Belief Chi-square Divergence And Its Applications In Information Fusion

With the rapid development of big data and artificial intelligence technology,humanity has entered an era that is more data-driven and intelligent.In the face of massive data from different sources,dimensions,and formats,how to effectively and accurately fuse such information has become a hot research topic.In the field of information fusion,ensuring the accuracy and reliability of the original information is key to ensuring effective fusion.However,due to external factors such as mechanical failures,weather conditions,and enemy interference,the obtained information may be incomplete,inaccurate,or even highly conflicting.In this case,if traditional information fusion algorithms are still used,the results may be inconsistent with the actual situation.Therefore,the main research content of this thesis is how to effectively fuse uncertain information under the situation of incomplete and inaccurate information and finally obtain reasonable evaluation predictions.There are many types of information fusion technologies,among which the Dempster-Shafer(D-S)evidence theory has attracted attention due to its ability to deal with uncertain information.The D-S evidence theory generalizes sets to power sets based on probability theory,replaces probability with basic probability assignment functions,and provides a set of combination rules,enabling it to fuse evidence in situations of uncertainty.Based on the D-S evidence theory,this thesis studies how to perform more effective information fusion,including:(1)Study on conflict measurement based on belief chi-square divergenceThe classic chi-square(χ~2)divergence is an asymmetric measure that measures the difference between two probability distributions.The main contribution of this thesis is to extend the chi-square divergence to the D-S evidence theory and propose a belief chi-square(Bχ~2)divergence.Compared with the traditional chi-square divergence,the Bχ~2 divergence is a symmetric measure that can measure the uncertainty of basic probability assignment in the evidence theory.Then,on the basis of the Bχ~2 divergence,a novel belief chi-square divergence measure called Rχ~2 divergence was proposed by incorporating belief and likelihood functions.With further research on the Rχ~2 divergence,it was found that the Rχ~2 divergence has limitations in measuring the uncertainty of multiple subset elements,which are important components of the D-S evidence theory.Therefore,we finally proposed a reinforced belief chi-square divergence model called the IB divergence,which satisfies good mathematical properties,including boundedness,non-degeneracy conditions,and symmetry.Finally,by comparing the three types of belief chi-square divergence proposed in this thesis with the existing divergence measure,the efficiency of the IB divergence in measuring information conflicts was verified.(2)Study on multi-source information fusion method based on the reinforced belief chi-square divergenceBased on the reinforced belief chi-square divergence,a multi-source information fusion method was proposed,which is mainly divided into two parts.First,the original data set is converted into basic probability assignment,and the method adopted in this thesis is the basic probability assignment generation method based on Gaussian distribution.Second,a new multi-source information fusion method was proposed based on the IB divergence,which uses the IB divergence to measure the discrepancy between basic probability assignments,and uses Deng entropy to measure the information volume of basic probability assignment from two perspectives,thus effectively improving the effectiveness and reliability of the fusion results.Finally,by applying the proposed method to the identification of automobile faults and public dataset,the effectiveness and accuracy of the model were verified.