Monte Carlo Analysis has been an accepted method for circuit tolerance analysis, but the heavy computational complexity has always prevented its applications. Based on random set theory, this paper presents a simple and flexible tolerance analysis method to estimate circuit yield. It is the alternative to Monte Carlo analysis, but reduces the number of calculations dramatically.
The particle Probability Hypotheses Density (particle-PHD) filter is a tractable approach for Random Finite Set (RFS) Bayes estimation, but the particle-PHD filter can not directly derive the target track. Most existing approaches combine the data association step to solve this problem. This paper proposes an algorithm which does not need the association step. Our basic ideal is based on the clustering algorithm of Finite Mixture Models (FMM). The intensity distribution is first derived by the particle-PHD filter, and then the clustering algorithm is applied to estimate the multitarget states and tracks jointly. The clustering process includes two steps: the prediction and update. The key to the proposed algorithm is to use the prediction as the initial points and the convergent points as the es- timates. Besides, Expectation-Maximization (EM) and Markov Chain Monte Carlo (MCMC) ap- proaches are used for the FMM parameter estimation.
Liu WeifengHan ChongzhaoLian FengXu XiaobinWen Chenglin
Simultaneous faults often occur in running equipments, in order to solve the problems of the simultaneous faults, a new approach based on random sets and Dezert-Smarandache Theory (DSmT) is proposed in this paper. Firstly, the simultaneous faults' model is built based on the generalized frame of discernment in DSmT. Secondly, according to the unified description of combination rules in evidence reasoning based on random sets, a new combination rule for simultaneous faults diagnosis is proposed. Thirdly, according to the working characteristics and environment of the sensors used to acquire fault characteristic information, a new method to construct basic probability assignment function is pro- posed based on membership. Finally, diagnosis result is obtained by use of the new combination rule combined with decision rules. A case pertaining to the fault diagnosis for a multi-function rotor test-bed is given, and the result shows that the proposed diagnosis approach is feasible and efficient.
Natural-language information is often mathematically expressed by fuzzy sets. With the random set theory as a bridge, this kind of information can be transformed into fuzzy evidence in Dempster-Shafer (DS) theory. Then Dempster's combination rule or other combination rules of evi- dence can be used perfectly for fusing natural-language and other information. However, this traditional transformation involves the use of α -cutsets to construct the focal elements which have to be repre- sented as consonant sets. This construction is very inflexible and unreasonable in some practical ap- plications. In this paper, with the desire to overcome this limitation, a method for constructing more general non-consonant focal elements is proposed based on the random set theory. Some examples are given to show the generality and the efficiency of this new method. Finally, we validate that non-consonant constructions provide less degrees of total uncertainty than that of the consonant case in these examples by using the evaluation criterion of total uncertainty.
