Robust Reliability Theory And Optimization Methods

Uncertain factors are critical in the applications of reliability engineering. The study on methods of reliability theory has been gaining increasing attentions to many researchers. During the past several decades, the traditional reliability approach based on probability theory has been widely applied to various engineering fields and has demonstrated its maturity. However, that method is not capable to deal with the situation when the statistical data or information is lacking. It can not overcome the limitations of the probability theory either. To overcome those barriers, a new reliability theory called the non-probabilistic reliability is proposed as a complement to the traditional reliability theory. This dissertation further develops the non-probabilistic reliability theory and studies its applications based on the exiting work in literature. The contributions of this paper include the following aspects:(1) The robust reliability theory of mechanical static strength is investigated and analyzed. The corresponding design criterion for mechanical components is proposed. The robust reliability of vibration components is analyzed, and the corresponding design criterion is established. We also compare the present robust reliability method with the traditional reliability method.(2) A new measure and a design criterion of the robust reliability theory are proposed. They are applied to study the system robust reliability. An example of the robust reliability analysis of a simple vibration system is used to demonstrate the validity of the proposed method. We compare the proposed robust reliability index with the Ben-Haim's robust reliability index.(3) Considering the variety and complexity of the uncertain factors with impact on the reliability in engineering practice, it is necessary to study the combination of the robust reliability, the traditional reliability, and the fuzzy reliability. To handle the real reliability problems, hybrid reliability models are established to fully utilizing available data. When we have sufficient data to describe the probabilistic characteristics of uncertain parameters, probabilistic reliability models or fuzzy reliability models can be adopted. When there is insufficient data, non-probabilistic set models should be chosen. When the above three conditions exist at the same time, we may choose to use hybrid reliability models. In engineering analysis, the ability of different possible reliability methods allows for mutual compensation for the disadvantages inherent in each individual method. After establishing the hybrid models, programs can be built to obtain corresponding solutions.(4) The robust reliability optimization methods are studied. In the lacking of data or deficiency of information on the uncertain structures, non-probabilistic models are proposed to be used to solve robust reliability optimization design problems. Based on convex modelsfor uncertainty description, structural design models of the non-probabilistic optimization are established. Furthermore, non-probabilistic reliability models are proposed in the presence of both probabilistic and non-probabilistic information. Based on the physical programming method, the robust reliability optimization of mechanical structures is investigated. The uncertainties in mechanical structures are described by convex models. The unsatisfactory functions are created by means of the physical programming. The robustness of objective functions is achieved by minimizing the unfavorable unsatisfactory functions. The robustness of constraints is ensured by a sub-optimization of the worst case scenario. Treating the reliability index as constraint functions or objective functions, another new method of the robust reliability optimization is presented by adding sensitivities as additive objectives. Three models of the robust reliability optimization are developed based on the conventional reliability optimization models with the additive objective functions. They are created respectively considering the sensitivity of objective functions, constraint functions, and the objective and constraint functions, with respect to design parameters. Optimization problems are solved by the optimization toolbox of MATLAB.The research on the robust reliability theory is important not only in academic research, but also in engineering applications. Although the robust reliability theory is not yet a mature theory, its idea is innovative providing a new method for the reliability engineering. This method is suited to the scarce statistical information, severe uncertainties, and the problems which the traditional reliability methods can deal with.