To analyze the effect of basic variable on failure probability in reliability analysis,a moment-independent importance measure of the basic random variable is proposed,and its properties are analyzed and verified.Base...To analyze the effect of basic variable on failure probability in reliability analysis,a moment-independent importance measure of the basic random variable is proposed,and its properties are analyzed and verified.Based on this work,the importance measure of the basic variable on the failure probability is compared with that on the distribution density of the response.By use of the probability density evolution method,a solution is established to solve two importance measures,which can efficiently avoid the difficulty in solving the importance measures.Some numerical examples and engineering examples are used to demonstrate the proposed importance measure on the failure probability and that on the distribution density of the response.The results show that the proposed importance measure can effectively describe the effect of the basic variable on the failure probability from the distribution density of the basic variable.Additionally,the results show that the established solution on the probability density evolution is efficient for the importance measures.展开更多
Dempster-Shafer (DS) theory of evidence has been widely used in many data fusion ap- plication systems. However, how to determine basic probability assignment, which is the main and the first step in evidence theory, ...Dempster-Shafer (DS) theory of evidence has been widely used in many data fusion ap- plication systems. However, how to determine basic probability assignment, which is the main and the first step in evidence theory, is still an open issue. In this paper, a new method to obtain Basic Probability Assignment (BPA) is proposed based on the similarity measure between generalized fuzzy numbers. In the proposed method, species model can be constructed by determination of the min, average and max value to construct a fuzzy number. Then, a new Radius Of Gravity (ROG) method to determine the similarity measure between generalized fuzzy numbers is used to calculate the BPA functions of each instance. Finally, the efficiency of the proposed method is illustrated by the classi- fication of Iris data.展开更多
This paper studies the emitter recognition problem. A new recognition method based on attribute measure for emitter recognition is put forward. The steps of the method are presented. The approach to determining the we...This paper studies the emitter recognition problem. A new recognition method based on attribute measure for emitter recognition is put forward. The steps of the method are presented. The approach to determining the weight coefficient is also discussed. Moreover, considering the temporal redundancy of emitter information detected by multi-sensor system, this new recognition method is generalized to multi-sensor system. A method based on the combination of attribute measure and D-S evidence theory is proposed. The implementation of D-S reasoning is always restricted by basic probability assignment function. Constructing basic probability assignment function based on attribute measure is presented in multi-sensor recognition system. Examples of recognizing the emitter purpose and system are selected to demonstrate the method proposed. Experimental results show that the performance of this new method is accurate and effective.展开更多
The main achievement of this paper is the finding and proof of Central Limit Theorem(CLT,see Theorem 12)under the framework of sublinear expectation.Roughly speaking under some reasonable assumption,the random sequenc...The main achievement of this paper is the finding and proof of Central Limit Theorem(CLT,see Theorem 12)under the framework of sublinear expectation.Roughly speaking under some reasonable assumption,the random sequence{1/√n(X1+···+Xn)}i∞=1 converges in law to a nonlinear normal distribution,called G-normal distribution,where{Xi}i∞=1 is an i.i.d.sequence under the sublinear expectation.It’s known that the framework of sublinear expectation provides a important role in situations that the probability measure itself has non-negligible uncertainties.Under such situation,this new CLT plays a similar role as the one of classical CLT.The classical CLT can be also directly obtained from this new CLT,since a linear expectation is a special case of sublinear expectations.A deep regularity estimate of 2nd order fully nonlinear parabolic PDE is applied to the proof of the CLT.This paper is originally exhibited in arXiv.(math.PR/0702358v1).展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos NSFC1057211, 50875213)New Century Excellent Talents in University of China (Grant No NCET-05-0868)+2 种基金Aviation Science Foundation of China (Grant No 2007ZA53012)National High Technology Research and Development Program of China (Grant No 2007AA04Z401)the Important National Science & Technology Specific Projects (Grant No 2009ZX04014-015-03)
文摘To analyze the effect of basic variable on failure probability in reliability analysis,a moment-independent importance measure of the basic random variable is proposed,and its properties are analyzed and verified.Based on this work,the importance measure of the basic variable on the failure probability is compared with that on the distribution density of the response.By use of the probability density evolution method,a solution is established to solve two importance measures,which can efficiently avoid the difficulty in solving the importance measures.Some numerical examples and engineering examples are used to demonstrate the proposed importance measure on the failure probability and that on the distribution density of the response.The results show that the proposed importance measure can effectively describe the effect of the basic variable on the failure probability from the distribution density of the basic variable.Additionally,the results show that the established solution on the probability density evolution is efficient for the importance measures.
基金Supported by National High Technology Project (863)(No. 2006AA02Z320)the National Natural Science Founda-tion of China (No.30700154, No.60874105)+1 种基金Zhejiang Natural Science Foundation (No.Y107458, RY1080422)the School Youth Found of Shanghai Jiaotong University
文摘Dempster-Shafer (DS) theory of evidence has been widely used in many data fusion ap- plication systems. However, how to determine basic probability assignment, which is the main and the first step in evidence theory, is still an open issue. In this paper, a new method to obtain Basic Probability Assignment (BPA) is proposed based on the similarity measure between generalized fuzzy numbers. In the proposed method, species model can be constructed by determination of the min, average and max value to construct a fuzzy number. Then, a new Radius Of Gravity (ROG) method to determine the similarity measure between generalized fuzzy numbers is used to calculate the BPA functions of each instance. Finally, the efficiency of the proposed method is illustrated by the classi- fication of Iris data.
基金This work was supported by the National Natural Science Foundation of China(Grant No.60172033)Excellent Ph.D Paper Author Foundation of China(Grant No.200036).
文摘This paper studies the emitter recognition problem. A new recognition method based on attribute measure for emitter recognition is put forward. The steps of the method are presented. The approach to determining the weight coefficient is also discussed. Moreover, considering the temporal redundancy of emitter information detected by multi-sensor system, this new recognition method is generalized to multi-sensor system. A method based on the combination of attribute measure and D-S evidence theory is proposed. The implementation of D-S reasoning is always restricted by basic probability assignment function. Constructing basic probability assignment function based on attribute measure is presented in multi-sensor recognition system. Examples of recognizing the emitter purpose and system are selected to demonstrate the method proposed. Experimental results show that the performance of this new method is accurate and effective.
文摘The main achievement of this paper is the finding and proof of Central Limit Theorem(CLT,see Theorem 12)under the framework of sublinear expectation.Roughly speaking under some reasonable assumption,the random sequence{1/√n(X1+···+Xn)}i∞=1 converges in law to a nonlinear normal distribution,called G-normal distribution,where{Xi}i∞=1 is an i.i.d.sequence under the sublinear expectation.It’s known that the framework of sublinear expectation provides a important role in situations that the probability measure itself has non-negligible uncertainties.Under such situation,this new CLT plays a similar role as the one of classical CLT.The classical CLT can be also directly obtained from this new CLT,since a linear expectation is a special case of sublinear expectations.A deep regularity estimate of 2nd order fully nonlinear parabolic PDE is applied to the proof of the CLT.This paper is originally exhibited in arXiv.(math.PR/0702358v1).