基于粗糙集理论的齿轮箱故障诊断研究
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摘要
齿轮箱是机械系统的重要传动部件,故障发生率较高,其振动信号呈现非线性非平稳的特点,故障程度、部位和类型等对特征参量的影响很大。在对齿轮箱进行监测与故障诊断时,若监测点选择不当就不能采集到有效的故障信息,从而导致故障发生部位不易确定,敏感特征参量提取困难、故障模式识别率低。局域波分解方法将非平稳时变信号自适应地分解展开并映射到时频分析平面,能够同时展示信号的时域和频域信息的全貌；粗糙集理论的属性约简技术能够优化故障特征参量集,提取出敏感的故障特征参量；最小二乘支持向量机的函数逼近效果良好,模式识别能力强,本文在采用局域波分解法处理故障信号以及深入研究粗糙集理论的基础上,将粗糙集与最小二乘支持向量机相结合,建立了基于粗糙集支持向量机的齿轮箱智能故障诊断系统。本文的主要研究内容与结论如下：
(1)在分析齿轮箱振动特性的基础上,提出采用局域波分解技术对齿轮箱故障信号进行处理并提取了初始的故障特征参量集。在局域波分解过程中,采用镜像延拓与窗函数相结合的方法缓解了端点效应问题,采用总体经验模态分解方法有效解决了模态混叠问题,实验结果表明这两种方法在齿轮箱故障信号分解中取得了较好的效果。根据衡量故障特征参量集的指标,提出采用每个工况的均方根有效值衡量故障特征参量集的稳定性,采用每个特征参量在六个工况之间的最小均值差衡量故障特征参量集的敏感性。实验中分别提取了基于EEMD的归一化能量特征参量集和基于EEMD的近似熵特征参量集,通过实际计算结果表明,前者与后者的敏感性基本一致,但是稳定性要优于后者,因此本文采用了基于EEMD的归一化能量特征参量集进行齿轮箱故障诊断。
(2)提出一种基于改进Naive Scaler算法的全局动态寻优离散化算法。通过对Naive Scaler算法过程进行改进,确保能够得到所有保证不可分辨关系的断点；通过断点均分样本集、逐渐增加断点的方法动态地从候选集中选择断点集,保证了整个信息系统分类能力不变的条件下断点个数最少。通过与其它算法对比,实验结果表明该算法得到的断点个数较少,体现了其在连续属性离散化方面的优越性。
(3)提出一种基于条件等价类的属性约简算法。该算法在核属性集的基础上,直接针对核属性的条件类中不能正确划入决策类的类,在核属性之外的其余条件属性中找到能够区分该类的属性,并添加到核属性集中,从而得到最小属性约简集。而基于启发式信息的属性约简算法无法保证所求约简集一定是最小属性约简集,实验结果表明该算法计算复杂度较低,提高了约简效率。
(4)提出采用粗糙集的属性约简技术对故障监测点进行优化配置。该方法将六个故障监测点的最小属性约简集融合成一个大决策表进行属性约简,根据每个监测点的故障特征参量在最终约简集中出现的频次判定相应监测点的分类能力,实验结果表明该方法不需要对监测对象建模,也不需要对其进行动力学分析,而是直接对监测到的振动信号进行处理,根据各个测点的故障特征参量与故障种类之间的关联程度选择最佳测点,是一种行之有效的测点优化配置方法。
(5)基于粗糙集理论提取决策规则的过程没有学习归纳的能力,故障模式识别率较低。粗糙集理论的属性约简技术能够提取敏感的故障特征参量,最小二乘支持向量机的模式识别能力强,因此为了充分利用两者在特征参量提取与模式识别方面的优势,构建了基于粗糙集支持向量机的智能故障诊断系统。理论与实践都表明该系统在一定程度上提高了齿轮箱故障诊断性能,为非线性非平稳故障信号的处理与识别提供了一种较通用的解决方案。
Gearbox is one of the most important transmission parts in the mechanical systems, but, for some uncertain reasons, the failure rate is higher, the vibration signal shows nonlinear and nonstationary, fault type and location as well as extent affect the characteristic parameters greatly. While monitoring and diagnosing the gearbox, selecting monitoring points improperly usually fails to gain the fault information effectively, determine the fault position, extract sensitive characteristic parameters and obtain high fault recognition rate. The method of local wave decomposition(LMD) could decompose the nonstationary signal adaptively and map to the time-frequence analysis plane, which could display signals in time domain and frequence domain simultaneously. Attributes reduction technology in rough sets (RS) could optimize the characteristic parameter set and extract the sensitive fault characteristic parameters. Least squares support vector machine (LSSVM) has good function approximation and high pattern recognition ratio. A method of combining RS with LSSVM through studying on LWD and RS deeply is proposed, intelligent fault diagnosis system of gearbox based on RS and LSSVM is established. The main work is as follows:
(1) LWD is employed to process the vibration signal of gearbox and extract the initial characteristic parameters based on analying the vibration property. A method of combining mirror extension with window function is used to relieve endpoint effect, ensemble empirical mode decomposition (EEMD) method is utilized to solve the mode mixing problem effectively, experiments show that these methods have achieved good results in fault signal decomposition. According to the measurable indicators of fault characteristic parameter set, it is proposed to use the rms values of the fault characteristic parameters to measure the stability and the minimal mean difference of each characteristic parameters in six working conditions to measure the sensitivity. The normalized energy and approximate entropy characteristic parameter sets based on EEMD are extracted in the paper, calculating results show that the sensitivity of the former and the latter are basically the same, but the stability is superior to the latter, so the normalized energy characteristic parameter set would be used for gearbox fault diagnosis.
(2) A global dynamic optimization algorithm for discretization based on improved Naive Scaler is proposed. The process of Naive Scaler algorithm is improved so that all breakpoints which warranties indiscernible relation would be got. The method of selecting breakpoints from the candidate set dynamically through separating the samples evenly by breakpoints and increasing the breakpoints gradually ensures the least breakpoints under the condition of keeping the classification ability of the whole information system. The experimental results show that the algorithm got the least breakpoints by comparison with other algorithms, which reflects the superiority in discretization aspects.
(3) A new reduction algorithm based on condition equivalence classifications is proposed to delete the redundant features. The minimal attributes reduction set can be got through finding the attributes in the rest of the properties which can distinguish the samples in the condition equivalence classifications not assigned to decision classes properly only by the core attributes. Attribute reduction algorithms based on heuristic information can not guarantee the minimal attributes reduction set, experimental results show that computational complexity of the algorithm proposed in the paper is low relatively, which improves the reduction efficiency.
(4) A method based on condition attribute reduction technology in Rough Sets is proposed to optimize the sampling points. The minimal attribute reduction sets of six fault monitoring points fuse into one big decision table for reduction, the classification ability of every monitoring point is determined according to the frequency of fault characteristic parameters in each point which appear in the final reduction set of the big decision table. Experimental results show the method needs neither modeling for the monitoring object nor dynamics analysis, but selects the effective sampling point directly according to the relationship between the fault characteristic parameters and fault types through processing the vibration signal, which is convenient and efficient to optimize the measuring points.
(5) The method of extracting decision rules based on rough set theory does not possess the ability to learn and induction, so fault pattern recognition rate is low relatively. Attribute reduction technique in rough set theory could extract sensitive fault characteristic parameters, least squares support vector machine has strong pattern recognition ability, so in order to make full use of their advantages in the characteristic parameter extraction and pattern recognition, the intelligent fault diagnosis system is constructed based on RS and LSSVM. The theoretical and practical results have proved that the system improves the gearbox fault diagnosis performance and provides a relatively generic solution for processing and recognizing nonlinear and non-stationary fault signal.
(1)在分析齿轮箱振动特性的基础上,提出采用局域波分解技术对齿轮箱故障信号进行处理并提取了初始的故障特征参量集。在局域波分解过程中,采用镜像延拓与窗函数相结合的方法缓解了端点效应问题,采用总体经验模态分解方法有效解决了模态混叠问题,实验结果表明这两种方法在齿轮箱故障信号分解中取得了较好的效果。根据衡量故障特征参量集的指标,提出采用每个工况的均方根有效值衡量故障特征参量集的稳定性,采用每个特征参量在六个工况之间的最小均值差衡量故障特征参量集的敏感性。实验中分别提取了基于EEMD的归一化能量特征参量集和基于EEMD的近似熵特征参量集,通过实际计算结果表明,前者与后者的敏感性基本一致,但是稳定性要优于后者,因此本文采用了基于EEMD的归一化能量特征参量集进行齿轮箱故障诊断。
(2)提出一种基于改进Naive Scaler算法的全局动态寻优离散化算法。通过对Naive Scaler算法过程进行改进,确保能够得到所有保证不可分辨关系的断点；通过断点均分样本集、逐渐增加断点的方法动态地从候选集中选择断点集,保证了整个信息系统分类能力不变的条件下断点个数最少。通过与其它算法对比,实验结果表明该算法得到的断点个数较少,体现了其在连续属性离散化方面的优越性。
(3)提出一种基于条件等价类的属性约简算法。该算法在核属性集的基础上,直接针对核属性的条件类中不能正确划入决策类的类,在核属性之外的其余条件属性中找到能够区分该类的属性,并添加到核属性集中,从而得到最小属性约简集。而基于启发式信息的属性约简算法无法保证所求约简集一定是最小属性约简集,实验结果表明该算法计算复杂度较低,提高了约简效率。
(4)提出采用粗糙集的属性约简技术对故障监测点进行优化配置。该方法将六个故障监测点的最小属性约简集融合成一个大决策表进行属性约简,根据每个监测点的故障特征参量在最终约简集中出现的频次判定相应监测点的分类能力,实验结果表明该方法不需要对监测对象建模,也不需要对其进行动力学分析,而是直接对监测到的振动信号进行处理,根据各个测点的故障特征参量与故障种类之间的关联程度选择最佳测点,是一种行之有效的测点优化配置方法。
(5)基于粗糙集理论提取决策规则的过程没有学习归纳的能力,故障模式识别率较低。粗糙集理论的属性约简技术能够提取敏感的故障特征参量,最小二乘支持向量机的模式识别能力强,因此为了充分利用两者在特征参量提取与模式识别方面的优势,构建了基于粗糙集支持向量机的智能故障诊断系统。理论与实践都表明该系统在一定程度上提高了齿轮箱故障诊断性能,为非线性非平稳故障信号的处理与识别提供了一种较通用的解决方案。
Gearbox is one of the most important transmission parts in the mechanical systems, but, for some uncertain reasons, the failure rate is higher, the vibration signal shows nonlinear and nonstationary, fault type and location as well as extent affect the characteristic parameters greatly. While monitoring and diagnosing the gearbox, selecting monitoring points improperly usually fails to gain the fault information effectively, determine the fault position, extract sensitive characteristic parameters and obtain high fault recognition rate. The method of local wave decomposition(LMD) could decompose the nonstationary signal adaptively and map to the time-frequence analysis plane, which could display signals in time domain and frequence domain simultaneously. Attributes reduction technology in rough sets (RS) could optimize the characteristic parameter set and extract the sensitive fault characteristic parameters. Least squares support vector machine (LSSVM) has good function approximation and high pattern recognition ratio. A method of combining RS with LSSVM through studying on LWD and RS deeply is proposed, intelligent fault diagnosis system of gearbox based on RS and LSSVM is established. The main work is as follows:
(1) LWD is employed to process the vibration signal of gearbox and extract the initial characteristic parameters based on analying the vibration property. A method of combining mirror extension with window function is used to relieve endpoint effect, ensemble empirical mode decomposition (EEMD) method is utilized to solve the mode mixing problem effectively, experiments show that these methods have achieved good results in fault signal decomposition. According to the measurable indicators of fault characteristic parameter set, it is proposed to use the rms values of the fault characteristic parameters to measure the stability and the minimal mean difference of each characteristic parameters in six working conditions to measure the sensitivity. The normalized energy and approximate entropy characteristic parameter sets based on EEMD are extracted in the paper, calculating results show that the sensitivity of the former and the latter are basically the same, but the stability is superior to the latter, so the normalized energy characteristic parameter set would be used for gearbox fault diagnosis.
(2) A global dynamic optimization algorithm for discretization based on improved Naive Scaler is proposed. The process of Naive Scaler algorithm is improved so that all breakpoints which warranties indiscernible relation would be got. The method of selecting breakpoints from the candidate set dynamically through separating the samples evenly by breakpoints and increasing the breakpoints gradually ensures the least breakpoints under the condition of keeping the classification ability of the whole information system. The experimental results show that the algorithm got the least breakpoints by comparison with other algorithms, which reflects the superiority in discretization aspects.
(3) A new reduction algorithm based on condition equivalence classifications is proposed to delete the redundant features. The minimal attributes reduction set can be got through finding the attributes in the rest of the properties which can distinguish the samples in the condition equivalence classifications not assigned to decision classes properly only by the core attributes. Attribute reduction algorithms based on heuristic information can not guarantee the minimal attributes reduction set, experimental results show that computational complexity of the algorithm proposed in the paper is low relatively, which improves the reduction efficiency.
(4) A method based on condition attribute reduction technology in Rough Sets is proposed to optimize the sampling points. The minimal attribute reduction sets of six fault monitoring points fuse into one big decision table for reduction, the classification ability of every monitoring point is determined according to the frequency of fault characteristic parameters in each point which appear in the final reduction set of the big decision table. Experimental results show the method needs neither modeling for the monitoring object nor dynamics analysis, but selects the effective sampling point directly according to the relationship between the fault characteristic parameters and fault types through processing the vibration signal, which is convenient and efficient to optimize the measuring points.
(5) The method of extracting decision rules based on rough set theory does not possess the ability to learn and induction, so fault pattern recognition rate is low relatively. Attribute reduction technique in rough set theory could extract sensitive fault characteristic parameters, least squares support vector machine has strong pattern recognition ability, so in order to make full use of their advantages in the characteristic parameter extraction and pattern recognition, the intelligent fault diagnosis system is constructed based on RS and LSSVM. The theoretical and practical results have proved that the system improves the gearbox fault diagnosis performance and provides a relatively generic solution for processing and recognizing nonlinear and non-stationary fault signal.
引文
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