Limit laws of the empirical Wasserstein distance: Gaussian distributions

Detection and Isolation of Incipiently Developing Fault Using Wasserstein Distance

This paper develops an incipient fault detection and isolation method using the Wasserstein distance, which measures the difference between the probability distributions of normal and faulty data sets from the aspect of optimal transport. For fault detection, a moving window based approach is introduced, resulting in two monitoring statistics that are constructed based on the Wasserstein distance. From analysis of the limiting distribution under multivariate Gaussian case, it is proved that the difference measured by the Wasserstein distance is more sensitive than conventional quadratic statistics like Hotelling’s T2 and Squared Prediction Error (SPE). For non-Gaussian distributed data, a project robust Wasserstein distance (PRW) model is proposed and the Riemannian block coordinate descent (RBCD) algorithm is applied to estimate the Wasserstein distance, which is fast when the number of sampled data is large. In addition, a fault isolation method is further proposed once the incipiently developing fault is detected. Application studies to a simulation example, a continuous stirred tank reactor (CSTR) process and a real-time boiler water wall over-temperature process demonstrate the effectiveness of the proposed method.