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摘要:
将辐射源威胁评估作为多属性决策问题进行处理时，侦察方无法获取敌方辐射源的所有信息，而逼近理想解排序（TOPSIS）法在处理“贫信息”问题时很难得到完美结果，而且其仅仅考虑指标之间的欧氏距离，无法反映各指标间的关联性。针对TOPSIS法存在的问题，将灰色关联分析（GRA）和TOPSIS法结合，提出一种基于博弈论的GRA-TOPSIS辐射源威胁评估模型。在构建辐射源目标综合评价指标体系的基础上，运用博弈论（GT）思想将区间层次分析法（IAHP）所得主观权重和信息熵所得客观权重进行组合得到综合权重，能够较大程度减少单独赋权带来的信息损失。在基于GRA-TOPSIS辐射源威胁评估模型下，构建了关于战场态势的决策信息系统，通过与传统TOPSIS法进行对比仿真，验证了所提方法的有效性，有助于对辐射源进行更精细准确地排序。
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关键词:
- 逼近理想解排序(TOPSIS) /
- 灰色关联分析(GRA) /
- 博弈论(GT) /
- 辐射源威胁评估 /
- 区间层次分析法(IAHP) /
- 信息熵 /
- 综合权重
Abstract:When the radiation source threat assessment is handled as a multi-attribute decision problem, the scouting party cannot obtain all the information of the enemy radiation source, the method of Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) is hard to get perfect results in dealing with "poor information", and it only considers the Euclidean distance between the indicators and cannot reflect the correlation between different indicators. Aimed at the problems of TOPSIS method, a radiation source threat assessment model based on game theory is proposed by combining Grey Relational Analysis (GRA) and TOPSIS method. On the basis of constructing the comprehensive evaluation index system of radiation source targets, Game Theory (GT) idea is used to combine the subjective weights of Interval Analytic Hierarchy Process (IAHP) and the objective weights obtained by information entropy to obtain comprehensive weights, which can greatly reduce the information loss caused by the weight alone. Based on the GRA-TOPSIS radiation source threat assessment model, a decision information system for battlefield situation is constructed. By comparing with the traditional TOPSIS method, the effectiveness of the proposed method is verified, which is helpful for sorting radiation sources more precisely and accurately.
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表 1 脉冲样本图参数
Table 1. Parameters of pulse sequence pattern
目标 RF/MHz PRI/μs PW/μs AOA/(°) PA/dB Ts/μs Te/μs N X1 9 500 3 1.2 11 10 1.00 3 072.00 1 024 X2 9 800 11.4 0.29 2 12 1 340.20 2 799.40 128 X3 9 000 3.1 1.1 30 6 4 510.00 6 097.20 512 X4 1 500 100 1.1 15 11 4 670.00 11 070.00 64 X5 10 000 3 0.5 45 5 7 910.00 9 446.00 512 
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表 2 辐射源特征参数
Table 2. Character parameters of emitter
目标 Pt/kW 
Fn/dB L/dB (S/N)min/dB tfa/s X1 12 40 4 6 [12, 20] [60, 90] X2 12 40 4 6 [12, 20] [60, 90] X3 13.5 45 3 4 [10, 20] [60, 90] X4 50 48 2 7 [8, 16] [90, 120] X5 15 50 3 6 [10, 18] [50, 80]
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表 3 目标平台态势参数
Table 3. Situation parameters of target platform
目标 A1(l) A2 A3(k) R/km v/(m·s-1) h/m X1 3 80 285 6 000 5 X2 3 50 290 5 500 5 X3 4 120 250 7 000 5 X4 2 400 0 0 2 X5 6 150 0 0 8
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表 4 规范化决策矩阵
Table 4. Normalization decision matrix
目标 R Rr RS, N Pd Pfa/10-9 ΔR Rmax Δv vmax C X1 0.303 6 0.030 5 0.278 5 0.377 7 0.668 3 0.596 5 0.006 9 0.215 7 0.569 0 0.495 1 X2 0.871 2 0.102 6 0.682 3 0.481 1 0.334 2 0.248 5 0.006 9 0.410 3 0.540 5 0.383 6 X3 0.223 6 0.060 8 0.352 3 0.480 6 0.611 5 0.530 2 0.007 0 0.441 4 0.581 2 0.514 1 X4 0.276 0 0.992 0 0.483 7 0.407 1 0.204 2 0.532 0 0.228 5 0.656 6 0.108 1 0.318 8 X5 0.145 2 0.029 6 0.314 3 0.478 7 0.161 4 0.142 5 0.973 5 0.398 9 0.185 9 0.491 6
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表 5 博弈论所赋各指标集化权重
Table 5. Combinational index weights obtained by using game theory
指标层 区间AHP法权重 熵权法权重 GT权重 C1 0.071 3 0.080 9 0.074 8 C2 0.071 3 0.336 2 0.168 5 C3 0.082 9 0.021 2 0.060 3 C4 0.117 9 0.001 9 0.075 4 C5 0.117 9 0.051 3 0.093 5 C6 0.086 2 0.040 7 0.069 5 C7 0.086 2 0.382 6 0.194 9 C8 0.132 8 0.020 8 0.091 7 C9 0.132 8 0.058 5 0.105 5 C10 0.100 8 0.005 8 0.066 0
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表 6 加权规范化决策矩阵
Table 6. Weighted normalization decision matrix
目标 R Rr RS, N Pd Pfa/10-9 ΔR Rmax Δv vmax C X1 0.022 9 0.005 1 0.016 8 0.028 5 0.062 5 0.041 5 0.001 3 0.019 8 0.060 0 0.032 7 X2 0.065 3 0.017 3 0.041 1 0.036 3 0.031 2 0.017 3 0.001 3 0.037 6 0.057 0 0.025 3 X3 0.016 7 0.010 2 0.021 2 0.036 2 0.057 2 0.036 8 0.001 4 0.040 5 0.061 3 0.033 9 X4 0.020 6 0.167 2 0.029 2 0.030 7 0.019 1 0.037 0 0.044 5 0.060 2 0.011 4 0.021 0 X5 0.010 9 0.005 0 0.019 0 0.036 1 0.015 1 0.009 9 0.189 7 0.036 6 0.019 6 0.032 4
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表 7 灰色关联系数矩阵
Table 7. Grey relational coefficient matrix
目标 R Rr RS, N Pd Pfa/10-9 ΔR Rmax Δv vmax C X1 0.571 9 0.998 2 0.699 3 0.979 2 1 0.641 4 1 1 0.537 7 0.979 2 X2 0.996 4 0.821 2 1 0.877 3 0.630 6 0.884 2 1 0.760 4 0.553 4 0.867 9 X3 0.529 1 0.915 7 0.739 5 0.882 8 0.915 7 0.677 5 0.998 2 0.731 9 0.531 1 1 X4 0.558 9 0.258 5 0.826 1 0.929 2 0.579 5 0.675 9 0.566 7 0.583 1 1 0.814 1 X5 0.509 6 1 0.718 9 0.892 6 0.543 8 1 0.230 7 0.770 8 0.873 3 0.974 1
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表 8 不同赋权方法的威胁评估结果
Table 8. Threat assessment results of different weighting methods
目标 主观赋权法 客观赋权法 组合赋权法 相对贴近度 排序结果 相对贴近度 排序结果 相对贴近度 排序结果 X1 0.353 2 3 0.365 2 2 0.614 8 2 X2 0.681 4 1 0.930 5 1 0.628 7 1 X3 0.331 5 4 0.304 0 3 0.568 0 3 X4 0.317 5 5 0.133 5 5 0.331 3 5 X5 0.365 4 2 0.267 7 4 0.458 8 4
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