Abstract
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.
Highlights
Recent forecasts show that renewable energy sources will be generating more than 25% of world’s electricity by 2035, with a quarter of this coming from wind [1]
The results show that the nonlinear quadratic deterministic trend was successfully removed in both cases
The method has been illustrated using three different time series data sets, that is, one with a nonlinear quadratic deterministic trend, another with a nonlinear exponential deterministic trend, and one experimental data set from a wind turbine drivetrain
Summary
Recent forecasts show that renewable energy sources will be generating more than 25% of world’s electricity by 2035, with a quarter of this coming from wind [1]. The cointegration approach—originally developed in the field of Econometrics in the late 1980s and early 1990s [14,15,16]—has been successfully employed as a reliable tool for dealing with the problem of operational and environmental variability in Process Engineering [17] and Structural Health Monitoring (SHM) [18,19,20,21,22,23,24] All these applications utilized the linear cointegration concept that is intimately connected with the concept of linear error correction models. The latter addresses two existing problems with heteroscedasticity and nonlinear trend removal in nonlinear cointegration method when used for trend monitoring/analysis.
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