Gradient-based Fuzzy Fault Isolation in Residual-based Fault Detection Systems

We introduce a fault isolation technique based on the analysis of the deformation of data-driven models produced by an incoming fault. Combining the gradients within a model, with the confidence of the model in terms of its quality influenced by the degree of violation of the uncertainty measure used in the fault detection phase allows us to successfully identify faults from the fault alarms produced by a residual-based fault-detection system relying on data-driven models. These models are built from scratch fully automatically on the basis of measurements recorded online and collected off-line in a preliminary batch phase (no physical or expert knowledge required). We used Partial Least Squares (PLS) regression and fuzzy modeling techniques with the inclusion of time lags in the input variables to establish time-varying prediction models. The deformation analysis is performed throughout the warning-models (those signaling the presence of a fault), and combines the contributions of all channels to the model prediction and then proposes a candidate faulty channel. We also introduce the concept of a Fault Isolation Likelihood Curve (FILC), inspired by the well-known Receiver Operating Characteristic (ROC) curves, in order to (i) show the isolation rates in a convenient and interpretable way and (ii) allow comparison between the detection and isolation capabilities of a fault detection system. In tandem with the FILC, we introduce the concept of the Fault Isolation Gap (FIG) as a tool for measuring the isolation capabilities of an algorithm with regards to the (fault) detection capabilities achieved by a fault detection method.