15 Exploring Environmental and Operational Variations in SHM Data Using Heteroscedastic Gaussian Processes 151 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 First component 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 Second component Mean prediction Confidence intervals Fig. 15.9 Heteroscedastic GP prediction of the 2nd component based on 1st component for the AANN manifold -5 -4 -3 -2 -1 0 1 2 3 LLE second component -1.5 -1 -0.5 0 0.5 1 1.5 AANN first component Mean prediction Confidence intervals Fig. 15.10 Classical GP prediction of the 1st component for the AANN manifold component based on 2nd component of the LLE manifold As an extra step one can “play” with several regression combinations, not only between the unfolded manifold branches of the same algorithm but also to make inferences between revealed manifolds of different methodologies as can be in seen in Fig. 15.10, 15.11 where GPs predict components based on components of different manifolds and in this case between LLE and AANN. Here, again the performance of the classical GP is very poor compared to heteroscedastic GP as it masks the fault’s indication. 15.6 Conclusion The purpose of this paper is to highlight the key utility of some specific machine learning methods, not only for novelty detection analysis but also as a method of investigating the uncertainty of the space where data clusters are lying. The main benefit of the heteroscedastic GP approach taken here is that gives more robust determination regarding the presence or absence of novelty when the normal condition set is under the suspicion that it may already include multiple abnormalities due to benign variations.
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