Damage detection under temperature variability using closed-loop mode shapes

Abstract

The dynamic characteristics of any structural system depend on the temperature. This poses a challenge in vibration-based damage detection, as temperature variability can mask damage-induced shifts in the vibration features. Different means for resolving the issue have been put forth, and two general method types can be distinguished; (i) those mitigating the effect of temperature variability on the features and (ii) those increasing the sensitivity to damage of the features. The present paper explores the use of features composed of closed-loop (CL) mode shapes, which combine attributes from both method groups by offering adequate sensitivity to damage and robustness to temperature variability. The CL mode shapes are designed using an eigenstructure assignment scheme formulated as a bi-objective optimization problem. The first objective is the reciprocal of the spectral norm of the CL mode shape Jacobian matrix, which is thus to be minimized to maximize the sensitivity to damage. The second objective, whose implementation hinges on the assumptions that temperature variability induces spatially uniform stiffness changes and that homogeneous sensing is employed, is a measure of how much the damping in each of the assigned CL modes deviates from a classical distribution. Since classically damped mode shapes obtained using homogeneous sensing are invariant under spatially uniform stiffness changes, the latter objective is minimized to promote robustness to temperature variability. The designed CL mode shape features can be used in any damage detection method, but in the paper we restrict the use to outlier analysis and assess the merit of the proposed scheme in the context of numerical examples. The damage detection results are compared to findings obtained using cointegration (a well-established method for mitigating the effect of temperature variability), and it is seen how the proposed scheme outperforms the cointegration-based method.