基于EEMD-SVD-PE的轨道波磨趋势项提取

钢轨波磨检测是保障行车安全的重要手段,针对复杂钢轨线路波磨数据中的轨道起伏趋势提取问题,提出了一种基于排列组合熵(Permutation Entropy, PE)选取低复杂度奇异值分量重构趋势的EEMD-SVD信号去趋方法.相比已有的经验模式分解去趋算法,该方法考虑到原始IMF可能存在的信号成分混杂问题(如含有白噪声与信号的低频成分),首次提出通过奇异值分解来精确提取隐藏在多维IMF矩阵中的趋势项成分作为奇异值分量.由于协方差矩阵构建的奇异值分量排列时只考虑了能量的分布而未考虑趋势项信号低复杂度、高幅的特点,使用排列组合熵来选出符合趋势项特征的奇异值分量,最后对满足要求的奇异值分量进行重建得到最终的趋势项.为验证本文方法的有效性,分别进行了数字仿真和实际钢轨波磨数据去趋实验.数字仿真实验结果表明该方法整体去趋性能优于低通滤波法、与EMD结合的线性规划法和小波分解法,尤其在多信噪比的仿真实验中,当信噪比较低时,提趋准确率最大提高约30%.同时,实际钢轨波磨数据去趋实验说明本文方法能够适用于钢轨波磨检测.

An EEMD-SVD-PE approach to extract the trend of track irregularity

Rail corrugation detection is an important method to ensure traffic safety. In order to solve the problem of the extraction of the trend of track irregularity in complex rail lines, a novel de-trending method named EEMD-SVD is proposed, which uses permutation entropy (PE) to select relevant singular-value components to reconstruct the trend. Compared with the existing methods based on EMD, this method considers the problem of mixed signal components in the original IMFs, and initially proposes the use of SVD to extract the trend accurately hidden in multi-dimensional IMF matrix. Since the singular-value components are arranged in the order of energy reduction without considering low-complexity and high-energy of signal, the proposed method modifies the EEMD-SVD, uses PE to select relevant low-complexity singular-value components, and finally reconstructs the trend with the relevant singular-value components selected above. Numerical simulation and track irregularity data test were carried out to evaluate the performance of the method. The numerical simulation experimental results showed that the proposed method outperformed the low-pass filter algorithm, the linear programming de-trending algorithm combined with EMD, and the WD de-noising algorithm. In particular, in the simulation of multiple signal-noise ratio, the improvement accuracy was about 30% when the signal-noise ratio was low. The track irregularity data test proved that the method is effective for de-trending the trend of track irregularity.