Non-probabilistic reliability sensitivity analysis of the model of structural systems with interval variables whose state of dependence is determined by constraints

Non-probabilistic reliability sensitivity analysis for structural systems plays an important role in determining key design variables that affect structural reliability strongly. Traditional non-probabilistic model assumes that all interval variables are mutually independent. However, this assumption may not be true in practical engineering. In this article, the dependency of interval variables is introduced into the non-probabilistic model by using both inequality and equality constraints. The non-probabilistic index model and optimization method for structural systems with interval variables, whose state of dependence is determined by constraints, are proposed on the basis of the existing non-probabilistic index theory. The linear optimization model is alternative when nonlinear optimization model cannot find any solution. Non-probabilistic reliability sensitivity analysis model and optimization method for structural systems, with the interval variables whose state of dependence is determined by constraints, are established based upon the finite difference theory. The proposed method is demonstrated via several examples.