﻿ 基于EMD-ARIMA模型的地铁门传动系统早期故障预测
 计算机系统应用  2019, Vol. 28 Issue (9): 110-117 PDF

1. 兰州理工大学 能源与动力工程学院, 兰州 730050;
2. 兰州轨道交通有限公司 机电设备处, 兰州 730030

Early Fault Prediction of Metro Door Transmission System Based on EMD-ARIMA Model
LI Bo-Xu1, NAN Xi-Kang1, ZHENG Xiang-Dong2, GAO Wen-Ke1
1. School of Energy and Power Engineering, Lanzhou University of Technology, Lanzhou 730050, China;
2. Department of Electromechanical Equipment, Lanzhou Rail Transit Co. Ltd., Lanzhou 730030, China
Foundation item: National Natural Science Foundation of China (71561016)
Abstract: The peak of clamping force data of Metro doors can reflect the degradation of the transmission system to a certain extent. Based on this, this study uses the developed data acquisition system to collect, store, display, and query the clamping force of the new on-line metro door in real time. ARIMA model and EMD-ARIMA model are used to predict the trend of mean and standard deviation of peak clamping force with cumulative running time, and the probability of early failure of door transmission system is determined based on the prediction results. The comparison of the two models shows that EMD-ARIMA model can predict the change trend of peak clamping force of metro doors, and the improved prediction method can provide a new idea for predicting the deterioration of metro doors in debugging period.
Key words: metro door     transmission system     fault prediction     time serious model     EMD-ARIMA prediction model

1 地铁门传动系统结构及工作原理

 图 1 传动系统结构示意图

 $F = \frac{{2{\text{π}} \eta {T_2}}}{L} = \frac{{2{\text{π}} \eta }}{L}\frac{{{Z_2}}}{{{Z_1}}}{T_1} = {\rm{ }}\frac{{19100{\text{π}} \eta {Z_2}}}{{L{Z_1}}}\frac{P}{{{n_1}}}$ (1)

2 地铁门数据采集系统设计

 图 2 地铁门夹紧力采集装置结构

 图 3 数据接收界面

3 EMD-ARIMA模型预测原理及方法 3.1 EMD分解法

 $x(t) = \sum\limits_{j = 1}^n {IM{F_j}} + res.$ (2)

 图 4 EMD-ARIMA预测算法

3.2 时间序列建模

 ${X_t} = F({X_{t - 1}},{X_{t - 2}}, \cdots ,{a_t})$ (3)

ARIMA(p, d, q)模型:

 ${\nabla ^d}{X_t} = {\varphi _1}{\nabla ^d}{X_{t - 1}} + \cdots + {\varphi _p}{\nabla ^d}{X_{t - p}} + {a_t} - {\theta _1}{a_{t - 1}} - \cdots {\theta _q}{a_{t - q}}$ (4)

 $\left[ \begin{gathered} {{\hat \gamma }_{q + 1}} \\ {{\hat \gamma }_{q + 2}} \\ \vdots \\ {{\hat \gamma }_{q + p}} \\ \end{gathered} \right] = \left[ {\begin{array}{*{20}{c}} {{{\hat \gamma }_q}}&{{{\hat \gamma }_{q - 1}}}& \cdots &{{{\hat \gamma }_{q - p + 1}}} \\ {{{\hat \gamma }_{q + 1}}}&{{{\hat \gamma }_q}}& \cdots &{{{\hat \gamma }_{q - p + 2}}} \\ \vdots & \vdots & \ddots & \vdots \\ {{{\hat \gamma }_{q + p - 1}}}&{{{\hat \gamma }_{q + p - 2}}}& \cdots &{{{\hat \gamma }_q}} \end{array}} \right]\left[ \begin{gathered} {\phi _1} \\ {\phi _2} \\ \vdots \\ {\phi _p} \\ \end{gathered} \right]$ (5)

 $\mathop {{Z_t}}\limits^ \sim - \left({\phi _1}{\mathop Z\limits^ \sim _{t - 1}} + \cdots + {\phi _p}{\mathop Z\limits^ \sim _{t - p}}\right) = {a_t} - {\theta _1}{a_{t - 1}} - \cdots - {\theta _q}{a_{t - q}}$ (6)

 $\mathop {{X_t}}\limits^ \sim = \mathop {{Z_t}}\limits^ \sim - \left({\phi _1}{\mathop Z\limits^ \sim _{t - 1}} + \cdots + {\phi _p}{\mathop Z\limits^ \sim _{t - p}}\right),\;t = p + 1,p + 2, \cdots ,n$ (7)

 ${Q_{lb}} = n\left( {n + 2} \right)\sum\limits_{k = 1}^m {\left( {\frac{{{{\hat \rho }_k}^2}}{{n - k}}} \right)} \sim {\chi ^2}\left( m \right)$ (8)

4 实例分析

(1)经数据处理后, 第一次开关门动作时夹紧力峰值的均值及标准差数据如表2所示.

 图 5 ARIMA建模算法流程图

 图 6 夹紧力峰值均值变化曲线

 图 7 夹紧力峰值标准差变化曲线

 图 8 均值的EMD分解

 图 9 标准差的EMD分解

 图 10 均值预测对比图

 图 11 标准差预测对比图

(2)第二次开关门动作与第三次开关门动作夹紧力峰值分布情况的ARIMA及EMD-ARIMA模型预测步骤及方法与第一次基本相同.

 图 12 均值预测对比图

 图 13 标准差预测对比图

(3)通过对第三次开关门的均值及标准差数据数据进行单根检验, 均值及标准差序列为非平稳序列. 经过2次差分后, 两者均为平稳序列. 因此, 均值预测模型为ARIMA(1,2,0), 标准差预测模型为ARIMA(1,2,0). 峰值的均值预测模型为 ${\nabla ^2}{\mu _t} = - 0.111439{\nabla ^2}{\mu _{t - 1}}$ ; 峰值的标准差预测模型为 ${\nabla ^2}{\sigma _t} = - 0.11144{\nabla ^2}{\sigma _{t - 1}}$ .

 图 14 均值预测对比图

 图 15 标准差预测对比图

5 结论

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