有砟轨道轮轨力功率谱曲线的拟合模型

Curve Fitting Model for Wheel-Rail Force Power Spectrum of Ballasted Track

通过研究同一轨道区段的轮轨力检测数据,时域分析表明不同速度条件下轮轨力检测数据具有很强的相似性,其服从正态分布特性,且满足平稳随机过程的检验条件;频域分析表明轮轨力检测数据的功率谱曲线中包含周期性谐波成分和随机成分,周期性谐波成分出现的频段对应特定的空间波长且与车速有关,而随机成分随着速度的不同呈现出相似的变化规律,可用曲线拟合模型对其进行描述。基于此,提出轮轨力功率谱曲线的有理式函数拟合模型(Rational Wheel-rail Force Model,RFM),先采用五点三次平滑算法对原始曲线进行平滑处理,再采用非线性最小二乘法中的Levenberg-Marquardt算法进行拟合,并采用拟合优度R2检验拟合结果。利用实测轮轨力数据进行其功率谱曲线的拟合结果表明,RFM拟合模型的结构简单,拟合优度高,普适性强。

The study on the wheel-rail force test data measured from the same track section shows that there is a strong similarity among the wheel-rail force measured data of different speed levels in time domain. The wheel-rail force measured data obey normal distribution characteristics and satisfy the test conditions for stationary random processes. The study also shows that there are periodic harmonic compo- nents which appear in frequency band corresponding to the specific spatial wavelength and the speed of the inspection car, and random components with different speeds appear similar change rule that can be used to describe the curve fitting modal in the power spectrum density curve of the wheel-rail force measured data. Based on this, a rational function fitting model （Rational Wheel-rail Force Model, RFM） of wheel-rail force power spectrum curve is proposed. Firstly, the original curve is smoothed by the five point three smoothing algorithm. Secondly, the Levenberg-Marquardt algorithm in the nonlinear least square method is used to fit the curve. Finally, the R2 test is used to test the fitting results. The fitting results of the power spectrum curve of the measured wheel-force data from different tracks show that the RFM with simple structure has high goodness of fitting and strong adaptability.