﻿ 航空兵协同对海打击时间协同模型研究
 舰船科学技术  2016, Vol. 38 Issue (3): 147-150 PDF

1. 海军航空工程学院, 山东烟台 264001;
2. 黄海水产研究所, 山东青岛 266000

Research on the Time constraint Model of Aviation Air to Sea Cooperative Operation
MA Hai-yang1, LI Dong1, SUN Huai-liang2
1. Naval Aeronautical Engineering Institute, Yantai 264001;
2. Yellow Sea Fisheries Research Institute, QingDao, 266000
Abstract: Time factor become more and more important in the cooperative operations. Firstly, STCN was analyzed, and then, according to the STCN, quantified aviation cooperative time constraint, turned TC into inequality that STCN required, the process of time cooperative model of STCN was given. Finally, model of d actions was built based on STCN.
Key words: aviation    cooperative actions    TCN    time constraint model
0 引言

1 协同时间约束关系描述

 $CA = \left\{ {C{A_1}，C{A_2}，\cdots，C{A_d}} \right\} 。$ (1)

 $TC = \left\{ {{T_S}{\rm{，}}{T_E}{\rm{，}}{T_{Dur}}{\rm{，}}{T_D}} \right\}。$ (2)

2 简单时间约束网络

TCN 不仅能够形象准确地表达许多实际问题和系统，而且通过相关的算法能够支持对时间的推理，如检测系统内各个活动时间约束的一致性等。目前己经在许多规划和调度系统中得到了较为广泛应用[3, 4, 5]

 $VA = \left\{ {V{A_1}，V{A_2}， \cdots ，V{A_k}} \right\}，$ (3)

 $C = \left\{ {{C_1}，{C_2}，\cdots ，{C_k}} \right\}。$ (4)

 $\left\{ {V{A_1} = v{a_1}，V{A_2} = v{a_2}， \cdots ，V{A_k} = v{a_k}} \right\} 。$ (5)

 $VA = \left\{ {v{a_1}，v{a_2}， \cdots ，v{a_k}} \right\}，$ (6)

 $G = \left\langle {V，E} \right\rangle。$ (7)

 $V{A_i} - V{A_j} \in \{ {I_1}，{I_2}，\cdot \cdot \cdot {I_n}\}。$ (8)

 ${G_D} = \left( {{V_D},{E_D}} \right)，$ (9)

STCN 是一个支持对二元时间约束系统进行描述和推理的通用模型，并能够在多项式时间内检测出一致性结果。STCN 同样包括一组时间点变量

 $VA = \left\{ {V{A_1}，V{A_2}， \cdots，V{A_d}} \right\}，$ (10)

 $T{L_{ij}} \leqslant V{A_j} - V{A_i} \leqslant T{U_{ij}}，$ (11)

 $0 \leqslant T{L_{ij}} \leqslant T{U_{ij}}，$ (12)

 $\begin{array}{*{20}{l}} {V{A_j} - V{A_i} \le T{U_{ij}}，}\ {V{A_i} - V{A_j} \le - T{L_{ij}}} \end{array}。$ (13)

 $V{A_j} - V{A_i} \leqslant T{U_{ij}}，$ (14)

VAjVAi 标注权值 -TLij，表示线性不等式

 $V{A_i} - V{A_j} \leqslant - T{L_{ij}}，$ (15)

 图 1 两顶点 STCN 示意图 Fig. 1 STCN of 2 vertices

 $\left\{ {\begin{array}{*{20}{l}} {{T_S} - {T_R} \le 40，{\rm{,}}}\\ {{T_E} - {T_S} \le 10，{\rm{,}}}\\ {{T_E} - {T_R} \le 55。} \end{array}} \right.{\rm{ }}$ (16)

 图 2 突击动作的 STCN Fig. 2 STCN of assault

 $A\left( {{G_D}} \right) = {\left( {{a_{ij}}} \right)_{\left( {2d + 1} \right) \times \left( {2d + 1} \right)}}，$ (17)
d 个协同动作组成的 STCN —— GD 的权值矩阵，其中

 ${a_{ij}} = \left\{ {\begin{array}{*{20}{l}} {\infty {\rm{，}}i = j{\rm{，}}}\\ {{W_{ij}}{\rm{，}}i \to j{\rm{，}}i \ne j{\rm{，}}}\\ {\infty {\rm{，}}i \to j{\rm{，}}} \end{array}} \right.$ (18)

3 基于时间约束网络的时间协同模型 3.1 时间约束的定量计算

 ${T_S}\left( {C{A_{di}}} \right) = \frac{{{T_{Sa}}\left( {C{A_{di}}} \right) + 4{T_{Sm}}\left( {C{A_{di}}} \right) + {T_{Sb}}\left( {C{A_{di}}} \right)}}{6}。$ (19)

3.2 时间协同模型的建立

 ${T_E}\left( {C{A_1}} \right)\langle {T_S}\left( {C{A_2}} \right)。$ (20)

 ${T_R}\left( {C{A_0}} \right) = 0，$ (21)

 $\begin{array}{*{20}{c}} {\begin{array}{*{20}{c}} {{T_R}\left( {C{A_0}} \right) - {T_S}\left( {C{A_1}} \right) \le {W_{S1R0}}，}\\ {{T_S}\left( {C{A_1}} \right) - {T_E}\left( {C{A_1}} \right) \le {W_{E1S1}}，}\\ {{T_E}\left( {C{A_1}} \right) - {T_R}\left( {C{A_0}} \right) \le {W_{R0E1}}，} \end{array}}\\ {{T_R}\left( {C{A_0}} \right) - {T_S}\left( {C{A_2}} \right) \le {W_{S2R0}}，}\\ {{T_S}\left( {C{A_2}} \right) - {T_E}\left( {C{A_2}} \right) \le {W_{E2S2}}，}\\ {\begin{array}{*{20}{c}} {{T_E}\left( {C{A_2}} \right) - {T_R}\left( {C{A_0}} \right) \le {W_{R0E2}}，}\\ {{T_E}\left( {C{A_1}} \right) - {T_S}\left( {C{A_2}} \right) \le {W_{S2E1}}。} \end{array}} \end{array}$ (22)

 图 3 两动作的 STCN 模型 Fig. 3 STCN model of 2 actions

 图 4 时间协同模型建立流程 Fig. 4 Flow of time coordination model establishment

 图 5 d 个协同动作 STCN 模型示意图 Fig. 5 STCN model of d actions
4 结语

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