﻿ 基于PCA-MPSO-ELM的空战目标威胁评估
 文章快速检索 高级检索

Target threat assessment in air combat based on PCA-MPSO-ELM algorithm
XI Zhifei, XU An, KOU Yingxin, LI Zhanwu, YANG Aiwu
College of Aeronautics Engineering, Air Force Engineering University, Xi'an 710038, China
Abstract: Target threat assessment is a key link in air combat. Due to the complex and diverse factors affecting the threat assessment of air combat targets and the correlation between the indicators, traditional assessment algorithm cannot obtain accurate and objective assessment results. This paper proposes a target threat assessment algorithm based on a Principal Component Analysis method and an Modified Particle Swarm Algorithm Optimized for Extreme Learning Machines (PCA-MPSO-ELM). Indicators affecting the degree of target threat values were comprehensively analyzed first, followed by linear changes in the original evaluation indicators using the principal component analysis method to obtain comprehensive variables, eliminating the correlation between the evaluation indicators and achieving dimensionality reduction of the evaluation data. On the basis of data pretreatment, the ELM neural network was established and the improved particle swarm algorithm was applied to the optimization of the input weights and threshold values of ELM to improve the accuracy of the target threat assessment model. Finally, air combat data was selected from the air combat maneuvering instrument, and sample data for target threat assessment was constructed using the threat index method. The accuracy analysis and real-time analysis of the assessment were carried out in simulation experiments, and the results showed that the proposed algorithm can achieve accurate and rapid target threat assessment in air combat.
Keywords: target threat assessment    index correlation    improved particle swarm optimization    extreme learning machines    principal component analysis

1 主成分分析法

 $\left\{ {\begin{array}{*{20}{l}} {{\mathit{\boldsymbol{F}}_1} = {l_{11}}{\mathit{\boldsymbol{X}}_1} + {l_{12}}{\mathit{\boldsymbol{X}}_2} + {l_{13}}{\mathit{\boldsymbol{X}}_3} + \cdots + {l_{1p}}{\mathit{\boldsymbol{X}}_p}}\\ {{\mathit{\boldsymbol{F}}_2} = {l_{21}}{\mathit{\boldsymbol{X}}_1} + {l_{22}}{\mathit{\boldsymbol{X}}_2} + {l_{23}}{\mathit{\boldsymbol{X}}_3} + \cdots + {l_{2p}}{\mathit{\boldsymbol{X}}_p}}\\ \vdots \\ {{\mathit{\boldsymbol{F}}_m} = {l_{m1}}{\mathit{\boldsymbol{X}}_1} + {l_{m2}}{\mathit{\boldsymbol{X}}_2} + {l_{m3}}{\mathit{\boldsymbol{X}}_3} + \cdots + {l_{mp}}{\mathit{\boldsymbol{X}}_p}} \end{array}} \right.$ （1）

 ${{z_{ij}} = \frac{{{x_{ij}} - {{\bar x}_j}}}{{\sqrt { {\rm{Var}}{ _j}} }}}$ （2）
 ${{{\bar x}_j} = \frac{1}{m}\sum\limits_{i = 1}^m {{x_{ij}}} }$ （3）
 $\begin{array}{*{20}{l}} { {\rm{Va}}{{\rm{r}}_j} = \frac{1}{{m - 1}}\sum\limits_{i = 1}^m {{{({x_{ij}} - {{\bar x}_j})}^2}} }\\ {{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} i = 1,2, \cdots ,n;j = 1,2, \cdots ,p} \end{array}$ （4）

 ${\sigma _{ij}} = \frac{{\sum\limits_{k = 1}^n {({z_{ki}} - \overline {{Z_i}} )} ({z_{kj}} - \overline {{Z_j}} )}}{{\sqrt {\sum\limits_{k = 1}^n {{{({z_{ki}} - \overline {{Z_i}} )}^2}} \sum\limits_{k = 1}^n {{{({z_{kj}} - \overline {{Z_j}} )}^2}} } }}$ （5）

 ${\mathit{\boldsymbol{U}}^{\rm{T}}}\mathit{\boldsymbol{ \boldsymbol{\varSigma} U}} = \mathit{\boldsymbol{ \boldsymbol{\varLambda} }} = \left[ {\begin{array}{*{20}{l}} {{\lambda _1}}&{}&{}&{}\\ {}&{{\lambda _2}}&{}&{}\\ {}&{}& \ddots &{}\\ {}&{}&{}&{{\lambda _p}} \end{array}} \right]$ （6）

 $\mathit{\boldsymbol{U}} = [{\mathit{\boldsymbol{u}}_1},{\mathit{\boldsymbol{u}}_2}, \cdots ,{\mathit{\boldsymbol{u}}_p}]$ （7）

 ${ {\rm{cov}} ({\mathit{\boldsymbol{F}}_i},{\mathit{\boldsymbol{F}}_j}) = \mathit{\boldsymbol{u}}_i^{\rm{T}}\mathit{\boldsymbol{ \boldsymbol{\varSigma} }}{\mathit{\boldsymbol{u}}_j} = {\bf{0}}}$ （8）
 ${ {\rm{Var}} ({\mathit{\boldsymbol{F}}_i}) = {\rm{Var }}(\mathit{\boldsymbol{u}}_i^{\rm{T}}\mathit{\boldsymbol{Z}}) = \mathit{\boldsymbol{u}}_i^{\rm{T}}\mathit{\boldsymbol{ \boldsymbol{\varSigma} }}{\mathit{\boldsymbol{u}}_i} = {\lambda _i}}$ （9）

 ${w_i} = {\lambda _i}/\sum\limits_{j = 1}^p {{\lambda _j}}$ （10）

 $\rho = \sum\limits_{i = 1}^d {{w_i}}$ （11）

 $\begin{array}{l} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \mathit{\boldsymbol{F}} = [{\mathit{\boldsymbol{F}}_1},{\mathit{\boldsymbol{F}}_2}, \cdots ,{\mathit{\boldsymbol{F}}_d}] = {[{\mathit{\boldsymbol{F}}_{ij}}]_{d \times p}}\\ \left\{ {\begin{array}{*{20}{c}} {{\mathit{\boldsymbol{F}}_1} = {u_{11}}{\mathit{\boldsymbol{Z}}_1} + {u_{12}}{\mathit{\boldsymbol{Z}}_2} + \cdots + {u_{1p}}{\mathit{\boldsymbol{Z}}_p}}\\ {{\mathit{\boldsymbol{F}}_2} = {u_{21}}{\mathit{\boldsymbol{Z}}_1} + {u_{22}}{\mathit{\boldsymbol{Z}}_2} + \cdots + {u_{2p}}{\mathit{\boldsymbol{Z}}_p}}\\ \vdots \\ {{\mathit{\boldsymbol{F}}_d} = {u_{d1}}{\mathit{\boldsymbol{Z}}_1} + {u_{d2}}{\mathit{\boldsymbol{Z}}_2} + \cdots + {u_{dp}}{\mathit{\boldsymbol{Z}}_p}} \end{array}} \right. \end{array}$ （12）
2 ELM神经网络

 ${O_j} = \sum\limits_{i = 1}^L {{\beta _i}} g({\mathit{\boldsymbol{w}}_i}{\mathit{\boldsymbol{x}}_j} + {b_i})\quad j = 1,2, \cdots ,N$ （13）

 $\sum\limits_{i = 1}^L {{\beta _i}} g({\mathit{\boldsymbol{w}}_i}{\mathit{\boldsymbol{x}}_j} + {b_i}) = {t_j}\quad j = 1,2, \cdots ,N$ （14）

 $\mathit{\boldsymbol{H\beta }} = \mathit{\boldsymbol{T}}$ （15）
 $\mathit{\boldsymbol{H}}({w_1},{w_2}, \cdots ,{w_L},{b_1},{b_2}, \cdots ,{b_L},{x_1},{x_2}, \cdots ,{x_N}) = \left[ {\begin{array}{*{20}{c}} {g({w_1}{x_1} + {b_1})}&{g({w_2}{x_1} + {b_2})}& \cdots &{g({w_L}{x_1} + {b_L})}\\ {g({w_1}{x_2} + {b_1})}&{g({w_2}{x_2} + {b_2})}& \cdots &{g({w_L}{x_2} + {b_L})}\\ \vdots & \vdots &{}& \vdots \\ {g({w_1}{x_N} + {b_1})}&{g({w_2}{x_N} + {b_2})}& \cdots &{g({w_L}{x_N} + {b_L})} \end{array}} \right]$ （16）

 $\left\| {\mathit{\boldsymbol{H\hat \beta }} - \mathit{\boldsymbol{T}}} \right\| = \left\| {\mathit{\boldsymbol{H}}{\mathit{\boldsymbol{H}}^\dagger }\mathit{\boldsymbol{T}} - \mathit{\boldsymbol{T}}} \right\| = \mathop {{\rm{min}}}\limits_\mathit{\boldsymbol{\beta }} \left\| {\mathit{\boldsymbol{H\beta }} - \mathit{\boldsymbol{T}}} \right\|$ （17）

 $\mathit{\boldsymbol{\hat \beta }} = {\mathit{\boldsymbol{H}}^\dagger }\mathit{\boldsymbol{T}}$ （18）

3 改进的粒子群算法

 $\omega = \left\{ {\begin{array}{*{20}{l}} {{\omega _{{\rm{min}}}} + \frac{{({\omega _{{\rm{max}}}} - {\omega _{{\rm{min}}}})(f - {f_{{\rm{min}}}})}}{{{f_{{\rm{ avg }}}} - {f_{{\rm{min}}}}}}}&{f \le {f_{{\rm{ avg }}}}}\\ {{\omega _{{\rm{max}}}}}&{f > {f_{{\rm{ avg }}}}} \end{array}} \right.$ （19）

 $\left\{ {\begin{array}{*{20}{l}} {{c_1} = {c_{{\rm{1s}}}} - \frac{{t({c_{{\rm{1s}}}} - {c_{{\rm{1e}}}})}}{{{T_{{\rm{max}}}}}}}\\ {{c_2} = {c_{{\rm{2s}}}} - \frac{{t({c_{{\rm{2s}}}} - {c_{{\rm{2e}}}})}}{{{T_{{\rm{max}}}}}}} \end{array}} \right.$ （20）

4 基于PCA-MPSO-ELM的目标威胁评估模型 4.1 构建目标威胁评估指标体系

 图 1 双机空战态势图 Fig. 1 Dual air combat situation map

1) 速度威胁

 ${T_V} = \left\{ {\begin{array}{*{20}{l}} {0.1}&{{v_{\rm{T}}} < 0.6{v_{\rm{F}}}}\\ { - 0.5 + {v_{\rm{T}}}/{v_{\rm{F}}}}&{0.6{v_{\rm{F}}} \le {v_{\rm{T}}} \le 1.5{v_{\rm{F}}}}\\ {1.0}&{{v_{\rm{T}}} > 1.5{v_{\rm{F}}}} \end{array}} \right.$ （21）

2) 角度威胁

 ${T_A} = \frac{{(|{\varphi _{\rm{F}}}| + |{q_{\rm{T}}}|)}}{{{{360}^\circ }}}$ （22）

3) 高度威胁

 ${T_H} = \left\{ {\begin{array}{*{20}{l}} {1.0}&{H \ge 5{\kern 1pt} {\kern 1pt} {\kern 1pt} 000}\\ {0.5 + 0.000{\kern 1pt} {\kern 1pt} {\kern 1pt} 1H}&{ - 5{\kern 1pt} {\kern 1pt} {\kern 1pt} 000 \le H \le 5{\kern 1pt} {\kern 1pt} {\kern 1pt} 000}\\ {0.1}&{H < - 5{\kern 1pt} {\kern 1pt} {\kern 1pt} 000} \end{array}} \right.$ （23）

4) 距离威胁

 ${T_D} = \left\{ {\begin{array}{*{20}{l}} 0&{D \ge {D_{{\rm{ Rmax }}}}}\\ {0.5{{\rm{e}}^{ - \frac{{D - {D_{{\rm{MAmax}}}}}}{{{D_{{\rm{MAmax}}}} - {D_{{\rm{Rmax}}}}}}}}}&{{D_{{\rm{MAmax}}}} \le D < {D_{{\rm{Rmax}}}}}\\ {{2^{ - \frac{{D - {D_{{\rm{MEmax}}}}}}{{{D_{{\rm{MAmax}}}} - {D_{{\rm{MEmax}}}}}}}}}&{{D_{{\rm{MEmax}}}} \le D < {D_{{\rm{MAmax}}}}}\\ 1&{{D_{{\rm{MEmin}}}} \le D < {D_{{\rm{MEmax}}}}} \end{array}} \right.$ （24）

5) 空战能力威胁

 $C = \left[ {{\rm{ln}}{\varepsilon _1} + {\rm{ln}}({\varepsilon _2} + 1) + {\rm{ln}}(\sum {{\varepsilon _3}} + 1)} \right]{\varepsilon _4}{\varepsilon _5}{\varepsilon _6}{\varepsilon _7}$ （25）

 ${T_C} = ({C_{\rm{F}}} - {C_{\rm{T}}} + 1)/2$ （26）

4.2 基于结构熵确定评估指标权重

1) 通过咨询领域内专家，形成“典型排序”。

 专家编号 TC TA TD TV TH 专家1 a11 a12 a13 a14 a15 专家2 a21 a22 a23 a24 a25 ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ 专家k ak1 ak2 ak3 ak4 ak5

2) 基于信息熵定性转化专家意见。

 $F(x) = - \frac{{(m - x)/{\rm{ln}}(m - x)}}{{(m - 1){\rm{ln}}(m - 1)}} + \frac{{(m - x)}}{{(m - 1)}}$ （27）

 $1 - F(x)/\left( {\frac{{m - x}}{{m - 1}}} \right) = D(x)$ （28）

 $D(x) = {\rm{ln}}(m - x)/{\rm{ln}}(m - 1)$ （29）

 $\mathit{\boldsymbol{D}} = \left[ {\begin{array}{*{20}{c}} {{d_{11}}}&{{d_{12}}}&{{d_{13}}}&{{d_{14}}}&{{d_{15}}}\\ \vdots & \vdots & \vdots & \vdots & \vdots \\ {{d_{i1}}}&{{d_{i2}}}&{{d_{i3}}}&{{d_{i4}}}&{{d_{i5}}}\\ \vdots & \vdots & \vdots & \vdots & \vdots \\ {{d_{k1}}}&{{d_{k2}}}&{{d_{k3}}}&{{d_{k4}}}&{{d_{k5}}} \end{array}} \right]$ （30）

3) 对专家形成的重要性排序进行盲度分析，优化因主观导致的不确定性偏差。

 ${d_j} = ({d_{1j}} + {d_{2j}} + \cdots + {d_{kj}})/k$ （31）

 $\begin{array}{*{20}{l}} {{Q_j} = |\{ [{\rm{max}}({d_{1j}},{d_{2j}}, \cdots ,{d_{kj}}) - {d_j}] + }\\ {{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} [{\rm{min}}({d_{1j}},{d_{2j}}, \cdots ,{d_{kj}}) - {d_j}]\} /2|} \end{array}$ （32）

 ${\mu _j} = {d_j}(1 - {Q_j})$ （33）

4) 对综合认识度进行归一化处理

 $\mu _j^* = \frac{{{\mu _j}}}{{\sum\limits_{k = 1}^5 {{\mu _k}} }}$ （34）

4.3 目标威胁评估样本数据构造

 图 2 空战对抗轨迹图 Fig. 2 Trajectories of air combat

4.4 目标威胁评估模型结构与算法流程

 图 3 目标威胁评估模型结构图 Fig. 3 Structure of target threat assessment model

1) 基于威胁指数法，构建空战目标威胁评估指标体系。

2) 基于结构熵确定威胁评估指标权重。

3) 空战数据提取。

4) 构建空战目标威胁评估的样本。

1) 对目标威胁指标进行分析，利用主成分分析对原始指标进行线性组合得到综合变量，消除原始评估指标之间的相关性，实现对数据的降维。

2) 构建ELM神经网络并利用改进粒子群算法优化其输入权值和阈值。

3) 基于步骤1中所构建的样本完成对PAC-MPSO-ELM目标威胁评估模型的训练。

ELM神经网络以经过PCA算法处理之后的综合变量为输入，目标的威胁值为输出。评估模型实施步骤2的流程如图 4所示。

 图 4 算法求解流程图 Fig. 4 Flow chart of proposed algorithm

5 仿真实验 5.1 实验设置

5.2 目标威胁评估指标权重的确定及结构熵法有效性验证

 专家 TC TA TD TV TH 1 3 8 5 2 7 2 2 9 1 5 6 3 3 6 3 4 7 4 1 8 4 6 4 5 3 7 2 4 5 6 3 6 2 5 6 7 1 7 3 2 5 8 1 7 8 6 7 9 2 7 3 2 8 10 1 8 2 4 7

 评估指标 权重 权值 层次分析法 结构熵法 空战能力 w1 0.167 8 0.103 6 角度威胁 w2 0.108 4 0.335 1 距离威胁 w3 0.361 0 0.148 9 速度威胁 w4 0.224 3 0.116 3 高度威胁 w5 0.138 5 0.296 1

5.3 ELM神经网络隐含层节点数的确定

ELM神经网络的隐含层节点数对于模型的预测精度的影响较大。如若隐含层的节点数过少，ELM神经网络将很难学习样本，导致模型预测精度较低；如果隐含层的节点数过多，将会大大增加网络的学习训练时间，降低了算法的实时性，并且因为过多的节点数容易造成过拟合[38]。在ELM神经网络的实际应用中，最佳的隐含层节点数大都是通过样本测试实验的方法来确定。根据Kolmogorov定理可知，对于单隐含层的神经网络输入层节点数p、输出层节点数q以及其隐含层节点数m满足m=sqrt(p+q)+a关系，其中a为[1,10]之间的常数。故本文为了兼顾ELM网络的预测性能以及算法的训练学习时间成本，采用测试仿真实验的方法，利用测试样本在[3,50]范围内找到使得ELM神经网络性能最好的隐含层节点数L

 图 5 隐含层节点数测试结果 Fig. 5 Testing results of hidden layer nodes

5.4 目标威胁评估精度对比分析

 图 6 测试样本评估结果 Fig. 6 Assessment results of test sample

 图 7 粒子群算法收敛曲线对比 Fig. 7 Comparison of convergence curves of PSO

 ${ {\rm{MAE}} = \frac{1}{N}\sum\limits_{i = 1}^N | {{\hat y}_i} - {y_i}|}$ （35）
 ${ {\rm{MSE}} = \frac{1}{N}\sum\limits_{i = 1}^N {{{({{\hat y}_i} - {y_i})}^2}} }$ （36）
 ${{\rm{MAPE}} = \frac{1}{N}\sum\limits_{i = 1}^N {\frac{{{{\hat y}_i} - {y_i}}}{{{y_i}}}} }$ （37）
 ${{\rm{NMSE}} = \frac{{\sum\limits_{i = 1}^N {{{({y_i} - {{\hat y}_i})}^2}} }}{{\sum\limits_{i = 1}^N {{{({y_i} - \bar y)}^2}} }}}$ （38）

 算法 MAE/10-4 MSE/10-7 MAPE/10-4 NMSE TIME PCA-MPSO-ELM 0.580 6 0.057 2 1.357 2 0.010 3 3.546 8 PCA-ELM 2.961 5 1.324 6 6.919 7 0.234 4 6.363 9 MPSO-ELM 0.789 8 0.093 6 1.844 9 0.016 6 5.188 7 ELM 3.082 7 1.301 9 7.202 3 0.233 9 8.879 6 BP 9.970 6 19.770 0 23.000 0 3.550 7 3.858 1 PCA-BP 3.284 4 1.280 1 7.674 0 0.226 6 4.675 7

 图 8 多种算法训练时间对比 Fig. 8 Comparison of training time of multiple algorithms

5.5 目标威胁评估指标不确定性影响分析

 态势参数 MAE/10-5 MSE/10-8 MAPE/10-4 NMSE qT 8.613 8 1.169 9 2.011 6 0.021 0 φF 8.431 1 1.120 4 1.968 3 0.020 1 ΔH 1.098 0 1.889 9 2.564 4 0.034 0 vF 0.606 0 0.617 9 1.415 9 0.011 1 vT 0.626 8 0.710 6 1.465 0 0.012 8 D 0.601 8 1 406.6 1.406 6 0.010 6
 图 9 不确定性分析 Fig. 9 Uncertainty analyses

 态势参数 因素改变量/% 平均改变量/10-4 重要性 因素改变量/% 平均改变量/10-4 重要性 qT +10 1.613 8 0.154 4 -10 1.078 3 0.120 5 φT +10 2.373 4 0.227 0 -10 2.084 9 0.233 1 vT +10 1.257 5 0.120 3 -10 1.044 1 0.116 7 vF +10 1.127 5 0.107 8 -10 1.376 9 0.153 9 ΔH +10 2.898 1 0.277 2 -10 2.685 1 0.300 2 D +10 1.184 5 0.113 3 -10 0.676 1 0.075 6

6 结论

1) 选取ACMI中的空战数据可以有效提高样本数据的质量，同时可以克服传统威胁评估方法因样本数据过少而导致的模型训练不充分的问题。

2) 主成分分析法可以对数据进行有效降维，可以很好地消除参数之间的相关性。

3) 改进的粒子群算法可以很好地优化ELM神经网络的输入层和隐含层之间的权值和阈值，从而有效提高模型的训练时间和预测精度。

4) 态势参数获取不准确对目标威胁评估结果存在一定的影响。

 [1] HUMA N, ASIF M. An optimal dynamic threat evaluation and weapon scheduling technique[J]. Knowledge-Based Systems, 2010, 23(3): 337-342. Click to display the text [2] 曾守桢, 穆志民. 基于Zhenyuan积分的直觉模糊多属性决策方法[J]. 控制与工程, 2018, 33(3): 542-548. ZENG S Z, MU Z M. Method based on Zhenyuan integral for intuitionistic fuzzy multiple attribute decision making[J]. Control and Decision, 2018, 33(3): 542-548. (in Chinese) Cited By in Cnki | Click to display the text [3] FENG J F, ZHANG Q, HU J H, et al. Dynamic assessment method of air target threat based on improved GIFSS[J]. Journal of Systems Engineering and Electronics, 2019, 30(3): 525-534. Click to display the text [4] 李闯, 端木京顺, 雷英杰, 等. 基于认知图和直觉模糊推理的态势评估方法[J]. 系统工程与电子技术, 2012, 34(10): 2064-2068. LI C, DUANMU J S, LEI Y J, et al. Situation assessment based on cognitive maps and intuitionistic fuzzy reasoning[J]. Systems Engineering and Electronics, 2012, 34(10): 2064-2068. (in Chinese) Cited By in Cnki (16) | Click to display the text [5] XU Y, MIU X. Multi-attribute decision making method for air target threat evaluation based on intuitionistic fuzzy sets[J]. Journal of Systems Engineering and Electronics, 2012, 23(6): 891-897. Click to display the text [6] 夏博龄, 贺正洪, 雷英杰. 基于直觉模糊推理的威胁评估改进算法[J]. 计算机工程, 2009, 35(16): 195-197. XIA B L, HE Z H, LEI Y J. Improved algorithm of threat assessment based on intuitionistic fuzzy reasoning[J]. Computer Engineering, 2009, 35(16): 195-197. (in Chinese) Cited By in Cnki (13) | Click to display the text [7] 李卫忠, 李志鹏, 江洋, 等. 混沌海豚群优化灰色神经网络的空中目标威胁评估[J]. 控制与决策, 2018, 33(11): 1997-2003. LI W Z, LI Z P, JIANG Y, et al. Air-targets threat assessment using grey neural network optimized by chaotic dolphin swarm algorithm[J]. Control and Decision, 2018, 33(11): 1997-2003. (in Chinese) Cited By in Cnki (5) | Click to display the text [8] BRYNIELSSON J, ARNBORG S. Bayesian games for threat prediction and situation analysis[C]//7th International Conference on Information Fusion, 2004: 1125-1132. Click to display the text [9] AZIMIRAD E, HADDADNIA J. Target threat assessment using fuzzy sets theory[J]. International Journal of Advances in Intelligent Informatics, 2015, 1(2): 57-74. Click to display the text [10] CHEN D F, FENG Y, LIU Y X. Threat assessment for air defense operations based on intuitionistic fuzzy logic[J]. Procedia Engineering, 2012, 29(4): 3302-3306. Click to display the text [11] MA S D, ZHANG H Z, YANG G Q. Target threat level assessment based on cloud model under fuzzy and uncertain conditions in air combat simulation[J]. Aerospace Science and Technology, 2017, 67: 49-53. Click to display the text [12] QU C W, HE Y. A method of threat assessment using multiple attribute decision making[C]//6th International Conference on Signal Processing, 2002: 1091-1095. Click to display the text [13] LIANG Q, CHENG X. Knowledge-based ubiquitous and persistent sensor networks for threat assessment[J]. IEEE Transactions on Aerospace and Electronic Systems, 2008, 44(3): 1060-1069. Click to display the text [14] 王俊, 姜长生. 基于LSRBF神经网络的空战目标威胁评估[J]. 电光与控制, 2007, 14(4): 43-48. WANG J, JIANG C S. Target threat assessment based on LSRBF neural network for air combat[J]. Electronic Optics & Control, 2007, 14(4): 43-48. (in Chinese) Cited By in Cnki (14) | Click to display the text [15] 邱浪波, 刘作良, 刘明. 一种应用神经网络技术的威胁估计算法[J]. 空军工程大学学报(自然科学版), 2002, 3(6): 25-28. QIU L B, LIU Z L, LIU M. A threat assessment algorithm by using the neural network techniques[J]. Journal of Air Force Engineering University:Natural Science Edition, 2002, 3(6): 25-28. (in Chinese) Cited By in Cnki (42) | Click to display the text [16] 王向华, 覃征, 刘宇, 等. 径向基神经网络解决威胁排序问题[J]. 系统仿真学报, 2004, 16(7): 1576-1579. WANG X H, QIN Z, LIU Y, et al. RBF neural network for threat sequencing[J]. Journal of System Simulation, 2004, 16(7): 1576-1579. (in Chinese) Cited By in Cnki (55) | Click to display the text [17] 郭辉, 徐浩军, 刘凌. 基于回归型支持向量机的空战目标威胁评估[J]. 北京航空航天大学学报, 2010, 36(1): 123-126. GUO H, XU H J, LIU L. Target threat assessment of air combat based on support vector machines for regression[J]. Journal of Beijing University of Aeronautics and Astronautics, 2010, 36(1): 123-126. (in Chinese) Cited By in Cnki (45) | Click to display the text [18] 王改革, 郭立红, 段红, 等. 基于萤火虫算法优化BP神经网络的目标威胁估计[J]. 吉林大学学报(工学版), 2013, 43(4): 1064-1069. WANG G G, GUO L H, DUAN H, et al. Target threat assessment using glowworm swarm optimization and BP neural network[J]. Journal of Jilin University (Engineering and Technology Edition), 2013, 43(4): 1064-1069. (in Chinese) Cited By in Cnki (63) | Click to display the text [19] 罗艳春, 郭立红, 姜晓莲, 等. 基于模糊神经网络的空中目标威胁评估[J]. 微计算机信息, 2007, 34(23): 268-270. LUO Y C, GUO L H, JIANG X L, et al. Threat assessment for aerial target based on fuzzy neural network[J]. Microcomputer Information, 2007, 34(23): 268-270. (in Chinese) Cited By in Cnki (12) | Click to display the text [20] LAM H K, LAUBER J. Membership-function-dependent stability analysis of fuzzy-model-based control systems using fuzzy Lyapunov functions[J]. Informantion Science, 2013, 232(20): 253-266. Click to display the text [21] HUANG G B, WANG D H, LAN Y. Extreme learning machines:A survey[J]. International Journal of Machine Learning and Cybernetics, 2011, 2(2): 107-122. Click to display the text [22] LAW A, GHOSG A. Multi-label classification using a cascade of stacked autoencoder and extreme learning machines[J]. Neurocomputing, 2019, 358: 222-234. Click to display the text [23] 赵春晖, 胡春梅, 石红. 采用选择性分段PCA算法的高光谱图像异常检测[J]. 哈尔滨工程大学学报(英文版), 2011, 32(1): 109-113. ZHAO C H, HU C M, SHI H. Anomaly detection for a hyperspectral image by using a selective section principal component analysis algorithm[J]. Journal of Harbin Engineering University, 2011, 32(1): 109-113. (in Chinese) Cited By in Cnki (23) | Click to display the text [24] 吕伏, 梁冰, 孙维吉, 等. 基于主成分回归分析法的回采工作面瓦斯涌出量预测[J]. 煤炭学报, 2012, 37(1): 113-116. LV F, LIANG B, SUN W J, et al. Gas emission quantity prediction of working face based on principal component regression analysis method[J]. Journal of China Coal Society, 2012, 37(1): 113-116. (in Chinese) Cited By in Cnki (110) | Click to display the text [25] HUANG G B. An insight into extreme learning machines:random neurons, random features and Kernels[J]. Cognitive Computation, 2014, 6(3): 376-390. Click to display the text [26] HUANG G B, ZHU Q Y, SIEW C K. Real-time learning capability of neural networks[J]. Neurocomputing, 2006, 70: 863-878. Click to display the text [27] LAN Y, SOH Y C, HUANG G B. Ensemble of online sequential extreme learning machine[J]. Neurocomputing, 2009, 72(13): 3391-3395. Click to display the text [28] HUANG G B, DING X J, ZHOU H M. Optimization method based extreme learning machine for classification[J]. Neurocomputing, 2010, 74(1): 155-163. Click to display the text [29] LUO X, CHANG X H, BAN X J. Regression and classification using extreme learning machine based on L-1-norm and L-2-norm[J]. Neurocomputing, 2016, 174: 179-186. Click to display the text [30] QIN Q, FENG Y W, LI F. Structural reliability analysis using enhanced cuckoo search algorithm and artificial neural network[J]. Journal of Systems Engineering and Electronics, 2018, 29(6): 1317-1326. Click to display the text [31] QUAN H, SRINIVASAN D, KHOSRAVI A. Short-term load and wind power forecasting using neural network-based prediction intervals[J]. IEEE Transactions on Neural Networks and Learning Systems, 2014, 25(2): 303-315. Click to display the text [32] 顾佼佼, 刘卫华. 基于攻击区和杀伤概率的视距内空战态势评估[J]. 系统工程与电子技术, 2015, 37(6): 1306-1312. GU J J, LIU W H. WVR air combat situation assessment model based on weapon engagement zone and kill probability[J]. Systems Engineering and Electronics, 2015, 37(6): 1306-1312. (in Chinese) Cited By in Cnki (31) | Click to display the text [33] 徐西蒙, 杨任农, 符颖, 等. 基于ELM_AdaBoost强预测器的空战目标威胁评估[J]. 系统工程与电子技术, 2018, 40(8): 1760-1768. XU X M, YANG R N, FU Y, et al. Target threat assessment in air combat based on ELM_AdaBoost strong predictor[J]. Systems Engineering and Electronics, 2018, 40(8): 1760-1768. (in Chinese) Cited By in Cnki (6) | Click to display the text [34] ZHANG K, KONG W R, LIU P P, et al. Assessment and sequencing of air target threat based on intuitionistic fuzzy entropy and dynamic VIKOR[J]. Journal of Systems Engineering and Electronics, 2018, 29(2): 305-310. Click to display the text [35] KOJADINOVIC I, MARICHAL J L. Entropy of bi-capacities[J]. European Journal of Operational Research, 2007, 178(1): 164-184. Click to display the text [36] GUO R F, HUANG G B, LIN Q P, et al. Error minimized extreme learning machine with growth of hidden nodes and incremental learning[J]. IEEE Transactions on Neural Networks and Learning Systems, 2009, 20(8): 1352-1357. Click to display the text [37] 陈洁钰, 姚佩阳, 王勃, 等. 基于结构熵和IGSO-BP算法的动态威胁评估[J]. 系统工程与电子技术, 2015, 37(5): 1076-1083. CHEN J Y, YAO P Y, WANG B, et al. Dynamic threat assessment based on structure entropy and IGSO-BP algorithm[J]. Systems Engineering and Electoronics, 2015, 37(5): 1076-1083. (in Chinese) Cited By in Cnki (27) | Click to display the text [38] 高大文, 王鹏, 蔡臻超. 人工神经网络中隐含层节点数与训练次数的优化[J]. 哈尔滨工业大学学报, 2003, 35(2): 207-209. GAO D W, WANG P, CAI Z C. Optimization of hidden nodes and training times in artificial neural network[J]. Journal of Harbin Institute of Technology, 2003, 35(2): 207-209. (in Chinese) Cited By in Cnki (133) | Click to display the text
http://dx.doi.org/10.7527/S1000-6893.2020.23895

0

#### 文章信息

XI Zhifei, XU An, KOU Yingxin, LI Zhanwu, YANG Aiwu

Target threat assessment in air combat based on PCA-MPSO-ELM algorithm

Acta Aeronautica et Astronautica Sinica, 2020, 41(9): 323895.
http://dx.doi.org/10.7527/S1000-6893.2020.23895