Reliability Robust Design Of Mechanical Structural System With Dependent Failure Modes Based On Moment Method

During the mechanical design process, uncertainty is unavoidable, and reliability methods are usually used to deal with these uncertainties. Meanwhile, the impact of the uncertainties on the mechanical structures and systems is different, and it is necessary to eliminate the negative impact of uncertainties in the design phase. As an effective tool to ensure the safety and reliability of products, uncertainty analysis and reliability-based robust optimization design enable designers to get the best performance indicators. Based on the studies on modern mathematics, mechanics and mechanical reliability theory, the uncertainty modeling and probabilistic correlation modeling are carried out. The quantitative model describing the impact of random factors on the mechanical system performance is built. The main random factors are integrated into the reliability optimization model of the mechanical structural system with the purpose to find the the best, the most reliable and robust product design project. The main contents of this paper include the following aspects:1. The basic framework of the theoretical system of uncertainty analysis and reliability robust design of mechanical structural systems with random parameters is described systematically and detailedly. The basic tasks and main contents of uncertainty modeling, probabilistic correlation modeling, reliability analysis, reliability sensitivity analysis and reliability-based robust design are explained. Research status and related theories are summarized and reviewed.2. A reliability-based risk assessment approach based on partial factor method is proposed. For the drawback of the traditional safety factors, based on the reliability theory and the first order second moment method, the partial factor method with respect to both the linear and nonlinear limit state equations is put forward. The structure with strength degradation caused by crack propagation is discussed and the partial factors are correlated with the reliability changes. A risk assessment approach of crackable structures is proposed based on the partial factors. 3. The reliability-based robust design of mechanical parts with multiple failure modes is studied. The reliability analysis with both independent and dependent failure modes is discussed. According to the property that only a few failure modes occur when a mechanical part fails, the reliability and reliability sensitivity methods are first presented based on the stochastic perturbation method, fourth moment method and higher moments standardized technology. Then the robust design model based on the reliability sensitivity is built with the reliability optimization model. When considering dependent failure modes, the Copula function is adopted to model the correlations. Based on the probability theory and the nature of the Archimedean Copula functions, the calculation of the reliability and reliability sensitivity with dependent failure modes are discussed, the reliability-based robust optimization is further performed.4. The reliability-based robust design of structural systems is studied. A practical method for reliability analysis of structural systems with arbitrary distribution parameters is presented by integrating the techniques of the stochastic perturbation method, Edgeworth series and its empirical remedy expression. According to the probabilistic network estimation technique, the Pearsonian correlation coefficient is used to describe the correlation between failure modes. The reliability sensitivity problem of structural systems with arbitrary distribution parameters is discussed based on the reliability analysis. A reliability-based robust design model for structural systems with arbitrary distribution parameters is built by combning the reliability-based optimization theory with the reliability sensitivity analysis technique.5. The reliability sensitivity problem of complex mechanical structures is discussed. Due to the implicit limit state function problem caused by the complexity of the mechanical structures, an analytical framework is presented to solve the problem with the integration of Pro/E, Hypermesh, MSC.Patran, MSC.Nastran, iSIGHT and Matlab. The responses of the structures are determined with experiment design and finite element analysis, then the explicit limit state functions are built based on the surrogate modeling technique. The reliability, reliability sensitivity and robust optimal design problem of the complex mechanical structures with dependent failure modes are discussed with the proposed analytical method.