Bayesian Method For Model-based Diagnosis

Model-based diagnosis is an important theory in the field of artificial intelligence. It has a rapid development by applied widely in various fields, and plays an important role in improving the reliability of complexity of engineering equipments. In recent decades, Model-based diagnosis has become the focus of research gradually in the field of artificial intelligence.Model-based is an important intelligent reasoning technology. In recent years, model-based diagnosis has been successfully applied in many field, examples include: space probes, robot automotive systems diagnosis and so on.The basic idea of model-based diagnosisis: using the model of the structure and behaviors of a system to establish the reason of malfunctioning. We determine a system is faulty, when some differences happen between the results of the model and the observations of the actual system. Then we have to make a trouble shoot to the system, by using logical reasoning. Model-based diagnosis is the process of identifying the set of components of the system, whose fault could explains the malfunctions of the system. But the limitation of the model-based is that it could not deal with uncertainty very well.Model-based diagnosis has two methods, which is consistency-based diagnosis and abductive diagnosis. This paper builds on the work in consistency-based diagnosis. Consistency-base diagnosis is a method of assumption-based. And the result of the diagnosis could be real as long as no refuting evidence is available. Consistency-based diagnosis has many advantages for trouble shooting, but could not quantify the uncertainty clearly. All the possible diagnoses are assumed to be equally likely in consistency-based diagnosis, but the situation is rare in the actual cases.Many researchers have done a great deal of research on the uncertainty in the model-based diagnosis. It has been proven that supplementing the logical-based framework with probabilistic reasoning is an effective method for dealing with uncertainty. And the possibility of failure of each component is described explicitly with mathematically sound ways.De Kleer and Williams proposed a mathematical method in the model-based firstly. They applied the Bayes'rule to get the posterior probability, and used the minimal entropy techniques to select the variable to be observed next. Shenoy proposed a valuation-based systems, but only be used in a valuation-based model whose variables with finite domains. Kohlas et al. proposed a General method ,which is a logic-based approach ,to found the real fault. This paper analysis these probabilistic method, and improved Kohlas et al's method whose is more reasonable than others.The basic ideas of Kohlas et al's theory is that, using the information of possible and impossible states of components as obtained by consistency-based reasoning:Let N d denote the set of system states that are consistent with the observations. ( A system state x∈Nd means that it is a possible explanation of the observations.)Let N c denote the set of system states that are inconformity with the observations. (A system state x∈Nc is a conflict. ) Kohlas et al adjust the probability distribution on the sets by Bayes'rule: Kohlas et al's method also exists some problems, one the one hand,the algorithm has very high computational complexity; on the other hand, the algorithm assumed the components are mutually independent, but it's not according with reality. And this paper improves the method in the two aspects, proposed a more reasonable method with a low computational complexity.Method proposed in this paper is still based on the logical model with the consistency-based diagnosis. The traditional method is improved with a mathematically ways. And the equivalence between the the traditional method and the proposed approach is also proved. The complexity and the completeness of the method are analyzed. The time complexity of the traditional method is ( )o mn2.m is the number of the diagnosis, and n is the number of the component of the system. The time complexity of the method in this paper is only ( )o n2.It means the time complexity and the space complexity are reduced in the improved method greatly.The experiment in this paper also illustrate that the improved method has a better executive efficiency than the traditional method in general. In fact, the executive efficiency may be improved up to two orders of magnitude in some cases.Furthermore, some unrealistic assumptions are made in the traditional method. This paper integrates the Bayesian network with the improved method, and optimizing the method in a reasonable way. Bayesian network is the extention of the Bayes'rule, and it offers a proper framework for dealing with uncertainty. And the posterior probability of each component can be computed without unrealistic assumptions. We also take an example for certification. It proves that the method in this paper is more reasonable.But, there is still a lot of work to do on Bayesian network for reducing computational complexity. The Bayesian network model should be simplified in a reasonable way.