Gray Prediction for Internal Corrosion Rate of Oil and Gas Pipelines Based on Markov Chain and Particle Swarm Optimization

Accurate prediction of the internal corrosion rate is crucial for the safety management and maintenance planning of oil and gas pipelines. However, this task is challenging due to the complex, multi-factor nature of corrosion and the scarcity of available inspection data. To address this, we propose a novel hybrid prediction model, GM-Markov-PSO, which integrates a gray prediction model with a Markov chain and a particle swarm optimization algorithm. A key innovation of our approach is the systematic incorporation of symmetry principles—observed in the spatial distribution of corrosion factors, the temporal evolution of the corrosion process, and the statistical fluctuations of monitoring data—to enhance model stability and accuracy. The proposed model effectively overcomes the limitations of individual components, providing superior handling of small-sample, non-linear datasets and demonstrating strong robustness against stochastic disturbances. In a case study, the GM-Markov-PSO model achieved prediction accuracy improvements ranging from 0.93% to 13.34%, with an average improvement of 4.51% over benchmark models, confirming its practical value for informing pipeline maintenance strategies. This work not only presents a reliable predictive tool but also enriches the application of symmetry theory in engineering forecasting by elucidating the inherent order within complex corrosion systems.