CN102520341A - Analog circuit fault diagnosis method based on Bayes-KFCM (Kernelized Fuzzy C-Means) algorithm - Google Patents

Analog circuit fault diagnosis method based on Bayes-KFCM (Kernelized Fuzzy C-Means) algorithm Download PDF

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CN102520341A
CN102520341A CN2011103965629A CN201110396562A CN102520341A CN 102520341 A CN102520341 A CN 102520341A CN 2011103965629 A CN2011103965629 A CN 2011103965629A CN 201110396562 A CN201110396562 A CN 201110396562A CN 102520341 A CN102520341 A CN 102520341A
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罗慧
王友仁
林华
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Nanjing University of Aeronautics and Astronautics
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Abstract

本发明公开了一种基于Bayes-KFCM算法的模拟电路故障诊断方法。本发明采用核模糊C均值聚类算法进行故障诊断，首先判断测试样本是否是新故障，如果是，则训练新类故障样本的诊断模型加入诊断系统，如果不是，则依据Bayes故障分类准则对测试样本进行故障定位。本发明对故障样本进行小波变换预处理，将样本的小波系数能量值和小波系数分形维数值进行多特征融合，提取故障特征；以最大类内类间距离作为依据，选择最优可测节点和/或测试信号频率。相比现有技术，本发明方法能有效的诊断出模拟电路的新故障，并能提高诊断准确度。

Figure 201110396562

The invention discloses an analog circuit fault diagnosis method based on Bayes-KFCM algorithm. The present invention adopts nuclear fuzzy C-means clustering algorithm to carry out fault diagnosis, first judges whether the test sample is a new fault, if so, then trains the diagnostic model of the new fault sample and adds it to the diagnostic system, if not, then tests the test sample according to the Bayes fault classification criterion Sample fault location. The present invention performs wavelet transform preprocessing on fault samples, performs multi-feature fusion on the wavelet coefficient energy value and wavelet coefficient fractal dimension value of the sample, and extracts fault features; based on the maximum distance between classes within a class, selects the optimal measurable node and /or test signal frequency. Compared with the prior art, the method of the invention can effectively diagnose the new fault of the analog circuit, and can improve the diagnosis accuracy.

Figure 201110396562

Description

一种基于Bayes-KFCM算法的模拟电路故障诊断方法A Fault Diagnosis Method for Analog Circuits Based on Bayes-KFCM Algorithm

技术领域 technical field

本发明涉及一种模拟电路故障诊断方法，尤其涉及一种基于Bayes-KFCM算法的模拟电路故障诊断方法。 The invention relates to an analog circuit fault diagnosis method, in particular to an analog circuit fault diagnosis method based on Bayes-KFCM algorithm.

背景技术 Background technique

模拟电路的测试和诊断主要针对电路的功能测试，目前根据仿真在测试过程的顺序划分可分为测前仿真和测后仿真，根据近几年研究文献和专利资料表明，智能故障诊断方法是现在的研究的热点和重点，该方法属于测前仿真方法，智能诊断方法能部分解决模拟电路故障的模糊性、不确定性等问题。最常见和广泛应用的智能诊断方法是神经网络法，近几年基于SVM的模拟电路故障诊断方法获得了较大发展，成为智能诊断方法得一个重要分支。然而，这两种传统智能方法均属于有导师学习算法，即训练诊断模型时必须已知故障样本已有的属类标签，然而当一个新的故障发生时，这两种故障诊断算法均不能有效的诊断出新故障。另外，当电路发生新的故障类，基于有导师学习算法的诊断系统需要重新训练所有样本集，诊断效率低。因此，为了能够有效的诊断新故障，同时也能诊断已知故障类，基于无导师学习的故障分类算法是一种合适的诊断智能算法。 The test and diagnosis of analog circuits are mainly aimed at the functional test of the circuit. At present, according to the order of simulation in the test process, it can be divided into pre-test simulation and post-test simulation. According to the research literature and patent data in recent years, the intelligent fault diagnosis method is now This method belongs to the pre-test simulation method, and the intelligent diagnosis method can partially solve the problems of ambiguity and uncertainty of analog circuit faults. The most common and widely used intelligent diagnosis method is the neural network method. In recent years, the SVM-based analog circuit fault diagnosis method has achieved great development and has become an important branch of the intelligent diagnosis method. However, both of these two traditional intelligent methods belong to the tutor learning algorithm, that is, when training the diagnosis model, the existing category labels of the fault samples must be known. However, when a new fault occurs, these two fault diagnosis algorithms cannot be effective. A new fault is diagnosed. In addition, when a new fault type occurs in the circuit, the diagnosis system based on the tutor learning algorithm needs to retrain all sample sets, and the diagnosis efficiency is low. Therefore, in order to effectively diagnose new faults and diagnose known faults at the same time, the fault classification algorithm based on unsupervised learning is a suitable diagnostic intelligent algorithm.

此外，故障特征的选择和提取是模拟电路故障诊断中的一项关键技术，由于模拟电路的元器件具有容差特点，使电路的输出响应在一定范围内具有随机性，且电路的输出往往呈现非线性特征。因此模拟电路的不同故障的故障特征可能存在交叉或重叠现象，成为模糊故障，无法被正确诊断定位。为了解决模糊故障特征的识别问题，模拟电路故障诊断中采用信号处理和降维方法对故障响应信号进行特征提取和选择。最常见的信号处理方法是小波变换，计算小波系数的能量熵值作为故障特征，该方法已经被证明能有效的提取故障特征。然而仅仅采用单一的故障特征并不能彻底解决模糊故障特征的重叠和交叉现象，如果选择多种特征信息从不同侧面反映故障特征，则具有一定的信息互补性。因此，借助信息融合技术实现不同特征融合是模拟电路故障特征提取的有效途径。 In addition, the selection and extraction of fault features is a key technology in fault diagnosis of analog circuits. Due to the tolerance characteristics of the components of analog circuits, the output response of the circuit is random within a certain range, and the output of the circuit often appears non-linear features. Therefore, the fault characteristics of different faults of the analog circuit may overlap or overlap, and become fuzzy faults, which cannot be correctly diagnosed and located. In order to solve the problem of identifying fuzzy fault features, signal processing and dimensionality reduction methods are used in analog circuit fault diagnosis to extract and select fault response signals. The most common signal processing method is wavelet transform, which calculates the energy entropy value of wavelet coefficients as fault features. This method has been proven to be effective in extracting fault features. However, only using a single fault feature cannot completely solve the overlapping and crossing phenomena of fuzzy fault features. If multiple feature information is selected to reflect fault features from different aspects, there is a certain degree of information complementarity. Therefore, the fusion of different features by means of information fusion technology is an effective way to extract fault features of analog circuits.

发明内容 Contents of the invention

本发明所要解决的技术问题在于克服现有故障诊断方法采用有导师学习算法所带来的诊断效率低，且无法对新故障进行有效诊断的不足，提供一种基于Bayes-KFCM算法的模拟电路故障诊断方法，该算法为无导师学习算法，具有更高的诊断效率，且能够对新故障进行有效诊断。 The technical problem to be solved by the present invention is to overcome the low diagnostic efficiency brought by the tutor learning algorithm in the existing fault diagnosis method and the inability to effectively diagnose new faults, and to provide an analog circuit fault based on the Bayes-KFCM algorithm Diagnosis method, the algorithm is a tutor-less learning algorithm, which has higher diagnosis efficiency and can effectively diagnose new faults.

一种基于Bayes-KFCM算法的模拟电路故障诊断方法，包括以下步骤： A method for fault diagnosis of analog circuits based on the Bayes-KFCM algorithm, comprising the following steps:

步骤A、选择待侧电路的最优可测节点和测试信号频率； Step A, selecting the optimal measurable node and test signal frequency of the circuit to be tested;

步骤B、对待测电路输入测试信号，模拟各种典型的故障状态，采集最优可测节点的电压输出值，得到故障数据作为训练数据；在相同的测试信号和可测节点下，采集测试电路在实际工作状态下的数据作为测试数据； Step B. Input the test signal to the circuit to be tested, simulate various typical fault states, collect the voltage output value of the optimal measurable node, and obtain the fault data as training data; under the same test signal and measurable node, collect the test circuit The data in the actual working state is used as the test data;

步骤C、分别提取故障数据和测试数据的特征，并进行去噪，生成训练样本集和测试样本集； Step C, extracting the features of the fault data and test data respectively, and performing denoising to generate a training sample set and a test sample set;

步骤D、利用训练样本集对故障诊断模型进行训练，并利用训练好的故障诊断模型对测试样本集进行故障诊断； Step D, using the training sample set to train the fault diagnosis model, and using the trained fault diagnosis model to perform fault diagnosis on the test sample set;

所述步骤D具体包括以下步骤： Described step D specifically comprises the following steps:

步骤D1、利用KFCM聚类算法对故障诊断模型进行训练，具体为：通过核函数将训练样本集映射到高维空间；然后通过模糊C均值方法进行聚类，当正确聚类的样本数与所有的聚类样本数之比大于或等于一预设的阈值，则算法停止，训练结束，将训练好的聚类模型作为诊断模型，同时得到各类训练样本的聚类中心，以及每类训练样本中与该类聚类中心距离最大的训练样本的距离值                                               

Figure 2011103965629100002DEST_PATH_IMAGE002
，其中
Figure 2011103965629100002DEST_PATH_IMAGE004
，n为训练样本的类数； Step D1, use the KFCM clustering algorithm to train the fault diagnosis model, specifically: map the training sample set to a high-dimensional space through the kernel function; then cluster through the fuzzy C- means method, when the number of correctly clustered samples is equal to all If the ratio of the number of cluster samples is greater than or equal to a preset threshold, the algorithm stops, the training ends, and the trained cluster model is used as a diagnostic model, and the cluster centers of various training samples and each type of training samples are obtained. The distance value of the training sample with the largest distance from the cluster center of this class
Figure 2011103965629100002DEST_PATH_IMAGE002
,in
Figure 2011103965629100002DEST_PATH_IMAGE004
, n is the number of classes of training samples;

步骤D2、将测试样本通过核函数映射到高维空间，在高维空间中计算测试样本到各类聚类中心的距离

Figure 2011103965629100002DEST_PATH_IMAGE006
，其中
Figure 548275DEST_PATH_IMAGE004
；当
Figure 2011103965629100002DEST_PATH_IMAGE008
时，则测试样本为新故障类样本，对新故障类样本采用KFCM聚类算法进行聚类，将新的聚类模型加入诊断系统；否则利用Bayes故障分类准则对测试样本进行故障定位，其中Bayes故障分类准则如下式： Step D2. Map the test sample to the high-dimensional space through the kernel function, and calculate the distance between the test sample and various cluster centers in the high-dimensional space
Figure 2011103965629100002DEST_PATH_IMAGE006
,in
Figure 548275DEST_PATH_IMAGE004
;when
Figure 2011103965629100002DEST_PATH_IMAGE008
, the test sample is a new fault sample, and the KFCM clustering algorithm is used to cluster the new fault sample, and the new clustering model is added to the diagnosis system; otherwise, the Bayes fault classification criterion is used to locate the fault of the test sample, where Bayes The fault classification criteria are as follows:

Figure 2011103965629100002DEST_PATH_IMAGE010
Figure 2011103965629100002DEST_PATH_IMAGE010

式中，

Figure 2011103965629100002DEST_PATH_IMAGE012
是第i类的训练样本数，
Figure 2011103965629100002DEST_PATH_IMAGE014
是所有的训练样本数，是测试样本x离第i类训练样本聚类中心的距离，
Figure 2011103965629100002DEST_PATH_IMAGE018
是所有第i类训练样本与其聚类中心距离的求和平均值，Bayes故障分类表示测试样本x属于具有最大
Figure 2011103965629100002DEST_PATH_IMAGE020
值的故障类。 In the formula,
Figure 2011103965629100002DEST_PATH_IMAGE012
is the number of training samples of class i ,
Figure 2011103965629100002DEST_PATH_IMAGE014
is the number of all training samples, is the distance between the test sample x and the cluster center of the i- th training sample,
Figure 2011103965629100002DEST_PATH_IMAGE018
is the summed average of the distances between all i -th training samples and their cluster centers, and the Bayesian fault classification indicates that the test sample x belongs to the class with the largest
Figure 2011103965629100002DEST_PATH_IMAGE020
The fault class for the value.

    进一步地，本发明在特征提取时采用多故障特征融合和选择的方法，来克服单一故障特征不能彻底解决模糊故障特征的重叠和交叉现象的问题，具体如下： Further, the present invention adopts the method of multi-fault feature fusion and selection during feature extraction to overcome the problem that a single fault feature cannot completely solve the overlapping and crossing phenomena of fuzzy fault features, as follows:

步骤C中所述特征提取具体按照以下方法： The feature extraction described in step C specifically follows the following methods:

步骤C1、将采集的电压值进行多层小波分解，分解成细节系数和近似系数； Step C1, performing multi-layer wavelet decomposition on the collected voltage value, decomposing it into detail coefficients and approximate coefficients;

步骤C2、计算每层细节系数和近似系数的能量熵值，由多层小波系数能量熵值组成的向量作为电压信号的第一个特征表示；  Step C2, calculating the energy entropy value of each layer of detail coefficients and approximate coefficients, the vector composed of multi-layer wavelet coefficient energy entropy values is used as the first characteristic representation of the voltage signal;

步骤C3、计算每层细节系数和近似系数的分形维数值，由多层小波系数分形维数值组成的向量作为电压信号的第二个特征表示； Step C3, calculating the fractal dimension values of the detail coefficients and approximation coefficients of each layer, the vector composed of the fractal dimension values of the multi-layer wavelet coefficients is used as the second characteristic representation of the voltage signal;

步骤C4、采用线性求和方法融合两种特征，其中线性求和融合公式如下表示： Step C4, using the linear summation method to fuse the two features, wherein the linear summation fusion formula is expressed as follows:

Figure 2011103965629100002DEST_PATH_IMAGE022
Figure 2011103965629100002DEST_PATH_IMAGE022

式中，表示融合的特征向量，

Figure 2011103965629100002DEST_PATH_IMAGE026
和
Figure 2011103965629100002DEST_PATH_IMAGE028
分别代表由信号的一层小波分解系数D计算得到的能量熵值和分形维数值，
Figure 2011103965629100002DEST_PATH_IMAGE030
和
Figure 2011103965629100002DEST_PATH_IMAGE032
分别代表小波系数能量值和小波系数分形维数值在融合中所占的权重，且； In the formula, Represents the fused feature vector,
Figure 2011103965629100002DEST_PATH_IMAGE026
and
Figure 2011103965629100002DEST_PATH_IMAGE028
Represent the energy entropy value and fractal dimension value calculated by one layer of wavelet decomposition coefficient D of the signal, respectively,
Figure 2011103965629100002DEST_PATH_IMAGE030
and
Figure 2011103965629100002DEST_PATH_IMAGE032
Represent the weights of wavelet coefficient energy value and wavelet coefficient fractal dimension value in the fusion, and ;

步骤C5、计算融合特征向量

Figure 672874DEST_PATH_IMAGE024
中每一个特征与其余特征的总体相关性大小，并由高到低进行排序，选择特征相关累计贡献值大于K％的前h个特征，进行特征降维，K的取值范围为（0，100）；设样本
Figure 2011103965629100002DEST_PATH_IMAGE036
中含有P个样本，每个样本的特征维数为W，则样本
Figure 327977DEST_PATH_IMAGE036
的特征相关系数向量按照以下方法得到： Step C5, calculate the fusion feature vector
Figure 672874DEST_PATH_IMAGE024
The overall correlation between each feature and the rest of the features is sorted from high to low, and the first h features with a cumulative contribution value of feature correlation greater than K % are selected for feature dimensionality reduction. The value range of K is (0, 100); set the sample
Figure 2011103965629100002DEST_PATH_IMAGE036
There are P samples in , and the feature dimension of each sample is W , then the sample
Figure 327977DEST_PATH_IMAGE036
The characteristic correlation coefficient vector of is obtained as follows:

首先，计算样本

Figure 97088DEST_PATH_IMAGE036
的样本均值向量为： First, calculate the sample
Figure 97088DEST_PATH_IMAGE036
The sample mean vector for is:

Figure 2011103965629100002DEST_PATH_IMAGE038
；
Figure 2011103965629100002DEST_PATH_IMAGE038
;

然后，计算样本

Figure 786827DEST_PATH_IMAGE036
的协方差矩阵，其中由字符
Figure 2011103965629100002DEST_PATH_IMAGE040
表示协方差矩阵中的每一个元素： Then, calculate the sample
Figure 786827DEST_PATH_IMAGE036
The covariance matrix of , where the characters
Figure 2011103965629100002DEST_PATH_IMAGE040
Represent each element in the covariance matrix:

Figure 2011103965629100002DEST_PATH_IMAGE042
Figure 2011103965629100002DEST_PATH_IMAGE044
；
Figure 2011103965629100002DEST_PATH_IMAGE042
Figure 2011103965629100002DEST_PATH_IMAGE044
;

接着，根据矩阵计算相关矩阵： Then, according to the matrix Compute the correlation matrix:

Figure 2011103965629100002DEST_PATH_IMAGE048
  ；
Figure 2011103965629100002DEST_PATH_IMAGE048
;

最后，分别计算每个特征对其余W-1特征的相关系数之和： Finally, the sum of the correlation coefficients of each feature to the remaining W -1 features is calculated separately:

Figure 2011103965629100002DEST_PATH_IMAGE050
  ；
Figure 2011103965629100002DEST_PATH_IMAGE050
;

则特征维数为W的样本

Figure 45507DEST_PATH_IMAGE036
的特征相关系数向量为：
Figure 2011103965629100002DEST_PATH_IMAGE052
； Then the sample whose feature dimension is W
Figure 45507DEST_PATH_IMAGE036
The characteristic correlation coefficient vector of is:
Figure 2011103965629100002DEST_PATH_IMAGE052
;

    其中特征相关累计贡献值

Figure 2011103965629100002DEST_PATH_IMAGE054
根据以下公式计算： Among them, the feature-related cumulative contribution value
Figure 2011103965629100002DEST_PATH_IMAGE054
Calculated according to the following formula:

Figure 2011103965629100002DEST_PATH_IMAGE056
  。
Figure 2011103965629100002DEST_PATH_IMAGE056
.

更进一步地，为了使最优可测节点和/或测试信号频率的选择更具有代表性，从而提高故障可诊性，本发明还采用最大类内类间距离作为选择依据，对最优可测节点和/或测试信号频率进行选择，具体如下： Furthermore, in order to make the selection of the optimal measurable node and/or the frequency of the test signal more representative, thereby improving the fault diagnosability, the present invention also uses the maximum intra-class distance as the selection basis, and the optimal measurable node and/or test signal frequency as follows:

所述测试信号频率通过以下方法选择： The test signal frequency is selected by the following methods:

步骤A1、获取待测电路的幅频响应曲线； Step A1, obtaining the amplitude-frequency response curve of the circuit to be tested;

步骤A2、选择幅频响应曲线上的拐点及其附近的频率，作为待选频率集合； Step A2, select the inflection point on the amplitude-frequency response curve and the frequencies near it as the frequency set to be selected;

步骤A3、人工模拟一些典型的测试故障,在电路的输出端采集待测电路在所有待选频率激励下电路的响应电压值作为故障样本值，计算不同测试故障类样本的类内类间距离，并选择测试故障类的类内类间距离最大的待选频率作为测试频率。 Step A3, manually simulating some typical test faults, collecting the response voltage value of the circuit under test under all frequencies to be selected at the output of the circuit as the fault sample value, and calculating the distance between classes within a class of different test fault class samples, And select the candidate frequency with the largest inter-class distance within the test fault class as the test frequency.

    所述最优可测节点通过以下方法选择： The optimal measurable node is selected by the following method:

步骤A4、将待测电路中所有可测的测试节点作为待选测试节点，人工模拟一些典型的测试故障，将选择的测试信号作为激励源加载到待测电路，采集所有待选测试节点上所有测试故障的电压值作为故障样本值； Step A4. Use all test nodes in the circuit to be tested as test nodes to be selected, artificially simulate some typical test faults, load the selected test signal as an excitation source to the circuit to be tested, and collect all test nodes on all test nodes to be selected. The voltage value of the test fault is used as the fault sample value;

步骤A5、计算各待选测试节点中测试故障类样本的类内类间距离，选择所有故障类的类内类间距离最大的前M个测试节点，M为预先设定的小于待选测试节点总数的整数。 Step A5, calculate the intra-class inter-class distance of the test fault class samples in each test node to be selected, select the first M test nodes with the largest intra-class inter-class distance of all fault classes, M is the preset value smaller than the test node to be selected An integer of the total.

    相比现有技术，本发明的模拟电路故障诊断方法具有以下有益效果： Compared with the prior art, the analog circuit fault diagnosis method of the present invention has the following beneficial effects:

（1）同时提取小波变换后的能量熵和分形维数两种特征，并通过线性求和方法进行特征融合，从多种侧面提取故障信号的特征，具有一定的互补性，弥补了单一特征的片面性。 (1) Simultaneously extract two features of energy entropy and fractal dimension after wavelet transform, and perform feature fusion by linear summation method to extract fault signal features from multiple sides, which has certain complementarity and makes up for the single feature. One-sidedness.

（2）通过计算特征向量中每种特征分量的相关性大小并进行排序，选择特征相关累计贡献值大于90％的前h个特征，可有效去除特征向量中冗余的和不相关的特征，降低故障特征向量的维数，提升诊断算法的效率。 (2) By calculating and sorting the correlation of each feature component in the feature vector, selecting the first h features whose cumulative contribution value of feature correlation is greater than 90%, can effectively remove redundant and irrelevant features in the feature vector, Reduce the dimensionality of the fault feature vector and improve the efficiency of the diagnosis algorithm.

（3）采用基于无导师学习的核模糊C均值聚类（KFCM）算法作为故障诊断算法，克服了传统有导师学习算法需要故障类标签的局限性，能有效诊断出新故障类。另外，面对出现新的故障类，传统的智能诊断系统需要重新训练所有样本集，诊断效率低，采用无导师学习算法只需训练新故障类的诊断模型，并加入诊断系统中即可。 (3) The kernel-fuzzy C-means clustering (KFCM) algorithm based on unsupervised learning is used as the fault diagnosis algorithm, which overcomes the limitation that the traditional tutor-based learning algorithm requires fault class labels, and can effectively diagnose new fault classes. In addition, in the face of new fault types, the traditional intelligent diagnosis system needs to retrain all sample sets, and the diagnosis efficiency is low. Using the tutor-free learning algorithm only needs to train the diagnosis model of the new fault type and add it to the diagnosis system.

（4）根据KFCM算法的特点并依据Bayes决策理论构造了一种故障分类准则，该准则能够快速和准确的判断和定位出故障。 (4) According to the characteristics of KFCM algorithm and Bayes decision theory, a fault classification criterion is constructed, which can quickly and accurately judge and locate faults.

附图说明 Description of drawings

图1是本发明的模拟电路故障诊断方法的流程图； Fig. 1 is the flowchart of analog circuit fault diagnosis method of the present invention;

图2是本发明方法中多故障特征融合和选择方法的流程图。 Fig. 2 is a flow chart of the multi-fault feature fusion and selection method in the method of the present invention.

具体实施方式 Detailed ways

下面结合附图对本发明的技术方案进行详细说明： The technical scheme of the present invention is described in detail below in conjunction with accompanying drawing:

本发明的模拟电路故障诊断方法，如图1所示，包括以下步骤： Analog circuit fault diagnosis method of the present invention, as shown in Figure 1, comprises the following steps:

步骤A、选择待侧电路的最优可测节点和测试信号频率。 Step A. Select the optimal measurable node and test signal frequency of the circuit to be tested.

为了使最优可测节点和/或测试信号频率的选择更具有代表性，从而提高故障可诊性，本发明采用最大类内类间距离作为选择依据，对最优可测节点和/或测试信号频率进行选择。具体地，步骤A具体包括： In order to make the selection of the optimal measurable node and/or test signal frequency more representative, thereby improving the fault diagnosability, the present invention uses the maximum intra-class distance as the selection basis, and the optimal measurable node and/or test signal frequency Select the signal frequency. Specifically, step A specifically includes:

步骤A1、获取待测电路的幅频响应曲线； Step A1, obtaining the amplitude-frequency response curve of the circuit to be tested;

步骤A2、选择幅频响应曲线上的拐点及其附近的频率，作为待选频率集合； Step A2, select the inflection point on the amplitude-frequency response curve and the frequencies near it as the frequency set to be selected;

步骤A3、人工模拟一些典型的测试故障,在电路的输出端采集待测电路在所有待选频率激励下电路的响应电压值作为故障样本值，计算不同测试故障类样本的类内类间距离，并选择测试故障类的类内类间距离最大的待选频率作为测试频率；其中，类内类间距离

Figure DEST_PATH_IMAGE058
的计算为现有技术，其计算公式如下： Step A3, manually simulating some typical test faults, collecting the response voltage value of the circuit under test under all frequencies to be selected at the output of the circuit as the fault sample value, and calculating the distance between classes within a class of different test fault class samples, And select the candidate frequency with the largest intra-class distance of the test fault class as the test frequency; among them, the intra-class inter-class distance
Figure DEST_PATH_IMAGE058
The calculation of is the prior art, and its calculation formula is as follows:

Figure 2011103965629100002DEST_PATH_IMAGE060
Figure 2011103965629100002DEST_PATH_IMAGE060

其中 in

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Figure DEST_PATH_IMAGE064

Figure DEST_PATH_IMAGE066
Figure DEST_PATH_IMAGE066

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Figure DEST_PATH_IMAGE068

式中，其中c为类别数，n i 为i类的样本数，P i 是第i类样本的先验概率，分别为i类的特征向量，

Figure DEST_PATH_IMAGE072
表示第i类样本集的均值向量，m表示所有各类的样本集总均值向量，
Figure DEST_PATH_IMAGE074
称为类间离散度矩阵，
Figure DEST_PATH_IMAGE076
为类内离散度矩阵，一般认为类间离散度尽量大，类内离散度尽量小，有利于分类； where c is the number of categories, n i is the number of samples of class i , P i is the prior probability of samples of class i , are the feature vectors of class i , respectively,
Figure DEST_PATH_IMAGE072
represents the mean vector of the i- th sample set, m represents the total mean vector of all types of sample sets,
Figure DEST_PATH_IMAGE074
is called the between-class scatter matrix,
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It is the intra-class dispersion matrix. It is generally believed that the inter-class dispersion is as large as possible, and the intra-class dispersion is as small as possible, which is conducive to classification;

    步骤A4、将待测电路中所有可测的测试节点作为待选测试节点，人工模拟一些典型的测试故障，将选择的测试信号作为激励源加载到待测电路，采集所有待选测试节点上所有测试故障的电压值作为故障样本值； Step A4. Use all test nodes in the circuit to be tested as test nodes to be selected, artificially simulate some typical test faults, load the selected test signal as an excitation source to the circuit to be tested, and collect all test nodes on all test nodes to be selected. The voltage value of the test fault is used as the fault sample value;

步骤A5、计算各待选测试节点中测试故障类样本的类内类间距离，选择所有故障类的类内类间距离最大的前M个测试节点，M为预先设定的小于待选测试节点总数的整数。 Step A5, calculate the intra-class inter-class distance of the test fault class samples in each test node to be selected, select the first M test nodes with the largest intra-class inter-class distance of all fault classes, M is the preset value smaller than the test node to be selected An integer of the total.

步骤B、对待测电路输入测试信号，模拟各种典型的故障状态，采集最优可测节点的电压输出值，得到故障数据作为训练数据；在相同的测试信号和可测节点下，采集测试电路在实际工作状态下的数据作为测试数据。 Step B. Input the test signal to the circuit to be tested, simulate various typical fault states, collect the voltage output value of the optimal measurable node, and obtain the fault data as training data; under the same test signal and measurable node, collect the test circuit The data in the actual working state is used as the test data.

步骤C、分别提取故障数据和测试数据的特征，并进行去噪，生成训练样本集和测试样本集。 Step C, extracting features of the fault data and test data respectively, and performing denoising to generate a training sample set and a test sample set.

本发明在特征提取时采用多故障特征融合和选择的方法，来克服单一故障特征不能彻底解决模糊故障特征的重叠和交叉现象的问题，具体如图2所示，包括： The present invention adopts the method of multi-fault feature fusion and selection during feature extraction to overcome the problem that a single fault feature cannot completely solve the overlapping and crossing phenomena of fuzzy fault features, specifically as shown in Figure 2, including:

步骤C1、将采集的电压值进行多层小波分解，分解成细节系数和近似系数； Step C1, performing multi-layer wavelet decomposition on the collected voltage value, decomposing it into detail coefficients and approximate coefficients;

步骤C2、计算每层细节系数和近似系数的能量熵值，由多层小波系数能量熵值组成的向量作为电压信号的第一个特征表示；  Step C2, calculating the energy entropy value of each layer of detail coefficients and approximate coefficients, the vector composed of multi-layer wavelet coefficient energy entropy values is used as the first characteristic representation of the voltage signal;

步骤C3、计算每层细节系数和近似系数的分形维数值，由多层小波系数分形维数值组成的向量作为电压信号的第二个特征表示； Step C3, calculating the fractal dimension values of the detail coefficients and approximation coefficients of each layer, the vector composed of the fractal dimension values of the multi-layer wavelet coefficients is used as the second characteristic representation of the voltage signal;

步骤C4、采用线性求和方法融合两种特征，其中线性求和融合公式如下表示： Step C4, using the linear summation method to fuse the two features, wherein the linear summation fusion formula is expressed as follows:

Figure 371928DEST_PATH_IMAGE022
Figure 371928DEST_PATH_IMAGE022

式中，

Figure 882412DEST_PATH_IMAGE024
表示融合的特征向量，
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和
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分别代表由信号的一层小波分解系数D计算得到的能量熵值和分形维数值，
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和
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分别代表小波系数能量值和小波系数分形维数值在融合中所占的权重，且
Figure 870966DEST_PATH_IMAGE034
；本具体实施方式中，权重
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和
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的取值均为0.5； In the formula,
Figure 882412DEST_PATH_IMAGE024
Represents the fused feature vector,
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and
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Represent the energy entropy value and fractal dimension value calculated by one layer of wavelet decomposition coefficient D of the signal, respectively,
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and
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Represent the weights of wavelet coefficient energy value and wavelet coefficient fractal dimension value in the fusion, and
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; In this specific implementation, the weight
Figure 113860DEST_PATH_IMAGE030
and
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The value of is 0.5;

步骤C5、计算融合特征向量

Figure 4510DEST_PATH_IMAGE024
中每一个特征与其余特征的总体相关性大小，并由高到低进行排序，选择特征相关累计贡献值大于K％的前h个特征，进行特征降维，K的取值范围为（0，100），本具体实施方式中，选择特征相关累积贡献值大于90%的前h个特征；设样本
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中含有P个样本，每个样本的特征维数为W，则样本
Figure 858513DEST_PATH_IMAGE036
的特征相关系数向量按照以下方法得到： Step C5, calculate the fusion feature vector
Figure 4510DEST_PATH_IMAGE024
The overall correlation between each feature and the rest of the features is sorted from high to low, and the first h features with a cumulative contribution value of feature correlation greater than K % are selected for feature dimensionality reduction. The value range of K is (0, 100), in this specific implementation mode, select the first h features whose correlation cumulative contribution value is greater than 90%; set the sample
Figure 710298DEST_PATH_IMAGE036
There are P samples in , and the feature dimension of each sample is W , then the sample
Figure 858513DEST_PATH_IMAGE036
The characteristic correlation coefficient vector of is obtained as follows:

首先，计算样本

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的样本均值向量为： First, calculate the sample
Figure 649752DEST_PATH_IMAGE036
The sample mean vector for is:

Figure 40151DEST_PATH_IMAGE038
；
Figure 40151DEST_PATH_IMAGE038
;

然后，计算样本

Figure 600445DEST_PATH_IMAGE036
的协方差矩阵，其中由字符
Figure 247458DEST_PATH_IMAGE040
表示协方差矩阵中的每一个元素： Then, calculate the sample
Figure 600445DEST_PATH_IMAGE036
The covariance matrix of , where the characters
Figure 247458DEST_PATH_IMAGE040
Represent each element in the covariance matrix:

Figure 198097DEST_PATH_IMAGE042
Figure 392187DEST_PATH_IMAGE044
；
Figure 198097DEST_PATH_IMAGE042
Figure 392187DEST_PATH_IMAGE044
;

接着，根据矩阵

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计算相关矩阵： Then, according to the matrix
Figure 806987DEST_PATH_IMAGE046
Compute the correlation matrix:

Figure 624902DEST_PATH_IMAGE048
  ；
Figure 624902DEST_PATH_IMAGE048
;

最后，分别计算每个特征对其余W-1特征的相关系数之和： Finally, the sum of the correlation coefficients of each feature to the remaining W -1 features is calculated separately:

Figure 374421DEST_PATH_IMAGE050
  ；
Figure 374421DEST_PATH_IMAGE050
;

则特征维数为W的样本

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的特征相关系数向量为：
Figure 142974DEST_PATH_IMAGE052
； Then the sample whose feature dimension is W
Figure 857355DEST_PATH_IMAGE036
The characteristic correlation coefficient vector of is:
Figure 142974DEST_PATH_IMAGE052
;

    其中特征相关累计贡献值

Figure 318740DEST_PATH_IMAGE054
根据以下公式计算： Among them, the feature-related cumulative contribution value
Figure 318740DEST_PATH_IMAGE054
Calculated according to the following formula:

Figure 555555DEST_PATH_IMAGE056
  。
Figure 555555DEST_PATH_IMAGE056
.

本具体实施方式中，采用传统的小波变换软阈值方法进行去噪。 In this specific implementation manner, the traditional wavelet transform soft threshold method is used for denoising.

步骤D、利用训练样本集对故障诊断模型进行训练，并利用训练好的故障诊断模型对测试样本集进行故障诊断。 Step D, using the training sample set to train the fault diagnosis model, and using the trained fault diagnosis model to perform fault diagnosis on the test sample set.

    本发明提出了一种KFCM算法与Bayes分类准则相结合的新算法，本发明中称其为Bayes-KFCM算法。 The present invention proposes a new algorithm combining the KFCM algorithm and the Bayes classification criterion, which is called the Bayes-KFCM algorithm in the present invention.

KFCM是一种无导师学习算法，通过核函数将原始特征空间数据映射到高维空间，然后通过模糊C均值方法进行聚类。假设训练样本中有k类故障，则聚类数是k个，以某一预设的准确率为KFCM聚类算法停止的条件，其中准确率通过以下公式计算得到： KFCM is an unsupervised learning algorithm that maps the original feature space data to a high-dimensional space through a kernel function, and then performs clustering through the fuzzy C-means method. Assuming that there are k types of faults in the training samples, the number of clusters is k , and the KFCM clustering algorithm stops at a certain preset accuracy rate, where the accuracy rate is calculated by the following formula:

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Figure DEST_PATH_IMAGE078

KFCM算法的目标函数为： The objective function of the KFCM algorithm is:

Figure DEST_PATH_IMAGE080
Figure DEST_PATH_IMAGE080

约束条件为：

Figure DEST_PATH_IMAGE082
，
Figure DEST_PATH_IMAGE086
，
Figure DEST_PATH_IMAGE088
The constraints are:
Figure DEST_PATH_IMAGE082
,
Figure DEST_PATH_IMAGE086
,
Figure DEST_PATH_IMAGE088

其中，

Figure DEST_PATH_IMAGE090
，
Figure DEST_PATH_IMAGE092
。 in,
Figure DEST_PATH_IMAGE090
,
Figure DEST_PATH_IMAGE092
.

式中

Figure DEST_PATH_IMAGE094
是隶属矩阵，表示隶属度，是加权指数，v j 是输入空间中的聚类中心，c是聚类的类别数，是非线性映射，K是核函数。 In the formula
Figure DEST_PATH_IMAGE094
is the membership matrix, Indicates the degree of membership, is the weighting index, v j is the cluster center in the input space, c is the number of categories of the cluster, is a nonlinear mapping, and K is a kernel function.

根据Bayes最优决策原理，一个新的样本应该被分到具有最优的后验概率的类别中： According to the Bayes optimal decision principle, a new sample should be classified into the category with the optimal posterior probability:

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Figure DEST_PATH_IMAGE102

其中先验概率

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,类别相关密度
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可由伪密度函数
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得到，
Figure DEST_PATH_IMAGE110
，因此后验概率
Figure 2011103965629100002DEST_PATH_IMAGE112
等于： where the prior probability
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, the category correlation density
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Pseudo-density function
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get,
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, so the posterior probability
Figure 2011103965629100002DEST_PATH_IMAGE112
equal:

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其中

Figure 2011103965629100002DEST_PATH_IMAGE116
通常是一个常量，其中
Figure 987322DEST_PATH_IMAGE012
是第i类的训练样本数，是所有的训练样本数，是测试样本x离第i类故障聚类中心的距离，
Figure 932647DEST_PATH_IMAGE018
是所有第i类训练样本与其聚类中心距离的求和平均值。所以上述基于Bayes最优决策原理的分类准则，可表示成以下形式： in
Figure 2011103965629100002DEST_PATH_IMAGE116
is usually a constant where
Figure 987322DEST_PATH_IMAGE012
is the number of training samples of class i , is the number of all training samples, is the distance between the test sample x and the i -th fault cluster center,
Figure 932647DEST_PATH_IMAGE018
is the summed average of the distances between all i -th class training samples and their cluster centers. Therefore, the above classification criteria based on Bayesian optimal decision-making principle can be expressed in the following form:

Figure 2011103965629100002DEST_PATH_IMAGE118
  。
Figure 2011103965629100002DEST_PATH_IMAGE118
.

具体而言，步骤B具体包括： Specifically, Step B specifically includes:

步骤D1、利用KFCM聚类算法对故障诊断模型进行训练，具体为：通过核函数将训练样本集映射到高维空间；然后通过模糊C均值方法进行聚类，当正确聚类的样本数与所有的聚类样本数之比大于或等于一预设的阈值，则算法停止，训练结束，将训练好的聚类模型作为诊断模型，同时得到各类训练样本的聚类中心，以及每类训练样本中与该类聚类中心距离最大的训练样本的距离值

Figure 396864DEST_PATH_IMAGE002
，其中
Figure 391496DEST_PATH_IMAGE004
，n为训练样本的类数； Step D1, use the KFCM clustering algorithm to train the fault diagnosis model, specifically: map the training sample set to a high-dimensional space through the kernel function; then cluster through the fuzzy C- means method, when the number of correctly clustered samples is equal to all If the ratio of the number of cluster samples is greater than or equal to a preset threshold, the algorithm stops, the training ends, and the trained cluster model is used as a diagnostic model, and the cluster centers of various training samples and each type of training samples are obtained. The distance value of the training sample with the largest distance from the cluster center of this class
Figure 396864DEST_PATH_IMAGE002
,in
Figure 391496DEST_PATH_IMAGE004
, n is the number of classes of training samples;

步骤D2、将测试样本通过核函数映射到高维空间，在高维空间中计算测试样本到各类聚类中心的距离

Figure 643486DEST_PATH_IMAGE006
，其中
Figure 854893DEST_PATH_IMAGE004
；当
Figure 483321DEST_PATH_IMAGE008
时，则测试样本为新故障类样本，对新故障类样本采用KFCM聚类算法进行聚类，将新的聚类模型加入诊断系统；否则利用Bayes故障分类准则对测试样本进行故障定位，其中Bayes故障分类准则如下式： Step D2. Map the test sample to the high-dimensional space through the kernel function, and calculate the distance between the test sample and various cluster centers in the high-dimensional space
Figure 643486DEST_PATH_IMAGE006
,in
Figure 854893DEST_PATH_IMAGE004
;when
Figure 483321DEST_PATH_IMAGE008
, the test sample is a new fault sample, and the KFCM clustering algorithm is used to cluster the new fault sample, and the new clustering model is added to the diagnosis system; otherwise, the Bayes fault classification criterion is used to locate the fault of the test sample, where Bayes The fault classification criteria are as follows:

Figure 598038DEST_PATH_IMAGE010
Figure 598038DEST_PATH_IMAGE010

式中，是第i类的训练样本数，

Figure 719633DEST_PATH_IMAGE014
是所有的训练样本数，
Figure 151751DEST_PATH_IMAGE016
是测试样本x离第i类训练样本聚类中心的距离，
Figure 229298DEST_PATH_IMAGE018
是所有第i类训练样本与其聚类中心距离的求和平均值，Bayes故障分类表示测试样本x属于具有最大
Figure 88669DEST_PATH_IMAGE020
值的故障类。 In the formula, is the number of training samples of class i ,
Figure 719633DEST_PATH_IMAGE014
is the number of all training samples,
Figure 151751DEST_PATH_IMAGE016
is the distance between the test sample x and the cluster center of the i- th training sample,
Figure 229298DEST_PATH_IMAGE018
is the summed average of the distances between all i -th training samples and their cluster centers, and the Bayesian fault classification indicates that the test sample x belongs to the class with the largest
Figure 88669DEST_PATH_IMAGE020
The fault class for the value.

Claims (7)

1. A fault diagnosis method for an analog circuit based on a Bayes-KFCM algorithm comprises the following steps:
a, selecting an optimal measurable node and a test signal frequency of a circuit to be tested;
b, inputting test signals to the circuit to be tested, simulating various typical fault states, and collecting voltage output values of the optimal measurable nodes to obtain fault data serving as training data; under the same test signal and measurable node, collecting data of the test circuit in the actual working state as test data;
c, respectively extracting the characteristics of the fault data and the test data, and denoising to generate a training sample set and a test sample set;
step D, training the fault diagnosis model by using the training sample set, and performing fault diagnosis on the test sample set by using the trained fault diagnosis model;
the method is characterized in that the step D specifically comprises the following steps:
step D1, training the fault diagnosis model by using a KFCM clustering algorithm, which specifically comprises the following steps: mapping the training sample set to a high-dimensional space through a kernel function; then by blurringCClustering by using a mean method, stopping the algorithm when the ratio of the number of correctly clustered samples to all the clustered samples is greater than or equal to a preset threshold value, finishing the training, taking the trained clustering model as a diagnosis model, and simultaneously obtaining the clustering centers of various training samples and the distance value of the training sample with the largest distance from the clustering center in each training sample
Figure 2011103965629100001DEST_PATH_IMAGE002
Wherein
Figure 2011103965629100001DEST_PATH_IMAGE004
，nClass number of training sample;
step D2, mapping the test sample to a high-dimensional space through a kernel function, and calculating the distance from the test sample to various cluster centers in the high-dimensional space
Figure 2011103965629100001DEST_PATH_IMAGE006
Wherein
Figure 791804DEST_PATH_IMAGE004
(ii) a When in use
Figure 2011103965629100001DEST_PATH_IMAGE008
If so, the test sample is newThe fault sample is clustered by adopting a KFCM clustering algorithm on the new fault sample, and a new clustering model is added into the diagnosis system; otherwise, fault location is carried out on the test sample by using a Bayes fault classification criterion, wherein the Bayes fault classification criterion is as follows:
Figure 2011103965629100001DEST_PATH_IMAGE010
in the formula,
Figure 2011103965629100001DEST_PATH_IMAGE012
is the firstiThe number of training samples of a class,
Figure 2011103965629100001DEST_PATH_IMAGE014
is the number of all the training samples,
Figure 2011103965629100001DEST_PATH_IMAGE016
is a test specimenxFrom the first to the secondiThe distance between the cluster centers of the class training samples,
Figure 2011103965629100001DEST_PATH_IMAGE018
is all thatiThe mean value of the distance between the class training sample and the cluster center thereof, Bayes fault classification and representation test samplexBelong to have the largest
Figure 2011103965629100001DEST_PATH_IMAGE020
Fault class of value.
2. The analog circuit fault diagnosis method based on the Bayes-KFCM algorithm according to claim 1, wherein the value of the threshold in step D1 is 90%.
3. The analog circuit fault diagnosis method based on the Bayes-KFCM algorithm as claimed in claim 1, wherein said feature extraction in step C is specifically according to the following method:
step C1, carrying out multilayer wavelet decomposition on the acquired voltage value to decompose the voltage value into detail coefficients and approximation coefficients;
step C2, calculating the energy entropy of each layer of detail coefficients and approximation coefficients, and using a vector formed by the energy entropy of the multilayer wavelet coefficients as a first feature representation of the voltage signal;
step C3, calculating the fractal dimension value of each layer of detail coefficient and approximation coefficient, and using the vector formed by the fractal dimension values of the multi-layer wavelet coefficients as a second feature representation of the voltage signal;
and step C4, fusing the two characteristics by adopting a linear summation method, wherein the linear summation fusion formula is expressed as follows:
Figure 2011103965629100001DEST_PATH_IMAGE022
in the formula,a feature vector representing the fusion is represented by,
Figure 2011103965629100001DEST_PATH_IMAGE026
and
Figure 2011103965629100001DEST_PATH_IMAGE028
respectively representing an energy entropy value and a fractal dimension value which are obtained by calculating a layer of wavelet decomposition coefficient D of the signal,and
Figure 2011103965629100001DEST_PATH_IMAGE032
respectively represent the weight of wavelet coefficient energy value and wavelet coefficient fractal dimension value in fusion, and
Figure DEST_PATH_IMAGE034
；
step C5, calculating fusion characteristic vector
Figure 585536DEST_PATH_IMAGE024
The total correlation magnitude of each feature and the rest features in the database are sorted from high to low, and the cumulative contribution value of the correlation of the selected features is larger than that of the correlation of the other featuresK% of the total amount ofhAnd (4) carrying out feature dimension reduction on each feature,Kthe value range of (1) is (0, 100); sample setting
Figure DEST_PATH_IMAGE036
Therein containPSamples, each sample having a feature dimension ofWThen sampleThe characteristic correlation coefficient vector is obtained according to the following method:
first, a sample is calculated
Figure 813441DEST_PATH_IMAGE036
The sample mean vector of (d) is:
Figure DEST_PATH_IMAGE038
；
then, the samples are calculated
Figure 847256DEST_PATH_IMAGE036
The covariance matrix of (1), wherein the character is represented by
Figure DEST_PATH_IMAGE040
Represents each element in the covariance matrix:
Figure DEST_PATH_IMAGE042
Figure DEST_PATH_IMAGE044
；
then, according to the matrix
Figure DEST_PATH_IMAGE046
Calculating a correlation matrix:
Figure DEST_PATH_IMAGE048
；
finally, the rest of each feature pair is calculated respectivelyW-1 sum of correlation coefficients of features:
Figure DEST_PATH_IMAGE050
；
the feature dimension is thenWOf (2) a sample
Figure 18516DEST_PATH_IMAGE036
The feature correlation coefficient vector of (a) is:
Figure DEST_PATH_IMAGE052
；
wherein the feature-dependent cumulative contribution valueCalculated according to the following formula:
Figure DEST_PATH_IMAGE056
。
4. the analog circuit fault diagnosis method based on Bayes-KFCM algorithm as claimed in claim 3, wherein the weight occupied by wavelet coefficient energy value and wavelet coefficient fractal dimension value in feature fusion
Figure 132971DEST_PATH_IMAGE030
And
Figure 334145DEST_PATH_IMAGE032
all values of (A) are 0.5.
5. The analog circuit fault diagnosis method based on Bayes-KFCM algorithm as claimed in claim 3,Kis at a value of 90.
6. The analog circuit fault diagnosis method based on the Bayes-KFCM algorithm according to any of claims 1 to 5, characterized in that the test signal frequency is selected by:
a1, obtaining an amplitude-frequency response curve of a circuit to be tested;
a2, selecting an inflection point on an amplitude-frequency response curve and frequencies near the inflection point as a frequency set to be selected;
step A3, simulating some typical test faults manually, collecting the response voltage value of the circuit to be tested under the excitation of all the frequency to be tested at the output end of the circuit as a fault sample value, calculating the intra-class inter-class distance of different test fault class samples, and selecting the frequency to be tested with the maximum intra-class inter-class distance of the test fault class as the test frequency.
7. A method of fault diagnosis for an analog circuit based on the Bayes-KFCM algorithm according to any of claims 1-5 wherein the optimal measurable node is selected by:
step A4, taking all testable test nodes in the circuit to be tested as test nodes to be selected, manually simulating some typical test faults, taking selected test signals as excitation sources to be loaded to the circuit to be tested, and collecting voltage values of all test faults on all test nodes to be selected as fault sample values;
step A5, calculating the inter-class distance of the test fault class samples in each test node to be selected, and selecting all fault classesFront of maximum distance between classesMA plurality of test nodes, each of which is connected to a test node,Mthe test nodes are preset integers which are smaller than the total number of the test nodes to be selected.
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