Nonlinear compensation algorithm for multidimensional temporal data: A missing value imputation for the power grid applications

Abstract In smart grid, the missing values do influence the real-time grid monitoring and bring biases of conclusions from the grid data mining. From the analysis on the data from smart grid, every variable shows global variation and local variation. Based on these characters, a novel statistical and machine learning-based imputation method is proposed, taking advantage of the global trend capturing by one-dimension interpolation of the variable of interest and the local variation capturing by linear compensation of multidimensional variables. By using KCPA, the multidimensional nonlinear variables are mapped into a feature space, and obtained new variables linearly couple with the variable of interest. Then these new variables together with the multidimensional linear variables are used for that linear compensation. The comparative experiment indicates that the proposed method outperforms the commonly used methods by reducing the RMSE by 29.19% and MAE by 44.73% on average, and having the best R 2 closest to 1. A test on public dataset shows that the proposed method still has a good performance. At last, the sensitivity analysis on missing rate shows that the imputation error of the proposed methods remains steady for all the variables with the increase of missing rates from 5% to 10%.