Frequency-Domain Model Updating through Branch and Bound with Convex Relaxation

通过凸松弛的分支定界更新频域模型

• 批准号: 2211343
• 负责人: Yang Wang
• 金额: $ 64.98万
• 依托单位: Georgia Tech Research Corporation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-01-01 至 2025-12-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2211343&HistoricalAwards=false
• 关键词: Frequency; Domain; Model; Updating; through

A variety of engineering disciplines use computer models to describe the mechanical and dynamical behavior of structures. Examples include buildings, bridges, airframes, and ship structures, spanning various disciplines including civil, mechanical, and aerospace engineering. Despite decades of progress in computer simulation of structural behaviors, simulation by a computer model usually differs from the response measured in-situ at the as-built structure. Particularly when dynamic structural performance is of interest, the difference between simulation and measurement can be significant. The process of improving model accuracy by identifying structural parameter values is termed structural model updating. This project will study numerical algorithms that can improve model accuracy by effectively finding more optimized parameter values for the structural model. These model updating algorithms can be useful in a variety of real applications. This project has the potential to greatly improve the accuracy of simulation response of structures subject to dynamic loading conditions such as earthquake, blast, and impacts.Although many research efforts have been dedicated to model updating, the underlying optimization problems are known to be non-convex. In general, off-the-shelf optimization algorithms cannot guarantee global optimality of a non-convex problem that has unknown number of local optima. This project investigates convex relaxation and branch-and-bound algorithms that can guarantee global optimality toward solving non-convex model updating problems. Providing an optimality certificate, the approach offers transformative solutions for the model updating of various engineering structures. In particular, to find a high-quality underestimating bound, multiple convex relaxations will be comparatively studied, including the convex quadratic, the semi-definite programing, and the second-order cone programing relaxations. The branch-and-bound solution is applicable to both deterministic and probabilistic versions of the modal property difference formulation in model updating. In addition to numerical examples, densely instrumented sensor data from a number of as-built structures will be used to validate the model updating algorithms.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

各种工程学科使用计算机模型来描述结构的机械和动力学行为。 例如，建筑物，桥梁，飞机场和船舶结构，涵盖了各种学科，包括民用，机械和航空航天工程。 尽管在计算机模拟结构行为方面进行了数十年的进展，但计算机模型的仿真通常与在原始结构下测得的原位响应不同。 特别是在感兴趣的动态结构性能时，模拟和测量之间的差异可能很大。 通过识别结构参数值来提高模型准确性的过程称为结构模型更新。 该项目将研究数值算法，通过为结构模型找到更优化的参数值，可以提高模型准确性。 这些模型更新算法在各种真实应用程序中可能很有用。 该项目有可能极大地提高受动态载荷条件（例如地震，爆炸和影响）结构的模拟响应的准确性。尽管许多研究工作已致力于建模更新，但已知潜在的优化问题是非 - 凸。 通常，现成的优化算法无法保证非凸局问题的全局最优性，该问题的本地优化数量未知。 该项目调查了凸放松和分支结合算法，这些算法可以保证全球最优性，以解决非凸模型更新问题。 该方法提供了最佳证书，为各种工程结构的模型更新提供了变革性解决方案。 特别是，要找到高质量的界限，将对多个凸松弛进行相对研究，包括凸二次，半定义编程和二阶锥形编程松弛。 分支结合的解决方案适用于模型更新中模态属性差异公式的确定性和概率版本。 除了数字示例外，还将使用来自许多未建造的结构的密集仪器传感器数据来验证更新算法的模型。该奖项反映了NSF的法定任务，并被认为是通过基金会的知识分子和广泛的评估来支持的支持影响审查标准。