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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