A Study Of Uncertainty Quantification And Reliability Analysis Method Based On Ellipsoid Model

With the development of space technology,the reliability problems,taking the accuracy and reliability of mechanism movement as the main index,have become increasingly prominent.For one thing,the deployable arm and other aerospace mechanisms are affected by the complex environmental conditions on the orbit,which causes the uncertain parameters such as shape,size,quality and material performance varying with time.For another thing,it is difficult to obtain enough samples of these uncertain parameters.For the problem of time varying parameters,some methods are proposed in probabilistic reliability studies.But these methods are complex in terms of algorithms and lack of precision.Concerning the problem of insufficient sample and failing in measuring probability density,researchers have established the convex model and adopted the non-probabilistic reliability method to conduct their studies.However,the existing convex set model does not consider the time factor.Even in the convex-probability hybrid model,the problem of time varying is not solved.Instead,it is transformed and treated as the issue of the probabilistic reliability.Moreover,the convex set theory is still developing and not mature yet.Further research is needed in model construction and quantification methods to enrich the convex set theory.To address these problems in reliability,this thesis takes the ellipsoid model,which can reflect the correlation between variables,as the research object.It studies the efficient construction of the model,new uncertainty quantification method,reliability analysis method based on imprecise probability,hybrid model reliability analysis method,the reliability analysis method of timevarying ellipsoid model based on the crossing theory.In so doing,the corresponding methods are applied to reliability analysis in this study.This thesis has completed the following work:Firstly,the morphology features of the ellipsoidal model was analyzed and the numeric variables of midpoint,radius,variance,and covariance related to the ellipsoidal model were identified.During transforming the interval model and joint normal distribution model into the ellipsoid model,the construction method based on the digital features of each model was found.Further,the characteristics of samples constructing the ellipsoidal model and the mode of complete substitution were proposed.The method was modeled directly by using the sample characteristics instead of using the minimal closure idea of the Khachiyan method.Concerning time-varying uncertain parameters modeling,the time variability was transformed into the digital feature of the ellipsoid model.The time-varying parameters ellipsoidal model was proposed,algorithm was developed,evaluation was administrated,and the Khachiyan method was improved under incomplete sample data.Secondly,the method of uncertainty quantification was proposed based on the ellipsoid model and principle of indifference reduction.That is,the ellipsoid model was normalized to a round ball model,and the reduced semi triangle membership function in fuzzy mathematics was normalized as a one-dimensional probability density function.The uni-dimension was extended to multidimension by using radical uniform distribution extended method.Based on this,imprecise probability was processed,and joint probability density function was obtained.The methods of importance sampling and the directional sampling for the analyses of reliability of ellipsoid model were developed.Numerical examples were given to illustrate the accuracy and efficiency of the present method.The method was also applied to the motion accuracy and motion function reliability analysis of a deployable mechanism.It shows that the algorithm is efficient.In addition,it verifies that the non-probabilistic reliability is not robust when the boundary is smaller.Thirdly,ellipsoid-probability hybrid reliability problem was transformed to probabilistic reliability problem.Specifically,method of hybrid reliability was proposed by means of improving the important sampling method,changing state function to probability instruction function and the probability of each sampling point in the critical domain was obtained.In doing so,the problem of uncertainty caused by unknown but bounded variables in critical value bounds was solved.In view of the inefficiency of the improved method,the important sampling method of the hybrid model was further proposed.That is,making important sampling by calculating the mixed design points of the limit function in their standardized space,and transforming the joint probability density function of basic variables into the product of probability density function and nonprobability(imprecise probability)density function.A numerical example was given to verify the accuracy of the proposed algorithm.Further,the algorithm was applied to the reliability analysis of mechanisms with mixed parameters.In doing so,the application of related methods was verified in production practice.Finally,limit state function in standard space was obtained by the time-varying ellipsoid model.By analyzing the application scope of the time point method,we got the spanning domain in the standard sphere model,and proposed an important sampling method based on the time varying ellipsoid model,which was guided by the solution of the crossing probability.This method used the design point as the intermediary to set up another unit ball,truncated the standard round ball to reduce the sampling range,and improved the operation efficiency significantly.In addition,on the basis of the PHI2 method,the E-PHI2 method to the time-varying ellipsoid probability mixed model was proposed to obtain the crossing rate.The method used critical important sampling method or mixed model important sampling method to solve the reliability of mixed model,and then conversed to solve the reliability coefficient.Finally,an example was used to verify the method proposed.The results show that this method is more reasonable.