﻿ 基于遗传算法DDBN参数学习的UUV威胁评估
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 哈尔滨工程大学学报  2018, Vol. 39 Issue (12): 1972-1978  DOI: 10.11990/jheu.201711072 0

### 引用本文

YAO Hongfei, WANG Hongjian, WANG Ying, et al. Threat assessment of UUV based on genetic algorithm DDBN parameter learning[J]. Journal of Harbin Engineering University, 2018, 39(12), 1972-1978. DOI: 10.11990/jheu.201711072.

### 文章历史

1. 哈尔滨工程大学 自动化学院, 黑龙江 哈尔滨 150001;
2. 齐齐哈尔大学 机电工程学院, 黑龙江 齐齐哈尔 161006;
3. 国网黑龙江省电力有限公司 经济技术研究院, 黑龙江 哈尔滨 150036

Threat assessment of UUV based on genetic algorithm DDBN parameter learning
YAO Hongfei 1,2, WANG Hongjian 1, WANG Ying 1,3, LI Qing 1
1. College of Automation, Harbin Engineering University, Harbin 150001;
2. College of Mechanical Engineering, Qiqihar University, Qiqihar 161006, China;
3. Economic Research Institute, State Grid Heilongjiang Electric Power Company Limited, Harbin 150036, China
Abstract: Considering the uncertain events in complex marine environments, threat assessment is very important for the safety of unmanned underwater vehicles (UUVs) during autonomous operations. In this study, a threat assessment model and a decision reasoning model are designed based on dynamic Bayesian network. The genetic algorithm is used to realize the discrete dynamic Bayesian network (DDBN) parameter learning, and finally, the optimal model parameters are obtained; this enhances the rapid response of the reasoning model to the marine environment. The simulation experiment results show that the real DDBN parameters can be obtained using the proposed algorithm. Thus, the UUV threat assessment problem in complex marine environment can be effectively solved, and the parameters for optimal UUV autonomous decision making can be provided.
Keywords: parameter learning    threat assessment    discrete dynamic Bayesian network (DDBN)    genetic algorithm    unmanned underwater vehicle (UUV)    decision making

1 任务描述与动态贝叶斯网络构建 1.1 任务决策需求

1.2 动态贝叶斯网络构建

 Download: 图 1 DBN表示图 Fig. 1 DBN representation
 $P\left( {{X_t}|{X_{t - 1}}} \right) = \prod\limits_{i = 1}^N P \left( {X_t^i|Pa\left( {X_t^i} \right)} \right)$ (1)

 $\begin{array}{c} P\left( {X_{1:T}^{\left( {1:N} \right)}} \right) = \prod\limits_{i = 1}^N {{P_{{B_1}}}} \left( {X_1^i|Pa\left( {X_1^i} \right)} \right) \times \\ \prod\limits_{t = 2}^T {\prod\limits_{i = 1}^N {{P_{B \to }}} \left( {X_t^i|Pa\left( {X_t^i} \right)} \right)} \end{array}$ (2)

 Download: 图 2 基于动态贝叶斯网络的UUV威胁估计模型 Fig. 2 Threat estimation model of UUV based on dynamic Bayesian network
 Download: 图 3 基于动态贝叶斯网络的UUV决策推理模型 Fig. 3 Decision reasoning model of UUV based on dynamic Bayesian network

2 动态贝叶斯网络参数学习

2.1 最大似然估计(MLE)

 $P\left( {D|\theta ,G} \right) = \prod\limits_{i = 1}^N P \left( {{Y_i}|\theta ,G} \right)$ (3)

MLE参数可以通过最大似然函数来获得，或等价地使用对数似然，即

 $\begin{array}{c} L\left( \theta \right) = \sum\limits_{i = 1}^N {\log P\left( {{Y_i}|\theta ,G} \right)} = \\ \sum\limits_{i = 1}^N {\sum\limits_{j = 1}^{{q_j}} {P\left( {Y_i^j|Y_i^{pa\left( j \right)},{\theta ^j}} \right)} } = \\ \sum\limits_{i = 1}^N {\sum\limits_{j = 1}^{{q_j}} {\sum\limits_{k = 1}^{{m_j}} {{n_{ijk}}\log \left( {{\theta _{ijk}}} \right)} } } \end{array}$ (4)

 ${n_{ijk}} = \left\{ \begin{array}{l} 1,在{Y_j}中,{P_a}\left( j \right) = k\\ 0,其他 \end{array} \right.$ (5)

2.2 DDBN参数学习遗传算法设计

1) 初始化DDBN的网络参数θ0，同时对威胁估计模型进行实时采样，得到一组数据。

2) 编码方式采用二进制编码，对GA种群进行初始化。这里的参数为各节点条件概率的集合, 即{Z(t), L(t), D(t), M(t), C(t), J(t), Q(t), N(t)}, 集合中元素介于区间[0, 1]内，为了减小个体长度，元素编码的时候只用小数位来表示。例如0.23，则小数位相应的二进制表示为00111011，保留小数点后8位精度。即集合的元素个体长度为8，集合中8个元素，所以集合的长度大小为64，种群大小为100，初始种群是随机产生的。

3) 给定最大遗传代数为100，判断是否满足结束条件。

4) 取最大似然函数L(θ)作为遗传算法的适应度函数F(x)，保留最优个体。

 $F\left( x \right) = \max \left\{ { - \sum\limits_{i = 1}^N {\sum\limits_{j = 1}^{{q_j}} {\sum\limits_{k = 1}^{{m_j}} {{n_{ijk}}\log \left( {{\theta _{ijk}}} \right)} } } } \right\}$ (6)

5) 选择策略：正比选择策略，对于个体i，设其适应值为Fi，种群规模为100，则该个体的选择概率可以表示为式(7)，得到选择概率后，采用轮盘赌来实现选择操作。

 ${P_i} = \frac{{{F_i}}}{{\sum\limits_{i = 1}^{100} {{F_i}} }}$ (7)

PP0=0, $P{P_i} = \sum\limits_{j = 1}^i {P{P_j}}$，每次随机产生ξkU(0, 1)，当PPi-1ξk < PPi，则选择个体i

6) 不断更新遗传算法的种群，目标函数如式(8)所示，将通过计算得到的网络参数θt+1替换上一时刻网络参数θt，同时进行实时数据采样。

 $L\left( \theta \right) = \sum\limits_{i = 1}^N {\sum\limits_{j = 1}^{{q_j}} {\sum\limits_{k = 1}^{{m_j}} {{n_{ijk}}\log \left( {{\theta _{ijk}}} \right)} } }$ (8)
3 仿真分析与验证

3.1 GA进行参数学习的有效性验证

 Download: 图 4 遗传算法的迭代优化曲线 Fig. 4 Iterative optimization curve of genetic algorithm
3.2 DDBN威胁评估方法验证

 Download: 图 5 UUV海洋环境任务决策概率推理 Fig. 5 Marine environment task decision probability reasoning of UUV
4 结论

1) 设计的基于动态贝叶斯网络的威胁评估模型以及决策推理模型，采用遗传算法实现了DDBN参数学习，能够使决策推理模型中的贝叶斯网络参数随海洋环境实时更新，随着数据数量的增加并进行不断地修正，最终趋近于真实的网络参数。

2) 通过仿真实验以及参数学习前后模型的似然度比较，验证了遗传算法进行参数学习的有效性，为UUV的海洋环境任务决策提供准确的参数保证，确保了UUV自主动态任务决策的合理性和准确性。

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