Fault isolation for a complex decentralized waste water treatment facility

Decentralized waste water treatment facilities monitor many features that are complexly related. The ability to detect the onset of a fault and to identify variables accurately that have shifted because of the fault are vital to maintaining proper system operation and high quality produced water. Various multivariate methods have been proposed to perform fault detection and isolation, but the methods require data to be independent and identically distributed when the process is in control, and most require a distributional assumption. We propose a distribution-free retrospective change-point-detection method for auto-correlated and non-stationary multivariate processes. We detrend the data by using observations from an in-control time period to account for expected changes due to external or user-controlled factors. Next, we perform the fused lasso, which penalizes differences in consecutive observations, to detect faults and to identify shifted variables. To account for auto-correlation, the regularization parameter is chosen by using an estimated effective sample size in the extended Bayesian information criterion. We demonstrate the performance of our method compared with a competitor in simulation. Finally, we apply our method to waste water treatment facility data with a known fault, and the variables identified by our proposed method are consistent with the operators' diagnosis of the fault's cause.