In practical engineering applications, uncertainty quantification is essential for predicting and preventing catastrophic failures. Reliability analysis methods have been introduced to calculate the probability that a system performs its intended functionality, and reliability-based design optimization (RBDO) has been widely applied to solve engineering design problems with the consideration of various sources of uncertainties. Optimum system design that has the best compromise between cost and system reliability can be achieved by solving RBDO problems.

This paper proposes a transfer learning method to solve the sampling-based RBDO problem. In this method, the sample space where the initial design point is located and its distribution are called the source domain, and the sample space where the updated design point is located and its distribution are called the target domain during the optimization process. Domain-adversarial regression neural networks are constructed by Monte Carlo simulation (MCS) samples and their responses of the source domain and MCS samples of the target domain to achieve high-precision response prediction of the target domain. According to the predicted response of MCS samples, the failure probability of the target domain is calculated, and the first-order score function is used to approximated the sensitivity information of the failure probability. By providing the estimated reliability, cost function value, and corresponding sensitivity information to the optimizer, an updated design point can be achieved accordingly. The iterative design process will be repeated until an optimal design is achieved. The core innovation of this method is to use the transfer learning model to solve the repeated reliability analysis in the sampling-based RBDO with only the computational cost of reliability analysis in the source domain. The efficiency and accuracy of the proposed method were demonstrated using numerical examples.