Reliability Analysis And Optimal Design Methods For Mechanical Systems Under Aleatory And Epistemic Uncertainties

With the rapid development of modern industrial technologies such as aerospace,deep-sea exploration and rail transit,mechanical products are becoming more and more huge,precise and complicated day by day.Many engineering machinery and weapons are subjected to extremely severe service environment,in addition to the effects of various uncertainties,which results in frequent breakdowns and has caused a lot of catastrophic accidents.High reliability is the basis for ensuring that the product can performs its proper function.In order to save costs or meet other performance requirements,lightweight designs for vehicles,high-speed trains,aeroplanes and satellites are also needed.To meet the design requirements of high reliability,long life and lightweight,reliability optimization design has increasingly applied to complex mechanical products.Several key problems need to be solved in the reliability optimization design of complex mechanical products,including 1)multisource mixed uncertainty quantification;2)high precision reliability evaluation under complex loading;3)reliability evaluation for multistate systems;4)efficient reliability optimization design.Reliability models established on the traditional stress-strength interference theory do not consider the effect of loading on mechanical products in the service,in addition,mechanical products are affected by many uncertainties during the whole life cycle,the existing methods of reliability analysis are no longer applicable,research on new dynamic reliability analysis method is urgent.Thus,in view of these key issues,this dissertation studies the dynamic reliability model under complex loading,the reliability analysis methods under mixed uncertainties,the fuzzy reliability analysis method for multi-state systems considering the correlation,and the reliability optimization design method under the mixed variables,respectively,to extend and improve the existing dynamic reliability models and analysis methods,and provide theoretical foundation and information support for the safety and reliability of mechanical system or mechanical products during the service,preventing accidents and reducing cost.The main research contents and innovations of this dissertation are listed as follows:(1)Development of a system reliability analysis method under the effects of complex load and strength degradation.This dissertation takes the comprehensive effects of shock load and strength degradation into consideration,studies the system dynamic reliability model and analysis method under complex load and strength degradation,and sets up a dynamic reliability model considering complex load and strength degradation.GaussLegendre integral formula is used for the calculation of dynamic reliability,the validity and accuracy are verified with Monte Carlo simulation.(2)Development of a system reliability analysis method based on entropy invariance.In the design process of mechanical products or systems,affected by incomplete information,insufficient data,and other uncertainties,it is often difficult to even cannot obtain the distribution types and distribution parameters of certain variables,but set them as fuzzy variables or interval variables.For reliability issues that only contain fuzzy variables,well-developed methods such as level cut sets,stochastic finite element can be used.In practical engineering,there are few cases where only fuzzy variable is present,and the opposite is often a mixture of variables.Thus,it is necessary to study the reliability analysis methods under mixed variables.This dissertation proposes an equivalent conversion method based on the theory of entropy,which can convert the fuzzy random variables to the normal random variables,and studies the system reliability analysis method under mixed uncertainties combined with saddlepoint approximation.(3)Development of a fuzzy reliability analysis method for multi-state systems considering the correlation.With the large dimension,complication and multi-function of mechanical products,the fault of a certain part or subsystem usually does not lead to the failure of the whole mechanical products,but results in a decline in the performance of the products gradually,and presents polymorphism.On the other hand,in practical engineering,due to the limitations of conditions,insufficient data,or incomplete information,etc.,people sometimes can only give rough ranges for the performance levels of the system and the corresponding probabilities.In addition,there is usually a connection between the components or subsystems that make up the system.This dissertation adds the correlation to fuzzy universal generating function,and proposes a new fuzzy reliability analysis method for multi-state systems considering the correlation.(4)Development of a reliability optimization design method under the mixture of fuzzy and interval variables.At present,scholars have done some research works on optimization design under the mixed uncertainties,and obtained some effective methods,but there is little research on reliability optimization design method under the mixture of fuzzy variables and interval variables,and lack effective treatment methods.In this dissertation,reliability optimization design under fuzzy variables and interval variables is converted to reliability optimization design under random variables and interval variables based on entropy invariability,and a new reliability optimization design method is proposed under the mixture of fuzzy variables and interval variables.