Structural Reliability-based Design Optimization Method And Its Application To Highly Nonlinear System

With the improvement of the performance requirements of mechanical equipment and its complex service environment,how to ensure the reliability of mechanical structures has become the key to the good operation of mechanical equipment.The reliability assessment and optimization design of mechanical structures are essential components to ensure the reliability of mechanical structures.Due to the complexity and variety of failure modes of mechanical structures,structural performance functions that reflect the performance of mechanical structures are usually highly nonlinear.However,when solving the reliability of highly nonlinear performance functions,the traditional reliability evaluation method is not efficient and the solution results may appear nonconvergence of periodic oscillation.On the other hand,in order to ensure the reliability of the mechanical structure and optimize its design,it is necessary to optimize the reliability of the mechanical structure.In reliability-based optimization design,the reliability optimization algorithm also has the problems of low efficiency and low stability when solving optimization problems with highly nonlinear performance functions.Therefore,ensuring the fast convergence of the reliability method for solving highly nonlinear performance functions and improving the efficiency and stability of the reliability-based optimization method have important significance for the reliability evaluation and optimization of mechanical structures.In view of the above problems,the main contents of this article are as follows:1)Firstly introduce the basic theory and related concepts of reliability modeling,then analyze and compare the characteristics and limitations of common reliability assessment methods in terms of solution efficiency and accuracy.2)In order to evaluate the reliability of the cylindrical worm drive mechanism,the Taylor series expansion is used to expand the state function of the worm gear mechanism and the first four-order center moments of the structural state function are obtained.Regarded this as a constraint condition,the probability density functions of the worm gear tooth surface contact strength and tooth root bending strength structural state function are obtained by combining the maximum entropy principle.On the basis of the probability density functions,the reliability of the two failure modes of the worm gear is analyzed.On the other hand,considering the correlation between the two failure modes of worm gear tooth surface contact and tooth root bending,the reliability model under failurerelated conditions is established,and the correlation coefficient between the two failure modes and the overall reliability of worm gear are given.Taking the worm gear of a reducer as an example,the proposed method was verified by Monte Carlo simulation.The results show that the reliability method based on the fourth moment and the maximum entropy principle has higher precision,and there is a certain correlation between the two failure modes of the worm wheel.3)In structural reliability analysis,the HL-RF algorithm in the first order reliability method(FORM)is a widely used solution tool.However,for some highly nonlinear reliability problems,non-convergence phenomena such as periodic cycles may occur in the iterative process.In order to improve the efficiency of the firstorder reliability method for solving nonlinear reliability problems,an adaptive firstorder reliability method(AFORM)is proposed in this paper by introducing an adaptive factor.Based on the two-parameter approximate reliability method,the AFORM method obtains the corresponding angle based on the new iteration point and the previous iteration point,and uses the angle condition to determine the convergence of the result.On this basis,according to the degree of convergence of the results,the two iterative parameters of the approximate reliability method are continuously adjusted by adaptive factors,and the iteration step size is adjusted by changing the parameters to improve the efficiency and robustness of the primary reliability method.In this paper,four numerical examples and two engineering reliability evaluation examples are used to verify the proposed method.The results show that compared with some other primary reliability algorithms,the method has the characteristics of high efficiency and good robustness.4)To improve the efficiency of structural reliability-based design optimization(RBDO)based onthe performance measure approach(PMA),a modified conjugate gradient approach(MCGA)is proposed forRBDO with nonlinear performance function.In PMA,the advanced mean value(AMV)approach is widelyused in engineering because its simplicity and efficiency.However,the AMV method shows the inefficientand unstable results for structural performance function with high nonlinearity in RBDO.To overcome thisshortcoming,the proposed MCGA method improves the efficiency of solution by modifying the relevantparameters of conjugate gradient approach(CGA)and the direction of conjugate gradient algorithm forsearching the optimal design point.Finally,four numerical examples with highly nonlinear performance function and an optimization design example of speed reducer are presented.Compared with the differen methods including chaos control(CC)method,modified chaos control(MCC)method and CGA,the results show that the MCGA method exhibited the better efficiency and robustness in structural reliability and RBDO analyses.