New dynamics concepts for vibration-based damage detection: wavelet modal curvatures

Modal curvatures are widely used in damage detection in beams and plates, allowing not only indication of damage occurrence but also determination of damage location, with no need for prior knowledge of the structure being inspected. Notably, however, modal curvatures have an intrinsic deficiency of susceptibility to noise involved in measurement, the noise effect easily masking genuine damage feature in the modal curvature. To overcome this deficiency, a new philosophy of adopting wavelet transform theory to create wavelet modal curvatures is formulated, from which a series of new concepts are derived, including 1D wavelet modal curvature, 2D wavelet modal curvature, and complex wavelet modal curvature. The multiscale property of wavelets endows these newly developed modal curvatures with the predominant characteristics of robustness against noise together with intensification of slight damage. A set of experimental cases is provided to demonstrate the capability of wavelet modal curvatures to identify complex damage in aluminum and composite structures

Effective filtering of modal curvatures for damage identification in beams

In this work, we investigate the effectiveness of a damage identification technique recently proposed in [1] and assess how it is affected by the number and position of the sensors used. Mode shapes and curvatures have been claimed to contain local information on damage and to be less sensitive to environmental variables than natural frequencies. It is known that notch-type damage produces a localized and sharp change in the curvature that unfortunately could be difficult to detect experimentally without the use of an adequate number of sensors. However, we have recently shown that even a coarse description of the modal curvature can still be employed to identify the damage, provided that it is used in combination with other modal quantities. Here, by exploiting the perturbative solution of the Euler-Bernoulli equation, we consider the inverse problem of damage localisation based on modal curvatures only and we ascertain the feasibility of their sole use for recostructing the damage shape. To do so, we set up a filtering procedure acting on modal curvatures which are expressed in a discrete form enabling further investigation on the effect of using a reduced number of measurement points. The sensitivity of the procedure to damage extension is further assessed

Numerical and experimental assessment of the modal curvature method for damage detection in plate structures

Use of modal curvatures obtained from modal displacement data for damage detection in isotropic and composite laminated plates is addressed through numerical examples and experimental tests. Numerical simulations are carried out employing COMSOL Multiphysics as finite element solver of the equations governing the Mindlin-Reissner plate model. Damages are introduced as localized non-smooth variations of the bending stiffness of the baseline (healthy) configuration. Experiments are also performed on steel and aluminum plates using scanning laser vibrometry. The obtained results confirm that use of the central difference method to compute modal curvatures greatly amplifies the measurement errors and its application leads to unreliable predictions for damage detection, even after denoising. Therefore, specialized ad hoc numerical techniques must be suitably implemented to enable structural health monitoring via modal curvature changes. In this study, the Savitzky-Golay filter (also referred to as least-square smoothing filter) is considered for the numerical differentiation of noisy data. Numerical and experimental results show that this filter is effective for the reliable computation of modal curvature changes in plate structures due to defects and/or damages

Modal curvature-based damage localization in weakly damaged continuous beams

Abstract Modal curvatures have been claimed to contain local information on damage and to be less sensitive to environmental variables than natural frequencies. However, simply using the difference between modal curvatures in the undamaged and damaged states can result into localization errors, due to the complex pattern that this quantity presents when considering broad damages or higher order modes. In this paper, we consider weakly damaged continuous beam and we exploit a perturbative solution of the beam equation of motion to obtain an analytical expression of the modal curvature variations in terms of damage distribution. The solution is then used to introduce a filtering technique of the modal curvature variation and to set up the inverse problem of damage localization based on modal curvatures only. Using numerical examples and experimental tests, we show that modal curvatures can be used for precise damage localization, once properly filtered

Numerical and experimental assessment of the modal curvature method for damage detection in plate structures

This paper is concerned with the use of numerically obtained modal curvatures for damage detection in both isotropic and composite laminated plates. Numerical simulations are carried out by using COMSOL Multiphysics as FEM solver of the governing equations, in which a Mindlin-Reissner plate model is assumed and defects are introduced as localized smoothed variations of the baseline (healthy) configuration. Experiments are also performed on steel and aluminum plates using scanning laser vibrometry. This study confirms that the central difference method greatly amplifies the measurement errors and its application leads to ineffective predictions for damage detection, even after denoising. As a consequence, different numerical techniques should be explored to allow the use of numerically obtained modal curvatures for structural health monitoring. Herein, the Savitzky-Golay filter (or least-square smoothing filter) is considered for the numerical differentiation of noisy data

Damage identification in a concrete beam using curvature difference ratio

Previous studies utilising changes in mode shape or curvature to locate damage rely on the fact that the greatest change occurs around the defect. However, in concrete beams this fact is undermined due to the nature of the defect as distributed multi-site cracks. In addition, differences in mode shape and curvature as ways to locate the damage is unstable because of occurrence of modal nodes and inflection points. In this paper, one interesting solution to this problem is being tested by establishing a new non-dimensional expression designated the 'Curvature Difference Ratio (CDR)'. This parameter exploits the ratio of differences in curvature of a specific mode shape for a damaged stage and another reference stage. The expression CDR is reasonably used to locate the damage and estimate the dynamic bending stiffness in a successively loaded 6m concrete beam. Results obtained by the proposed technique are tested and validated with a case study results done by Ren and De Roeck [1] also by Maeck and De Roeck [2]. Another contribution of this work is that relating changes in vibration properties to the design bending moment at beam sections as defined in Eurocode 2 specifications [3]. Linking between a beam section condition and the change in vibration data will help to give a better comprehension on the beam condition than the applied load

Vortex-induced vibration of catenary riser: reduced-order modeling and lock-in analysis using wake oscillator

A new reduced-order model capable of analyzing the vortex-induced vibration of catenary riser in the ocean current has been developed. This semi analytical-numerical approach is versatile and allows for a significant reduction in computational effort for the analysis of fluid-riser interactions. The incoming current flow is assumed to be steady, uniform, unidirectional and perpendicular to the riser plane of initial equilibrium curvatures

The minimum variance distortionless response beamformer for damage identification using modal curvatures

This study presents a damage identification procedure in beams based on the use of beamforming algorithms, which are mostly utilized in inverse problems of source identification and image reconstruction. We choose the modal curvatures as observed quantities and compare the performance of the Bartlett beamformer, minimum variance distortionless response (MVDR) processor, and of a conventional objective function based on the modal curvatures. By means of a set of experiments, we show that the MVDR processor can overcome some of the difficulties encountered with other estimators, especially in cases of slight damage, or damage located between two sensors

Nonlinear multi-mode interactions in subsea risers undergoing vortex-induced vibrations

This paper investigates nonlinear multi-mode interactions in subsea risers undergoing vortex-induced vibrations based on a computationally efficient reduced-order fluid-structure interaction model. Cross-flow responses as a result of a steady uniform current are considered. The geometrically nonlinear equations of riser motion are coupled with nonlinear wake oscillators which have been modified to capture the effect of initial curvatures of curved cylinder and to approximate the space-time varying hydrodynamic lift forces. The main objectives are to provide new insights into the vortex-induced vibration characteristics of risers under external and internal resonances and to distinguish nonlinear dynamic behaviors between curved catenary and straight toptensioned risers. The analyses of multi-mode contributions, lock-in regimes, response amplitudes, resonant nonlinear modes and curvatures are carried out and several interesting aspects are highlighted