Research On Evidence Theory And Its Reliability Analysis Methods And Applications For Complex Systems

With the tendencies of great size and large tonnage, complexity and preciseness of the industrial systems and manufacturing equipments, their reliability performances are gaining an increasing concern. In order to ensure the general operations of the system, it reliability has become one of the key issues. During reliability analysis of complex systems, it is very difficult to attain enough statistical data because of its complexity of system structure and mechanism with the limits of the daily conditions (human sources, economic resources and time, etc.). Moreover, the initial data contain a great deal of epistemics and uncertainties. The traditional analysis method based on the probability theory has the obviously restrictions. Consequently, there is an urgent need for investigating the uncertainty in reliability engineering of complex system to facilitate the reliability assessment and enhancement for the complex systems.Supported by the NSFC project:’Reliability analysis and design optimization of mechanical systems based on the possibility and evidence theory (50775026)’and the NHTRDP (863program):’Reliability analysis and design techniques of major equipment under the lack of data (2007AA04Z403)’, in this dissertation, some drawbacks of probability theory and epistemics and random uncertainties quantification and propagation in reliability analysis has been considered based on the investigating the question of evidence theory. The questions of using evidence theory to quantify and propagate the uncertainties of complex system are studied. The corresponding quantitative framework and propagating model are constructed respectively.In combination with theoretical researches and methodological method, integrating qualitative and quantitative uncertainty analysis of the aeroengine system, the dissertation proposes the following contributions:(1) The algorithm of quantification classification of multiple sources of evidence is proposed. The stochastic interpretation of basic probability assignment function is analyzed. The measurable space of frame of discernment is constructed. It is proved that countable intersection of the measurable space of the frame of discernment is close. This space is satisfied with the property of closed under finite countable intersection, finite countable union and difference operation. The vector and matrix of basic probability assignment function are defined. A common precondition underlying methods of the combination paradox is that conflict evidence has been known and existed, which, however, is not always true. Moreover, it has been verified that the conflict factor cannot accurately characterize the degree of conflict. In order to avoid the counter-intuitive results, multiple sources of evidence should be classified firstly. This paper proposes a novel algorithm for quantification classification of multiple sources of evidence based on a core vector method and the Jousselme distance has been regarded as quantification criterion for the degree of conflict because of its promising properties. Demonstrated by numerical studies and examples, the proposed methodology can classify the multi-sources evidence effectively and avoid the paradox of combination using the Dempster combination rule.(2) A combination rule of evidence compatibility is proposed based on the novel conflict degree of evidence. For the conflict factor of evidence can not fully describe the level of conflict between two pieces of evidence in Dempster-Shafer (Dempster) evidence theory, the deficiencies of present several methods to describe the conflict degree of evidence are analyzed and a novel conflict factor is proposed in this dissertation. The non-negativity, symmetry and boundedness of novel conflict factor are confirmed respectively. Based on the researches above, compatibility degree between two pieces of evidence is constructed according to the mutual compatibility degree among all pieces of evidence, the vector of compatibility degree is constructed. Then a correction factor of evidence is determined. The correction factor is used to modify the evidence respectively. A novel combination rule to deal with the conflict evidence is proposed. Based upon the proposed method, the novel combination rule can deal with the combination paradox effectively. When the novel combination rule is used to combine the evidence, the efficiency of combination to multi-sources evidence is better with comparison to other rules.(3) The method of risk evaluation and ranking for failure modes and effects analysis is proposed using Dempster-Shafer evidence theory under uncertainty. Dempster evidence theory is adopted to aggregate the risk evaluation information of multiple experts, which may be inconsistent, imprecise and uncertain. The modified evidence theory is proposed for dealing with different opinions of multiple experts, multiple failure modes and three risk factors in risk priority number analysis of failure mode and effects analysis. In this method, the simplified frames of discernment are provided according to our practical engineering application. The different frame of discernment and the corresponding power set is constructed respectively. The basic probability assignment function of risk rank of different risk factor is modified by the expert weights weight matrix. The combination rule of different evaluation information of multiple experts on the three risk factors of failure modes is proposed. Meanwhile, the fused three risk factors are regarded as the discrete random variables. Consequently, the risk priority number is a function of the discrete random variable. The mean value of risk priority number is utilised to the risk priority ranking of failure modes. The proposed method is demonstrated by an application of risk priority ranking of failure modes in failure mode and effects analysis of compressor blades of an aeroengine. The consequence is demonstrated that the novel method can manage the uncertainty risk evaluation and ranking to failure modes in failure mode and effects analysis.(4) Uncertainties of reliability analysis of complexity system based on the evidence network has been analyzed. Fault tree analysis, as one of the powerful tools in reliability engineering, has been widely used to enhance system quality attributes. In most cases of fault tree analyses, precise values are adopted to represent the probabilities of occurrence of those events. Due to the lack of sufficient data or imprecision of existing data at the early stage of product design, it is usually difficult to estimate the failure rates of individual events or the probabilities of occurrence of the events accurately. Therefore, such imprecision and uncertainty need to be taken into account in reliability analysis. The evidential networks is employed to quantify and propagate the aforementioned uncertainty and imprecision in fault tree analysis. The detailed conversion processing of some logiec gates to evidential networks is developed, respectively. The figures of the logic gates and the converted equivalent evidential networks, together with the associated truth tables and the conditional belief mass tables, are also presented in this work. The step of fault tree mapping into evidential networks is constructed. The computing of probability importance, structure importance is illustrated by evidential networks respectively. The novel uncertainty importance is proposed. For the design of the planetary gear is improve in the reducer, the information about experimental observations or tests is limited. Evidence network is adopted to quantify and propagate the uncertainty and imprecise probability in reliability prediction of improved aero-engine reducer. The evidence network of the system is constructed. The range of system reliability is attained by evidence theory. From the consequence of the computing, it is can be attained that the parallel system can decrease the uncertainty of the system because the sub-components includes the uncertainty in the parallel system. The series system can increase the uncertainty of the system because the sub-components involve the uncertainty in the series system. When one component has uncertainty in the series system, the overall uncertainty of the component is unrelated to the other components in system. This conclusion provides the qualitative criterion for uncertainty analysis in reliability engineering.