本文選題：不確定性量化 + 隨機(jī)集理論　； 參考：《中國(guó)工程物理研究院》2016年博士論文

【摘要】：裕量與不確定性量化(Quantification of Margins and Uncertainties, QMU)是美國(guó)核安全部門(mén)為了在實(shí)驗(yàn)受限的情況下評(píng)估復(fù)雜系統(tǒng)的可靠性、安全性而提出的一種性能分析理念。其體現(xiàn)了科研工程中系統(tǒng)分析方式由實(shí)驗(yàn)數(shù)據(jù)統(tǒng)計(jì)向基于物理特性進(jìn)行建模仿真的轉(zhuǎn)變趨勢(shì),在航空航天、核能、土木等領(lǐng)域都有廣闊的應(yīng)用前景。從具有廣泛適用性的數(shù)學(xué)層面來(lái)講,不確定性量化以及模型確認(rèn)是支撐QMU分析所需的關(guān)鍵技術(shù),現(xiàn)有的這方面研究在實(shí)際應(yīng)用時(shí)仍存在諸多不足。包括不確定性量化過(guò)程中對(duì)樣本信息所做的假設(shè)過(guò)于主觀、變量間的相關(guān)性被忽略、確認(rèn)推斷過(guò)程中未考慮模型響應(yīng)間定量聯(lián)系的非精確性、QMU度量不具有明確的數(shù)學(xué)意義等。本文針對(duì)這些問(wèn)題,研究完善基于隨機(jī)集理論的不確定性量化方法,并以此為基礎(chǔ)提出有關(guān)模型確認(rèn)以及QMU度量的改進(jìn)方法,文中具體工作如下：(1)針對(duì)數(shù)據(jù)樣本有限,且其中同時(shí)含有點(diǎn)數(shù)據(jù)以及區(qū)間數(shù)據(jù)的測(cè)試信息,研究了相應(yīng)的隨機(jī)集表示方法。通過(guò)bootstrap抽樣與核密度估計(jì)相結(jié)合的方式將此類測(cè)試信息中的不確定性由概率分布包絡(luò)表示出來(lái),再將其離散為隨機(jī)集的表示形式。除此以外,還討論了變量間存在相關(guān)性時(shí)基于隨機(jī)集理論的不確定性量化方法,該方法根據(jù)變量間的相關(guān)系數(shù)矩陣,通過(guò)Nataf變換產(chǎn)生相關(guān)樣本,進(jìn)而獲取多維焦元的聯(lián)合基本概率賦值。算例分析顯示了該方法在變量相關(guān)條件下的有效性。(2)針對(duì)現(xiàn)有確認(rèn)度量缺乏對(duì)模型響應(yīng)中認(rèn)知不確定性的考慮這一不足,采用Pignistic概率轉(zhuǎn)換方法將基于隨機(jī)集的模型認(rèn)知不確定性量化結(jié)果轉(zhuǎn)換為便于決策的Pignistic概率分布形式,通過(guò)考察其與實(shí)驗(yàn)觀測(cè)數(shù)據(jù)的概率分布距離來(lái)量化模型的準(zhǔn)確性。并將Kolmogorov-Smirnov置信包絡(luò)與優(yōu)化問(wèn)題求解結(jié)合起來(lái)給出了與實(shí)驗(yàn)觀測(cè)樣本量相對(duì)應(yīng)的確認(rèn)度量的置信區(qū)間。在此基礎(chǔ)上,通過(guò)構(gòu)造實(shí)驗(yàn)觀測(cè)數(shù)據(jù)的協(xié)方差矩陣,提出了一種多響應(yīng)條件下基于概率分布距離的確認(rèn)度量方法。該方法考慮了各確認(rèn)點(diǎn)／模型輸出變量之間的相關(guān)性,能夠在模型多響應(yīng)的條件下給出對(duì)于模型整體準(zhǔn)確性的量化結(jié)果。(3)針對(duì)現(xiàn)有基于貝葉斯網(wǎng)絡(luò)的確認(rèn)推斷方法未考慮網(wǎng)絡(luò)節(jié)點(diǎn)間非精確條件概率這一常見(jiàn)情況的不足,采用區(qū)間概率描述不同網(wǎng)絡(luò)節(jié)點(diǎn)間的聯(lián)系,而后基于修正區(qū)間條件概率的Gibbs近似推理獲得貝葉斯網(wǎng)絡(luò)中缺乏實(shí)驗(yàn)觀測(cè)的節(jié)點(diǎn)在特定模型響應(yīng)處的后驗(yàn)概率。在此基礎(chǔ)上利用區(qū)間數(shù)排序的方式對(duì)比特定網(wǎng)絡(luò)節(jié)點(diǎn)所表示的模型響應(yīng)的后驗(yàn)／先驗(yàn)區(qū)間概率,最終得到能夠反映模型準(zhǔn)確性的擴(kuò)展貝葉斯因子以及有關(guān)模型準(zhǔn)確性的置信度,由此實(shí)現(xiàn)了貼近科研工程中實(shí)際條件的確認(rèn)推斷。(4)研究了將系統(tǒng)性能特征的隨機(jī)集量化結(jié)果與系統(tǒng)性能閾值的Logistic回歸分析結(jié)果相結(jié)合的QMU度量方式。相比區(qū)間形式的性能閾值描述,采用Logistic回歸分析能夠由分類實(shí)驗(yàn)觀測(cè)數(shù)據(jù)得到關(guān)于性能閾值的概率分布描述,在此基礎(chǔ)上圍繞系統(tǒng)性能特征與性能閾值的特定分位點(diǎn)所定義的QMU度量能夠與系統(tǒng)可靠度指標(biāo)聯(lián)系起來(lái),且具有固定的臨界值。通過(guò)該度量值可以直觀地向決策人員反映系統(tǒng)的可靠性狀況。(5)研究了將隨機(jī)集不確定性表示方式與現(xiàn)代優(yōu)化算法相結(jié)合的系統(tǒng)參數(shù)設(shè)計(jì)方法。該方法能夠在指定系統(tǒng)輸出包絡(luò)的情況下得到優(yōu)化的系統(tǒng)參數(shù)概率分布包絡(luò),且在此過(guò)程中不需要如貝葉斯方法一樣為系統(tǒng)參數(shù)設(shè)定任何先驗(yàn)分布。由此可以為系統(tǒng)設(shè)計(jì)過(guò)程中的不確定性指標(biāo)分配提供依據(jù)。
[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.
【學(xué)位授予單位】：中國(guó)工程物理研究院
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2016
【分類號(hào)】：O211

【相似文獻(xiàn)】

相關(guān)期刊論文 前10條

1 孔紹文;隨機(jī)集與集合套理論[J];解放軍測(cè)繪學(xué)院學(xué)報(bào);1987年02期

2 李西和;;一般隨機(jī)集的中心統(tǒng)計(jì)定理[J];數(shù)學(xué)季刊;1989年03期

3 汪培莊,張文修;隨機(jī)集及其模糊落影分布簡(jiǎn)化定義與性質(zhì)[J];西安交通大學(xué)學(xué)報(bào);1982年06期

4 閻建平,江佩榮;隨機(jī)集與模糊集運(yùn)算之間的關(guān)系[J];沈陽(yáng)機(jī)電學(xué)院學(xué)報(bào);1984年02期

5 郭嗣琮;F集值統(tǒng)計(jì)[J];阜新礦業(yè)學(xué)院學(xué)報(bào);1986年04期

6 李華貴,張文修;隨機(jī)集序列在拓?fù)湟饬x下收斂定理[J];科學(xué)通報(bào);1987年02期

7 李世楷,孔慶隆;關(guān)于隨機(jī)集積分序列的收斂定理[J];科學(xué)通報(bào);1987年07期

8 毛超林;;某些隨機(jī)集合的復(fù)蓋性質(zhì)[J];深圳大學(xué)學(xué)報(bào);1987年Z2期

9 曹顯兵;隨機(jī)集序列的收斂域[J];益陽(yáng)師專學(xué)報(bào);1993年06期

10 閆彥宗,米據(jù)生;基于隨機(jī)集的可能性測(cè)度[J];寧夏大學(xué)學(xué)報(bào)(自然科學(xué)版);2002年02期

相關(guān)會(huì)議論文 前1條

1 梁學(xué)軍;;二型隨機(jī)集與隸屬程度分析[A];數(shù)學(xué)及其應(yīng)用文集——中南模糊數(shù)學(xué)和系統(tǒng)分會(huì)第三屆年會(huì)論文集（上卷）[C];1995年

相關(guān)博士學(xué)位論文 前4條

1 趙亮;基于隨機(jī)集理論的QMU關(guān)鍵技術(shù)研究[D];中國(guó)工程物理研究院;2016年

2 孟凡彬;基于隨機(jī)集理論的多目標(biāo)跟蹤技術(shù)研究[D];哈爾濱工程大學(xué);2010年

3 徐曉濱;不確定性信息處理的隨機(jī)集方法及在系統(tǒng)可靠性評(píng)估與故障診斷中的應(yīng)用[D];上海海事大學(xué);2009年

4 歐陽(yáng)成;基于隨機(jī)集理論的被動(dòng)多傳感器多目標(biāo)跟蹤[D];西安電子科技大學(xué);2012年

相關(guān)碩士學(xué)位論文 前10條

1 程旭陽(yáng);未知雜波環(huán)境隨機(jī)集強(qiáng)度濾波器研究[D];西安電子科技大學(xué);2014年

2 魏軻;隨機(jī)集與非線性數(shù)學(xué)期望[D];山東大學(xué);2010年

3 孫璐;基于隨機(jī)集樣本的統(tǒng)計(jì)學(xué)習(xí)理論基礎(chǔ)[D];河北大學(xué);2009年

4 汪百川;隨機(jī)集理論在通信中的應(yīng)用研究[D];杭州電子科技大學(xué);2010年

5 鄭學(xué)_";復(fù)雜環(huán)境下基于隨機(jī)集的多目標(biāo)跟蹤算法研究[D];西安電子科技大學(xué);2013年

6 朱孟凱;基于隨機(jī)集理論的多目標(biāo)跟蹤算法研究[D];吉林大學(xué);2013年

7 周承興;基于隨機(jī)集的多目標(biāo)跟蹤算法研究[D];西安電子科技大學(xué);2011年

8 李末;一種基于隨機(jī)集的異類信息表示與融合方法[D];哈爾濱工程大學(xué);2011年

9 瑚成祥;基于隨機(jī)集理論的多目標(biāo)跟蹤方法[D];西安電子科技大學(xué);2014年

10 鄒其兵;多伯努利濾波器及其在檢測(cè)前跟蹤中的應(yīng)用[D];西安電子科技大學(xué);2012年

，

本文編號(hào)：2003966