Basic belief assignment approximations using degree of non-redundancy for focal element

Dempster-Shafer evidence theory, also called the theory of belief function, is widely used for uncertainty modeling and reasoning. However, when the size and number of focal elements are large, the evidence combination will bring a high computational complexity. To address this issue, various methods have been proposed including the implementation of more efficient combination rules and the simplifications or approximations of Basic Belief Assignments (BBAs). In this paper, a novel principle for approximating a BBA into a simpler one is proposed, which is based on the degree of non-redundancy for focal elements. More non-redundant focal elements are kept in the approximation while more redundant focal elements in the original BBA are removed first. Three types of degree of non-redundancy are defined based on three different definitions of focal element distance, respectively. Two different implementations of this principle for BBA approximations are proposed including a batch and an iterative type. Examples, experiments, comparisons and related analyses are provided to validate proposed approximation approaches.     

Novel moderate transformation of fuzzy membership function into basic belief assignment

In information fusion, the uncertain information from different sources might be modeled with different theoretical frameworks. When one needs to fuse the uncertain information represented by different uncertainty theories, constructing the transformation between different frameworks is crucial. Various transformations of a Fuzzy Membership Function (FMF) into a Basic Belief Assignment (BBA) have been proposed, where the transformations based on uncertainty maximization and minimization can determine the BBA without preselecting the focal elements. However, these two transformations that based on uncertainty optimization emphasize the extreme cases of uncertainty. To avoid extreme attitudinal bias, a trade-off or moderate BBA with the uncertainty degree between the minimal and maximal ones is more preferred. In this paper, two moderate transformations of an FMF into a trade-off BBA are proposed. One is the weighted average based transformation and the other is the optimization-based transformation with weighting mechanism, where the weighting factor can be user-specified or determined with some prior information. The rationality and effectiveness of our transformations are verified through numerical examples and classification examples.     

A novel approximation of basic probability assignment based on rank-level fusion

Belief functions theory is an important tool in the field of information fusion. However, when the cardinality of the frame of discernment becomes large, the high computational cost of evidence combination will become the bottleneck of belief functions theory in real applications. The basic probability assignment (BPA) approximations, which can reduce the complexity of the BPAs, are always used to reduce the computational cost of evidence combination. In this paper, both the cardinalities and the mass assignment values of focal elements are used as the criteria of reduction. The two criteria are jointly used by using rank-level fusion. Some experiments and related analyses are provided to illustrate and justify the proposed new BPA approximation approach.     

Epistemic uncertainty quantification in flutter analysis using evidence theory

Aimed at evaluating the structural stability and flutter risk of the system, this paper manages to quantify epistemic uncertainty in flutter analysis using evidence theory, including both parametric uncertainty and method selection uncertainty, on the basis of information from limited experimental data of uncertain parameters. Two uncertain variables of the actuator coupling system with unknown probability distributions, that is bending and torsional stiffness, which are both described with multiple intervals and the basic belief assignment(BBA) extricated from the modal test of actuator coupling systems, are taken into account. Considering the difference in dealing with experimental data by different persons and the reliability of various information sources, a new combination rule of evidence––the generalized lower triangular matrices method is formed to acquire the combined BBA. Finally the parametric uncertainty and the epistemic uncertainty of flutter analysis method selection are considered in the same system to realize quantification. A typical rudder of missile is selected to examine the present method, and the dangerous range of velocity as well as relevant belief and plausibility functions is obtained. The results suggest that the present method is effective in obtaining the lower and upper bounds of flutter probability and assessing flutter risk of structures with limited experimental data of uncertain parameters and the belief of different methods.     

An information-volume-based distance measure for decision-making

D-S evidence theory, as a general framework for reasoning with uncertainty, allows combining pieces of evidence from different information sources to derive a degree of belief function that is a type of fuzzy measure. However, the mass assignments given by unknown information sources are disordered. How to measure the difference between the mass assignments has aroused people’s interest. In this paper, inspired by the information volume, a novel distance-based measure is proposed to measure the difference between mass assignments. The method can refine the uncertain information given by experts and compare the refined information to obtain the difference between mass assignments. At the same time, it is verified that the measure not only meets the properties of distance, but also proves the superiority of the proposed Information Volume Distance (IVD) through simulation experiments. Meanwhile, in the process of information fusion, the reliability of each source could be quantified through IVD. Therefore, based on IVD, a new multi-source information algorithm is proposed to solve the problem of multi-source information fusion. Moreover, algorithm is applied to decision-making problem and compare with other methods to verify the effectiveness.     

基于证据理论的航空发动机早期故障诊断方法

在分析航空发动机早期故障特点和数据融合的基础上,将证据理论应用于发动机故障征兆级别的数据融合中,提出了构造基本信任指派函数的方法,从而得到了更准确的早期故障征兆.在此基础上,应用模糊聚类分析方法,依据最大隶属度原则得到发动机早期故障源.该方法考虑了发动机早期故障征兆不明确、不精确、不肯定等特点,应用模糊测度来表示征兆,更符合发动机早期故障的实际情况.      

多传感器协同探测证据理论分类融合方法

随着智能化、网络化集群作战等理念和技术的兴起,精确制导武器越来越向智能化、协同化方向发展。多传感器协同探测能够针对不同的探测任务背景和作战需求,提升目标探测性能,还可以跨域整合多种探测平台。但是由于信息的不确定性等特点,使得多传感器数据直接融合可能造成决策困难。因此,在证据理论体系下对信息融合的有效性进行合理分析与度量是很有必要的。提出了一种基于Deng熵的证据理论分类融合算法,以熵减为主要思想,将证据进行分类融合。在决策过程中,将含有证据数最多的类别融合结果作为总体融合结果,避免高冲突证据的影响,提升融合结果的信息有效性。采用算例说明了所提方法不仅能够得到合理正确的结果,并且融合可靠性较高,便于决策与后续的信息处理。     

信息融合图像识别算法及其在三维飞机图像识别中的应用研究

将D S证据推理与不变矩理论相结合,提出了信息融合图像识别算法,并应用于三维飞机图像的识别。构造了基本置信指派函数,建立了分类规则,针对Dempster组合规则只适用于高置信度、低冲突性的情况,应用可解决证据冲突的加权分配冲突法及吸收法,完成了三维飞机图像识别的仿真,比较了3种组合规则的识别效果,结果表明吸收法识别率最高。     

基于DSmT的航空发动机早期振动故障融合诊断方法

提出在航空发动机多个部位安装多个振动传感器组成传感器网络.采用多传感器信息融合技术进行早期振动故障的诊断方法,并引入Dezert-Smarandache理论(DSmT)来处理由早期微弱故障本身所导致的各个传感器信息相互冲突的问题.在构建的早期微弱故障诊断系统框架中,采用基于本征模态函数(IMF)的信息熵特征提取方法提取各路振动数据的特征,采用反向传播(BP)神经网络完成对故障属性的判断并生成各种故障模式的基本置信分配,最后根据DSmT融合规则得到最终的诊断结果.算例表明采用该方法可以有效地解决早期微弱故障条件下的高冲突信息融合问题,故障诊断结果准确可靠.      

机载探测设备目标识别算法的研究

针对机载探测设备多传感器系统具有多目标,大量观测数据的特点,提出了一种基于Demp-ster-Shafer（D-S）证据理论和主观Bayesian方法组合的数据融合算法。在数据融合过程中,为保证融合的实时性,融合系统采用时域融合和空域融合相结合的方法,首先对相同传感器的各次抽样值进行时域融合,然后传感器之间的融合采用D-S方法进行融合;最后,其融合结果经概率转化后,与来自于ELINT（Electronic Intelligence）的信息通过主观Bayesian方法进行识别级融合。最后给出一个实例,经过仿真计算证明了该算法的可行性和实用性。     

Combination of classifiers with incomplete frames of discernment

The methods for combining multiple classifiers based on belief functions require to work with a common and complete(closed) Frame of Discernment(Fo D) on which the belief functions are defined before making their combination. This theoretical requirement is however difficult to satisfy in practice because some abnormal(or unknown) objects that do not belong to any predefined class of the Fo D can appear in real classification applications. The classifiers learnt using different attributes inform...     

基于D-S证据理论的目标属性辨识研究

D—S证据组合理论已经成为不确定性推理的一种重要方法，基于该理论的多传感器决策层信息融合已得到广泛应用。本文在简要介绍D—S证据组合理论框架基础上，阐述了基于D—S证据组合理论的信息融合一般步骤及决策层判决方法；分析了发生证据严重冲突时，Dempster证据组合规则出现的不可靠和不合理的本质原因，介绍了针对D—S证据组合规则进行修正的几种主要方法；最后，提出了需要继续深入探讨的问题。     

证据冲突下自适应融合目标识别算法

 利用证据理论对空中目标识别系统的观测信息融合时,Dempster规则对低冲突信息的融合结果较为理想,但无法对高冲突信息有效融合。Dubois &; Prade(DP)规则及证据折扣法可对高冲突信息进行合理融合。为使不同融合方法发挥各自优势,提出一种自适应融合算法。首先将矛盾因子和证据距离两者结合以更全面地表示证据冲突程度,当冲突较小时,选用Dempster规则,反之,根据冲突的具体情况选择使用DP规则或证据折扣法。通过目标识别实验对多种算法进行了对比,表明本文算法既能对高冲突证据进行合理融合,又能使融合结果快速收敛,可以有效地提高识别速度及正确率。     

基于序列图像的自动目标识别算法

由于利用单幅二维图像进行三维目标识别存在识别的多义性,提出了一种基于二维序列图像的三维目标自动识别算法。首先以修正的Hu不变矩构造目标的图像识别特征,进而采用BP神经网络分类器构造关于目标融合识别的基本置信指派函数,以神经网络的训练误差构造证据理论不确定性度量,采用基于吸收法的DS证据理论实现高冲突证据的贯序式融合。对各姿态飞机图像识别的仿真表明,该算法对飞机的空间姿态变化具有很强的鲁棒性,能快速地准确识别飞机类型。此外,算法对先验性参数具有一定的鲁棒性。     

An improved α-cut approach to transforming fuzzy membership function into basic belief assignment

In practical applications, pieces of evidence originated from different sources might be modeled by different uncertainty theories. To implement the evidence combination under the Dempster–Shafer evidence theory(DST) framework, transformations from the other type of uncertainty representation into the basic belief assignment are needed. a-Cut is an important approach to transforming a fuzzy membership function into a basic belief assignment, which provides a bridge between the fuzzy set theory and the DST. Some drawbacks of the traditional a-cut approach caused by its normalization step are pointed out in this paper. An improved a-cut approach is proposed, which can counteract the drawbacks of the traditional a-cut approach and has good properties. Illustrative examples, experiments and related analyses are provided to show the rationality of the improved a-cut approach.     

全源定位与导航的统一理论框架构建

针对多导航传感器的信息融合复杂性的问题,提出了一种基于全源定位与导航的信息融合统一理论框架。该框架将目前导航领域的主要定位导航技术分成了与时间无关的定位导航技术方法以及与时间相关的定位导航技术。首先,主要从数学的角度将各种导航技术的测量模型抽象为统一的表达形式,提出了位置、姿态、速度函数的概念,讨论了各种测量方法的测量函数及其应用;其次,分析了航位、航姿、航速的推算方法;最后根据测量模型和运动模型构建了信息融合的基本方程,并讨论了基于贝叶斯估计的导航参数一般性估计方法。     

Sequence comparison techniques for multisensor data fusion andtarget recognition

A new class of techniques for multisensor fusion and target recognition is proposed using sequence comparison by dynamic programming and multiple model estimation. The objective is to fuse information on the kinematic state and “nonkinematic” signature of unclassified targets, assessing the joint likelihood of all observed events for recognition. Relationships are shown to previous efforts in pattern recognition and state estimation. This research applies “classical” speech processing-related and other sequence comparison methods to moving target recognition, extends the efforts of previous researchers through improved fusion with kinematic information, relates the proposed techniques to Bayesian theory, and applies parameter identification methods to target recognition for improved understanding of the subject in general. The proposed techniques are evaluated and compared with existing approaches using the method of generalized ambiguity functions, which lends to a form of Cramer-Rao lower bound for target recognition     

信息融合在空战中的应用

主要讨论航空电子系统中的信息融合及在空战中的应用,介绍了信息融合的结构和一般方法,在综合应用场合,信息融合通常先进行同类信息融合,再进行不同类信息融合,在现代空战的应用中,信息融合可帮助分析,处理和综合各类信息源信息及人类专家知识,并结合空战中信息融合应用实例,讨论基于Ｋａｌｍａｎ滤波,模糊逻辑和专家诉信息融合的设计及实现。     

An ECR-PCR rule for fusion of evidences defined on a non-exclusive framework of discernment

In the research of uncertain information processing, Dempster-Shafer Theory (DST) provides a framework for dealing with uncertain information, where evidence is defined on a Frame of Discernment (FOD) consisting of mutually exclusive elements. However, the requirement of exclusiveness on FOD sometimes is not satisfied, as shown in Dezert-Smarandache Theory(DSmT), a derivative of DST. In DSmT, the non-exclusiveness is expressed by propositions’ intersection and the fusion of evidence is realized through a Proportional Conflict Redistribution (PCR) rule. In order to handle non-exclusive FODs, a new framework called D Number Theory (DNT) has been proposed recently, which quantifies the non-exclusive degree between propositions different from DSmT. In previous studies, an Exclusive Conflict Redistribution (ECR) rule has been designed in DNT to implement the fusion of evidence defined on a non-exclusive FOD, but there are some deficiencies in the ECR rule. In this paper, a new rule called ECR-PCR rule is proposed by combining the ECR and PCR rules to better implement the fusion of evidence defined on a non-exclusive FOD. Within the proposed rule, the definition of conflict utilizes the idea of ECR’s exclusive conflict, and the disposal of conflict is following the idea of PCR’s proportional redistribution. Properties of the ECR-PCR rule are presented. The effectiveness of the proposed new rule is verified through numerical examples and applications, in comparison with other fusion methods.     

An Application of Evidential Networks to Threat Assessment

Decision makers operating in modern defence theatres need to comprehend and reason with huge quantities of potentially uncertain and imprecise data in a timely fashion. An automatic information fusion system is developed which aims at supporting a commander's decision making by providing a threat assessment, that is an estimate of the extent to which an enemy platform poses a threat based on evidence about its intent and capability. Threat is modelled by a network of entities and relationships between them, while the uncertainties in the relationships are represented by belief functions as defined in the theory of evidence. To support the implementation of the threat assessment functionality, an efficient valuation-based reasoning scheme, referred to as an evidential network, is developed. To reduce computational overheads, the scheme performs local computations in the network by applying an inward propagation algorithm to the underlying binary join tree. This allows the dynamic nature of the external evidence, which drives the evidential network, to be taken into account by recomputing only the affected paths in the binary join tree.