Ahmadreza Chokhachian

Ahmadreza Chokhachian, V. Roshan Joseph, Yu Ding

Accurate modeling of wind turbine power curves is crucial for optimal wind farm operation. Nearly all existing power curve models focus on temporal variables such as wind speed and temperature while overlooking the influence of terrain covariates, which governs inflow wind conditions and thus also affects wind power production. This paper proposes a nonparametric spatio-temporal Gaussian process model that integrates temporal environmental covariates with spatial terrain features. The model falls in the category of spatial-temporal Gaussian process models with data on a grid. The challenge to be addressed is that the spatio-temporal modeling require certain temporal alignment among the data, a property that the wind farm data does not have. Our solution strategy is to construct a shared representative temporal covariate set which not only aligns the temporal inputs but also has a size an order of magnitude smaller than the original data size. With this transformation, our resulting model is able to employ a separable kernel structure that captures both spatial and temporal dependencies. Empirical analysis on a real wind farm dataset shows that our method improves predictive accuracy over existing baselines and can be used to quantify the various impact of the terrain characteristics on turbine performance.

Ahmadreza Chokhachian, Matthias Katzfuss, Yu Ding

This paper is concerned with the problem of how to speed up computation for Gaussian process models trained on autocorrelated data. The Gaussian process model is a powerful tool commonly used in nonlinear regression applications. Standard regression modeling assumes random samples and an independently, identically distributed noise. Various fast approximations that speed up Gaussian process regression work under this standard setting. But for autocorrelated data, failing to account for autocorrelation leads to a phenomenon known as temporal overfitting that deteriorates model performance on new test instances. To handle autocorrelated data, existing fast Gaussian process approximations have to be modified; one such approach is to segment the originally correlated data points into blocks in which the blocked data are de-correlated. This work explains how to make some of the existing Gaussian process approximations work with blocked data. Numerical experiments across diverse application datasets demonstrate that the proposed approaches can remarkably accelerate computation for Gaussian process regression on autocorrelated data without compromising model prediction performance.