基于符号有向图和支持向量机的故障诊断方法的研究
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摘要
符号有向图(Signed Directed Graph, SDG)是在图论的基础上发展起来的一种基于定性分析的故障诊断方法,能够有效地表达复杂系统的各个变量之间的相互关系,具有很强的完备性同时又具有灵活的推理方式和有效的推理算法能够提供故障传播的路径,给出故障发生的详细解释。然而由于SDG是基于定性的故障诊断方法,测量信号中许多有用的定量信息被忽略或无法被考虑,导致故障诊断分辨率不高。支持向量机(Support Vector Machine, SVM)是在统计学习理论的基础上发展起来的一种新的机器学习方法。采用结构风险最小化思想的SVM同时考虑了经验风险和置信区间的最小,能够获得最好的泛化能力,是专门研究小样本情况下机器学习的理论。其次,SVM巧妙地采用“核函数”,将低维非线性空间映射到高维线性特征空间的同时,并没有增加求解最优分类面的复杂度,解决了高维空间中计算带来的“维数灾难”问题。SVM以其深厚的数学基础和极强的泛化能力,被认为是十几年来机器学习和模式识别领域最有影响的成果之一。本文将SDG和SVM有机结合起来,利用SDG的完备性和推理机制,找到故障传播的相容通路,提取故障发生时的上要相关变量;利用SVM优良的分类性能对相关的主要变量进行训练,根据训练获得的最优分类面进行故障诊断。本文主要内容包括两大部分：一是基于“去心法”的支持向量预选取方法及其模式识别应用；二是基于SDG和SVM的故障诊断算法及其工程应用,这部分是本文的核心部分。具体内容包括以下几部分：(1)在深入研究支持向量机的理论基础及工作原理的基础上,提出了基于“去心法”(Central Samples Discarded Method,CSDM)的支持向量预选取方法。支持向量是决定最优超平面位置的关键元素,去掉非支持向量,重新对样本进行训练,能够得到相同的最优超平面。基于这个思想,提出了利用标准差去掉各类样本中靠近中心位置的样本,保留边界样本的“去心法”,以此来进行支持向量的预选取,该方法显著提高了SVM的训练速度。和已有的支持向量预选取方法进行对比,论证了该方法的可行性。
(2)提出了一次相容通路的概念。一次相容通路是指故障发生初期的相容通路。当故障发生时,系统状态变量的响应有3个阶段：初始响应、中间响应和最终响应。故障诊断最主要的性能指标之一是实时性,因此一次相容通路的获取对故障诊断非常重要,可以解决故障发生的不同时期,其相容通路不同而导致的分辨率不高的问题。一次相容通路是符号有向图理论的一个扩充。
(3)提出了符号有向图和支持向量机相结合的故障诊断方法。利用一次相容通路中的一次相容变量为基础进行SVM的训练,达到了降维的目的,提高训练和诊断速度；利用SVM优良的分类性可以提高故障诊断的准确率。以火电厂除氧器的故障诊断为例验证了该方法的可行性。
(4)将基于符号有向图和支持向量机的故障诊断方法应用在Tennessee-Eastman Process (TEP)仿真系统的故障诊断中。通过对TEP仿真系统的实验结果分析,对该故障诊断方法的适用范围进行了探讨。
本文的创新性成果如下
(1)提出了基于“去心法”的支持向量预选取方法；
(2)根据故障传播的特点,提出了一次相容通路的概念；
(3)本文将定性的SDG和定量的SVM有机结合起来,提出了一种基于SDG和SVM的故障诊断算法。
(4)针对多故障诊断中特征故障的特点,提出了将基于“二叉树”的多类分类算法与基于决策导向无环图(DDAG)的多类分类算法相结合的混合多类分类算法,并应用于除氧器的故障诊断中
(5)基于一次相容通路的概念,在基于决策导向无环图(DDAG)的多类分类算法中,提出了针对不同的两分类问题,选用不同的变量进行分类器的训练,提高了算法的训练速度。
Signed Directed Graph is a fault diagnosis method developed on the basis of graph theory, and not only can efficiently express the interrelations among variables of complex systems and has strong completeness, flexible reasoning ways and effective reasoning algorithm, but also shows failure propagation paths and faults detailed explanations. However, SDG is an qualitative analysis method, many useful quantitative information in measured signals are ignored or cannot be considered, which leads to low fault resolution. Support Vector Machine (S VM) is a new kind of machine learning method developed on the basis of statistical learning theory, which uses structural risk minimization thought. SVM takes the minimum of experience risk and confidence interval into account, and can gain the best generalization ability, and specializes in small sample. Then, SVM ingeniously uses "Kernel function", which can map low-dimensional nonlinear space to higher dimensional linear character space, in the process of which don't increase the complexity of solution of optimal classification, and solve problem of "dimension disaster" brought by calculation in higher-dimensional space. With profound mathematics base and strong generalization ability, SVM is considered to be one of the most influential achievements in pattern recognition and machine learning domain in ten years.
The qualitative SDG and quantitative SVM are combined in this paper. Mainly related variables in compatible pathways can be got by SDG's completeness and reasoning mechanisms; main variables are trained to acquire optimal hyperplanes.
This paper mainly includes two parts:first, support vector pre-selected method based on Central Samples Discarded Method is proposed and is applied in Pattern Recognition; second, fault diagnosis algorithm based on SDG and SVM is proposed and applied in engineering fault diagnosis, which is this paper's core.
The main research and innovative achievements in this paper can be classed as follows:
(1) On the basis of the thorough research in theoretical basis of support vector machine and the basic principle, support vector pre-selected was proposed based on the method of "Central Samples Discarded Method, CSDM". Support vector is the key elements deciding the optimal hyperplanes location, and removing the non-support vector and restarting training the sample can get the same optimal hyperplanes. Based on thought above, the method of "CSDM", which removes the samples near the center and keeps the boundary samples to have support vector pre-selected, is put forward, thus the purpose of improving the training speed is achieved. Compared with pre-existing support vector pre-selected method, the feasibility is demonstrated.
(2) Put forward the concept of Initial Consistent Path. Initial Consistent Path refers to consistent path at the beginning of the faults. When a fault occurs, the response of the system state variables has three stages:the initial response, middle response and eventual response. One of the main performance indexes of fault diagnosis is real-time. Therefore, the gain of consistent path of the initial response phase for fault diagnosis is very important, which can effectively solve the problem that different compatible pathways in different fault period can lead to low resolution. Initial Consistent Path is an extension to SDG.
(3) Put forward to fault diagnosis method of the combination of SDG and SVM. Proposed compatible pathways can look for fluctuating variables at the begining of the faults occurance. SVM training based on these variables can achieve the purpose of reducing the dimension, improve training and diagnosis velocity; SVM excellent classification can improve fault diagnosis accuracy. Fault diagnosis for deaerator of coal-fired plants demonstrated the feasibility of this method.
(4) Fault diagnosis method based on SDG and SVM is applied into Tennessee-Eastman Process (TEP) simulation fault diagnosis system. By analyzing the experimental results of the TEP simulation system, this paper discusses the applicable scope of the fault diagnosis method.
Innovative achievements in this paper can be classed as follows:
(1) Support vector pre-selected was proposed based on the method of Central Samples Discarded Method.
(2) Put forward to the concept of Initial Consistent Path by failure propagation characteristics.
(3) Put forward to fault diagnosis algorithm based on SDG and SVM.
(4) On account of the characteristics of special faults in multi-fault diagnosis, mix multi-class classification algorithm constituted with the combination of classification algorithms based on binary tree and DDAG are proposed and applied in fault diagnosis for deaerator of power plants.
(5) In DDAG-classification algorithm, the concept that different variables for classifier training in different two classification problem is put forward base on Initial Consistent Path, which improves training speed of algorithms.
(2)提出了一次相容通路的概念。一次相容通路是指故障发生初期的相容通路。当故障发生时,系统状态变量的响应有3个阶段：初始响应、中间响应和最终响应。故障诊断最主要的性能指标之一是实时性,因此一次相容通路的获取对故障诊断非常重要,可以解决故障发生的不同时期,其相容通路不同而导致的分辨率不高的问题。一次相容通路是符号有向图理论的一个扩充。
(3)提出了符号有向图和支持向量机相结合的故障诊断方法。利用一次相容通路中的一次相容变量为基础进行SVM的训练,达到了降维的目的,提高训练和诊断速度；利用SVM优良的分类性可以提高故障诊断的准确率。以火电厂除氧器的故障诊断为例验证了该方法的可行性。
(4)将基于符号有向图和支持向量机的故障诊断方法应用在Tennessee-Eastman Process (TEP)仿真系统的故障诊断中。通过对TEP仿真系统的实验结果分析,对该故障诊断方法的适用范围进行了探讨。
本文的创新性成果如下
(1)提出了基于“去心法”的支持向量预选取方法；
(2)根据故障传播的特点,提出了一次相容通路的概念；
(3)本文将定性的SDG和定量的SVM有机结合起来,提出了一种基于SDG和SVM的故障诊断算法。
(4)针对多故障诊断中特征故障的特点,提出了将基于“二叉树”的多类分类算法与基于决策导向无环图(DDAG)的多类分类算法相结合的混合多类分类算法,并应用于除氧器的故障诊断中
(5)基于一次相容通路的概念,在基于决策导向无环图(DDAG)的多类分类算法中,提出了针对不同的两分类问题,选用不同的变量进行分类器的训练,提高了算法的训练速度。
Signed Directed Graph is a fault diagnosis method developed on the basis of graph theory, and not only can efficiently express the interrelations among variables of complex systems and has strong completeness, flexible reasoning ways and effective reasoning algorithm, but also shows failure propagation paths and faults detailed explanations. However, SDG is an qualitative analysis method, many useful quantitative information in measured signals are ignored or cannot be considered, which leads to low fault resolution. Support Vector Machine (S VM) is a new kind of machine learning method developed on the basis of statistical learning theory, which uses structural risk minimization thought. SVM takes the minimum of experience risk and confidence interval into account, and can gain the best generalization ability, and specializes in small sample. Then, SVM ingeniously uses "Kernel function", which can map low-dimensional nonlinear space to higher dimensional linear character space, in the process of which don't increase the complexity of solution of optimal classification, and solve problem of "dimension disaster" brought by calculation in higher-dimensional space. With profound mathematics base and strong generalization ability, SVM is considered to be one of the most influential achievements in pattern recognition and machine learning domain in ten years.
The qualitative SDG and quantitative SVM are combined in this paper. Mainly related variables in compatible pathways can be got by SDG's completeness and reasoning mechanisms; main variables are trained to acquire optimal hyperplanes.
This paper mainly includes two parts:first, support vector pre-selected method based on Central Samples Discarded Method is proposed and is applied in Pattern Recognition; second, fault diagnosis algorithm based on SDG and SVM is proposed and applied in engineering fault diagnosis, which is this paper's core.
The main research and innovative achievements in this paper can be classed as follows:
(1) On the basis of the thorough research in theoretical basis of support vector machine and the basic principle, support vector pre-selected was proposed based on the method of "Central Samples Discarded Method, CSDM". Support vector is the key elements deciding the optimal hyperplanes location, and removing the non-support vector and restarting training the sample can get the same optimal hyperplanes. Based on thought above, the method of "CSDM", which removes the samples near the center and keeps the boundary samples to have support vector pre-selected, is put forward, thus the purpose of improving the training speed is achieved. Compared with pre-existing support vector pre-selected method, the feasibility is demonstrated.
(2) Put forward the concept of Initial Consistent Path. Initial Consistent Path refers to consistent path at the beginning of the faults. When a fault occurs, the response of the system state variables has three stages:the initial response, middle response and eventual response. One of the main performance indexes of fault diagnosis is real-time. Therefore, the gain of consistent path of the initial response phase for fault diagnosis is very important, which can effectively solve the problem that different compatible pathways in different fault period can lead to low resolution. Initial Consistent Path is an extension to SDG.
(3) Put forward to fault diagnosis method of the combination of SDG and SVM. Proposed compatible pathways can look for fluctuating variables at the begining of the faults occurance. SVM training based on these variables can achieve the purpose of reducing the dimension, improve training and diagnosis velocity; SVM excellent classification can improve fault diagnosis accuracy. Fault diagnosis for deaerator of coal-fired plants demonstrated the feasibility of this method.
(4) Fault diagnosis method based on SDG and SVM is applied into Tennessee-Eastman Process (TEP) simulation fault diagnosis system. By analyzing the experimental results of the TEP simulation system, this paper discusses the applicable scope of the fault diagnosis method.
Innovative achievements in this paper can be classed as follows:
(1) Support vector pre-selected was proposed based on the method of Central Samples Discarded Method.
(2) Put forward to the concept of Initial Consistent Path by failure propagation characteristics.
(3) Put forward to fault diagnosis algorithm based on SDG and SVM.
(4) On account of the characteristics of special faults in multi-fault diagnosis, mix multi-class classification algorithm constituted with the combination of classification algorithms based on binary tree and DDAG are proposed and applied in fault diagnosis for deaerator of power plants.
(5) In DDAG-classification algorithm, the concept that different variables for classifier training in different two classification problem is put forward base on Initial Consistent Path, which improves training speed of algorithms.
引文
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