Exploring Environmental and Operational Variations in SHM Data Using Heteroscedastic Gaussian Processes

  • N. DervilisEmail author
  • H. Shi
  • K. Worden
  • E. J. Cross
Conference paper
Part of the Conference Proceedings of the Society for Experimental Mechanics Series book series (CPSEMS)


The higher levels of Structural Health Monitoring (SHM)—localisation, classification, severity assessment—are only accessible using supervised learning in the data-based approach. Unfortunately, one does not often have data from damaged structures; this forces a dependence on unsupervised learning i.e. novelty detection. This means that detection is sensitive to benign environmental and operational variations (EOVs) in or around the structure. In this paper a two-stage procedure is presented: identify EOVs in training data using a nonlinear manifold approach and remove EOVs by utilising the interesting tool of heteroscedastic Gaussian processes (GPs). In Classical GPs models, the data noise is assumed to have constant variance throughout the input space. This assumption is a drawback most of the time, and a more robust Bayesian regression tool where GP inference is tractable is needed. In this work a combination of data projection and a non-standard heteroscedastic GP is presented as means of visualising and exploring SHM data.


Environmental and operational variations Manifold learning Pattern recognition Gaussian processes 



The support of the UK Engineering and Physical Sciences Research Council (EPSRC) through grant reference number EP/J016942/1 and EP/K003836/2 is gratefully acknowledged.


  1. 1.
    Dervilis, N., Antoniadou, I., Cross, E.J., Worden, K.: A non-linear manifold strategy for SHM approaches. Strain 51(4), 324–331 (2015)CrossRefGoogle Scholar
  2. 2.
    Titsias, M.K., Lázaro-gredilla, M.: Variational heteroscedastic gaussian process regression. In: Proceedings of the 28th International Conference on Machine Learning (ICML-11), pp. 841–848 (2011)Google Scholar
  3. 3.
    Dervilis, N., Choi, M., Taylor, S.G., Barthorpe, R.J., Park, G., Farrar, C.R., Worden, K.: On damage diagnosis for a wind turbine blade using pattern recognition. J. Sound Vib. 333(6), 1833–1850 (2014)CrossRefGoogle Scholar
  4. 4.
    Cross, E.J.: On structural health monitoring in changing environmental and operational conditions. Ph.D Thesis, University of Sheffield (2012)Google Scholar
  5. 5.
    Cross, E.J., Worden, K., Chen, Q.: Cointegration: a novel approach for the removal of environmental trends in structural health monitoring data. Proc. R. Soc. A Math. Phys. Eng. Sci. 467(2133), 2712–2732 (2011)CrossRefzbMATHGoogle Scholar
  6. 6.
    Figueiredo, E., Park, G., Farrar, C.R., Worden, K., Figueiras, J.: Machine learning algorithms for damage detection under operational and environmental variability. Struct. Health Monit. 10(6), 559–572 (2011)CrossRefGoogle Scholar
  7. 7.
    Cross, E.J., Manson, G., Worden, K., Pierce, S.G.: Features for damage detection with insensitivity to environmental and operational variations. Proc. R. Soc. A Math. Phys. Eng. Sci. 468(2148), 4098–4122 (2012)CrossRefGoogle Scholar
  8. 8.
    Yi, T.-H., Li, H.-N., Sun, H.-M.: Multi-stage structural damage diagnosis method based on “energy-damage” theory. Smart Struct. Syst. 12(3–4), 345–361 (2013)CrossRefGoogle Scholar
  9. 9.
    Worden, K., Cross, E.J., Antoniadou, I., Kyprianou, A.: A multiresolution approach to cointegration for enhanced SHM of structures under varying conditions–an exploratory study. Mech. Syst. Signal Process. 47(1), 243–262 (2014)CrossRefGoogle Scholar
  10. 10.
    Zheng, W., Yu, W.: Probabilistic approach to assessing scoured bridge performance and associated uncertainties based on vibration measurements. J. Bridg. Eng. 20(6), 04014089 (2014)CrossRefGoogle Scholar
  11. 11.
    Reynders, E., Wursten, G., De Roeck, G.: Output-only structural health monitoring in changing environmental conditions by means of nonlinear system identification. Struct. Health Monit. 13(1), 82–93 (2014)Google Scholar
  12. 12.
    Dervilis, N., Worden, K., Cross, E.J.: On robust regression analysis as a means of exploring environmental and operational conditions for SHM data. J. Sound Vib. 347(0), 279–296 (2015)Google Scholar
  13. 13.
    Dervilis, N., Cross, E.J., Barthorpe, R.J., Worden, K.: Robust methods of inclusive outlier analysis for structural health monitoring. J. Sound Vib. 333(20), 5181–5195 (2014)CrossRefGoogle Scholar
  14. 14.
    Cross, E.J., Koo, K.Y., Brownjohn, J.M.W., Worden, K.: Long-term monitoring and data analysis of the Tamar bridge. Mech. Syst. Signal Process. 35(1), 16–34 (2013)CrossRefGoogle Scholar
  15. 15.
    Peeters, B., Maeck, J., De Roeck, G.: Vibration-based damage detection in civil engineering: excitation sources and temperature effects. Smart Mat. Struct. 10(3), 518 (2001)Google Scholar
  16. 16.
    Alampalli, S.: Effects of testing, analysis, damage, and environment on modal parameters. Mech. Syst. Signal Process. 14(1), 63–74 (2000)CrossRefGoogle Scholar
  17. 17.
    Cornwell, P., Farrar, C.R., Doebling, S.W., Sohn, H.: Environmental variability of modal properties. Exp. Tech. 23(6), 45–48 (1999)CrossRefGoogle Scholar
  18. 18.
    Bishop, C.M.: Pattern Recognition and Machine Learning, vol. 4. Springer, New York (2006)zbMATHGoogle Scholar
  19. 19.
    Bishop, C.M.: Neural Networks for Pattern Recognition. Clarendon press, Oxford (1995)zbMATHGoogle Scholar
  20. 20.
    Nabney,. I.T.: NETLAB: Algorithms for Pattern Recognition. Springer, New York (2004)Google Scholar
  21. 21.
    Saul, L.K., Roweis, S.T.: An introduction to locally linear embedding. Available at: (2000)
  22. 22.
    Roweis, S.T., Saul, L.K.: Nonlinear dimensionality reduction by locally linear embedding. Science 290(5500), 2323–2326 (2000)CrossRefGoogle Scholar
  23. 23.
    Bourlard, H., Kamp, Y.: Auto-association by multilayer perceptrons and singular value decomposition. Biol. Cybern. 59(4), 291–294 (1988)MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Scholz, M., Vigário, R.: Nonlinear PCA: a new hierarchical approach. In: Proceedings ESANN, pp. 439–444 (2002)Google Scholar
  25. 25.
    Japkowicz, N., Hanson, S.J., Gluck, M.A.: Nonlinear auto-association is not equivalent to PCA. Neural Comput. 12(3), 531–545 (2000)CrossRefGoogle Scholar
  26. 26.
    Kramer, M.A.: Nonlinear principal component analysis using auto-associative neural networks. AlChE J. 37(2), 233–243 (1991)CrossRefGoogle Scholar
  27. 27.
    Worden, K.: Structural fault detection using a novelty measure. J. Sound Vib. 201(1), 85–101 (1997)MathSciNetCrossRefGoogle Scholar
  28. 28.
    Tarassenko, L., Nairac, A., Townsend, N., Buxton, I., Cowley, P.: Novelty detection for the identification of abnormalities. Int. J. Syst. Sci. 31(11), 1427–1439 (2000)CrossRefzbMATHGoogle Scholar
  29. 29.
    Rasmussen, C.E., Williams, C.K.I.: Gaussian Processes for Machine Learning.MIT, Cambridge (2006)Google Scholar
  30. 30.
    De Roeck, G.: The state-of-the-art of damage detection by vibration monitoring: the SIMCES experience. J. Struct. Control 10, 127–134 (2003)CrossRefGoogle Scholar

Copyright information

© The Society for Experimental Mechanics, Inc. 2016

Authors and Affiliations

  1. 1.Dynamics Research Group, Department of Mechanical EngineeringUniversity of SheffieldSheffieldUK

Personalised recommendations