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的这项合作研究的目标是开发一种新的概率动力分析框架，用于处理不确定条件下的大型结构。特别是，研究小组的目标是解决一些研究挑战，例如计算成本高和难以表征这类分析中经常遇到的模型不确定性。本研究中的方法建立在混合建模和分析策略的基础上，使用结构模态响应的计算和测量。它的特点是结构动力学模型降阶、贝叶斯响应预测(基于一组可行的候选模型)和递归模型更新和多阶段验证相结合。为了能够对高维系统进行概率分析，将开发一个高效的自适应马尔可夫链蒙特卡罗求解程序，并将其嵌入到分析框架中。这一框架使我们能够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求解技术的同步进步。结构不确定性及其对振动响应的影响信息可以用来指导结构产品的稳健设计，也可以用来确定基于振动响应的结构在线监测的阈值。研究的协作性和跨学科性质将为参与其中的所有级别的学生提供独特的学习机会。传播计划将广泛提供成果，通过在专业会议上发表演讲、在被推荐的期刊上发表文章以及在大学一级的课程中授课，为培训分析师和工程师做出贡献。

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.