A confidence-based reliability optimization with single loop strategy and second-order reliability method

Abstract

The statistical model is commonly used in the reliability-based design optimization (RBDO). However, it is difficult to obtain sufficient data to construct a reasonable statistical model in the practical engineering. The biased statistical model seriously reduces the accuracy of uncertainty modeling and further affects the validity of the optimal result of RBDO. In this paper, the uncertainty of statistical model caused by the insufficient data is taken into consideration, which is quantified by the confidence of failure probability. Confidence-based design optimization (CBDO) is used to ensure the validity of the optimal result, and thus the double-loop RBDO is replaced by the time-consuming treble-loop CBDO. To reduce the heavy computational cost, a complete performance measure approach (PMA) with single-loop strategy is proposed in this paper and performance measure value is applied in the whole optimization process. The modified second-order reliability method (SORM) is employed to replace the time-consuming MCS and calculate the minimum performance target point (MPTP) of the reliability constraint function. Then, the reliability analysis is integrated into the confidence level evaluation process by single-loop strategy. Four examples are used to verify the performance of the proposed method in this paper. All results have demonstrated that the proposed method only needs much lower computational cost but its accuracy is similar to the previous CBDO.