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

各种工程学科使用计算机模型来描述结构的力学和动力行为。例子包括建筑、桥梁、机身和船舶结构，跨越各种学科，包括土木、机械和航空航天工程。尽管计算机模拟结构行为已经取得了几十年的进展，但计算机模型的模拟通常与在建成结构中现场测量的响应不同。特别是当对动态结构性能感兴趣时，模拟和测量之间的差异可能是显著的。通过识别结构参数值来提高模型精度的过程称为结构模型更新。本项目将研究数值算法，通过有效地为结构模型寻找更优化的参数值来提高模型精度。这些模型更新算法在各种实际应用中都很有用。该项目具有极大提高结构在地震、爆炸、冲击等动荷载条件下的模拟响应精度的潜力。尽管许多研究工作致力于模型更新，但已知潜在的优化问题是非凸的。一般来说，现有的优化算法不能保证具有未知数量的局部最优的非凸问题的全局最优性。这个项目研究凸松弛和分支定界算法，它们可以保证解决非凸模型更新问题的全局最优性。该方法提供了最优性证明，为各种工程结构的模型更新提供了变革性的解决方案。特别是，为了找到一个高质量的低估界，我们将比较研究多个凸松弛，包括凸二次规划、半确定规划和二阶锥规划松弛。分支定界解适用于模型更新中模态属性差公式的确定性和概率两种形式。除了数值示例外，还将使用来自许多已建成结构的密集仪器传感器数据来验证模型更新算法。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.