基于Volterra级数和神经网络的非线性电路故障诊断研究
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摘要
随着电子技术的飞速发展，非线性模拟电路在工程上广泛应用。但是，测试和故障诊断问题一直是生产和使用这些非线性模拟电路的瓶颈。由于元件的非线性，不存在一种普遍适用的非线性电路模型，缺乏通用的非线性电路仿真程序，导致电路的故障特性无统一的分析计算方法。非线性系统的Volterra级数核是系统的本质特征，基于Volterra级数的非线性系统分析和系统辨识已经引起了国际学术界的重视。神经网络具有较强的模式识别和非线性函数逼近能力。因此，本文针对非线性电路的特点，利用Volterra级数和神经网络等理论系统的研究了非线性模拟电路自动故障诊断系统结构，故障特征的提取方法和测试激励信号参数优化方法。作者主要做了如下几个方面的工作：
1．基于神经网络的模拟电路故障诊断系统
研究了基于神经网络的模拟电路故障诊断系统的结构，包括特征提取，神经网络训练样本的形成、结构确定和学习算法。
2．频域法非线性模拟电路故障特征提取
①基于非线性模拟电路频率响应的故障诊断。本文首先利用Volterra级数分析非线性模拟电路的频率响应，然后研究了如何从频率响应提取故障特征。频率响应法诊断故障的关键是激励信号的频率设计。本文提出了两种激励信号设计方法，一种方法是以尽量少的谐波信号获得尽量大的故障特征向量的方法设计激励信号；另一种方法是把激励信号的设计当作一个优化问题，即用Volterra级数建立非线性模拟电路的数学模型，然后用遗传算法搜索使故障电路和无故障电路响应区别最大的激励信号的方法。在用Volterra级数建模的过程中，Volterra核的测量是关键，因此，本文还研究了Volterra级数显著阶的确定和Volterra核的测量。
②基于非线性模拟电路的Volterra频域核的故障特征提取方法。非线性模拟电路的Volterra频域核不依赖于系统的输入，完全反映了系统的本质特性。因此本文提出用非线性模拟电路的Volterra频域核作故障特征进行故障诊断，并提出一种直接利用电路的频率响应快速测量Volterra频域核的方法，测量精度高。
3．瞬态响应法非线性模拟电路故障特征提取
①研究了应用小波分析从电路的瞬态响应中提取电路故障特征的方法。应用小波多分辨分析从电路的瞬态响应中提取故障电路和无故障电路的特征，作为神经网络的输入，对故障类别进行辨识，该方法减少了神经网络的输入数目，简化了结构和减少了训练时间，提高了故障辨识能力。本文分析了各种小波函数对故障诊断率的影响，并提出一种利用总体类间离散度的方法选择诊断效率最高的小波的方法。
②研究了瞬态测试故障诊断的激励信号的优化。本文提出用反馈神经网络建立动态非线性模拟电路的数学模型，然后用遗传算法搜索激励信号的最佳参数的方法，以提高故障识别率。
通过对举例电路的仿真表明，利用所提出的方法，能较好地分析非线性模拟电路的故障响应，较准确地完成非线性模拟电路的故障诊断，并且具有良好的可行性。
With the advancement in electronic technology, nonlinear analog are being used aggressively in industry. Nevertheless, fault diagnosis continues to be the bottleneck in producing and using these circuits. For the circuits with nonlinear component, there are no generally proper math model and common simulation program for nonlinear circuits. So the unified method is lacking for computing fault character of nonlinear circuits. The Volterra kernels of nonlinear analog circuits are the inherent characteristic of the system. System identification and nonlinear system analysis based on Volterra series are widely used in resent years. Neuron network has strong patter identification ability and can approximate a nonlinear system accurately. Therefore, this dissertation studied the structure of nonlinear analog circuits fault diagnosis system and the methods of how to extract the fault signatures from the respose of the circuit based on Volterra series and neural networks. Author's main work concentrates on three aspects as follows:
1. Faults diagnosis system of analog circuits based on neural networks.
Researched the structure of nonlinear analog circuits fault diagnosis system based on neural network. Include the methods of extract fault signatures, generate the train samples, design the neural network structure and the learn arithmetic.
2. How to extract fault signatures from frequency response of nonlinear analog circuits
①Nonlinear analog circuits fault diagnose based on frequency response. This dissertation researched the character of the frequency response of nonlinear analog circuits with Volterra series, and presented a method of how to extract the fault signatures from frequency response of the nonlinear analog circuit. Because the key of fault diagnosis based on frequency response is how to design the stimulus, this dissertation presented two methods to solve this problem. One is designing the frequency of stimulus with least multisine to generate most fault signature. The other is using optimization that used the Volterra kernels as the models of the fault circuits and fault free circuits and search the optimum stimulus based on genetic algorithm. To develop the precision models of nonlinear analog circuits, this dissertation researched how to determine the highest significant order of nonlinear analog circuit and how to measure all the Volterra kernels.
②How to use the Volterra frequency kernels as the fault signatures in diagnosis nonlinear analog circuit. The Volterra kernels of nonlinear analog circuits which are independent of the input are the inherent characteristic of the circuits. So this dissertation presented that using the Volterra frequency kernels as the fault signatures to diagnosis. This dissertation presented a Volterra frequency kernels measurement method that used the frequency response of nonlinear analog circuits directly.
3. How to extract fault signatures from transient response of nonlinear analog circuit
①This dissertation presented that use wavelet analysis to extract the transient response signature of nonlinear circuits and compress the signature data, and fed it into neural networks to execute fault identification. This method can largely reduces the input number and training time, simplifies the construction and improves the ability of fault identification for neural networks. This dissertation presented a selecting the best wavelet function method based on the between-category total scatter of signature.
②Studied how to optimum the transient testing stimulus. This dissertation present that use Elman network to develop the models of the fault circuits and fault free circuit and search the optimum stimulus based on genetic algorithm.
The simulation results of examples given in this dissertation show that the fault diagnosis methods proposed above have good diagnosis effect and feasibility in analyzing the fault response of nonlinear analog circuits and can locate the fault correctly.
1．基于神经网络的模拟电路故障诊断系统
研究了基于神经网络的模拟电路故障诊断系统的结构，包括特征提取，神经网络训练样本的形成、结构确定和学习算法。
2．频域法非线性模拟电路故障特征提取
①基于非线性模拟电路频率响应的故障诊断。本文首先利用Volterra级数分析非线性模拟电路的频率响应，然后研究了如何从频率响应提取故障特征。频率响应法诊断故障的关键是激励信号的频率设计。本文提出了两种激励信号设计方法，一种方法是以尽量少的谐波信号获得尽量大的故障特征向量的方法设计激励信号；另一种方法是把激励信号的设计当作一个优化问题，即用Volterra级数建立非线性模拟电路的数学模型，然后用遗传算法搜索使故障电路和无故障电路响应区别最大的激励信号的方法。在用Volterra级数建模的过程中，Volterra核的测量是关键，因此，本文还研究了Volterra级数显著阶的确定和Volterra核的测量。
②基于非线性模拟电路的Volterra频域核的故障特征提取方法。非线性模拟电路的Volterra频域核不依赖于系统的输入，完全反映了系统的本质特性。因此本文提出用非线性模拟电路的Volterra频域核作故障特征进行故障诊断，并提出一种直接利用电路的频率响应快速测量Volterra频域核的方法，测量精度高。
3．瞬态响应法非线性模拟电路故障特征提取
①研究了应用小波分析从电路的瞬态响应中提取电路故障特征的方法。应用小波多分辨分析从电路的瞬态响应中提取故障电路和无故障电路的特征，作为神经网络的输入，对故障类别进行辨识，该方法减少了神经网络的输入数目，简化了结构和减少了训练时间，提高了故障辨识能力。本文分析了各种小波函数对故障诊断率的影响，并提出一种利用总体类间离散度的方法选择诊断效率最高的小波的方法。
②研究了瞬态测试故障诊断的激励信号的优化。本文提出用反馈神经网络建立动态非线性模拟电路的数学模型，然后用遗传算法搜索激励信号的最佳参数的方法，以提高故障识别率。
通过对举例电路的仿真表明，利用所提出的方法，能较好地分析非线性模拟电路的故障响应，较准确地完成非线性模拟电路的故障诊断，并且具有良好的可行性。
With the advancement in electronic technology, nonlinear analog are being used aggressively in industry. Nevertheless, fault diagnosis continues to be the bottleneck in producing and using these circuits. For the circuits with nonlinear component, there are no generally proper math model and common simulation program for nonlinear circuits. So the unified method is lacking for computing fault character of nonlinear circuits. The Volterra kernels of nonlinear analog circuits are the inherent characteristic of the system. System identification and nonlinear system analysis based on Volterra series are widely used in resent years. Neuron network has strong patter identification ability and can approximate a nonlinear system accurately. Therefore, this dissertation studied the structure of nonlinear analog circuits fault diagnosis system and the methods of how to extract the fault signatures from the respose of the circuit based on Volterra series and neural networks. Author's main work concentrates on three aspects as follows:
1. Faults diagnosis system of analog circuits based on neural networks.
Researched the structure of nonlinear analog circuits fault diagnosis system based on neural network. Include the methods of extract fault signatures, generate the train samples, design the neural network structure and the learn arithmetic.
2. How to extract fault signatures from frequency response of nonlinear analog circuits
①Nonlinear analog circuits fault diagnose based on frequency response. This dissertation researched the character of the frequency response of nonlinear analog circuits with Volterra series, and presented a method of how to extract the fault signatures from frequency response of the nonlinear analog circuit. Because the key of fault diagnosis based on frequency response is how to design the stimulus, this dissertation presented two methods to solve this problem. One is designing the frequency of stimulus with least multisine to generate most fault signature. The other is using optimization that used the Volterra kernels as the models of the fault circuits and fault free circuits and search the optimum stimulus based on genetic algorithm. To develop the precision models of nonlinear analog circuits, this dissertation researched how to determine the highest significant order of nonlinear analog circuit and how to measure all the Volterra kernels.
②How to use the Volterra frequency kernels as the fault signatures in diagnosis nonlinear analog circuit. The Volterra kernels of nonlinear analog circuits which are independent of the input are the inherent characteristic of the circuits. So this dissertation presented that using the Volterra frequency kernels as the fault signatures to diagnosis. This dissertation presented a Volterra frequency kernels measurement method that used the frequency response of nonlinear analog circuits directly.
3. How to extract fault signatures from transient response of nonlinear analog circuit
①This dissertation presented that use wavelet analysis to extract the transient response signature of nonlinear circuits and compress the signature data, and fed it into neural networks to execute fault identification. This method can largely reduces the input number and training time, simplifies the construction and improves the ability of fault identification for neural networks. This dissertation presented a selecting the best wavelet function method based on the between-category total scatter of signature.
②Studied how to optimum the transient testing stimulus. This dissertation present that use Elman network to develop the models of the fault circuits and fault free circuit and search the optimum stimulus based on genetic algorithm.
The simulation results of examples given in this dissertation show that the fault diagnosis methods proposed above have good diagnosis effect and feasibility in analyzing the fault response of nonlinear analog circuits and can locate the fault correctly.
引文
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