Uncertain Observations

Abstract

In diagnosis of dynamic systems each observation has a logical content, representing what has been observed, a temporal content, specifying when it has been observed, and a source content, stating which is the source component of each piece of observed evidence. The observation of an active system is an untimed DES observation, therefore its logical and temporal contents are the observed symbols and their precedence relationships, respectively, while the source content is the sender component of each observed event, as it can be hypothesized given the observation and the structural model of the system. While the source content of an active system observation is allowed to be ambiguous, the logical and temporal contents are not. This certainty principle, whilst being a useful simplification for a variety of contexts, may become inappropriate for a wide range of real systems, where the communication between the system and the observer, combined with the possibly limited ability of the observer to observe, is either bound to generate spurious observed events, to randomly lose some events, or to lose temporal constraints among them. To cope with these uncertainties, a number of principles affecting both the observations and the modeled behavior of a system are introduced, that are independent of any processing technique. Furthermore, the notion of an uncertain observation for an untimed DES is introduced and accommodated within a graph whose nodes are labeled by logically uncertain observed events, while edges define a partial temporal ordering among them. This way, an uncertain observation implicitly defines a finite set of observations in the traditional sense, i.e. sequences of logically certain observed events. Thus, solving an uncertain diagnostic problem inherent to an active system amounts to solving in one shot several traditional diagnostic problems.