Analytic Confusion Matrix Bounds for Fault Detection and Isolation Using a Sum-of-Squared-Residuals Approach

Given a system which can fail in 1 of n different ways, a fault detection and isolation (FDI) algorithm uses sensor data to determine which fault is the most likely to have occurred. The effectiveness of an FDI algorithm can be quantified by a confusion matrix, also called a diagnosis probability matrix, which indicates the probability that each fault is isolated given that each fault has occurred. Confusion matrices are often generated with simulation data, particularly for complex systems. In this paper, we perform FDI using sum-of-squared residuals (SSRs). We assume that the sensor residuals are s-independent and Gaussian, which gives the SSRs chi-squared distributions. We then generate analytic lower, and upper bounds on the confusion matrix elements. This approach allows for the generation of optimal sensor sets without numerical simulations. The confusion matrix bounds are verified with simulated aircraft engine data.