The Reliability Analysis And It’s Application Based On The Non-probabilistic Convex Model

Uncertainty widely exists in practical engineering problems. Reliability theorygradually developed with considering the uncertainty in engineering structures.Probabilistic method is generally considered as an effective tool to measure theuncertainty. However, probabilistic model needs enough data to determine thedistribution of the uncertain variables. Some times, it is difficult to obtain sufficientdata. It may bring some large errors if assuming the probability distribution of thevariables. So which may led to the limitations of probabilistic methods in someengineering problems. Non-probabilistic convex models use interval or ellipsoid todescribe the uncertainty of the variables, and it just need a small number of samplepoints, hence it has the characteristics of convenience and economy in the aspect ofbuilding the model. The main work of this paper is the reliability analysis model andthe development of the efficient algorithms, as follows:Firstly, interval reliability analysis method is introduced to the truncatedprobability problems and construct a hybrid reliability model. Different types ofpositional relations between the limit state function and the uncertainty domain aredescribed. If the intersection set is formed by them is empty, the interval reliabilityanalysis method will be used. If the intersection set is nonempty, the probabilisticreliability analysis method will be adopted.Secondly, the two kinds of Fist Order Reliability Method(FORM) based on themulti-dimensional ellipsoidal convex model are discussed based on thenon-probabilistic reliability measure which is widely used in the convex model field.in addition, the non-probabilistic reliability measure is used to solve the systemreliability problems, but it is inapplicable.Thirdly, constructing an efficient approximate method to solve thenon-probabilistic reliability model based on the volume ratio. A first orderapproximate method is used to solve the reliability model based on a linearapproximation to the limit-state function at the design point.Fourth, building an efficient reliability optimization design method based onmulti-dimensional ellipsoidal convex model through the extension of the existingreliability optimization techniques. Compared to the nested reliability optimization design methods, which greatly reduces the number of the calculation of the limit statefunction and significantly improve the efficiency of optimization.