Abstract
We develop a novel method aimed at estimating the relationship between a drifting process parameter and some operational variables of a component under fault. The method is to be used for condition monitoring and tracking, and it is based on Gaussian Process (GP) models, which are widely used Bayesian models for nonlinear regression. These models provide great flexibility for regression and the capability of quantifying uncertainty in the form of a posterior predictive distribution. Their main limitation is the difficulty to handle large data sets. For this reason, over the past decade different approximations have been proposed to reduce the computational burden, either global or local. For global approximations of time- dependent data, a proper selection of the set of inducing points is crucial for maintaining accuracy and effectiveness, while also reducing the computational costs. In this paper, we propose a strategy to select the inducing points for nonlinear regression of time-dependent data: the algorithm adaptively computes the inducing points as sparse means over moving time-windows. The time windows are selected in order to maximize the similarity between the target variable and the inputs within each window. We finally combine the sparse functional learning of inducing point positions with an approximate GP model for nonlinear regression, with the aim of estimating the relationship between the target variable and the inputs. The effectiveness of the proposed strategy is shown on a case study with real data from a Nuclear Power Plant (NPP) component.
