Collaborative Research: Efficient Probabilistic Approach Using Order Reduction and Hybrid Models -- A New Paradigm for Structural Dynamic Analysis

康涅狄格大学和德克萨斯农工大学合作研究的目标是开发一种新的动态分析概率框架，用于处理不确定情况下的大型结构。特别是，研究团队的目标是解决一些研究挑战，如高计算成本和难以表征模型不确定性，在这类分析中经常遇到。本研究的方法是建立在混合建模和分析策略之上，同时使用结构模态响应的计算和测量。它结合了结构动态模型降阶、贝叶斯响应预测（基于一组可行的候选模型）和多阶段递归模型更新和验证。为了实现高维系统的概率分析，将开发一个高效的自适应马尔可夫链蒙特卡罗解程序并嵌入到分析框架中。该框架允许我们同时评估结构的不确定性及其对振动响应的影响。如果成功，这项研究的结果将导致概率结构分析和基于蒙特卡罗的解决方案技术的同步进步。结构不确定性及其对振动响应的影响信息可用于指导结构产品的鲁棒设计，也可用于制定基于振动响应的在线结构监测的阈值。该研究的合作和跨学科性质将为各个层次的学生提供独特的学习机会。传播计划将使研究成果广为流传，通过在专业会议上发表论文、在经过审查的期刊上发表文章和在大学一级的课程中授课，对培训分析人员和工程师作出贡献。

The objective of this collaborative research between University of Connecticut and Texas A&M University is to develop a new probabilistic framework of dynamic analysis for handling large-scale structures under uncertainties. In particular, the research team aims at tackling a number of research challenges such as high computational cost and difficulty in characterizing model uncertainties, often encountered in this type of analysis. The approach in this research is built upon a hybrid modeling and analysis strategy, using both the computations and measurements of structural modal responses. It features the combination of structural dynamic model order-reduction, Bayesian response prediction (based on a set of viable candidate models), and recursive model updating and verification at multiple stages. To enable the probabilistic analysis of high dimensional systems, a highly efficient adaptive Markov Chain Monte Carlo solution procedure will be developed and embedded into the analysis framework. This framework allows us to evaluate simultaneously the structural uncertainties and their impact to vibration responses.If successful, the outcome of this research will lead to the concurrent advancements in both probabilistic structural analysis and Monte Carlo-based solution techniques. The information of structural uncertainties and their impact to vibration responses can be used to guide the robust design of structural products, and also be used to develop thresholds for vibration response-based online structural monitoring. The collaborative and interdisciplinary nature of the research will provide unique learning opportunities for students involved at all levels. The plan for dissemination will make results widely available, contributing to training analysts and engineers by presenting at professional conferences, publishing in refereed journals, and teaching at university-level courses.