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.

For surface crack detection in in-service concrete buildings, this study proposes DCFYOLO, a lightweight crack instance segmentation algorithm improved from YOLO11n-seg, which enhances feature representation and multi-scale contextual fusion to improve crack detection and segmentation performance in complex scenarios. Frequency Channel Attention (FCA) is introduced into the C3k2 units of the backbone network, where multi-scale pooling extracts multi-spectral information to enhance channel-level feature discrimination. Context Anchor Attention (CAA) is added to the PAN-FPN structure in the neck to address multi-scale feature fusion and long-range context modeling in complex scenes. A Dynamic Snake Convolution with Efficient Channel Attention (DSECA) module is constructed by combining dynamic snake convolution and efficient channel attention. Through a serial design, this module provides the multi-scale feature fusion process with both geometrically adaptive sampling and channel-discriminative optimization. Experimental results on the DeepCrack dataset show that DCFYOLO achieves 73.2% Box mAP@0.5 and 67.4% Mask mAP@0.5 with 2.47 M parameters, improving the baseline YOLO11n-seg by 2.8 and 2.7 percentage points, respectively. Ablation experiments verify the independent contribution of each improved module. The algorithm demonstrates a balance between segmentation accuracy and inference efficiency under lightweight constraints on the DeepCrack dataset, and can provide a reference for research on concrete surface crack instance segmentation.