Research On Reliability Analysis And Design Of Complex Structure

Reliability analysis and design are important in engineering. When the availablereliability methods well established in theory, e.g. stochastic reliability, fuzzy reliabilityand robust reliability etc. are applied to the engineering, some problems, such ascomputational cost and narrow applicability, are needed to be solved.For these problems encountered in engineering application, some improvedmethods based on traditional stochastic and fuzzy reliability are setup to reduce thecomplexity of analysis and design. A new robust reliability index is defined to deal withvarious uncertain convex models. The corresponding robust reliability analysis anddesign methods are established to perfect the robust reliability theory. The contents aredetailed as following.(1) By means of high-order correction term and equivalent probability transform, anadvanced response surface method(RSM) is established with lower computationalcost. A combination RSM is presented to the problem with high nonlinearity. Itimpoves the computational pression by introducing a set of linear response surfacesto approximate the actually nonlinear limit state equation. Through non-linearregression, the approximately analytical relationship between the synthesizedvariables and the basic variables are constructed. Then using the chain derivativerule, the reliability sensitivity, measured by the partial derivatives of the failureprobability with respect to the distribution parameters of basic variables, ispresented by the first order and second moment method.(2) The numerical simulation based on intelligent optimization is presented to analyzethe fuzzy random reliability. In the presented method, the fuzzy variable istransformed into random one first, then the simulated annealing method is adoptedto optimize the mean of the importance sample density function for each failuremode, in which the weighted importance sampling is constructed, to complete thereliability analysis.(3) The scale factor of size parameter is defined to map the multiple size parameters ofconvex models to a single one. The minimum value of the scale factor, determinedby the intersection between the uncertainty convex and failure region, is defined asthe robust reliability index, and the corresponding intersection point is defined asthe design point. They can be applied to various uncertain convex models.(4) The analytical formulae of robust reliability index and the corresponding design points are derived for the linear limit state function. By linearizing nonlinear limitstate equation, and defining the convergence rule on the convex distance, a firstorder design point method is set up to approximately slove the reliability index ofthe problem with low nonlinearity. For the problem with high nonlinearity,numerical simulation algorithms, incuding Monte-Carlo method, the advancedMonte-Carlo method and Markov Chain method, are estabilshed on probabilitydensity function constructed in convex model and the convergence rule on theconvex distance. By constructing the optimization function determined by the robustreliability index and introducing the convergence rule on the convex distance, theoptimization methods for solving the robust reliability are constructed on thesimulated annealing algorithm and the genetic algorithm.(5) For implicit limit state function, the linear RSM, the linear weighted RSM and thequadratic RSM are presente by refining the steps in traditional RSM and introducingthe convergence rule on convex distance; The neural network method is alsopresented to analyze the robust reliability by combining the B-P neural network(NN)and genetic algorithm(GA), in witch the B-P NN is used to construct the explicitexpression of the implict limit state function by trial and error, and GA is used tocalculate the corresponding robust reliability.(6) The optimal design model of the robust reliability is proposed on the basis of thefirst order design point method and the genetic optimization.(7) Observing the robust reliability analysis methods, the relationship between thestochastic reliability and the robust reliability is pointed, on which thestochastic-robust reliability analysis methods are presented.In general, by improving the traditional reliability analysis and design methods,defining a general robust reliability index and the establishing the corresponding robustreliability analysis and design methods, the above works increase the feasibility of theavailable method in the application to the complicated structural systems, which isdemonstrated by the examples of an aero engine turbine disk and the rotating shaft of ahorizontal tail of a aircraft.