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.
An intricacy in vibration-based structural damage detection (VSDD) relates to environmental variabilities imposing limitations to the damage detectability. One method that has been put forth to resolve the issue is cointegration. Here, non-stationary vibration features are linearly combined into stationary residuals, which are then employed as damage indices under the assumption that the non-stationarity is governed by environmental variabilities. In the present paper, the feasibility of using cointegration to mitigate environmental variabilities while retaining sensitivity to damage is examined through an experimental study with a steel beam. A temperature-based environmental variability is introduced to the beam by use of a heating cable, while damage is emulated by adding local mass perturbations. The vibration response of the beam in different environmental and structural states is captured and utilized as features in a cointegration-based damage detection scheme. The performance of the scheme is assessed and compared to that of a scheme not accounting for the variability on the basis of the false positive ratio (FPR), the true positive ratio (TPR), and the area under the receiver operating characteristic curve (AUC). The results show that cointegration effectively mitigates the temperature variability and allows for an improved damage detectability compared to that of the scheme without a mitigation strategy.
The recently proposed Shaped Damage Locating Input Distribution (SDLID) method locates structural damage by active interrogation with controllable inputs. The methodological premise is to shape these inputs such that certain steady-state vibration features (depending on the type of damage to be located) are rendered dormant in one subdomain at a time. As such, damage is localized when the vibration response induced by the shaped inputs in the damaged state corresponds to that stored for the reference state. Previously, the SDLID method, which operates free of system identification, has been tested through numerical simulations and, in this context, demonstrated its merits; namely, a low demand on output sensors, robustness towards noise, and conceptual simplicity. This paper presents an experimental application study, in which the SDLID method is used to locate different mass perturbations in a frame structure investigated using two actuators delivering harmonic excitation. Based on steady-state acceleration measurements, it is shown how the method succeeds in locating all the added mass perturbations.
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