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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 978156, 11 pages
Research Article

Nonlinear Cointegration Approach for Condition Monitoring of Wind Turbines

1Department of Robotics and Mechatronics, AGH University of Science and Technology, Aleja Mickiewicza 30, 30-059 Krakow, Poland
2Institute of Mathematics, Jagiellonian University, Ulica Prof. Stanisława Łojasiewicza 6, 30-348 Krakow, Poland

Received 16 April 2015; Revised 14 July 2015; Accepted 22 July 2015

Academic Editor: Yan-Jun Liu

Copyright © 2015 Konrad Zolna et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Monitoring of trends and removal of undesired trends from operational/process parameters in wind turbines is important for their condition monitoring. This paper presents the homoscedastic nonlinear cointegration for the solution to this problem. The cointegration approach used leads to stable variances in cointegration residuals. The adapted Breusch-Pagan test procedure is developed to test for the presence of heteroscedasticity in cointegration residuals obtained from the nonlinear cointegration analysis. Examples using three different time series data sets—that is, one with a nonlinear quadratic deterministic trend, another with a nonlinear exponential deterministic trend, and experimental data from a wind turbine drivetrain—are used to illustrate the method and demonstrate possible practical applications. The results show that the proposed approach can be used for effective removal of nonlinear trends form various types of data, allowing for possible condition monitoring applications.