Reconstructing coupled blade pitch moments of large wind turbines using multidimensional copula-based method

Interactions among the aerodynamic, structural and control systems of wind turbines induce nonlinear coupling of blade pitch moments and trigger load fluctuations. Most existing studies focus on single-blade pitch behavior and lack effective methods for characterizing multi-blade coupling effects. However, effectively modeling and reconstructing the coupling behavior of multi-blade pitch moments with limited SCADA data remains an unresolved challenge in current research. To address this issue, this study proposes a multidimensional Archimedean Copula-based reconstruction method to analyze the evolution of pitch moment coupling during turbine operation. The proposed method allows robust, quantitative characterization and reconstruction of pitch moment coupling using small-sample data, thereby reducing the need for long-term field testing and additional sensors.Finite-element analysis identifies the coupling characteristics of pitch moments, and copula theory is used to quantify the coupling coefficients. Using SCADA data from a southern wind farm, four typical Archimedean Copulas (Clayton, Gumbel, Frank, and Joe) are combined with the Laplace transform and empirical probability distribution to reconstruct the coupled pitch moments of three blades. Results show that Archimedean Copulas effectively characterize the probability distribution of pitch moments, with the Frank Copula providing the best fit. The reconstructed samples pass the univariate Kolmogorov–Smirnov test and the multidimensional non-parametric test, accurately reproducing the coupling evolution of pitch moments and verifying the validity of the proposed method.