Feature Extraction Methods in Fault Diagnosis of Analog Circuits

1. Introduction

Fault feature extraction is the key to analog circuit fault diagnosis. However, due to the complexity of fault models, tolerance of component parameters, nonlinearity, noise, and large-scale integration, analog circuit fault information is presented as a multi-feature, high-noise, and nonlinear data set. In addition, it is restricted by the means of characteristic signal observation, symptom extraction methods, state recognition technology, completeness of diagnostic knowledge, and diagnostic economy. As a result, the fault diagnosis technology of analog circuits lags behind the fault diagnosis technology of digital circuits and faces huge challenges. Analog circuit fault diagnosis is essentially equivalent to the problem of pattern recognition. Therefore, it is an important topic to study how to compress the original features of the circuit state from the high-dimensional feature space to the low-dimensional feature space and extract effective fault features to improve the fault diagnosis rate. This article will briefly introduce the principle steps and advantages and disadvantages of some feature extraction methods used in analog circuit fault diagnosis, laying a foundation for further research.

2. Feature extraction based on statistical theory

The traditional feature extraction method based on statistical theory considers the first-order moment and second-order moment of the measurement point data, and reduces the dimension of the feature space according to the important statistical characteristics of these measurement point data to achieve the purpose of effective feature extraction, including feature extraction methods based on separability criterion, KL transformation, principal component analysis, etc.

Principal component analysis is a data feature analysis method based on the variance-covariance (correlation coefficient) matrix of data samples. From the perspective of feature validity, it uses linear transformation to find a set of vectors in the data space that can explain the variance of the data as much as possible, and maps the data from the original high-dimensional space to a low-dimensional vector space. After dimensionality reduction, the main information of the data is retained, and the principal components are independent of each other, making the data easier to process. In analog circuit fault diagnosis [1,2], the process of using principal component analysis to achieve data compression and feature extraction is: first, standardize the original feature data to eliminate the influence of different dimensions and large numerical differences of the original variables; then establish the correlation matrix of the data, calculate the eigenvalues ​​and eigenvectors of the matrix, and sort the obtained eigenvalues; finally, select the principal component according to the variance contribution rate of the eigenvalue, usually requiring the cumulative variance contribution rate to reach 80% to 90%. The structure of the diagnostic system is shown in Figure 1. After the eigenvector is reduced in dimension by principal component analysis, the input of the diagnostic neural network is reduced, the network training speed is improved, and the computational complexity of the neural network is reduced.

Fig.1 Analog circuit fault diagnosis system based on principal component analysis

Feature extraction based on statistical theory is often difficult to calculate in applications due to the distribution of probability density functions, and the mapping required for high-resolution feature extraction is often nonlinear, so the linear transformation method based on statistical theory is limited in use. Further research directions are nonlinear extensions of its methods, such as nonlinear principal component transformation and its integration with other feature extraction methods.

3. Feature extraction based on wavelet analysis[3-8]

In the feature extraction of circuit signals, spectrum analysis is often used. However, Fourier analysis based on statistical analysis is only very effective for stationary signals that do not change with time. It cannot effectively extract fault features for analog circuit response signals that usually contain non-stationary or time-varying information. In addition, analog circuits contain a lot of noise. If the high-frequency components are directly discarded as noise components, it will cause the loss of effective components. If the output of the circuit is simply analyzed, it will result in a large number of fault fuzzy sets and low resolution [5]. The time-frequency localization characteristics, good denoising ability, and the advantage of not requiring a system model structure make wavelet analysis an effective tool for analyzing and processing such signals. It is also the most commonly used feature extraction method in the field of analog circuit fault diagnosis, and is applicable to both soft and hard faults in analog circuits.

The basic principle of wavelet analysis is to analyze the signal by scaling the wavelet mother function in scale and frequency shifting in time domain. Appropriate selection of the mother function can make the expansion function have good locality, which is very suitable for singular value analysis of non-stationary signals to distinguish signal mutations from noise. At present, wavelet transform, wavelet packet transform and multi-wavelet transform are used in the literature of analog circuit fault diagnosis [3-8] to extract the features of circuit fault information, which has a good effect on the extraction of transient signals of analog circuits, elimination of circuit noise and component parameter tolerance unique to analog circuits.

There are two ways to combine wavelet analysis technology with neural networks: one is loose combination, and the other is compact combination. The loose structure is the most common way of data preprocessing. At present, the wavelet neural network with compact structure has also been successfully used for denoising and feature extraction of analog circuits [5]. Since the compact wavelet neural network uses nonlinear wavelet basis to replace the nonlinear sigmoid function, the connection between wavelet transform and neural network is established through affine transformation, which has stronger approximation ability and convergence speed. It has obvious advantages whether it is used for feature extraction or fault diagnosis. The structure of compact wavelet neural network is shown in Figure 2.

Figure 2 Compact wavelet neural network structure diagram

The multi-resolution analysis in wavelet analysis technology only decomposes the low-frequency part of the signal each time, while the high-frequency part remains unchanged, resulting in a very low resolution of the high-frequency part. However, the wavelet packet transform provides a more sophisticated analysis method, which can decompose the low-frequency and high-frequency parts at the same time to adaptively determine the resolution of the signal in different frequency bands, so that the decomposition sequence has a higher time-frequency resolution and the same bandwidth in the entire time-frequency domain, and more effectively extracts features. The multiwavelet transform can simultaneously possess important properties such as symmetry, orthogonality, short support, and high-order vanishing moments, which makes up for the shortcomings of a single wavelet and has begun to become a hot topic in feature extraction research. The difference between it and the multi-resolution analysis of a single wavelet is that its multi-resolution analysis is generated by multiple scale functions, and its construction method can generally use the orthogonality, symmetry, short support and approximation order of multiwavelets to construct corresponding multi-scale functions and multiwavelet functions.

[page] The advantage of wavelet analysis in feature extraction is mainly the ability of wavelet basis to approximate a class of actual functions with fewer non-zero wavelet coefficients. The selection of wavelet basis should be based on the maximum amount of wavelet coefficients close to zero. This ability of wavelet basis mainly depends on its mathematical properties - orthogonality, vanishing moment, regularity, symmetry and support length. When selecting different mother wavelets for feature extraction, the effect will be very different. There is no perfect theoretical guidance on which wavelet function to choose in the characteristic analysis of circuits. It is mostly determined based on experience or experiments. Therefore, the optimization of wavelet mother function, wavelet coefficients, wavelet network structure and learning algorithm are all problems that need to be solved urgently.

4. Feature extraction based on fault information

The feature extraction method based on the amount of fault information is a new method based on different ideas [9-11]. If a fault occurs during the operation of an analog circuit, the characteristic parameters of the circuit will deviate from the normal state and the characteristic vector will also change. Therefore, as long as the fault source exists, the fault information will be expressed through the characteristic parameters [11]. If the amount of information is used as a measure of the occurrence of a fault, the state of the circuit can be diagnosed. According to the viewpoint of information theory, the goal of feature extraction is to maximize the information of the channel and minimize the channel loss through a special channel, that is, the feature extraction method used. The principle is shown in Figure 3.

Figure 3 Comparison between information transmission model and feature extraction model

Feature extraction based on mutual information entropy is one of the methods. Its theoretical basis is that when a feature obtains the maximum mutual information entropy, the feature can obtain the maximum recognition entropy increment and the minimum misidentification probability, thus having the best characteristics. Therefore, feature extraction is to find a set with the maximum mutual information entropy or the minimum feature condition entropy in the initial feature set of the circuit. The maximum mutual information entropy is determined by the system entropy and the posterior entropy. The system entropy is certain. Therefore, the smaller the posterior entropy, the greater the mutual information and the better the classification effect. Therefore, effective feature extraction is transformed into finding a set with the maximum mutual information entropy or the minimum posterior entropy after the initial feature set is given. In the process of feature optimization, as features are deleted, information loss will occur, causing the posterior entropy to increase. The value of the posterior entropy increment reflects the information loss caused by deleting the feature vector. Arrange the posterior entropy from small to large to obtain the corresponding feature deletion sequence.

References [9,10] expand the measurement points in the circuit to any characteristic quantity that can carry circuit fault information. After performing AC small signal analysis on the circuit, the phase-frequency and amplitude-frequency characteristics of the voltage measured from the accessible nodes are sampled. The diagnostic information of these sampling points is then used to complete the selection of effective measurement points (i.e., features), providing an effective fault feature set with a large amount of diagnostic information and guaranteed fault identification accuracy for subsequent diagnosis.

In the fault feature extraction method based on the amount of fault information, as long as the information containing the uncertain state can be transmitted in the circuit system and reach the output port, the uncertain state in the circuit can be obtained through the detected output signal, the abnormal signs of the system can be extracted, and effective feature data can be provided for fault diagnosis. This method can be used not only for linear circuits, but also for nonlinear circuits.

At present, the feature extraction methods based on fault information include multiple measures such as information entropy, mutual information, and negative entropy. Most of them need to obtain the posterior probability distribution function of various faults and the density function of the measurement value of the measuring point. However, it is difficult to obtain these parameters, and they are mostly approximated by estimation methods. Therefore, different estimation methods of probability density functions and different search algorithms will affect whether the fault feature set generated in the end is the best fault feature set. These are all issues that need further exploration in the current feature extraction work.

5. Feature extraction based on kernel function [4,12-13]

Nonlinear feature extraction based on kernel functions is particularly suitable for dealing with nonlinear problems that are widely present in analog circuits. It transforms the nonlinear problem in the original feature sample space into a linear problem in the mapping space through nonlinear mapping, as shown in Figure 4. Its goal is to minimize the sum of the distances between the data point and the curve or surface it represents, so that the input vector has better separability. Commonly used kernel functions include polynomial kernels and Gaussian kernels.

Figure 4 Nonlinear embedding mapping of kernel function

[page] Reference [12] uses kernel function to expand linear feature extraction. Through simulation analysis, it is shown that the approach of nonlinear feature extraction based on kernel function can improve the separability of fault modes, thereby improving the accuracy of circuit fault identification. Reference [3] proposes a method of extracting analog circuit fault features using binary tree support vector machine, and constructs different binary tree structures based on the separability strategy of pattern class space distribution. The results of these methods are compared, and it is concluded that balanced binary tree support vector machine has better speed for diagnosis of multi-fault analog circuits, while adaptive support vector machine has better classification effect.

The calculation cost and classification effect of kernel function-based nonlinear feature extraction are different when different kernel functions are selected. In addition, kernel function-based nonlinear feature extraction has a good classification effect on fault diagnosis of small sample data, but when extracting features in the case of a large number of samples, such as when using kernel principal component analysis, it is necessary to calculate the kernel matrix. Since the dimension of the kernel matrix is ​​equal to the number of samples, the calculation of the kernel matrix will become very difficult. Therefore, how to select a suitable kernel function and reduce the calculation amount of the kernel matrix while keeping the distribution structure of the feature samples unchanged requires further research.

6. Feature extraction methods from other theories

Rough set theory is a new mathematical tool for dealing with incompleteness and uncertainty problems, and has been successfully applied in the field of pattern recognition. Its main advantage is that it does not require any prior or additional data information. It can discover the implicit knowledge and rules by simply using the information provided by the measured data. Therefore, it is more objective in describing and dealing with the uncertainty of the problem. The feature extraction method based on rough sets uses the data simplification capability of rough sets to transform the feature extraction process into a simplification process [14]. The conditional attributes and decision attributes of the system to be diagnosed are simplified to obtain the best training sample set that eliminates redundant and repeated information, that is, the optimal decision attribute set, so as to simplify the neural network structure and improve the system diagnosis speed. It provides a new idea for feature extraction of analog circuits under incomplete symptom information.

With the development of nonlinear dynamic system theory, fractal theory reveals the regularity of various complex phenomena in nature and human society from its special perspective. It provides another new idea and new method for dealing with nonlinear system problems. The parameter that quantitatively describes fractal characteristics is the fractal dimension, which quantitatively describes the complexity of the fractal set. Therefore, the dimension of the detail signal can be used as a feature for classification and recognition. Commonly used dimensions are box dimension and information dimension. The box dimension reflects the geometric scale of the fractal set, and the information dimension reflects the information of the fractal set in distribution. Reference [15] uses wavelet transform to decompose the communication signal in view of the non-stationary and large signal-to-noise ratio variation range of the communication signal. The box dimension and information dimension of the obtained detail signal are calculated. The dimension contains the main information such as amplitude, frequency and phase required to distinguish different modulation types. Then the dimension of these detail signals is used as the feature of communication signal modulation type recognition. The classifier designed based on this feature is simple and efficient, and has certain noise resistance performance. The characteristic signal of the analog circuit operation status has fractal characteristics within a certain scale range. Combining it with wavelet transform and neural network can increase the number of feature extraction and improve the effectiveness and reliability of fault diagnosis.

7. Conclusion

Feature extraction is the basic link of pattern recognition and is equally important for fault diagnosis of analog circuits. It strongly affects the design and performance of classifiers, so it is a key issue in fault diagnosis of analog circuits. This paper summarizes some feature extraction methods commonly used in the field of fault diagnosis of analog circuits in recent years. Traditional statistical analysis methods such as principal component analysis use linear transformation to solve the dimensionality reduction problem of circuit response feature vectors; wavelet analysis can decompose the non-stationary signal of analog circuit response into sequences of different levels and channels, and has very good time-frequency characteristics; and feature extraction methods based on information entropy, fuzzy theory and rough sets can solve the uncertainty problem of fault modes in analog circuits. Feature extraction methods based on kernel functions have excellent generalization capabilities in nonlinear approximation and small sample conditions. The above methods each have their own advantages and disadvantages, and one method cannot completely replace another. Therefore, how to optimize various feature extraction methods or construct a feature extraction fusion method that gives full play to their respective advantages, complements their functions, and is efficient and practical, and effectively extracts the fault signs of analog circuits, will be a topic for future research.
[page] References

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