摘要
粗糙集理论是近年来国际上研究智能决策技术的一个新成果，是对不完整、不精确、不确定信息的表达、学习、归纳的理论。它可以将测量所得的数据信息进行分类、约简、挖掘和形成规则。其重要特点在于其具有很强的定性分析能力，即不需要预先给定某些特征或属性的数量描述，而直接从给定问题的描述集合出发，通过不可分辨关系和不可分辨类确定给定问题的近似域，从而找出该问题的内在规律。
旋转机械是机械设备的重要组成部分，它们以转子及其回转部件为工作的主体，一旦发生故障，将造成巨大损失。同时现代设备管理要求采用“故障维修”策略，消除“过剩维修”。因此世界各国都非常重视旋转机械故障诊断研究。目前，国内外故障诊断技术已取得了重大的进展，诊断方法由简易型向智能化、集成化方向发展，出现了遗传算法、模糊数学、神经网络等智能决策系统。但是，这些决策系统数学模型难以建立，物理意义不明确，需专家参与，且数据处理和学习时间过长而失去它在线控制的意义。
目前，国内外学者对粗糙集的研究主要集中在如何应用它的方法，处理一些简单的故障诊断信息表，探讨这种方法的可行性。而从机械故障的数据采集，信号处理，知识库和决策表的形成，直到应用粗糙集理论对决策表进行约简，形成决策规则，这方面的报导还很少见。因此，如何将粗糙集理论应用到处理旋转机械故障的工程实际中，已成为大家十分关心的课题。本课题组在2001年得到了江苏省自然科学基金的立项资助（BK2001095），为深入地开展研究提供了良好的基础。
本文的主要工作体现在：
1、确定了基于粗糙集理论的旋转机械故障在线诊断的技术路线。以旋转机械为对象，侧重研究转子不对中、转子不平衡、油膜涡动和转轴的局部摩擦四种典型的旋转机械故障,分析了这几种故障的机理及其特征表现。在旋转机械故障诊断方法中，振动分析法是成熟的方法之一。本研究通过速度传感器、加速度传感器和位移传感器采集特征信息和敏感性参数，同时通过时域分析、频域分析、时间序列分析得到不同故障的特征信息，构成了故障信息的知识库。通过对图形的语义化和对数据的数学处理，形成决策表。通过粗糙集理论对决策表进行约简，并优选出最简决策表，形成标准特征库。从运行中的旋转设备，检测出状态信号，与标准信息库相比较，确定状态模式，作出故障诊断决策。
2、提出了模拟四种故障的力学模型和实现的方法。在模拟实验中，转子不对中
故障是通过提高轴承支座的高度，产生轴线角度不对中；转子不平衡故障的模拟，是在对经过动平衡试验转子上，配载一定质量的偏心载荷；油膜涡动故障是用带有油杯的轴承座，轴和轴颈之间有较大的配合间隙；转轴的碰摩故障是通过远离动力源端，靠近支座处，安装摩擦螺钉。在模拟实验时，应用CRAS5.1数据采集系统，对实验数据采集、信号与系统分析和时间与振动趋势测定。
3、建立了故障诊断的决策表。从转子故障实验图表及其相关数据中，根据不同的条件属性和决策属性的对应关系，结合机械故障诊断的专业知识，对图表进行语义化，和实验数据一起，按照粗糙集理论的要求，建立旋转机械故障诊断的数据库。论文中，根据实验处理软件所提供的数据和图形，提出了六大类，十七个条件属性，一个决策属性。六大类条件属性分别是特征频率、时间-振动曲线特性、轴心轨迹、振动随转速的变化规则、振动的稳定性以及峭度特性；一个决策属性是联轴节的不对中、转子的不平衡、转轴的碰摩和轴承的油膜振荡。用语义法描述了图形库的知识，实现了将知识库向决策表的过渡。为了应用粗糙集理论对数据库进行约简，就必须按某种数学模型或计算方法，对采集的连续数据离散化，对图形语义化，并用符号代替语义定义，构造符合粗糙集理论要求的决策表，
4、形成了旋转机械故障诊断的决策规则。由于在故障诊断的决策表中，有些特征信息是相关的，有些是独立的。独立的特征能提供互补信息，因而加以保留，相关性特征产生冗余信息。在对决策表约简时，首先进行条件属性的简化，消去重复列，然后对每一决策规则进行冗余属性值的简化，合并重复行，导出简化决策表，形成旋转机械故障诊断的决策规则，并对决策规则进行可信度研究。
5、确定了决策表的核和最小解。通过区分矩阵和区分方程寻找决策表的约简和核。对于一个决策表有可能有多种约简形式，属性子集可以不只是一种简化，一个知识表达系统的决策表的简化不是唯一，问题的最小解不是唯一的，通过优化方法，鳞选得出决策表的最小的约简形式。
应用粗糙集理论对四种典型的旋转机械故障形成的决策表的约简，从十七个条件属性简化成三个条件属性，极大地减少数据库中数据的数量。对四种故障的决策规则和相关的设备故障诊断标准规则相一致。验证了应用粗糙集理论对数据库约简的有效性，证明了基于粗糙集理论的旋转机械故障诊断是可行的。
Rough Sets Theory (RS) is a new fruit in the field of studying artificial intelligent decision-making technology in recent years in the world. RS researches into knowledge of expression, learning and conclusion of inexact, incomplete or uncertain. This method can be used for the classification, reduction, data-mining and regulation establishment from obtained data. The main feature of the theory is the strong qualitative-analysis ability, i.e. without advance quantity description for some character or attributes, the internal regulation can be found out directly from the description aggregation by the application of approximation universe produced by indiscernible relation and attributes.
The rotating machinery is the major part of machinery, and its work mainly depends on rotor and rotating part of this mechanical device. Once some fault occurs，there will be a great loss. Due to the strategy of "fault maintenance" instead of strategy of "overmuch maintenance" in management of equipment at present, many countries pay more attention to the study of fault diagnosis in rotating machinery. Recently, some great achievement in the field has been obtained in the world. There is a trend for the method of fault diagnosis from simple to intelligent and integration. Some intelligent decision-making systems come out, such as genetic algorithm, fuzzy mathematics and neural network. But it is difficult to establish the mathematics models of these decision-making systems, and the physical meanings of the mathematics models of these decision-making systems are else not clear. In addition, due to the long time on data treatment and self-studying, the on-line control becomes impossible.
For the time being, study of RS focus mainly on how to deal with some simple fault diagnosis information tables and its feasibility of the method. But it has been less reported about the data collection of mechanical failure, signal treatment from sensor, forming of knowledge database and decision-table, and decision-table reduction using RS. Therefore, the applying study based on RS of rotating machinery fault diagnosis has become to a very attractive task. The project has been gotten financially aid by the Natural Science Fund of Jiangsu province in 2001(BK2001095). This provided a good foundation for further studying.
The major innovations in the present study are as follows:
1. Techno-way is ascertained for rotating machinery fault diagnosis on line based on RS. This paper mainly studies four kinds of typical rotating machinery faults including rotor misalignment, rotor unbalance, bear oil whip and shaft friction and hitting. Four kinds of typical fault principles and characteristic behavior are analyzed. Vibration analysis method
is a very important fault diagnoses way for rotating machinery. Characteristic information and sensitive parameter are collected by velocity sensor, displacement sensor and acceleration sensor. The different fault characteristic information is gotten by analysis of time domain, frequency domain and time sequence. Decision table is built by figure semantization and data treatment. Decision table is reduced using RS, the simplest decision table is made a choice, and standard characteristic database is done. State information checking and measuring from running rotating machinery is contrasted with standard information database, and then decision-making of fault diagnosis is made out.
2. Mechanics model and achieving method are proposed about the four kinds of faults. In simulative experiment, bearing stands are hoisted through putting shim and bringing axis-line angle misalignment in rotor misalignment. Fixing eccentricity load in the rotor that is tested in dynamic balancing forms rotor unbalance fault. Oil whip fault is gotten, as clearance is big enough between axis and axis neck. Shaft friction and hitting fault are produced by friction bolt that is away from power and near bearing stand. CRAS5.1 data collection system is applied in rotor fault simulative experiment to collect information, analyze
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