Research On Fusion Theory Of Possibility Distribution And Its Engineering Application

Possibility distribution, as an important content in the possibility theory, is able to forecasthow things change, and has some advantages that it is suitable for representation andmeasurement of a small amount of data and description the variable mapping between sets,also it has low computational complexity, which has extensive application value in reliabilityanalysis of systems, failure diagnosis and risk assessment, and other fields. After constructingpossibility distributions of multiple information sources, the information of each possibilitydistribution is fused according to certain rules or methods, thus we can obtain more accurateand reliable results than a single possibility distribution, so that the fused results changecorrespondingly along with the change of distribution value. Therefore, in this paper, fusiontheory of possibility distribution and its engineering application are studied, and the maincontents are as follows:(i) Study of possibility distribution construction: the transformation rules are revealedfrom the different forms of probability distribution to possibility distribution, and thecorresponding possibility distribution functions are obtained, and the rules are proved. Aimingat the characteristics of small sample data, a possibility distribution construction method isproposed based on uncertainty information of small sample. Different confidence intervals arerepresented by possibility according to the relationship between the confidence level inprobability distribution and cut sets in possibility distribution. Then parabola interpolationmethod is used for interpolation to realize the characterization and measurement of smallsample data. Finally the effectiveness of the proposed method is validated by simulation.Possibility distribution construction is direct premise of possibility distribution fusion. Weonly grasp the construction characteristics of different types of possibility distribution to lay afoundation for targeted fusion of possibility distributions. (ii) Study of the relevant fusion theory of possibility distributions: basic concept ofpossibility distribution fusion is summarized by analyzing its properties, characteristics andfusion modes (e.g. a single point, only increase, only decrease, and increase and decrease).Basic operations of possibility distribution is analysed and used for fusion of infrared images.The classification of possibility distribution fusion methods is studied, and it can be dividedinto: fusion method based on fuzzy operators, weighted fusion method based on similarmeasure and weighted fusion method based on certainty degree. Possibility distribution fusionis the core content in fusion theory of possibility distribution, and its relevant theoreticalresearch provides effective basis to establish different types of possibility distribution fusionmethods.(iii) Study of different possibility distribution fusion methods: a more general fusionmethod based on fuzzy operators is proposed by comparison and analysis of the differentforms of T-module operator, and each possibility distribution are fused after choosing theappropriate T-module operator according to the relationship of independent variables in thepractical problems. For fusion of nonlinear fuzzy numbers, this paper gives a similaritycalculation method based on the perimeter, area, height, distance and the center of mass ofnonlinear fuzzy numbers, and a logarithm regression weighted fusion method based onsimilar measure is put forward by constructing logarithmic function of sum of error square.For fusion of general possibility distribution, the certainty degrees of possibility distributionsare determined according to the cut sets and possibility mean, and a weighted fusion methodbased on certainty degree is proposed. Taken acoustic excitation test of metal and nonmetaladhesive structure as an example, the effectiveness of the proposed methods are illustrated.According to different types of possibility distributions, this paper gives the correspondingfusion strategy, which provides new ideas for possibility distribution fusion.(iv) Study of decision-making method based on possibility distribution fusion: this paperputs forward a transformation from possibility distribution to mass function and reliabilitydecision-making method in view of attribute weights of the distributions are unknown. Atransformation method based on weighted center of gravity is given by moment characteristics of possibility distribution (e.g. the mean, variance and skewness), and thereliability of each information source is determined according to the flows of body ofevidence, thus decision result is obtained via decision-making rule. In view of attributeweights are known, an extended TOPSIS method based on possibility theory is proposed.Relative close coefficients of possibility mean and ideal solution for the alternatives can becalculated according to the distance between the positive and negative ideal solution ofpossibility mean, and similarly the coefficients of possibility standard deviation and idealsolution can be determined based on the distance between the positive and negative idealsolution of possibility standard deviation. Then comprehensive close coefficients of thealternatives are constructed. The effectiveness of the proposed method is verified bysimulation. Practical decision-making problems drive study of possibility distribution fusion,and meanwhile possibility distribution fusion provides effective means for decision-makingproblems, so in fusion theory of possibility distribution, study of decision-making methodbased on possibility distribution fusion is necessary.(v) Study of engineering application about fusion theory of possibility distribution: onthe basis of further studying monitoring data of a certain tailings dam, possibility distributionsof reservoir water level, dam displacement, length of dry beach and phreatic lines of eachmonitoring point are constructed, then possibility distributions of different monitoring pointsare fused. On this basis, according to the relationship between monitoring indicators and riskstates, the risk state is judged and evaluated by a transformation from possibility distributionto mass function and reliability decision-making method, in order to verify the validity andpracticability of fusion theory of possibility distribution.