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 PDFInfo
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Abstract
The invention discloses an analog circuit fault diagnosis method based on a Bayes-KFCM (Kernelized Fuzzy C-Means) algorithm, which comprises the following steps of: carrying out fault diagnosis by adopting a kernelized fuzzy C-means clustering algorithm and firstly judging whether a new fault exits in a test sample, if YES, a diagnostic model of a new fault sample is trained to join a diagnosis system, or else, the fault positioning is carried out on the test sample according to a Bayes fault classification standard. In the invention, the wavelet transform pretreatment is carried out on the fault sample, and the multi-feature fusion is carried out on the wavelet coefficient energy value and the wavelet coefficient fractal dimension value of the sample to extract fault characteristics; and the frequency of an optimal measurable node and/or a test signal is selected through taking a maximum class inter-class distance as a basis. Compared with the prior art, the analog circuit fault diagnosis method realizes that the analog circuit fault diagnosis method, the new fault of an analog circuit can be effectively diagnosed, and the diagnosis accuracy can be improved.
Description
Technical Field
The invention relates to a fault diagnosis method for an analog circuit, in particular to a fault diagnosis method for an analog circuit based on a Bayes-KFCM algorithm.
Background
The test and diagnosis of the analog circuit mainly aim at the functional test of the circuit, the current sequence division in the test process according to the simulation can be divided into simulation before test and simulation after test, research documents and patent data in recent years show that the intelligent fault diagnosis method is the focus and key point of the current research, the method belongs to the simulation before test, and the intelligent diagnosis method can partially solve the problems of fuzziness, uncertainty and the like of the analog circuit fault. The most common and widely applied intelligent diagnosis method is a neural network method, and in recent years, an analog circuit fault diagnosis method based on SVM has been greatly developed and becomes an important branch of the intelligent diagnosis method. However, both of the two conventional intelligent methods belong to the instructor learning algorithm, that is, the existing generic labels of the fault samples must be known when the diagnostic model is trained, but when a new fault occurs, neither of the two fault diagnosis algorithms can effectively diagnose the new fault. In addition, when a circuit generates a new fault class, the diagnosis system based on the instructor learning algorithm needs to retrain all sample sets, and the diagnosis efficiency is low. Therefore, in order to effectively diagnose new faults and also diagnose known fault classes, a fault classification algorithm based on the learning of no instructor is a suitable intelligent diagnosis algorithm.
In addition, the selection and extraction of fault characteristics are a key technology in fault diagnosis of the analog circuit, and because components of the analog circuit have tolerance characteristics, the output response of the circuit has randomness in a certain range, and the output of the circuit often presents nonlinear characteristics. Therefore, the fault characteristics of different faults of the analog circuit may have a cross or overlapping phenomenon, which becomes a fuzzy fault and cannot be correctly diagnosed and positioned. In order to solve the problem of identification of fuzzy fault characteristics, a signal processing and dimension reduction method is adopted to extract and select the characteristics of a fault response signal in the fault diagnosis of an analog circuit. The most common signal processing method is wavelet transform, which calculates the energy entropy of wavelet coefficients as fault features, and has been proven to be effective in extracting fault features. However, the overlapping and crossing phenomena of fuzzy fault features cannot be completely solved by only adopting a single fault feature, and if a plurality of kinds of feature information are selected to reflect the fault features from different sides, certain information complementarity exists. Therefore, the method for realizing the fusion of different characteristics by means of the information fusion technology is an effective way for extracting the fault characteristics of the analog circuit.
Disclosure of Invention
The invention aims to solve the technical problems that the diagnosis efficiency is low and new faults cannot be effectively diagnosed due to the fact that the existing fault diagnosis method adopts a teacher learning algorithm, and provides an analog circuit fault diagnosis method based on a Bayes-KFCM algorithm.
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 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
Wherein
，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
Wherein
(ii) a When in use
If so, the test sample is a new fault sample, clustering the new fault sample by adopting a KFCM clustering algorithm, and adding a new clustering model 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:
in the formula,
is the firstiThe number of training samples of a class,
is the number of all the training samples,is a test specimenxFrom the first to the secondiThe distance between the cluster centers of the class training samples,
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
Fault class of value.
Further, the invention adopts a method of multi-fault feature fusion and selection during feature extraction to overcome the problem that the overlapping and crossing phenomena of fuzzy fault features cannot be thoroughly solved by a single fault feature, which is specifically as follows:
the feature extraction in the step C is specifically carried out 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:
in the formula,a feature vector representing the fusion is represented by,
and
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
respectively representing the wavelet coefficient energy value and the wavelet coefficient fractal dimension value in the fusionA weight, and；
step C5, calculating fusion characteristic vector
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
Therein containPSamples, each sample having a feature dimension ofWThen sample
The characteristic correlation coefficient vector is obtained according to the following method:
first, a sample is calculated
The sample mean vector of (d) is:
then, the samples are calculated
The covariance matrix of (1), wherein the character is represented by
Represents each element in the covariance matrix:
then, according to the matrixCalculating a correlation matrix:
finally, the rest of each feature pair is calculated respectivelyW-1 sum of correlation coefficients of features:
the feature dimension is thenWOf (2) a sample
The feature correlation coefficient vector of (a) is:
；
wherein the feature-dependent cumulative contribution value
Calculated according to the following formula:
furthermore, in order to make the selection of the optimal measurable node and/or the test signal frequency more representative and thus improve the fault diagnosis, the invention also adopts the maximum intra-class inter-class distance as the selection basis to select the optimal measurable node and/or the test signal frequency, which specifically comprises the following steps:
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.
The optimal measurable node is selected by the following method:
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 sample in each test node to be selected, and selecting the front point with the maximum inter-class distance of all fault 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.
Compared with the prior art, the analog circuit fault diagnosis method has the following beneficial effects:
(1) the method has the advantages that two characteristics of the energy entropy and the fractal dimension after wavelet transformation are extracted simultaneously, characteristic fusion is carried out through a linear summation method, the characteristics of fault signals are extracted from various side faces, certain complementarity is achieved, and the one-sidedness of single characteristics is compensated.
(2) Selecting the top with the accumulated contribution value of the feature correlation larger than 90 percent by calculating the correlation size of each feature component in the feature vector and sorting the correlation sizeshThe characteristic can effectively remove redundant and irrelevant characteristics in the characteristic vector, reduce the dimension of the fault characteristic vector and improve the efficiency of a diagnosis algorithm.
(3) A kernel fuzzy C-means clustering (KFCM) algorithm based on instructor-free learning is adopted as a fault diagnosis algorithm, so that the limitation that the traditional instructor-based learning algorithm needs a fault class label is overcome, and a new fault class can be effectively diagnosed. In addition, in the face of new fault classes, the traditional intelligent diagnosis system needs to retrain all sample sets, diagnosis efficiency is low, and only a diagnosis model of the new fault classes needs to be trained by adopting a guide-free learning algorithm and is added into the diagnosis system.
(4) A fault classification criterion is constructed according to the characteristics of a KFCM algorithm and a Bayes decision theory, and the criterion can quickly and accurately judge and position faults.
Drawings
FIG. 1 is a flow chart of an analog circuit fault diagnostic method of the present invention;
FIG. 2 is a flow chart of a method of multiple fault signature fusion and selection in the method of the present invention.
Detailed Description
The technical scheme of the invention is explained in detail in the following with the accompanying drawings:
the analog circuit fault diagnosis method of the present invention, as shown in fig. 1, includes the steps of:
and A, selecting the optimal measurable node and the test signal frequency of the circuit to be tested.
In order to enable the selection of the optimal measurable node and/or the optimal frequency of the test signal to be more representative and improve the fault diagnosis, the method adopts the maximum intra-class inter-class distance as a selection basis to select the optimal measurable node and/or the optimal frequency of the test signal. Specifically, step a specifically includes:
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;
a3, simulating some typical test faults manually, collecting the response voltage values of the circuit to be tested under the excitation of all the to-be-selected frequencies at the output end of the circuit as fault sample values, calculating the intra-class inter-class distances of different test fault class samples, and selecting the to-be-selected frequency with the maximum intra-class inter-class distance of the test fault class as the test frequency; wherein, the inter-class distance
The calculation of (a) is the prior art, and the calculation formula is as follows:
wherein
In the formula (I), whereincAs the number of the categories,n i is composed ofiThe number of samples of a class,P i is the firstiThe prior probability of a class sample,are respectively asiThe feature vector of a class is then calculated,
is shown asiThe mean vector of the class sample set is,mrepresents the sample lumped mean vector of all classes,
referred to as the inter-class dispersion matrix,
the intra-class dispersion matrix is generally considered that the inter-class dispersion is as large as possible, and the intra-class dispersion is as small as possible, so that classification is facilitated;
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 sample in each test node to be selected, and selecting the front point with the maximum inter-class distance of all fault classesMA plurality of test nodes, each of which is connected to a test node,Mto prepareFirstly, setting an integer less than the total number of the test nodes to be selected.
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, data of the test circuit in the actual working state is collected as test data.
And C, respectively extracting the characteristics of the fault data and the test data, denoising, and generating a training sample set and a test sample set.
The invention adopts a method of multi-fault feature fusion and selection during feature extraction to overcome the problem that the overlapping and crossing phenomena of fuzzy fault features cannot be thoroughly solved by a single fault feature, and specifically as shown in fig. 2, the method comprises the following steps:
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:
in the formula,
a feature vector representing the fusion is represented by,
and
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
respectively represent the weight of wavelet coefficient energy value and wavelet coefficient fractal dimension value in fusion, and
(ii) a In this embodiment, the weight
And
all values of (A) are 0.5;
step C5, calculating fusion characteristic vector
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,Kis (0, 100), in the present embodiment, the top of the feature correlation cumulative contribution value greater than 90% is selectedhA feature; sample setting
Therein containPSamples, each sample having a feature dimension ofWThen sample
The characteristic correlation coefficient vector is obtained according to the following method:
first, a sample is calculated
The sample mean vector of (d) is:
then, the samples are calculated
The covariance matrix of (1), wherein the character is represented by
Represents each element in the covariance matrix:
then, according to the matrix
Calculating a correlation matrix:
finally, the rest of each feature pair is calculated respectivelyW-1 sum of correlation coefficients of features:
the feature dimension is thenWOf (2) a sample
The feature correlation coefficient vector of (a) is:
；
wherein the feature-dependent cumulative contribution value
Calculated according to the following formula:
in this embodiment, the denoising is performed by using a conventional wavelet transform soft threshold method.
And 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 invention provides a new algorithm combining a KFCM algorithm and a Bayes classification criterion, which is called Bayes-KFCM algorithm in the invention.
KFCM is a guiding-free learning algorithm, original characteristic space data are mapped to a high-dimensional space through a kernel function, and then clustering is carried out through a fuzzy C mean value method. Suppose there are training sampleskClass failure, then the number of clusters iskAnd taking a certain preset accuracy as a condition for stopping the KFCM clustering algorithm, wherein the accuracy is calculated by the following formula:
the objective function of the KFCM algorithm is:
the constraint conditions are as follows:
，
，
wherein,
，
。
in the formula
Is a membership matrix which is a matrix of membership,the degree of membership is represented by,is a weighted index of the number of bits in the bit stream,v j is the center of the cluster in the input space,cis the number of categories of the cluster and,the non-linear mapping is carried out,Kis a nuclear letterAnd (4) counting.
According to the Bayes optimal decision principle, a new sample should be classified into the category with the optimal posterior probability:
wherein the prior probability
Class correlation density
Can be determined by a pseudo-density function
So as to obtain the compound with the characteristics of,
hence posterior probability
Equal to:
wherein
Is usually a constant, wherein
Is the firstiThe number of training samples of a class,is the number of all the training samples,is a test specimenxFrom the first to the secondiThe distance between the centers of the fault-like clusters,
is all thatiThe summed average of class training samples and their cluster center distances. The classification criterion based on Bayes' optimal decision principle described above can be expressed in the form:
specifically, step B specifically includes:
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
Wherein
，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
Wherein
(ii) a When in use
If so, the test sample is a new fault sample, clustering the new fault sample by adopting a KFCM clustering algorithm, and adding a new clustering model 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:
in the formula,is the firstiThe number of training samples of a class,
is the number of all the training samples,
is a test specimenxFrom the first to the secondiThe distance between the cluster centers of the class training samples,
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
Fault class of 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
Wherein
，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
Wherein
(ii) a When in use
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:
in the formula,
is the firstiThe number of training samples of a class,
is the number of all the training samples,
is a test specimenxFrom the first to the secondiThe distance between the cluster centers of the class training samples,
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
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:
in the formula,a feature vector representing the fusion is represented by,
and
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
respectively represent the weight of wavelet coefficient energy value and wavelet coefficient fractal dimension value in fusion, and
；
step C5, calculating fusion characteristic vector
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
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
The sample mean vector of (d) is:
then, the samples are calculated
The covariance matrix of (1), wherein the character is represented by
Represents each element in the covariance matrix:
then, according to the matrix
Calculating a correlation matrix:
finally, the rest of each feature pair is calculated respectivelyW-1 sum of correlation coefficients of features:
the feature dimension is thenWOf (2) a sample
The feature correlation coefficient vector of (a) is:
；
wherein the feature-dependent cumulative contribution valueCalculated according to the following formula:
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
And
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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