﻿ 轨道车辆振动实测环境的谱归纳技术
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 同济大学学报(自然科学版)  2019, Vol. 47 Issue (10): 1514-1519.  DOI: 10.11908/j.issn.0253-374x.2019.10.018 0

### 引用本文

DENG Chenxin, ZHOU Jinsong, GONG Dao, LUO Min. Spectral Induction Method of Vibration in Rail Vehicles' Measurement Environment[J]. Journal of Tongji University (Natural Science), 2019, 47(10): 1514-1519. DOI: 10.11908/j.issn.0253-374x.2019.10.018

### 文章历史

Spectral Induction Method of Vibration in Rail Vehicles' Measurement Environment
DENG Chenxin , ZHOU Jinsong , GONG Dao , LUO Min
Institute of Railway Transit, Tongji University, Shanghai 201804, China
Abstract: The measured acceleration data of vibration in rail vehicles show strong non-normality, and Johnson's law is used to improve the criterion of inducing vibration data. A universal induction method of vibration spectrum is proposed in this paper. By using the measured data, the difference between the ordinary method and the modified method is compared, and the universality of the method is tested. The results show that the modified method can adapt to the non-normal environment and the induced spectrum can reflect the actual vibration.
Key words: rail vehicle    random vibration    power spectrum    process of abnormal data

1 归纳方法原理 1.1 非正态处理

Slifker等[6]提出，使用一簇分布可将数据正态化，如下所示:

 $\widetilde{x}=\gamma+\eta k_{a}(x ; \lambda, \varepsilon)$ (1)

 $k_{a}(x ; \lambda, \varepsilon)=\left\{\begin{array}{ll}{\sinh ^{-1}\left(\frac{x-\varepsilon}{\lambda}\right), } & {a=1} \\ {\ln \left(\frac{x-\varepsilon}{\lambda+\varepsilon-x}\right), } & {a=2} \\ {\ln \left(\frac{x-\varepsilon}{\lambda}\right), } & {a=3}\end{array}\right.$ (2)

1.2 时域处理

 $x_{1}=\bar{x}+Q_s$ (3)

1.3 频域处理 1.3.1 特征样本

 $\left\{ {\begin{array}{*{20}{l}} {{X_i} = \frac{1}{{{M_1}}}\sum\limits_{j = 1}^{{M_1}} {{\alpha _{{\rm{RMS}}}}} (i, j)}\\ {S_i^2 = \frac{1}{{{M_1} - 1}}\sum\limits_{j = 1}^{{M_1}} {{{\left( {{\alpha _{{\rm{RMS}}}}(i, j) - {X_i}} \right)}^2}} } \end{array}} \right.$ (4)

 $\left\{\begin{array}{l}{F(i, m)=\frac{S_{i}^{2}}{S_{m}^{2}}, \quad i \neq m} \\ {t(i, m)=\frac{X_{i}-X_{m}}{\sqrt{\left(S_{i}^{2}+S_{m}^{2}\right) / M_{1}}}, \quad i \neq m}\end{array}\right.$ (5)

 $\left\{\begin{array}{l}{F_{\left(M_{1}-1, M_{1}-1\right) ; \alpha / 2} \leqslant F(i, m) \leqslant F_{\left(M_{1}-1, M_{1}-1\right) ;(1-\alpha / 2)}} \\ {|t(i, m)| \leqslant t_{2\left(M_{1}-1\right) ;(1-\alpha / 2)}}\end{array}\right.$ (6)

1.3.2 实测谱

 $x_{k}(p, q)=\sqrt{\widetilde{G}_{k}(p, q)}$ (7)

 $\left\{ {\begin{array}{*{20}{l}} {{X_k}(p) = \frac{1}{{{Q_p}}}\sum\limits_{q = 1}^{{Q_p}} {{x_k}} (p, q)}\\ {S_k^2(p) = \frac{1}{{{Q_p} - 1}}\sum\limits_{q = 1}^{{Q_p}} {{{\left( {{x_k}(p, q) - {X_k}(p)} \right)}^2}} } \end{array}} \right.$ (8)

 ${F_{11}} = \frac{{{t_{\left( {{Q_p} - 1} \right);(1 - \alpha )}}}}{{\sqrt {{Q_p}} }} + {Z_\beta }\sqrt {\frac{{{Q_p} - 1}}{{\chi _{\left( {{Q_q} - 1} \right);\alpha }^2}}}$ (9)

 $G_{k}(p)=\left(X_{k}(p)+F_{11} S_{k}(p)\right)^{2}$ (10)

1.3.3 规范谱

 $\left\{\begin{array}{l}{F(k, k+1)=\frac{S_{k}^{2}(p)}{S_{k+1}^{2}(p)}} \\ {t(k, k+1)=\frac{X_{k}(p)-X_{k+1}(p)}{\sqrt{\left(S_{k}^{2}(p)+S_{k+1}^{2}(p)\right) / Q_{p}}}}\end{array}\right.$ (11)

 $\left\{\begin{array}{l}{F_{\left(Q_{q}-1, Q_{q}-1\right) ; a / 2} \leqslant F(k, k+1) \leqslant F_{\left(Q_{q}-1, Q_{q}-1\right) ;(1-\alpha / 2)}} \\ {|t(k, k+1)| \leqslant t_{2\left(Q_{q}-1\right) ;(1-\alpha / 2)}}\end{array}\right.$ (12)

 $\left\{ {\begin{array}{*{20}{l}} {{X_h}(p) = \frac{1}{{{Q_p}{N_h}}}\sum\limits_{q = 1}^{{Q_p}} {\sum\limits_{k = {k_{h1}}}^{{k_{h2}}} {{x_k}} } (p, q)}\\ {S_h^2(p) = \frac{1}{{{Q_p}{N_h} - 1}}\sum\limits_{q = 1}^{{Q_p}} {\sum\limits_{k = {k_{h1}}}^{{k_{h2}}} {{{\left( {{x_k}(p, q) - {X_k}(p)} \right)}^2}} } } \end{array}} \right.$ (13)

 ${F_{12}} = \frac{{{t_{\left( {{Q_p}{N_h} - 1} \right);(1 - \alpha )}}}}{{\sqrt {{Q_p}{N_h}} }} + {Z_\beta }\sqrt {\frac{{{Q_p}{N_h} - 1}}{{\chi _{\left( {{Q_q}{N_h} - 1} \right);\alpha }^2}}}$ (14)

 $G_{h}(p)=\left(X_{h}(p)+F_{12} S_{h}(p)\right)^{2}$ (15)

 图 1 谱归纳流程 Fig.1 Flow chart of spectral induction
2 基于实测振动数据的谱归纳分析 2.1 实测背景

2.2 时域处理

 $J=\frac{N}{6}\left(\gamma_{\mathrm{s}}^{2}+\frac{\left(\gamma_{\mathrm{k}}-3\right)^{2}}{4}\right)$ (16)

 图 2 处理前后部分时域数据对比 Fig.2 Comparison of time domain data before and after processing

2.3 频域分析

 图 3 旧车轴箱垂向振动归纳谱与标准谱对比 Fig.3 Comparison between induced spectrum and standard spectrum of axle box's vertical vibration of old vehicle
 图 4 新车轴箱垂向振动归纳谱与标准谱对比 Fig.4 Comparison between induced spectrum and standard spectrum of axle box's vertical vibration of new vehicle

2.4 偏差分析

 $\delta_{k}=\frac{G_{k {\rm o}}-G_{k {\rm j}}}{G_{k {\rm o}}} \times 100 \%$ (17)

 图 5 偏差分布 Fig.5 Deviation distribution

 图 6 谱线值分布 Fig.6 Distribution of spectral line values

 图 7 旧车车体横向振动归纳谱 Fig.7 Induced spectrum of body's lateral vibration of old vehicle
 图 8 旧车构架横向振动归纳谱 Fig.8 Induced spectrum of frame's lateral vibration of old vehicle
3 结语

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