基于解轨迹多项式分解的非线性电路故障诊断研究
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摘要
上世纪八十年代以来,计算机技术和微电子技术在测试领域的运用,带动了测控技术的飞速发展。航天、军工等领域对系统安全性、可靠性要求的日益提升,电子装备的可测性设计、故障诊断和容错控制技术正日益引起人们的重视。其中,非线性模拟电路的测试、诊断问题既不可避免又极其困难,已成为现代测试领域最具挑战性的课题之一。
非线性模拟电路故障诊断可分为：系统建模、激励设计、特征提取和故障识别四个部分。由于非线性模拟电路(或系统)中故障传播机理的非线性,极易导致故障信息的重叠、交叉,因此,非线性模拟电路故障诊断技术的核心是故障特征提取。由于解轨迹分析能最大程度地获取电路信息,因此,本文以解轨迹多项式分解为基础,围绕提高故障特征的有效性(聚类性)为目标,展开非线性模拟电路故障诊断的研究。概括来说,主要做了如下几个方面的研究工作：
1.研究了斜坡激励下的非线性电阻网络故障诊断方法,目的是建立非线性电阻网络的故障诊断方程,实现软故障、多故障诊断。方法是通过解轨迹多项式分解将非线性静态电路转化成线性电路序列,再在线性电路中实现软故障、多故障的诊断。重点讨论了斜坡激励下解轨迹多项式系数间的迭代关系和解轨迹多项式系数的性质；在此基础上,提出了基于静态解轨迹多项式系数的故障诊断方程和基于多轨迹分析的多故障诊断方法。
2.研究了基于动态解轨迹Volterra响应分解的非线性动态电路故障诊断方法,目的是提高故障特征的聚类性。方法是根据动态解轨迹谐波多项式与Volterra响应分量间的对应关系,利用谐波分解方法和V子带参数估计方法提取Volterra线性子电路中的故障特征,以消除故障传播的非线性叠加效应。重点讨论了Volterra谐波分量的故障信息全息性；给出了基于响应空间正交投影的主元特征提取方法。
3.研究了基于相干检测的故障特征提取方法,目的是建立非线性动态电路的故障诊断方程,实现非线性动态电路的软故障、多故障诊断。方法是利用相干检测方法提取满足动态电路复节点方程的静态故障特征,建立动态电路故障诊断方程。重点讨论了相位驻留特征提取的物理意义和实现方法；提出了基于相位驻留法的故障诊断方程建立方法。
4.研究了基于动态增量Volterra级数(DDVS)的故障特征提取方法,目的是提高较大截尾误差情况下故障特征提取的数值稳定性,使Volterra方法适用于高维非线性电路的故障分析。方法是通过重组Volterra级数实现“截尾不截维”,来提高参数估计的数值稳定性。重点讨论了DDVS与Volterra级数的关系,分析了DDVS在参数估计中的数值稳定性和故障特征聚类性；提出了基于DDVS参数估计的故障特征提取方法。DDVS的显著特点是具有模块化结构,容易扩展成更高阶非线性系统。
5.研究了基于时频基函数多项式(BFP)的非线性电路故障特征提取方法,目的是实现高维复杂非线性电路的故障特征提取。方法是通过对被测信号的BFP拟合来提取故障特征。重点讨论了框架基函数时频域描述的完备性和基于BFP的非线性系统建模问题；分析了BFP在故障诊断应用中存在的问题,提出了基于平移联动的BFP基函数族简化方法。BFP模型的特点是具有更强的非线性适应能力和更好的数值稳定性。
总体而言,本文以故障特征提取方法为中心；以解轨迹多项式分解和参数估计为手段；以实现非线性电路的软故障、多故障诊断为目的。考虑到非线性电路的静态和动态、非线性程度的强与弱等情况,重点分析了参数估计的稳定性、故障特征的聚类性和非线性模型的线性化能力等问题。仿真结果表明：所提方法是有效的。
Since the 1980s, with the development of computer and microelectronics technology, the system security and reliability demands in aerospace, military and other fields have been leading the rapid progress of testing-controlling technology. Measurability design, fault diagnosis and tolerant control are becoming more and more important in electronic equipments. Among them, the problem of nonlinear analog circuit fault diagnosis is not only inevitable but also extremely difficult. Fault diagnosis theory and methods of nonlinear analog circuits have become one of the challenging topics in international test research domain.
A typical process of nonlinear analog circuit fault diagnosis includes system modeling, stimulation design, feature extraction and fault identification. For the nonlinear mechanism of fault propagation, fault information can be very likely to be overlapped and interleaved, thus the key point of fault diagnosis is fault characteristics extraction. This dissertation is mainly focused on nonlinear system modeling and improvement of characteristics extraction approach, based on the trajectory polynomial decomposition analysis. Author's main work concentrates on five aspects as follows:
1. An approach of static trajectory polynomial (STP) for nonlinear resistance network fault diagnosis was studied with ramp power supplies. The purpose is to build the fault diagnosis equation, and to realize multi-faults diagnosis. With the trajectory polynomial decomposition, the iterative relationship of STP's coefficients was discussed, and the properties of STP's coefficients on fault diagnosis were analyzed. Based on STP modeling, nonlinear circuit can be transformed into linear circuit series, and fault diagnosis equation was built with STP's coefficients. Finally, multi-faults diagnosis method of nonlinear resistance network was discussed based on multi-STP analysis.
2. A fault diagnosis approach for nonlinear dynamic circuit with some special AM stimulation was studied based on trajectory harmonic polynomial (THP) decomposition. The purpose is to enhance clustering property of fault characteristics. First, the relationship between dynamic trajectory spectrum components and Volterra spectrum components were discussed under some special AM stimulation. Then the holography of fault information in THP components was analyzed. And two approaches of Volterra responses decomposition were represented based on ARMA harmonic decomposition and Volterra sub-band decomposition. Finally, an approach of characteristics extraction was presented based on orthogonal projection of sub-space.
3.In order to solve the diagnosis problem of soft-faults and multi-faults for dynamic nonlinear circuit, an approach of fault diagnosis was studied based on coherent measurement. Based on the correlation between Volterra spectrum components and equivalent exciting signals, the phase resident method was presented by coherent measurement, and dynamic circuit can be transformed into static parameter circuit on phase cut-slide. Then the fault information included in phase cut-slide was discussed, and fault diagnosis equation was established based on circuit configuration.
4. The dissertation studied fault characteristics extracting method based on dynamic deviation Volterra serise (DDVS), which is designed to improve stability of the process of characteristic extraction for higher dimension nonlinear circuit. Discussion has been done on relationship between DDVS and Volterra series, and DDVS stability in parameter estimation and fault information capability have been analyzed. Then fault characteristics extracting method based on DDVS parameter estimation was represented. DDVS have distinct modularization structure, so it's easy to extend to higher dimension nonlinear system..
5. In chapter six, we studied nonlinear circuit fault characteristics extracting method based on basis-function polynomial (BFP), which is to solve the difficult problem for characteristics extraction of high dimension and longer delay nonlinear system. Based on the principle of time-frequency basic function frame, the paper analyzed existing problem of BFP fitting in nonlinear circuit diagnosis. Then an approach for simplifying the basic function tribe of BFP was presented based on fixed scale and joint translation. The virtue of BFP is higher stability in parameter estimation and stronger adaptability of various nonlinear circuits.
In one word, this dissertation focuses on the fault characteristic extraction based on trajectory polynomial decomposition. In order to achieve the aim of soft-fault and multi-fault diagnosis of nonlinear circuit, the importance of both the stability and clustering performance of fault characteritics were emphasized in this paper, and the ability for linearization decomposition of nonlinear modeling was also analyzed emphatically. Some examples to illuminate the proposed approaches are available.
非线性模拟电路故障诊断可分为：系统建模、激励设计、特征提取和故障识别四个部分。由于非线性模拟电路(或系统)中故障传播机理的非线性,极易导致故障信息的重叠、交叉,因此,非线性模拟电路故障诊断技术的核心是故障特征提取。由于解轨迹分析能最大程度地获取电路信息,因此,本文以解轨迹多项式分解为基础,围绕提高故障特征的有效性(聚类性)为目标,展开非线性模拟电路故障诊断的研究。概括来说,主要做了如下几个方面的研究工作：
1.研究了斜坡激励下的非线性电阻网络故障诊断方法,目的是建立非线性电阻网络的故障诊断方程,实现软故障、多故障诊断。方法是通过解轨迹多项式分解将非线性静态电路转化成线性电路序列,再在线性电路中实现软故障、多故障的诊断。重点讨论了斜坡激励下解轨迹多项式系数间的迭代关系和解轨迹多项式系数的性质；在此基础上,提出了基于静态解轨迹多项式系数的故障诊断方程和基于多轨迹分析的多故障诊断方法。
2.研究了基于动态解轨迹Volterra响应分解的非线性动态电路故障诊断方法,目的是提高故障特征的聚类性。方法是根据动态解轨迹谐波多项式与Volterra响应分量间的对应关系,利用谐波分解方法和V子带参数估计方法提取Volterra线性子电路中的故障特征,以消除故障传播的非线性叠加效应。重点讨论了Volterra谐波分量的故障信息全息性；给出了基于响应空间正交投影的主元特征提取方法。
3.研究了基于相干检测的故障特征提取方法,目的是建立非线性动态电路的故障诊断方程,实现非线性动态电路的软故障、多故障诊断。方法是利用相干检测方法提取满足动态电路复节点方程的静态故障特征,建立动态电路故障诊断方程。重点讨论了相位驻留特征提取的物理意义和实现方法；提出了基于相位驻留法的故障诊断方程建立方法。
4.研究了基于动态增量Volterra级数(DDVS)的故障特征提取方法,目的是提高较大截尾误差情况下故障特征提取的数值稳定性,使Volterra方法适用于高维非线性电路的故障分析。方法是通过重组Volterra级数实现“截尾不截维”,来提高参数估计的数值稳定性。重点讨论了DDVS与Volterra级数的关系,分析了DDVS在参数估计中的数值稳定性和故障特征聚类性；提出了基于DDVS参数估计的故障特征提取方法。DDVS的显著特点是具有模块化结构,容易扩展成更高阶非线性系统。
5.研究了基于时频基函数多项式(BFP)的非线性电路故障特征提取方法,目的是实现高维复杂非线性电路的故障特征提取。方法是通过对被测信号的BFP拟合来提取故障特征。重点讨论了框架基函数时频域描述的完备性和基于BFP的非线性系统建模问题；分析了BFP在故障诊断应用中存在的问题,提出了基于平移联动的BFP基函数族简化方法。BFP模型的特点是具有更强的非线性适应能力和更好的数值稳定性。
总体而言,本文以故障特征提取方法为中心；以解轨迹多项式分解和参数估计为手段；以实现非线性电路的软故障、多故障诊断为目的。考虑到非线性电路的静态和动态、非线性程度的强与弱等情况,重点分析了参数估计的稳定性、故障特征的聚类性和非线性模型的线性化能力等问题。仿真结果表明：所提方法是有效的。
Since the 1980s, with the development of computer and microelectronics technology, the system security and reliability demands in aerospace, military and other fields have been leading the rapid progress of testing-controlling technology. Measurability design, fault diagnosis and tolerant control are becoming more and more important in electronic equipments. Among them, the problem of nonlinear analog circuit fault diagnosis is not only inevitable but also extremely difficult. Fault diagnosis theory and methods of nonlinear analog circuits have become one of the challenging topics in international test research domain.
A typical process of nonlinear analog circuit fault diagnosis includes system modeling, stimulation design, feature extraction and fault identification. For the nonlinear mechanism of fault propagation, fault information can be very likely to be overlapped and interleaved, thus the key point of fault diagnosis is fault characteristics extraction. This dissertation is mainly focused on nonlinear system modeling and improvement of characteristics extraction approach, based on the trajectory polynomial decomposition analysis. Author's main work concentrates on five aspects as follows:
1. An approach of static trajectory polynomial (STP) for nonlinear resistance network fault diagnosis was studied with ramp power supplies. The purpose is to build the fault diagnosis equation, and to realize multi-faults diagnosis. With the trajectory polynomial decomposition, the iterative relationship of STP's coefficients was discussed, and the properties of STP's coefficients on fault diagnosis were analyzed. Based on STP modeling, nonlinear circuit can be transformed into linear circuit series, and fault diagnosis equation was built with STP's coefficients. Finally, multi-faults diagnosis method of nonlinear resistance network was discussed based on multi-STP analysis.
2. A fault diagnosis approach for nonlinear dynamic circuit with some special AM stimulation was studied based on trajectory harmonic polynomial (THP) decomposition. The purpose is to enhance clustering property of fault characteristics. First, the relationship between dynamic trajectory spectrum components and Volterra spectrum components were discussed under some special AM stimulation. Then the holography of fault information in THP components was analyzed. And two approaches of Volterra responses decomposition were represented based on ARMA harmonic decomposition and Volterra sub-band decomposition. Finally, an approach of characteristics extraction was presented based on orthogonal projection of sub-space.
3.In order to solve the diagnosis problem of soft-faults and multi-faults for dynamic nonlinear circuit, an approach of fault diagnosis was studied based on coherent measurement. Based on the correlation between Volterra spectrum components and equivalent exciting signals, the phase resident method was presented by coherent measurement, and dynamic circuit can be transformed into static parameter circuit on phase cut-slide. Then the fault information included in phase cut-slide was discussed, and fault diagnosis equation was established based on circuit configuration.
4. The dissertation studied fault characteristics extracting method based on dynamic deviation Volterra serise (DDVS), which is designed to improve stability of the process of characteristic extraction for higher dimension nonlinear circuit. Discussion has been done on relationship between DDVS and Volterra series, and DDVS stability in parameter estimation and fault information capability have been analyzed. Then fault characteristics extracting method based on DDVS parameter estimation was represented. DDVS have distinct modularization structure, so it's easy to extend to higher dimension nonlinear system..
5. In chapter six, we studied nonlinear circuit fault characteristics extracting method based on basis-function polynomial (BFP), which is to solve the difficult problem for characteristics extraction of high dimension and longer delay nonlinear system. Based on the principle of time-frequency basic function frame, the paper analyzed existing problem of BFP fitting in nonlinear circuit diagnosis. Then an approach for simplifying the basic function tribe of BFP was presented based on fixed scale and joint translation. The virtue of BFP is higher stability in parameter estimation and stronger adaptability of various nonlinear circuits.
In one word, this dissertation focuses on the fault characteristic extraction based on trajectory polynomial decomposition. In order to achieve the aim of soft-fault and multi-fault diagnosis of nonlinear circuit, the importance of both the stability and clustering performance of fault characteritics were emphasized in this paper, and the ability for linearization decomposition of nonlinear modeling was also analyzed emphatically. Some examples to illuminate the proposed approaches are available.
引文
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