Chen Baixi, Shen Luming, Zhang Hao
School of Civil Engineering, The University of Sydney, Sydney, NSW, 2006, Australia.
Sci Rep. 2022 Feb 22;12(1):3017. doi: 10.1038/s41598-022-06870-9.
Describing the material flow stress and the associated uncertainty is essential for the plastic stochastic structural analysis. In this context, a data-driven approach-heteroscedastic sparse Gaussian process regression (HSGPR) with enhanced efficiency is introduced to model the material flow stress. Different from other machine learning approaches, e.g. artificial neural network (ANN), which only estimate the deterministic flow stress, the HSGPR model can capture the flow stress and its uncertainty simultaneously from the dataset. For validating the proposed model, the experimental data of the Al 6061 alloy is used here. Without setting a priori assumption on the mathematical expression, the proposed HSGPR-based flow stress model can produce a better prediction of the experimental stress data than the ANN model, the conventional GPR model, and Johnson Cook model at elevated temperatures. After the HSGPR-based flow stress model is implemented into finite element analysis, two numerical examples with synthetic material properties are performed to demonstrate the model's capability in stochastic plastic structural analysis. The results have shown that with sufficient data, the distribution of the structural load carrying capacity at elevated temperatures and the variation of load-displacement curves during the loading and unloading processes can be accurately predicted by the HSGPR-based flow stress model.
描述材料流动应力及其相关不确定性对于塑性随机结构分析至关重要。在此背景下，引入了一种具有更高效率的数据驱动方法——异方差稀疏高斯过程回归（HSGPR）来对材料流动应力进行建模。与其他机器学习方法不同，例如仅估计确定性流动应力的人工神经网络（ANN），HSGPR模型能够从数据集中同时捕捉流动应力及其不确定性。为了验证所提出的模型，这里使用了Al 6061合金的实验数据。在不对数学表达式进行先验假设的情况下，所提出的基于HSGPR的流动应力模型在高温下比ANN模型、传统GPR模型和Johnson Cook模型能更好地预测实验应力数据。将基于HSGPR的流动应力模型应用于有限元分析后，进行了两个具有合成材料属性的数值示例，以证明该模型在随机塑性结构分析中的能力。结果表明，在有足够数据的情况下，基于HSGPR的流动应力模型能够准确预测高温下结构承载能力的分布以及加载和卸载过程中载荷-位移曲线的变化。
