The belief noisy-or model applied to network reliability analysis

One difficulty faced in knowledge engineering for Bayesian Network (BN) is the quan-tification step where the Conditional Probability Tables (CPTs) are determined. The number of parameters included in CPTs increases exponentially with the number of parent variables. The most common solution is the application of the so-called canonical gates. The Noisy-OR (NOR) gate, which takes advantage of the independence of causal interactions, provides a logarithmic reduction of the number of parameters required to specify a CPT. In this paper, an extension of NOR model based on the theory of belief functions, named Belief Noisy-OR (BNOR), is proposed. BNOR is capable of dealing with both aleatory and epistemic uncertainty of the network. Compared with NOR, more rich information which is of great value for making decisions can be got when the available knowledge is uncertain. Specially, when there is no epistemic uncertainty, BNOR degrades into NOR. Additionally, different structures of BNOR are presented in this paper in order to meet various needs of engineers. The application of BNOR model on the reliability evaluation problem of networked systems demonstrates its effectiveness

Time-Sliced temporal evidential networks : the case of evidential HMM with application to dynamical system analysis.

International audienceDiagnostics and prognostics of health states are important activities in the maintenance process strategy of dynamical systems. Many approaches have been developed for this purpose and we particularly focus on data-driven methods which are increasingly applied due to the availability of various cheap sensors. Most data-driven methods proposed in the literature rely on probability density estimation. However, when the training data are limited, the estimated parameters are no longer reliable. This is particularly true for data in faulty states which are generally expensive and difficult to obtain. In order to solve this problem, we propose to use the theory of belief functions as described by Dempster, Shafer (Theory of Evidence) and Smets (Transferable Belief Model). A few methods based on belief functions have been proposed for diagnostics and prognostics of dynamical systems. Among these methods, Evidential Hidden Markov Models (EvHMM) seems promising and extends usual HMM to belief functions. Inference tools in EvHMM have already been developed, but parameter training has not fully been considered until now or only with strong assumptions. In this paper, we propose to complete the generalization of HMM to belief functions with a method for automatic parameter training. The generalization of this training procedure to more general Time-Sliced Temporal Evidential Network (TSTEN) is discussed paving the way for a further generalization of Dynamic Bayesian Network to belief functions with potential applications to diagnostics and prognostics. An application to time series classification is proposed

Prognostics in switching systems: Evidential markovian classification of real-time neuro-fuzzy predictions.

International audienceCondition-based maintenance is nowadays considered as a key-process in maintenance strategies and prognostics appears to be a very promising activity as it should permit to not engage inopportune spending. Various approaches have been developed and data-driven methods are increasingly applied. The training step of these methods generally requires huge datasets since a lot of methods rely on probability theory and/or on artificial neural networks. This step is thus time-consuming and generally made in batch mode which can be restrictive in practical application when few data are available. A method for prognostics is proposed to face up this problem of lack of information and missing prior knowledge. The approach is based on the integration of three complementary modules and aims at predicting the failure mode early while the system can switch between several functioning modes. The three modules are: 1) observation selection based on information theory and Choquet Integral, 2) prediction relying on an evolving real-time neuro-fuzzy system and 3) classification into one of the possible functioning modes using an evidential Markovian classifier based on Dempster-Shafer theory. Experiments concern the prediction of an engine health based on more than twenty observations