Optimal Spatiotemporal Reduced Order Modeling for Nonlinear Structural Dynamics

该项目的总体目标是制定最佳的，数据驱动的，降低顺序建模（ROM）框架，以显着更快和更准确的非线性动力系统的计算预测。建模框架以最优预测形式为基础，以相关时空相关性的形式包含信息。为了实现整个项目目标，工作将a)将该方法应用于变分（弱）形式，b)使用ROM方法和完全解决的模拟，研究非线性结构动力学中的两个问题，这些问题预计会表现出复杂的空间和时间（尺度）特征。研究的两个具体问题是：1)各向同性板振动的湍流行为和2)具有各向异性本构关系的三维连续体的振动特性。降阶建模是工程设计过程中不可或缺的一部分，因为完全解析的仿真仍然过于昂贵，无法用于参数化和优化研究。该工作提供的减少订单模拟的进展将对提供快速可靠的模拟的能力产生重大影响，以帮助新工程产品的创新。项目产生的结果和想法将通过同行评议的出版物和出席会议的方式传播。为了向学生介绍降阶模拟的重要概念，俄克拉荷马大学将开设一门新的研究生课程。为了进一步扩大这项工作的影响，将积极征聘人数不足的群体（一般本科生、妇女和少数民族学生）直接参加研究活动，并通过一门新课程间接参加。

The overall goal of this project is to formulate optimal, data driven, reduced order modeling (ROM) frameworks for significantly faster and more accurate computational predictions of nonlinear dynamical systems. The modeling framework is based upon the optimal prediction formalism and includes information in the form of relevant spatiotemporal correlations. To achieve the overall project goal, the work will a) apply the method to variational (weak) forms and b) investigate, using the ROM methodology and fully resolved simulation, two problems in nonlinear structural dynamics which are expected to exhibit complex spatial and temporal (scale) characteristics. The two specific problems to be investigated are: 1) turbulent behavior of isotropic plate vibration and 2) vibration characteristics of three-dimensional continua with anisotropic constitutive relationships.Reduced order modeling is an integral part of the engineering design process as fully resolved simulation is still too expensive to be practical for parametric and optimization studies. The advances in reduced order simulation provided by the work will have significant impact on the ability to provide fast and reliable simulation to aid in the innovation of new engineering products. Results and ideas generated from the project will be disseminated through peer-reviewed publication and conference attendance. In order to introduce students to the important concept of reduced order simulation, a new graduate level course on the subject will be developed at The University of Oklahoma. To further broaden the impact of the work, underrepresented groups (undergraduates in general, women and minority students) will be actively recruited to participate both directly in the research activities and indirectly through a new course.