(285g) Unification of Contribution Analysis for Process Monitoring

Abstract

Industrial processes have made successful use of
statistical methods to perform detection and diagnosis of faults [5, 9]. These
methods use statistical indices for fault detection, being the most popular the
squared prediction error (SPE), Hotelling's T² statistic and a
combination both indices [6].

Several methods have been developed for fault
diagnosis. Among these methods, contribution plots are popular and are used to
diagnose the cause of a fault by determining the contribution of each variable
to the fault detection statistics calculated [4, 5, 8]. The assumption behind
the contribution plot method is that faulty variables have high contributions
to the fault detection index. However, contribution plots not always point to
the right source of a fault, and it has been demonstrated that they do not
guarantee correct diagnosis of simple faults, which are sensor faults with very
large magnitudes [1].

Other proposed methods for fault diagnosis have been
the reconstruction-based contribution (RBC) [1], the sensor validity index
(SVI) [3], the identification index [2] and angle-information methods [7, 10].
The RBC, SVI and identification index use the reconstruction of a faulty index
along a variable direction; in this work, they will be called
reconstruction-based methods. The SVI is used to diagnose sensor faults; the
identification index is a generalization of the SVI and can be used for
diagnosis of sensor and process faults; the RBC method is also used for
diagnosis of process and sensor faults. On the other hand, angle-information
methods look at the angle between a faulty measurement and the direction of a
given variable or fault; in this work, an angle-based contribution (ABC) will
be defined and used for fault diagnosis.

Reconstruction-based and angle-based methods have
been developed under different criteria; however, in this work, it will be
shown that both kinds of methods are interrelated. Furthermore, since it has
been proven that RBC guarantees correct diagnosis of simple faults, it will be
shown that both reconstruction-based and angle-based methods guarantee correct
diagnosis of simple faults. The diagnosability analysis will be performed in a
unified way for the diagnosis methods, and a general fault detection index will
be used instead of treating each index individually. Reconstruction-based and
angle-based methods will be used to diagnose faults in an industrial polyester
process and the results will be compared.

References

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