Parameterized Consistency Learning-based Deep Polynomial Chaos Neural Network Method for Reliability Analysis in Aerospace Engineering

• URL: http://arxiv.org/abs/2203.15655v1
• Date: Tue, 29 Mar 2022 15:15:12 GMT
• Title: Parameterized Consistency Learning-based Deep Polynomial Chaos Neural Network Method for Reliability Analysis in Aerospace Engineering
• Authors: Xiaohu Zheng, Wen Yao, Yunyang Zhang, Xiaoya Zhang
• Abstract summary: Polynomial chaos expansion (PCE) is a powerful surrogate model reliability analysis method in aerospace engineering. To alleviate this problem, this paper proposes a parameterized consistency learning-based deep chaos neural network (Deep PCNN) method. The Deep PCNN method can significantly reduce the training data cost in constructing a high-order PCE model.
• Score: 3.541245871465521
• License: http://creativecommons.org/publicdomain/zero/1.0/
• Abstract: Polynomial chaos expansion (PCE) is a powerful surrogate model-based reliability analysis method in aerospace engineering. Generally, a PCE model with a higher expansion order is usually required to obtain an accurate surrogate model for some non-linear complex stochastic systems. However, the high-order PCE increases the labeled training data cost for solving the expansion coefficients. To alleviate this problem, this paper proposes a parameterized consistency learning-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 high-order main model are parameterized into the learnable weights of the polynomial chaos neural network. The auxiliary model uses a proposed unsupervised consistency loss function to assist in training the main model. The Deep PCNN method can significantly reduce the training data cost in constructing a high-order PCE model without losing surrogate model accuracy by using a small amount of labeled data and many unlabeled data. A numerical example validates the effectiveness of the Deep PCNN method, and the Deep PCNN method is applied to analyze the reliability of two aerospace engineering systems.

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