BACKGROUND OF THE PRESENT INVENTION

Field of Invention

The invention belongs to the technical field of circuit testing, and particularly relates to a method for diagnosing analog circuit fault based on cross wavelet features.

Description of Related Arts

2. DESCRIPTION OF RELATED ART

With the development of integrated circuit technology, large-scale digital-analog hybrid integrated circuits have been widely applied to the fields of consumer electronics, industrial control and aerospace. Analog circuits, as an important constituent part of integrated circuits, used for signal transmission, filter, amplification and conversion are indispensible for normal operation of a system. Therefore, it is necessary to carry out a study on the fault diagnosis technique of analog circuits to ensure the reliability of the system.

However, due to the difficult simulation of analog circuit faults and the influences of non-linearity and tolerance of circuit elements, there are still many problems in fault diagnosis of analog circuits. For example, the disturbance from external noises, the unknown unpredictability of faults and the uncertainty of the deviation of parameters from normal ranges all have a significant influence on the accuracy and efficiency of fault diagnosis methods.

In view of these problems, many domestic and foreign researchers have carried out a great number of studies on fault feature extraction methods. For example, in the literature “Spina R, Upadhyaya S. Linear circuit fault diagnosis using neuromorphic analyzers[J], Circuits & Systems II Analog & Digital Signal Processing IEEE Transactions on, 1997, 44(3): 188-196. Negnevitsky M, Pavlovsky V. Neural networks approach to online identification of multiple failures of protection systems[J], IEEE Transactions on Power Delivery, 2005, 20(2):588-594.”, fault response signals of a circuit under test are directly used as inputs of a classifier without being preprocessed, and consequentially, the training time of the classifier is too long, and the structural size is too large. For another example, in the literature “He Xing, Wang Hongli, Lu Jinghui, etc. Analog circuit fault diagnosis method based on preferred wavelet packet and ELM [J]. Chinese Journal of Scientific Instrument, 2013,34 (11):2614-2619” and the literature “Xiao Yufei, Liu Zurun, Li Mu. Analog circuit fault diagnosis based on wavelet energy entropy and SVM [J], 2011, 34(6):110-113.”, the wavelet coefficient energy value or energy entropy is calculated and used as a fault feature to be input to a classifier to realize fault recognition; however, the feature values of nodes are small, and the features cannot be clearly distinguished. For another example, in the literature “Yuan L, He Y, Huang J, et al. A New Neural-Network-Based Fault Diagnosis Approach for Analog Circuits by Using Kurtosis and Entropy as a Preprocessor[J]. IEEE Transactions on Instrumentation & Measurement, 2010, 59(3):586-595. Long Y, Xiong Y, He Y, et al. A new switched current circuit fault diagnosis approach based on pseudorandom test and preprocess by using entropy and Haar wavelet transform [J]. Analog Integrated Circuits & Signal Processing, 2017(3):1-17”, the author uses the higher-order statistics of fault response signals as fault features to be input to the classifier to be recognized and obtains a good diagnosis effect; however, the performance of the fault diagnosis method in case of multiple faults (namely the fault categories overlap to a large extent) fails to be taken into consideration.

Thus, it is necessary to work out an analog circuit fault diagnosis method which can effectively improve the circuit fault diagnosis efficiency and can diagnose different types of faults.

SUMMARY OF THE PRESENT INVENTION

The technical issue to be settled by the invention is to overcome the aforementioned defects of the prior art by providing an analog circuit fault diagnosis method based on cross wavelet features, which can effectively improve the circuit fault diagnosis efficiency and can diagnose different types of faults.

The technical solution adopted by the invention to settle the aforesaid technical issue is as follows.

A method for diagnosing analog circuit fault based on cross wavelet features, comprises steps of:

step (1): inputting an excitation signal to an analog circuit under test, and collecting time domain response output signals under a normal condition and time domain response output signals under a fault condition to form an original data sample set, wherein the time domain response output signals under the normal condition and the time domain response output signals under the fault condition are sequentially arrayed in the original data sample set according to a collection sequence;

then, selecting 50% of the time domain response output signals under the normal condition and the domain response output signals under the fault condition from the original data sample set to form a training sample set, and selecting a residual 50% of the time domain response output signals under the normal condition and the time domain response output signals under the fault condition from the original data sample set to form a test sample set;

step (2): performing cross wavelet decomposition on both the training sample set and the test sample set to respectively acquire a wavelet cross spectrum of the training sample set and a wavelet cross spectrum of the test sample set, wherein the wavelet cross spectra is in a form of two-dimensional matrixes;

step (3): applying bidirectional two-dimensional linear discriminant analysis to process the wavelet cross spectrum of the training sample set, extracting fault feature vectors of the training sample set; and applying bidirectional two-dimensional linear discriminant analysis to process the wavelet cross spectrum of the test sample set, extracting fault feature vectors of the test sample set; and

step (4): submitting the fault feature vectors of the training sample set to a support vector machine for training an SVM classifier, and constructing a support vector machine fault diagnosis model based on the fault feature vectors of the training sample set; and after the model is trained, inputting the fault feature vectors of the test sample set to the model to perform fault classification.

Furthermore, in the step (2), the wavelet cross spectrum of the training sample set is acquired through steps of:

firstly, performing wavelet decomposition on the time domain output signals under the fault circuit condition and the time domain response output signals under the normal circuit condition in the training sample set to acquire corresponding signal wavelet coefficients which are expressed as:

Wx⁡(a,τ)=1a⁢∫-∞+∞⁢x⁡(t)⁢ψ*⁡(t-τa)⁢dt,a>0;Wy⁡(a,τ)=1a⁢∫-∞+∞⁢y⁡(t)⁢ψ*⁡(t-τa)⁢dt,a>0;

wherein t is a time point; x(t) is the time domain response output signals under the fault circuit condition in the training sample set, y(t) is the time domain response output signals under the normal circuit condition in the training sample set; α is a scale parameter; τ is a time shift parameter; * is complex number conjugation; ψ is a wavelet basis function; a Monet function is adopted as a basis function and is expressed as:

ψ⁡(t)=e-t2/2⁢ej⁢⁢Ω⁢⁢t;

secondly, performing cross processing on the time domain response output signals under the normal circuit condition and the time domain response output signals under the fault circuit condition in the training sample set to acquire the wavelet cross spectrum Sx,y(α, τ) of the training sample set, wherein a process is expressed as:
Cx,y(α,τ)Wx(α,τ)W*y(α,τ);
Sx,y(α,τ)=Cx,y(α,τ)C*x,y(α,τ)=|Cx,y(α,τ)|2

acquiring wavelet cross spectrum of the test sample set in an identical way;

wherein the wavelet cross spectrum of the training sample set and the wavelet cross spectrum of the test sample set are both in a form of a matrix.

Furthermore in step (3) applying bidirectional two-dimensional linear discriminant analysis to process the wavelet cross spectrum of the training sample set to extract fault feature vectors of the training sample set is specifically implemented as:

first, performing dimensionality reduction in a row direction of the matrix, namely the wavelet cross spectrum of the training sample set; wherein suppose there are C types of training samples in the training sample set, M is the number of all training samples in the training sample set, namely the number of all the time domain response output signals in the training sample set, and Miis the number of the ithtype of training samples in the training sample set (namely the number of time domain response output signals corresponding to the ithfault class in the training sample set),

(1≤i≤C,M=∑i=1c⁢Mi);
suppose that m*n matrix Aijrepresents the jthelement in the ithtype of training samples, an inter-class scatter matrix Sband an intra-class scatter matrix Sw, are defined as:

Sb=1M⁢∑i=1c⁢Mi⁡(A_i-A_)T⁢(A_i-A_)Sw=1M⁢∑i=1c⁢∑j=1Mi⁢(Ai-A_)γ⁢(Aij-A_i);

wherein Aiis a mean of the ithtype of training samples in the training sample set, and Ā is a grand mean of all the training samples in the training sample set;

then, resolving d maximum feature values of matrix Sw−1Sband d corresponding orthogonal feature vectors: x1, x2, . . . , xd, wherein the orthogonal feature vectors x1, x2, . . . , xdare an optimum projection of the wavelet cross spectrum of the training sample set in the row direction, and d≤(C−1);

a vector set consisting of the orthogonal feature vectors x1, x2, . . . , xdis an n*d matrix X=[x1, x2, . . . , xd], and a given m*n sample matrix A is:
B=AX;

wherein B is a feature matrix of the matrix A and is an m*d matrix;

then, by a two-dimensional linear discriminant analysis (2DLDA) method performing dimensionality reduction in a column direction of the matrix to obtain formulas of:

S_b=1M⁢∑i=1c⁢Mi⁡(A_i-A_)⁢(A_i-A_)PS~w=1M⁢∑i=1c⁢∑j=1Mi⁢(Ai-A_i)⁢(Aij-A_i)Y;then, resolving f maximum feature values of matrix {tilde over (S)}w−1{tilde over (S)}band f corresponding orthogonal feature vectors {tilde over (x)}1, {tilde over (x)}2, . . . , {tilde over (x)}f; wherein the orthogonal feature vectors {tilde over (x)}1, {tilde over (x)}2, . . . , {tilde over (x)}fare an optimum projection of the wavelet cross spectrum of the training sample set in the column direction, and f≤(C−1); a vector set consisting of the orthogonal feature vectors {tilde over (x)}1, {tilde over (x)}2, . . . , {tilde over (x)}fis an m*f matrix {tilde over (X)}=[{tilde over (x)}1, {tilde over (x)}2, . . . , {tilde over (x)}f];

thus, the projection of the sample matrix A in the row and column directions is:
Z={tilde over (X)}TAX

wherein, Z is a feature matrix extracted from the sample matrix A by means of bidirectional linear discriminant analysis (B2DLDA), and a dimensionality is f*d.

transforming the feature matrix Z extracted by the formula into a one-directional vector to constitute the fault feature vectors of the training sample set;

similarly, by bidirectional two-dimensional linear discriminant analysis, processing the wavelet cross spectrum of the test sample set to extract the fault feature vectors of the test sample set.

In step (4), as described in Literature “Sun Yongkui, Chen Guang, Li Hui. Analog circuit fault diagnosis based on adaptive wavelet decomposition and SVM [J]. Chinese Journal of Scientific Instrument, 2008, 29 (10): 2105-2109”, a support vector machine (SVM) fault diagnosis model based on feature vectors of training samples is constructed first, wherein penalty parameters and kernel parameters in the SVM model are obtained by optimization through a grid search method; and after the model is constructed, fault feature vectors of a test sample set is input to the model to recognize fault classes.

According to the invention, output response signals of a circuit under test are processed by means of cross wavelets, and wavelet cross spectra are generated after the output signals are subjected to cross wavelet transform and are stored in the form of two-dimensional matrixes; because the wavelet cross spectra cannot be directly used for training and testing a fault diagnosis model, bidirectional two-dimensional linear discriminant analysis is applied in this invention to extract feature vectors of the wavelet cross spectra to facilitate subsequent training and testing of the fault diagnosis model.

The Invention has the Following Beneficial Effects

According to the invention, useful information in fault signals and normal signals of a circuit under test are comprehensively acquired through cross wavelet transform; compared with conventional signal processing techniques, wavelet cross spectra obtained by cross wavelet transform visually and comprehensively represent the time-frequency-energy information of the signals in the form of images.

B2DLDA is adopted to directly extract the features of image matrixes to clearly distinguish different fault features. Rapid and accurate fault classification is automatically fulfilled through SVM.

Soft-fault and multi-fault simulation experiments of the circuit show that: the method of the invention can distinguish fault response features from normal response features of the analog circuit and can clearly distinguish different fault response features, and essential information of various faults is fully reflected by feature vectors; and fault diagnosis based on SVM is accurate and rapid.

