Active learning with generalized sliced inverse regression for high-dimensional reliability analysis. (January 2022) - Yin, Jianhua; Du, Xiaoping
Highlights: Dimension is reduced by the generalized sliced inverse regression – a nonlinear dimension reduction method. The curse of dimensionality is mitigated with the constructed Gaussian process model in the low-dimensional space. The new method can deal with nonlinear functions and small probabilities of failure. Abstract: It is computationally expensive to predict reliability using physical models at the design stage if many random input variables exist. This work introduces a dimension reduction technique based on generalized sliced inverse regression (GSIR) to mitigate the curse of dimensionality. The proposed high dimensional reliability method enables active learning to integrate GSIR, Gaussian Process (GP) modeling, and Importance Sampling (IS), resulting in an accurate reliability prediction at a reduced computational cost. The new method consists of three core steps, 1) identification of the importance sampling region, 2) dimension reduction by GSIR to produce a sufficient predictor, and 3) construction of a GP model for the true response with respect to the sufficient predictor in the reduced-dimension space. High accuracy and efficiency are achieved with active learning that is iteratively executed with the above three steps by adding new training points one by one in the region with a high chance of failure.