The Temporal Overfitting Problem with Applications in Wind Power Curve Modeling

Abstract

This article is concerned with a nonparametric regression problem in which the input variables and the errors are autocorrelated in time. The motivation for the research stems from modeling wind power curves. Using existing model selection methods, like cross-validation, results in model overfitting in presence of temporal autocorrelation. This phenomenon is referred to as temporal overfitting, which causes loss of performance while predicting responses for a time domain different from the training time domain. We propose a Gaussian process (GP)-based method to tackle the temporal overfitting problem. Our model is partitioned into two parts—a time-invariant component and a time-varying component, each of which is modeled through a GP. We modify the inference method to a thinning-based strategy, an idea borrowed from Markov chain Monte Carlo sampling, to overcome temporal overfitting and estimate the time-invariant component. We extensively compare our proposed method with both existing power curve models and available ideas for handling temporal overfitting on real wind turbine datasets. Our approach yields significant improvement when predicting response for a time period different from the training time period.

KEYWORDS:

• Autocorrelation
• Gaussian process
• Nonparametric regression
• Time series

5 Supplementary Materials

Supplementary Material: The PDF file contains: (S1) Results for Case Study II with different covariance functions, (S2) PACF plots for WT1, (S3) Hyperparameter estimates, (S4) Actual RMSEs for Case Study II, (S5) Prediction intervals for select turbines, and (S6) Experiments on a simulated function.

Computer Code: The computer code to reproduce all the results in this article are available on GitHub at https://github.com/TAMU-AML/tempGP-Paper. A generic R function for applying the tempGP algorithm to any dataset is available in DSWE package in R available through CRAN at https://CRAN.R-project.org/package=DSWE.

Acknowledgments

The authors would like to thank the Editor, the Associate Editor and the Reviewers for providing valuable feedback. Their comments has led to a significant improvement in the article. The authors would also like to thank Texas A&M’s high performance research computing (HPRC), which enabled the authors to efficiently run their experiments.

Funding

Prakash and Ding’s research is partially supported by NSF IIS-1741173; Tuo’s research by NSF DMS-1914636; and Ding and Tuo’s research also by NSF grant CCF-1934904.

Additional information

Funding

Prakash and Ding’s research is partially supported by NSF IIS-1741173; Tuo’s research by NSF DMS-1914636; and Ding and Tuo’s research also by NSF grant CCF-1934904.