(268e) Parity Space Based Fault Detection Schemes Using Subspace Approaches

The use of multivariate statistical methods such as principal component analysis (PCA) for fault detection and isolation (FDI) received significant attention recently. Originally proposed as a quality monitoring technique in Jackson and Mudholkar (1979) and process monitoring method in Kresta et al. (1991), these methods are applied to a variety of process monitoring problems and sensor validation based on normal process data. Fault diagnosis is made possible by the use of contribution plots (Miller et al., 1993) and a sensor validity index (SVI), (Dunia et al., 1996), and fault identification index (Dunia and Qin, 1998). Gertler et al. (1999) uses a bank of PCA models to enhance fault isolation, similar to the design of a fault incidence matrix. Qin and Li (1999) improve the structured residual approach to fault identification (Gertler and Singer, 1990) with maximized sensitivity for fault isolation. These approaches provide explicit design methods for FDI.

While the multivariate statistical monitoring methods are easy to apply since they only make use of process data, they are inherently steady state methods that can cause false alarms in a dynamically operated process. To deal with dynamic processes, in Ku et al., 1995 a dynamic PCA (DPCA) is discussed by including time lagged variables in PCA. This extension, however, gives poor dynamic models as demonstrated in Negiz and Cinar (1997) and Li and Qin (2001).

To build a sound dynamic model from process data, subspace identification methods (SIM) are promising alternatives to PCA (Overschee and De Moor, 1996). Among these SIM algorithms are the canonical variate analysis (CVA, Larimore 1983, 1990), N4SID (Van Overschee and De Moor, 1994), MOESP (Verhaegen and Dewilde, 1992), and the use of parity space and PCA (SIMPCA, Wang and Qin, 2002, 2006). SIM offers consistent estimate of state-space models, e.g., the state space matrices {A, B, C, D} for multivariable dynamic systems with proper selection of the system order. A typical SIM contains two steps: (1) identification of the extended observability matrix and/or the state sequence; and (2) calculation of {A, B, C, D}. While most SIM approaches appear as numerical algorithms, statistical properties such as consistency have also been explored (Bauer et al., 1999; Deistler et al., 1995; Heij and Scherrer, 1999; Jansson and Wahlberg, 1998). The error-in-variables (EIV) situation can be considered as well (Li and Qin, 2001; Chou and Verhaegen, 1997; Huang et al., 2005).

The SIM formulation is attractive not only because of its numerical simplicity and stability, but also for its general state space form. The SIM state space formulation allows not only the implementation of FDI schemes designed totally in the well known model-based approaches, but also, designed totally in the data-based approaches, which provides great flexibility for comparing and analyzing various methods. In Qin and Li, 2001; Lin and Qin, 2005, it is presented the use of SIM for the implementation of an FDI scheme designed in the framework of Parity Space.

This work presents different forms of subspace based residual generators obtained in the parity space approach. The set of residual generators can be divided into two subsets: (i) the ones based in the conventional approach of decoupling the initial states (Chow and Willski, 1984; Qin and Li, 2001); and (ii) those based in avoiding such decoupling of states. Though the general performance of all of the residual generators is similar, in this paper it is highlighted the subtle features of each residual generator, e.g. some have the ability to yield white residuals which is valuable to specify reliable control limits. Two examples are considered here, a 4x4 MIMO system and a VTOL aircraft system. By means of simulations it is shown how the particular features in the dynamics of the VTOL aircraft system affect the performance of the residual generators based in the conventional approach while such situation is overcome by the remaining residual generators.

It is also important to note that with the SIM formulation the proposed residual generators can be identified in a direct way from noisy input-output data (EIV problem), instead of explicitly identify the system matrices {A, B, C, D}.

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