用于隐式边坡可靠性分析和不确定性量化的多项式响应面信息神经网络

IF 5.3 1区 工程技术 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS
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引用次数: 0

摘要

在边坡可靠性分析中,通常设计代用模型来替代计算成本高昂的性能函数。对于考虑土壤空间变异性高维模拟的边坡可靠性问题,必须使用足够多的采样点来构建代用模型,以覆盖模型参数的高维域,这可能会使其稳健性对采样大小非常敏感。本文提出了一种新的代用建模框架--PRS-informed NN(物理信息神经网络的替代方案,PINN),它将多项式响应面(PRS,代表小尺度物理规律指标)与神经网络代用模型(NN,代表大尺度模型性能)集成在一起,以提高不同样本量下的建模性能并降低不确定性。基于卡尔胡宁-洛夫扩展技术,首先降低了随机场离散化所涉及的变量维度,从而简化了边坡坍塌概率(Pf)的计算。通过调整训练损失函数,将作为边坡稳定性模型基本物理规律的 PRS 集成到神经网络中。通过合成斜坡模型和实际斜坡案例研究,证明了所提方法的可行性。结果表明,所提出的框架提高了神经网络代用模型的准确性,尤其是在样本量较小的情况下。最后,量化了代用模型中的不确定性和认识不确定性,并详细讨论了 Pf 估计的置信区间。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Polynomial response surface-informed neural network for implicit slope reliability analysis and uncertainty quantification
In slope reliability analysis, surrogate models are usually designed to replace the computationally expensive performance functions. For slope reliability problems considering high dimensional simulation of soil spatial variability, the surrogate model must be constructed using sufficient sampling points in order to cover the high dimension domain of model parameters, potentially making its robustness sensitive to the sample size. This paper proposes a novel surrogate modelling framework, the PRS-informed NN (alternative to the physics-informed neural network, PINN), which integrates a polynomial response surface (PRS, representing a small-scale physical law indicator) with a neural network surrogate model (NN, representing a large-scale model performance) to enhance the modelling performance across various sample sizes and reduce uncertainty. Based on the Karhunen-Loeve expansion technique, the dimension of variables involved in random field discretization is firstly reduced, simplifying the computation for probability of slope failure (Pf). The PRS that plays a role of basic physical law of slope stability model, is integrated into the neural network by adjusting the training loss function. The feasibility of the proposed method is demonstrated through a synthetic slope model and a real-world slope case study. Results show that the proposed framework improves the accuracy of neural network surrogate models, especially with smaller sample sizes. At last, both aleatory and epistemic uncertainties in the surrogate modelling are quantified, followed by a detailed discussion of the confidence interval for the Pf estimation.
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来源期刊
Computers and Geotechnics
Computers and Geotechnics 地学-地球科学综合
CiteScore
9.10
自引率
15.10%
发文量
438
审稿时长
45 days
期刊介绍: The use of computers is firmly established in geotechnical engineering and continues to grow rapidly in both engineering practice and academe. The development of advanced numerical techniques and constitutive modeling, in conjunction with rapid developments in computer hardware, enables problems to be tackled that were unthinkable even a few years ago. Computers and Geotechnics provides an up-to-date reference for engineers and researchers engaged in computer aided analysis and research in geotechnical engineering. The journal is intended for an expeditious dissemination of advanced computer applications across a broad range of geotechnical topics. Contributions on advances in numerical algorithms, computer implementation of new constitutive models and probabilistic methods are especially encouraged.
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