September 2022 Parameter calibration in wake effect simulation model with stochastic gradient descent and stratified sampling
Bingjie Liu, Xubo Yue, Eunshin Byon, Raed Al Kontar
Author Affiliations +
Ann. Appl. Stat. 16(3): 1795-1821 (September 2022). DOI: 10.1214/21-AOAS1567


As the market share of wind energy has been rapidly growing, wake effect analysis is gaining substantial attention in the wind industry. Wake effects represent a wind shade cast by upstream turbines to the downwind direction, resulting in power deficits in downstream turbines. To quantify the aggregated influence of wake effects on the power generation of a wind farm, various simulation models have been developed, including Jensen’s wake model. These models include parameters that need to be calibrated from field data. Existing calibration methods are based on surrogate models that impute the data under the assumption that physical and/or computer trials are computationally expensive, typically at the design stage. This, however, is not the case where large volumes of data can be collected during the operational stage. Motivated by the wind energy application, we develop a new calibration approach for big data settings without the need for statistical emulators. Specifically, we cast the problem into a stochastic optimization framework and employ stochastic gradient descent to iteratively refine calibration parameters using randomly selected subsets of data. We then propose a stratified sampling scheme that enables choosing more samples from noisy and influential sampling regions and thus reducing the variance of the estimated gradient for improved convergence. Through both theoretical and numerical studies on wind farm data, we highlight the benefits of our variance-conscious calibration approach.

Funding Statement

The first and third authors were supported by the U.S. National Science Foundation, Division of Information and Intelligent Systems (IIS), under Grant IIS-1741166.


The authors thank the Editor, Associate Editor, and reviewers for suggestions that helped us greatly improve this manuscript. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.


Download Citation

Bingjie Liu. Xubo Yue. Eunshin Byon. Raed Al Kontar. "Parameter calibration in wake effect simulation model with stochastic gradient descent and stratified sampling." Ann. Appl. Stat. 16 (3) 1795 - 1821, September 2022.


Received: 1 October 2020; Revised: 1 July 2021; Published: September 2022
First available in Project Euclid: 19 July 2022

MathSciNet: MR4455900
zbMATH: 1498.62333
Digital Object Identifier: 10.1214/21-AOAS1567

Keywords: Jensen’s wake model , stochastic optimization , variance reduction , wind energy

Rights: Copyright © 2022 Institute of Mathematical Statistics


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Vol.16 • No. 3 • September 2022
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