CN113283176B - Optimization method and system for dielectric response extended debye model - Google Patents
Optimization method and system for dielectric response extended debye model Download PDFInfo
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Abstract
The invention discloses a dielectric response extended debye model optimization method and a dielectric response extended debye model optimization system, wherein the method comprises the following steps: constructing and obtaining an optimized objective function based on a dielectric response extended debye model; carrying out parameter solving on the dielectric response expansion debye model by utilizing a genetic algorithm to obtain a rough solution; taking the rough solution as an initial value, and carrying out parameter optimization on the dielectric response expansion debye model by utilizing a Gaussian-Newton algorithm to obtain the dielectric response expansion debye model after parameter optimization; and determining RC branch numbers of the dielectric response extended debye model by using the fitting goodness based on the dielectric response extended debye model after the parameter optimization, and completing dielectric response extended debye model optimization. The extended Debye model obtained by the method has accurate parameters, and can effectively solve the technical problems of low matching precision, weak applicability to different test objects, poor model stability and the like of the dielectric response extended Debye equivalent model in the present stage.
Description
Technical Field
The invention belongs to the technical field of electrical equipment insulation state evaluation, and particularly relates to an optimization method and system of a dielectric response extended debye model.
Background
The demand for electric energy by various industries has been continuously increasing since the 21 st century, and the installed capacity of electric power and the scale of the electric network have been continuously expanding. Statistical analysis shows that more than 50% of grid accidents are caused by faults of power transmission and transformation equipment, and the equipment problems are the first cause of the faults. The oil paper composite insulation is widely applied to power equipment due to the advantages of good insulation performance, excellent heat dissipation performance and the like, and the insulation condition and the health level of the power equipment are directly related to the safe and stable operation of a power grid.
The dielectric response (Dielectric Response, DR) is a nondestructive testing method of the oil paper insulation equipment, has the advantages of low testing voltage, strong field testing anti-interference performance and abundant insulation information, and is widely applied to field detection and evaluation of the insulation state of the oil paper insulation equipment.
At present, the dielectric response-based electric equipment insulation state evaluation is mostly limited to qualitative evaluation of a simple comparison test curve, and is lack of an equivalent model of the dielectric response of a tested object, and the accurate and reliable quantitative evaluation based on the dielectric response is still immature. In recent years, excitation voltage of dielectric response is not limited to one sweep frequency of sinusoidal signals with different frequencies, and novel dielectric response testing methods such as impact dielectric response and the like are more concerned due to wider application prospects, and accurate dielectric response model establishment is the basis of related research.
Debye relaxation theory is the most classical and widely accepted dielectric response theory basis, and because the oiled paper insulating dielectric response contains multiple dielectric relaxation processes, an extended debye model capable of simultaneously representing multiple dielectric relaxation processes is evolved. The corresponding extended debye model has a certain difference due to the difference of physical structure and dielectric property of the actual measured object. Most of the existing Debye model building methods are based on least square method curve fitting methods, the solving efficiency is low, further accurate optimization cannot be performed, influence of differences of different test objects on the parameter precision of the extended Debye model cannot be eliminated, the finally obtained extended Debye model is low in precision, and deep research and wide application of dielectric response are limited.
In summary, a new dielectric response extended debye model building method is needed.
Disclosure of Invention
The present invention is directed to a method and system for optimizing a dielectric response extended debye model, which solve one or more of the above-mentioned problems. The invention provides an optimization method combining a genetic algorithm and a Gaussian-Newton algorithm, and a dielectric response expansion Debye model optimization method formed based on the optimization method; the extended Debye model obtained by the method has accurate parameters, and can effectively solve the technical problems of low matching precision, weak applicability to different test objects, poor model stability and the like of the dielectric response extended Debye equivalent model in the present stage.
In order to achieve the above purpose, the invention adopts the following technical scheme:
the invention discloses an optimization method of a dielectric response extended debye model, which comprises the following steps:
the real part and the imaginary part of the complex capacitance of the dielectric response are selected as optimization targets, a multi-target optimization problem is converted into a single-target optimization problem based on a least square method and through a weighting method, and an optimization target function based on a dielectric response expansion debye model is constructed and obtained;
based on the optimized objective function, carrying out parameter solving on the dielectric response extended debye model by utilizing a genetic algorithm to obtain a rough solution;
based on the optimization objective function, taking the rough solution as an initial value, and carrying out parameter optimization on the dielectric response expansion debye model by utilizing a Gaussian-Newton algorithm to obtain a dielectric response expansion debye model after parameter optimization;
and determining RC branch numbers of the dielectric response extended debye model by using the fitting goodness based on the dielectric response extended debye model after the parameter optimization, and completing dielectric response extended debye model optimization.
The invention further improves that in the dielectric response extended debye model, the insulation resistance and the geometric capacitance of the dielectric are represented by adopting parallel connection of a resistor and a capacitor, and then the polarization process with different relaxation times in the dielectric is represented by parallel connection of a resistance-capacitance serial branch with different time constants, so that a mixed connection branch with parallel resistance-capacitance and serial multi-branch resistance-capacitance is formed.
The invention further improves that the dielectric response complex capacitance real part and the imaginary part are selected as optimization targets, the multi-target optimization problem is converted into a single-target optimization problem based on a least square method and through a weighting method, and the step of constructing and obtaining the optimization target function based on the dielectric response extended debye model specifically comprises the following steps:
complex capacitor C * The method comprises the following steps:
the real part C 'and the imaginary part C' of the complex capacitance are respectively:
wherein ω is the power angular frequency, C 0 Is the geometric capacitance, C 0 Is insulation resistance, R i 、C i For extended debye model parameters to be optimized, subscript i represents the extended debye model branch sequence number;
the weighted least squares optimization objective function is established as follows:
wherein C' Measuring And C' Measuring To test the complex capacitance real part and imaginary part omega of the dielectric response at different frequencies 1i 、ω 2i For each frequency point weight omega 1i ＝1/C' Measuring (ω)，ω 2i ＝1/C″ Measuring (ω)；
Converting the multi-objective optimization problem into a single-objective optimization problem to be solved by constructing a characteristic evaluation function, wherein the evaluation function is as follows:
y＝ω c1 y 1 +ω c2 y 2 (5)
wherein omega C1 And omega C2 Setting omega for the weight of the real part and the imaginary part of the complex capacitance C1 And omega C2 Are all 1;
substituting equation (4) into equation (5) to obtain the final optimized objective function:
bringing equations (2) and (3) into equation (6) yields an optimized objective function based on the dielectric response extended debye model as:
the function is R i 、C i Is a multiple objective function of a variable, abbreviated as y=f (R 1 ,R 2 ,…,R n ；C 1 ,C 2 ,…,C n )。
A further improvement of the invention is that the measurement values of the real part and the imaginary part of the complex capacitance are obtained by carrying out frequency domain dielectric spectrum test on the oilpaper insulation.
The invention further improves that the step of utilizing a genetic algorithm to carry out parameter solution on the dielectric response extended debye model based on the optimized objective function to obtain a rough solution specifically comprises the following steps:
calling a genetic algorithm function, and taking an optimized objective function based on a dielectric response extended debye model as an fitness function; setting population number N, termination evolution algebra T and crossover probability P in genetic algorithm function c Probability of variation P m A value;
and obtaining a rough solution by the genetic algorithm function when the minimum value of the optimized objective function is obtained.
The invention is further improved in that the value range of N is 20-100, the value range of T is 100-500, and P c The value range is 0.4-0.99, and the value range of Pm is 0.001-0.1.
The invention further improves that the rough solution is used as an initial value based on the optimized objective function, and the dielectric response extended debye model is subjected to parameter optimization by utilizing a Gaussian-Newton algorithm, so that the dielectric response extended debye model after parameter optimization is obtained:
the iterative formula of the Gaussian-Newton algorithm is as follows:
x k+1 ＝x k -(J(x k ) T J(x k )) -1 J(x k ) T f(x k ) (8)
wherein x= [ R ] 1 ,R 2 ,…,R n ,C 1 ,C 2 ,…,C n ] T The subscript k represents the iteration order;
a preset threshold value epsilon is set,when f (x k+1 )-f(x k )<And epsilon, obtaining an accurate value of the optimal solution, and obtaining a dielectric response extended debye model after parameter optimization.
The invention further improves that the dielectric response extended debye model after the parameter optimization is based on the dielectric response extended debye model, and the step of determining the RC branch number of the dielectric response extended debye model by utilizing the fitting goodness to complete the dielectric response extended debye model optimization specifically comprises the following steps:
respectively selecting the number n of the RC branches of the extended debye model as a preset value, repeating the parameter solving and optimizing process, and determining the number of the RC branches of the extended debye model by using the fitting goodness;
wherein, the definition of the goodness of fit R is:
wherein y is i As the raw data is to be processed,for fitting data, +.>R is the average value of the original data, and the distribution interval (0, 1) of R is defined; and determining the RC branch number of the extended debye model through the size of the goodness-of-fit value based on a preset threshold range.
The invention relates to an optimization system of dielectric response extended debye model, which comprises:
the optimization objective function acquisition module is used for selecting a dielectric response complex capacitance real part and an imaginary part as optimization targets, converting a multi-target optimization problem into a single-target optimization problem by adopting a weighting method based on a least square method, and constructing and obtaining an optimization objective function based on a dielectric response extended debye model;
the rough solution acquisition module is used for carrying out parameter solution on the dielectric response expansion debye model by utilizing a genetic algorithm according to the optimization objective function to obtain a rough solution;
the parameter optimization module is used for carrying out parameter optimization on the dielectric response expansion debye model by using the rough solution as an initial value and utilizing a Gaussian-Newton algorithm according to the optimization objective function to obtain the dielectric response expansion debye model after parameter optimization;
and the RC branch number determining module is used for determining the RC branch number of the dielectric response extended debye model by utilizing the fitting goodness according to the dielectric response extended debye model after the parameter optimization, so as to complete the dielectric response extended debye model optimization.
Compared with the prior art, the invention has the following beneficial effects:
1. most of the existing Debye model building methods are based on least square method curve fitting methods, further difference accurate optimization can not be conducted on tested objects with different physical structures and dielectric properties, and influence of difference of different tested objects on parameter accuracy of an extended Debye model can not be eliminated. The invention optimizes the parameters of the debye model by combining a genetic algorithm and a Gaussian-Newton algorithm, and increases the application range of the debye model building method.
2. The fusion genetic algorithm and the Gaussian-Newton algorithm are used for carrying out parameter optimization on the extended Debye model, the advantages of the two algorithms in global searching and local searching are fully exerted, the problems that the traditional algorithm is large in initial value dependence and prone to being trapped in a local convergence trap are solved, and meanwhile the efficiency and the accuracy of a modeling process are improved.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following description of the embodiments or the drawings used in the description of the prior art will make a brief description; it will be apparent to those of ordinary skill in the art that the drawings in the following description are of some embodiments of the invention and that other drawings may be derived from them without undue effort.
FIG. 1 is a schematic diagram of a process for establishing an optimized parameter extended Debye model in an embodiment of the present invention;
FIG. 2 is a schematic illustration of goodness-of-fit of different RC branch extended Debye models in an embodiment of the present invention;
fig. 3 is a schematic diagram of the extended debye model complex electricity Rong Shibu C' and imaginary part c″ after optimizing parameters in an embodiment of the invention.
Detailed Description
In order to make the purposes, technical effects and technical solutions of the embodiments of the present invention more clear, the technical solutions of the embodiments of the present invention are clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention; it will be apparent that the described embodiments are some of the embodiments of the present invention. Other embodiments, which may be made by those of ordinary skill in the art based on the disclosed embodiments without undue burden, are within the scope of the present invention.
The dielectric response extended debye model optimizing method is a dielectric response extended debye model establishing method based on a genetic algorithm and a Gaussian-Newton algorithm, parameter optimization is carried out on the extended debye model through the fusion genetic algorithm and the Gaussian-Newton algorithm, the branch number of the extended debye model is determined by using the goodness of fit, and the extended debye model which is reliable, accurate and wide in application range is established.
In the method of the embodiment of the invention, a rough solution near the optimal solution of the objective function is obtained by adopting a genetic algorithm, then the accurate optimal solution of the objective function is solved by adopting a Gaussian-Newton algorithm, the advantages of the two algorithms in global searching and local searching are respectively exerted, and the influence of different physical structures and dielectric properties of the measured object on the model accuracy is avoided. In the embodiment of the invention, a genetic algorithm is adopted to obtain a rough solution near the optimal solution of the objective function. After the model parameter objective function is established, a Gaussian-Newton algorithm is adopted to solve the accurate optimal solution of the objective function, so that a global optimal solution of a plurality of parameters of the extended Debye model is obtained, and global errors caused by local convergence are avoided. In the embodiment of the invention, each parameter of the extended debye model is optimized by using a Gaussian-Newton algorithm, and rough solutions near the optimal solution of the objective function obtained by the genetic algorithm are optimized to be the optimal accurate solution.
In the embodiment of the invention, the branch number of the extended debye model is determined through the goodness of fit. And selecting a plurality of RC branch numbers for verification, determining the proper RC branch number, and considering the simplicity and the fitting goodness of an optimization algorithm, so as to ensure the feasibility of the extended Debye model building process of the same type of measured objects.
In summary, the least square method curve fitting method based on most of the existing debye model building methods cannot be used for further differential accurate optimization of the tested objects with different physical structures and dielectric properties, and cannot exclude the influence of the differences of different tested objects on the parameter accuracy of the extended debye model. The invention optimizes the parameters of the debye model by combining a genetic algorithm and a Gaussian-Newton algorithm, and increases the application range of the debye model building method. The fusion genetic algorithm and the Gaussian-Newton algorithm are used for carrying out parameter optimization on the extended Debye model, the advantages of the two algorithms in global searching and local searching are fully exerted, the problems that the traditional algorithm is large in initial value dependence and prone to being trapped in a local convergence trap are solved, and meanwhile the efficiency and the accuracy of a modeling process are improved.
According to the dielectric response extended debye model building method based on the genetic algorithm and the Gaussian-Newton algorithm, a dielectric response complex capacitance real part and an imaginary part are selected as optimization targets, a multi-target optimization problem is converted into a single-target optimization problem by a weighting method on the basis of a least square method, an optimization objective function is built, and parameter identification and optimization are carried out on the extended debye model through fusion of the genetic algorithm and the Gaussian-Newton algorithm. The method comprises the steps of determining the branch number of an extended debye model by adopting the goodness of fit, establishing a reliable, accurate and wide-application-range extended debye model, obtaining a rough solution near an optimal solution of an objective function by adopting a genetic algorithm, then solving the accurate optimal solution of the objective function by adopting a Gaussian-Newton algorithm, respectively exerting the advantages of the two algorithms in global searching and local searching, and realizing the accurate establishment of the dielectric response extended debye model of the tested object with different physical structures and dielectric properties.
In the embodiment of the invention, the insulation resistance and the geometric capacitance of the dielectric medium are represented by adopting parallel connection of the resistance and the capacitance, and then the polarization processes with different relaxation times in the dielectric medium are represented by parallel connection of the resistance-capacitance serial branches with different time constants, so that a mixed connection branch with parallel resistance-capacitance and serial connection of multiple branches is formed and used for accurately representing a dielectric medium dielectric response calculation model. And (3) carrying out frequency domain dielectric spectrum test on the oilpaper insulation to obtain measured values of a complex capacitance real part and an imaginary part of the oilpaper insulation, and using the measured values as extended debye model fitting target data of the dielectric response calculation model and the fitting formula.
Referring to fig. 1 and 2, a method for optimizing a dielectric response extended debye model according to an embodiment of the invention includes the following steps:
an optimization objective function is first established based on an extended debye model. The extended debye model basic circuit is shown in fig. 2, and according to the circuit principle, the complex capacitance can be obtained as follows:
the real and imaginary parts of the complex capacitance are:
wherein ω is the power angular frequency, C 0 Is the geometric capacitance, C 0 Is insulation resistance, R i 、C i For the extended debye model parameters to be optimized, the subscript i represents the extended debye model branch sequence number. A weighted least squares optimization objective function is established based on these parameters:
wherein C' Measuring And C' Measuring For experimental testing of the obtained dielectric response parameters, i.e. complex capacitive real and imaginary parts, ω, at different frequencies 1i 、ω 2i For each frequency point weight, is set as the reciprocal of the measured value, i.e., ω 1i ＝1/C' Measuring (ω)，ω 2i ＝1/C″ Measuring (ω), i.e. the objective function is a relative least squares construction. The formula (4) is a multi-objective optimization function, so that it is difficult for each optimization objective to reach the comprehensive optimal value at the same time, and solutions for each objective to reach the comprehensive optimal value at the same time basically do not exist. According to the importance degree, the multi-objective optimization problem is converted into a single-objective optimization problem to be solved by constructing a characteristic evaluation function. The following evaluation functions were constructed using the weighting method:
y＝ω c1 y 1 +ω c2 y 2 (5)
wherein omega C1 And omega C2 Is the weight of the real part and the imaginary part of complex capacitance due to y 1 And y 1 The weight of each data is expressed by relative value, and there is no priority of complex capacitance part and imaginary part, so omega is set C1 And omega C2 Are all 1. Substituting equation (4) into equation (5) yields the final optimized objective function:
bringing equations (2) and (3) into equation (6) yields an optimized objective function based on the extended debye model of:
the function is R i 、C i Is a multiple objective function of a variable, abbreviated as y=f (R 1 ,R 2 ,…,R n ；C 1 ,C 2 ,…,C n )。
And carrying out parameter solving on the extended debye model by utilizing a genetic algorithm. Based on the optimization objective function y=f (R 1 ,R 2 ,…,R n ；C 1 ,C 2 ,…,C n ) The parameter optimization is converted into genetic algorithm data fitting. Calling genetic algorithm functions (GA functions) in matlab toolkits, wherein an optimization objective function y=f is an fitness function, andthe main key parameters of the genetic algorithm are set by oneself, including the number N of population, terminate the evolution algebra T and cross probability P c Probability of variation P m The value range of N is generally 20-100, T is generally 100-500, and P c The value range is generally 0.4-0.99, and Pm is generally 0.001-0.1. The GA function returns the extended Debye model parameter R while obtaining the minimum value of the optimized objective function i 、C i The value of (2) is a rough solution near the optimal solution of the parameter, and is taken as an initial value of a Gaussian-Newton algorithm.
And carrying out parameter optimization on the extended debye model by using a Gaussian-Newton algorithm. R obtained by genetic algorithm i And C i As an initial iteration value, y=f (R using a gaussian-newton algorithm 1 ,R 2 ,…,R n ；C 1 ,C 2 ,…,C n ) And carrying out further optimal accurate solution. The iterative formula of the Gaussian-Newton algorithm is as follows:
x k+1 ＝x k -(J(x k ) T J(x k )) -1 J(x k ) T f(x k ) (8)
wherein x= [ R ] 1 ,R 2 ,…,R n ,C 1 ,C 2 ,…,C n ] T The subscript k denotes the iteration order. The Gaussian-Newton method overcomes the iteration defect that the step length is increased when the Jacobi matrix in the Newton method has an odd or bad condition. Selecting a suitable ε, when f (x k+1 )-f(x k )<Epsilon, obtaining the accurate value of the optimal solution, and ending the parameter optimization process.
And determining the RC branch number of the extended debye model by using the goodness of fit. The number n of the RC branches of the extended debye model is respectively selected as 3, 4, 5, 6 and 7, the parameter solving and optimizing process is repeated, the number of the RC branches of the extended debye model is determined by using the fitting goodness, and the fitting goodness is defined as follows:
in which y i As the raw data is to be processed,fitting data,/->For the raw data average, the smaller R indicates a worse fit and the larger R indicates a better fit for the R distribution interval (0, 1). And the fitting goodness and the optimization algorithm simplicity are considered, and the proper RC branch number of the extended debye model is determined for the objects to be measured of the same type. And obtaining the dielectric response extended debye model after parameter optimization.
The embodiment of the invention discloses a dielectric response extended debye model building method based on a genetic algorithm and a Gaussian-Newton algorithm, which is characterized in that the parameters of the extended debye model are optimized by fusing the genetic algorithm and the Gaussian-Newton algorithm, the branch number of the extended debye model is determined by using the goodness of fit, and a reliable, accurate and wide-application-range extended debye model is built. The combination of the two different algorithms can respectively exert the advantages of the two algorithms in global search and local search, comprehensively and effectively optimize model parameters, avoid the influence of different physical structures and dielectric properties of the tested object on model accuracy, and effectively solve the problems of low matching precision of the dielectric response extended debye equivalent model, weak applicability to different tested objects, poor model stability and the like in the current stage.
In the embodiment of the invention, the measured object is an oil immersed paper sample with the thickness of 130um, the fitting goodness corresponding to different branch numbers is shown in figure 2, the fitting goodness and the optimization algorithm simplicity are considered, and the RC branch number n is determined to be 6. The optimal accurate solution of the parameters of the extended debye model is obtained on the basis of a genetic algorithm and a Gauss-Newton algorithm on oil-immersed paper samples with different water contents, the imaginary part of the optimized extended debye model complex electricity Rong Shibu is shown in figure 3, and the fitting of the optimized result and measured data is excellent.
TABLE 1 parameters of insulation extended Debye model for oiled papers with different moisture contents
In summary, the embodiment of the invention discloses a dielectric response extended debye model optimization method based on a genetic algorithm and a Gaussian-Newton algorithm. And carrying out parameter optimization on the extended debye model by using a fusion genetic algorithm and a Gaussian-Newton algorithm, determining the branch number of the extended debye model by using the goodness of fit, and establishing the extended debye model with reliability, accuracy and wide application range. The combination of the two different algorithms can respectively exert the advantages of the two algorithms in global search and local search, comprehensively and effectively optimize model parameters, avoid the influence of different physical structures and dielectric properties of a tested object on model accuracy, effectively solve the problems of low matching accuracy of a dielectric response extended debye equivalent model, weak applicability to different tested objects, poor model stability and the like, and provide an application basis for novel test methods such as dielectric response accurate evaluation and impact dielectric response.
It will be appreciated by those skilled in the art that embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The above embodiments are only for illustrating the technical solution of the present invention and not for limiting the same, and although the present invention has been described in detail with reference to the above embodiments, one skilled in the art may make modifications and equivalents to the specific embodiments of the present invention, and any modifications and equivalents not departing from the spirit and scope of the present invention are within the scope of the claims of the present invention.
Claims (9)
1. A method of optimizing a dielectric response extended debye model, comprising the steps of:
the real part and the imaginary part of the complex capacitance of the dielectric response are selected as optimization targets, a multi-target optimization problem is converted into a single-target optimization problem based on a least square method and through a weighting method, and an optimization target function based on a dielectric response expansion debye model is constructed and obtained;
based on the optimized objective function, carrying out parameter solving on the dielectric response extended debye model by utilizing a genetic algorithm to obtain a rough solution;
based on the optimization objective function, taking the rough solution as an initial value, and carrying out parameter optimization on the dielectric response expansion debye model by utilizing a Gaussian-Newton algorithm to obtain a dielectric response expansion debye model after parameter optimization;
and determining RC branch numbers of the dielectric response extended debye model by using the fitting goodness based on the dielectric response extended debye model after the parameter optimization, and completing dielectric response extended debye model optimization.
2. The method of optimizing a dielectric response extended debye model according to claim 1, wherein in the dielectric response extended debye model, a resistor and a capacitor are used to represent an insulation resistor and a geometric capacitor of a dielectric in parallel, and then a series resistance-capacitance branch with different time constants is connected in parallel to represent a polarization process with different relaxation times in the dielectric, so as to form a mixed branch with a parallel resistance-capacitance and a series resistance-capacitance of multiple branches.
3. The optimization method of dielectric response extended debye model according to claim 1, wherein the step of selecting the real part and the imaginary part of the complex capacitance of the dielectric response as the optimization targets, converting the multi-target optimization problem into a single-target optimization problem based on the least square method and by a weighting method, and constructing and obtaining the optimization target function based on the dielectric response extended debye model specifically comprises:
complex capacitor C * The method comprises the following steps:
the real part C 'and the imaginary part C' of the complex capacitance are respectively:
wherein ω is the power angular frequency, C 0 Is the geometric capacitance, C 0 Is insulation resistance, R i 、C i For extended debye model parameters to be optimized, subscript i represents the extended debye model branch sequence number;
the weighted least squares optimization objective function is established as follows:
wherein C' Measuring And C' Measuring To test the complex capacitance real part and imaginary part omega of the dielectric response at different frequencies 1i 、ω 2i For each frequency point weight omega 1i ＝1/C' Measuring (ω)，ω 2i ＝1/C” Measuring (ω)；
Converting the multi-objective optimization problem into a single-objective optimization problem to be solved by constructing a characteristic evaluation function, wherein the evaluation function is as follows:
y＝ω c1 y 1 +ω c2 y 2 (5)
wherein omega C1 And omega C2 Setting omega for the weight of the real part and the imaginary part of the complex capacitance C1 And omega C2 Are all 1;
substituting equation (4) into equation (5) to obtain the final optimized objective function:
bringing equations (2) and (3) into equation (6) yields an optimized objective function based on the dielectric response extended debye model as:
the function is R i 、C i Is a multiple objective function of a variable, abbreviated as y=f (R 1 ,R 2 ,…,R n ；C 1 ,C 2 ,…,C n )。
4. A method of optimizing a dielectric response spread debye model according to claim 3 wherein the measurements of the real and imaginary parts of the complex capacitance are obtained by frequency domain dielectric spectroscopy of the oiled paper insulation.
5. The method for optimizing the dielectric response spread debye model according to claim 1, wherein said step of performing a parametric solution to the dielectric response spread debye model using a genetic algorithm based on said optimization objective function, the step of obtaining a rough solution specifically comprises:
calling a genetic algorithm function, and taking an optimized objective function based on a dielectric response extended debye model as an fitness function; setting population number N, termination evolution algebra T and crossover probability P in genetic algorithm function c Probability of variation P m A value;
and obtaining a rough solution by the genetic algorithm function when the minimum value of the optimized objective function is obtained.
6. The method of optimizing a dielectric response spread debye model as claimed in claim 5 wherein N is in the range of 20 to 100, T is in the range of 100 to 500, and P is c The value range is 0.4-0.99, and the value range of Pm is 0.001-0.1.
7. The method for optimizing the dielectric response spread debye model according to claim 1, wherein the coarse solution is used as an initial value based on the optimization objective function, and the dielectric response spread debye model is subjected to parameter optimization by using a gauss-newton algorithm, so that the parameter-optimized dielectric response spread debye model is obtained:
the iterative formula of the Gaussian-Newton algorithm is as follows:
x k+1 ＝x k -(J(x k ) T J(x k )) -1 J(x k ) T f(x k ) (8)
wherein x= [ R ] 1 ,R 2 ,…,R n ,C 1 ,C 2 ,…,C n ] T The subscript k represents the iteration order;
a preset threshold epsilon, when f (x k+1 )-f(x k )<And epsilon, obtaining an accurate value of the optimal solution, and obtaining a dielectric response extended debye model after parameter optimization.
8. The method for optimizing the dielectric response spread debye model according to claim 1, wherein the step of determining the RC branch number of the dielectric response spread debye model by using the goodness-of-fit based on the parameter-optimized dielectric response spread debye model, and completing the dielectric response spread debye model optimization specifically comprises:
respectively selecting the number n of the RC branches of the extended debye model as a preset value, repeating the parameter solving and optimizing process, and determining the number of the RC branches of the extended debye model by using the fitting goodness;
wherein, the definition of the goodness of fit R is:
wherein y is i As the raw data is to be processed,for fitting data, +.>R is the average value of the original data, and the distribution interval (0, 1) of R is defined; and determining the RC branch number of the extended debye model through the size of the goodness-of-fit value based on a preset threshold range.
9. An optimization system for a dielectric response extended debye model, comprising:
the optimization objective function acquisition module is used for selecting a dielectric response complex capacitance real part and an imaginary part as optimization targets, converting a multi-target optimization problem into a single-target optimization problem by adopting a weighting method based on a least square method, and constructing and obtaining an optimization objective function based on a dielectric response extended debye model;
the rough solution acquisition module is used for carrying out parameter solution on the dielectric response expansion debye model by utilizing a genetic algorithm according to the optimization objective function to obtain a rough solution;
the parameter optimization module is used for carrying out parameter optimization on the dielectric response expansion debye model by using the rough solution as an initial value and utilizing a Gaussian-Newton algorithm according to the optimization objective function to obtain the dielectric response expansion debye model after parameter optimization;
and the RC branch number determining module is used for determining the RC branch number of the dielectric response extended debye model by utilizing the fitting goodness according to the dielectric response extended debye model after the parameter optimization, so as to complete the dielectric response extended debye model optimization.
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