Deep Learning-Based Multi-Fidelity Surrogate Modeling for High Dimensional Reliability Prediction

Luojie Shi, Baisong Pan, Weile Chen, Zequn Wang
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Abstract

Multi-fidelity surrogate modeling offers a cost-effective approach to reduce extensive evaluations of expensive physics-based simulations for reliability predictions. However, considering spatial uncertainties in multi-fidelity surrogate modeling remains extremely challenging due to the curse of dimensionality. To address this challenge, this paper introduces a deep learning-based multi-fidelity surrogate modeling approach that fuses multi-fidelity datasets for high-dimensional reliability analysis of complex structures. It first involves a heterogeneous dimension transformation approach to bridge the gap in terms of input format between the low-fidelity and high-fidelity domains. Then, an explainable deep convolutional dimension-reduction network is proposed to effectively reduce the dimensionality of the structural reliability problems. To obtain a meaningful low dimensional space, a new knowledge reasoning-based loss regularization mechanism is integrated with the covariance matrix adaptation evolution strategy to encourage an unbiased linear pattern in the latent space for reliability predictions. Then, the high-fidelity data can be utilized for bias modeling using Gaussian process regression. Finally, Monte Carlo simulation is employed for the propagation of high-dimensional spatial uncertainties. Two structural examples are utilized to validate the effectiveness of the proposed method.
基于深度学习的多保真度代用模型用于高维可靠性预测
多保真度代理建模提供了一种经济有效的方法,可减少对昂贵的可靠性预测物理模拟的大量评估。然而,由于维度诅咒,在多保真度代理建模中考虑空间不确定性仍然极具挑战性。为应对这一挑战,本文介绍了一种基于深度学习的多保真度代理建模方法,该方法可融合多保真度数据集,用于复杂结构的高维可靠性分析。它首先涉及一种异构维度转换方法,以弥合低保真域和高保真域之间在输入格式上的差距。然后,提出一种可解释的深度卷积降维网络,以有效降低结构可靠性问题的维度。为了获得有意义的低维空间,一种新的基于知识推理的损失正则化机制与协方差矩阵自适应演化策略相结合,鼓励在潜在空间中形成无偏的线性模式,用于可靠性预测。然后,利用高斯过程回归对高保真数据进行偏差建模。最后,采用蒙特卡罗模拟来传播高维空间不确定性。我们利用两个结构实例来验证所提方法的有效性。
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