基于稀疏表示的轨道波磨检测方法研究

Rail Corrugation Detection Method Based on Sparse Representation Research

摘要: 波磨是轨道交通运行过程中常见的问题之一，为了检测钢轨波磨，不同于传统波磨检测方法，在MATLAB环境下处理车辆轴箱振动信号得到钢轨波磨波形。进行动力学建模，建立列车集总参数简化模型推导波磨状态下的列车振动信号。采用信号稀疏表示方法对轻微故障特征进行提取与诊断，其中L1范数作为正则化的方法是目前最常用的，但基于该方法容易低估重构信号幅值，可能会造成较大误差，因此采用基于GMC罚函数的稀疏表示方法解决此问题。建立目标函数，研究目标函数的保凸条件，利用前向后向分裂算法(FBS)求解稀疏表示目标函数，对比两种方法在重构信号方面的表现。结果显示，GMC罚函数在信号重构方面的性能更好，优于L1罚函数。接着基于GMC罚函数的稀疏表示方法进行仿真和实测，验证所提方法的有效性，并针对不足之处加以分析。

Abstract: Corrugation is one of the common problems in the operation of rail transit. In order to detect rail corrugation, different from the traditional corrugation detection method, the vibration signal of the vehicle axle box is processed in a MATLAB environment to obtain the rail corrugation waveform. The dynamic modeling is carried out, and the simplified model of train lumped parameters is es-tablished to derive the train vibration signal under the condition of corrugation. The signal sparse representation method is used to extract and diagnose the minor fault features. The L1 norm as the regularization method is the most commonly used method at present. However, based on this method, it is easy to underestimate the amplitude of the reconstructed signal, which may cause large errors. Therefore, the sparse representation method based on the GMC penalty function is used to solve this problem. The objective function is established, and the convexity-preserving con-ditions of the objective function are studied. The forward-backward splitting algorithm (FBS) is used to solve the sparse representation objective function, and the performance of the two methods in reconstructing the signal is compared. The results show that the GMC penalty function has better performance in signal reconstruction than the L1 penalty function. Then, the sparse representation method based on the GMC penalty function is simulated and measured to verify the effectiveness of the proposed method, and the shortcomings are analyzed.