基于不确定度的复杂过程建模与模拟的模型确认方法研究及其应用

With the rapid development of computational technique, numerical simulation is one of important role of scientific research, so people pay more and more attentions on the confidence of numerical simulating result. This project studies the method of model validation of modeling and simulation for complex process. Based on evidence and interval theory a optimal representation method is proposed for modeling and simulation of complex process. It is considered to be solved that the difficulty of constructing likelihood functions in Bayesian calibration. According to the uncertainty of numerical result and experimental data a validation metric is developed to measure the gap between the numerical result and experimental data of the complex process. At last we use the validation method to study the interface instability problem of strength material driven by detonation. The success of this project has an important role in verification and validation of our country, and also it is a beneficial reference of technique and application for modeling calibration and validation.

随着计算技术的飞速发展，数值模拟成为流体力学研究的重要手段之一，因此人们越来越关心数值模拟结果的可信度。本课题针对复杂过程的建模与模拟开展模型确认方法研究，提出基于模型标定的模型确认方法。根据证据理论和区间理论针对复杂过程的特点给出认知不确定性区间概率的的优化均值表征方法，利用近似贝叶斯计算解决复杂模型贝叶斯标定中的似然函数不能解析给出或者需要大计算量构造的难题，重点研究非点点对应数据的近似贝叶斯计算方法，基于模拟结果和实验数据的不确定度给出模型确认度量，有效量化模拟结果与实验结果的吻合程度。最终面向强度材料界面不稳定问题开展实际问题的建模与模拟模型确认研究。本课题的成功实施能够有力推动我国复杂过程建模与模拟的不确定度量化研究，为模型的标定与确认提供方法技术积累和应用研究经验。

随着计算技术的飞速发展，数值模拟成为流体力学研究的重要手段之一，因此人们越来越关心数值模拟结果的可信度。由于很多实际问题响应因素众多，因此本课题开展了基于压缩感知的稀疏重构技术研究；为了提高样本的质量，本课题提出了一种考虑响应量空间的自适应抽样策略；针对复杂物理问题本课题还建立了考虑物理信息的Kriging模型方法；基于Rosenthal距离给出了一个统一的区间变量的定义。最终针对圆筒实验、爆轰驱动的强度材料界面不稳定性问题、新冠肺炎疫情开展了应用研究，达到了预期的效果。