The Entropy Algorithm and Its Variants in the Fault Diagnosis of Rotating Machinery: A Review <s> B. BELIEF ENTROPY <s> A modified average method to combine belief function based on distance measures of evidence is proposed. The weight of each body of evidence (BOE) is taken into account. A numerical example is shown to illustrate the use of the proposed method to combine conflicting evidence. Some open issues are discussed in the final section. <s> BIB001 </s> The Entropy Algorithm and Its Variants in the Fault Diagnosis of Rotating Machinery: A Review <s> B. BELIEF ENTROPY <s> The multi-sensor data fusion technique plays a significant role in fault diagnosis and in a variety of such applications, and the Dempster–Shafer evidence theory is employed to improve the system performance; whereas, it may generate a counter-intuitive result when the pieces of evidence highly conflict with each other. To handle this problem, a novel multi-sensor data fusion approach on the basis of the distance of evidence, belief entropy and fuzzy preference relation analysis is proposed. A function of evidence distance is first leveraged to measure the conflict degree among the pieces of evidence; thus, the support degree can be obtained to represent the reliability of the evidence. Next, the uncertainty of each piece of evidence is measured by means of the belief entropy. Based on the quantitative uncertainty measured above, the fuzzy preference relations are applied to represent the relative credibility preference of the evidence. Afterwards, the support degree of each piece of evidence is adjusted by taking advantage of the relative credibility preference of the evidence that can be utilized to generate an appropriate weight with respect to each piece of evidence. Finally, the modified weights of the evidence are adopted to adjust the bodies of the evidence in the advance of utilizing Dempster’s combination rule. A numerical example and a practical application in fault diagnosis are used as illustrations to demonstrate that the proposal is reasonable and efficient in the management of conflict and fault diagnosis. <s> BIB002 </s> The Entropy Algorithm and Its Variants in the Fault Diagnosis of Rotating Machinery: A Review <s> B. BELIEF ENTROPY <s> Abstract Similarity of nodes is a basic structure quantification in complex networks. Lots of methods in research on complex networks are based on nodes’ similarity such as node’s classification, network’s community structure detection, network’s link prediction and so on. Therefore, how to measure nodes’ similarity is an important problem in complex networks. In this paper, a new method is proposed to measure nodes’ structure similarity based on relative entropy and each node’s local structure. In the new method, each node’s structure feature can be quantified as a special kind of information. The quantification of similarity between different pair of nodes can be replaced as the quantification of similarity in structural information. Then relative entropy is used to measure the difference between each pair of nodes’ structural information. At last the value of relative entropy between each pair of nodes is used to measure nodes’ structure similarity in complex networks. Comparing with existing methods the new method is more accuracy to measure nodes’ structure similarity. <s> BIB003
Belief entropy was first proposed by Deng et al. BIB001 to measure the uncertain information of time series. A larger belief entropy value means the evidence contains more information BIB003 . Xiao BIB002 proposed a hybrid methodology based on belief entropy and fuzzy preference relation analysis to accomplish the motor rotor fault diagnosis. Details about symplectic entropy can refer to BIB001 .