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 哈尔滨工程大学学报  2019, Vol. 40 Issue (5): 953-959  DOI: 10.11990/jheu.201801005 0

### 引用本文

ZHI Pengfei, LIU Sheng, ZHU Wanlu, et al. A risk prediction and assessment method for an integrated electric propulsion system[J]. Journal of Harbin Engineering University, 2019, 40(5), 953-959. DOI: 10.11990/jheu.201801005.

### 文章历史

1. 江苏科技大学 电子信息学院, 江苏 镇江 212003;
2. 哈尔滨工程大学 自动化学院, 黑龙江 哈尔滨 150001

A risk prediction and assessment method for an integrated electric propulsion system
ZHI Pengfei 1, LIU Sheng 2, ZHU Wanlu 1, YE Hui 1
1. College of Electronic Information, Jiangsu University of Science and Technology, Zhenjiang 212003, China;
2. College of Automation, Harbin Engineering University, Harbin 150001, China
Abstract: This paper proposes a novel risk prediction and assessment method for an integrated electric propulsion system in order to solve the problems of numerous delays in the risk assessment of integrated electric propulsion systems in complex environment and the difficulty in formulating strategies to cope with such delays in real time. The MHMM-Viterbi algorithm proposed, which combines the traditional HMM algorithm, the Viterbi algorithm, and statistics theory to predict the system work state probabilities in the continuous time points in the future. According to the system operation status and the impact of external environment, the working states of the subsystems of the system components are predicted by the MHMM-Viterbi algorithm. Subsequently, the risk assessment model of network topology of the system was built, and the system state under abnormal condition was simulated using the Monte Carlo method, thus yielding the risk prediction and assessment results. Furthermore, this paper considers a ship integrated electric propulsion system as an example to validate the proposed method. Results are in accordance with the actual risk record of the marine navigation of the ship's integrated electric propulsion system.
Keywords: integrated electric propulsion system    risk prediction    risk assessment    Viterbi algorithm    Markov model    Monte Carlo simulation    network topology

1 MHMM-Viterbi算法

 $S=\left\{S_{1}, S_{2}, \cdots, S_{M}\right\}$ (1)

 $S_{t} \in\left(S_{1}, S_{2}, \cdots, S_{M}\right)$ (2)

 $O=\left\{O_{1}, O_{2}, \cdots, O_{N}\right\}$ (3)

t时刻的观测值可以被定义为，其中

 $o_{t}=\left(O_{1}, O_{2}, \cdots, O_{N}\right)$ (4)

 $\mathit{\boldsymbol{\pi }} = \left\{ {{\pi _1},{\pi _2}, \cdots ,{\pi _M}} \right\}$ (5)
 $\mathit{\boldsymbol{\pi }} = P\left( {{q_t} = {S_i}} \right),\quad 1 \le i < M$ (6)

 $\mathit{\boldsymbol{A}} = {\left( {{a_{ij}}} \right)_{M \times M}}$ (7)
 ${a_{ij}} = P\left( {\left( {{q_{t + 1}} = {S_j}} \right)/\left( {{q_t} = {S_i}} \right)} \right),\quad 1 \le i,j \le M$ (8)

 $\boldsymbol{B}=\left(b_{j k}\right)_{M \times N}$ (9)
 $\left\{ {\begin{array}{*{20}{l}} {{b_{jk}} = P\left( {\left( {{o_i} = {O_k}} \right)/\left( {{q_t} = {S_j}} \right)} \right),}\\ {1 \le j < M,1 \le k < N} \end{array}} \right.$ (10)

 Download: 图 1 时间T内单元状态转移图 Fig. 1 States transition diagram of unit in time T

 $P(Q | o)=(P(Q) P(o | Q)) / P(o)$ (11)

 $g_{Q}(o)=P(Q) P(Q | o)$ (12)

 $\begin{array}{c}{P(o | Q)=P\left(q_{1}, q_{2}, \cdots, q_{T}\right) P\left(q_{1}\right)} \\ {P\left(q_{2} | q_{1}\right) \cdots P\left(q_{T} | q_{T-1}\right)}\end{array}$ (13)

 $\begin{array}{*{20}{c}} {P(o|Q) = P\left( {{o_1},{o_2}, \cdots ,{o_T}} \right)P\left( {{q_1},{q_2}, \cdots ,{q_T}} \right) = }\\ {P\left( {{O_1}|{q_1}} \right)P\left( {{O_2}|{q_2}} \right) \cdots P\left( {{O_T}|{q_T}} \right)} \end{array}$ (14)

 $\begin{array}{*{20}{c}} {{g_Q}(o) = P\left( {{q_1}} \right) \cdots P\left( {{q_T}|{q_{T - 1}}} \right)P\left( {{o_1}|{q_1}} \right) \cdots P\left( {{o_T}|{q_T}} \right) = }\\ {P\left( {{q_1}} \right)\prod\limits_{t = 2}^T P \left( {{q_t}|{q_{t - 1}}} \right)\prod\limits_{t = 1}^T P \left( {{o_t}|{q_t}} \right)} \end{array}$ (15)

 \begin{aligned} \ln q_{Q}=& \ln P\left(q_{1}\right)+\sum\limits_{i=2}^{T} \ln P\left(q_{t} | q_{t-1}\right)+\\ & \sum\limits_{t=1}^{T} \ln P\left(o_{t} | q_{t}\right) \end{aligned} (16)

 \begin{aligned} \operatorname{ln}g_{Q}(o)=& \ln P\left(q_{1}\right)+\ln P\left(o_{1} | q_{1}\right)+\\ & \sum\limits_{i=2}^{T}\left(\ln P\left(q_{t} | q_{t-1}\right)+\ln P\left(o_{t} | q_{t}\right)\right) \end{aligned} (17)

 $\boldsymbol{H}=\left[H_{1}, H_{2}, \cdots, H_{i}, \cdots, H_{p}\right]^{\mathrm{T}}$ (18)

 $H_{i}=\left\{S_{i_{1}}, S_{i_{2}}, \cdots, S_{i_{T}}\right\}, \quad i=1,2, \cdots, P$ (19)

 $\mathit{\boldsymbol{H}} = \left[ {\begin{array}{*{20}{c}} {{S_{11}}}& \cdots &{{S_{1T}}}\\ \vdots &{}& \vdots \\ {{S_{p1}}}& \cdots &{{S_{PT}}} \end{array}} \right]$ (20)

 $S_{i_{(t-1)}}=1$ (21)

 ${f_t} = \frac{{\sum\limits_{j = 2}^M {{Q_J}} }}{Q}$ (22)

 $F=\left\{f_{1}, f_{2}, \cdots, f_{T}\right\}$ (23)

MHMM-Viterbi算法将评估对象的内因和外因相结合，同时在很大程度上消除了小概率误差，使状态预测结果更准确。

2 综合电力推进系统风险预测评估方法

2.1 综合电力推进系统拓扑建模

 Download: 图 2 风险拓扑建模原则 Fig. 2 The principle for network topology modeling
2.2 综合电力推进系统风险模拟

 Download: 图 3 系统风险模拟流程图 Fig. 3 The flow chart of system risk simulation

1) 单元失效模拟：对节点矩阵和支路矩阵的每个单元独立取[0, 1]的随机数，随机数小于单元失效率则认为该单元失效，反之则认为该单元未失效，单元失效模拟过程可以表达为：

 $S_{i}=\left\{\begin{array}{ll}{1,} & {\lambda>a_{i}} \\ {0,} & {\lambda_{i} \leqslant a_{i}}\end{array}\right.$ (24)

2) 单元失效后矩阵重组：首先对失效单元进行分类，确定单元所属矩阵，之后对综合电力推进系统拓扑模型进行该单元失效后的结构重组。

3) 单元失效下潮流分析：采用单元失效下的最优潮流分析方法，对单元失效下的重组节点矩阵、支路矩阵和发电矩阵进行潮流分析，潮流分析结果为各节点功率矩阵，矩阵参数包括节点类型、节点编号、节点实际注入有功、实际注入无功、负载有功、负载无功、实际电压和相角等参数。

4) 最后将单元失效引发风险后的潮流分析结果与正常工作状态下的潮流分析结果进行对比分析，则得到该次单元风险失效引发的系统风险评估结果。

2.3 综合电力推进系统风险评估参数计算

1) 系统风险发生概率PRO。

 $\mathrm{PRO}_{k}=\sum\limits_{i=1}^{N_{\mathrm{k}}} P_{i k}$ (25)

 $\mathrm{PRO}=\sum\limits_{k=1}^{N_{\mathrm{U}}} \mathrm{PRO}_{k}$ (26)

2) 系统期望缺供电力EDNS。

 $\mathrm{EDNS}_{k}=\sum\limits_{i=1}^{N_{k}} P_{i k} L_{k}$ (27)

 $\mathrm{EDNS}=\sum\limits_{k=1}^{N_{\mathrm{U}}} \mathrm{EDNS}_{k}$ (28)

3) 系统期望缺供电量EENS。

 $\mathrm{EENS}=\mathrm{EDNS} \times T$ (29)

 $\mathrm{EENS}=\sum\limits_{k=1}^{N_{\mathrm{U}}}\left(\sum\limits_{S \in F_{k}} P(s) C(s)\right) \times T$ (30)

3 船舶综合电力推进系统风险预测评估

3.1 综合电力推进系统风险评估参数计算

 Download: 图 4 船舶综合电力推进系统构成图 Fig. 4 The structure diagram of ship integrated electric propulsion system

 Download: 图 5 船舶综合电力推进系统简略风险拓扑图 Fig. 5 The brief network topology figure of ship integrated electric propulsion system

3.2 风险预测建模

 Download: 图 6 船舶综合电力推进系统单元HMM状态转换示意 Fig. 6 The state transition diagram of ship integrated electric propulsion system unit HMM

 ${\mathit{\boldsymbol{A}}_{MG1}} = \left[ {\begin{array}{*{20}{l}} {0.85}&{0.05}&{0.10}\\ {0.05}&{0.08}&{0.87}\\ {0.85}&{0.05}&{0.10} \end{array}} \right]$ (31)

MG1的可观测特征分布概率矩阵BMG1为：

 $\boldsymbol{B}_{M G 1}=\left[ \begin{array}{cccc}{0.45} & {0.35} & {0.15} & {0.05} \\ {0.10} & {0.15} & {0.30} & {0.45} \\ {0.08} & {0.17} & {0.34} & {0.41}\end{array}\right]$ (32)

3.3 风险预测评估仿真

 Download: 图 7 2种工况下PRO、EDNS与EENS曲线对比 Fig. 7 The PRO, EDNS and EENS curve contrast figure under two states

4 结论

1) 本文提出的基于MHMM-Viterbi算法的工作状态预测分析方法，将HMM算法、Viterbi算法与统计学理论相结合，可以对系统各单元和子系统在未来连续时间点所处的工作状态概率进行预测分析。

2) 本文提出的综合电力推进系统风险预测评估方法，能够对综合电力推进系统在未来一段时间内的风险进行预测和评估。该风险预测评估方法也适用于很多其他领域的系统，如果加入一些新的高速率智能算法，便可以实现对系统的实时风险预测评估。

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