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On the Choice of Optimisation Scheme for Gaussian Process Hyperparameters in SHM Problems



Within Structural Health Monitoring a number of problems exist which require estimation and prediction of quantities such as load, strain, or acceleration. This can be achieved through Gaussian Process (GP) regression models, which provide a powerful framework for Bayesian machine learning. The ability of GP models to automatically return confidence intervals and not needing to specify a topology, as with Artificial Neural Networks, makes them an appealing choice in engineering problems where quantifying uncertainty is important to the model application. Although GP models are nonparametric, at the heart of the model is the optimisation of the marginal likelihood of the data with respect to the hyperparameters which govern the covariance function. Within many software packages that implement GP models, this optimisation is achieved via a conjugate gradient descent, since the derivatives of the marginal likelihood are cheap to compute once the function value is obtained. This paper investigates the effect of choice of hyperparameter optimisation scheme on the quality of fit of the model and the training time — to determine if a conjugate gradient optimisation is sufficient to identify the covariance function hyperparameters. A number of optimisation schemes are tested on synthetic data, and also on data from in-flight monitoring of aircraft dynamics. Specifically the problem of strain prediction for fatigue monitoring of a Tucano TMk1 trainer aircraft is considered. The effect of input data dimensionality on the ability of the optimisation schemes to find hyperparameters which suitably describe the data is also considered. This paper aims to begin a discussion into when the cost of more complex optimisation schemes is justified for Gaussian process hyperparameter optimisation.


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