*Article* **Research on the Diffusion Model of Cable Corrosion Factors Based on Optimized BP Neural Network Algorithm**

**Shiya Li 1,2, Guowen Yao 1,2, Wei Wang 3,\*, Xuanrui Yu 1,2, Xuanbo He 1,2, Chongyang Ran 1,2 and Hong Long 1,2**


**\*** Correspondence: 622220080005@mails.cqjtu.edu.cn

**Abstract:** Corrosion factors enter the cable via diffusion and penetration from the defect position of the cable or the connection position between the anchoring system and the cable section, seriously affecting the cable's durability. Exploring the transmission mechanism of corrosion factors in the cable structure is essential to reveal the durability and the long-term performance of the cable structure and to judge the corrosion damage of steel wires in the cable structure. Based on the machine learning (ML) method and the analytical solution of Fick's second law, the laws between different temperatures, humidity, cable inclinations, cable defect areas, etc., and the diffusion coefficient of corrosion factors and the concentration of surface corrosion factors are obtained, also a spatial diffusion model of corrosion factors is established. According to the research, the optimum simulation result is achieved by employing the optimized back propagation (BP) neural network algorithm, which has a faster convergence speed and better robustness. Although ambient temperature, humidity, and corrosion time all impact the diffusion rate of corrosion factors, the tilt angle of the cable and the size of cable defects are the main factors influencing the diffusion coefficient of corrosion factors and the concentration of surface corrosion factors. The error between the concentration of corrosion factors calculated by the model in this article and the measured values at each spatial point of the cable is controlled within 15%, allowing for the spatial diffusion of corrosion factors to be effectively predicted and evaluated in practical engineering.

**Keywords:** bridge engineering; stay cable; corrosion factors; neural networks; spatial diffusion model
