Research on the method of guided wave mode excitation in rails based on mathematical model

Ultrasonic guided waves have emerged as an essential technique for rail nondestructive evaluation(NDE) owing to long-range propagation and high defect sensitivity, yet multimode coexistence produces strongly overlapping responses that challenge conventional excitation-based mode selection. This study develops a mathematical model in which excitation position and input energy are treated as optimization variables to identify the most effective configuration for the selective excitation of targeted guided wave modes. Optimization is cast with mode purity (the ratio of the target-mode response amplitude to the overall guided-wave response) as the primary objective and directional matching as an auxiliary constraint to enhance excitation selectivity. Leveraging particle swarm optimization (PSO) the proposed scheme identifies optimal excitation parameters that realize efficient selective mode generation with only two excitation points and yields a simplified and practical transducer configuration. Numerical simulations and full-scale rail experiments across multiple frequency bands, including 400 Hz and 35 kHz, indicate that the proposed approach markedly enhances target-mode purity and enables reliable detection of defect echoes not observable with conventional single-point excitation. Taken together, these results support a new route to selective mode generation for rail NDE while avoiding complex phased array systems.