不确定性信息处理的随机集方法及在系统可靠性评估与故障诊断中的应用
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摘要
由于环境的复杂性、传感器或观测者本身的局限性、信息获取技术或方法的不完善性等因素的影响,使得描述系统可靠性和系统故障的信息通常表现出随机、非精确、未知、不完全等多种不确定性。研究者常常根据不同的情况和需要,在一定的假设或条件下采用相应的不确定性理论和方法,有针对性地分析某种类型的不确定性信息,所以各种理论处理信息的类型较为单一。并且,信息采集手段及途径的多样化,将进一步导致信息类型更多形式更复杂。面对这种情况,已有理论及其方法都逐步显示出自身的局限性。现有研究表明,随机集理论是一种能够有效地统一诸如概率论、模糊集理论、Dempster-Shafer证据理论、可能性理论和粗糙集理论等多种不确定性理论的有效的数学工具,已有的大多数类型的不确定性信息都能用随机集理论加以描述与分析。本文旨在利用随机集理论研究不确定性信息统一表示与建模等理论问题,基于此再以特定的电路系统、机电设备等为应用研究对象,将随机集理论和其他多种不确定性理论相结合生成新方法,解决对象系统可靠性评估与故障诊断中的不确定性信息处理问题,以期克服已有方法在处理相应问题时的不足。
全文的主要工作包含以下几个方面:
1)首先基于对不确定性信息的分类,评述了系统可靠性评估与故障诊断中常用的不确定性信息处理方法,并分析了这些方法在应用中存在的不足。然后引入随机集理论基础,综合论述了该理论与几种常用的不确定性理论之间的相互关系,从而论证了用随机集理论统一表示和建模多类不确定性信息的可行性。
以该项研究内容为基础,又逐步展开了以下工作:
2)基于随机变量的随机集表示形式及随机集扩展准则等随机集特性,结合所建立的电路系统性能可靠性评估的概率模型,给出了一种简便灵活的方法判断电路性能的可靠性;并用实例说明该方法在计算量远远小于蒙特卡罗方法的情况下,可以得到与其相当的可靠性评估效果。
3)基于Dempster证据组合规则的随机集表示以及广义集值映射和随机集联合条件概率,给出了DS证据理论中包含Dempster组合规则在内的多种经典组合规则的随机集统一表示模型。并且,文中利用这个模型构造了一种新的组合规则,它能很好的避免Dempster规则应用中存在的一类不合理现象,并以设备故障诊断中冲突证据的融合决策为例,说明了新规则的有效性。
4)基于模糊集的随机集表示和随机集似然测度,给出了一种从模糊故障特征信息(故障样板模式与待检模式)中获取诊断证据的新方法。然后结合证据理论,利用Dempster证据组合规则融合多组证据得出诊断结果。该方法可以克服基于单一特征的传统诊断方法和基于单个观测数据的待检模式匹配融合诊断方法的不足,显著提高对故障的识别能力。最后通过在多功能电机柔性转子试验台上的诊断实验,验证了新方法的有效性。
Because of the complexity of environments, limitation of sensor performance and imperfection of information acquisition technique, multisoures information reflecting system reliability and faults is usually uncertain (such as random, imprecise, vague and incomplete). These uncertain information is described and modeled by the corresponding knew theories under certain assumptions. Moreover, the more diverse the ways and means of information acquisition are, the more complex and various the types of information are. In this case, the limitations of knew theories become more and more unnegligible. For several years, researchers have explored the unification of theories dealing with different uncertainties of information and have finally considered random set theory, because it can unifies several uncertain theories such as probability theory, fuzzy set theory, Dempster-Shafer evidence theory, possibility Theory, rough set Theory. This doctoral dissertation is devoted to study on the random set methods of unified describing and modeling different-types uncertain information. Based on which, for specific objects in application such as circuit system, electromechanical equipments, some new methods are generated using random set theory and knew theories comprehensively. They can be used in reliability evaluation and fault diagnosis of specific system objects and are better than knew methods.
The main works in the thesis are introduced as follows:
1. Firstly, the available information is classified according to different uncertain types. The methods of uncertain information processing are reviewed in reliability evaluation and fault diagnosis. Their shortcomings are analyzed. We introduce the random set theory as a possible framework for unification and detail how the individual theories can fit in this framework.
Based on this research, other works are developed as follow
2. Based on the random set description of random variables and the extension principles of random set, a simple and flexible method is given for evaluating reliability of circuit performance by virtue of the proposed probability model of circuit system performance evaluation. This method is alternative to Monte-Carlo analysis, but reduces the number of calculations required drastically.
3. On the basis of random set representation of Dempster combination rule, the proposed extended set-valued mapping and joint conditional probability of random sets, a unified random set model of classical combination rules is presented. By use of this model, a new combination rule is constructed for overcoming a class of counterintuitive phenomena. The example of fault diagnosis using conflict evidence is given to show the effectiveness of new rule.
4. Based on the random set description of fuzzy set and the likelihood function of random set, new method is proposed to obtain fuzzy evidence from fuzzy fault features, and then, Dempster combination rule are used to fusion several pieces of fuzzy evidence to get diagnosis results. The proposed method of fuzzy evidence extraction can reduces uncertainties in fusion-makings and improves fault identifications. It is better than the traditional single-feature fault diagnosis and fusion diagnosis method based on single observation data matching. Finally, the diagnosis results of machine rotor show that the proposed method can enhance diagnostic accuracy and reliability.
全文的主要工作包含以下几个方面:
1)首先基于对不确定性信息的分类,评述了系统可靠性评估与故障诊断中常用的不确定性信息处理方法,并分析了这些方法在应用中存在的不足。然后引入随机集理论基础,综合论述了该理论与几种常用的不确定性理论之间的相互关系,从而论证了用随机集理论统一表示和建模多类不确定性信息的可行性。
以该项研究内容为基础,又逐步展开了以下工作:
2)基于随机变量的随机集表示形式及随机集扩展准则等随机集特性,结合所建立的电路系统性能可靠性评估的概率模型,给出了一种简便灵活的方法判断电路性能的可靠性;并用实例说明该方法在计算量远远小于蒙特卡罗方法的情况下,可以得到与其相当的可靠性评估效果。
3)基于Dempster证据组合规则的随机集表示以及广义集值映射和随机集联合条件概率,给出了DS证据理论中包含Dempster组合规则在内的多种经典组合规则的随机集统一表示模型。并且,文中利用这个模型构造了一种新的组合规则,它能很好的避免Dempster规则应用中存在的一类不合理现象,并以设备故障诊断中冲突证据的融合决策为例,说明了新规则的有效性。
4)基于模糊集的随机集表示和随机集似然测度,给出了一种从模糊故障特征信息(故障样板模式与待检模式)中获取诊断证据的新方法。然后结合证据理论,利用Dempster证据组合规则融合多组证据得出诊断结果。该方法可以克服基于单一特征的传统诊断方法和基于单个观测数据的待检模式匹配融合诊断方法的不足,显著提高对故障的识别能力。最后通过在多功能电机柔性转子试验台上的诊断实验,验证了新方法的有效性。
Because of the complexity of environments, limitation of sensor performance and imperfection of information acquisition technique, multisoures information reflecting system reliability and faults is usually uncertain (such as random, imprecise, vague and incomplete). These uncertain information is described and modeled by the corresponding knew theories under certain assumptions. Moreover, the more diverse the ways and means of information acquisition are, the more complex and various the types of information are. In this case, the limitations of knew theories become more and more unnegligible. For several years, researchers have explored the unification of theories dealing with different uncertainties of information and have finally considered random set theory, because it can unifies several uncertain theories such as probability theory, fuzzy set theory, Dempster-Shafer evidence theory, possibility Theory, rough set Theory. This doctoral dissertation is devoted to study on the random set methods of unified describing and modeling different-types uncertain information. Based on which, for specific objects in application such as circuit system, electromechanical equipments, some new methods are generated using random set theory and knew theories comprehensively. They can be used in reliability evaluation and fault diagnosis of specific system objects and are better than knew methods.
The main works in the thesis are introduced as follows:
1. Firstly, the available information is classified according to different uncertain types. The methods of uncertain information processing are reviewed in reliability evaluation and fault diagnosis. Their shortcomings are analyzed. We introduce the random set theory as a possible framework for unification and detail how the individual theories can fit in this framework.
Based on this research, other works are developed as follow
2. Based on the random set description of random variables and the extension principles of random set, a simple and flexible method is given for evaluating reliability of circuit performance by virtue of the proposed probability model of circuit system performance evaluation. This method is alternative to Monte-Carlo analysis, but reduces the number of calculations required drastically.
3. On the basis of random set representation of Dempster combination rule, the proposed extended set-valued mapping and joint conditional probability of random sets, a unified random set model of classical combination rules is presented. By use of this model, a new combination rule is constructed for overcoming a class of counterintuitive phenomena. The example of fault diagnosis using conflict evidence is given to show the effectiveness of new rule.
4. Based on the random set description of fuzzy set and the likelihood function of random set, new method is proposed to obtain fuzzy evidence from fuzzy fault features, and then, Dempster combination rule are used to fusion several pieces of fuzzy evidence to get diagnosis results. The proposed method of fuzzy evidence extraction can reduces uncertainties in fusion-makings and improves fault identifications. It is better than the traditional single-feature fault diagnosis and fusion diagnosis method based on single observation data matching. Finally, the diagnosis results of machine rotor show that the proposed method can enhance diagnostic accuracy and reliability.
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