The Reliability Index Solving And The Robust Design Based On The Interval Model

Probabilistic reliability analysis is extremely sensitive to the distribution forms ofmodel and model parameters, they appear a very small deviation, reliability analysismay lead to large errors. Non-probabilistic reliability describe uncertain parameterswith a convex sets, which need less information. When the sample space is small, usethe non-probabilistic reliability analysis of the reliability of the structure is moresuitable. Interval model is a kind of non-probabilistic reliability models, whichdescribes as uncertain parameters an interval uncertain variables. Compared to theother models, interval model has the advantage of the need for less data andconservative results, the research of this article is based on interval model. Thenon-probabilistic reliability index is the most important indicator of the reliability ofthe measurement system, due to its unique form of expression, how to solve indicatorsfast and accurate is the difficulties and the key of the study of non-probabilisticreliability. The robust design based on interval model is the non-probabilisticreliability’s applications in engineering, the interval model is different from theprobability model, the robust design of the study interval model has its practicalsignificance.This paper focuses on the algorithms of the solving the reliability index androbust design based on the interval model. This paper solves the problem of thereliability index solving of the interval model, improves the response surface methodto study reliability index of solving the problem in the case analytic expression doesnot exist, and explore the robust design of interval model. The specific contents are asfollows:First, in the case that limit state equation expressions exist, for the unconvergencein the iteration, that projection gradient method solves the reliability index, this paper analyzes its reasons, and put forward the space dimension reduction to solve theunconvergence in the iteration, give the conditions that the iterative reduces thedimension, fast method of dimensionality reduction, and the convergence of theiteration basis, the algorithm is verified by example.Secondly, in the case that the limit state equation of expression does not exist, itsanalytical expression by the response surface method gets, due to the interval modelreliability indicators solving more demanding on the accuracy of the response surfacemethod, this article is construct a new form of response surface expression accordingto structural features, the new method depends on the users’ experience, the examplesshow that the algorithm can solve complex structures’ reliability index, compared withthe traditional response surface method, it has higher accuracy;Finally, study the robust design of the interval model, this paper redefine thestructure robustness of interval model, which is described as reliability index, reducethe robust design of the structure to a two-tier plan, solve this problem by linearizationconstraint equations and the objective function, the algorithm was validated by someexamples.