爆轰驱动问题数值模拟不确定度量化方法研究

Numerical simulation of detonation driven problems has been witnessed its role under substantial and far-reaching transition. The traditional role is to reproduce experiment results and improve in-depth understanding of the mechanisms underlying complex processes. The new trend is to improve the credibility for numerical simulation to support design optimizations and overall performance assessments of complex engineering facilities, the core of which is the effective methodology for uncertainty quantification (UQ). Following the UQ requirements for the numerical simulation of detonation problems, this project will develop the general methods for unified metrics of both aleatory and epistemic uncertainty under the frame of evidence theory. The polynomial chaos method with high precision and robust multi-resolution wavelet method will be combined for effective uncertainty quantification with the help of adaptive decomposition of stochastic space for smooth or discontinuous stochastic problems. We will improve the precision of interpolation and fitting methods to form an effective stochastic collocation approach for uncertainty quantification for arbitrary domain in multidimensional stochastic space. This approach has the advantage of reuse of the already existed data samples, which is very important for practical engineering problems where the data sample is quite costly. All the above UQ methods will be applied to practical detonation problems to determine the key input stochastic parameters as well as their contributions to the uncertainties of overall outputs. All the efforts of this project would provide a flexible, robust and effective UQ approach for engineering problems.

爆轰驱动数值模拟的作用正在发生深远的转变，其主要标志是从传统的重复实验结果、加深对复杂过程机理的认识，逐渐转到建立高置信度数值模拟能力以支持复杂工程装置优化设计和总体性能评估，而高置信度数值模拟的核心问题是建立有效的不确定度量化分析方法。本项目密切结合爆轰驱动问题数值模拟应用背景，在证据理论框架下发展完善认知和随机不确定性的统一表征度量方法；充分利用非嵌入式多项式混沌方法高精度和多分辨率小波方法鲁棒性特点，建立基于随机空间自适应局域细分、能有效处理间断现象的不确定度量化分析方法；深入研究能够复用已有数据点的高精度插值/拟合方法，形成适用于任意局域随机空间、基于多维散点插值/拟合的不确定度量化分析能力；运用上述方法开展典型爆轰驱动问题不确定度量化评估应用研究，确定主要影响因素及其对数值模拟结果整体不确定度的贡献，为实际工程数值模拟提供灵活、健壮、有效的不确定度量化分析手段。

爆轰驱动数值模拟的作用正在发生深远的转变，其主要标志是从传统的重复实验结果、加深对复杂过程机理的认识，逐渐转到建立高置信度数值模拟能力以支持复杂工程装置优化设计和总体性能评估，而高置信度数值模拟的核心问题是建立有效的不确定度量化分析方法。本项目密切结合爆轰驱动问题数值模拟应用背景，重点开展了基于实验数据的贝叶斯模型参数标定方法研究、多项式混搭理论研究、全局敏感性分析等不确定度量化理论研究。特别是利用贝叶斯参数标定方法开展了炸药爆轰驱动飞片试验、圆筒试验、柱面爆轰驱动金属界面不稳定性试验研究，利用试验数据、模拟数据获得了物理模型参数，参数得到实验的确认，说明了贝叶斯参数标定方法在确定炸药参数方面的有效性。本项目研究的不确定度量化方法理论为实际工程数值模拟提供灵活、健壮、有效的分析手段。