为了降低计算量,多可信度代理模型技术通过融合不同精度和计算量的分析模型构建高精度分析模型的代理模型,在基于仿真的工程优化中得到广泛应用。现有的多可信度建模方法在面对高维问题时往往仍需要大量高精度样本点,计算量很大,且大都...为了降低计算量,多可信度代理模型技术通过融合不同精度和计算量的分析模型构建高精度分析模型的代理模型,在基于仿真的工程优化中得到广泛应用。现有的多可信度建模方法在面对高维问题时往往仍需要大量高精度样本点,计算量很大,且大都基于高斯随机过程理论,超参数估计时长随着问题维数和非线性程度的增加明显增长且不够稳健。为此,充分利用深度神经网络在高维信息提取和近似方面的巨大潜能,以及元学习理论在小样本学习领域的优势,提出一种基于元学习的多可信度深度神经网络(Meta-learning based multi-fidelity deep neural networks, MLMF-DNN)代理模型方法。通过若干数学算例和NACA0012翼型稳健优化问题的应用,表明提出的MLMF-DNN方法相比于经典的Co-Kriging方法,在预测精度和训练时长上均有明显改善,对于高维问题优势更明显。展开更多
The classic polynomial chaos method(PCM), characterized as an intrusive methodology,has been applied to uncertainty propagation(UP) in many dynamic systems. However, the intrusive polynomial chaos method(IPCM) r...The classic polynomial chaos method(PCM), characterized as an intrusive methodology,has been applied to uncertainty propagation(UP) in many dynamic systems. However, the intrusive polynomial chaos method(IPCM) requires tedious modification of the governing equations, which might introduce errors and can be impractical. Alternative to IPCM, the non-intrusive polynomial chaos method(NIPCM) that avoids such modifications has been developed. In spite of the frequent application to dynamic problems, almost all the existing works about NIPCM for dynamic UP fail to elaborate the implementation process in a straightforward way, which is important to readers who are unfamiliar with the mathematics of the polynomial chaos theory. Meanwhile, very few works have compared NIPCM to IPCM in terms of their merits and applicability. Therefore, the mathematic procedure of dynamic UP via both methods considering parametric and initial condition uncertainties are comparatively discussed and studied in the present paper. Comparison of accuracy and efficiency in statistic moment estimation is made by applying the two methods to several dynamic UP problems. The relative merits of both approaches are discussed and summarized. The detailed description and insights gained with the two methods through this work are expected to be helpful to engineering designers in solving dynamic UP problems.展开更多
文摘为了降低计算量,多可信度代理模型技术通过融合不同精度和计算量的分析模型构建高精度分析模型的代理模型,在基于仿真的工程优化中得到广泛应用。现有的多可信度建模方法在面对高维问题时往往仍需要大量高精度样本点,计算量很大,且大都基于高斯随机过程理论,超参数估计时长随着问题维数和非线性程度的增加明显增长且不够稳健。为此,充分利用深度神经网络在高维信息提取和近似方面的巨大潜能,以及元学习理论在小样本学习领域的优势,提出一种基于元学习的多可信度深度神经网络(Meta-learning based multi-fidelity deep neural networks, MLMF-DNN)代理模型方法。通过若干数学算例和NACA0012翼型稳健优化问题的应用,表明提出的MLMF-DNN方法相比于经典的Co-Kriging方法,在预测精度和训练时长上均有明显改善,对于高维问题优势更明显。
基金supported by the National Natural Science Foundation of China (No. 51105034)the Doctoral Thesis Build Project of Beijing 2012 (China)
文摘The classic polynomial chaos method(PCM), characterized as an intrusive methodology,has been applied to uncertainty propagation(UP) in many dynamic systems. However, the intrusive polynomial chaos method(IPCM) requires tedious modification of the governing equations, which might introduce errors and can be impractical. Alternative to IPCM, the non-intrusive polynomial chaos method(NIPCM) that avoids such modifications has been developed. In spite of the frequent application to dynamic problems, almost all the existing works about NIPCM for dynamic UP fail to elaborate the implementation process in a straightforward way, which is important to readers who are unfamiliar with the mathematics of the polynomial chaos theory. Meanwhile, very few works have compared NIPCM to IPCM in terms of their merits and applicability. Therefore, the mathematic procedure of dynamic UP via both methods considering parametric and initial condition uncertainties are comparatively discussed and studied in the present paper. Comparison of accuracy and efficiency in statistic moment estimation is made by applying the two methods to several dynamic UP problems. The relative merits of both approaches are discussed and summarized. The detailed description and insights gained with the two methods through this work are expected to be helpful to engineering designers in solving dynamic UP problems.