证据理论中信任函数的合成方法研究与应用

发布时间：2018-01-12 22:17

本文关键词：证据理论中信任函数的合成方法研究与应用　出处：《中国科学技术大学》2016年博士论文　论文类型：学位论文

【摘要】：在实际问题中,无论是传感器测量信息还是专家经验知识,一般都存在定程度的不确定性或不完备性。研究不确定信息的建模和推理决策问题具有重要意义。证据理论是一种常用的不确定推理方法,其中表征信息的信任函数是定义在识别框架幂集上的一个置信分布,能够区分无知与等可能性,比概率分布的表示更加灵活准确：并且证据推理的过程与人类专家的思维方式比较相似。因此,证据理论已成为一种重要的信息融合方法,在多个领域中得以应用。鉴于证据理论处理不确定知识的能力,许多研究将其与其它理论方法相结合,置信规则库推理方法就是其中之一。经典证据理论中通过Dempster规则合成多条证据,实现推理决策过程。然而使用Dempster规则需要满足一定的前提条件,如证据独立性、证据可靠性等,这些条件在实际问题中不一定能够满足；而且Dempster规则合成冲突证据时可能出现合成悖论问题。为避免合成悖论,并更好的符合实际应用条件,本文对信任函数的合成方法进行研究,主要从冲突证据的分析与合成、证据重要性与可靠性的处理、相关证据的合成等方面展开。此外,针对置信规则库推理方法存在模型训练缓慢、规则约简方法复杂等问题,提出一种新的模型结构以解决这些问题。首先,研究了合成悖论问题,并提出一种新的冲突衡量方法和证据折扣方法。利用规范分解对典型合成悖论进行了分析,总结出了它们的共同特点,并证明证据折扣可以避免这一问题。因此,提出一种模糊折扣方法。该方法考虑了证据之间的冲突和自身不确定性两方面因素,不仅能够取得较快的信度收敛速度,并且对异常证据也具有较好的鲁棒性。为衡量证据冲突和不确定性,分别定义了基于奇异值的冲突衡量方法和基于pignistic概率的区分度。其次,研究了证据推理(ER)规则的相关性质及其存在的问题,并用其对隔振系统的故障诊断问题进行研究。分析了ER规则与证据折扣方法之间的关系、权重归一化对其合成结果的影响,以及它在重要性与可靠性表示上存在的缺陷,并提出一种改进的方法。针对隔振系统的故障诊断问题,给出了证据重要性与可靠性的评估方法,提取了合适的特征参数并用以生成证据,利用改进的ER规则对多传感器信息进行融合,实现故障的诊断发现。在多种故障情况下对所提方法进行了验证。然后，研究了相关源证据已知和未知两种情况下的相关证据合成问题。在相关源证据未知的情况下,借助证据推理规则处理相对重要性的能力,将其与谨慎合成规则相结合,得到加权谨慎合成规则：此外，基于最小承诺准则和证据似然排序、众信度排序,分别提出一种相关证据合成方法,设计优化方法求解符合条件的信仟函数。在相关源证据已知情况下,利用合成规则的众信度函数表达形式,得到一种直接计算合成结果的方法,该方法对相关源证据的形式没有要求。最后,研究了基于加权平均推理的置信规则库方法。对已有文献中一些置信规则库的计算表明,被激活规则的置信分布一般存在较大冲突,而加权平均比较适合这种情况。因此在推理环节使用加权平均代替ER算法,对相应置信规则库的基本结构进行了推导,并证明其仍然具有全局逼近能力。为避免过拟合和降低模型复杂度,利用新置信规则库的特殊结构,提出一种简单有效的前提属性参考值约简方法。针对动态系统的时变特性,在正态输出假设条件下,对新置信规则库的参数在线更新方法进行了推导。通过数值仿真对新置信规则库及其属性约简方法和参数更新方法进行了验证。
[Abstract]:In fact, whether sensor information or expertise, generally have the degree of uncertainty or imperfection. Study the uncertainty modeling and reasoning decision-making problems is of great significance. Evidence theory is an uncertainty reasoning method commonly used, the trust function is to define a representation of information in the identification of frame power set confidence distribution, to distinguish between ignorance and possibility, than the probability distribution is more flexible and accurate representation: process and human expert evidence reasoning mode of thinking is similar. Therefore, evidence theory has become an important method of information fusion has been applied in many fields. In view of the evidence theory to deal with the uncertain knowledge, many of its combination with other theories, rimer is one of them. In the classical theory of evidence Dempster rule of combination of multiple evidence reasoning, implementation of the decision-making process. However, the use of Dempster rules to meet certain preconditions, such as evidence of independence, evidence of reliability, these conditions in practical problems can not meet the Dempster rules; and conflicting evidence combination possible synthesis paradox. In order to avoid the synthesis of paradox, and better in line with the actual application conditions, this paper studies the synthesis method of trust function, mainly from the analysis and synthesis of conflicting evidence, evidence the importance and reliability of the evidence combination and other aspects. In addition, the rimer model training is slow, the rules of the complex reduction method, put forward a new models to solve these problems. First, studied the synthesis of paradox, and proposed a new conflict measure and evidence discount The typical synthesis method. Analyzed the canonical paradox, summarizes their common features, and evidence of discount can avoid this problem. Therefore, this paper proposes a fuzzy discount method. This method considers the conflict between the evidence and the uncertainty of the two factors, not only can achieve fast convergence reliability, and also has good robustness to abnormal evidence. As a measure of evidence conflict and uncertainty, defines the measure method based on singular value conflict and discrimination based on the probability of pignistic. Secondly, the study of evidence reasoning (ER) properties of rules and problems, and use it to study the fault diagnosis of vibration isolation system. Analysis of the relationship between the ER rules and evidence discount method, influence of weighting normalization on the synthesis results, and it said in importance and reliability. The existence of defects, and put forward an improved method to solve the problem of fault diagnosis of vibration isolation system, gives the assessment of the importance of evidence and the reliability of the method, feature parameters are extracted and used to generate the appropriate evidence of multi-sensor information fusion based on improved ER rules, realize fault diagnosis found in a variety of fault. The case to verify the proposed method. Then, study the synthesis problems related to evidence of evidence known and unknown in two cases. In the case of unknown source of relevant evidence, the evidence reasoning rules relative importance of ability, combined with the cautious synthesis rules, weighted cautious synthesis in addition, the minimum commitment rules: guidelines and evidence likelihood based sorting, the reliability sorting, put forward a relevant evidence synthesis method respectively, trust function design optimization method in line with the conditions. Relevant evidence is known, the use of the public expression of reliability function synthesis rules, a method of direct calculation result, this method does not require the form of relevant evidence. Finally, study the belief rule base inference based on the weighted average method. The have showed some belief rule base calculation in the literature that is activated confidence distribution rules are generally larger conflict, and the weighted average for this situation. So using the weighted average instead of the ER algorithm in reasoning link, the basic structure of the corresponding belief rule base was deduced, and prove that it still has global approximation ability. In order to avoid overfitting and reduce the complexity of the model, using the the special structure of the new belief rule base, puts forward a simple and effective reference attribute value reduction method. According to the dynamic time-varying characteristic of the systems in the normal output hypothesis Then, the online updating method of the new belief rule base is derived. The new belief rule base and its attribute reduction method and parameter update method are verified by numerical simulation.

【学位授予单位】：中国科学技术大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TP202

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