基于内积变换的机械故障特征提取原理与早期识别方法研究
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摘要
本文针对关键机泵、燃气轮机、往复式压缩机风力透平等机械装备健康监控中的故障特征提取和早期识别问题，开展了理论、实验和工程应用研究。
在理论研究方面，本文在前人总结的内积变换和机械故障诊断关系的基础上，基于泛函分析中的Riesz表示定理和振动力学中的Duhamel积分原理，阐明了以下观点：（1）当且仅当机械故障特征提取采用了线性变换时，特征提取可以归结为内积变换；（2）线性机械系统的响应可以视为故障激振力与其物理响应函数的内积。此外，赋予信号处理理论中基于内积变换的框架和对偶框架关系式以物理意义，可作为机械故障动态信号特征提取的统一数学模型——内积变换模型。该模型在振动信号压缩、冲击性振动故障特征提取、往复机示功图故障特征提取三种场合下有不同的具体形式。
针对采油平台机泵和风力发电机组在线监测的大数据量——昂贵传输带宽的突出矛盾，研究了振动加速度信号压缩方法。提出了基于小波变换和最优稀疏表达的压缩方法。该方法可以视为内积变换模型在基于稀疏表达的加速度信号压缩情形下的具体形式。实验研究表明：基于sym8小波和匹配追踪（MP）的压缩方法具有相对最优的压缩效果。工程应用研究结果表明：该方法能够将振动加速度信号数据压缩至20%，且不丢失振动故障特征。为后续振动故障特征提取和早期识别打好了基础。
针对风力发电机组齿轮箱故障、机泵和双转子燃气轮机滚动轴承故障特征提取和早期识别，研究了它们机理上共有的冲击性。提出两种最优化参数的冲击性振动故障特征提取方法—最优高通滤波包络解调方法、最优反对称实Laplace(ARLW)小波滤波包络解调方法；并指出两种方法均为内积变换模型在冲击性特征提取时的具体形式。实验和工程应用研究表明：这两种方法对早期或微弱冲击性故障特征提取与识别性能相较传统高通滤波包络解调有提升。
针对往复式压缩机故障的示功图特征提取和早期识别，提出了基于Curvelet变换的往复压缩机故障示功图特征提取和基于支持向量机的故障识别方法。阐述了内积变换模型在该种情况下的具体物理意义。实验研究表明：Curvelet变换比一般小波变换能够更清晰地提取示功图特征，而结合支持向量机就能够自动检测不同往复机故障示功图间的差异；该结果可用于自动化示功图故障诊断，具有成为构建往复机故障诊断专家系统支撑技术的潜力。
In this paper, the faults feature extraction and early identification of keyfans and pumps, gas turbines, reciprocating compressors and wind turbines arestudied. Theoretical and application researches are made.
Theoretical research is made following the relation between inner productand machine fault diagnosis which was summarized by the former researchers.Two main points are presented based on Riesz representation theorem andDuhamel integral. First, if and only if linear transform is adopted by faultfeature extraction, the feature extraction process can be taken as inner product.Second, the response of linear machine system excited by fault forces is theinner product of the forces and the system’s physical response function.Furthermore, by giving the physical meaning to frames and dual framesrelation proposed in signal processing field, this relation can be taken as ageneral machine fault feature extraction model termed inner product transform (IPT) model. Different concrete forms of this model are shown in thesituations of signal compression, impulsive vibration fault feature extractionand indicator diagram feature extraction of reciprocating compressors.
The problem of huge amount of data and expensive bandwidth isencountered in the monitoring of key pumps on oil platforms and windturbines. Hence, vibration acceleration signal compression is researched.Compression approach based on wavelet transform and sparse representationis presented. This approach is a special form of the IPT model. Experimentaland application studies reveal that relatively optimal results are obtained bysym8wavelet and Matching Pursuit. Without loss of fault features,80%ofdata is compressed.
The same mechanism—impulsive vibration of gearbox fault of windturbines and rolling bearing faults of fans, pumps, and double-rotor gasturbines is clarified and used in this work. Two envelope demodulationmethods based on optimal high-pass filter and optimal Antisymmetric RealLaplace Wavelet (ARLW) filter are proposed. These two methods share asame form of IPT model. More effective results of feature extraction andidentification of early or weak impulsive fault are obtained by experimentaland application study.
Indicator diagram feature extraction based on Curvelet transform which isalso a special form of IPT model is proposed in the last part of this work. AndSVM is used to reciprocating compressors fault recognition. More clear features can be extracted by Curvelet transform than wavelet transform in theexperimental study. Combination of Curvelet transform and SVM can be usedto construct fault diagnosis expert system.
在理论研究方面，本文在前人总结的内积变换和机械故障诊断关系的基础上，基于泛函分析中的Riesz表示定理和振动力学中的Duhamel积分原理，阐明了以下观点：（1）当且仅当机械故障特征提取采用了线性变换时，特征提取可以归结为内积变换；（2）线性机械系统的响应可以视为故障激振力与其物理响应函数的内积。此外，赋予信号处理理论中基于内积变换的框架和对偶框架关系式以物理意义，可作为机械故障动态信号特征提取的统一数学模型——内积变换模型。该模型在振动信号压缩、冲击性振动故障特征提取、往复机示功图故障特征提取三种场合下有不同的具体形式。
针对采油平台机泵和风力发电机组在线监测的大数据量——昂贵传输带宽的突出矛盾，研究了振动加速度信号压缩方法。提出了基于小波变换和最优稀疏表达的压缩方法。该方法可以视为内积变换模型在基于稀疏表达的加速度信号压缩情形下的具体形式。实验研究表明：基于sym8小波和匹配追踪（MP）的压缩方法具有相对最优的压缩效果。工程应用研究结果表明：该方法能够将振动加速度信号数据压缩至20%，且不丢失振动故障特征。为后续振动故障特征提取和早期识别打好了基础。
针对风力发电机组齿轮箱故障、机泵和双转子燃气轮机滚动轴承故障特征提取和早期识别，研究了它们机理上共有的冲击性。提出两种最优化参数的冲击性振动故障特征提取方法—最优高通滤波包络解调方法、最优反对称实Laplace(ARLW)小波滤波包络解调方法；并指出两种方法均为内积变换模型在冲击性特征提取时的具体形式。实验和工程应用研究表明：这两种方法对早期或微弱冲击性故障特征提取与识别性能相较传统高通滤波包络解调有提升。
针对往复式压缩机故障的示功图特征提取和早期识别，提出了基于Curvelet变换的往复压缩机故障示功图特征提取和基于支持向量机的故障识别方法。阐述了内积变换模型在该种情况下的具体物理意义。实验研究表明：Curvelet变换比一般小波变换能够更清晰地提取示功图特征，而结合支持向量机就能够自动检测不同往复机故障示功图间的差异；该结果可用于自动化示功图故障诊断，具有成为构建往复机故障诊断专家系统支撑技术的潜力。
In this paper, the faults feature extraction and early identification of keyfans and pumps, gas turbines, reciprocating compressors and wind turbines arestudied. Theoretical and application researches are made.
Theoretical research is made following the relation between inner productand machine fault diagnosis which was summarized by the former researchers.Two main points are presented based on Riesz representation theorem andDuhamel integral. First, if and only if linear transform is adopted by faultfeature extraction, the feature extraction process can be taken as inner product.Second, the response of linear machine system excited by fault forces is theinner product of the forces and the system’s physical response function.Furthermore, by giving the physical meaning to frames and dual framesrelation proposed in signal processing field, this relation can be taken as ageneral machine fault feature extraction model termed inner product transform (IPT) model. Different concrete forms of this model are shown in thesituations of signal compression, impulsive vibration fault feature extractionand indicator diagram feature extraction of reciprocating compressors.
The problem of huge amount of data and expensive bandwidth isencountered in the monitoring of key pumps on oil platforms and windturbines. Hence, vibration acceleration signal compression is researched.Compression approach based on wavelet transform and sparse representationis presented. This approach is a special form of the IPT model. Experimentaland application studies reveal that relatively optimal results are obtained bysym8wavelet and Matching Pursuit. Without loss of fault features,80%ofdata is compressed.
The same mechanism—impulsive vibration of gearbox fault of windturbines and rolling bearing faults of fans, pumps, and double-rotor gasturbines is clarified and used in this work. Two envelope demodulationmethods based on optimal high-pass filter and optimal Antisymmetric RealLaplace Wavelet (ARLW) filter are proposed. These two methods share asame form of IPT model. More effective results of feature extraction andidentification of early or weak impulsive fault are obtained by experimentaland application study.
Indicator diagram feature extraction based on Curvelet transform which isalso a special form of IPT model is proposed in the last part of this work. AndSVM is used to reciprocating compressors fault recognition. More clear features can be extracted by Curvelet transform than wavelet transform in theexperimental study. Combination of Curvelet transform and SVM can be usedto construct fault diagnosis expert system.
引文
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