of the ring gear rim thickness in the large aviation planetary system of the specified model is determined by NSGA-II genetic algorithm to be 26.87 mm. At this point, the mass of the ring gear is reduced by 10.06% compared to the original design, achieving the purpose of weight reduction. Conceptualization, M.L. ; methodology, L.X. ; software, M.L. and Y.L. ; validation, M.L. ; formal analysis, M.L. ; investigation, M.L. and L.X. ; resources, M.L. ; data curation, M.L. and Y.L. ; writing--original draft preparation, M.L. ; writing--review and editing, M.L., Y.L. and L.X. ; visualization, L.X. ; supervision, M.L. ; project administration, M.L. ; funding acquisition, M.L. All authors have read and agreed to the published version of the manuscript. This research was funded by the National Natural Science Foundation of China (NSFC), (Grant No.52005350), Scientific Research Foundation of Education Department of Liaoning Province, (Grant No.