Residual-Sensitive Fault Detection Filter
Robert H. Chen and Jason L. Speyer
Mechanical and Aerospace Engineering Department
University of California, Los Angeles, California 90095-1597
A fault detection and identiﬁcation algorithm, called the residual-sensitive fault detection
ﬁlter, is presented. The objective of the ﬁlter is to monitor certain faults called target faults
and block other faults which are called nuisance faults. This ﬁlter is derived from solving a
min-max problem which makes the residual sensitive to the target fault, but insensitive to
the nuisance faults. It is shown that this ﬁlter approximates the properties of the classical
fault detection ﬁlter such that in the limit where the weighting on the nuisance faults is zero,
the residual-sensitive fault detection ﬁlter is equivalent to the unknown input observer and
there exists a reduced-order ﬁlter. Fault detection ﬁlter designs can be obtained for both
linear time-invariant and time-varying systems.
Any system under automatic control demands a high degree of system reliability and this requires
a health monitoring system capable of detecting any system, actuator and sensor fault as it occurs
and identifying the faulty component. One approach, analytical redundancy which reduces the
need for hardware redundancy, uses a modeled dynamic relationship between system inputs and
measured system outputs to form a residual process used for detecting and identifying faults.
Nominally, the residual is nonzero only when a fault has occurred and is zero at other times.
A popular approach to analytical redundancy is the detection ﬁlter which was ﬁrst introduced
by (Beard, 1971) and reﬁned by (Jones, 1973). It is also known as the Beard-Jones fault detection
ﬁlter. A geometric interpretation of this ﬁlter is given in (Massoumnia, 1986). Design algorithms
have been developed (White and Speyer, 1987; Douglas and Speyer, 1996, 1999) which improved
detection ﬁlter robustness. The idea of a detection ﬁlter is to put the reachable subspace of each
fault into invariant subspaces which do not overlap with each other. Then, when a nonzero
residual is detected, a fault can be announced and identiﬁed by projecting the residual onto
each of the invariant subspaces. Therefore, multiple faults can be monitored in one ﬁlter.
Another related approach, the unknown input observer (Massoumnia
, 1989), simpliﬁes
the detection ﬁlter problem by dividing the faults into a target fault and nuisance fault group
where the nuisance faults are placed into one unobservable subspace. Although only one fault can
be detected in each unknown input observer, additional ﬂexibility in fault detection ﬁlter design
for robustness and time-varying system is obtained by using an approximate fault detection ﬁlter
(Chung and Speyer, 1998; Lee, 1994; Brinsmead
, 1997; Chen and Speyer, 1999).