  Polynomial chaos expansion (PCE) is a powerful surrogate model-based
reliability analysis method. Generally, a PCE model with a higher expansion
order is usually required to obtain an accurate surrogate model for some
complex non-linear stochastic systems. However, the high-order PCE increases
the number of labeled data required for solving the expansion coefficients. To
alleviate this problem, this paper proposes a consistency regularization-based
deep polynomial chaos neural network (Deep PCNN) method, including the
low-order adaptive PCE model (the auxiliary model) and the high-order
polynomial chaos neural network (the main model). The expansion coefficients of
the main model are parameterized into the learnable weights of the polynomial
chaos neural network, realizing iterative learning of expansion coefficients to
obtain more accurate high-order PCE models. The auxiliary model uses a proposed
consistency regularization loss function to assist in training the main model.
The consistency regularization-based Deep PCNN method can significantly reduce
the number of labeled data in constructing a high-order PCE model without
losing accuracy by using few labeled data and abundant unlabeled data. A
numerical example validates the effectiveness of the consistency
regularization-based Deep PCNN method, and then this method is applied to
analyze the reliability of two aerospace engineering systems.
