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

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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.