基于梯度增强Stochastic Co-Kriging的CFD非嵌入式不确定性量化方法研究

CFD problems often come with expensive computation, high dimensionality and strong nonlinearity. This puts forward a great challenge to Non-intrusive uncertainty quantification. In order to address the problem, the study on stochastic and statistical approaches has become an inevitable trend in the future. Based on this, a statistics-based Gradient Enhanced Stochastic Co-Kriging will be proposed in this project on the basis of existing work on Stochastic Kriging by defining Mean Square Error, applying reasonable assumptions and developing strategies to solve the intrinsic and extrinsic uncertainty covariance parameters through the introduction of gradient and multi-fidelity. In the meanwhile, a three-stage sequential Design of Experiment method will be constructed based on the proposed Gradient Enhanced Stochastic Co-Kriging method to fully use of the limited computing resources, in which the criterions of Design of Experiment would be established through the integration of Mean Square Error. Moreover, the proposed method is going to bring into effect in CFD Non-intrusive uncertainty quantification, which will greatly reduce heavy computation through accurate and effective statistical predictions, and provide effective means and technical support for CFD uncertainty-based research.

CFD问题通常都具有计算量大、空间维度高和非线性效应显著的特点，这给非嵌入式不确定性量化研究提出了巨大的挑战。为了解决这一问题，开展随机方法和统计学方法的研究已成为必然的发展趋势。基于此，本项目拟在已有Stochastic Kriging建模工作的基础上，研究以统计学理论为背景的梯度增强Stochastic Co-Kriging随机代理模型，通过引入梯度和变置信度对模型均方差的定义、假设的合理运用和固有、非固有不确定性相关性参数的求解方案进行探索；同时以均方差积分为基础构建试验设计准则，发展基于该随机代理模型的三阶段序贯试验设计方法，以合理分配有限的计算资源；并将所构建方法运用于CFD非嵌入式不确定性量化问题，通过所构建随机代理模型精准高效的统计信息预测大幅缩减非嵌入式不确定性量化过程中的计算量，为基于CFD的不确定性研究提供有效手段和技术支撑。

CFD通常都具有计算量大、空间维度高和非线性效应显著的特点，这无疑给非嵌入式不确定性量化研究工作提出了巨大的挑战。为了解决此问题，开展随机方法和统计学方法为背景的理论研究已成为未来的发展趋势。因此，本课题在已有Stochastic Kriging建模工作的基础上，建立了以统计学理论为背景的Stochastic Co-Kriging代理模型，通过趋势模型的引入对模型均方差的定义、假设的合理运用和固有、非固有不确定性相关性参数的求解方案进行探索，再引入高低置信度数据，加快模型构建，获得了适用性更强的随机代理模型理论；同时基于均方差构建了采样准则，发展了基于所构建随机代理模型的序贯采样方法，进而合理分配有限的计算资源；并将所构建方法运用于CFD的非嵌入式不确定性量化问题，通过所构建方法精准高效的统计信息预测大幅缩减非嵌入式不确定性量化过程中的计算量，为基于CFD的不确定性研究工作提供高效手段和技术支撑。