CN118051761A - Analog circuit fault diagnosis method based on matrix model parameter identification - Google Patents
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Abstract
The invention discloses a matrix model parameter identification-based analog circuit fault diagnosis method. On the matrix model and the diagnosis method thereof: the matrix construction link adopts Laplace operator to reduce the dimension, and reduces the matrix order while retaining the high-dimension fault characteristics; in the parameter identification link, the solution of the comprehensive trace and the spectrum radius in the corresponding fitting equation is used as the final identification error. The method is applied to a Sallen_Key band-pass filter circuit and a frog-leaping low-pass filter circuit, can realize parameter identification, and can control the error within 1%; the fault diagnosis rate reaches 100 percent. The invention realizes the integration of fault diagnosis, positioning and parameter identification, has high positioning precision and small parameter identification error, and is suitable for occasions requiring high-precision parameter identification such as residual life estimation of a circuit system, element failure mechanism analysis and the like.
Description
Technical Field
The invention relates to the field of analog circuit fault diagnosis, in particular to an analog circuit fault diagnosis method based on matrix model parameter identification.
Background
With the increase of Circuit integration and complexity, the reliability, maintainability and testability of modern electronic devices and systems for Analog circuits (AC for short) are increasingly high. Analog circuits have problems of component tolerance, nonlinearity, lack of fault models and the like, so that the fault diagnosis research of the analog circuits becomes a popular and challenging research subject. In recent years, the research on fault diagnosis of analog circuits is mainly focused on artificial intelligence algorithms, and methods such as neural networks, support vector machines, machine learning and the like are used in many cases. However, these methods are essentially classification algorithms, often only a limited number of fault states or fault intervals can be diagnosed, and parameter identification is difficult. In the links of residual life estimation of a circuit system, circuit fault identification, component failure mechanism analysis and the like, parameter identification is precisely needed for a fault component so as to provide more specific fault information. Fault parameter identification is much more difficult than fault detection and fault localization.
In the field of fault diagnosis of analog circuits, mature fault parameter identification methods are rarely reported. The sub-band filtering method can detect the parameter faults of the analog circuit, but the method is difficult to locate the faults; the fuzzy analysis method based on sensitivity calculation can realize the parameter type fault diagnosis of the linear analog circuit, but the method has poor effect on tolerance characteristics in fault diagnosis. In the method for extracting the fault characteristics of the analog circuit, the wavelet analysis can embed the original data into a high-dimensional characteristic space through nonlinear mapping, and has good time-frequency localization and multi-resolution analysis properties, but the calculation is complex.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a matrix model parameter identification-based analog circuit fault diagnosis method.
According to the invention, an analog circuit fault diagnosis model is established according to the rule that the characteristics of the circuit output response matrix change along with the change of the device parameters, so that the integration of fault diagnosis, positioning and parameter identification is realized, and the problems that the subband filtering method is difficult to perform fault positioning and the artificial intelligent algorithm cannot realize parameter identification are solved; the invention adopts the numerical value characteristic of the output response matrix characteristic as the fault characteristic, and avoids the problem of complex wavelet analysis and calculation.
The aim of the invention is realized by the following technical scheme:
the analog circuit fault diagnosis method based on matrix model parameter identification comprises the following steps:
A pre-measurement stage:
step one, numbering the diagnosed device and setting the fault state of the diagnosed device;
Sampling output signals of each fault state of each diagnosed device according to time sequence to form an ordered matrix, using Laplace operator to reduce dimension and sharpen to obtain trace and spectrum radius of the matrix as fault characteristics;
Performing least square fitting on the obtained numerical values of the discrete fault characteristics to obtain a continuous fitting equation;
Diagnosis stage:
Step four, inputting the same excitation as the previous stage to the fault circuit, obtaining an output response sequence of the circuit in each fault state, forming an output response matrix, and obtaining a measured value of a trace of the matrix and a measured value of a spectrum radius after dimension reduction by using a Laplace operator;
Substituting the measured value of the trace into the fitted equation of the trace of each fault device to obtain a series of solutions, substituting the solutions as independent variables into the fitted equation of the spectrum radius of the corresponding device again to obtain a series of calculated values of the spectrum radius;
Step six, finding out the closest measured value of the spectrum radius from a series of calculated values of the spectrum radius, and judging that the circuit has no fault if the solution of the measured value of the corresponding trace is within the tolerance range of the device; otherwise, the device corresponding to the calculated value of the spectrum radius is a fault element, so that fault positioning is realized;
And step seven, after fault positioning, using the spectrum radius measurement value to replace the fitting equation of the spectrum radius of the positioned fault device, solving the parameter value of the fault device calculated by using the spectrum radius, and averaging the parameter value of the fault device calculated by using the trace before as the final identification parameter of the fault device.
The invention firstly extracts the characteristics of the output response matrix of the circuit output points, and then establishes a model according to the rule that the characteristics change along with the change of the device parameters, thereby realizing the parameter identification of the fault diagnosis of the analog circuit.
The method is based on a matrix model, and innovations are provided on the construction of a matrix output response matrix: the output response matrix is generally extracted by sampling according to the time sequence of the output voltage, and then extracting the numerical characteristics of the matrix. This presents two problems, if the matrix dimension of the output response sequence is small, the obtained circuit information is limited, which results in a low final failure diagnosis rate; if the matrix dimension formed by the output response sequence is large, the calculation amount of the method can be increased sharply, and the cost of diagnosis time is increased. Therefore, there is a need to use a relatively simple dimension reduction method that does not introduce random amounts. The invention adopts Laplace operator and output matrix convolution, and reduces matrix order while retaining high-dimensional fault characteristics.
In the fault diagnosis link, the fault device can be reversely pushed through the measured fault characteristics according to the rule that the fault characteristics change along with the device parameter change, but due to multiple solutions, two fault characteristics are required to be cross-verified so as to actually locate the fault. According to the principle of error reduction, after the fault is positioned, the invention synthesizes the identification of two characteristics to the fault components and parts, and finally determines the identification error. By doing so, the stability of error identification can be improved, and the identification error can be reduced to a certain extent.
The invention has various advantages, such as no need of training samples, less test nodes, low test time cost and favorable engineering realization.
The invention has the effects or advantages that:
The invention establishes a fault diagnosis model of the analog circuit according to the rule that the characteristics of the output response matrix of the circuit change along with the change of the parameters of the device. Because the change rule of the output response matrix characteristic is explored, but not discrete fault characteristics, the parameter identification of the fault components can be realized. Taking Sallen_Key band-pass filter circuit and frog-leaping low-pass filter circuit as example experiments, the result shows that the method can realize parameter identification, and the parameter identification error is controlled within 1%; the fault diagnosis rate reaches 100 percent. The invention realizes the integration of fault diagnosis, positioning and parameter identification, has the characteristics of high positioning precision and small parameter identification error because of being capable of realizing parameter identification, is suitable for occasions requiring high-precision parameter identification such as residual life estimation of a circuit system, element failure mechanism analysis and the like, is easy for engineering application, is easy to realize on-line test, and meets the requirement of large-scale integrated analog circuit test.
Drawings
FIG. 1 is a fault diagnosis flow chart of an analog circuit fault diagnosis method based on matrix model parameter identification;
FIG. 2 is a graph of trace of output response matrix as a function of device value;
FIG. 3 is a graph of spectral radius of the output response matrix as a function of device value;
FIG. 4 is a schematic diagram of a Sallen_key band-pass filter circuit;
fig. 5 is a schematic diagram of a frog low pass filter circuit.
Detailed Description
The invention will now be further described with reference to the drawings and examples, which are not intended to limit the scope of the invention.
For a better understanding of the present invention, the basic principles and related concepts of the invention are briefly described below.
Matrix disturbance analysis:
Y (nT s) is defined as a sampling sequence of the output signal Y (T) at the output point of the tested circuit, where T S is a sampling period, and if n is an integer of k×k, the sampling sequence may be expressed as a k-th order square matrix:
This k-th order square matrix is called a response matrix, whose rows represent sample values at k times T S intervals, and whose column elements represent consecutive sample values over a period of time at T S intervals. Under the same test point and the same test condition, the output response matrix changes due to the change of the device parameters, which is called disturbance of the response matrix.
According to Rouche's theory and the Ostrowski theorem, it can be demonstrated that the eigenvalues of a matrix are continuous functions of the matrix elements. Definition matrix a= (a ij)∈Cn×n, definition variable)
ai′＝(ai1,…,ai,i-1,ai,i+1,…,ain)T (2)
Gi(A)＝{z∈C:|z＝aii|≤||ai′||1},i＝1,…,n (3)
Thus, the eigenvalue λ (a) of matrix a can be found to satisfy the rule of the guerre disk
In addition, the Ostrowski theorem gives the upper bound of matrix eigenvalue perturbation versus matrix element perturbation quantity:
Where λ' is the eigenvalue of matrix (A+εB), λ is the eigenvalue of matrix A, n is the matrix order, ε is a constant arbitrarily greater than 0, and the elements of matrices A and B satisfy |a ij|＜1,|bij | < 1. From formulas (4) and (5), it can be derived that: the change of the matrix eigenvalues corresponds to the change of the matrix elements one by one. According to the disturbance analysis of the previous response matrix, it can be known that the disturbance caused by the circuit component can be further transferred to the eigenvalue of the response matrix through the response matrix, which is the complete matrix disturbance analysis. And the next step can be to build a fault model through the change rule of the matrix eigenvalue, and complete fault diagnosis and parameter identification.
The Laplace operator optimizes the response matrix:
Laplace operator is a type of sharpening filter that is used quite much in the field of image processing. The Laplacian is a second order differential operator in the n-dimensional Euclidean space, and the Laplacian of a function f (x, y) is defined as
Where x, y is the argument of the function f (x, y),Representing the divergence of the gradient of the function f (x, y)/>Representing the second partial derivative of f (x, y) with respect to x,/>Representing the second partial derivative of f (x, y) to y;
The second order differential of a function is defined as
Where f (x+1, y), f (x-1, y) are the front and rear state amounts of the f (x, y) that are discrete in the x direction, respectively.
Thus combining equation (6) and equation (7) yields the Laplace operator discrete form as
Where f (x, y+1), f (x, y-1) are the front and rear state amounts of the f (x, y) that are discrete in the y direction, respectively.
According to the discrete form of the Laplace operator, the Laplace operator is constructed into a matrix, the original matrix can be sharpened by convolution with the original matrix, and the Laplace operator is called a filter template, and the form is as follows:
This filter achieves an isotropic result of the laplace operator rotating in 90 degree increments. If the diagonal direction is considered, the following templates will be generated:
Because the theory principle is based on matrix disturbance, considering that the Laplace operator can make the mutation part of the data more obvious, if the Laplace operator is added in the process of extracting the response matrix and convolved with the original matrix, the disturbance can be amplified, and meanwhile, the matrix order can be reduced because of convolution operation, so that the method has two purposes. However, unlike sharpening pictures, the sharpening of the response matrix should take into account its need for different degrees of sharpening, so the filter template of the Laplace operator is defined as:
Where n is a positive integer, and the greater n, the higher the degree of sharpening.
Fault feature extraction:
If the characteristic values of the response matrix after optimization are directly taken as characteristics, two points are difficult, namely (1) an n-order square matrix has n characteristic values, if only partial characteristic values are taken, information can be lost, and if the complete taking is too complex; (2) Because of the influence of noise and measurement errors, complex eigenvalues of the actual response matrix appear, and the fault model needs to be researched on a complex plane at this time, which is very difficult.
There are a number of eigenvalue-related quantities in the matrix principle, where the spectrum of the matrix is defined as the set of overall eigenvalues of the matrix, denoted as σ (a), and the spectral radius ρ (a) is defined as
ρ(A)＝sup{|λ|:λ∈σ(A)} (9)
Where λ is the eigenvalue of the matrix, equation (9) states that ρ (a) is always real, so ρ (a) can be a fault signature. Because ρ (a) is the modulus of the matrix maximum eigenvalue, in conjunction with matrix perturbation analysis, the process of continually deviating from the nominal value for a device results in a regular change in ρ (a), i.e., perturbation of ρ (a). If this rule is grasped, the degree to which the device deviates from the nominal value can be deduced back from ρ (a). However, a circuit often has many devices, and it is likely that the corresponding situation can be found on several devices only by judging through ρ (a), so that the second fault feature is needed together for fault diagnosis.
In matrix theory, there is a simple and magic quantity, the trace of the matrix, which is equal to not only the sum of the matrix eigenvalues, but also the sum of the matrix diagonal elements, defined as:
Where lambda p represents the p-th eigenvalue of matrix a. According to matrix theory, the complex eigenvalues of the matrix always appear in pairs. The trace of the matrix is the sum of the characteristic values of the matrix, so that the trace of the matrix is always real, and the overall situation of the characteristic values can be reflected. The trace of the matrix can thus also be a fault feature and the trace inherits the disturbance of the matrix. Therefore, the trace tr (A) and the spectrum radius rho (A) of the matrix can be used as two fault characteristics, and a fault model is established according to the disturbance rule of the fault model under a real number coordinate system, so that fault positioning and fault parameter identification are realized.
Fault model built based on pre-test simulation:
And taking four devices in the circuit as an example to study the change rule of fault characteristics. The four devices were varied from 70% to 130% of their nominal values, stepped by 10% to obtain a total of 28 states. And obtaining 28 output response matrixes, and then optimizing the output response matrixes through a Laplace operator to obtain 28 tracks and spectrum radiuses. The trace and spectral radius are plotted as a function of device value, respectively, and the results are shown in fig. 2 and 3. Wherein the abscissa represents the normalized value of the parameter of the device and the ordinate represents the value of the corresponding state trace or spectral radius. From fig. 2 and 3, it is found that the relationship between trace and spectral radius as a function of device value can be approximated by a second order equation:
Ti,j＝aix2 i,j+bixi,j+ci (11)
Zi,j＝ai′x2 i,j+bi′xi,j+ci′ (12)
Where x i,j represents the normalized parameters of the j-th fault state of the i-th device, T i,j and Z i,j are the trace and the spectral radius corresponding to x i,j, respectively, and the equation coefficients a i,bi,ci,ai′,bi 'and c i' corresponding to the i-th device can be obtained by using least squares fitting on them.
Examples:
As shown in fig. 1, the method for diagnosing the fault of the analog circuit based on the matrix model parameter identification comprises the following steps:
A pre-measurement stage:
S1, numbering i diagnosed devices, setting 7 different fault states for each diagnosed device, for example, R1 can be stepped by 10% from 70% to 130% of the nominal value;
S2, testing the circuit in each fault state to obtain an output response sequence, forming an output response matrix by the output response sequence, then performing dimension reduction by using a Laplace operator to obtain a matrix after dimension reduction, and obtaining the trace and the spectrum radius of the matrix;
s3, performing curve fitting on a series of traces and spectrum radiuses of each device obtained in the S2 by taking the nominal value of the device as an independent variable to obtain a fitting equation of the trace of each device:
Ti,j＝aix2 i,j+bixi,j+ci (11)
fitting equation for spectral radius:
Zi,j＝ai′x2 i,j+bi′xi,j+ci′ (12)
Wherein x i,j represents the normalized parameter of the j-th fault state of the i-th device, T i,j and Z i,j are the trace and the spectrum radius corresponding to x i,j respectively, and the equation coefficients a i,bi,ci,ai′,bi 'and c i' corresponding to the i-th device can be obtained by using least square fitting on the trace and the spectrum radius corresponding to x i,j; the fitting effect is shown in fig. 2 and 3;
Diagnosis stage:
S4, inputting excitation which is the same as that of the pre-measurement stage aiming at a fault circuit, obtaining an output response sequence, forming an output response matrix, and obtaining a measured value L T of a trace of the matrix and a measured value L Z of a spectrum radius after dimension reduction by using a Laplace operator;
S5, substituting the measured value L T of the trace into the fitting equation of the trace of each device in S3, namely equation (11), obtaining p solutions, namely x i, i=1, 2, …, p, substituting the x i as an independent variable x i,j into the fitting equation of the spectrum radius of the corresponding device again, namely equation (12), and obtaining a series of calculated values of the spectrum radius, namely z i, wherein i=1, 2, …, p;
S6, calculating error delta Z i＝|Zi-LZ I between Z i and spectrum radius L Z, finding out the minimum element delta Z q in delta Z i, and judging that the circuit has no fault if x i corresponding to delta Z q does not exceed the tolerance of the device; if x i exceeds the tolerance of the devices, the ith device corresponding to x i is the fault device; to achieve fault location;
And S7, under the condition that a fault element is found, substituting the measured value L Z of the spectrum radius into a fitting equation of a corresponding fault device, namely, in equation (12), if the fitting equation is 2 times, 2 solutions can be obtained, finding out a solution close to x i, taking the average of the solution and x i as the final parameter of the fault device, and realizing parameter identification.
Sallen_Key circuit fault diagnosis and analysis:
taking a Sallen_Key band-pass filter circuit fault diagnosis model as an example, how the method can realize fault diagnosis, fault positioning and parameter identification is described in detail. After the model is built, other experiments are performed to verify the correctness of the model.
The simulation environment was processed using software OrCAD Pspice V16.0.0 and data import Matlab2023a, and the simulation was run on a personal computer using Intel (R) Core (TM) i5-8500 CPU. The Sallen_Key band-pass filter circuit is an international standard circuit and is often used for verifying the correctness of a method in the field of analog circuit fault diagnosis. The sallen_key bandpass filter circuit schematic diagram with a center frequency of 31kHz is shown in fig. 4, and these component amounts are resistors r1=1kΩ, r2=2kΩ, r3=2kΩ, r4=4kΩ, r5=4kΩ, capacitors c1=5nf and c2=5nf, the tolerance of all devices is ±5%, and the input test stimulus of the power supply circuit is a sinusoidal signal with a amplitude of 1V and a frequency of 31 kHz.
The pre-measurement simulation is performed as follows:
1) The diagnosed device is first numbered:
R1, R2, R4 and C1 are respectively numbered as 1, 2,3 and 4, after OrCAD Pspice is drawn with a circuit diagram, each diagnostic device is respectively stepped by 10% from 70% to 130% of the nominal value, and output data of each diagnostic device is recorded.
2) Sampling the time output sequence of each fault state into an output response matrix, then performing dimension reduction by using a Laplace operator to obtain a matrix after dimension reduction, and obtaining the trace and the spectrum radius of the matrix. Thus, each fault condition of each diagnostic device has a corresponding trace and spectral radius value.
3) And fitting each diagnostic device by taking the fault value (compared with the nominal value) as an independent variable and the trace as a dependent variable to obtain a trace fitting equation of each device, wherein the effect is shown in figure 2. The same fit was made to the spectral radii, with the effect shown in figure 3. The fitting coefficients are shown in table 1.
TABLE 1 values of partial parameters during diagnosis
| Parameters (parameters) | Device 1 (R1) | Device 2 (R2) | Device 3 (R4) | Device 4 (C1) |
| ai | 0.9343 | 1.2134 | -3.2260 | -0.4415 |
| bi | -4.1703 | -4.6456 | 11.9673 | 0.4592 |
| ci | 6.5610 | 6.3869 | -15.6490 | 4.0572 |
| di | -1.6282 | -1.2569 | 8.5995 | -2.3796 |
| ai′ | 0.5041 | 0.2156 | -4.4794 | -0.3800 |
| bi′ | -2.1919 | -0.8997 | 16.7911 | 0.4279 |
| ci′ | 2.9606 | 1.4055 | -22.3304 | 3.6190 |
| di′ | 1.5882 | 2.1394 | 12.8735 | -0.8068 |
A i,bi,ci,di is the coefficient of the third equation of the trace fitting according to the order of times from high to low; a i′,bi′,ci 'and d i' are coefficients of the cubic equation of the spectral radius fit;
Diagnosis stage:
To ensure simplicity and efficiency of the description, this takes as an example a fault in which R1 varies to 70% of nominal.
4) Inputting excitation which is the same as that of the pre-measurement stage aiming at a fault circuit with the R1 reduced to 70% of a nominal value, obtaining an output response sequence to form an output response matrix, and obtaining a measured value= -3.1384 of a trace of the matrix after the dimension reduction by using a Laplace operator, wherein the measured value of a spectrum radius = 3.6658; selecting 3 by using the sharpening degree n of the Laplace operator;
5) Substituting the measured values of the traces into the fitting equation of the traces of each device in the step 3) respectively, and solving a series of corresponding solutions. The solution of R1 is 0.7000, 3.3978 and 3.3978, the solution of R2 is 0.2566, 1.8332 and 1.8332, the solution of R4 is 0.8114, 1.5122 and 1.5122, the solution of C1 is 1.6007, 1.7212 and 1.7212, and if the solution is complex, only the real part is taken; substituting the 12 solutions into respective spectrum radius equations to obtain calculated values of spectrum radii, and subtracting measurement values of the spectrum radii to obtain 12 deviations, R1:0.0001, -0.5659, -0.5659;
R2：0.2642、-0.7258、-0.7258；R4:0.1528、-1.2804、-1.2804；C1:0.2108、0.3008、0.3008；
6) Finding the smallest absolute value in the spectrum radius deviation value, namely 0.0001 of R1, considering the solution 0.7000 of the trace of R1, which is not within the tolerance of 5%, and then locating the fault as R1 fault;
7) Substituting measured value= 3.6658 of the spectral radius of R1 into the spectral radius equation of R1 yields solutions 0.7001,3.7154, -7.0077. And 0.7001, which is closest to 0.7000, is found out, and the average is carried out to obtain the final fault parameter value 0.70005, so that fault location and parameter identification are completed.
In this way, a total of 84 kinds of faults were diagnosed, and the results are shown in Table 2.
TABLE 2 diagnostic results
As can be seen from Table 2, the diagnostic accuracy was 100%, and the maximum diagnostic error was 0.32%. The result proves that the method has the characteristics of high positioning precision and small parameter identification error. However, the Sallen_key circuit is simpler, so that another complex frog-leaping low-pass filter is used for further verification.
Fault diagnosis and analysis of the frog low-pass filter circuit:
The circuit diagram of the frog-leaping low-pass filter is shown in figure 5, and a sine voltage source with the voltage amplitude of 6V and the frequency of 1kHz is selected as an excitation source of the circuit. The voltage output out is selected as the test input, and the circuit device parameters are set to + -5% as shown in figure 5. The pre-test simulation and test method is the same as the Sallen_key circuit, and considers faults of 4 passive devices C4, R5 and R7 in total, 7 parameter states are simulated for each device before test, and 21 parameter states are simulated for each device in the test stage. Through experimental calculation, 84 faults are all correctly positioned, and the maximum error of parameter identification is 0.98%. Comparing the diagnosis results with the matrix model method without improvement, and obtaining the results shown in table 3:
TABLE 3 comparison of diagnostic effects of different methods
| Project | Calculation time/ms | Fault location/% | Parameter identification | Maximum identification error |
| Matrix model | 107 | 98.5 | Can be used for | 1.72 |
| The invention is that | 134 | 100 | Can be used for | 0.98 |
The results in Table 3 show that the calculation time of the invention is slightly higher than that of the unmodified matrix model method, because the invention introduces a link for optimizing the matrix response by the Laplace operator and a change in the diagnostic algorithm. But the invention directly improves the fault location to 100%, and the maximum parameter identification error is greatly reduced and controlled within 1%. Therefore, the invention is advantageous if it is used in situations where the positioning requirements and the identification errors are high.
The preferred embodiments of the invention disclosed above are merely to aid in the description of the invention and are not intended to limit the invention to the specific embodiments described. Obviously, many modifications and variations are possible in light of the above teaching. The embodiments were chosen and described in order to best explain the principles of the invention and the practical application, to thereby enable others skilled in the art to best understand and utilize the invention.
Claims (8)
1. The analog circuit fault diagnosis method based on matrix model parameter identification is characterized by comprising the following steps:
A pre-measurement stage:
step one, numbering the diagnosed device and setting the fault state of the diagnosed device;
Sampling output signals of each fault state of each diagnosed device according to time sequence to form an ordered matrix, using Laplace operator to reduce dimension and sharpen to obtain trace and spectrum radius of the matrix as fault characteristics;
Performing least square fitting on the obtained numerical values of the discrete fault characteristics to obtain a continuous fitting equation;
Diagnosis stage:
Step four, inputting the same excitation as the previous stage to the fault circuit, obtaining an output response sequence of the circuit in each fault state, forming an output response matrix, and obtaining a measured value of a trace of the matrix and a measured value of a spectrum radius after dimension reduction by using a Laplace operator;
Substituting the measured value of the trace into the fitted equation of the trace of each fault device to obtain a series of solutions, substituting the solutions as independent variables into the fitted equation of the spectrum radius of the corresponding device again to obtain a series of calculated values of the spectrum radius;
Step six, finding out the closest measured value of the spectrum radius from a series of calculated values of the spectrum radius, and judging that the circuit has no fault if the solution of the measured value of the corresponding trace is within the tolerance range of the device; otherwise, the device corresponding to the calculated value of the spectrum radius is a fault element, so that fault positioning is realized;
And step seven, after fault positioning, using the spectrum radius measurement value to replace the fitting equation of the spectrum radius of the positioned fault device, solving the parameter value of the fault device calculated by using the spectrum radius, and averaging the parameter value of the fault device calculated by using the trace before as the final identification parameter of the fault device.
2. The method for diagnosing a fault in an analog circuit based on matrix model parameter identification as recited in claim 1, wherein in step one, i diagnosed devices are numbered, and 7 different fault states are set for each diagnosed device.
3. The method for diagnosing faults of an analog circuit based on matrix model parameter identification as claimed in claim 1, wherein in the third step, curve fitting is performed on a series of traces and spectrum radii of each device obtained in the second step by taking a nominal value of the device as an independent variable, so as to obtain a fitting equation of the trace of each device:
Ti,j＝aix2 i,j+bixi,j+ci (11)
fitting equation for spectral radius:
Zi,j＝a′ix2 i,j+b′ixi,j+c′i (12)
wherein x i,j represents a normalized parameter of the jth fault state of the ith device, T i,j and Z i,j are a trace and a spectrum radius corresponding to x i,j, respectively, and a least squares fit is used for the trace and the spectrum radius corresponding to x i,j to obtain equation coefficients a i,bi,ci,a′i,b′i and c' i corresponding to the ith device.
4. The method for diagnosing faults in an analog circuit based on matrix model parameter identification as claimed in claim 1, wherein in step five, the measured value L T of the trace is substituted into the fitting equation of the trace of each device in S3, namely equation (11), p solutions are obtained, which are denoted as x i, i=1, 2, …, p, and these x i are substituted again as independent variables x i,j into the fitting equation of the spectral radius of the corresponding device, namely equation (12), and a series of calculated values of the spectral radius are obtained, which are denoted as z i, i=1, 2, …, p.
5. The method for diagnosing faults of an analog circuit based on matrix model parameter identification as claimed in claim 1, wherein in step six, error Δz i＝|Zi-LZ |betweenz i and spectrum radius L Z is calculated, the smallest element Δz q in Δz i is found out, if x i corresponding to Δz q does not exceed the tolerance of the device, then the circuit is judged to be fault-free; if x i exceeds the tolerance of the devices, the ith device corresponding to x i is the fault device; to this end, fault localization is achieved.
6. The method for diagnosing a fault in an analog circuit based on matrix model parameter identification as claimed in claim 1, wherein in step seven, when a fault element is found, the measured value L Z of the spectrum radius is substituted into a fitting equation of a corresponding fault device, namely equation (12), if the fitting equation is2 times, 2 solutions can be obtained, a solution close to x i is found, and the average of the solution and x i is taken as the parameter of the final fault device, thereby realizing parameter identification.
7. The matrix model parameter identification-based analog circuit fault diagnosis method of any one of claims 1 to 6 is used for sallen_key band-pass filter circuit fault diagnosis.
8. The matrix model parameter identification-based analog circuit fault diagnosis method of any one of claims 1 to 6 is used for fault diagnosis of a frog-leaping low-pass filter circuit.
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