Fault diagnosis method for analog circuits based on fractal analysis and generalized eigenvalue decomposition

Abstract

The application relates to a simulation circuit fault diagnosis method based on fractal analysis and generalized eigenvalue decomposition, and aims at the nonlinear simulation circuit fault diagnosis problem with fractal characteristics of output response. The fractal analysis-based fault diagnosis method is researched, and key problems such as fault feature extraction and fault mode classification are mainly solved. The fractal dimension spectrum algorithm is adopted to extract the fault features of the nonlinear simulation circuit, the principal component analysis technology is used for fault feature compression, the generalized eigenvalue decomposition-based multi-classification recognition method is combined, and the simulation circuit fault diagnosis is realized. Through the inverter circuit fault diagnosis example of an electric servo mechanism control system, it is verified that the method can realize the nonlinear simulation circuit fault diagnosis, and has high diagnosis precision and efficiency.

Description

TECHNICAL FIELD

[0001] The application relates to the field of circuit test methods, in particular to a simulation circuit fault diagnosis method based on fractal analysis and generalized eigenvalue decomposition. BACKGROUND

[0002] There are 12 IGBTs in the inverter circuit of the electric servo mechanism control system, according to statistical data, 80% of inverter failures are caused by IGBT failures, mainly IGBT open circuit failure and short circuit failure. Since the short circuit failure exists for a short time, and the protection circuit in the inverter can detect the short circuit current and start the protection action, it is very difficult to solve the fault characteristic parameters through mathematical expressions for the inverter circuit, and it is also difficult to detect the switching state of the power device, therefore, only the output voltage, current and other easily measured quantities can be selected for fault diagnosis. SUMMARY

[0003] The application aims to solve the above problems, and provides a simulation circuit fault diagnosis method based on fractal analysis and generalized eigenvalue decomposition.

[0004] To solve the above technical problems, the application adopts the following technical scheme:

[0005] The simulation circuit fault diagnosis method based on fractal analysis and generalized eigenvalue decomposition comprises the following steps:

[0006] Step 1, a training circuit simulation model is built, the components in the training circuit are set to be normal or faulty, normal state training circuits and training circuits in multiple fault states are obtained, all the normal state training circuits are classified as normal types, the training circuits in multiple fault states are classified according to preset fault types, a working input signal is applied to each training circuit, and the output voltage is sampled to obtain training voltage sequence values of each training circuit;

[0007] Step 2, the Higuchi fractal dimension spectrum method is used to calculate the HFDS (Higuchi Fractal Dimension Spectrum) waveform diagram of the circuit output voltage by using the training voltage sequence values, the HFDS waveform diagram of each training circuit is obtained, the principal component analysis technology is used to extract the principal components of the HFDS waveform diagram of each training circuit, the first N principal components constitute a fault feature vector representing the current training circuit state, and the fault feature vectors corresponding to all the training circuits are obtained;

[0008] Step 3, the training feature vectors corresponding to the training circuits of the same type are classified into a training set, a plurality of type training sets are obtained, a one-to-many SVM (Support Vector Machine) classification method is used to train the plurality of type training sets respectively, and a binary classifier corresponding to each fault type and a binary classifier corresponding to a normal type are obtained;

[0009] Step 4, applying a working input signal to the analog circuit to be tested, sampling the output voltage to obtain test voltage sequence values;

[0010] Step 5, using the Higuchi fractal dimension spectrum method to calculate the HFDS waveform of the circuit output voltage by using the test voltage sequence values, obtaining the HFDS waveform of the analog circuit to be tested, and using principal component analysis technology to extract the principal components of the HFDS waveform of the analog circuit to be tested, the first N principal components extracted constitute a test feature vector representing the state of the analog circuit to be tested;

[0011] Step 6, inputting the test feature vector into each binary classifier corresponding to a fault type and a binary classifier corresponding to a normal type respectively, obtaining a test result corresponding to each type, if the smallest test result value is the minimum value of the binary classifier corresponding to the α fault type, then the analog circuit to be tested is of the α fault type, and if the smallest test result value is the minimum value of the binary classifier corresponding to the normal type, then the analog circuit to be tested is normal.

[0012] Further, the N = 6.

[0013] Further, the method for obtaining a plurality of state training circuits in step 1 is: setting all components in the training circuit to parameters within the nominal parameter tolerance range, obtaining a plurality of normal state circuits by adjusting the parameter values, and arbitrarily selecting one or more components, setting the components to parameters outside the nominal parameter tolerance range, and setting the remaining components to parameters within the nominal parameter tolerance range, to obtain a plurality of fault state circuits.

[0014] The above technical scheme is adopted in the present application, and compared with the prior art, the present application has the following advantages:

[0015] (1) proposed based on Higuchi fractal dimension spectrum of analog circuit fault feature extraction method. Based on the generalized distance calculation, the HFD algorithm is extended to Higuchi fractal dimension spectrum algorithm, which can mine more and more rich implicit information.(2) Design of analog circuit fault diagnosis algorithm based on fractal analysis and generalized eigenvalue decomposition. The Higuchi fractal dimension spectrum algorithm is used to extract the fault features of nonlinear analog circuits, and the principal component analysis technology is used for fault feature compression, combined with the multi-classification recognition method based on generalized eigenvalue decomposition, the analog circuit fault diagnosis is realized. Finally, through the inverter circuit fault diagnosis example of the electric servo mechanism control system, it is verified that the method proposed in the invention can realize the fault diagnosis of nonlinear analog circuit, and has high diagnosis precision and efficiency.

[0016] The application will be described in detail below with reference to the accompanying drawings and examples. BRIEF DESCRIPTION OF DRAWINGS

[0017] Figure 1 is the overall flowchart of the application;

[0018] Figure 2 is the inverter circuit;

[0019] Figure 3 is the space control vector diagram;

[0020] Figure 4 is the Higuchi fractal dimension spectrum calculation result of single fractal sequence;

[0021] Figure 5 is the Higuchi fractal dimension spectrum calculation result diagram of multiple fractal sequence;

[0022] Figure 6 is the Duffing oscillator circuit diagram;

[0023] Figure 7 is the Duffing circuit V(U3)-V(U4) chaotic phase diagram;

[0024] Figure 8 is the output voltage waveform of Duffing circuit under different states;

[0025] Figure 9 is the output voltage HFDS curve of Duffing circuit under different states. DETAILED DESCRIPTION

[0026] The principles and characteristics of the application will be described below in conjunction with the accompanying drawings, and the examples are only used to explain the application, and are not used to limit the scope of the application.

[0027] Fault diagnosis process based on fractal analysis and generalized eigenvalue decomposition

[0028] The fault diagnosis of nonlinear analog circuit mainly completes two aspects of work: one is fault feature extraction, the Higuchi fractal dimension spectrum method is used to calculate the HFDS of the output voltage of the circuit, which can represent the fault feature of the circuit, but the HFDS dimension is high, and the principal component analysis technology is used for dimension reduction processing, which can significantly compress the feature space and greatly reduce the calculation amount of the classification algorithm; the other is fault mode recognition, a multi-classification method based on generalized eigenvalue decomposition is used for fault classification, which has higher classification efficiency compared with the support vector machine method. The analog circuit fault diagnosis process based on fractal analysis and generalized eigenvalue decomposition is shown in Figure 1 . First, the analog circuit in different states (including normal state and all fault states) is excited by a signal, the output voltage is sampled, the Higuchi fractal dimension spectrum method is used to calculate the HFDS of the output voltage of the circuit, the principal component analysis technology is used to compress the HFDS, and the fault feature quantity representing the state of the circuit is obtained as the training set, and the GEPSVM (Proximal Support Vector Machine via Generalized Eigenvalues, Proximal Support Vector Machine via Generalized Eigenvalues) classifier is trained to obtain multiple binary classifiers, and the training process is shown in Figure 1 (a); secondly, the trained multi-class GEPSVM classifier is used for fault recognition of the to-be-tested circuit, and the test process is shown in Figure 1 (b); finally, the diagnosis result is output.

[0029] Example study

[0030] The inverter circuit of the electric servo mechanism control system is shown in Figure 2 There are 12 IGBTs in the inverter circuit, according to the statistics, 80% of the inverter faults are caused by IGBT faults, mainly IGBT open circuit faults and short circuit faults. Since the short circuit fault exists for a short time, and the protection circuit in the inverter can detect the short circuit current and start the protection action, therefore, the present application only considers the open circuit fault of IGBT. Considering that the possibility of multiple IGBTs failing simultaneously in actual work is very small, the present application assumes that at most two IGBTs fail simultaneously, and the IGBT faults in the circuit are divided into 5 large categories and 79 small categories according to the structure of the inverter circuit, and the specific fault types are shown in Table 1.

[0031] Table 1 Inverter circuit fault types

[0032]

[0033]

[0034] For the inverter circuit, it is very difficult to solve the fault characteristic parameters by mathematical expression, and it is also difficult to detect the switching state of power device, so only the output voltage, current and other easily measured quantities can be selected for fault diagnosis. Considering that the output current will change with the load, the three-phase output voltage is selected for analysis. The DC supply voltage in the inverter circuit is 160V, and the voltage space vector control method (SVPWM) is used to control the on-off state of IGBT, and the space control vector is as shown in Figure 3 The six large vectors divide the vector space into six large sectors, and each large sector is divided into six small areas by the medium and small vectors. The input three-phase voltage is set as: Twelve typical fault modes as shown in the table are selected from 79 fault modes for diagnostic analysis. The Higuchi fractal dimension spectrum method is used to calculate the HFDS of three-phase output voltage, and the principal component analysis technology is used to extract the first three principal components in the HFDS. The characteristic vector curve composed of the principal components of three-phase voltage output HFDS can be known: the characteristic vectors of all fault modes are significantly different, and can be easily distinguished.

[0035] Table 2 Typical state setting of inverter

[0036]

[0037] The three-phase input voltage is set as a sinusoidal signal, so as to ensure that the space voltage vector traverses all 6 large sectors. The three-phase input voltage amplitudes U are set as 30V, 50V and 70V respectively, the step size is 0.02V, 30V-31V (50 groups, the space voltage vector traverses 1 / 2 small sector), 50V-51V (50 groups, the space voltage vector traverses 1 / 2 / 4 / 5 small sector), 70V-71V sampling data (50 groups, the space voltage vector traverses 3 / 4 / 5 / 6 small sector), 20000 voltages are sampled in each state, and 50x12x20000 data of three types are obtained. 30x12x20000 groups of data are randomly selected from the measured data as the test set, and the remaining 20x12x20000 groups of data are used as the training set, and the fault diagnosis method is used for diagnosis. Considering that there are noise and measurement error in actual measurement, therefore, the measured voltage signal in the test set is increased by 95, 80 and 65 of the signal-to-noise ratio of the Gaussian white noise, and the Higuchi fractal dimension spectrum feature extraction method and the MF-DFA feature extraction method are compared and analyzed, the minimum value and the maximum value of the singular value, the singular value width, the multi-fractal spectrum width, the maximum value and the minimum value of the multi-fractal spectrum are selected as six variables to form a fault feature vector (6 dimensions in total), and the first six principal components of the HFDS are extracted by the method to form a fault feature vector, and the measured data of the A-phase, A / B-phase and A / B / C-phase output voltage are used to form a feature vector for fault diagnosis, and the diagnosis results are shown in Table 3, from which it can be seen that the fault diagnosis accuracy of the Higuchi fractal dimension spectrum feature extraction method is similar to that of the MF-DFA algorithm, and both are not sensitive to noise.

[0038] Table 3 Fault diagnosis results when the input voltage amplitude is 30V

[0039]

[0040] Table 4 Fault diagnosis results when the input voltage amplitude is 50V

[0041]

[0042]

[0043] Table 5 Fault diagnosis results when the input voltage amplitude is 70V

[0044]

[0045] Summary

[0046] The present application is aimed at the fault diagnosis problem of nonlinear analog circuit with fractal characteristics of output response, and studies a fault diagnosis method based on fractal analysis, and focuses on solving key problems such as fault feature extraction and fault mode classification. The main work is summarized as follows:

[0047] (1) A method for extracting analog circuit fault features based on Higuchi fractal dimension spectrum is proposed. Based on generalized distance calculation, the HFD algorithm is expanded to the Higuchi fractal dimension spectrum algorithm, which can mine more and richer implicit information.

[0048] (2) A fault diagnosis algorithm for analog circuits based on fractal analysis and generalized eigenvalue decomposition is designed. The Higuchi fractal dimension spectrum algorithm is used to extract fault features of nonlinear analog circuits, principal component analysis technology is used for fault feature compression, and a multi-classification recognition method based on generalized eigenvalue decomposition is used to realize analog circuit fault diagnosis.

[0049] Finally, through the fault diagnosis example of the inverter circuit of the electric servo mechanism control system, it is verified that the method proposed in the application can realize the fault diagnosis of nonlinear analog circuits, and has high diagnosis accuracy and efficiency.

[0050] Fractal feature extraction based on Higuchi fractal dimension spectrum

[0051] The HFD algorithm can depict the similarity characteristics and irregularity of fractal time series, and has high accuracy and simple operation, and is widely used in signal feature extraction. The application applies it to the fault feature extraction of nonlinear analog circuits.

[0052] 1. HFD algorithm steps

[0053] The specific process of calculating the Higuchi fractal dimension by using the HFD algorithm is as follows:

[0054] Step 1: Use X(1), X(2), …, X(N) to represent the time series with length N, select the delay time interval constant k to extract the time series, and obtain a new time series

[0055]

[0056] Expand the above time series to obtain the following time series matrix:

[0057]

[0058] Where i and m represent the row number and column number of the time series matrix respectively; floor(·) represents the rounding operation; the number of rows in the last row of the time series matrix is The data in this row is And the last data is X(N).

[0059] For example, when k=3 and N=100, the extracted time series matrix is

[0060]

[0061] Step 2: Calculate the curve length L of each column of the time series matrix m (k), get

[0062]

[0063] Wherein is a normalization factor, after adjustment

[0064]

[0065] Step 3: Use the average of the curve length of all columns in the time series matrix to describe the total curve length of the matrix, get

[0066]

[0067] Step 4: When k takes different values, steps 1-3 are calculated respectively, and finally a set of k and L(k) related array data is obtained, and linear fitting is performed on the array data to obtain

[0068] log(L(k))=FD*log(1 / k)+C,

[0069] Wherein the slope FD of the straight line is the calculated fractal dimension.

[0070] 2. Higuchi fractal dimension spectrum algorithm

[0071] Through steps 1-3 of the HFD algorithm, the curve length L(k) of the time series is obtained

[0072]

[0073] In step 2 of the HFD algorithm, the absolute value distance is used to calculate the time series curve distance, and the absolute value distance

[0074]

[0075] is extended to generalized Minkowski distance

[0076]

[0077] When q takes different values, the Higuchi fractal dimension spectrum is calculated by using the HFD algorithm based on the generalized distance. Since the generalized Minkowski distance involves multiplication and square root operations, divergence may occur when q takes negative values, therefore, the invention only discusses the case when q takes positive values: when q=2, the generalized distance degenerates into Euclidean distance

[0078]

[0079] When q→∞, the generalized distance degenerates into Chebyshev distance

[0080] max(|x(m+ki)-x(m+k(i-1))|).

[0081] 3. Fractal feature extraction example

[0082] 3.1 Fractal feature extraction of time series

[0083] The present application selects typical single and multiple fractal time series as research objects, and discusses the influence of the value of q on the calculated value of generalized HFD. When calculating the Higuchi fractal dimension spectrum, the value of q is uniformly set as q=1:50.

[0084] (1) Single fractal time series analysis

[0085] Taking WMCF sequence and TF sequence as research objects, the Higuchi fractal dimension spectrum of each sequence is calculated. By parameter setting, the fractal dimension FD of the time series is set as 1.1-1.9, the step length is set as 0.1, and 131072 (2 17 ) time series data are intercepted, and the calculated Higuchi fractal dimension spectrum is shown in Figure 4 As shown in Figure 4 , the Higuchi fractal dimension of the two kinds of fractal time series has the same trend with the change of q; when q=1, the Higuchi fractal dimension takes the maximum value, which is close to the theoretical fractal dimension; for the time series with fixed fractal dimension, the Higuchi fractal dimension converges to a stable value with the increase of q.

[0086] The multiple fractal characteristics of the binomial sequence are derived from the long-range correlation characteristics. The time series is generated by iteration: at the initial iteration, the data set X(i) only contains a single value X (0) (1)=1; after k iterations, X (k) (2i-1)=pX (k-1) (i) and X (k) (2i)= (1-p)X (k-1) (i) generate the data set {X (k) (i): i=1,2,...,2 k}, (i=1,2,...,2 k-1 ); when k→∞, X (k) (i) is approximately a binomial measure.

[0087] The multiple fractal characteristics of the Levy sequence are derived from the wide probability density function. The Levy sequence is a search strategy model, and the Mantegna calculation formula is usually used when calculating the Levy search path: s=μ / |v| 1 / βwhere 1 < β < 2, the parameters v and μ take random numbers obeying normal distribution σ v = 1 and

[0088] The Higuchi fractal dimension spectrum of the binomial sequence and the Levy sequence are calculated respectively. The parameters of the binomial sequence are set as p = 0.05:0.05:0.45, and the iteration is 17 times. The parameters of the Levy sequence are set as β = 1.005:0.005:1.995, and 131072 (2 17 ) time series data are extracted respectively. The Higuchi fractal dimension spectrum obtained by calculation is shown in Figure 5 It can be seen from Figure 5 that the change trend of the Higuchi fractal dimension of the two kinds of fractal time series is consistent. When q = 1, the Higuchi fractal dimension takes the maximum value, which is about 2. For the fractal time series with fixed model parameters, the Higuchi fractal dimension converges to a stable value HFDS_inf as q increases. The HFDS_inf changes with the parameter q or β. The HFDS_inf of the binomial sequence is a monotone decreasing function of the parameter q when 0 < p < 0.5. The relationship between the HFDS_inf of the Levy sequence and the parameter β is relatively complex, and there is a general decreasing trend.

[0089] 3.2 Fault feature extraction of analog circuit

[0090] The Higuchi fractal dimension spectrum method is used to extract the fault features of the Duffing oscillator circuit shown in the figure. The nominal parameters of the components are shown in Figure 6 . The test excitation signal is set as a sine signal with an amplitude of 0.707 V and a frequency of 0.159 Hz. The V(U3)-V(U4) phase diagram under the nominal parameters is shown in Figure 7 . It can be seen from Figure 7 that the circuit has strong chaotic characteristics.

[0091] Six circuit states are set as shown in Table 6:

[0092] Table 6 Fault mode setting

[0093]

[0094] In the table It is shown that the resistance R1 is increased by 20%, and the resistance R2 is decreased by 20%, the output curve of the circuit is obtained by simulation, the circuit output response has strong nonlinearity, and the output voltage cannot be directly used for distinguishing various states of the circuit, and needs to be further analyzed and processed. The Higuchi fractal dimension spectrum of the output voltage of the circuit is calculated by using the method, and the result is shown in the figure. As shown in the figure, the Higuchi fractal dimension spectrum of the output voltage of the circuit in different states is significantly different, and various circuit states can be easily distinguished, so the Higuchi fractal dimension spectrum can fully represent the fault characteristics of the circuit.

[0095] The above is an example of the best embodiment of the present application, wherein the parts not described in detail are all the common knowledge of ordinary skilled in the art. The protection scope of the present application is subject to the content of the claims, and any equivalent transformation based on the technical inspiration of the present application is also within the protection scope of the present application.

Claims

1. A method for analog circuit fault diagnosis based on fractal analysis and generalized eigenvalue decomposition, characterized by, The method comprises the following steps: Step 1, a training circuit simulation model is built, components in the training circuit are set to normal or fault, a normal state training circuit and a plurality of fault state training circuits are obtained, all normal state training circuits are classified as a normal type, the plurality of fault state training circuits are classified according to a preset fault type, a working input signal is applied to each training circuit, and a training voltage sequence value of each training circuit is obtained by sampling an output voltage; Step 2, a Higuchi fractal dimension spectrum method is used to calculate an HFDS waveform diagram of the circuit output voltage by using the training voltage sequence value, an HFDS waveform diagram of each training circuit is obtained, principal component analysis technology is used to extract principal components of the HFDS waveform diagram of each training circuit, the first N principal components constitute a fault feature vector representing a current training circuit state, and a fault feature vector corresponding to all training circuits is obtained; Step 3, training feature vectors corresponding to training circuits belonging to the same type are classified into a training set, a plurality of type training sets are obtained, and a one-versus-all SVM classification method is used to train a plurality of GEPSVM classifiers respectively, to obtain a two-classifier corresponding to each fault type and a two-classifier corresponding to the normal type; Step 4, a working input signal is applied to the to-be-tested analog circuit, and a test voltage sequence value is obtained by sampling an output voltage; Step 5, a Higuchi fractal dimension spectrum method is used to calculate an HFDS waveform diagram of the circuit output voltage by using the test voltage sequence value, an HFDS waveform diagram of the to-be-tested analog circuit is obtained, principal component analysis technology is used to extract principal components of the HFDS waveform diagram of the to-be-tested analog circuit, and the first N principal components constitute a test feature vector representing a state of the to-be-tested analog circuit; Step 6, the test feature vector is input into the two-classifier corresponding to each fault type and the two-classifier corresponding to the normal type respectively, a test result corresponding to each type is obtained, if a minimum test result value is a minimum value of the two-classifier corresponding to the α fault type, the to-be-tested analog circuit is of the α fault type, and if the minimum test result value is a minimum value of the two-classifier corresponding to the normal type, the to-be-tested analog circuit is normal.

2. The method of claim 1, wherein the method is characterized by: The N is 6.

3. The method of claim 1, wherein the method is characterized by: In step 1, the method for obtaining the plurality of state training circuits is as follows: all components in the training circuit are set to parameters within a nominal parameter tolerance range, a plurality of normal state circuits are obtained by adjusting the parameter values, one or more components are selected at random, the components are set to parameters outside the nominal parameter tolerance range, and the remaining components are set to parameters within the nominal parameter tolerance range, and a plurality of fault state circuits are obtained.

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