﻿ 电磁式先进阻拦装置可靠性分析方法
 舰船科学技术  2021, Vol. 43 Issue (7): 168-172    DOI: 10.3404/j.issn.1672-7649.2021.07.034 PDF

Research on reliability analysis method of electromagnetic advanced arresting gear device
ZHANG Xiao-xu, CHENG Hong-wei, TAN Da-li, WANG Qing-yu, TENG Teng
Naval Research Academy, Beijing 100161, China
Abstract: In this paper, the reliability analysis method for electromagnetic advanced arresting gear device is studied. Firstly, the system composition and working principle of the device are described. Then, the key link in the reliability analysis of the device is analyzed. Finally, considering with the system characteristics of the electromagnetic advanced arresting gear device, the system-level reliability analysis method based on mathematical statistics. What's more, the fixed time censoring method based on Weibull distribution, the parametric Bootstrap method and the equipment-level reliability analysis method considering the degradation of the rope diameter are analyzed and summarized. It provides a theoretical reference for the reliability design, application and evaluation of electromagnetic advanced arresting gear device.
Key words: electromagnetic advanced arresting gear     reliability analysis     Weibull distribution     fixed time censoring     degradation of the rope diameter
0 引　言

1 电磁式先进阻拦装置组成

 图 1 电磁阻拦装置构成图 Fig. 1 Electromagnetic arresting device principle

2 电磁阻拦装置可靠性分析关键环节

2.1 装置可靠性的指标

2.2 装置可靠性的分析流程

1）对于电磁阻拦装置系统级可靠性的分析流程，主要围绕着其核心指标−阻拦次数进行，包含如下步骤：记录实验次数、统计故障次数、计算平均故障间隔次数和评估可靠性结果。对应的可靠性分析流程，如图2所示。

 图 2 系统级可靠性分析流程 Fig. 2 System level reliability analysis process

2）对于阻拦索的设备级可靠性分析过程相对复杂，因为阻拦索的疲劳失效存在一个过程。而且相比于其他机械及电气设备，阻拦索的失效对系统带来的负面影响最大，且修护难度和工作量也是最大的。综合考虑上述因素，将阻拦索的使用寿命评估作为电磁阻拦系统可靠性分析的关键组成部分。阻拦索寿命评估流程，如图3所示。

 图 3 阻拦索寿命可靠性估算流程 Fig. 3 Reliability life estimation process of arresting gear

2.3 装置的故障分类、判定与统计原则

3 电磁阻拦装置可靠性分析方法

3.1 基于数理统计的可靠性分析

 $MCB{F_Q} = \frac{{2N}}{{\chi _{1 - Q}^2\left( {2R + 2} \right)}}\text{。}$ (1)

3.2 基于Weibull分布定时截尾的可靠寿命点估算

 $\begin{split} & {F(t) = 1 - {e^{ - {t^m}/\beta }}}, \qquad {t \geqslant 0}\text{，} \\ & {P(t) = \dfrac{{m{t^{m - 1}}}}{\beta }{e^{ - {t^m}/\beta }}} , \quad {t \geqslant 0} \text{。} \end{split}$ (2)

 $L\left( {m,\beta } \right) = \frac{{{m^r}}}{{{\beta ^r}}}\prod\limits_{i = 1}^r {t_i^{m - 1}} \exp \left\{ { - \frac{1}{\beta }\left[ {\sum\limits_{i = 1}^r {t_i^m + (n - r)t_r^m} } \right]} \right\}\text{。}$ (3)

 $\sum {^*} t_i^m = \sum\limits_{i = 1}^r {t_i^m + (n - r) \cdot } t_r^m\text{，}$ (4)

 $\begin{split} & \dfrac{\partial }{{\partial m}}\left( {\displaystyle\sum {^*t_i^m} } \right) \!\!=\!\! \displaystyle\sum\limits_{i = 1}^r {t_i^m\ln {t_i}} \! +\! (n - r)t_r^m\ln {t_r}\!\! = \!\!\displaystyle\sum {^*t_i^m} \ln {t_i} \text{，} \\ & \dfrac{{{\partial ^2}}}{{\partial {m^2}}}\left( {\displaystyle\sum {^*t_i^m} } \right) = \displaystyle\sum {^*t_i^m} {(\ln {t_i})^2}\text{。} \end{split}$ (5)

 $\ln L = r\ln m - r\ln \beta + (m - 1)\sum\limits_{i = 1}^r {\ln {t_i}} - \frac{1}{\beta }\sum {^*t_i^m}\text{，}$ (6)

 $\begin{split} & \frac{{\partial \ln L}}{{\partial m}} = \frac{r}{m} + \sum\limits_{i = 1}^r {\ln {t_i}} - \frac{1}{\beta }\sum {^{\rm{*}}t_i^m\ln {t_i}}\text{，} \\ & \frac{{\partial \ln L}}{{\partial \beta }} = - \frac{r}{\beta } + \frac{1}{{{\beta ^2}}}\sum {^*t_i^m} \text{，} \end{split}$ (7)

 $\begin{split} &{\beta = \frac{1}{r}\sum {^*t_i^m} }\text{，} \\ & {\frac{{\displaystyle\sum {^*t_i^m\ln {t_i}} }}{{\displaystyle\sum {^*t_i^m} }} - \frac{1}{m} = \frac{1}{r}\sum {\ln {t_i}} } \text{，} \end{split}$ (8)

 $E\left( T \right) = \eta \Gamma \left(1 + \frac{1}{m}\right)\text{，}$ (9)

 $R\left( {{t_r}} \right) = {e^{ - \frac{{t_r^m}}{\beta }}} = r\text{，}$ (10)

 $- \frac{{t_r^m}}{\beta } = \ln r\text{，}$ (11)

 ${t_r} = \sqrt[m]{{\beta \ln \frac{1}{r}}} = \eta \sqrt[m]{{\ln \frac{1}{r}}}\text{。}$ (12)

3.3 采用参数Bootstrap方法的可靠寿命区间估算

1）采用极大似然估计法对定时截尾实验数据中的5个数据样本进行计算，得到Weibull分布参数估计值 $\hat m$ $\hat \eta$

2）再由Weibull分布 $W(\hat m,\hat \eta )$ 产生5个随机数，构成自助样本。由该样本数据估计Weibull分布参数可记为： $\tilde m$ $\tilde \eta$

3）将 $\tilde m$ $\tilde \eta$ 代入Weibull分布平均寿命计算公式（9）和可靠寿命计算公式（12），计算得到对应的寿命自助估计值： $\tilde E(T)$ ${\tilde t_r}$

4）重复上述过程步骤1～步骤3B次，即可得到B个平均寿命和可靠寿命估计值：

 $\left\{ {\tilde E{{(T)}^{(i)}},{{\tilde t}_r}^{(i)},i = 1,2, \cdots ,B} \right\}{\text；}$ (13)

5）将B $\tilde E(T)$ 数值按从小到大的顺序排列，给定置信度α，则排列在第[αB]位的数值即为平均寿命的置信度为α的单侧置信下限估计值；

6）将B ${\tilde t_r}$ 数值按从小到大的顺序排列，给定置信度α，则排列在第[αB]位的数值即为可靠度为r条件下的置信度为α的可靠寿命单侧置信下限估计值。

 图 4 Weibull寿命预测与可靠度归一化曲线 Fig. 4 Weibull life prediction and reliability normalization curve

3.4 基于绳径退化数据的寿命评估

1）间隔一定时间测量阻拦索绳径数据，对其中有效样本阻拦索绳径数据虽试验次数增加的退化规律进行数学拟合，得到拟合斜率、拟合截距和拟合优度，建立阻拦索绳径退化数学模型；

2）根据上述模型对阻拦索的使用寿命进行预测。当阻拦索的绳径下降到阈值Z需要更换时，可得到个样本的预测寿命值；

3）根据上一步骤得到的预测寿命值，再采用Weibull寿命分布极大似然估计法，得到分布参数估计值为 $\hat m$ $\hat \eta$ ，再次通过式（9）～式（12）和参数Bootstrap方法进一步推导计算获得可靠函数、可靠寿命点估计值和可靠寿命区间估计值。

1）同一阻拦索使用次数为故障结尾且小于绳径退化预测次数的，在可靠寿命评估过程中采信使用次数；

2）同一阻拦索使用次数为故障结尾且大于绳径退化预测次数的，在可靠寿命评估过程中采信绳径退化预测次数；

3）同一阻拦索使用次数为定时结尾的，在可靠寿命评估过程中采信绳径退化预测次数。

 图 5 绳径退化寿命预测与可靠度归一化曲线 Fig. 5 Life prediction of rope path and reliability normalization curve
4 结　语

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