Optimal stochastic multiple-fault detection filter

A class of robust fault detection filters is generalized from detecting single fault to multiple faults. This generalization is called the optimal stochastic multiple-fault detection filter since in the formulation, the unknown fault amplitudes are modeled as white noise. The residual space of the filter is divided into several subspaces and each subspace is sensitive to only one fault (target fault), but not to other faults (nuisance faults), in the sense that the transmission from nuisance faults to the target residual space is small while the transmission from target fault is large. It is shown that this filter approximates the properties of the classical fault detection filter such that in the limit where the nuisance fault weighting goes to infinity, the optimal stochastic multiple-fault detection filter is equivalent to the Beard-Jones fault detection filter when there is no complementary subspace. A numerical example also shows that this filter is an approximate Beard-Jones fault detection filter even when complementary subspace exists. This filter combines the advantages of the robust single-fault detection filter and Beard-Jones fault detection filter.