﻿ 基于DBN效能拟合的舰艇编队作战效能敏感性分析
 文章快速检索 高级检索

1. 西北工业大学 电子信息学院, 西安 710072;
2. 中国电子科技集团公司 数据链技术重点实验室, 西安 710077

Sensitivity analysis of ship formation operational effectiveness based on DBN effectiveness fitting
LI Bo1,2, LUO Haoran1, TIAN Linyu1, WANG Yuanxun1
1. School of Electronics and Information, Northwestern Polytechnical University, Xi'an 710072, China;
2. Key Laboratory of Data Link Technology, CETC, Xi'an 710077, China
Abstract: Aiming at the problem of insufficient data utilization and high requirements for data integrity in the traditional ship formation combat effectiveness analysis analysis method, this paper proposes a performance analysis fitting model based on deep belief network. Start with the most representative sensitivity analysis method-Sobol index method, and then take characteristic learning ability of deep learning, constructing a effectiveness fitting network based on Deep Belief Network(DBN), with network training and parameter optimization combined with unsupervised pre-training and supervised tuning. Finally, the experiments are simulated and analyzed based on the formation of air defense combat. Simulation results verify the applicability and effectiveness of the model.
Keywords: effectiveness analysis     effectiveness fitting model     Deep Belief Network(DBN)     sensitivity analysis     ship formation air defense

1 基于Sobol指数法的全局敏感性

Sobol敏感性分析法[8-10]是最具有代表性的全局敏感性分析方法，它基于模型分解思想，可以分别得到参数1、2次及更高次的敏感度。它的核心思想是方差分解，把模型分解为单个参数及参数之间相互组合的函数，通过计算单个输入参数或输入参数集的方差对总输出方差的影响来分析参数的重要性以及各个参数之间的交互效应。

1) 利用Sobol序列对输入的作战性能指标进行抽样，得到抽样矩阵(N×2n维)，将矩阵前n列设置为矩阵A，后n列设置为矩阵B :

 $\mathit{\boldsymbol{A}} = \left[ {\begin{array}{*{20}{c}} {{x_{11}}}&{{x_{12}}}& \cdots &{{x_{1n}}}\\ {{x_{21}}}&{{x_{22}}}& \cdots &{{x_{2n}}}\\ \vdots & \vdots & \vdots & \vdots \\ {{x_{N1}}}&{{x_{N2}}}& \cdots &{{x_{Nn}}} \end{array}} \right],\mathit{\boldsymbol{B}} = \left[ {\begin{array}{*{20}{c}} {x_{11}^\prime }&{x_{12}^\prime }& \cdots &{x_{1n}^\prime }\\ {x_{21}^\prime }&{x_{22}^\prime }& \cdots &{x_{2n}^\prime }\\ \vdots & \vdots & \vdots & \vdots \\ {x_{N1}^\prime }&{x_{N2}^\prime }& \cdots &{x_{Nn}^\prime } \end{array}} \right]$

2) 基于输出列向量计算相应的估计量。

 $\begin{array}{l} V\left( \mathit{\boldsymbol{Y}} \right) = \frac{1}{N}\mathit{\boldsymbol{Y}}_\mathit{\boldsymbol{A}}^{\rm{T}}\left( {{\mathit{\boldsymbol{Y}}_\mathit{\boldsymbol{A}}} - {\mathit{\boldsymbol{Y}}_\mathit{\boldsymbol{B}}}} \right) = \frac{1}{N}\sum\limits_{r = 1}^N {{F^2}} \left( {{x_{{r_1}}},{x_{{r_2}}}, \cdots ,} \right.\\ \;\;\;\;\;\;\;\;\;\;\;\left. {{x_{{r_n}}}} \right) - f_0^2 \end{array}$ （1）
 $V\left( {E\left( {\mathit{\boldsymbol{Y}}|{\mathit{\boldsymbol{X}}_i}} \right)} \right) = \frac{1}{N}\mathit{\boldsymbol{Y}}_A^{\rm{T}}\left( {{\mathit{\boldsymbol{Y}}_{{\mathit{\boldsymbol{M}}_{\rm{i}}}}} - {\mathit{\boldsymbol{Y}}_\mathit{\boldsymbol{B}}}} \right)$ （2）

 $\begin{array}{l} f_0^2 = \frac{1}{N}\mathit{\boldsymbol{Y}}_A^{\rm{T}}{\mathit{\boldsymbol{Y}}_\mathit{\boldsymbol{B}}} = \frac{1}{N}\sum\limits_{r = 1}^N {F\left( {{x_{{r_1}}},{x_{{r_2}}}, \cdots ,{x_{{r_n}}}} \right)} \cdot \\ \;\;\;\;\;\;F\left( {{{x'}_{{r_1}}},{{x'}_{{r_2}}}, \cdots ,{{x'}_{{r_n}}}} \right) \end{array}$
 $\begin{array}{l} {U_i} = \frac{1}{N}\mathit{\boldsymbol{Y}}_\mathit{\boldsymbol{A}}^{\rm{T}}{\mathit{\boldsymbol{Y}}_{{\mathit{\boldsymbol{M}}_i}}} = \frac{1}{N}\sum\limits_{r = 1}^N {F\left( {{x_{{r_1}}},{x_{{r_2}}}, \cdots ,{x_{{r_n}}}} \right)} \cdot \\ \;\;\;\;\;\;F\left( {{{x'}_{{r_1}}},{{x'}_{{r_2}}}, \cdots ,{{x'}_{{r_{\left( {i - 1} \right)}}}},{x_{{r_i}}},{{x'}_{{r_{\left( {i + 1} \right)}}}}, \cdots ,{{x'}_{{r_n}}}} \right) \end{array}$
 $\begin{array}{l} {U_{ - i}} = \frac{1}{N}\mathit{\boldsymbol{Y}}_\mathit{\boldsymbol{A}}^{\rm{T}}{\mathit{\boldsymbol{Y}}_{{\mathit{\boldsymbol{M}}_{ - i}}}} = \frac{1}{N}\sum\limits_{r = 1}^N {F\left( {{x_{{r_1}}},{x_{{r_2}}}, \cdots ,{x_{{r_n}}}} \right)} \cdot \\ \;\;\;\;\;\;F\left( {{x_{{r_1}}},{x_{{r_2}}}, \cdots ,{x_{{r_{\left( {i - 1} \right)}}}},{{x'}_{{r_i}}},{x_{{r_{\left( {i + 1} \right)}}}}, \cdots ,{x_{{r_n}}}} \right) \end{array}$

3) 计算敏感性指标对应的主效应指数和二阶交互效应指数。

 ${S_{{\mathit{\boldsymbol{X}}_i}}} = \frac{{{U_i} - f_0^2}}{{V\left( \mathit{\boldsymbol{Y}} \right)}}$

 ${S_{{\mathit{\boldsymbol{X}}_i}{\mathit{\boldsymbol{X}}_j}}} = \frac{{{U_{ij}} - f_0^2}}{{V\left( \mathit{\boldsymbol{Y}} \right)}} - {S_{{\mathit{\boldsymbol{X}}_i}}} - {S_{{\mathit{\boldsymbol{X}}_j}}}$

2 舰艇编队防空作战效能分析指标体系

 图 1 与拦截概率相关的系统性能指标与效能指标 Fig. 1 System performance indicators and effectiveness indicators related to interception probability

1) 简洁性：为了减少分析的复杂程度，尽可能去除不必要的指标来评估整个系统。

2) 客观性：所选择的指标应尽量保持客观，可以通过实验等方法得到具体的值，不能主观性太强。

3) 完整性：选择的指标对于评估的各个方面都有所涉及，可以衡量待评估的所有内容。

4) 独立性：所选择的指标不能重复，尽量互不干扰。

 ${P_{{\rm{lj}}}} = {P_{{\rm{fx}}}}{P_{{\rm{sxx}}}}{P_{{\rm{ss}}}}$ （3）

 ${P_{{\rm{fx}}}} = \int\limits_{{R_{\min }}}^{{R_{\max }}} {{P_{\rm{d}}}{\rm{d}}R/\left( {{R_{\max }} - {R_{\min }}} \right)}$ （4）

 系统 参数 输入参数含义 信息探测类 x1 = P 发射脉冲功率 x2 = G 天线增益 x3 = λ 雷达工作波长 x4 = σ 目标的有效散射截面积 x5 = L 损失系数 x6 = Fn 雷达接收机噪声系数 x7 = nEi(n) 积累效率 x8 = δR 天气常数 x9 = Rmax 雷达最大探测距离 x10 = Rmin 雷达最小探测距离 指挥控制类 x11 = tbg 发现敌情到指挥部收到情报的时间 x12 = txd 收到敌情报告到战斗任务下达完毕时间 x13 = tzb 兵力收到战斗任务到完成准备的时间 打击武器类 x14 = Rhs 导弹的毁伤半径 x15 = σ 导弹的射击误差 x16 = n1 导弹射击枚数

 ${P_{{\rm{sxx}}}}\left( t \right) = {{\rm{e}}^{ - \gamma {t_{{\rm{sxx}}}}}}$ （5）

 ${P_{{\rm{ss}}}} = 1 - {\left( {1 - {P_{\rm{m}}}} \right)^n}$ （6）

3 基于深度信念网络的效能拟合模型

3.1 效能拟合模型网络结构

 图 2 基于DBN的效能拟合模型 Fig. 2 DBN-based effectiveness fitting model

3.2 效能拟合模型的预训练及调优

RBM[20-23]网络结构如图 3所示。

 图 3 受限玻尔兹曼机的网络结构 Fig. 3 Restricted Boltzmann machine network structure

DBN的训练过程[24]如下：先对受限玻尔兹曼机按逐层贪婪的方法进行逐层无监督预训练，再利用反向传播算法进行有监督调优。

 图 4 深度信念网络的逐层训练过程 Fig. 4 Layer-by-layer training process of deep belief network

1) 采用最小均方误差准则来衡量参数的更新效果，当代价函数最小时表示参数更新完成。其中代价函数定义为

 $E = \frac{1}{N}\sum\limits_{i = 1}^N {{{\left( {{{\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}} \over Y} }_i}\left( {{W^{\left( 1 \right)}},{b^{\left( 1 \right)}}} \right) - {Y_i}} \right)}^2}}$ （7）

2) 采用反向传播算法，求解网络各层梯度值，并利用求解的梯度值来更新网络的权重和偏置参数，更新过程为

 $\left( {{W^{\left( 1 \right)}},{b^{\left( 1 \right)}}} \right) \leftarrow \left\{ {\left( {{W^{\left( 1 \right)}},{b^{\left( 1 \right)}}} \right) - \varepsilon \cdot \frac{{\partial E}}{{\partial \left( {{W^{\left( 1 \right)}},{b^{\left( 1 \right)}}} \right)}}} \right\}$ （8）

3) 通过上述权值更新规则，逐渐调整权重，以使误差函数值达到最小，从而得出最优的权重组合。

4 作战效能分析仿真实验 4.1 实验环境

4.2 效能拟合模型搭建及分析

 ${\rm{MAPE}} = \frac{1}{N}\sum\limits_{i = 1}^N {\left| {\frac{{{y_1} - {y_2}}}{{{y_2}}}} \right|}$ （9）
 ${\rm{RMSE}} = \sqrt {\frac{1}{N}\sum\limits_{i = 1}^N {{{\left| {{y_1} - {y_2}} \right|}^2}} }$ （10）
4.2.1 模型参数与结构对效能拟合效果的影响

 隐含层数 隐层单元数 平均绝对百分误差/% 均方根误差/% 时间/s 1 (GRBM) 10 4.9776 3.651 10.38 20 3.79 2.636 10.97 30 3.878 2.645 11.30 40 3.851 2.656 11.71 2 (1GRBM, 1BRBM) 10 3.727 3.670 26.17 20 2.953 2.618 26.84 30 2.207 3.587 27.75 40 2.208 3.581 28.64 3 (1GRBM, 2BRBM) 10 1.923 2.061 34.55 20 1.519 1.988 35.50 30 1.117 1.260 36.99 40 1.366 1.436 36.89

1) 随着隐含层数以及节点数的增加，利用该模型得到的拟合数据的精度在一定范围内会有所提升，训练网络所用时间也在增长。当模型特别复杂时，可能会存在过拟合、训练参数需要不断动态调整等问题，导致拟合效果反而不太好。所以在构建模型时也需要考虑模型复杂度、训练难度以及训练时间等因素。

2) 当网络结构包含两个隐含层时，拟合数据的RMSE相对较大，表示结果具有较大的波动性，可能与受限玻尔兹曼机种类的更改有关。

3) 对于本文选择的数据集，效能拟合模型选择3个隐含层结构，并且第1个隐含层选择20个节点、第2个隐含层选择30个节点、第3个隐含层选择30个节点时模型的拟合效果比较好，此时模型为5层结构。

4.2.2 不完备数据下拟合模型有效性

 图 5 500和1 000组数据训练模型输出拦截概率 Fig. 5 Output interception probability of 500 and 1 000 data training models

4.2.3 敏感性分析效果对比

1) 对于主效应指数，2种方式得到的输入变量的主效应指数对比如表 3图 6所示。

 指标 SXi S′Xi x1 0.001 841 0.007 09 x2 0.122 358 0.155 81 x3 0.000 139 0.008 62 x4 0.000 063 0.001 96 x5 0.075 703 0.088 95 x6 0.010 333 0.040 24 x7 0.000 112 0.002 48 x8 0.004 047 0.005 79 x9 0.133 080 0.145 97 x10 0.030 291 0.051 37 x11 0.007 314 0.018 50 x12 0.111 860 0.159 60 x13 0.065 481 0.069 25 x14 0.115 553 0.129 66 x15 0.101 984 0.083 29 x16 0.006 978 0.040 48
 图 6 2种方式下各个指标的主效应指数值对比 Fig. 6 Comparison of main effect index values of each index under two modes

 方式 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 完备 x9 x2 x14 x12 x15 x5 x13 x10 x6 x11 x16 x8 x1 x3 x7 x4 拟合 x12 x2 x9 x14 x5 x15 x13 x10 x16 x6 x11 x3 x1 x7 x4 x4

2) 对于二阶交互效应指数，两种方式下每一个指标与其他指标的交互效应值见图 7~图 9

 图 7 不完备数据条件下的全局敏感性分析结果 Fig. 7 Global sensitivity analysis results under incomplete data conditions
 图 8 不同条件下指标间的交互作用值 Fig. 8 Interaction value of indicators under different conditions
 图 9 交互效应值对应的指标组合及排序对比 Fig. 9 Combination and ranking comparison of indicators corresponding to interactive effect values

 方式 1 2 3 4 5 6 7 8 9 10 11 12 13 14 完备 x14/x15 x15/x16 x2/x9 x2/x5 x5/x9 x6/x8 x3/x9 x9/x12 x9/x15 x1/x6 x5/x6 x4/x6 x6/x12 x6/x11 拟合 x14/x15 x15/x16 x2/x9 x2/x5 x3/x9 x5/x9 x6/x8 x6/x11 x9/x15 x13/x15 x5/x6 x9/x12 x1/x6 x6/x7

5 结论

1) 建立了基于Sobol指数法的效能分析模型。通过Sobol指数法来分析多个输入因素的同时改变对系统效能的影响，便可以确定影响系统效能的主要因素，为系统优化提供相应的支撑。

2) 提出了基于深度信念网络的效能拟合模型。利用深度信念网络的学习能力，对数据进行特征提取，深入探索输入与输出的复杂关系，构建了效能拟合模型。模型通过预训练及网络调优，实现了模拟作战系统产生数据的功能，进而得到足够数据来完成作战系统的效能分析。

3) 针对舰艇编队防空作战效能分析分别给出了不同的仿真案例。对于效能拟合模型，探究了不同数据量对于所提出的效能拟合模型拟合数据效果的影响，并与其他方法进行了对比，验证了提出的方法的有效性；对于数据量不足的作战系统，将所提出的效能拟合模型应用于其中得到完备数据，然后进行效能分析得到相应结果，并与完备数据条件下的效能分析结果进行对比。验证了本文提出的效能拟合模型对于不完全数据下的舰艇编队作战系统敏感性分析的有效性。

 [1] 李国伟, 王付明, 王南星. 基于模糊AHP法的网络空间联合反恐作战指挥体系效能评估[J]. 兵器装备工程学报, 2016, 37(4): 111-113, 117. LI G W, WANG F M, WANG N X. Joint terrorism combat command system effectiveness evaluation based on fuzzy AHP in cyberspace[J]. Journal of Ordnance Equipment Engineering, 2016, 37(4): 111-113, 117. (in Chinese) Cited By in Cnki (10) | Click to display the text [2] 雷志良, 秦开兵, 许明, 等. 基于AHP-云模型的雷达对抗装备组网作战效能评估[J]. 舰船电子对抗, 2014, 37(6): 77-82. LEI Z L, QIN K B, XU M, et al. Efficiency evaluation of radar countermeasure equipment joint netting operation based on AHP-Cloud model[J]. Shipboard Electronic Countermeasure, 2014, 37(6): 77-82. (in Chinese) Cited By in Cnki (4) | Click to display the text [3] 周经伦, 傅攀峰, 罗鹏程. 基于方差的全局敏感性方法在空战效能分析中的运用[J]. 现代防御技术, 2007(6): 22-27. ZHOU J L, FU P F, LUO P C. Variance based global sensitivity analysis method using in air combat effectiveness analysis[J]. Modern Defence Technology, 2007(6): 22-27. (in Chinese) Cited By in Cnki (17) | Click to display the text [4] 谢瑞煜, 赵建军, 蒋涛. 基于蒙特卡洛法的武器系统标定误差分析[J]. 兵器装备工程学报, 2019, 40(1): 130-134, 158. XIE R Y, ZHAO J J, JIANG T. Error analysis of weapon system calibration based on Monte Carlo method[J]. Journal of Ordnance Equipment Engineering, 2019, 40(1): 130-134, 158. (in Chinese) Cited By in Cnki (2) | Click to display the text [5] 姚裕盛, 徐开俊. 基于BP神经网络的飞行训练品质评估[J]. 航空学报, 2017, 38(S1): 24-32. YAO Y S, XU K J. Quality assessment of flight training based on BP neural network[J]. Acta Aeronautica et Astronautica Sinica, 2017, 38(S1): 24-32. (in Chinese) Cited By in Cnki (14) | Click to display the text [6] 郭媛媛, 孙有朝, 李龙彪. 基于蒙特卡罗方法的民用飞机故障风险评估方法[J]. 航空学报, 2017, 38(10): 155-163. GUO Y Y, SUN Y C, LI L B. Failure risk assessment method of civil aircraft based on Monte Carlo method[J]. Acta Aeronautica et Astronautica Sinica, 2017, 38(10): 155-163. (in Chinese) Cited By in Cnki (2) | Click to display the text [7] 周智超. 面向武器装备系统效能的敏感性分析[J]. 火力与指挥控制, 2013, 38(2): 98-102. ZHOU Z C. Sensitivity analysis of oriented to system effectiveness of weapons and equipment[J]. Fire Control and Command Control, 2013, 38(2): 98-102. (in Chinese) Cited By in Cnki (4) | Click to display the text [8] 衡德正, 陈伟, 胡轶敏, 等. 基于Sobol序列的装配公差分析[J]. 机械设计与制造, 2016(12): 227-230. HENG D Z, CHEN W, HU Y M, et al. Assembly tolerance analysis based on the Sobol sequence[J]. Machinery Design & Manufacture, 2016(12): 227-230. (in Chinese) Cited By in Cnki (3) | Click to display the text [9] JOE S, KUO F Y. Constructing Sobol sequences with better two-dimensional projections[J]. SIAM Journal on Scientific Computer, 2008, 30(5): 2635-2654. Click to display the text [10] BRATLEY P, FOX B L. Algorithm 659:Implementing Sobol's quasirandom sequence generator[J]. ACM Transactions on Mathematical Software, 1988, 14(1): 88-100. Click to display the text [11] 陈国生, 马良, 张明. 舰艇编队协同防空作战效能评估[J]. 舰船科学技术, 2011, 33(2): 105-107. CHEN G S, MA L, ZHANG M. Effect evaluation of coordinated-air defense of warships[J]. Ship Science and Technology, 2011, 33(2): 105-107. (in Chinese) Cited By in Cnki (11) | Click to display the text [12] SONGLEI N, YAN J. Research on coordination air-defense decision-making optimum model of naval ship formation[J]. Computer Engineering & Applications, 2013, 49(6): 257-261. Click to display the text [13] 罗鹏程, 周经伦, 金光, 等. 武器装备体系作战效能与作战能力评估分析方法[M]. 北京: 国防工业出版社, 2014. LUO P C, ZHOU J L, JIN G, et al. Analysis on assessment methods for combat capability of weapon SoS[M]. Beijing: National Defense Industry Press, 2014. (in Chinese) [14] 罗亚民, 宋贵宝. 海军导弹装备采办综合绩效评价体系构建[J]. 兵器装备工程学报, 2018(2): 146-152. LUO Y M, SONG G B. Construction of comprehensive performance evaluation system for navy missile equipment acquisition[J]. Journal of Ordnance Equipment Engineering, 2018(2): 146-152. (in Chinese) Cited By in Cnki | Click to display the text [15] 苏建刚.武器装备效能评估指标体系研究[A].北京: 中国自动化学会, 2017: 4. SU J G. Research on effectiveness evaluation index system of weapon equipment[A]. Beijing: Chinese Association of Automation, 2017: 4(in Chinese). [16] 周静杨.舰艇编队分布式协同防空建模与仿真[D].西安: 西北工业大学, 2016. ZHOU J Y. Modeling and simulation of distributed cooperative air defense for warship fleet[D]. Xi'an: Northwestern Polytechnical University, 2016(in Chinese). [17] 张晓海, 操新文, 耿松涛, 等. 基于深度学习的军事辅助决策智能化研究[J]. 兵器装备工程学报, 2018, 39(10): 162-167. ZHANG X H, CAO X W, GENG S T, et al. Research on intelligence of military auxiliary decision-Making system based on deep learning[J]. Journal of Ordnance Equipment Engineering, 2018, 39(10): 162-167. (in Chinese) Cited By in Cnki (3) | Click to display the text [18] JABARDI M H, AL-FATLAWI A H, LING S. Jabardi diagnosis system for parkinson's disease using speech characteristics of patients and deep belief network[J]. CAAI Transaction on Intelligence Technology, 2017, 2(9): 246-253. [19] HINTON G E, OSINDERO S, TEH Y W. A fast learning algorithm for deep belief nets[J]. Neural Computation, 2014, 18(7): 1527-1554. Click to display the text [20] FISCHER A, IGEL C. Training restricted boltzmann machines:An introduction[J]. Pattern Recognition, 2014, 47: 25-39. Click to display the text [21] HOCHREITER S, MOZER M C. Monaural speech separation by support vector machines:Bridging the divide between supervised and unsupervised learning methods[M]. Blind Speech Separation. Berlin: Springer, 2008: 18. [22] HINTON G E, OSINDERO S, TEH Y W. A fast learning algorithm for deep belief nets[J]. Neural Computation, 2014, 18(7): 1527-1554. Click to display the text [23] SUTSKEVER I, TIELEMAN T. On the convergence properties of contrastive divergence[J]. Journal of Machine Learing Research, 2010, 9(4): 789-795. Click to display the text [24] 陈春利, 金炜东. 一种改进的DNN算法在雷达信号分选中的应用[J]. 计算机应用研究, 2019(4): 1-5. CHEN C L, JIN W D. Application of improved DNN algorithm in radar signal sorting[J]. Application Research of Computers, 2019(4): 1-5. (in Chinese) Cited By in Cnki (2) | Click to display the text
http://dx.doi.org/10.7527/S1000-6893.2019.23214

0

#### 文章信息

LI Bo, LUO Haoran, TIAN Linyu, WANG Yuanxun

Sensitivity analysis of ship formation operational effectiveness based on DBN effectiveness fitting

Acta Aeronautica et Astronautica Sinica, 2019, 40(12): 323214.
http://dx.doi.org/10.7527/S1000-6893.2019.23214