Applying Bayesian networks to fault diagnosis

Diagnosis applications relying on artificial intelligence methods must deal with uncertain knowledge and fuzzy input data. Besides other methods, classical probability theory has been realized by many authors to be useful for such tasks, given that tools are available, making its application more handy. One such tool are Bayesian networks (causal probabilistic networks, belief networks). While the construction of the graph of a Bayesian network along causal dependencies is often quite easy, it is usually difficult to specify the necessary probabilities, i.e. for every node the probabilities that its variable assumes a certain value given the predecessors´ values. Instead, in practical applications, it is usually preferable to specify an unordered set of conditional probabilities, which does not necessarily match the set of probabilities in the network. Such a set of probabilities has the potential problem of being neither consistent nor complete with respect to the compound distribution of all random variables in the net. It is shown, that a test for consistency and completeness and answering queries about the compound probability can in general be done by solving a nonlinear equation system. However, due to the inherent complexity of solving such a system, this is in general not feasible. But some interesting special cases are presented for which an approximation yields useful results