Reliability Sensitivity Analysis Method for Mechanical Components

Based on the univariate dimension-reduction method (UDRM), Edgeworth series, and sensitivity analysis, a new method for reliability sensitivity analysis of mechanical components is proposed. The univariate dimension-reduction method is applied to calculate the response origin moments and their sensitivity with respect to distribution parameters (e.g., mean and standard deviation) of fundamental input random variables. Edgeworth series is used to estimate failure probability of mechanical components by using first few response central moments. The analytic formula of reliability sensitivity can be derived by calculating partial derivative of the failure probability P f with respect to distribution parameters of basic random variables. The nonnormal random parameters need not to be transformed into equivalent normal ones. Three numerical examples are employed to illustrate the accuracy and efficiency of the proposed method by comparing the failure probability and reliability sensitivity results obtained by the proposed method with those obtained by Monte Carlo simulation (MCS).

Reliability-based robust design optimization using anchored ANOVA expansion and truncated Edgeworth series approximation

Based on the basic concept of reliability-based design optimization and robust design optimization, a reliability-based robust design optimization is achieved with the moment method in this work. At the first step, two methods, i.e. the anchored ANOVA expansion and truncated Edgeworth series approximation, are combined to solve the reliability constraints in the optimization procedure. The computational effort of the reliability analysis involved in the reliability-based design optimization is then reduced by the moment method. The reliability-based robust design optimization is then formulated by introducing the reliability sensitivity into the reliability-based design optimization as a sub-objective function, which is derived based on the truncated Edgeworth series expansion. The numerical examples illustrate the effectiveness and applicability of the proposed methodology and that the moment-based reliability-based robust design optimization satisfies (1) the reliability target of each constraint and (2) the minimum reliability sensitivity with respect to the mean value of the input random variables. The proposed reliability-based robust design optimization procedure could be applied to the product design under uncertain environment.

Influence of Chemical Heterogeneities on Line Profiles

The chemical composition fluctuation in a material may cause line broadening due to the variation of the lattice parameter, which yields a distribution of the profile centers scattered from different volumes of the material. The nature of line broadening induced by chemical heterogeneities is similar to a microstrain-like broadening in the sense that the peak width increases with the magnitude of the diffraction vector. However, the dependence of compositional broadening on the orientation of diffraction vector (i.e. the anisotropic nature of this effect) differs very much from other types of strain broadening (e.g. from that caused by dislocations). The anisotropic line broadening caused by composition fluctuation is parameterized for different crystal systems and incorporated into the evaluation procedures of peak profiles. This chapter shows that the composition probability distribution function can be determined from the moments of the experimental line profiles using the Edgeworth series. The concentration fluctuations in decomposed solid solutions can also be determined from the intensity distribution in the splitted diffraction peaks.