Non-probabilistic Reliability Sensitivity Based On Ellipsoidal Convex Model

The reliability sensitivity can provide the information about the relationship between reli ability and the distribution parameters of uncertain variables, and therefore guide reliability an alysis and reliability-based optimization. In this paper, several issues about reliability sensitivi ty analysis based on ellipsoid convex model are investigated, which include the non-probabili stic index and its two approximate first order reliability methods, two reliability sensitivity an alysis methods, approximate analysis approach of and Monte Carlo simulation, the main conta in as follows:1. Based on the resemblances between non-probabilistic convex model and probabilistic model, we focus on the non-probabilistic reliability index for ellipsoidal convex model and its two first-order reliability methods(FORM). When the limit state function is linear, the consistency between the two forms of non-probabilistic reliability index is proved. When the limit state function is nonlinear, the invariant problem in mean-value method is revealed, which can be removed by using the design-point method, and based on which a discussion on the two first-order reliability methods is made.2. A novel non-probabilistic reliability sensitivity method based on ellipsoidal convex model is presented, in which non-probabilistic reliability sensitivity is defined as the partial derivative of non-probabilistic reliability index with respect to the distribution parameters of uncertain variables. The analytical equations of non-probabilistic reliability sensitivity for linear limit state functions are first derived. By treating the midpoint and the design point as the linearization point, the approximate functions of non-linear limit state functions are then obtained using the first-order Taylor expansion, and based on which the approximate analytical equations of non-probabilistic reliability sensitivity are given. Several numerical examples are used to demonstrate the effectiveness and feasibility of the proposed methods.3. By using a derivative rule of compound function, the analytical equations of non-probabilistic reliability sensitivity are derived, which is redefined as the partial derivative of non-probabilistic unreliability with respect to the distribution parameters of uncertain variables. A reliability sensitivity method based on Monte Carlo Simulation is also presented, which can provide the theoretical exact solutions.