Research On Key Technologies Of QMU Based On Random Set Theory

Quantification of Margins and Uncertainties (QMU) was originally introduced as a concept for reliability and safety assessment in complex system by American nuclear department. It reflects the change in the system assessment from experimental statistics to physics based model and simulation, and has broad application in aerospace engineering, nuclear engineering, civil engineering and so on. Uncertainty quantification and model validation are key techniques for QMU from the viewpoint of mathematics. Up to the present, the existing methods for the application of QMU are doubted for the subjective assumption on the distribution of variable, the ignorance for the dependence between variables, the insufficient consideration about the imprecise relationship between model responses during validate extrapolation, the ambiguity of the QMU metric,In this work, the uncertainty quantification based on the random set theory is investigated, then the methods for the model validation and QMU metric are presented. The major contributions in the dissertation are as follows:(1)The construction of random set from information which consists of limited point measurements and interval measurements is studied. Using bootstrap sampling and kernel density estimation, a probability box about the given measurements is obtained, then the random set is constructed from the probability box by an outer discretization method. Besides, the uncertainty quantification method based on random set theory considering the dependence among system variables is also discussed, the Nataf transformation is used to generate dependent random samples which are consistent with correlation coefficients matrix, then the joint basic probability assignments for the multidimensional focal elements are calculated to construct the random set. Simulation result shows that the method can get reasonable results with dependent variables.(2)The validation metric under epstemic uncertainty is considered. The result of unceratainty quantification based on random set theory is transformed into Pignistic probability distribution for the sake of decision, then it is compared with the probability distribution of the experimental observations to measure the accuracy of the model. The confidence interval for the validation metric is presented by calculating the infimum and supremum of the distance between the Pignistic probability distribution and the Kolmogorov-Smirnov confidence interval of the experimental distribution. Besides, a multiple response validation metric based on distance of probability distribution is proposed by constructing experimental covariance matrix. The metric considers the correlation among multiple model responses, and it provides a quantitative measurement about the model accuracy when there are multiple model responses.(3)The validation extrapolation based on Bayes network with imprecise conditional probabilities is considered. The relationships between model variables are characterized with interval probabilities. Then the posterior probability for the network node which lacks experimental observation is extrapolated by the Gibbs method based on the modificatory interval conditional probability. Finally, the extended Bayes factor which reflects the accuracy of the model is calculated by ranking the interval values of prior and posterior probabilities of the model prediction, and the confidence of the model is also obtained based on the extended Bayes factor. With the consideration of the imprecise conditional probabilities, the method of validation extrapolation consists with the practical applications.(4)The QMU metric which combines the system performance characteristic quantified by random set with the performance threshold obtained by Logistic regression is discussed. Compared with a determinated performance threshold, the Logistic regression provides more meaningful description for the performance threshold from the experimental observations. Based on the description, the QMU metric defined with the selected percentiles of the performance characteristic and performance threshold can be connected with the reliability index. Moreover, the critical value of the QMU metric is static, it is helpful to present the system status for the decision makers.(5)The system design method based on the uncertainty representation with random set and modern optimization algorithm is proposed. This method optimizes the probability box of the system parameters with the specified probability box of the system output. And the prior information for the system parameter is not crucial during the optimization procedure. With this method, the allocation of uncertainty for the system parameters can be more rational.