Adaptive second order step length algorithm for inverse reliability analysis. (August 2020) - Libotte, Gustavo Barbosa; Lobato, Fran Sérgio; Moura Neto, Francisco Duarte; Platt, Gustavo Mendes
Highlights: A novel algorithm for reliability-based design optimization is developed and validated. A second order approximation is used for optimal step length calculation. A principled scheme is presented to avoid calculating the Hessian matrix. Benchmark and engineering problems illustrate the behavior and advantages of the proposed method. The method presents weak sensitivity to the choice of control parameters and low computational cost. Abstract: In order to obtain reliable operating conditions, uncertainties must be taken into account in the mathematical modeling of systems and processes. An uncertainty is measured by the probability of failure of the process, which can be tackled by inverse reliability analysis. This analysis guarantees the achievement of the probabilistic constraints at a specified level. Here, we propose a new methodology for obtaining optimum operating conditions, considering certain probabilistic constraints. The method uses a second order approximation for the calculation of an adaptive step length, in a technique based on steepest descent method, to optimize the performance function. The efficiency of the proposed technique is evaluated in some benchmark problems and in an engineering problem, showing that it outperforms other recent methodologies in convergence capability and stability, while being robust in the choice of control parameters.