Research On Some Issues About Interval Model For Structural Reliability Analysis

The performance of structures in service will be affected by uncertainties from many aspects, such as structural material parameters, geometrical parameters, loads, and etc. To ensure proper performance of a structure for supporting loads and bearing environment and normally working, it is essential to give a reliability analysis of this structure under service environment, assigned condition and design lifetime. In order to set up a reasonable reliability model and guarantee validity of reliability analysis, well-understanding of these uncertainties should be emphasized. Because theory of interval analysis representing uncertainty with simple interval arithmetic computation has no need for consideration of probability distribution, it's more practical and can be easily done; and interval arithmetic could track truncated error and rounded error automatically during calculation. So reliability analysis based on theory of interval analysis, named structural interval reliability analysis prevails in recent years, which as one of the non-probabilistic reliability analysis methods is one useful supplement to probabilistic reliability analysis, and could make up some drawbacks of probabilistic methods, such as a great number of data are required to determine the probability density function for stochastic methods and membership function for fuzzy methods, and practically high cost will pay out for acquiring these probability information, and little error in initial probability information will result in big error in reliability analysis, and the like. Thus far, there is still a long way to go for integral and regular system info of structural interval reliability analysis. So, this paper pays more attentions to some problems of structural interval reliability analysis.In structural interval reliability analysis, comparison between two interval variables will often be involved, such as the comparison between generalized interval strength and generalized interval stress, etc. Thus a detailed survey on comparing interval numbers is presented; which provides us the premise for structural interval analysis.After the survey on methods for comparison between interval numbers and definition given on interval variable, structural interval reliability analysis methods based on interval performance function and interval stress-interval strength interference model are analyzed. The interval reliability index was modified, and its geometrical meaning is deeply investigated following the definition of a standard transformation. Possibility degree based method for structural interval reliability is presented, and structural safety possibility degree (SPD), to characterize the safety of structure, is given. The characters of SPD are analyzed. When strength and stress are uniformly distributed in their interval fields, the relationship between structural SPD based on interval analysis and probability reliability degree based on probability analysis is investigated. It is concluded that SPD could provide us a reasonable estimation for the safety state of structures, even if there is no enough data for probability reliability analysis.In the presence of upper bound and lower bound of elements'reliability degree and independence of reliability among elements, interval reliability of some typical systems and its relation to elements'interval reliability are investigated. It is concluded that the properties of system point reliability (i.e. traditional probability reliability) are hold with quasi-consistency by system interval reliability.