Fault detection based on optimal transport theory

Most of the existing methods for fault detection are residual-based, i.e., they reconstruct the expected values of the signals in normal condition by using large amounts of data collected in the past and require to formulate hypotheses on the distributions. Since in many industrial applications the available data do not cover all the possible operating conditions and data distributions are unknown, their performance can be unsatisfactory. In this work, we propose a data-driven fault detection method based on Optimal Transport (OT). The Wasserstein distance between the distribution of the signals measured under the current conditions and a baseline distribution derived from the signals measured under normal conditions is used as abnormality score, and the OT solution is computed using the Cumulative Distribution Transform (CDT). The proposed method is verified considering a real bearing dataset. The performance of the detection is evaluated in terms of missed and false alarm rates, and compared to that of other traditional fault detection methods.