基于随机集理论的QMU关键技术研究

发布时间：2018-06-10 17:07

本文选题：不确定性量化 + 随机集理论　；参考：《中国工程物理研究院》2016年博士论文

【摘要】：裕量与不确定性量化(Quantification of Margins and Uncertainties, QMU)是美国核安全部门为了在实验受限的情况下评估复杂系统的可靠性、安全性而提出的一种性能分析理念。其体现了科研工程中系统分析方式由实验数据统计向基于物理特性进行建模仿真的转变趋势,在航空航天、核能、土木等领域都有广阔的应用前景。从具有广泛适用性的数学层面来讲,不确定性量化以及模型确认是支撑QMU分析所需的关键技术,现有的这方面研究在实际应用时仍存在诸多不足。包括不确定性量化过程中对样本信息所做的假设过于主观、变量间的相关性被忽略、确认推断过程中未考虑模型响应间定量联系的非精确性、QMU度量不具有明确的数学意义等。本文针对这些问题,研究完善基于随机集理论的不确定性量化方法,并以此为基础提出有关模型确认以及QMU度量的改进方法,文中具体工作如下：(1)针对数据样本有限,且其中同时含有点数据以及区间数据的测试信息,研究了相应的随机集表示方法。通过bootstrap抽样与核密度估计相结合的方式将此类测试信息中的不确定性由概率分布包络表示出来,再将其离散为随机集的表示形式。除此以外,还讨论了变量间存在相关性时基于随机集理论的不确定性量化方法,该方法根据变量间的相关系数矩阵,通过Nataf变换产生相关样本,进而获取多维焦元的联合基本概率赋值。算例分析显示了该方法在变量相关条件下的有效性。(2)针对现有确认度量缺乏对模型响应中认知不确定性的考虑这一不足,采用Pignistic概率转换方法将基于随机集的模型认知不确定性量化结果转换为便于决策的Pignistic概率分布形式,通过考察其与实验观测数据的概率分布距离来量化模型的准确性。并将Kolmogorov-Smirnov置信包络与优化问题求解结合起来给出了与实验观测样本量相对应的确认度量的置信区间。在此基础上,通过构造实验观测数据的协方差矩阵,提出了一种多响应条件下基于概率分布距离的确认度量方法。该方法考虑了各确认点／模型输出变量之间的相关性,能够在模型多响应的条件下给出对于模型整体准确性的量化结果。(3)针对现有基于贝叶斯网络的确认推断方法未考虑网络节点间非精确条件概率这一常见情况的不足,采用区间概率描述不同网络节点间的联系,而后基于修正区间条件概率的Gibbs近似推理获得贝叶斯网络中缺乏实验观测的节点在特定模型响应处的后验概率。在此基础上利用区间数排序的方式对比特定网络节点所表示的模型响应的后验／先验区间概率,最终得到能够反映模型准确性的扩展贝叶斯因子以及有关模型准确性的置信度,由此实现了贴近科研工程中实际条件的确认推断。(4)研究了将系统性能特征的随机集量化结果与系统性能阈值的Logistic回归分析结果相结合的QMU度量方式。相比区间形式的性能阈值描述,采用Logistic回归分析能够由分类实验观测数据得到关于性能阈值的概率分布描述,在此基础上围绕系统性能特征与性能阈值的特定分位点所定义的QMU度量能够与系统可靠度指标联系起来,且具有固定的临界值。通过该度量值可以直观地向决策人员反映系统的可靠性状况。(5)研究了将随机集不确定性表示方式与现代优化算法相结合的系统参数设计方法。该方法能够在指定系统输出包络的情况下得到优化的系统参数概率分布包络,且在此过程中不需要如贝叶斯方法一样为系统参数设定任何先验分布。由此可以为系统设计过程中的不确定性指标分配提供依据。
[Abstract]:Quantification of Margins and Uncertainties (QMU) is a performance analysis concept proposed by the U. S. nuclear safety department to evaluate the reliability and security of complex systems in the case of limited experiment. It embodies the system analysis method in scientific research engineering from experimental data statistics to physical characteristics The changing trend of modeling and simulation has broad application prospects in aerospace, nuclear energy, civil and other fields. From the mathematical level of wide applicability, uncertainty quantification and model confirmation are the key technologies to support QMU analysis. There are still a lot of shortcomings in the practical application of the existing research. In the process of qualitative quantification, the hypothesis of sample information is too subjective, the correlation between variables is ignored, the inaccuracy of quantitative relation between model responses is not considered in the process of confirmation and inference, and the QMU measure does not have definite mathematical meaning. On the basis of this, the improvement methods of model confirmation and QMU measurement are proposed. The specific work in this paper is as follows: (1) the corresponding random set representation method is studied for the limited data samples, which contain point data and interval data at the same time. The method of combining bootstrap sampling with kernel density estimation will be used. The uncertainty in the test information is expressed by the probability distribution envelope, and then it is discrete as the representation of the random set. In addition, the uncertainty quantization method based on the random set theory is discussed. The method generates the related samples by the Nataf transformation according to the correlation coefficient matrix among the variables, and then the method is obtained. The combined basic probability assignment of the multidimensional focal element is taken. An example analysis shows the effectiveness of the method under the variable dependent condition. (2) in view of the deficiency of the existing confirmation measure that lacks the consideration of the cognitive uncertainty in the model response, the Pignistic probability conversion method is used to convert the quantitative results of the model cognitive uncertainty based on the random set. In order to facilitate the decision - making Pignistic probability distribution, the accuracy of the model is quantified by examining the probability distribution distance from the experimental observation data. The confidence interval of the Kolmogorov-Smirnov confidence envelope and the optimization problem is combined to give the confidence interval of the confirmation measure corresponding to the sample size of the experimental observation. The covariance matrix of experimental observation data is made, and a method of recognition based on probability distribution distance is proposed under the condition of multi response. This method considers the correlation between the output variables of each confirmation point / model, and can give the quantitative results for the overall accuracy of the model under the condition of multi response of the model. (3) the existing Bayesian method is based on the Bayesian network. The confirmation and inference method of Juliu network does not take into account the shortage of the inaccurate conditional probability between network nodes. The interval probability is used to describe the connection between different network nodes, and then based on the Gibbs approximation of the modified interval conditional probability, the nodes in the Bayesian network which lack the actual observation observation in the specific model response are obtained. On this basis, by comparing the posterior / prior interval probability of the model response expressed by a specific network node, the extended Bias factor which can reflect the accuracy of the model and the confidence of the accuracy of the model are finally obtained. Thus the confirmation of the actual conditions in the scientific research project is realized. (4) (4) a QMU measure which combines the results of the stochastic collection of the system performance characteristics with the Logistic regression analysis results of the system performance threshold is studied. Compared with the performance threshold description of the interval form, the Logistic regression analysis can be used to describe the probability distribution of the performance threshold from the classified experimental data, and on this basis. The QMU metric defined by the specific points of the system performance characteristics and performance thresholds can be linked to the system reliability index, and has a fixed critical value. Through this measure, the reliability status of the system can be directly reflected to the decision maker. (5) a study of the stochastic set uncertainty representation and the modern optimization algorithm is studied. A combined system parameter design method. This method can obtain the optimal probability distribution envelope of the system parameters in the case of the specified system output envelope, and in this process, it does not need to set any prior distribution for the system parameters as the Bayesian method, which can provide the allocation of uncertain indexes in the system setting process. Basis.
【学位授予单位】：中国工程物理研究院
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O211

【相似文献】