CN114239457A - Extended Debye model parameter identification method based on mixed frog-leaping particle swarm optimization - Google Patents

Extended Debye model parameter identification method based on mixed frog-leaping particle swarm optimization Download PDF

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CN114239457A
CN114239457A CN202111450600.4A CN202111450600A CN114239457A CN 114239457 A CN114239457 A CN 114239457A CN 202111450600 A CN202111450600 A CN 202111450600A CN 114239457 A CN114239457 A CN 114239457A
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林明星
陈扩松
林翊乾
郑宇�
李语菲
潘亦斌
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State Grid Fujian Electric Power Co Ltd
Putian Power Supply Co of State Grid Fujian Electric Power Co Ltd
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Abstract

The invention relates to an extended Debye model parameter identification method based on a mixed frog-leaping particle swarm algorithm, which comprises the following steps of: establishing an extended Debye model, establishing a calculation formula of the parameter to be identified and determining a target function; initializing a particle swarm to obtain n particles corresponding to the n-dimensional solution vector of the extended Debye model, and calculating the self-fitness of each particle according to a calculation formula of the parameter to be identified and a target function; introducing differential grouping of a frog-leaping algorithm, and dividing n particles into m ethnic groups according to the self fitness of each particle; iteration and optimization are carried out on each group, after an iteration termination condition is reached, the position of a particle with a global optimal value is output as a model identification parameter of an expanded Debye model, and differential grouping of a frog-leaping algorithm is added into a traditional particle swarm algorithm, so that the particle swarm is prevented from being concentrated in the same direction prematurely, and the mutual learning capacity of the particles in the same group is also improved.

Description

Extended Debye model parameter identification method based on mixed frog-leaping particle swarm optimization
Technical Field
The invention relates to an extended Debye model parameter identification method based on a mixed frog-leaping particle swarm algorithm, and belongs to the technical field of transformer equivalent circuit model parameter identification.
Background
The extended Debye model is used as a classical equivalent circuit model of the oil paper insulation system, and model parameters of the extended Debye model have great significance for analyzing microscopic dielectric reaction inside the oil paper insulation system. At present, the parameter identification method of the extended Debye model mostly adopts intelligent algorithm identification. The particle swarm algorithm is based on foraging and providing of the bird swarm, and the bird swarm can gather around the food source through mutual transmission of information of respective positions in the whole searching process. The influence factors influencing the foraging direction of birds mainly include two factors: one is the current position of the bird closest to the food among all birds, and the other is the previous position of each bird itself closest to the food. Compared with locust algorithm, chicken swarm algorithm and the like, the particle swarm algorithm has the advantages of high searching speed, simplicity in programming and the like, however, the learning object of the algorithm in the later period is single, and the algorithm is easy to fall into local optimum.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides an extended Debye model parameter identification method based on a mixed frog-leaping particle swarm algorithm.
The technical scheme of the invention is as follows:
on one hand, the invention provides an extended Debye model parameter identification method based on a mixed frog-leaping particle swarm optimization algorithm, which comprises the following steps:
establishing an extended Debye model, establishing a calculation formula of the parameter to be identified and determining a target function;
initializing a particle swarm to obtain n particles corresponding to the n-dimensional solution vector of the extended Debye model, and calculating the self-fitness of each particle according to a calculation formula of the parameter to be identified and a target function;
introducing differential grouping of a frog-leaping algorithm, and dividing n particles into m ethnic groups according to the self fitness of each particle;
and iterating and optimizing each group, and outputting the position of the particle with the global optimal value as a model identification parameter of the expanded Debye model after the iteration termination condition is reached.
As a preferred embodiment, the parameter to be identified includes a real complex capacitance part C', an imaginary complex capacitance part C ″ and a dielectric loss factor tan δ;
the self-fitness P of each particle is calculated by the formula:
Figure BDA0003385776060000021
wherein tan δ 1(ω), C1'(ω), and C1 "(ω) represent frequency-domain dielectric spectrum test values at ω frequency points, and tan δ (ω), C' (ω), and C" (ω) represent calculation formula values at ω frequency points obtained from a calculation formula of a parameter to be identified.
As a preferred embodiment, the step of introducing the differential grouping of the frog-leaping algorithm to divide n particles into m populations according to the self-fitness of each particle specifically includes:
defining the number of particle populations as:
n=m*z;
wherein n is the number of particle populations, m is the number of populations, and z is the number of population particles;
calculating the self-fitness P of each particle, and sequencing all the particles from large to small according to the self-fitness P;
the 1 st particle with the maximum self-fitness P is divided into the 1 st group, the 2 nd particle is divided into the 2 nd group …, the mth particle is divided into the mth group, and the m +1 th particle is divided into the 1 st group, and the steps are sequentially circulated until each particle is divided into the corresponding group.
As a preferred embodiment, the step of performing iteration and optimization on each population, and after the iteration termination condition is reached, outputting the model identification parameter of the extended debye model in which the position of the particle with the global optimal value is located specifically includes:
comparing according to the self fitness of each particle to obtain the optimal value A of the group in each groupbesObtaining global optimum G of whole particle groupbestAnd the individual optimum value Pibest(ii) a Each group is updated according to a particle position updating formula;
calculating the self fitness of the particles after the position updating, and determining whether to replace the optimal value A of the group in each groupbesObtaining global optimum G of whole particle groupbestAnd the individual optimum value Pibest
After the iteration times of the particle swarm reach the preset times, the particles with the updated positions enter the next difference grouping and continue to iterate;
after the iteration termination condition is reached, outputting a global optimal value GbestThe position of the particle is a model identification parameter of the extended debye model.
As a preferred embodiment, the particle position update formula is specifically:
Figure BDA0003385776060000031
wherein, c1、c2、c3Is a learning factor, a and b are random numbers within (0,1), PibestFor individual optimum value, G, of the particlesbestFor the global optimum, A, of the particlebestThe optimal value is the particle group.
In another aspect, the present invention further provides an electronic device, which includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the extended debye model parameter identification method according to any embodiment of the present invention.
In yet another aspect, the present invention further provides a computer readable storage medium, on which a computer program is stored, wherein the computer program is executed by a processor to implement the extended debye model parameter identification method according to any embodiment of the present invention.
The invention has the following beneficial effects:
1. the invention relates to an extended Debye model parameter identification method based on a mixed frog-leaping particle swarm algorithm, which adds the difference grouping of the frog-leaping algorithm into the traditional particle swarm algorithm, avoids that the particle swarm is prematurely concentrated in the same direction, and also increases the mutual learning capacity of particles in the same group;
2. the invention relates to an extended Debye model parameter identification method based on a mixed frog-leaping particle swarm algorithm, which optimizes a position updating mode of a particle swarm, introduces a quantum measurement inaccuracy principle, introduces random numbers obeying Gaussian distribution, combines an individual average to form a disturbance factor to influence the motion direction of particles, cancels a traditional particle flight speed item, replaces the traditional optimization mode with probability distribution, improves algorithm diversity, avoids the algorithm from falling into local optimization, and enhances the global optimization capability.
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FIG. 1 is a flow chart of an embodiment of the present invention;
FIG. 2 is a schematic diagram of the structure of the extended Debye model;
FIG. 3 is a comparison example diagram of complex capacitance imaginary part identification spectral lines for parameter identification using two algorithms according to an embodiment of the present invention;
FIG. 4 is a comparison example diagram of complex capacitance real part identification spectral lines for parameter identification using two algorithms according to an embodiment of the present invention;
fig. 5 is a comparison example diagram of the dielectric loss factor identification spectrum lines for parameter identification by using two algorithms in the embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
It should be understood that the step numbers used herein are for convenience of description only and are not intended as limitations on the order in which the steps are performed.
It is to be understood that the terminology used in the description of the invention herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. As used in the specification of the present invention and the appended claims, the singular forms "a," "an," and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise.
The terms "comprises" and "comprising" indicate the presence of the described features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof.
The term "and/or" refers to and includes any and all possible combinations of one or more of the associated listed items.
The first embodiment is as follows:
referring to fig. 1, the embodiment provides an extended debye model parameter identification method based on a mixed frog-leaping particle swarm algorithm, which includes the following steps:
establishing an extended debye model, wherein the extended debye model established in this embodiment is shown in fig. 2; the interior of the oil paper insulation system contains various dielectric response processes under the action of an alternating electric field, and the conductance and polarization response of the oil paper insulation system change correspondingly along with the change of the frequency of the electric field. The extended Debye model represents the insulating dielectric process of the complex oilpaper by constructing an RC parallel geometric equivalent circuit and N RC series polarization equivalent circuits. Wherein C isgThe capacitance is a lossless polarization equivalent capacitance, Rg is an insulation resistance, Rpi represents the energy loss of the ith relaxation polarization branch, and Cpi represents the capacitance of the ith relaxation polarization branch;
establishing a calculation formula of a parameter to be identified and determining a target function;
initializing a particle swarm, setting n particles in the swarm to be distributed in a solution space with a space dimension d, and setting a position X where the ith particle is locatedid=(Xi1,Xi2,…,Xid) Obtaining n particles corresponding to the n-dimensional solution vector of the extended Debye model, and calculating the self fitness of each particle according to a calculation formula of the parameter to be identified and an objective function;
the frog leaping algorithm is derived from frog foraging and migrating processes, the whole frog species of the wetland is randomly divided into different ethnic groups, and each ethnic group executes a local search strategy. Each individual in the ethnic group has a food foraging path, different individuals can exchange information and learn, and the group is guided to approach food through the optimization of the individuals in the ethnic group. After the local search among the groups is completed for a certain number of times, the information sharing among different groups can be performed. And then, the population is divided again, and the circulation is repeated, so that the global optimal search is realized. However, the leapfrog algorithm is only based on a single optimal solution, and not only has a slow convergence rate, but also is easy to fall into local optimal.
On the basis of the method, the traditional particle swarm algorithm is improved, the difference of the frog-leaping algorithm is grouped and introduced into the particle swarm algorithm, and n particles are divided into m ethnic groups according to the self fitness of each particle; by combining the frog-leaping algorithm and the particle swarm algorithm, the later searching capability of the algorithm is improved.
And iterating and optimizing each group, and outputting the position of the particle with the global optimal value as a model identification parameter of the expanded Debye model after the iteration termination condition is reached.
As a preferred embodiment of this embodiment, the parameter to be identified includes a real complex capacitance part C', an imaginary complex capacitance part C ″ and a dielectric loss factor tan δ; from fig. 2, the port equivalent admittance of the extended Debye model can be derived:
Figure BDA0003385776060000071
the equation of complex capacitance is introduced:
Figure BDA0003385776060000072
the formula of the real part and the imaginary part of the complex capacitance can be obtained:
Figure BDA0003385776060000073
Figure BDA0003385776060000074
dielectric loss factor equation:
Figure BDA0003385776060000075
after FDS measurement is carried out on the oiled paper insulation sample, real part and imaginary part of the actually measured complex capacitance and dielectric loss factor value can be obtained. And substituting the n-dimensional space solution vector of the particle into the formulas (3) to (5) to obtain a real part calculated value, an imaginary part calculated value and a dielectric loss factor calculated value of the complex capacitance of the expanded Debye model.
When the calculated value based on the formula is closer to the measured value, the better the parameter identification effect is, and a multi-objective optimization function formula (6) can be constructed based on the parameter identification effect. And (3) making the self-fitness P of the particles equal to the multi-objective optimization function, and when the parameter identification effect is better, the denominator is smaller, and the self-fitness P of the particles is larger at the moment. On the contrary, the worse the parameter identification, the larger the denominator, and the smaller the self-fitness P of the particle.
The self-fitness P of each particle is calculated by the formula:
Figure BDA0003385776060000081
wherein tan δ 1(ω), C1'(ω), and C1 "(ω) represent frequency-domain dielectric spectrum test values at ω frequency points, and tan δ (ω), C' (ω), and C" (ω) represent calculation formula values at ω frequency points obtained from a calculation formula of a parameter to be identified.
As a preferred implementation of this embodiment, the step of introducing the differential grouping of the leapfrog algorithm to divide n particles into m populations according to the self-fitness of each particle specifically includes:
defining the number of particle populations as:
n=m*z;
wherein n is the number of particle populations, m is the number of populations, and z is the number of population particles;
calculating the self-fitness P of each particle, and sequencing all the particles from large to small according to the self-fitness P;
the 1 st particle with the maximum self-fitness P is divided into the 1 st group, the 2 nd particle is divided into the 2 nd group …, the mth particle is divided into the mth group, and the m +1 th particle is divided into the 1 st group, and the steps are sequentially circulated until each particle is divided into the corresponding group.
As a preferred embodiment of this embodiment, after the division of the particle clusters is finished, iteration and optimization are performed on each cluster, and after an iteration termination condition is reached, the step of outputting the model identification parameter of the extended debye model where the position of the particle with the global optimal value is located is specifically:
comparing according to the self fitness of each particle to obtain the optimal value A of the group in each groupbesObtaining global optimum G of whole particle groupbestAnd the individual optimum value Pibest(ii) a Each group is updated according to a particle position updating formula;
calculating the self-fitness P of the particles after the position updating, and comparing the self-fitness P after each particle updating with the historical global optimal value GbestComparing if P is greater than the global optimum GbestThen, the self fitness P of the current particle is taken as the historical global optimal value GbestUpdating by using the current particle position;
calculating the self-fitness P of the particle with the updated position in each group and matching the self-fitness P with the optimal value A of the historical group in the corresponding groupbesComparing if there is P greater than the optimal value A for the historical populationbesThen, the self-fitness P of the current particle is used as the historical population to be optimalValue AbesUpdating by using the current particle position;
calculating the self-fitness P of the particles after the position updating, and comparing the self-fitness P of each particle after the updating with the historical individual optimal value PibestComparing if P is greater than the individual optimal value PibestTaking the self fitness P of the current particle as the optimal value P of the historical individualibestUpdating by using the current particle position;
the particles in each group update the positions thereof according to a particle position updating formula;
after the iteration times of the particle swarm reach the preset times, the particles with the updated positions enter the next difference grouping and continue to iterate;
after the iteration termination condition is reached, namely the optimization precision is met or the highest iteration frequency is reached, outputting a global optimal value GbestThe position of the particle is a model identification parameter of the extended debye model.
As a preferred implementation of this embodiment, the particle position update formula is specifically:
Figure BDA0003385776060000101
wherein, c1、c2、c3Is a learning factor, a and b are random numbers within (0,1), PibestFor individual optimum value, G, of the particlesbestFor the global optimum, A, of the particlebestThe optimal value is the particle group.
The method introduces a quantum measurement inaccuracy principle into a particle position updating formula, introduces random numbers a and b subject to Gaussian distribution, combines an individual average to form disturbance factors to influence the motion direction of particles, cancels a traditional particle flight speed item, replaces the conventional optimization mode with probability distribution, improves algorithm diversity, avoids algorithm falling into local optimization, and enhances global optimization capability.
To further verify the accuracy of the parameter identification method and the fitting degree of the spectral line, the model FDS curve and the actually measured FDS curve are identified hereinPerforming fitting degree analysis on the line, and selecting the fitting degree R2As evaluation parameters, the following formula was constructed:
Figure BDA0003385776060000102
in the formula: yck denotes the measured value of the spectrum at the k-th sampling frequency point; ytk denotes the spectral discrimination value at the k-th sampling frequency point; and n is the sampling times.
In this embodiment, a set of measured FDS data is selected, and parameter identification is performed by the hybrid frog-leaping particle swarm algorithm and the conventional particle swarm algorithm provided in this embodiment, respectively. The parameters after identification are fitted with spectral lines as shown in FIGS. 3-5, degree of fitting R2As shown in table 1:
table 1: two-algorithm identification parameter spectral line fitting degree R2
Days of aging Mixed frog-leaping quantum particle swarm algorithm Traditional particle swarm algorithm
Dielectric loss tan fitness R2 0.97 0.49
Degree of fitting R of real part c2 0.98 0.48
Degree of fitting R of imaginary part cc2 0.99 0.54
It can be seen that the identification capability of the mixed frog-leaping particle swarm optimization algorithm provided by the embodiment on the parameters of the expanded debye model is greatly improved, and the parameter fitting spectral line is more consistent with the actually measured spectral line. Compared with the traditional particle swarm algorithm, the method has the advantages of stronger searching capability and better global optimization effect.
Example two:
the present embodiment provides an electronic device, which includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the extended debye model parameter identification method according to any embodiment of the present invention when executing the computer program.
Example three:
the present embodiment provides a computer-readable storage medium, on which a computer program is stored, wherein the computer program, when executed by a processor, implements the extended debye model parameter identification method according to any embodiment of the present invention.
The above description is only an embodiment of the present invention, and not intended to limit the scope of the present invention, and all modifications of equivalent structures and equivalent processes performed by the present specification and drawings, or directly or indirectly applied to other related technical fields, are included in the scope of the present invention.

Claims (7)

1. An extended Debye model parameter identification method based on a mixed frog-leaping particle swarm algorithm is characterized by comprising the following steps:
establishing an extended Debye model, establishing a calculation formula of the parameter to be identified and determining a target function;
initializing a particle swarm to obtain n particles corresponding to the n-dimensional solution vector of the extended Debye model, and calculating the self-fitness of each particle according to a calculation formula of the parameter to be identified and a target function;
introducing differential grouping of a frog-leaping algorithm, and dividing n particles into m ethnic groups according to the self fitness of each particle;
and iterating and optimizing each group, and outputting the position of the particle with the global optimal value as a model identification parameter of the expanded Debye model after the iteration termination condition is reached.
2. The extended Debye model parameter identification method based on the mixed frog-leaping particle swarm optimization algorithm is characterized in that the parameters to be identified comprise a complex capacitance real part C ', a complex capacitance imaginary part C' and a dielectric loss factor tan delta;
the self-fitness P of each particle is calculated by the formula:
Figure FDA0003385776050000011
wherein tan δ 1(ω), C1'(ω), and C1 "(ω) represent frequency-domain dielectric spectrum test values at ω frequency points, and tan δ (ω), C' (ω), and C" (ω) represent calculation formula values at ω frequency points obtained from calculation formulas of parameters to be identified.
3. The extended debye model parameter identification method based on the mixed frog-leap particle swarm optimization algorithm according to claim 2, wherein the step of dividing n particles into m populations according to the self-fitness of each particle by introducing the differential grouping of the frog-leap algorithm is specifically:
defining the number of particle populations as:
n=m*z;
wherein n is the number of particle populations, m is the number of populations, and z is the number of population particles;
calculating the self-fitness P of each particle, and sequencing all the particles from large to small according to the self-fitness P;
the 1 st particle with the maximum self-fitness P is divided into the 1 st group, the 2 nd particle is divided into the 2 nd group …, the mth particle is divided into the mth group, and the m +1 th particle is divided into the 1 st group, and the steps are sequentially circulated until each particle is divided into the corresponding group.
4. The extended debye model parameter identification method based on the mixed frog-leaping particle swarm optimization algorithm according to claim 3, wherein the step of iterating and optimizing each population, and outputting the position of the particle with the global optimal value as the model identification parameter of the extended debye model after the iteration termination condition is reached is specifically as follows:
comparing according to the self fitness of each particle to obtain the optimal value A of the group in each groupbesObtaining global optimum G of whole particle groupbestAnd the individual optimum value Pibest(ii) a Each group is updated according to a particle position updating formula;
calculating the self fitness of the particles after the position updating, and determining whether to replace the optimal value A of the group in each groupbesObtaining global optimum G of whole particle groupbestAnd the individual optimum value Pibest
After the iteration times of the particle swarm reach the preset times, the particles with the updated positions enter the next difference grouping and continue to iterate;
after the iteration termination condition is reached, outputting a global optimal value GbestThe position of the particle is a model identification parameter of the extended debye model.
5. The method of claim 4, wherein the particle location update formula is specifically as follows:
Figure FDA0003385776050000031
wherein, c1、c2、c3Is a learning factor, a and b are random numbers within (0,1), PibestFor individual optimum value, G, of the particlesbestFor the global optimum, A, of the particlebestThe optimal value is the particle group.
6. An electronic device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the processor implements the extended debye model parameter identification method as claimed in any one of claims 1 to 5 when executing the program.
7. A computer-readable storage medium, on which a computer program is stored which, when being executed by a processor, carries out the extended debye model parameter identification method according to any one of claims 1 to 5.
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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116719275A (en) * 2023-07-08 2023-09-08 四川大学 Comprehensive process optimization method for part full cutting process

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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116719275A (en) * 2023-07-08 2023-09-08 四川大学 Comprehensive process optimization method for part full cutting process
CN116719275B (en) * 2023-07-08 2024-02-06 四川大学 Comprehensive process optimization method for part full cutting process

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