Techniques have recently been developed for early warning of slight changes in systems [. Benveniste 1987, Basseville 1993, Zhang 1994.], and they have been applied to condition-based maintenance and diagnosis (e.g., of gas turbines and of vibrations in offshore platforms). These techniques are based on the asymptotic local approach for change detection and classification, and we will build on our work in adaptive algorithms [.Arapostathis 1990.]. It is important to note that the methodology is specifically designed for the detection of small changes in the system.
In general, change detection algorithms can be viewed as consisting of three parts: (i) generation of residuals or change indicating basic statistics that are ideally close to zero when no change occurs and change when it occurs in the system; (ii) statistical decision rules based on these basic statistics; and (iii) diagnosis or classification of the change or fault. In the asymptotic local approach, the role of the basic statistics is played by the efficient score (gradient of the log-likelihood function) or, more generally, by the gradient of some other criterion such as prediction error, derived from an adaptive algorithm. By means of a nonstationary Central Limit Theorem, the decision rule becomes one of testing for changes in the mean of the basic statistic; for example, a cumulative sum (CUSUM) of the basic statistics is used, as if the basic statistics formed an independent Gaussian sequence. The asymptotic local approach gives a diagnosis technique based on a sensitivity method suited to the identification of the origin of small changes. This technique can be supplemented by an examination of the basic statistics for known failure signatures, as well as by a multiple model approach. Under quite general conditions, in particular when a reduced order model is used to compute the basic statistics, this approach can be shown to be asymptotically optimal.
In the initial phases of the research we will focus on the detection and recognition of changes in systems described by Hidden Markov Models and the generalizations of HMMs developed by Ostendorf [.Kimball 1996.]. These are nonstationary, nonlinear models; however, the asymptotic local approach is well suited to such systems. One must derive the appropriate statistics to monitor. In this case, the efficient score is too complicated to compute. However, in our work on adaptive state estimation for HMMs [.Arapostathis 1990.], we have developed the appropriate statistics that are recursively computable in real time. Using these statistics, we will employ the asymptotic local approach for detection and diagnosis in HMMs. In later phases of the research, this approach will be applied to models for mechanical systems. This may well involve the detection of changes in the autoregressive part of an ARMA model in which the moving-average part is nonstationary, as in the case of offshore platforms [.Zhang 1994.].