本文關(guān)鍵詞： 鐵路事故 預(yù)警 相關(guān)性 MIC 圖模型 聚類算法　出處：《北京交通大學(xué)》2016年博士論文　論文類型：學(xué)位論文

【摘要】：鐵路運(yùn)輸在整個(gè)交通運(yùn)輸體系中占有重要的地位,隨著我國鐵路的大規(guī)模建設(shè),鐵路運(yùn)輸進(jìn)入了跨越式快速發(fā)展階段,鐵路運(yùn)營里程不斷增加,貨運(yùn)及客運(yùn)量不斷增長。然而,與此同時(shí),重、特大鐵路事故仍然偶有發(fā)生,這給人民生命和財(cái)產(chǎn)安全造成極大的損失,確保鐵路運(yùn)輸安全仍然是鐵路運(yùn)輸中的一項(xiàng)重要工作。當(dāng)前,各種先進(jìn)電子電氣設(shè)備不斷地應(yīng)用到鐵路系統(tǒng)中,影響鐵路安全的因素越來越多。面對(duì)如此多影響鐵路安全的因素,首先需要分析這些因素之間的相關(guān)性,相比其它統(tǒng)計(jì)相關(guān)系數(shù),最大信息系數(shù)(theMaximalInformationCoefficient,MIC)具有良好的性質(zhì):廣泛性(Generality)和均勻性(Equitability),MIC可以發(fā)現(xiàn)不同類型的相關(guān)關(guān)系。本文具體分析了 Reshef等人提出的兩變量最大信息系數(shù)MIC的定義及其近似算法,針對(duì)其存在的不足,提出了計(jì)算大規(guī)模數(shù)據(jù)中兩變量以及多變量最大信息系數(shù)MIC的快速算法,并基于最大信息系數(shù)MIC,進(jìn)行了鐵路事故分析及預(yù)警研究。具體來說,本文主要?jiǎng)?chuàng)新點(diǎn)如下。1.提出了計(jì)算兩變量最大信息系數(shù)MIC的數(shù)學(xué)規(guī)劃模型并設(shè)計(jì)了面向大規(guī)模數(shù)據(jù)的快速算法。通過分析Reshef等人提出的兩變量最大信息系數(shù)MIC的定義,明確了求解兩變量最大信息系數(shù)MIC的目標(biāo)以及各種約束條件,給出了數(shù)學(xué)規(guī)劃模型;針對(duì)Reshef等人提出的計(jì)算兩變量最大信息系數(shù)MIC近似算法計(jì)算時(shí)間較長的問題,利用k-均值聚類算法,分別對(duì)兩個(gè)變量進(jìn)行劃分,得到兩個(gè)變量的格子劃分,提出了計(jì)算大規(guī)模數(shù)據(jù)中兩變量最大信息系數(shù)MIC的快速算法。數(shù)值實(shí)驗(yàn)表明,本文提出的快速算法計(jì)算得到的兩變量最大信息系數(shù)MIC保留了 MIC的兩個(gè)優(yōu)良的性質(zhì):廣泛性和均勻性;不同類型兩變量相關(guān)關(guān)系最大信息系數(shù)MIC的計(jì)算時(shí)間非常接近,而且,隨著數(shù)據(jù)規(guī)模的增大,計(jì)算時(shí)間的增長速度不快;分析了算法的時(shí)間復(fù)雜度,Reshef等人提出的近似算法的時(shí)間復(fù)雜度為O(n2.4),本文提出的快速算法的時(shí)間復(fù)雜度是O(n1.6),本文提出的快速算法更適合發(fā)掘大規(guī)模數(shù)據(jù)中的兩變量相關(guān)關(guān)系。2.給出了多變量最大信息系數(shù)MIC的定義,并提出了計(jì)算大規(guī)模數(shù)據(jù)中多變量最大信息系數(shù)MIC的快速算法。利用互信息的鏈?zhǔn)椒▌t,將多變量互信息分解為一個(gè)變量與多個(gè)變量之間互信息的和,從而將多變量分為因變量和自變量兩部分,得到多變量最大信息系數(shù)MIC的定義。利用二分k-均值聚類算法,將自變量和因變量分別劃分為不同數(shù)量的塊,提出了計(jì)算大規(guī)模數(shù)據(jù)中多變量最大信息系數(shù)MIC的快速算法。數(shù)值實(shí)驗(yàn)結(jié)果表明,提出的快速算法計(jì)算得到的多變量最大信息系數(shù)MIC保持了 MIC的優(yōu)越性質(zhì):廣泛性和均勻性,并且計(jì)算時(shí)間較短,計(jì)算時(shí)間增長速度較慢,本文提出的快速算法適合發(fā)掘大規(guī)模數(shù)據(jù)中的多變量相關(guān)關(guān)系。3.提出了基于最大信息系數(shù)MIC的鐵路事故復(fù)雜網(wǎng)絡(luò)模型。事故因素作為網(wǎng)絡(luò)節(jié)點(diǎn),根據(jù)兩點(diǎn)之間最大信息系數(shù)MIC值產(chǎn)生網(wǎng)絡(luò)中的邊,分析了不同依賴性水平下的網(wǎng)絡(luò)結(jié)構(gòu)變化情況,具體分析了網(wǎng)絡(luò)節(jié)點(diǎn)的度、度分布、孤立點(diǎn)、連通圖以及網(wǎng)絡(luò)平均連接度等指標(biāo)的變化情況。對(duì)某一固定因素,隨著依賴性水平的不斷增長,該因素的重要影響因素可以被識(shí)別出來。4.提出了一種基于最大信息系數(shù)MIC的鐵路事故預(yù)警方法�；谧畲笮畔⑾禂�(shù)MIC,對(duì)相關(guān)影響因素按照相關(guān)性程度進(jìn)行排序,利用人工神經(jīng)網(wǎng)絡(luò)模型,得到不同數(shù)量影響因素情況下的擬合曲線,由此得到目標(biāo)因素與影響因素之間的最優(yōu)擬合曲線。在此基礎(chǔ)上,給出危險(xiǎn)區(qū)域的概念,提出了一種鐵路事故預(yù)警方法。當(dāng)影響鐵路安全的因素進(jìn)入危險(xiǎn)區(qū)域時(shí),調(diào)整不正常影響因素指標(biāo),可以極大地避免鐵路事故的發(fā)生。
[Abstract]:Railway transportation plays an important role in the entire transportation system, with large-scale construction of China's railway, the railway transportation has entered a leapfrog stage of rapid development, the railway operating mileage increasing, freight and passenger traffic increased. However, at the same time, heavy, large railway accidents still happen occasionally, which caused great losses to people's life and property safety, ensure the safety of railway transportation is still an important part of the railway transportation. At present, a variety of advanced electronic and electrical equipment constantly applied to the railway system, railway safety influence factors more and more. In the face of so many influence factors of railway safety, first need to analyze the correlation between these factors, compared with other statistical correlation coefficient, maximum information coefficient (theMaximalInformationCoefficient, MIC) has good properties: wide (Generality) and evenness (Equit Ability), MIC can find different types of relationships. This paper analyses the definition of the two variable maximum information coefficient MIC proposed by Reshef et al and its approximation algorithm, for its shortcomings, proposes a fast algorithm for calculation of large-scale data in two variables and multi variable coefficient MIC and the maximum information, based on the maximum information coefficient MIC. The railway accident analysis and early warning research. Specifically, the main innovations are as follows:.1. proposes a mathematical programming model to calculate the two variable maximum information coefficient MIC and designed a fast algorithm for large-scale data. Through the definition of the two variable maximum information coefficient MIC analysis proposed by Reshef et al, the solution of the two variable maximum information the coefficients of MIC target and constraints, the mathematical model of planning are given; according to Reshef et al. Proposed the calculation of two variable maximum information system MIC Approximation algorithm for computing time, using k- means clustering algorithm, are divided respectively to two variables and two variables divided by the lattice algorithm, calculation of the two variables in large-scale data maximum information coefficient MIC. Numerical experiments show that the variable coefficient MIC two maximum information calculated by the fast algorithm proposed in this paper retained two excellent MIC properties: universality and uniformity; the computation time of two different types of variable correlation coefficient MIC is very close to the maximum information, and, with the increasing size of the data, the calculating time of the growth rate is not fast; analyzes the time complexity of the algorithm, the approximate algorithm proposed by Reshef et al. The time complexity is O (n2.4), this paper presents fast algorithms of time complexity is O (n1.6), a fast algorithm is proposed in this paper is more suitable for the excavation of two variables related to large-scale data in .2. defines a multivariate maximum information coefficient MIC, and proposes a fast algorithm for calculation of large-scale data in multi variable maximum information coefficient MIC. By using the chain rule of mutual information, the multivariate mutual information between a variable and decomposed into multiple variables and mutual information, which will be divided into multiple variables for the two part variables and independent variables, defined by multivariate maximum information coefficient MIC. Two using k- means clustering algorithm, the independent and dependent variables are divided into different number of blocks, proposes a fast algorithm for calculation of large-scale data in multi variable maximum information system number MIC. The numerical results show that the maximum coefficient of multivariate information MIC obtained a fast algorithm is proposed to maintain the superior properties of MIC: universality and uniformity, and the computation time is short, the computation time grows slower, suitable for the fast algorithm is proposed in this paper To explore large data in multivariate correlation.3. proposed complex network model of maximum information coefficient of MIC railway accidents based on accident factors. As a network node, between two points according to the maximum information coefficient MIC value generated edges in the network, analyzes the different levels of the dependent network structure changes, analyzes the degree of network nodes, degree distribution, outlier, change graph and network connectivity. The average index of a fixed factor, along with the increasing dependence of the level, the important factors influencing factors can be identified as.4. proposed a railway accident early warning method of maximum information coefficient based on MIC. The maximum information coefficient MIC based on the related influencing factors according to the correlation of the sort, using artificial neural network model, get the fitting curves under different number of factors affected by the The optimal fitting curve between the target and the influence factors of factors. On this basis, the concept is given the danger zone, proposed a railway accident early warning method. When the influence factors of railway safety into the danger area, adjust the abnormal factors, can greatly avoid the railway accident.

【學(xué)位授予單位】：北京交通大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2016
【分類號(hào)】：U298.5;TP301.6

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