基于支持向量机的模拟电路故障诊断方法研究
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摘要
模拟电路故障诊断理论和方法研究目前仍然是国际电路测试领域中极具挑战性的前沿和热点研究课题。半导体技术和工艺的飞速发展促进了模拟集成电路、模／数混合信号电路的广泛应用。为了有效缩短电子产品的上市时间和提高电子设备的可靠性，对模拟电路测试和故障诊断提出了更高、更新的要求。由于模拟电路响应的连续性、非线性性和元件参数的容差性等固有的特点以及故障的多样性、复杂性，常规或者传统故障诊断理论和方法对模拟电路进行故障诊断难以在实际工程中达到预期的效果。因此研究高效、适应模拟电路发展需求的故障诊断理论和方法显得尤为重要。近年来快速发展的基于统计学习理论的支持向量机(SupportVector Machine，SVM)为模拟电路故障诊断提供了一种有效的解决方法，是目前国内外研究的热点。本文以现代测试技术、信号处理、系统辨识和可测性分析等理论和技术为基础，深入研究了基于支持向量机的模拟电路故障诊断方法，完成的主要工作如下：
根据模拟电路故障的特点，结合支持向量机在解决小样本、非线性和高维模式识别问题中所具有结构简单、全局最优、泛化能力强等特点，提出了基于支持向量机的模拟电路故障诊断方法，并构建了基于支持向量的模拟电路故障诊断系统，建立了被测电路故障诊断的支持向量机模型，对支持向量机故障诊断模型性能的影响因数——核函数及其核参数、惩罚参数、多分类支持向量机不同组合方法进行了研究。
在时域和频域中给出了基于响应曲线波形有效点的模拟电路故障特征提取方法。为减少故障特征数据维数，提出了基于最大相关、最小冗余原则(Criteria ofMax-Relevance and Min Redundancy，MRMR)和支持向量机的故障特征选择方法，建立了电路最优故障特征的选择机制，有效地解决了支持向量机故障诊断模型的复杂性。
考虑到模拟电路的故障响应包含了非平稳或时变信息，研究了基于小波变换的模拟电路故障特征提取方法，定义了电路特征测度为电路故障特征与正常特征之差的均方根值，提出了基于电路特征测度的最优母小波选择原则，实现了自适应小波变换的模拟电路故障特征提取。
由于模拟电路工作状态的时变性和实际测得信号的不规则性，测得的信号在一定的尺度范围内具有分形特征，提出了基于多重分形分析的模拟电路故障特征提取方法，给出了基于小波极大模的多重分形奇异谱计算方法，并提取了与多重分形奇异谱有关的6个参数为故障特征。
有限测试节点的响应不足以表征模拟电路每个元件的状态，研究了模拟电路潜在故障可诊断元件集的选择方法。首先讨论了基于电路拓扑结构的可测性分析，通过可测矩阵的相关性获得了可测组和模糊组，从而把电路潜在的故障元件进行分组，实现了可诊断元件集的选择。其次给出了传递函数零极点与元件参数的变化关系，提出了基于零极点灵敏度分析的可诊断元件集确定方法，由极点模糊组和零点模糊组的关系确定可诊断元件集。最后通过研究被测电路可及节点输出响应的模糊聚类，提出了基于模糊聚类的可诊断元件集确定方法，采用聚类有效性指标来确定可诊断元件集。
在理论分析的基础上，以模／数信号测试的标准电路和文献中广泛研究的电路为实验对象，采用OrCAD10．5仿真了被测电路各种状态，获得了响应数据，在Matlab7．0中建立了基于支持向量机的模拟电路故障诊断模型，对被测电路的硬故障、软故障和多故障进行了诊断仿真实验。实验结果验证了本文提出方法的可行性和结论的正确性，与广泛研究的基于神经网络的模拟电路故障诊断方法相比，本文所提的基于支持向量机的模拟电路故障诊断方法具有结构简单，诊断准确率更优的特点，解决了神经网络的局部最优值、模型结构难以选择和小样本等问题。
Fault diagnosis theory and methods for analog circuits is still an extremelychallenging research topic in the circuit test field around the world.The rapiddevelopment of semiconductor technology has promoted the wide applications ofanalog integrated circuits and analog/digital mixed-signal circuits.In order to shortenthe time-to-market of the electronic product and increase its reliability,a new theory andfault diagnosis method needs to be established to meet the new requirements of analogcircuit test and fault diagnosis.However,due to the inherent characteristics of analogcircuits,such as its nonlinearity and continuous response,tolerances on componentparameters,etc,as well as the diversity and complexity of their faults,it is difficult forthe conventional or traditional fault diagnosis theories and methods to achieve theexpected results in the practical engineering.Hence,it is very important to explore somehighly efficient fault diagnosis theories and methods to meet the development of analogcircuits.Support vector machine (SVM) based on statistical learning theory,which is aresearch focus both at home and abroad,has provided an effective solution for faultdiagnosis in analog circuits.On the basis of the modern test technology,signalprocessing,system identification and testability analysis,etc,the fault diagnosis methodfor analog circuits based on SVM is deeply researched in the dissertation.The mainresearch contents and achievements are summarized as follows:
According to the characteristics of analog circuit faults and SVM with simplestructure,the global optimum solution,good generalization to solve pattern recognitionissues with a few samples,nonlinearity and high dimensionality,the fault diagnosismethod for analog circuit based on SVM is presented.At the same time,the faultdiagnosis system of analog circuit based on SVM and a SVM model of fault diagnosisfor the circuits under test (CUT) is established.The factors which influence theperformance of SVM fault diagnosis model,such as kernel function and kernelparameters,punishment parameters and the combination algorithm of multiclass SVM,are researched.
The feature extraction method based on efficient points of response curve is studied in time domain and frequency domain.In order to reduce the faults' featuredimensions,the fault feature selection method based on criteria of Max-Relevance andMin-Redundancy (MRMR) and SVM is presented,and the selection mechanism of theoptimal feature is established.As a result,the complexity of the SVM fault diagnosismodel is effectively reduced.
Due to analog circuit fault response included the non-stationary or time-varyinginformation,the fault feature extraction method based on wavelet analysis is studied,and the feature measure of CUT is defined as the RMS value of difference betweennormal and faulty features.Meanwhile,the selection principle of optimal motherwavelet based on feature measurement is presented so as to achieve the faults featureextraction in analog circuits based on adaptive wavelet analysis.
As a result of the time-variability of analog circuits and the irregularity of actualmeasured signals,the measured signals have fractal properties in certain scale rangesand the fault feature extraction method of analog circuits based on multfractal analysisis presented.In addition,the procedure for estimating multifractal singularity spectrabased on the wavelet's maximum modulus is researched and 6 parameters related tomultifractal singularity spectra are extracted as faults' features.
The response obtained from the limited test nodes is not enough to reflect the stateof each component in CUT,and there are some ambiguity groups in CUT.The study ofapproaches to selecting the diagnosable component set is very helpful for diagnosingthe potential fault in CUT.Firstly,the testability analysis based on the circuit topologyis studied,the potential fault components are grouped by the testable and ambiguitygroup which is attained by use of linear correlation of the testability matrix of CUT,andthe selection of diagnosable components set is realized.Secondly,according to therelationship between transfer function Pole-zero and parameters of components,theapproach to selecting the diagnosable component set is presented based on thePole-Zero sensitivity analysis of CUT.The diagnosable component set can beascertained by the relationship between the Pole and Zero ambiguity groups.Finally,bystudying the fuzzy cluster of the response obtained from accessible node,the approachto selecting the diagnosable component set is presented based on fuzzy cluster analysisand fuzzy cluster validity index theory.
Based on the theoretical analysis,targeted at the analog/digital signal benchmark circuits and the circuits widely studied in the references,and simulated the faultscenarios as well as the fault-free operation of CUT by OrCAD10.5,analog circuit faultdiagnosis model based on support vector machine is achieved in Matlab7.0 and asimulating experiment is also carried out to diagnose the soft faults,hard faults andmulti-faults in CUT.The experimental results have testified the feasibility of theproposed method and the validity of the conclusion in this dissertation.Compared withthe widely studied analog circuits fault diagnosis method based on neural network,theproposed method in this dissertation possesses the merits of simpler structure and higherdiagnostic accuracy,and it solves the disadvantage of neural network--local optimalsolution,over-fitting and under-fitting,difficulty in choosing model structures,etc,andrealizes the automatic choice of model structure and good generalization ability forsmall samples to account for the trade off between learning ability and generalizationability of learning machine by minimizing structural risk.
根据模拟电路故障的特点，结合支持向量机在解决小样本、非线性和高维模式识别问题中所具有结构简单、全局最优、泛化能力强等特点，提出了基于支持向量机的模拟电路故障诊断方法，并构建了基于支持向量的模拟电路故障诊断系统，建立了被测电路故障诊断的支持向量机模型，对支持向量机故障诊断模型性能的影响因数——核函数及其核参数、惩罚参数、多分类支持向量机不同组合方法进行了研究。
在时域和频域中给出了基于响应曲线波形有效点的模拟电路故障特征提取方法。为减少故障特征数据维数，提出了基于最大相关、最小冗余原则(Criteria ofMax-Relevance and Min Redundancy，MRMR)和支持向量机的故障特征选择方法，建立了电路最优故障特征的选择机制，有效地解决了支持向量机故障诊断模型的复杂性。
考虑到模拟电路的故障响应包含了非平稳或时变信息，研究了基于小波变换的模拟电路故障特征提取方法，定义了电路特征测度为电路故障特征与正常特征之差的均方根值，提出了基于电路特征测度的最优母小波选择原则，实现了自适应小波变换的模拟电路故障特征提取。
由于模拟电路工作状态的时变性和实际测得信号的不规则性，测得的信号在一定的尺度范围内具有分形特征，提出了基于多重分形分析的模拟电路故障特征提取方法，给出了基于小波极大模的多重分形奇异谱计算方法，并提取了与多重分形奇异谱有关的6个参数为故障特征。
有限测试节点的响应不足以表征模拟电路每个元件的状态，研究了模拟电路潜在故障可诊断元件集的选择方法。首先讨论了基于电路拓扑结构的可测性分析，通过可测矩阵的相关性获得了可测组和模糊组，从而把电路潜在的故障元件进行分组，实现了可诊断元件集的选择。其次给出了传递函数零极点与元件参数的变化关系，提出了基于零极点灵敏度分析的可诊断元件集确定方法，由极点模糊组和零点模糊组的关系确定可诊断元件集。最后通过研究被测电路可及节点输出响应的模糊聚类，提出了基于模糊聚类的可诊断元件集确定方法，采用聚类有效性指标来确定可诊断元件集。
在理论分析的基础上，以模／数信号测试的标准电路和文献中广泛研究的电路为实验对象，采用OrCAD10．5仿真了被测电路各种状态，获得了响应数据，在Matlab7．0中建立了基于支持向量机的模拟电路故障诊断模型，对被测电路的硬故障、软故障和多故障进行了诊断仿真实验。实验结果验证了本文提出方法的可行性和结论的正确性，与广泛研究的基于神经网络的模拟电路故障诊断方法相比，本文所提的基于支持向量机的模拟电路故障诊断方法具有结构简单，诊断准确率更优的特点，解决了神经网络的局部最优值、模型结构难以选择和小样本等问题。
Fault diagnosis theory and methods for analog circuits is still an extremelychallenging research topic in the circuit test field around the world.The rapiddevelopment of semiconductor technology has promoted the wide applications ofanalog integrated circuits and analog/digital mixed-signal circuits.In order to shortenthe time-to-market of the electronic product and increase its reliability,a new theory andfault diagnosis method needs to be established to meet the new requirements of analogcircuit test and fault diagnosis.However,due to the inherent characteristics of analogcircuits,such as its nonlinearity and continuous response,tolerances on componentparameters,etc,as well as the diversity and complexity of their faults,it is difficult forthe conventional or traditional fault diagnosis theories and methods to achieve theexpected results in the practical engineering.Hence,it is very important to explore somehighly efficient fault diagnosis theories and methods to meet the development of analogcircuits.Support vector machine (SVM) based on statistical learning theory,which is aresearch focus both at home and abroad,has provided an effective solution for faultdiagnosis in analog circuits.On the basis of the modern test technology,signalprocessing,system identification and testability analysis,etc,the fault diagnosis methodfor analog circuits based on SVM is deeply researched in the dissertation.The mainresearch contents and achievements are summarized as follows:
According to the characteristics of analog circuit faults and SVM with simplestructure,the global optimum solution,good generalization to solve pattern recognitionissues with a few samples,nonlinearity and high dimensionality,the fault diagnosismethod for analog circuit based on SVM is presented.At the same time,the faultdiagnosis system of analog circuit based on SVM and a SVM model of fault diagnosisfor the circuits under test (CUT) is established.The factors which influence theperformance of SVM fault diagnosis model,such as kernel function and kernelparameters,punishment parameters and the combination algorithm of multiclass SVM,are researched.
The feature extraction method based on efficient points of response curve is studied in time domain and frequency domain.In order to reduce the faults' featuredimensions,the fault feature selection method based on criteria of Max-Relevance andMin-Redundancy (MRMR) and SVM is presented,and the selection mechanism of theoptimal feature is established.As a result,the complexity of the SVM fault diagnosismodel is effectively reduced.
Due to analog circuit fault response included the non-stationary or time-varyinginformation,the fault feature extraction method based on wavelet analysis is studied,and the feature measure of CUT is defined as the RMS value of difference betweennormal and faulty features.Meanwhile,the selection principle of optimal motherwavelet based on feature measurement is presented so as to achieve the faults featureextraction in analog circuits based on adaptive wavelet analysis.
As a result of the time-variability of analog circuits and the irregularity of actualmeasured signals,the measured signals have fractal properties in certain scale rangesand the fault feature extraction method of analog circuits based on multfractal analysisis presented.In addition,the procedure for estimating multifractal singularity spectrabased on the wavelet's maximum modulus is researched and 6 parameters related tomultifractal singularity spectra are extracted as faults' features.
The response obtained from the limited test nodes is not enough to reflect the stateof each component in CUT,and there are some ambiguity groups in CUT.The study ofapproaches to selecting the diagnosable component set is very helpful for diagnosingthe potential fault in CUT.Firstly,the testability analysis based on the circuit topologyis studied,the potential fault components are grouped by the testable and ambiguitygroup which is attained by use of linear correlation of the testability matrix of CUT,andthe selection of diagnosable components set is realized.Secondly,according to therelationship between transfer function Pole-zero and parameters of components,theapproach to selecting the diagnosable component set is presented based on thePole-Zero sensitivity analysis of CUT.The diagnosable component set can beascertained by the relationship between the Pole and Zero ambiguity groups.Finally,bystudying the fuzzy cluster of the response obtained from accessible node,the approachto selecting the diagnosable component set is presented based on fuzzy cluster analysisand fuzzy cluster validity index theory.
Based on the theoretical analysis,targeted at the analog/digital signal benchmark circuits and the circuits widely studied in the references,and simulated the faultscenarios as well as the fault-free operation of CUT by OrCAD10.5,analog circuit faultdiagnosis model based on support vector machine is achieved in Matlab7.0 and asimulating experiment is also carried out to diagnose the soft faults,hard faults andmulti-faults in CUT.The experimental results have testified the feasibility of theproposed method and the validity of the conclusion in this dissertation.Compared withthe widely studied analog circuits fault diagnosis method based on neural network,theproposed method in this dissertation possesses the merits of simpler structure and higherdiagnostic accuracy,and it solves the disadvantage of neural network--local optimalsolution,over-fitting and under-fitting,difficulty in choosing model structures,etc,andrealizes the automatic choice of model structure and good generalization ability forsmall samples to account for the trade off between learning ability and generalizationability of learning machine by minimizing structural risk.
引文
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