Invariant system description of the stochastic realization

Statistical monitoring of multivariable dynamic processes with state‐space models

“…Several methods have been proposed for selecting the value of n. The ratio of the specific singular value to the sum of all the singular values provides a popular selection criterion (Aoki, 1990). An information theoretic approach, such as the Akaike information criterion (AIC), is also used frequently (Candy et al, 1979;Larimore, 1993). Both the inspection of the relative magnitude of singular values and the AIC criteria have been used in our studies for selecting n. While the ad hoc nature of the former approach may cause some arbitrariness in order selection, both approaches have given similar results in our studies.…”

“…K is chosen to be the maximum significant lag, after which the autocorrelation of autoregressive model residuals of all the variables becomes insignificant. In the information theoretic approach (Candy et al, 1979;Larimore, 1993) there is no penalty to the minimization criterion in terms of J or K . The parametrization penalty term includes the number of inputs, outputs, and the order of the system (number of state variables n).…”

Fault detection in dynamic processes using a simplified monitoring-specific CVA state space modelling approach

“…The origin of Eq. (41) is tied to the number of parameters required to parameterize the general state space canonical form which is far less than the number of elements in the various state space matrices (Candy, 1979). However, the numbers of parameters making up the matrices of the proposed state space model versus Larimore's model are given by Eq.…”

Development of Statistical Methods Using Predictive Inference and Entropy.

“…In fact for each distinct probability distn'buon there is an equivalence class of models of the form (4-12) and (4-13) with the same distrilutio. It can be shown (Candy, Bullock, and Warren, 1979) that the number of independent parameters is…”