Research On The Uncertainty Of Consistency-Based Diagnosis Applying Bayesian Network

Model-based diagnosis is a new type of intelligent reasoning technology, in order to overcome traditional fault-diagnosis methods'shortcomings. And model-based diagnosis is one of the active branches of Artificial Intelligence. In addition to circuit diagnosis and medical diagnosis, nowadays, MBD has been applied to more practical aspects, such as fault detection and location in VHDL, diagnosis of asynchronization discrete systems, diagnosis of network communications, automotive systems diagnosis, and so on.The basic idea of MBD is: expressing the system to be diagnosed as an abstract model according to all the components and their connections in products'design or production phase. Then predict the system behaviour with the model and compare it with the practical behaviour to find the fault components. So it has two main advantages. One is that it is symptom-oriented, avoiding blindness. The other is that it has a strong equipment-independence. It can be served a variety of equipment, avoid the cumbersome nature of the diagnosis, and applies to different kinds of application fields.MBD has two genres: consistency-based diagnosis (CBD) and abductive diagnosis (ABD). CBD requires the system descriptions (SD), observations (OBS), and abnormality assumptions(△) are consistent. ABD, in addition, requires that OBS can get from SD and△. So, ABD is a strong notion diagnosis. An ABD is a CBD, but a CBD is not always an ABD.Model-based diagnosis is one of the intensional approaches,it is very clear in semantic denotation, because of global consistency description model, there is no the problems of bidirectional-reasoning , and the related evidence-handling, but the contradiction between computation modular and semantic consistency is in existence. The Bayesian network is a balance scenario between simple and legible semantic denotation. As an intensional approach, semantic is joint probability distribution; the computation complexity is lowered with adoption of network structure representing independence. So it is the preferred method of treating with the uncertainty involved in consistency-based diagnosis.De Kleer proposed to represent this uncertainty as a joint probability distribution Pr(C) on a set of components C={C1,…,Cn}, where the adjustment of this probability distribution due to the observation of a particular finding O would be computed by Bayes'rule: Whereas the specification of the probability distribution is exponential in their number of variables, computation of the other probability is hard.Kohlas et al. proposed another approach; they adjust the joint probability distribution using knowledge of possible and impossible states of components as obtained by consistency-based diagnosis. Thsis may be viewed as determining the probabilistic diagnosis of faulty behavior:The different ways to incorporate uncertainty in model-based diagnosis discussed above, none is really satisfactory. It is assumed that the components are mutually independent, but the event of failure of one component is likely to be dependent of failure of the other components, so it is a strong assumption, and not accord with reality.After introducing consistency-based diagnosis, interrelated knowledge about probability, and Bayesian networks reasoning, we make condition independence assumption on the relation between system components, combine consistency-based diagnosis and Bayesian probability reasoning on this basis, and propose a framework which integrates Bayesian networks reasonning model into consistency-based diagnosis finally. As the theory foundation, we research three primary aspects on this combination: probability independence, probability reasoning, and observation handling.Probability independence: uncertainty with respect to the normal or faulty behavior of components is expressed by a joint probability distribution on the set of components COMPS: Pr (C1,…,Cn ) where Ci, for each i, 1≤i≤n, is a stochastic variable that when taking the value true, also denoted by ci, indicates component ci to be faulty; when taking the value false, also denoted by┓ci, indicates component ci to be normal. This yields a 1-1 correspondence between Ab formulae and Boolean expressions involving ci and its negation.Probability reasoning: If the diagnosis is for uncertain reasoning, it needs to be redefined probability of consistency-based diagnosis. System definition for S = (SD, COMPS, OBS), Pr (C)>0. Pr (OBS)>0, C is a conflict set, if and only if Pr (C|OBS) = 0. Set probability of conflict and systematic observation in the form of linked together to construct a strict probabilistic reasonning relationship. Observing into Bayesian model used to calculate conflict set of knowledge far more than the simple types of knowledge, which all knowledge is used to calculate the possibility of the consistency-based diagnosis.Observation handling: observations could in principle influence our knowledge of the likelihood of malfunction of certain component of the system. Therefore it is necessary to join the observation variables into Bayesian inference network model. For any diagnosis , as well as related observations OBS set. BΔs Bayesian network inference algorithm can calculate the probability Pr (Δ), its complexity depends on the network topology degrees. After all, due to the number of breakdown components nodes in the Bayesian network accounts for a relatively small proportion. So there can be set by calculating the probability of conflict to seek diagnosis probability, and in order to avoid double-counting probability, conflict set should only be considered maximum consistency. The unity of qualitative logical reasoning method and quantitative probability method produce the following results: 1. Consistency-based diagnosis logical method calculates all the likely diagnosis; confirm the space of diagnosis to be identified.2. Bayesian inference computes for each model by observing the possibility of the diagnosis; decide on the final findings.Finally, a Bayesian network inference model is proposed:The Bayesian observation model of System S = (SD, COMPS. OBS) is defined as a triple Bs= (V, E, Pr);V denotes independent nodes in Bayesian network reasoning model, contains three types of node, V=I∪O∪C, I denotes input observation; O denotes output observation, and C denotes component in system.E (?) V×V, is the set of direct arcs. Describes the stochastic independence relationship of variables.Pr is defined as a joint probability distribution on the basis of components set and observations set. Reflecting the dependence of components.And propose a system reasoning theorem: system S = (SD, COMPS. OBS), is a CBD, for the CBD system by applying Bayesian network reasoning model, PB = (Bs,ΔΩ), then SD UOBSUΔ⊥(?) P (Ω|Δ)≠0.The theorem shows that CBD which applies Bayesian model framework and the original diagnosis are exactly the same in the diagnosis conclusion. In this framework it is the basis for a diagnostic evaluation of the optimal. We introduce aΩ-Confidence function used to measure the size of diagnostic possibilities. P-value is higher shows that observations give greater support for diagnosis . Finally, we take an example for certification; the method is proved effectively in the handling process of uncertainty involved in consistency-based diagnosis. It provide a reference value for the differential diagnosis, fault location, and is necessary to do more research on Bayesian network model simplification, and reducing computational complexity.