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多传感器信息融合,由于传感器之间的数据冗余性增强了系统信息的可靠性,同时,多传感器之间互补数据和信息扩展了整个电子战系统的性能。如图 2所示,这里有多个传感器,传感器之间存在若干非全组合的重叠关系,表现在数据上就是A、B、C、D等重叠区域的冗余数据,同时非重叠部分的数据又构成数据互补。
1991年最早提出的数据融合处理模型如图 3所示,当时主要是面向军事领域的应用,自此一直被沿用于数据融合领域。信息融合的3个主要层次数据层融合、特征层融合及决策层融合,就是基于该原型,通过进一步改进与丰富所得。后期,“信息源”与“数据库管理系统”两个模块逐渐体现在数据层的融合上;而“源预处理”体现在特征层融合;“目标评估”、“态势评估”、“威胁评估”和“总过程评估”则是决策层的融合。
信息融合系统的融合层次,不仅限于3个层次的融合结构,根据不同的数据抽象,还可划分为像素层融合、特征层融合和决策层融合。决策层融合作为3层次融合的最终结果,直接指向具体的决策目标,其融合结果直接影响决策水平的高低。然而,决策层融合中要获得各自的判定结果,第一步要对原传感器信息进行预处理,所以预处理的代价更高。
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在DS证据理论中,识别框架表示对某一问题的所有可能性答案,是由互不相容的基本命题(假定)组成的完备集合,而其中只存在一个正确的答案。命题是该框架的子集部分,基本可信数(BPA,也称m函数),m(A)反映对A的信度大小,是分配给各命题的信任程度。具体基本定义如下:
定义 1 基本概率分配(BPA)
设U为已识别框架,则函数m:${2^U} \to [01]$满足下列条件:
1) m (Φ)=0;
2) $\sum\limits_{A \subset U} {\operatorname{m} (A)} {\rm{ = }}1$时,称$\operatorname{m} (A)$=0为A的基本赋值,$\operatorname{m} (A)$=0表示对A的信任程度,也称为mass函数。
定义 2 信任函数(belief function)
Bel:${2^U} \to [01]$
Bel(A)=$\sum\limits_{B \subset A} {{\mathop{\rm m}\nolimits} (B)} {\rm{ = }}1(\forall A \subset U)$
表示A的全部子集的基本概率分配函数之和。
定义 3 似然函数(plausibility function)
$${\rm{pl}}(A){\rm{ = }}1 - {\rm{Bel}}(\overline A ){\rm{ = }}$$ $$\sum\limits_{B \subset U} {{\rm{m}}(B)} - \sum\limits_{B \subset A} {{\rm{m}}(B)} = \sum\limits_{B \cap A \ne \phi } {{\rm{m}}(B)} $$ 似然函数是所有与A相交的子集的基本概率分配之和,表示不否认A的信任度。
定义 4 信任区间
[Bel(A), pl(A)]表示命题A的信任区间,Bel(A)表示信任函数为下限,pl(A)表示似然函数为上限。
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主成份分析法(PCA),旨在利用降维的思想,把多指标转化为少数几个综合指标(即主成份),其中每个主成份所含信息互不相同,都可以反映原始变量的大部分信息。该方法在引进多方面变量的同时将复杂因素归结为几个主成份,进而简单化问题处理过程。基于该方法,对多传感器数据进行融合,提取它们的共同特征,从而得到一个比较准确的采样信号,将该信号带入下述算法中,可以有效地减少因为恶劣环境或干扰引起的误差。
首先,PCA通过线性变换达到数据降维的目的:
$$Y = {\omega _1}{X_1} + {\omega _2}{X_2} + \cdots + {\omega _p}{X_p} = {\mathit{\boldsymbol{ \boldsymbol{\varOmega} }}^{\rm{T}}}\mathit{\boldsymbol{X}}$$ (1) 式中,X为多元变量,Xi为随机变量;Y是变换后所得的随机变量;Ω是线性变换矩阵,有:
$$\max {\rm{Var}}({\mathit{\boldsymbol{ \boldsymbol{\varOmega} }}^{\rm{T}}}\mathit{\boldsymbol{X}}) = \max {\mathit{\boldsymbol{ \boldsymbol{\varOmega} }}^{\rm{T}}}{\rm{Var}}(\mathit{\boldsymbol{X}})\mathit{\boldsymbol{ \boldsymbol{\varOmega} }},\mathit{\boldsymbol{ \boldsymbol{\varOmega} }}:||\mathit{\boldsymbol{ \boldsymbol{\varOmega} }}|| = 1$$ (2) 式中,Var(*)表示计算方差。实际中,线性变换矩阵根据特征值由大到小的顺序排列,由矩阵X的特征向量所组成,及特征向量为${{\mathit{\boldsymbol{\gamma}}} _1},{{\mathit{\boldsymbol{\gamma}}} _2}, \cdots ,{{\mathit{\boldsymbol{\gamma}}} _p}$,对应的特征值满足${{\mathit{\boldsymbol{\lambda}}} _1},{\lambda _2}, \cdots ,{{\mathit{\boldsymbol{\lambda}}} _p}$。因此,${\mathit{\boldsymbol{\gamma}}} _1^{\rm{T}}{\mathit{\boldsymbol{X}}}$为第一主成份,${\mathit{\boldsymbol{\gamma}}} _2^{\rm{T}}X$为第二主成份,由此类推。值得注意的是,该方法在很大程度上受影响于被处理数据的物理单位,所以同单位物理量是最好的选择。在诸多电子战系统装备中,大部分检测信号类型同一且均值为零的特性,刚好满足PCA方法的要求。
假设Xi是系统检测到的信号,i表示为第i次检测到的信号。因此多源随机变量为:
$$\mathit{\boldsymbol{X}} = [{X_1},{X_2}, \cdots ,{X_p}]$$ (3) 将以上检测到的测量信号集合${\mathit{\boldsymbol{X}}}$带入到PCA算法中,就可以得到一个p维向量集合为:
$${\bf{Score}} = [{\rm{IM}}{{\rm{F}}_1},{\rm{IM}}{{\rm{F}}_2}, \cdots ,{\rm{IM}}{{\rm{F}}_p}]$$ (4) 式中,IMFi为第i模态分量,即第i个主成份的数据。由于在实际检测中,数据${\mathit{\boldsymbol{X}}}$都是几乎差不多的同种类型的信号,便使得第一模态分量中的贡献值高达99%。因此,IMFi用来代替检测到的数组集合${\mathit{\boldsymbol{X}}}$是完全可行的。
在本文方法中,首先确定有不同种类的数据来源集合,如振动信号、磁光信号、热辐射信号和转速信号等,并且将它们组合成一个数组信号,如Sensors=[V1, V2, V3, …, Vn],其中Vi表示第i种传感器所得到的特征信号。为保证信号处理的一致性,首先对Vi信号的采样数据位数要统一;其次,由于PCA方法对单位的敏感性,需要对数据进行归一化处理。通过以上方法处理后,可以实现多数据特征的融合,进一步通过DS方法判定,从而达到综合判定的效果。
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根据定义1,给定一个识别框架Θ,或称为假设空间。在识别框架Θ上的基本概率分配(BPA)是一个2Θ → [0, 1] mass函数,简称为m,且满足如下关系:
$$\left\{ \begin{gathered} m(\Phi ) = 0 \\ \sum\limits_{A \subseteq \Theta } {m(A) = 1} \\ \end{gathered} \right.$$ (5) 式中,焦元(focal elements)是使得m(A) > 0的A。在识别框架Θ上,基于BPA及定义2,对于识别框架Θ中的某一个假设A,按照基本的概率分配BPA分别计算得出关于该假设的信任函数Bel(A)及似然函数pl(A),组成信任区间[Bel (A), pl (A)],以表示对某个假设的确认程度。由此,对于$\forall $A$ \subseteq $Θ,识别框架Θ上的有限个mass函数m1, m2, …, mn的Dempster合成规则为:
$$\begin{gathered} ({m_1} \oplus {m_2} \oplus \cdots \oplus {m_n})(A) = \\ \frac{1}{K}\sum\limits_{{A_1} \cap {A_2} \cap \cdots \cap {A_n} = A} {{m_1}} ({A_1}) \cdot {m_2}({A_2}) \cdots {m_n}({A_n}) \\ \end{gathered} $$ (6) 式中,
$$\begin{gathered} K = \sum\limits_{{A_1} \cap {A_2} \cap \cdots \cap {A_n} \ne \Phi } {{m_1}} ({A_1}) \cdot {m_2}({A_2}) \cdots {m_n}({A_n}) = \\ 1 - \sum\limits_{{A_1} \cap {A_2} \cap \cdots \cap {A_n} = \Phi } {{m_1}} ({A_1}) \cdot {m_2}({A_2}) \cdots {m_n}({A_n}) \\ \end{gathered} $$ (7) 通过以上数据处理技术和方案,对多数据进行融合优化处理,可以更加准确地判断设备故障和健康状态。PCA数据融合方案如图 4所示,主要步骤如下:
1) 不同种类数据采集及特征提取;
2) 对不同传感器获得不同种类的特征数据进行等采样率采集处理,使数据点数相同;
3) 对不同种类的数据进行归一化处理,使PCA对其更有普遍意义;
4) PCA处理,得到主成份向量及降维后的数据特征;
5) 数据对象两两进行DS判据处理,得到信息故障和健康检测,同时该数据会迭代校准数据。
Multi-Information PCA Fusion Scheme of Electronic Warfare Based on DS
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摘要: 该文提出一种新型主成份分析(PCA)电子战信息一体化融合方案。该方案基于信息融合DS理论,采用PCA分析法对数据进行收集和降维处理;再对特征层数据建立基本信任分配函数,实现基于特征的数据融合;最后对电子战系统信息进行智能诊断和挖掘等,有效实现电子战系统中故障检测和分离。进一步,通过大数据挖掘对设备状态进行评估,及时发送给控制系统,实现作战过程中对作战战略的合理指导、预警管控,从而对多系统协同工作提供有力保障。Abstract: In this paper, a new type of principal component analysis (PCA) for electronic warfare information integration fusion scheme is presented. Based on DS theory of information fusion, the PCA method is used to collect data and reduce dimensions, and the basic trust distribution function is established for feature layer data to realize further based data fusion. The electronic warfare system information is intelligently diagnosed and mined to effectively achieve the fault detection and separation of electronic warfare system. Furthermore, the device status is evaluated and timely sent the control system through the big data mining, thus implementing the reasonable guidance and early warning and control for operational strategy in warfare procedure.
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[1] AN Hong, DENG Yang-jian, LYU Lian-yuan. Research on sliding mode control for anti-lock braking system based state observability and wheel optimal slip estimation[J]. Computer Simulation, 2002, 19(1):66-68. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=jsjfz200201021 [2] LIN Zhi-yuan, LIU Gang. The integration of radar-electronic warfare-communication[J]. Aerospace Shanghai, 2004, 21(6):55-58. http://cn.bing.com/academic/profile?id=1fb870a3a8ab10e14330ccec13e8c4ca&encoded=0&v=paper_preview&mkt=zh-cn [3] WANG Xue-song, XIAO Shun-ping, FENG De-jun. Modeling and simulation of modern radar and electronic warfare systems[M].[S.l.]: Publishing House of Electronics Industry, 2010. [4] DING Wen-rui, HUANG Wen-qian. The survey of the development of anti-jamming technology for UAV data link[J]. Application of Electronic Technique, 2016, 42(10):6-10. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=dzjsyy201610005 [5] GAO Xiao-bin, HAO Chong-yang. Fuzzy evaluation method of the electronic warfare system effectiveness[J]. Fire Control & Command Control, 2005, 30(1):69-72. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=hlyzhkz200501021 [6] KEMKEMIAN S, NOUVEL-FIANI M, CHAMOUARD E. Radar and electronic warfare cooperation:how to improve the system efficiency[J]. IEEE Aerospace & Electronic Systems Magazine, 2011, 26(8):32-38. http://cn.bing.com/academic/profile?id=d6776d4e475252b6b624cf3a4f9c8a77&encoded=0&v=paper_preview&mkt=zh-cn [7] JIANG Yan, LIU Yi, QI Yuan-xiang. Key techniques of integrated electronic warfare system[J]. Electronic Test, 2017(9):85-86. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=dzcs201709039 [8] LIANG Cai-yun, XIE Ye-ping, LI Yong-fan, et al. Application of integrated aircraft/engine technology in aeroengine designing[J]. Aeroengine, 2015, 41(3):1-5. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=hkfdj201503001 [9] PAN Yang, LI Qiu-hong, GU Shu-wen, et al. Aeroengine thrust command model based on optimized intelligent networks[J]. Aeroengine, 2016, 42(2):51-56. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=hkfdj201602010 [10] ZHANG Liao-ning, QU Yang, ZHANG Zheng, et al. Ability to implement the mandate assessment of armored equipment weapons system based on technical detection[J]. Ordnance Industry Automation, 2016, 35(7):74-76. [11] WANG Dong. The research of data fusion perception rule mining in uavs cooperative network[D]. Chengdu: University of Electronic Science and Technology of China, 2015. [12] WANG Run-sheng. Information fusion[M].[S.l.]: Science Press, 2007. [13] JIANG Wen, ZHANG An, DENG Yong. A novel information fusion method based on our evidence conflict representation[J]. Journal of Northwestern Polytechnical University, 2010, 28(1):27-32. http://en.cnki.com.cn/CJFD_en_New/Detail.ashx?t=e&url=/Article_en/CJFDTOTAL-XBGD201001007.htm [14] JIAN Xiao-gang, JIA Hong-sheng, SHI Lai-de. Advances on multi-sensor information fusion technologies[J]. Chinese Journal of Construction Machinery, 2009, 7(2):227-232. http://cn.bing.com/academic/profile?id=4e90a4710b25ed86a2adab35b146c8a5&encoded=0&v=paper_preview&mkt=zh-cn [15] CHENG Xue-qi, JIN Xiao-long, Wang Yuan-zhuo, et al. Survey on big data system and analytic technology[J]. Journal of Software, 2014(9):1889-1908. http://cn.bing.com/academic/profile?id=1255197477698622c23cae4f51ca2138&encoded=0&v=paper_preview&mkt=zh-cn [16] VIE L L, SCHEIER L M, LESTER P B, et al. The U.S. amy person-event data environment:a military-civilian big data enterprise[J]. Big Data, 2015, 3(2):67-79. doi: 10.1089/big.2014.0055 [17] KULSHRESTHA S. Big data in military information & intelligence[J]. Social Science Electronic Publishing, 2016(2):107-108. http://d.old.wanfangdata.com.cn/Periodical/zhyxtsgzz201804004 [18] WANG Sheng-li, Analysis on development of C4ISAR systems in the era of big data[J]. Modern Radar, 2013, 35(5):1-5. [19] WU Rong-chun. Key technology research of information fusion in military information system[D]. Chengdu: University of Electronic Science and Technology of China, 2016. [20] MANDLER E, SCHUERMANN J. Combining the classification results of independent classifiers based on the Dempster/Shafer theory of evidence[J]. Machine Intelligence & Pattern Recognition 1988, 7:381-393. http://cn.bing.com/academic/profile?id=1144edbe245fad50d0d2cc522359a1e4&encoded=0&v=paper_preview&mkt=zh-cn [21] SENTZ K, FERSON S. Combination of evidence in Dempster-Shafer Theory[J]. Contemporary Pacific, 2002, 11(2):416-426. http://d.old.wanfangdata.com.cn/Periodical/glgcxb201803014 [22] LELANDAIS B, GARDIN I, MOUCHARD L, et al. Dealing with uncertainty and imprecision in image segmentation using belief function theory[J]. International Journal of Approximate Reasoning, 2014, 55(1):376-387. doi: 10.1016/j.ijar.2013.10.006 [23] HONG Zhao-yi, GAO Xun-zhang, LI Xiang. Research on temporal-spatial information fusion model based on DS theory[J]. Signal Processing, 2011, 27(1):14-19. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=xhcl201101003 [24] SHU Jian, LIANG Chang-yong. Dynamic trust model based on DS evidence theory under cloud computing environment[J]. Computer Science, 2016, 43(8):105-109. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=jsjkx201608022 [25] LI Ling-bo, YANG Zhao-min, FENG Ya-jun, et al. Target handoff of tracking-and-guiding radar to KEI using DS method[J]. Journal of Air Force Early Warning Academy, 2013(6):427-429. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=kjldxyxb201306010 [26] DU Yang, DONG Bin-hong, ZHAO Yan, et al. Performance analysis of message-driven direct sequence/frequency hopping spread spectrum communication system[J]. Journal of Signal Processing, 2015, 31(5):514-520. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=xhcl201505002 [27] CHENG Si-yi, SUO Zhong-ying, ZHNAG Jin. The method of rule fusion based on evidence theory and its application[J]. Journal of Air Force Engineering University (Natural Science Edition), 2010, 11(4):47-51. http://cn.bing.com/academic/profile?id=9a1d4437011d02f550b535218b2a7696&encoded=0&v=paper_preview&mkt=zh-cn [28] ZHOU Hao, LI Shao-hong. Combination of support vector machine and evidence theory in information fusion[J]. Chinese Journal of Sensors and Actuators, 2008, 21(9):1566-1570. http://cn.bing.com/academic/profile?id=fdb98c63d061845cb254a2242889272d&encoded=0&v=paper_preview&mkt=zh-cn [29] LIN Guo-ping. Connections between covering generization rough set and Dempster-Shafer theory of evidence[J]. Journal of Zhangzhou Normal University (Natural Science), 2010, 23(2):1-4. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=zzsfxyxb201002001 [30] LU Xue-yan, Zhao Zheng. Fault diagnosis of mill based on fuzzy clustering analysis and D-S evidence theory[J]. Electric Power Science and Engineering, 2011, 27(7):41-44. [31] XIAO Ting-ting, ZHANG Bing. Multi-sensor target recognition technology based on neural network and D-S evidence theory[J]. Shipboard Electronic Countermeasure, 2010, 33(2):90-93. http://cn.bing.com/academic/profile?id=360ba82d16ebdd49c3bd09cef5fc97f8&encoded=0&v=paper_preview&mkt=zh-cn