Adaptive parallel design criterion for failure probability estimation with Student-t likelihood

Most existing methods for system failure probability estimation typically concentrate on optimizing the learning function to locate global sampling points in sequential experimental designs. However, such techniques often generate many points that are distant from the failure boundary, potentially leading to inefficient use of computational resources. To address this issue, we develop an innovative t-likelihood-based adaptive parallel design criterion (t-APDC) by combining classical reliability analysis methods with novel machine learning techniques. Our approach begins with the introduction of a new sign loss function to enhance the optimization of Gaussian process regression hyperparameters. This significantly boosts the accuracy of the surrogate model in differentiating the sign of limit state functions, thereby reducing the need for costly computer experiments. Next, we utilize the Student’s t-distribution as the likelihood function, which mitigates the impact of outlier samples and improves prediction accuracy. By integrating the t-likelihood with a power prior, a tractable posterior distribution of the approximate failure boundary can be efficiently sampled by normalizing flow, which circumvents the optimization challenges inherent in traditional experimental design. Numerical experiments demonstrate the robust and outstanding performance of our proposed method, which supports parallel distributed processing and effectively handles multi-modal limit state scenarios.