PSI - Issue 54

J.V. Araújo dos Santos et al. / Procedia Structural Integrity 54 (2024) 575–584 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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5. Conclusions The proposed damage indicator is based on the norm of modal strains, obtained by smoothing and differentiating the modal displacements (mode shapes) with Savitzky-Golay filters. Our study reveals that filters with a relatively low number of points are preferable since applying a filter with a large number of points result in distortions in the shape of the norm of modal strains and will lead to damage identifications with poor quality. On the other hand, the polynomial degree seems to have a lower impact on the identifications. The proposed procedure allows to identify single and multiple damage, even in the presence of moderate and low noise levels. The damage identifications quality was assessed by computing the correlation coefficient between the norm of modal strains computed based on mode shapes with and without noise. A threshold value of 0.95 for this correlation coefficient was established in view of the damage identifications quality. It was also found that effective identifications of multiple damage require higher signal-to-noise ratios than those of single damage. Acknowledgements The authors would like to acknowledge the support of FCT, through IDMEC, under LAETA, project UIDB/50022/2020. References dos Santos, J.V.A., Katunin, A., Lopes, H., 2019. Vibration-based damage identification using wavelet transform and a numerical model of shearography. International Journal of Structural Stability and Dynamics 19, 1950038. Kuo, J. E., Wang, H., Pickup, S., 1991. Multidimensional least-squares smoothing using orthogonal polynomials. Analytical Chemistry 63, 630 – 635. Lopes, H., dos Santos, J. V. A., Moreno-Garcia, P., 2019. Evaluation of noise in measurements with speckle shearography. Mechanical Systems and Signal Processing 118, 259 – 276. Moreno-García, P., Lopes, H., dos Santos, J.V.A., 2016. Application of higher order finite differences to damage localization in laminated composite plates. Composite Structures 156, 385 – 392. Nikitas, P., Pappa-Louisi, A., 2000. Comments on the two-dimensional smoothing of data. Analytica Chimica Acta 415, 117 – 125. Oliveira, T., dos Santos, J.V.A., Lopes, H., 2022. On the use of finite differences for vibration-based damage localization in laminated composite plates. International Journal of Structural Integrity 14, 57 – 73. Petyt, M., 2010. Introduction to Finite Element Vibration Analysis. Cambridge University Press: New York. Ratzlaff, K.L., Johnson, J.T., 1989. Computation of two-dimensional polynomial least-squares convolution smoothing integers. Analytical Chemistry 61, 1303 – 1305. Rosso, M.M., Aloisio, A., Melchiorre, J., Huo, F., Marano, G. C., 2023. Noise effects analysis on subspace-based damage detection with neural networks. Structures 54, 23 – 37. Rucevskis, S., Janeliukstis, R., Akishin, P., Chate, A., 2016. Mode shape-based damage detection in plate structure without baseline data. Structural Control and Health Monitoring 23, 1180 – 1193. Rucka, M., 2011. Damage detection in beams using wavelet transform on higher vibration modes. Journal of Theoretical and Applied Mechanics 49, 399 – 417. Savitzky, A., Golay, M.J.E., 1964. Smoothing and differentiation of data by simplified least squares procedures. Analytical Chemistry 36, 1627 – 1639 Uwayed, A.N., Brethee, K.F., Muhammad, S.O., 2023. Improved vibration based damage detection in laminated composite plate structures under free and forced modal analysis. European Journal of Mechanics - A/Solids 100, 105031. Yang, Z.-B., Radzienski, M., Kudela, P., Ostachowicz, W., 2017. Fourier spectral-based modal curvature analysis and its application to damage detection in beams. Mechanical Systems and Signal Processing 84, 763 – 781. Zhong, H., Yang, M., 2016. Damage detection for plate-like structures using generalized curvature mode shape method. Journal of Civil Structural Health Monitoring 6, 141 – 152.