Research On The Kriging-based Reliability Analysis Method For Mechanical Structures

Reliability is one of the most important indicators to evaluate the quality of mechanical products.In recent years,with development of modern technology,mechanical structures are increasingly complex.Variables that may influence the reliability of mechanical structures become more than ever.Besides,performance function that measures the working state of a mechanical structure tends to much more time-consuming and complicated nolinear.All factors mentioned above make the efficiency and accuracy of existing methods insufficient to perform the reliability analysis of complex mechanical structures.Therefore,it is important for both theoretical research and engineerings to employ Kriging as the surrogate model,and systematically study the time-invariant and time-variant Kriging-based structural reliability methods for mechanical structures with complicated nolinear and time-consuming performance functions.The research is surrmarized as followed:(1)Deriving "the Kriging covariance matrix",which is also rigorously proved.In the procedure of reliability analysis,performance values at many untried points are needed.Therefore,the covariance matrix of performance values at untried points is derived based on the theory of the Kriging model,multidimensional normal distribution and conditional distribution,which is called "the Kriging covariance matrix".(2)Researching the measures that quantitatively evaluate the accuracy of the Kriging model in terms of reliability analysis.The probability that the sign of the performance value at a given point is different from that of Kriging-predicted value.Then,the method to estimate the proportion of points whose performance values are wrongly predicted in the sense of positive or negative by the Kriging model is developed,which is treated as the accuracy measure of the Kriging model for time-invariant reliability analysis.The variance of the failure probability,i.e.the mean mean squared error of the Kriging-based failure-probability estimate,is derived and calculated,which is one of the benefits of the Kriging covariance matrix.Then,Chebyshev's inequality is employed to construct the confidence interval and 'an upper bound of the error of the Kriging-based failure-probability estimate.(3)The time-invariant reliability analysis method based on the best next point of the Kriging model.The point that is potential to enhance the accuracy of the Kriging model most is defined as the best next point.Three methods for different accuracy measures of the Kriging model is constructed to search the best next point.And the time-invariant reliability analysis method based on the best next point of the Kriging model is proposed.The strategy for refreshing the Kriging model of the proposed method is to add the best next point into the current DoE one by one.The stopping criterion of the proposed method is based on the proposed upper bound of the error of the Kriging-based failure probability estimate.(4)The time-variant reliability method based on the best next point of the Kriging model.The explicit expressions of upper bounds of the Kriging-based failure probability function and the distribution function of a structural lifetime are derived,and the approximations of both are constructed.The point that is potential to most enhance the accuracy of the Kriging model for time-variant reliability is defined as the best next point.Then,the time-variant reliability method based on the best next point of the Kriging model is proposed,which is able to estimate the failure probability function,the distribution function of a structural lifetime and the failure rate of given time interval.The stopping criterion of the proposed method could be adjusted quantitatively according to the accuracy requirement of engineering.(5)The proposed time-invariant and time-variant reliability methods are employed to perform the reliability analysis of gear contact strength.Considering the manufacturing and installation errors,the APDL of ANAYS is used to establish the parametric model of the gears,based on which the parametric simulation of gear contact strength is carried out.The time-varinat reliability analysis method is employed to perform time-varinat reliability analysis of the gear contact strength.To demonstrate the engineering value of the proposed time-variant reliability analysis method,the time-variant loads and the degeneration of gear contact strength are considered,which makes the results of reliability analysis close to engineering practice.