Sur la décombinaison de fonctions de croyance

International audienceThe evidence combination is a kind of decision-level information fusion in the theory of belief functions. Given two basic belief assignments (BBAs) originated from different sources, one can combine them using some combination rule, e.g., Dempster's rule to expect a better decision result. If one only has a combined BBA, how to determine the original two BBAs to combine? This can be considered as a defusion of information. This is useful, e.g., one can analyze the difference or dissimilarity between two different information sources based on the BBAs obtained using evidence decombination. Therefore, in this paper, we research on such a defusion in the theory of belief functions. We find that it is a well-posed problem if one original BBA and the combined BBA are both available, and it is an under-determined problem if both BBAs to combine are unknown. We propose an optimization-based approach for the evidence decombination according to the criteria of divergence maximization. Numerical examples are provided illustrate and verify our proposed decombination approach, which is expected to be used in applications such the difference analysis between information sources in information fusion systems when the original BBAs are discarded, and performance evaluation of combination rules

Interval-valued Evidence Updating with Reliability and Sensitivity Analysis for Fault Diagnosis

Information fusion methods based on Dempster-Shafer evidence theory (DST) have been widely used in fault diagnosis. In DST-based methods, the monitoring information collected from sensors is modeled as multiple pieces of diagnosis evidence in the form of basic belief assignment (BBA), and Dempster’s rule is then used to combine these BBAs to obtain the fused BBA for diagnosis decision making. However, the belief structure with crisp singlevalued belief degrees in BBA may be too coarse to truthfully represent detailed fault information. Moreover, Dempster’s rule only uses a static combination process, which is unsuitable for dynamically fusing information collected at different time steps. In order to address these issues, the paper proposes a dynamic diagnosis method based on interval-valued evidential updating. First of all, the diagnosis evidence is constructed as an interval-valued belief structure (IBS), which provides a more informative scheme than BBA to model fault information. Secondly, the proposed evidential updating strategy can generate updated IBS as global diagnosis evidence by updating the previous evidence with the new incoming evidence recursively. Thirdly, the reliability and sensitivity indices are designed to evaluate and compare the performance of the proposed updating strategy with other commonly used strategies. Finally, the effectiveness of the proposed evidential updating strategy is demonstrated through some typical fault experiments of a machine rotor