复杂结构数值模拟模型确认与校正的不确定性反问题理论与方法研究

复杂结构数值模拟模型的确认和校正，对于提高建模可信度，实现高精度和高可靠模拟具有重要意义。本项目针对复杂结构建模中存在的高维相关多源不确定性、嵌套求解计算量大、不适定等难点，在概率框架下研究模型确认与校正的不确定性反问题理论和方法。首先，考虑高维模型参量的概率分布及相关性，研究解析的全局敏感性分析方法，实现建模不确定性参量的重要性排序；其次，发展基于多维相关响应的模型确认准则，开发高效的不确定性传播度量算法，基于贝叶斯假设检验实现模型可信度水平的定量化评估；再次，研究基于Copula函数的多源不确定性建模方法，发展自适应代理模型技术和病态反问题的正则化方法，基于高效的不确定性计算反求算法实现模型的校正和更新；最后，将相关模型、准则和算法进行模块化集成，并开展车辆碰撞建模的应用研究。本项目的完成为有望为分析、评估和缩减建模不确定性提供一条新的研究思路，将有效提高数值模拟的准确性和工程实用性。

Model validation and model calibration for the numerical simulation of complicated structures is of great significance for improving modeling credibility and achieving high accurate and reliable simulation. Some difficulties about high-dimensional, correlative, multi-source uncertainties, large computation requirement of nested calculation and ill-posed problem will arise in the modeling of complicated structures. So in this proposal the theory and methodology of uncertain inverse problems for model validation and calibration will be researched in the framework of probability. First, the analytical method for global sensitivity analysis will be investigated when considering the probability distributions and correlations of high-dimensional model parameters, and the importance levels of uncertain model parameters will be ranked. Second, study new validation metrics for models with multiple correlated responses, develop efficient algorithm of uncertainty propagation, and achieve quantitative evaluation of modeling credibility based on Bayesian hypothesis test. Third, establish the model of multi- source based on Copula function, develop the adaptive meta-model technology and regularization method for ill-posed inverse problems, and achieve model calibration and updating based efficient computational inverse techniques. Finally, the corresponding models,metrics and algorithms will be modularized integration, and the application on modeling of vehicle collision will be study. The completion of this proposal will provide a new approach to analysis, evaluate and reduce the modelling uncertainties, and improve the accuracy and engineering practice of numerical simulation.