Abstract
For some years, there has been interest in locating cracks in beams by detecting singularities in mode shape curvatures. Most of the work in the past has depended on the estimation of spatial derivatives (smoothed or otherwise) of the experimentally measured mode shape. This problem is made difficult by the fact that numerical differentiation is notorious for amplifying measurement noise, coupled with that fact that very precise estimates of mode shapes are difficult to obtain. One recent approach, introduced by one of the authors, circumvented the noise issue via a method which did not need numerical differentiation. Briefly, the method applied a Gaussian process regression to the data, using a covariance function that could switch between spatial regions; the switch point—which indicated the crack position—could be determined by a maximum likelihood algorithm. The object of the current paper is to present an alternative approach which uses Treed Gaussian Processes (TGPs). The idea is that separate Gaussian Processes, with standard covariance functions, can be fitted over different spatial regions of the beam, with any switching points learned as part of a decision tree structure. The paper also revisits the idea of using differentiated mode shapes, on the premise that the Gaussian process can ‘see through’ the noise created and perceive the underlying structure.
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In the full implementation of the TGP code [12], all the hyperparameters are dealt with in a principled manner, including the roughness parameters. In fact the hyperparameters are represented by prior densities, which have their own hyper-hyperparameters. The result of this extra generality is that a much more complex algorithm is needed than the basic Bayesian approach outlined earlier in this section.
References
Farrar, C.R., Worden, K.: Structural Health Monitoring: A Machine Learning Perspective. Wiley, New York (2013)
Salawu, O.: Detection of structural damage through changes in frequency: a review. Eng. Struct. 19, 718–723 (1997)
Hensman, J.J., Surace, C., Gherlone, M.: Detecting mode-shape discontinuities without differentiating - examining a Gaussian process approach. In: Proceedings of 9th International Conference in Damage Assessment (DAMAS 2011), Oxford (2011)
Rasmussen, C.E., Williams, C.: Gaussian Processes for Machine Learning. The MIT Press, New York (2006)
Corrado, N., Surace, C., Montanari, L., Spagnoli, A.: Comparing three derivative discontinuities detection methods for the localisation of cracks in beam-like structures. In: Proceedings of International Workshop on Structural Health Monitoring, Palo Alto, CA (2015)
Gramacy, R.B.: Bayesian treed Gaussian process models. PhD thesis, University of California (2005)
Breiman, L., Friedman, J., Stone, C.J., Olshen, R.A.: Classification and Regression Trees. Chapman and Hall/CRC, Boca Raton (1984)
Chipman, H.A., George, E.I., McCulloch, R.E.: Bayesian CART model search. J. Am. Stat. Assoc. 93, 935–948 (1998)
Chipman, H.A., George, E.I., McCulloch, R.E.: Bayesian treed models. Mach. Learn. 48, 299–320 (2002)
Kennedy, M.C., Anderson, C.W., Conti, S., O’Hagan, A.: Case studies in Gaussian process modelling of computer codes. Reliab. Eng. Syst. Saf. 91, 1301–1309 (2006)
Becker, W.E.: Uncertainty propagation through large nonlinear models. PhD thesis, Department of Mechanical Engineering, University of Sheffield (2011)
Gramacy, R.B.: tgp: An R package for Bayesian nonstationary, semiparametric nonlinear regression and design by treed Gaussian process models. J. Stat. Softw. 19 (2007). doi:10.18637/jss.v019.i09
Qian, G.L., Gu, S.N., Jiang, J.S.: The dynamic behaviour and crack detection of a beam with a crack. J. Sound Vib. 138 (2), 233–243 (1990)
Silverman, B.W.: Density Estimation for Statistics and Data Analysis. Monographs on Statistics and Applied Probability. Chapman and Hall, London (1986)
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Civera, M., Surace, C., Worden, K. (2017). Detection of Cracks in Beams Using Treed Gaussian Processes. In: Niezrecki, C. (eds) Structural Health Monitoring & Damage Detection, Volume 7. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-54109-9_10
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