﻿ 船舶脉冲负载柴油发电机运行可靠性研究
 舰船科学技术  2022, Vol. 44 Issue (18): 139-142    DOI: 10.3404/j.issn.1672-7649.2022.18.028 PDF

Research on operation reliability of marine pulse load diesel generator
WANG Can, YANG Zi-hang
College of Engineering Machinery Changan University, Xi′an 710018, China
Abstract: The safety and stability of ship navigation mainly depend on the operation reliability of ship diesel generator. In order to improve the safety of ships in operation, it is necessary to study and analyze the reliability of diesel generators. Therefore, the research method of the operational reliability of the marine pulse load diesel generator is proposed. By establishing the mathematical model of the marine pulse load diesel generator, the operational status of the diesel generator is obtained. Based on this, the operation reliability index of marine pulse load diesel generator is selected, and the state subspace of the generator is established by the nuclear principal component analysis method in combination with the above reliability index. The main included angle formed by the basis vector of the state subspace in the normal and current state of the generator is extracted, and the operation reliability of marine pulse load diesel generator is obtained by combining the mapping function. The experimental results show that the state detection accuracy and reliability analysis accuracy of the proposed method are high.
Key words: pulse load     marine diesel generator     nuclear principal component analysis     reliability index     main angle
0 引　言

1 柴油发电机数学模型及其运行可靠性指标 1.1 柴油发电机数学模型

 图 1 柴油发动机及调速系统 Fig. 1 Diesel engine and speed regulating system

1）转速调节器

PID控制方法是转速器中用于调节转速常用的方法，用 $H(s)$ 表示其传递函数，表达式如下：

 $H(s) = {K_P} + \frac{{{K_I}}}{s} + {K_D}s。$ (1)

2）油门执行器

 $G(s) = \frac{{L(s)}}{{u(s)}} = \frac{{{K_2}}}{{{T_1}s + 1}}。$ (2)

3）柴油发动机

 $G(s) = \frac{{{K_3}}}{{{T_2}s + 1}} 。$ (3)

 $G(s) = \frac{{{K_4}}}{{{T_3}s + 1}}。$ (4)

1.2 可靠性指标

1）强迫停运率

 ${F_{OR}} = \frac{{{F_{OH}}}}{{{S_H} + {F_{OH}}}} \times 100\text{%}。$ (5)

2）启动率

 ${C_R} = \frac{{{C_s}}}{{{S_H}}} 。$ (6)

3）可用系数

 ${A_F} = \frac{{{A_H}}}{{{P_H}}} \times 100\text{%} 。$ (7)

4）平均无故障可用小时

 ${M_A} = \frac{{{A_H}}}{{{N_{FO}}}}。$ (8)

5）不可用系数

 ${U_F} = \frac{{{F_{OH}} + {M_{OH}} + {P_{OH}}}}{{{P_H}}} \times 100\text{%} 。$ (9)

6）平均计划停运延续时间

 ${M_{POD}} = \frac{{{P_{OH}}}}{{{N_{PO}}}}。$ (10)

7）计划停运系数

 ${P_{OF}} = \frac{{{P_{OH}}}}{{{P_H}}} \times 100\text{%}。$ (11)
2 柴油发电机运行可靠性研究

 ${\boldsymbol{C}} = ({c_1},{c_2}, \cdots ,{c_m}) = \left( {\begin{array}{*{20}{c}} {{c_{11}}}&{{c_{12}}}& \cdots &{{c_{1m}}} \\ {{c_{21}}}&{{c_{22}}}& \cdots &{{c_{2m}}} \\ \cdots & \cdots & \cdots & \cdots \\ {{c_{n1}}}&{{c_{n2}}}& \cdots &{{c_{nm}}} \end{array}} \right) 。$ (12)

 $\left\{ \begin{gathered} C \to \gamma (C)，\\ \gamma (C) = [\gamma ({c_1}),\gamma ({c_2}), \cdots ,\gamma ({c_m})]。\\ \end{gathered} \right.$ (13)

 ${\boldsymbol{V}} = \frac{{\displaystyle \sum\limits_{j = 1}^m {\gamma ({c_j})\gamma {{({c_j})}^{\rm{T}}}} }}{m}。$ (14)

${\boldsymbol{b}}$ 表示特征矢量，用 ${\boldsymbol{\mu}}$ 表示特征值，两者之间的关系为 ${\boldsymbol{\mu b}} = {\boldsymbol{Vb}}$ 。特征矢量 $b$ 在特征空间中可利用线性映射 $\gamma (C)$ 描述：

 $b = \sum\limits_{j = 1}^m {{\beta _j}} \gamma ({c_j}) = \beta \gamma (C)。$ (15)

 $m\mu \beta = K\beta 。$ (16)

 $D = span[{\xi _1},{\xi _2}, \cdots ,{\xi _r}]。$ (17)

 $\left\{ \begin{gathered} {D_2} = span[\gamma (X){\chi _1},\gamma (X){\chi _2}, \cdots ,\gamma (X){\chi _q}]，\\ {D_1} = span[\gamma (U){\eta _1},\gamma (U){\eta _2}, \cdots ,\gamma (U){\eta _p}]。\\ \end{gathered} \right.$ (18)

 ${E_{ij}} = \eta _i^{\rm{T}}\gamma {(U)^{\rm{T}}}\gamma (X){\chi _j}。$ (19)

$f = \min (p,q)$ ，奇异值分解内积矩阵 $E$ ，获得 $f$ 个船舶脉冲负载柴油发电机的状态特征值 ${\lambda _1},{\lambda _2}, \cdots ,{\lambda _f}$ ，特征值对应的反余弦值即为子空间基矢量之间的主夹角为：

 ${\vartheta _i} = \arccos {\lambda _i}。$ (20)

2个子空间之间的相似性随着主夹角 ${\vartheta _i}$ 的减小而增大，利用主夹角分析船舶脉冲负载柴油发电机运行的可靠性为：

 $T = \cos \min ({\vartheta _i})。$ (21)

3 实验与分析

 图 2 不同方法的发电机状态检测结果 Fig. 2 Generator state detection results of different methods

4 结　语

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