Study On The Uncertainty Processing Based On Evidence Theory And Its Application In Test

The study on uncertainties processing based on evidence theory is focused by many scientists and engineers all over the world. The work is very useful to help to enrich the theoretical mechanism of evidence theory, to solve the problems in which exists imprecise information, simple sample data and epistemic uncertainty, but also to enhance the foundation and application of measurement technology.In this paper, the study is presented based on the evidence theory and the information process of the uncertainties. And the study is concentrated in 2 aspects. Firstly, the mathematic theory related to the evidence theory is discussed, including uncertainty quantification, relationship among the evidence theory, probability theory and possibility theory, and finally a modified combination rule for evidence. As for the second aspects, the study is focused on the application of the evidence theory into the uncertain data processing. The basic method for the uncertain data processing is presented. Based on the study of the probability boundary analysis, the computational equations for several uncertain input probability boxes are given. In addition, the computational method for probability boxes of the uncertain function is presented based on the conversion of probability boxes and evidence body. As for the third aspects, the study is made for the measured uncertainty data and information processing technology. The main task for this is to carryout the data statistics of the dynamic measured data based on the evidence theory and the expression of the measured data of the possibility distribution, based on which, several evaluation methods for the uncertainty measurement are put forward. Moreover, the fusion of the measurement data of multiple sensors are made with the modified evidence composition rule presented in this paper. In addition to the theoretical study, experimental results and simulation results are presented in this paper with fairly good accordance with each other.The major innovative of this paper is given as the follows.The unique performance of the evidence theory in dealing with the imprecise probability is described. And the related deductions are made to identify the similarity and difference of the evidence theory with other theories in dealing with uncertainty. Such concepts as basic mass assign, belief function, plausible function, the upper and lower probability are used for the process and statistics of the measurement data, so is applied to process neutrons data.Based on the discussion of the advantages and disadvantages of the various combination rules for evidence, a modified combination rule is presented to deal with consistence or inconsistence evidences obtained from multiple sources. The modified rule adapts AND-operation to combine consistent evidences and reflects the intersection of focal elements, and allocates the conflict probability to very inconsistence focus element according to its average supported degree. Experiments show that the new combination rule is very reliable and rational for all kinds of evidences including highly conflicting evidences.The measurement uncertainty is often evaluated by a probabilistic approach, but such approach is not always adapted to imprecise measurement data. After discussing the relation between Shannon entropy and measurement uncertainty, a general formula for evaluation of measurement uncertainty is proposed, which can be applied in both precise data and imprecise data.The conversion between the evidence body and probability boxes is discussed provide two methods for the probability boxes namely the average discretization and the external discretization. In accordance with the three principles in dealing with the probability boxes as rigor-preserving, best possible and sample uncertainty, the computational methods for the probability boxes with various uncertainty variables are given with known type of distribution or partially limited information. And the computational methods of the probability boxes of the uncertainty function are presented with conversion method of the probability boxes and evidence body.The study covers the possibility expression of the measurement error, the evaluation of the measurement uncertainty, the transformation from probability distribution into possibility distribution, and the modeling of the possibility distribution of the measurement data.