Research On Reliability Analysis Method Based On Polar Transformation And Techniques For Its Applications

Random factor is one of the most significant factors that influence the uncertainty of mechanical products'output performance including structure and vibration.And structural reliability theory is an efficient approach to deal with transfer law of random factor in mechanical models.The reliability problems of mechanical products tend to be multi-dimensional and implicit,which is the difficulty and focal point in reliability analysis,i.e.,existing reliability algorithms more or less show insufficient when facing this challenge,which is called "dimensionality disaster".Rolling bearings and gears are the most common and important components in transmission systems,and their well performance and stable work state will improve the performance and life of transmission system and entire machinery equipment.Analyzing and designing rolling bearings and gears utilizing the method of reliability is one of the hot issues of applications of reliability theory in engineering.Polar transformation is a dimensionality reduction and visualization method to project multidimensional data to two-dimensional plane,which displays clustering structure of reliability data through scatter diagram.In order to establish systematic analytical framework and research techniques for multi-dimensional and implicit reliability problems,the reliability theory and techniques for its applications are studied systematically in this dissertation based on the clustering feature of polar transformation,and further research is carried out in areas of reliability sensitivity analysis,random vibration,hybrid reality algorithm and reliability based design optimization.The main research contents are as follows:(1)A reliability sensitivity algorithm applying to multi-dimensional condition is proposed based on polar transformation.According to the clustering and distinguishability features of safe and failure classes of data in polar feature plane,the reliability sensitivity is defined by selecting failure data with visual aids.The results show that the algorithm has high efficiency and is not affected by dimensionality or nonlinearity,which is an effective method for analyzing multi-dimensional reliability sensitivity problems.Finally,on the basis of this algorithm,the influencing degree of each factor on rolling bearing clearance reliability is measured,which brings forward important theoretical basis for reliability design of rolling bearing.(2)The reliability and reliability sensitivity problems of random vibration are analyzed using polar transformation.Dimensionality reduction and visualization analysis of linear and nonlinear Duffing oscillator subjected to white noise is conducted.The results show that the clustering feature of data will appear only when the important direction exists.In the case of double random vibration systems,the influencing degree of random structural parameters on reliability is discussed.Finally,the reliability sensitivity of three degree of freedom gear transmission system subjected to random internal excitation is calculated,which provides theoretical foundation for the vibration reliability design of gear system.(3)An experiment design scheme based on polar transformation is raised,and a hybrid reliability algorithm combining it with sparse response surface is proposed.In every step of response surface construction,the critical samples are added and fitted according to the clustering feature of two classes of samples in a plane,and the most significant terms of polynomial response surface are chosen according to error prediction criteria and cross-validation method.The implicit limit state function of rolling bearing clearance is displayed using the algorithm,and the results turn out that the sampling method based on polar transformation is more reasonable,the overfitting phenomenon is overcome,and the convergence rate and precision of response surface is improved.Finally,the initial clearance of rolling bearing is selected according to the explicit limit state function and optimum working clearance interval,which offers theoretical direction for the reliability assurance of bearing clearance.(4)The active learing Kriging model is introduced in polar feature plane,and the samples are selected with learning functions.Taking advantage of stochastic characteristics of the Kriging model,two active learning functions EFF and U are combined with Kriging model,and the best samples are selected and added to update Kriging model.The results indicate that the accuracy and efficiency of reliability analysis based on surrogate model is improved due to the active learning functions.Further more,the algorithm is applied to the reliability based design optimization,which effectively improves the computation efficiency of optimization procedure.