The present work addresses the problem of missing data in multidimensional time series such as those collected during operational transients in industrial plants. We propose a novel method for missing data reconstruction based on three main steps: (1) computing a fuzzy similarity measure between a segment of the time series containing the missing data and segments of reference time series; (2) assigning a weight to each reference segment; (3) reconstructing the missing values as a weighted average of the reference segments. The performance of the proposed method is compared with that of an Auto Associative Kernel Regression (AAKR) method on an artificial case study and a real industrial application regarding shut-down transients of a Nuclear Power Plant (NPP) turbine. number of reference trajectories index of the reference trajectories number of dimensions of a trajectory index of the signal m-th reference trajectory time length of a reference trajectory time index value of signal j of trajectory m at time k test trajectory signal with missing data length of the time window with missing data present time in the test trajectory value of signal j at time k ≤ t in the test trajectory reconstruction of a missing datum time length used for the similarity computation segment of the most recent L t measurements of signal j in the test trajectory segment of length L t of signal j which ends at time k in reference trajectory m squared Euclidean distance between the monodimensional segment x ¯ m tr ( k , j ) and x ¯ t ( j ) squared Euclidean distance between X ¯ ¯ and the k-th segment of the m-th reference trajectory membership function value of the “approximately zero” fuzzy set computed in δ m 2 ( k ) parameter of μ m (k) parameter of μ m (k) distance score between X ¯ ¯ and the k-th segment of the m-th reference trajectory weight given to the k-th segment of the m-th reference trajectory 
Reconstruction of missing data in multidimensional time series by fuzzy similarity