A reduced-order diagnostic framework for pantograph-contact wire vibration response and reliability-oriented assessment

Pantograph–contact wire interaction is a complex distributed dynamic problem that usually requires multi-degree-of-freedom or finite-element modelling for detailed design verification. This paper does not attempt to replace such high-fidelity models. Instead, it proposes a reduced-order diagnostic framework for preliminary assessment of dominant vibration response, contact force variation, and reliability-oriented indicators of railway overhead contact lines. The contact network is first interpreted as a distributed multi-degree-of-freedom system, after which modal reduction is used to obtain a simplified representation of the dominant contact-wire vibration mode. To avoid an excessive simplification of pantograph-contact wire interaction, a two-coordinate reduced model is introduced, including the vertical displacement of the pantograph head and the dominant displacement of the contact wire. Wind excitation, stiffness degradation, and electrical-thermal effects are considered only through their influence on contact force stability, contact loss probability, and degradation-related reliability indicators. The limitations and possible errors caused by model-order reduction are explicitly discussed. An illustrative parametric example demonstrates how stiffness degradation changes natural frequency, contact force fluctuation, probability of contact loss, and preliminary reliability indicators. The proposed framework is intended for early-stage diagnostics and sensitivity analysis rather than full-scale design validation.