CN110907810A - Analog circuit single fault diagnosis method based on particle swarm algorithm - Google Patents

Analog circuit single fault diagnosis method based on particle swarm algorithm Download PDF

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CN110907810A
CN110907810A CN201911212967.5A CN201911212967A CN110907810A CN 110907810 A CN110907810 A CN 110907810A CN 201911212967 A CN201911212967 A CN 201911212967A CN 110907810 A CN110907810 A CN 110907810A
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杨成林
田书林
黄建国
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University of Electronic Science and Technology of China
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Abstract

The invention relates to a single fault diagnosis method of an analog circuit based on a particle swarm algorithm, which comprises the steps of firstly obtaining a transmission function of the analog circuit at a measuring point, obtaining element information and fuzzy group information of the analog circuit, measuring output voltage at the measuring point under a preset excitation signal when the analog circuit has a fault, then taking element parameter vectors as particles of the particle swarm algorithm, obtaining output voltage corresponding to each particle according to the transmission function, calculating the fitness value of the particles according to the difference value of the fault output voltage and the particle output voltage, wherein the smaller the fitness is, the more the particles are optimal, and after the iteration of the particle swarm algorithm is finished, screening out elements with element parameters exceeding the tolerance range from the global optimal position, wherein the fuzzy group corresponding to the element is a fault diagnosis result. According to the method, the storage in advance is not needed, and the particle swarm optimization is utilized to find the analog circuit transmission function parameter closest to the fault response according to the fault circuit response, so that the fault source is found.

Description

Analog circuit single fault diagnosis method based on particle swarm algorithm
Technical Field
The invention belongs to the technical field of analog circuit fault diagnosis, and particularly relates to an analog circuit single fault diagnosis method based on a particle swarm algorithm.
Background
Currently, in the field of analog circuit fault diagnosis, there are mainly a pre-test simulation (such as a fault dictionary method) and a post-test simulation method. Before-test emulation is to simulate possible faults of a circuit according to a circuit diagram, parameters and the like before testing, store fault responses, and measure the fault responses by using the excitation adopted in the process of constructing a dictionary before after the circuit has faults. The closest response is then looked up in the dictionary to find the fault. The advantage of this method is that the fault diagnosis is fast, but the disadvantage is also obvious, namely, when constructing the dictionary, all faults need to be exhausted. In addition, the simulation element parameters are continuously changed, so the space complexity of the exhaustive method is high. For an analog circuit with C devices, if 100 faults are sampled uniformly per element and stored in the fault dictionary, 100C storage units are needed to store the 100 single faults. If the double failure combination case is considered, then 100C 10 needs to be stored4C2A unit of storage. In addition, the required pre-survey simulation workload is also almost impossible to accomplish when constructing such a dictionary.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a particle swarm algorithm-based analog circuit single-fault diagnosis method.
In order to achieve the above purpose, the analog circuit single fault diagnosis method based on the particle swarm algorithm of the invention comprises the following steps:
s1: acquiring a transmission function of the analog circuit at a measuring point t;
s2: the number of elements in the analog circuit is marked as C, and the nominal value of the parameter of each element is marked as
Figure BDA0002298648850000012
C is 1,2, …, C; the tolerance ranges of the respective elements are expressed as
Figure BDA0002298648850000011
α represents tolerance parameters, 0 is less than α is less than 1, 1 measuring point is arranged according to the requirement, fuzzy group analysis for fault diagnosis of C elements through the measuring point is carried out, a representative fault element is selected for each fuzzy group, the number of the representative fault elements is recorded as N, obviously, the number of the fuzzy groups is also recorded as N, and the number of other non-representative fault elements is recorded as M;
s3: when the analog circuit has a fault, the output voltage at the measuring point t is measured under the preset excitation signal
Figure BDA0002298648850000021
S4: initializing the number of iterations q to 1 and initializing the velocity of each particle in the population
Figure BDA0002298648850000022
And position
Figure BDA0002298648850000023
K represents the number of particles in the population; the position vector of each particle corresponds to an element parameter vector, wherein
Figure BDA0002298648850000024
The parameter value of the nth fault element in the kth particle position vector is represented, wherein N is 1,2, …, N + M, the first N fault elements are representative fault elements, the parameters of the first N fault elements take values randomly, the last M fault elements are non-representative fault elements, and the parameters of the last M fault elements take values randomly in a corresponding tolerance range;
s5: positioning the particles under a predetermined excitation signal
Figure BDA0002298648850000025
Substituting the transmission function to calculate the output voltage at the measuring point t
Figure BDA0002298648850000026
Then, the fitness value of each particle in the current particle swarm is calculated according to the following formula
Figure BDA0002298648850000027
Figure BDA0002298648850000028
Initializing a locally optimal position for each particle
Figure BDA0002298648850000029
Its fitness value is recorded as f (Pbest)k) (ii) a Then selecting the position of the particle with the minimum fitness value in the current particle swarm as a global optimal position Gtest, and recording the corresponding fitness value as f (Gtest);
s6: the speed and the position of each particle are respectively updated to obtain the updated particle speed
Figure BDA00022986488500000210
And the position of the particles
Figure BDA00022986488500000211
For updated particle position
Figure BDA00022986488500000212
Order to
Figure BDA00022986488500000213
S7: calculating the fitness value of each particle in the updated particle swarm
Figure BDA00022986488500000214
S8: for each particle in the updated population of particles
Figure BDA00022986488500000215
If it is not
Figure BDA00022986488500000216
Then order
Figure BDA00022986488500000217
Otherwise, no operation is performed;
s9: the particle with the minimum fitness value in the updated particle group is selected and recorded as
Figure BDA00022986488500000218
If it is not
Figure BDA00022986488500000219
Then order
Figure BDA00022986488500000220
Otherwise, no operation is performed;
s10: let q be q + 1;
s11: judging whether the iteration number Q is less than or equal to Q, wherein Q represents the maximum iteration number, if so, returning to the step S6, otherwise, entering the step S12;
s12: and screening out the elements with the element parameters exceeding the tolerance range from the global optimal position Gbest, wherein the fuzzy group corresponding to the element is the fault diagnosis result.
The invention relates to a single fault diagnosis method of an analog circuit based on a particle swarm algorithm, which comprises the steps of firstly obtaining a transmission function of the analog circuit at a measuring point, obtaining element information and fuzzy group information of the analog circuit, measuring output voltage at the measuring point under a preset excitation signal when the analog circuit has a fault, then taking element parameter vectors as particles of the particle swarm algorithm, obtaining output voltage corresponding to each particle according to the transmission function, calculating the fitness value of the particles according to the difference value of the fault output voltage and the particle output voltage, wherein the smaller the fitness is, the better the particles are, and after the iteration of the particle swarm algorithm is finished, screening out elements with element parameters exceeding the tolerance range from the global optimal position, wherein the fuzzy group corresponding to the element is the fault diagnosis result. The invention relates to a post-test optimization diagnosis method without storing in advance after test, which finds out the analog circuit transmission function parameter closest to the fault response by utilizing a particle swarm algorithm according to the fault circuit response so as to find out the fault source.
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FIG. 1 is a block diagram of an embodiment of a single fault diagnosis method for an analog circuit based on particle swarm optimization according to the present invention;
fig. 2 is a circuit diagram of a second-order thomas analog filter circuit in the present embodiment.
Detailed Description
The following description of the embodiments of the present invention is provided in order to better understand the present invention for those skilled in the art with reference to the accompanying drawings. It is to be expressly noted that in the following description, a detailed description of known functions and designs will be omitted when it may obscure the subject matter of the present invention.
In order to better explain the technical solution of the present invention, first, the technical principle of the present invention is briefly explained.
For each analog circuit, there is a circuit transfer function H (j ω) as follows:
Figure BDA0002298648850000031
where ω denotes the angular frequency, j denotes the imaginary unit,
Figure BDA0002298648850000032
representing the inputs and outputs of an analog circuit. The transfer function H (j ω) is an element parameter X ═ X of the analog circuit1,x2,…,xC) Where C is the number of analog circuit elements. If the excitation frequency is not changed, outputting phasor
Figure BDA0002298648850000033
Is the element parameter X ═ X1,x2,…,xC) Function of xcThe parameter value of the c-th element is indicated. Recording nominal value of element parameter of analog circuit
Figure BDA0002298648850000034
The nominal value of the parameter for the c-th element is indicated. The fault diagnosis can be converted into an optimization problem when a circuit has a single fault, namely a certain element is out of tolerance
Figure BDA0002298648850000035
α denotes a tolerance parameter, typically 0.05, and the actual fault voltage of the circuit is measured as
Figure BDA0002298648850000041
The fault diagnosis is to find a set of element parameters X*So that the following equation is minimized:
Figure BDA0002298648850000042
wherein, | | | represents a two-norm, that is, a euclidean distance.
Figure BDA0002298648850000043
Obtained by transfer function calculation. Because the invention is single fault diagnosis, in the particle swarm algorithm, the fitness function of the particle X is defined as:
Figure BDA0002298648850000044
ultimately, the fault diagnosis translates into the following minimization problem:
Figure BDA0002298648850000045
based on the analysis, the invention provides a single fault diagnosis method for an analog circuit based on a particle swarm algorithm. Fig. 1 is a structural diagram of a single fault diagnosis method of an analog circuit based on a particle swarm optimization according to an embodiment of the present invention. As shown in fig. 1, the method for diagnosing single fault of analog circuit based on particle swarm optimization of the present invention comprises the following specific steps:
s101: acquiring a transmission function:
and acquiring the transmission function of the analog circuit at the measuring point t.
S102: acquiring analog circuit information:
the number of elements in the analog circuit is marked as C, and the nominal value of the parameter of each element is marked as
Figure BDA0002298648850000046
The tolerance ranges of the respective elements are expressed as
Figure BDA0002298648850000047
α denotes tolerance parameters, 0 < α < 1, tolerance parameters α are usually set to 0.05, 1 measuring point is set as required, fuzzy group analysis for fault diagnosis is performed on C elements through the measuring point, a representative fault element is selected for each fuzzy group, the number of the representative fault elements is recorded as N, obviously, N also denotes the number of fuzzy groups, the number of other non-representative fault elements is recorded as m, fuzzy group analysis is a common technical means for fault diagnosis of analog circuits, and the specific process is not repeated here.
S103: determining the current output of the analog circuit:
when the analog circuit has a fault, the output voltage at the measuring point t is measured under the preset excitation signal
Figure BDA0002298648850000048
In order to make the output voltage under the fault state more accurate, the output voltage can be averaged after measuring the output voltage for multiple times, so as to obtain the output voltage
Figure BDA0002298648850000049
S104: initializing particle swarm parameters:
initializing the number of iterations q to 1 and initializing the velocity of each particle in the population
Figure BDA0002298648850000051
And position
Figure BDA0002298648850000052
K represents the number of particles in the population. The position vector of each particle corresponds to an element parameter vector, wherein
Figure BDA0002298648850000053
Parameter value representing the nth faulty component in the kth particle position vector, n ═ n1,2, …, N + M, the first N faulty elements are representative faulty elements, the parameters of which take values randomly, and the last M faulty elements are non-representative faulty elements, the parameters of which take values randomly within the tolerance range.
S105: initializing local optimal positions and global optimal positions:
positioning the particles under a predetermined excitation signal
Figure BDA0002298648850000054
Substituting the transmission function to calculate the output voltage at the measuring point t
Figure BDA0002298648850000055
Then, the fitness value of each particle in the current particle swarm is calculated according to the following formula
Figure BDA0002298648850000056
Figure BDA0002298648850000057
Initializing a locally optimal position for each particle
Figure BDA0002298648850000058
Its fitness value is recorded as f (Pbest)k). And then selecting the position of the particle with the minimum fitness value in the current particle swarm as a global optimal position Gbest, and recording the corresponding fitness value as f (Gbest).
S106: update particle velocity and position:
the speed and the position of each particle are respectively updated to obtain the updated particle speed
Figure BDA0002298648850000059
And the position of the particles
Figure BDA00022986488500000510
The update formula of the particle velocity in this embodiment is:
Figure BDA00022986488500000511
wherein, omega represents inertia weight and has a value range of [0, 1%]，c1、c2Is a learning factor, r1、r2Is between [0,1]Random probability value between.
The update formula of the particle position is:
Figure BDA00022986488500000512
since the fault elements of the analog circuit are divided into the representative fault elements and the non-representative fault elements, and the invention is a diagnosis method for single fault, the parameter values of the non-representative fault elements in the updated particle positions need to be limited, that is, the parameter values cannot exceed the tolerance range, and the specific method is as follows:
for updated particle position
Figure BDA00022986488500000513
Order to
Figure BDA00022986488500000514
The nominal value of the parameter for the nth' element is indicated.
S107: calculating a particle fitness value:
calculating the fitness value of each particle in the updated particle swarm
Figure BDA0002298648850000061
S108: updating the local optimal position:
for each particle in the updated population of particles
Figure BDA0002298648850000062
If it is not
Figure BDA0002298648850000063
Then order
Figure BDA0002298648850000064
Otherwise, no operation is performed.
S109: updating the global optimal position:
the particle with the minimum fitness value in the updated particle group is selected and recorded as
Figure BDA0002298648850000065
If it is not
Figure BDA0002298648850000066
Then order
Figure BDA0002298648850000067
Otherwise, no operation is performed.
S110: let q be q + 1.
S111: and judging whether the iteration number Q is less than or equal to Q, wherein Q represents the maximum iteration number, if so, returning to the step S106, otherwise, entering the step S112.
S112: obtaining a fault diagnosis result:
and screening out the elements with the element parameters exceeding the tolerance range from the global optimal position Gbest, wherein the fuzzy group corresponding to the element is the fault diagnosis result.
Examples
In order to better illustrate the technical effects of the invention, the invention is verified by taking a second-order thomas analog filter circuit as an example. Fig. 2 is a circuit diagram of a second-order thomas analog filter circuit in the present embodiment. As shown in fig. 2, the second-order thomas analog filter circuit in this embodiment includes 3 amplifiers, 6 resistors and 2 capacitors, and the resistor R is used for providing a voltage to the second-order thomas analog filter circuit1The output of the 3 rd amplifier is used as the output of the whole circuit, namely the measuring point t. The transfer function of the circuit shown in fig. 2 is given by:
Figure BDA0002298648850000068
where ω represents the angular frequency.
The fuzzy group condition of the circuit can be known according to the symbol analysis method and the transmission functionComprises the following steps: { R1}，{R2}，{R4,R5,R6,C2}，{R3,C1}. Faults of elements inside the fuzzy sets are indistinguishable, and faults between fuzzy sets can theoretically be distinguished. In the present embodiment, the representative failure elements of the 4 fuzzy groups are R1,R2,R3,R4。
Randomly setting a fault, e.g. R2385 Ω, the other elements take values randomly within the tolerance range: r1＝9707Ω，R3＝9979Ω，R4＝9688Ω，R5＝9748Ω，R6＝10289Ω，C1＝9.7467nF，C29.8889 nF. Obtaining the fault voltage under the excitation of a sinusoidal signal with the voltage of 1V and the frequency of 1000Hz
Figure BDA0002298648850000071
The number of the population is set to be K-100, and the maximum iteration number Q is 100. In the obtained final global optimal position Gbest, R1＝9720Ω，R2＝405Ω，R3＝10124Ω，R4＝9928Ω，R5＝9997Ω，R6＝10497Ω，C1＝10.2nF，C210.194 nF. Obviously only the resistance R2And if the fault is beyond the tolerance range, the fault diagnosis is correct.
And then setting 100 times of faults for each representative fault element, wherein each fault is a different fault value, and other elements are randomly set within a tolerance range, and counting the diagnosis accuracy of the invention. Table 1 is a statistical table of the diagnosis accuracy of each representative faulty component in the present embodiment.
Component R1 R2 R3 R4
Accuracy of diagnosis 97％ 98％ 90％ 97％
TABLE 1
As can be seen from Table 1, the invention can realize post-test fault diagnosis with higher accuracy for the analog circuit.
Although illustrative embodiments of the present invention have been described above to facilitate the understanding of the present invention by those skilled in the art, it should be understood that the present invention is not limited to the scope of the embodiments, and various changes may be made apparent to those skilled in the art as long as they are within the spirit and scope of the present invention as defined and defined by the appended claims, and all matters of the invention which utilize the inventive concepts are protected.

Claims (1)

1. A single fault diagnosis method for an analog circuit based on a particle swarm algorithm is characterized by comprising the following steps:
s1: acquiring a transmission function of the analog circuit at a measuring point t;
s2: the number of elements in the analog circuit is marked as C, and the nominal value of the parameter of each element is marked as
Figure FDA0002298648840000011
C is 1,2, …, C; the tolerance ranges of the respective elements are expressed as
Figure FDA0002298648840000012
α represents tolerance parameters, 0 is less than α is less than 1, 1 measuring point is arranged according to the requirement, fuzzy group analysis for fault diagnosis of C elements through the measuring point is carried out, a representative fault element is selected for each fuzzy group, the number of the representative fault elements is recorded as N, obviously, the number of the fuzzy groups is also recorded as N, and the number of other non-representative fault elements is recorded as M;
s3: when the analog circuit has a fault, the output voltage at the measuring point t is measured under the preset excitation signal
Figure FDA0002298648840000013
S4: initializing the number of iterations q to 1 and initializing the velocity of each particle in the population
Figure FDA0002298648840000014
And position
Figure FDA0002298648840000015
i is 1,2, …, K, K represents the number of particles in the population; the position vector of each particle corresponds to an element parameter vector, wherein
Figure FDA0002298648840000016
The parameter value of the nth fault element in the kth particle position vector is represented, wherein N is 1,2, …, N + M, the first N fault elements are representative fault elements, the parameters of the first N fault elements take values randomly, the last M fault elements are non-representative fault elements, and the parameters of the last M fault elements take values randomly in a corresponding tolerance range;
s5: positioning the particles under a predetermined excitation signal
Figure FDA0002298648840000017
Substituting the transmission function to calculate the output voltage at the measuring point t
Figure FDA0002298648840000018
Then calculating the current particle size of each particle in the particle swarm according to the following formulaFitness value
Figure FDA0002298648840000019
Figure FDA00022986488400000110
Initializing a locally optimal position for each particle
Figure FDA00022986488400000111
Its fitness value is recorded as f (Pbest)k) (ii) a Then selecting the position of the particle with the minimum fitness value in the current particle swarm as a global optimal position Gbest, and recording the corresponding fitness value as f (best);
s6: the speed and the position of each particle are respectively updated to obtain the updated particle speed
Figure FDA00022986488400000112
And the position of the particles
Figure FDA00022986488400000113
For updated particle position
Figure FDA00022986488400000114
Order to
Figure FDA00022986488400000115
S7: calculating the fitness value of each particle in the updated particle swarm
Figure FDA00022986488400000116
S8: for each particle in the updated population of particles
Figure FDA00022986488400000117
If it is not
Figure FDA00022986488400000118
Then order
Figure FDA0002298648840000021
Otherwise, no operation is performed;
s9: the particle with the minimum fitness value in the updated particle group is selected and recorded as
Figure FDA0002298648840000022
If it is not
Figure FDA0002298648840000023
Then order
Figure FDA0002298648840000024
Otherwise, no operation is performed;
s10: let q be q + 1;
s11: judging whether the iteration number Q is less than or equal to Q, wherein Q represents the maximum iteration number, if so, returning to the step S6, otherwise, entering the step S12;
s12: and screening out the elements with the element parameters exceeding the tolerance range from the global optimal position Gbest, wherein the fuzzy group corresponding to the element is the fault diagnosis result.
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CN112347317B (en) * 2020-10-23 2022-07-12 四川长虹电器股份有限公司 Equipment fault diagnosis method based on particle swarm optimization improved negative selection algorithm
CN112485652A (en) * 2020-12-09 2021-03-12 电子科技大学 Analog circuit single fault diagnosis method based on improved sine and cosine algorithm
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