The Reliability Analysis And Evaluation Of Mechanical Systems Based On Possibilistic Measurements

With an ever-increasing tendency to take uncertainty factors into account in engineering design, reliability has now been an important concept in science and engineering as well as a primary quality index of guaranteeing stable performances. The traditional stochastic/ probabilistic reliability method is a successful tool to handling uncertainty and has been widely used in engineering. Yet considering complex mechanical systems with frequently variant working conditions (e.g. crane and transporter), necessary statistic data is often not available, and there exist vast subjective information and epistemic uncertainty in initial data. Due to the frequent faults and multiple fault modes of such mechanical systems, their reliability data is thus different according to the adopted statistical approach. Moreover, the reliability data is also variant according to different types of mechanical system, which leads to lack of data or limited belief in preliminary design. The stochastic method is strongly depends upon the available information, which greatly restricts its applications in engineering.Against the backgrounds of the NSFC project, in consideration of some drawbacks of stochastic reliability method in theory and applications, as well as the existence of insufficient and vague data in actual equipments design, the reliability analysis and evaluation problems of complex mechanical systems are investigated in this dissertation, by means of possibilistic measurements integrating possibilistic theoretical models and operational methodologies.The purpose of this study includes three aspects. First of all, it attempts to explore new reliability theories and methodologies in the context of possibility theory and measurement. Secondly, it attempts to build up a design framework from uncertainty formalization to integral/measure qualification, and then to application methodologies. Thirdly, it attempts to provide some technical supports and guarantees for possibilistic reliability design and possibilistic reliability management in the case of limited statistical data.In combination with theoretical research and methodological exploitation, and integrating qualitative analysis with quantitative computations, the dissertation includes the following contributions:(1) The representation, synthesize and qualification of epistemic uncertainty in reliability design and analysis are investigated when necessary statistical data is scarce. Starting with a holistic understanding of uncertainty, uncertainty factors inherent in reliability inputs, reliability models, reliability inferences and external operating environments are analyzed in detail to find out their essences, and then the behaviors and appearances of insufficient data in reliability engineering are presented, which reveal the handling of epistemic uncertainty plays an important role in reliability analysis with imprecise or incomplete parameters. After comparing probabilistic approach with non-probabilistic approach in reliability design, some vital factors in model errors such as character parameters, distribution types, sample capacities and prior distributions are pointed out in turn, which provides a theoretical background for uncertainty formalization and validation in reliability analysis.(2) The measurements of possibilistic uncertainty and its corresponding information are studied. With an explanation of information types and information semantic of possibilistic uncertainty, the duality of possibility measure and necessity measure, as well as the bipolarity of optimistic criterion and pessimistic criterion are explored for epistemic uncertainty validation computationally. By a comparative analysis of possibility theory with some relative theories, the connections and transformations between them are proposed. Then two approaches to constructions of possibility distributions are provided, respectively as possibility distribution generations based on membership functions and possibility distribution transformations from probability distribution. Especially, when there is limited objective reliability data, a new method of developing the possibility distribution by subjective assignment strategy is put forward, which makes use of the concept of interval-valued possibilistic mean value of a L-R fuzzy number and is then illustrated by the lifetime data from fatigue reliability tests. These works provide a possibilistic design framework on the measure and integral background.(3) The possbilistic reliability models of typically general systems are constructed. Characterizing the systems(components) failure behavior by possibility measures in place of probability measures, treating the systems (components) lifetime as fuzzy variables in the possibility space, and introducing possibilistic approaches into system reliability modeling and analysis, the possibilistic reliability theories are advanced based on possibilistic measurements. By expanding the universe of discourse, the derivation of Posbist reliability models is simplified without loss of the nature of the problems to be solved, and the proofs and calculations of Posbist reliability of typical systems including series, parallel, series-parallel, parallel-series, and cold standby systems are much more straightforward. The detailed application examples in system reliability analysis provide a possibilistic design framework on the general reliability models background.(4) The models of possibilistic FTA and the approach to possibilistic importance analysis in accord with possibilistic reliability theory are exploited. From one side, a Posbist fault tree model of coherent systems is constructed by means of possibilistic characterizations of state variables from the viewpoint of fault, along with redefinitions of structure functions of coherent systems and possibilistic fault tree. The MCS model for qualitative analysis and possibilistic operators of logic gates for quantitative analysis are then proposed, respectively. They are suitable for predicting and diagnosing failures and evaluating reliability and safety of systems, in which the statistical data is scarce or the failure probability is extremely small. From another side, combining the ability of possibility theory in handling natural language with the extension of non-addictive measures by GIT, a new importance measure is proposed based upon possibilistic information entropy. In a two-dimensional framework combining both the set theory and the measure theory, an axiomatic index of importance is defined in the possibility space and then the modeling principles are presented after investigating the possibilistic information semantics, measure-theoretic terms and entropy-like models. Not only uncertainty quantification but also sensitivity analysis of possibilistic uncertainty is concerned in this study, which provide a practical methodology on the reliability application background.From the above works, with the engineering application of the concept selection for mechanical systems, fault tree analysis of the crane rope and a comprehensive safety evaluation of crane machinery, our conclusions could be summarized as follows, i.e. the adjustability of epistemic uncertainty characterizations for the occurrences of insufficient data, the effectiveness of possibilistic measurements for the handling of epistemic uncertainty, and the feasibility of possibilistic system models and fault tree models for the application of possibilistic measurements in reliability analysis.In this dissertation, the proposed models and methodologies would be extended to applications in the overall reliability evaluations, fault diagnosis and safety control of other complex engineering machinery.