Evidence-theory Models Considering Dependence Among Parameters And Their Applications In Structural Reliability Analysis

Uncertainties widely exist in practical engineering problems, and they are often associated with the material property, boundary condition, load, etc. How to precisely quantify the uncertainty existing in the structure or system and whereby conduct a reliability design has become an extremely important issue for current product design. Probabilistic method is generally considered as an effective tool to measure the uncertainty. However, probabilistic model needs enough data to determine the distribution of the uncertain variables. Some times, it is difficult to obtain sufficient data. It may bring some large errors if assuming the probability distribution of the variables. So which may led to the limitations of probabilistic methods in some engineering problems. Evidence theory is practically the generalization of the above probability and non-probability uncertainty modeling techniques, and under some special cases it will degenerate to the probability model, possibility theory, fuzzy sets and convex models, respectively. It can deal with the limited or even conflicting information and more importantly it is able to combine aleatory and epistemic uncertainties in a very straightforward way. It just need a small number of sample points, hence it has the characteristics of convenience and economy in the aspect of building the model. The main work of this paper is trying to use the evidence theory in the reliability analysis model, as follows:Firstly, presents an evidence theory model considering the dependence among evidence variables and discusses its application in the Structural Reliability Analysis. By introducing an ellipsoidal model, a joint frame of discernment (FD) can be created for the multidimensional problem, in which the correlativity between the parameters can be well reflected by the shape of the ellipsoid. By combining the ellipsoidal model with the marginal basic probability assignments (BPAs) of all the parameters, a joint BPA structure can be constructed.Secondly, by using the Copula function into the evidence theory mode to deal with correlation between the variables, and applies the model to solve the structure reliability problems. The cumulative distribution function of uncertain variables can be constructed by using the Copula function. By combining the cumulative distribution function with the marginal basic probability assignments (BPAs) of all the parameters, a joint BPA structure can be constructed.