This paper presents a probabilistic method for processing and analyzing residuals for the purpose of fault detection. The method incorporates residuals from multiple models using a hybrid dynamic Bayesian network in order to yield a low-cost, complete, diagnostic system. Continuous residuals are used as evidence directly in the network, and this paper discusses options for representing their pr...

Comparing residuals from two earthquakes is difficult because earthquake locations interact with differences in three variables: (1) the spatial location of the source; (2) the set of stations that record each earthquake; and (3) the precision of individual arrival time measurements. Effective comparisons can be made by looking only at the components the residuals from two different earthquakes...

The Conjugate Gradient (CG) method is often used to solve a positive definite linear system Ax = b. This paper analyzes two hard cases for CG or any Krylov subspace type methods by either analytically finding the residual formulas or tightly bound the residuals from above and below, in contrast to existing results which only bound residuals from above. The analysis is based on a general framewo...

This paper deals with fault detection methods taking model uncertainties into account. It focuses on dynamic and structured uncertain models, where parameter uncertainties are described by bounded variables. In order to de-couple residuals from unknown physical variables, a parity space approach is proposed, where the parity matrix depends on uncertain parameters. In this way, residuals are not...