Issue 48

R. S. Y. R. C. Silva et alii, Frattura ed Integrità Strutturale, 48 (2019) 693-705; DOI: 10.3221/IGF-ESIS.48.65 694 The classical methods of damage detection are based on structural vibrations. Such methods rely on the fact that dynamic characteristics, such as natural frequencies, mode shapes and damping are influenced by the stiffness of the structure [1] (see, for example, detailed studies on damage detection methods based on structural vibrations [2, 3]). The most serious limitation of those methods is the need for a structural response of the healthy structure. Methods which can detect damage with information obtained from the damage condition of the bridge alone are more appropriate for bridges since their condition before damage is rarely known [4]. It is worth mentioning that another great advantage of wavelet-based methods is that they can be applied both in dynamic responses (mode shapes and frequencies) and in static responses (displacements) [5]. The direct application of Wavelet Transform (WT) to evaluate the structural integrity of bridges has been used by many researchers, see for example [4, 6, 7, 8, 9]. Another approach is the use of damage index, as proposed by [10]. This index is obtained from the ratio between the damaged and the intact acceleration responses. So far, few tests on damaged bridges have been carried out and made available to researchers working on computational methods to detect damage in structures. Further tests are necessary to provide more data concerning structural bridge variety, different bridge materials, sizes, traffic, environmental conditions and the type of damage. More data on real tests of bridges will contribute to the improvement of the numerical procedures to effectively detect damages in structures. In this context, no conclusive and efficient method for the effective detection of damages exists. The accuracy of these methods changes with boundary conditions, bridge geometry, material type and the quality of available information. This paper proposes a new methodology to contribute to the SHM methods, using interpolation and regularization techniques to increase the number of reference points and reduce oscillations of the signal data. The proposed methodology is based on real test data and numerical data. W AVELET TRANSFORM n the last decade, the wavelet theory has been widely used in various fields of engineering; it has been applied in solving static and dynamic, linear and nonlinear problems of damage detection in structures. Damage is typically a local phenomenon which may not be apparent in the global vibration response data of the structure. Wavelet Transform (WT) is a signal processing tool that has the ability to identify even small changes in the global response of a signal [11]. Continuous wavelet transform In this paper, the wavelet transform is applied to a given signal to provide enhanced frequency–time information of the signal and use that information to detect damage [12]. Generally speaking, the usual time variable employed in classical wavelet theory can be changed to any other variable in which the signal is a function of position. In this research, the wavelet transform will be applied to a set of displacements u(x) varying along a pre-defined x-axis of a structural member. A wavelet has an average value of zero, so that the following Eq. [1] can be written: 0 (X)DX      (1) In Eq. (1), the mother wavelet   Ψ x , defined later in this paper, can be used to calculate the analyzed wavelet coefficient a,b 0 Ψ (x ) defined in the following Eq. (2). Note that the coefficient a,b 0 Ψ (x ) is defined using ‘b’, a translation parameter, and ‘a’ a dilation parameter 7 , as follows:   0 , 0 1 Ψ Ψ  a b x b x a a         (2) Scaling, as a mathematical operation, either dilates or compresses a signal. Larger scales correspond to dilated (or stretched out) signals and smaller scales correspond to compressed signals. Thus in the graphical representation of a,b 0 Ψ (x ), a little spike corresponds to a high frequency component in the signal and a large spike corresponds to a low frequency component. I