Modal dynamic residual-based model updating through regularized semidefinite programming with facial reduction

Abstract

Structural model updating techniques optimize model parameter values for improving the predication accuracy of a numerical model. Formulated as optimization problems, the objective of these techniques is to minimize the difference between model prediction and the experimental data. Most of these optimization problems are nonconvex, and consequently, the global optimum is very hard to solve. The sum of squares (SOS) approach and its sparse variant have been reported to relax a nonconvex polynomial optimization problem into a convex semidefinite programming (SDP) problem, which is more readily solvable. However, the corresponding convex SDP problem may fail the Slater condition qualification. The failure increases the difficulty for numerical algorithms, e.g. the interior point method, to solve the SDP problem. This paper proposes to utilize the facial reduction technique to regularize an SDP problem which fails the Slater condition qualification. In addition, the regularized SDP problem has smaller size, which helps to improve the computation efficiency. The performance of the proposed model updating approach is evaluated through a plane truss example.