Polygonalization of the wheel describes the growth of out-of-round profiles of the wheels of railway vehicle. This problem was identified in the 1980s but its mechanism is still not well understood. The wheel-rail disturbance formed by wheel polygonalization will accelerate the fatigue fracture of the key parts of rail vehicles and seriously threaten the safety of rail vehicle. This fact has led to significant efforts in detecting and diagnosing wheel polygonalization, in particular in setting the criteria for health monitoring. Currently, the time-domain feature parameters extraction method based on data statistics and frequency-domain feature parameters extraction method based on spectrum estimation are widely applied to detect wheel polygonalization. However, the basis of spectral estimation is the Fourier transform, which is not good at dealing with non-linear vibration systems (such as vehicle-track coupled system). Aiming at the wheel polygonalization problem existing in high-speed train, the non-linear extent of vibration response of vehicle system caused by wheel polygonalization is analyzed based on vehicle-track coupled dynamics and adaptive data analysis method. A typical high-speed train model is established according to the vehicle-track coupled dynamics theory. The wheel polygonalization model is introduced and vehicle system vibration response is calculated by numerical integration. The vibration response signal is decomposed by empirical mode decomposition (EMD) to produce the intrinsic mode functions (IMFs). By calculating the intra-wave frequency modulation of IMFs, that is, the difference between instantaneous and mean frequencies and amplitudes, the non-linearity of the dynamic response is quantified. Influences of wheel polygonalization on the non-linearity of steady-state and unsteady vibration responses of vehicle system are analyzed in detail. An objective criterion for wheel polygonalization health monitoring based on Degree of Non-linearity is proposed, which provides an effective tool for prognostics and health management of trains.

车轮的多边形化描述了铁路车辆车轮不圆轮廓的增长。这个问题是在 1980 年代发现的，但其机制仍未得到很好的理解。车轮多边形化形成的轮轨扰动会加速轨道车辆关键部位的疲劳断裂，严重威胁轨道车辆的安全。这一事实导致在检测和诊断车轮多边形化方面做出了重大努力，特别是在设置健康监测标准方面。目前，基于数据统计的时域特征参数提取方法和基于谱估计的频域特征参数提取方法被广泛应用于车轮多边形检测。然而，谱估计的基础是傅立叶变换，不擅长处理非线性振动系统（如车轨耦合系统）。针对高速列车中存在的车轮多边形化问题，基于车轨耦合动力学和自适应数据分析方法，分析了车轮多边形化引起的车辆系统振动响应的非线性程度。根据车轨耦合动力学理论建立了典型的高速列车模型。引入车轮多边形化模型，通过数值积分计算车辆系统振动响应。振动响应信号通过经验模态分解 (EMD) 进行分解，以产生固有模态函数 (IMF)。通过计算 IMFs 的波内频率调制，即 瞬时和平均频率和幅度之间的差异，动态响应的非线性被量化。详细分析了车轮多边形化对车辆系统稳态和非稳态振动响应非线性的影响。提出了一种基于非线性度的车轮多边形化健康监测客观判据，为列车的预测和健康管理提供了有效的工具。