| The uncertainty of load,the strength degradation of parts with time and the correlation between failure modes of parts are widely found in the reliability analysis of mechanical system.Most of available work related to the reliability analysis still focus on the reliability analysis of static systems without considering the uncertainty of loads and the variation of parts’ strength with time,and also the relative research is still based on the assumption of independent failure modes of parts,which not only exert a great impact on the reliability analysis results,but also do not meet the actual situation.Therefore,it is urgent to investigate the dynamic reliability of the mechanical system when fully accounting for the uncertainty of load,the dynamic correlation of the failure modes and the varying strength of parts.In this paper,the dynamic correlation of failure modes for parts is firstly dealt with by introducing Copula function,the dynamic reliability of the series system and parallel system are respectively carried out when taking the randomness and fuzziness of loads into account.The main content of this thesis is as follows:(1)The stress-strength interference,fuzzy reliability and the concept and the properties of the Copula function are first introduced,which lays a theoretical basis for the following work.(2)In order to investigate the dynamic reliability of different failure-dependent systems under the stochastic excitations,a new method was proposed based on the dynamic reliability of the part with or without strength degradation and the Copula functions.With this method,values of the edge distribution function of stress-intensity interference samples of the systems and the parameter q of copula function are evaluated with the nonparametric kernel estimation.The method proposed can estimate the parameters q of the copula function more accurately without consideration of the prior hypothesis or calculation of the sample distribution law.Utilizing the difference method,the dynamic reliability for the different systems with or without the strength degradation of parts are then derived after inserting the dynamic reliability of the parts and parameter q into the dynamic Copula reliability models of different failure-dependent systems.Finally,the feasibility and validity of the method presented are verified with an example,whereby the computational results from the method presented agree well with those from Monte-carlosimulation method.(3)In order to investigate the dynamic fuzzy reliabilities of series system and parallel system under the fuzzy excitations,a method was proposed based on the dynamic fuzzy reliability of the parts with or without considering fuzzy strength degradation of parts and the Copula functions.With this method,the parameters of copula functions are representing with the Kendall rank correlation coefficient,and the influence of the Copula parameters on the dynamic fuzzy reliabilities of the series and parallel systems is further inspected.Based on the proposed model,the fuzzy dynamic reliability of the structural system in the example is calculated,and the results are compared with those obtained by Monte Carlo simulation method,which also verifies the feasibility of the proposed method.According to the results in the example,the most suitable type of Copula functions is determined and selected,which provides a reference for the dynamic fuzzy reliability analysis of such kind of problem. |
