Mode Shape Expansion Techniques for Model Error Localization and Damage Detection

Abstract

Abstract Several methods for mode shape expansion are investigated. The most popular methods use the dynamic equations of motions to obtain direct solutions, or use orthogonal projections. Both approaches can also be formulated as constrained optimization problems. To account for uncertainties in the measurements and in the prediction, a new expansion technique based on least squares minimization with quadratic inequality constraints (LSQI) is proposed. Each modal expansion technique is evaluated with experimental data obtained on the Micro-Precision Interferometer testbed, using both the pre-test and updated analytical models. The robustness of these methods is verified with respect to measurement noise and model error. It is shown that the proposed LSQI method has the best performance and can reliably predict mode shapes, and can be used to locate damage elements, even in very adverse situations. A new LSQI algorithm is also proposed which significantly decreases the solution time.