Sensitivity Analysis of Reliability‐Based Optimal Solution

The paper examines reliability‐based optimization problems formulated as the minimization of an objective function with reliability constraints that model the requirements for the reliability index of component failure modes. It is briefly described how these problems can be solved. The main contribution of the paper is given in the sensitivity analysis of the optimal solution at the optimal stationarity point, i.e., the sensitivity of the objective function and the optimal solution point due to changes in the various model parameters (nonoptimization variables). For the case of sensitivity analysis of the objective function with respect to a model parameter, it is shown by use of perturbation techniques that the total derivative of the objective function (taken at the optimal point) equals the partial derivative of the Lagrange function of the problem. Hereby, the sensitivities of the objective function can be achieved quickly and efficiently. In the case of sensitivity analysis of the optimal point due to a change in a model parameter, an equation system is presented. It is shown that the second‐order derivatives of the element reliability indices are necessary. Expressions for these second‐order derivatives are then derived by perturbation of the optimality conditions of the underlying reliability‐index‐optimization problem.