Formulation and application of SMU: An open-source MATLAB package for structural model updating

Abstract

This paper describes a MATLAB package for structural model updating, named SMU. The SMU package updates parameter values of a finite element model by solving optimization problems utilizing modal properties obtained from sensor measurements. In particular, the package offers three model updating formulations, namely, (1) the modal assurance criterion value approach, (2) the eigenvector difference approach, and (3) the modal dynamic residual formulation. The first two belong to the family of modal property difference formulations. For each formulation, the analytical Jacobian derivative of the objective function is derived and implemented in SMU. Since the formulated optimization problems are generally nonconvex, the global optimality of the solution cannot be guaranteed using off-the-shelf optimization algorithms. In order to increase the chance of finding a better local minimum, the SMU package can perform gradient search from randomly generated starting points. Several examples for the model updating of as-built structures are included in the GitHub package. This paper demonstrates the SMU functionality through model updating of an 18-DOF model and a concrete building frame model.