Reliability-Based Sensitivity And Reliability-Based Robust Design For Mechanical Components With Non-Normal Random Variables

The security and reliability of structural systems is realized through design, manufacturing and management. Among them the design determines the inherent reliability of the product. Therefore, design has an important contribution to the quality of the product, and endows the congenital essential characteristics of the product. Because of the existence of uncertain factors in structures, such as the load, material properties, and geometry parameters, the problem hence becomes a stochastic system with random parameters. The study of the reliability of stochastic structural systems is of important significance. The reliability analysis of mechanical structures can help the designer to establish acceptable tolerances on mechanical structures and govern the fluctuations of the system parameters for safe operations. In the end, the reasonable mechanical structures could be designed with enough reliability and little cost. Structural reliability which is of universal attention at home and abroad is the main index and on the most important technique index of product quality, and the reliability theory and reliability-based design methods have been developed rapidly in the past decades.Reliability sensitivity analysis of structural systems is the sensitivity design based on reliability, which can be used to evaluate the influence of the change of parameters on the reliability of structural systems. That is to say, the sensitivity of the reliability of structural systems with respect to the variance of design parameters can be determined by reliability sensitivity analysis. Reliability sensitivity analysis is of important implication in reliability design and modification, reliability based optimization design, reliability maintenance and so on. Nowadays, there are many methods in reliability analysis. In general, reliability analysis can always be performed based on the reliability analysis.The reliability-based robust design which is based on reliability based optimization design is a low cost and high quality design method. This method integrates the reliability sensitivity design into the reliability optimization design. Its basic concept is that the robust of the product quality can always be ensured when the design parameters have small variances. There the study of reliability based robust design is of very important significance in the field of reliability design of mechanical structures.Based on the stochastic perturbation method, fourth moment technique and reliability sensitivity method, an analytical method of reliability sensitivity with respect to random variables with non-normal distribution was proposed. A numerical comparison was made among other methods, such as Edgeworth method and Monte Carlo Simulation. The results showed out that the method proposed in the thesis is practical. The numerical example gave out the variation of the reliability sensitivity. The impact of mutative design parameters on the reliability of mechanical structures was widely studied.There are eight chapters in the thesis, the main contents are as follows:Chapter1We explicate the engineering background, the aim and meaning of the research; introduce the rise, the concept, the development of reliability theory, reliability sensitivity method and reliability-based robust design, and set forth the significant meaning of the study.Chapter2:The common methods for reliability design of mechanical components are introduced. Mathematics theories and methods used in this dissertation are briefly listed. Techniques from the perturbation method and the fourth moment method are used to propose a practical and effective numerical method of reliability analysis with arbitrary distribution parameters. A numerical comparison was made among other methods, such as Edgeworth method, Monte Carlo Simulation. The results showed out that the method proposed in the thesis is practical.Chapter3Based on the stochastic perturbation method, fourth moment technique and reliability sensitivity method, an analytical method of reliability sensitivity with respect to random variables with non-normal distribution was built. A numerical comparison was made among other methods, such as Edgeworth method. The results showed out that the method proposed here is practical. The numerical example gave out the variation of the reliability sensitivity. The impact of mutative design parameters on the reliability of mechanical structures was widely studied.Chapter4Based on the engineering optimization model, reliability optimization method, reliability sensitivity technique and robust design theory, a reliability-based robust design. method for mechanical components with non-normal parameters was proposed based on the fourth moment technique. A comparison was made among different methods, which proved that the reliability-based robust design method proposed herein is practical.Chapter5A method of reliability-based sensitivity with respect to correlation coefficients was proposed. The principle of choosing the correlation coefficients and criterions for determining correlation degree among the random parameters were put forward. Results of numerical examples indicated that the method proposed is a convenient and practical approach to obtain the values of the correlation coefficients among random parameters.Chapter6A deterministic static stress analysis on a turbine disk was conducted by using three-dimensional modeling software PRO/E and the finite element software PATRAN. By using ISIGHT, PRO/E and PATRAN/NASTRAN are integrated to carry out the stress and strain analysis. The randomness of parameters are taken into account, sample points of the dangerous area are generated by the experiment design of ISIGHT. Artificial neural network technology was adopted for the purpose of sample fitting. The approximate nonlinear function acquired by using Back Propagation network (BP network) was employed as the limit state function with an explicit expression. Hence, the reliability and reliability sensitivity analysis can be conducted with the method proposed herein. Using of the structural reliability analysis software NESSUS, a connector with PRO/E and PATRAN is established. The reliability and reliability sensitivity analysis are carried out in NESSUS. The results obtained in NESSUS are compared with that obtained by using the proposed method.Chapter7Two sets of software library on the reliability design were developed, which helps to solve the core problems on the analysis of reliability in the mechanical area in our country (A practical software library for reliability based design of mobile components:China,2009SR06661; A practical software library for reliability based design of mechanical components:China,2009SR06661).Chapter8The main conclusions of this dissertation are summarized and the prospects of the applications of reliability design in mechanical structures are discussed.