CN116562157A - Grading ring parameter model selection optimization method based on improved fully-connected neural network - Google Patents
Grading ring parameter model selection optimization method based on improved fully-connected neural network Download PDFInfo
- Publication number
- CN116562157A CN116562157A CN202310541462.3A CN202310541462A CN116562157A CN 116562157 A CN116562157 A CN 116562157A CN 202310541462 A CN202310541462 A CN 202310541462A CN 116562157 A CN116562157 A CN 116562157A
- Authority
- CN
- China
- Prior art keywords
- equalizing ring
- optimization
- ring
- particle
- neural network
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Pending
Links
- 238000005457 optimization Methods 0.000 title claims abstract description 65
- 238000000034 method Methods 0.000 title claims abstract description 46
- 238000013528 artificial neural network Methods 0.000 title claims abstract description 30
- 239000002245 particle Substances 0.000 claims abstract description 62
- 230000005684 electric field Effects 0.000 claims abstract description 30
- 238000004422 calculation algorithm Methods 0.000 claims abstract description 23
- 238000013461 design Methods 0.000 claims abstract description 16
- 238000012549 training Methods 0.000 claims abstract description 12
- 230000006870 function Effects 0.000 claims description 45
- 230000001133 acceleration Effects 0.000 claims description 17
- 239000012212 insulator Substances 0.000 claims description 15
- 239000000463 material Substances 0.000 claims description 12
- 230000004913 activation Effects 0.000 claims description 11
- 238000013507 mapping Methods 0.000 claims description 8
- 230000003044 adaptive effect Effects 0.000 claims description 5
- 238000004364 calculation method Methods 0.000 claims description 5
- 238000009434 installation Methods 0.000 claims description 4
- 239000011159 matrix material Substances 0.000 claims description 4
- 230000008569 process Effects 0.000 claims description 4
- 238000012360 testing method Methods 0.000 claims description 4
- 101000802640 Homo sapiens Lactosylceramide 4-alpha-galactosyltransferase Proteins 0.000 claims description 3
- 102100035838 Lactosylceramide 4-alpha-galactosyltransferase Human genes 0.000 claims description 3
- 230000008859 change Effects 0.000 claims description 3
- 230000007423 decrease Effects 0.000 claims description 3
- 238000012545 processing Methods 0.000 claims description 3
- 230000009466 transformation Effects 0.000 claims description 3
- 230000008901 benefit Effects 0.000 abstract description 5
- 230000007613 environmental effect Effects 0.000 abstract description 2
- 238000009413 insulation Methods 0.000 abstract description 2
- 230000005672 electromagnetic field Effects 0.000 description 3
- 238000005516 engineering process Methods 0.000 description 2
- 238000012986 modification Methods 0.000 description 2
- 230000004048 modification Effects 0.000 description 2
- 230000006978 adaptation Effects 0.000 description 1
- 230000005540 biological transmission Effects 0.000 description 1
- 238000010276 construction Methods 0.000 description 1
- 238000013135 deep learning Methods 0.000 description 1
- 238000011161 development Methods 0.000 description 1
- 238000010586 diagram Methods 0.000 description 1
- 238000002474 experimental method Methods 0.000 description 1
- 238000005290 field theory Methods 0.000 description 1
- 238000012423 maintenance Methods 0.000 description 1
- 238000013178 mathematical model Methods 0.000 description 1
- 238000013021 overheating Methods 0.000 description 1
- 238000006467 substitution reaction Methods 0.000 description 1
- 230000009897 systematic effect Effects 0.000 description 1
- 238000004804 winding Methods 0.000 description 1
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
- G06F30/27—Design optimisation, verification or simulation using machine learning, e.g. artificial intelligence, neural networks, support vector machines [SVM] or training a model
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/10—Geometric CAD
- G06F30/17—Mechanical parametric or variational design
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
- G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
- G06N3/00—Computing arrangements based on biological models
- G06N3/004—Artificial life, i.e. computing arrangements simulating life
- G06N3/006—Artificial life, i.e. computing arrangements simulating life based on simulated virtual individual or collective life forms, e.g. social simulations or particle swarm optimisation [PSO]
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
- G06N3/00—Computing arrangements based on biological models
- G06N3/02—Neural networks
- G06N3/04—Architecture, e.g. interconnection topology
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
- G06N3/00—Computing arrangements based on biological models
- G06N3/02—Neural networks
- G06N3/08—Learning methods
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2111/00—Details relating to CAD techniques
- G06F2111/06—Multi-objective optimisation, e.g. Pareto optimisation using simulated annealing [SA], ant colony algorithms or genetic algorithms [GA]
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y04—INFORMATION OR COMMUNICATION TECHNOLOGIES HAVING AN IMPACT ON OTHER TECHNOLOGY AREAS
- Y04S—SYSTEMS INTEGRATING TECHNOLOGIES RELATED TO POWER NETWORK OPERATION, COMMUNICATION OR INFORMATION TECHNOLOGIES FOR IMPROVING THE ELECTRICAL POWER GENERATION, TRANSMISSION, DISTRIBUTION, MANAGEMENT OR USAGE, i.e. SMART GRIDS
- Y04S10/00—Systems supporting electrical power generation, transmission or distribution
- Y04S10/50—Systems or methods supporting the power network operation or management, involving a certain degree of interaction with the load-side end user applications
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- Theoretical Computer Science (AREA)
- Evolutionary Computation (AREA)
- General Physics & Mathematics (AREA)
- General Engineering & Computer Science (AREA)
- Geometry (AREA)
- Artificial Intelligence (AREA)
- Software Systems (AREA)
- Biomedical Technology (AREA)
- Computational Linguistics (AREA)
- Mathematical Physics (AREA)
- Computing Systems (AREA)
- Molecular Biology (AREA)
- Computer Hardware Design (AREA)
- General Health & Medical Sciences (AREA)
- Health & Medical Sciences (AREA)
- Life Sciences & Earth Sciences (AREA)
- Data Mining & Analysis (AREA)
- Biophysics (AREA)
- Mathematical Optimization (AREA)
- Computer Vision & Pattern Recognition (AREA)
- Pure & Applied Mathematics (AREA)
- Mathematical Analysis (AREA)
- Computational Mathematics (AREA)
- Medical Informatics (AREA)
- Management, Administration, Business Operations System, And Electronic Commerce (AREA)
Abstract
An equalizing ring parameter model selection optimization method based on an improved fully-connected neural network belongs to the technical field of high-voltage insulation, and solves the problem of optimizing the parameter model selection of an equalizing ring on the basis of considering environmental factors; the method comprises the steps of collecting application parameters and related influence factors of the equalizing ring, performing model training through a fully-connected neural network, realizing input of corresponding application environments of the equalizing ring, outputting basic parameters of the equalizing ring, establishing a related finite element model in a comsol on the basis of the basic parameters, taking the minimum value of the field intensity along the surface and the degree of electric field non-uniformity as optimization targets, and further performing optimization design on structural parameters of the equalizing ring based on a particle swarm optimization algorithm; the method can realize the rapid model selection and basic design of the equalizing ring under different application environments manually and the design optimization of structural parameters of the equalizing ring under specific application environments; the invention is not limited by single parameter, has wider application range and higher economic benefit.
Description
Technical Field
The invention belongs to the technical field of high-voltage insulation, and relates to an equalizing ring parameter selection optimization method based on an improved fully-connected neural network.
Background
The choice and design of the grading ring becomes critical when high voltage applications are involved. Grading rings are an important component used in electrical equipment to balance the voltages of the different windings and to ensure that they are at the same potential. Its function is to eliminate leakage induced potential and avoid local overheating and damage due to non-uniform voltage distribution.
The selection of an appropriate grading ring requires consideration of a number of factors including voltage class, current load, ring material, structural form, and the like. Incorrect selection or design may result in uneven voltage distribution, increasing the failure rate of the device, reducing the reliability and efficiency of the system. In addition, the design of the grading ring also faces some challenges and difficulties. For example, how to realize a compact and lightweight design while ensuring electrical performance, so as to meet the requirements of modern power systems for high performance and high efficiency. Therefore, the grading ring design and design requires multiple factors to be considered in combination, and requires experienced engineers and specialists to make the assessment and decision.
The structural optimization of the equalizing ring refers to a technology for optimally designing the position, the size, the parameters and the like of the equalizing ring so that the equalizing ring can better play a role. Structural optimization of the equalizing ring has important theoretical significance and practical value. In theory, the structural optimization of the equalizing ring can improve the electrical uniformity of the equipment, reduce the corona initial field intensity of the equipment, reduce the discharge and pollution degree of the equipment and prolong the service life of the equipment. In practice, the structural optimization of the equalizing ring can save material cost, reduce equipment weight, reduce equipment occupation space, facilitate equipment installation and maintenance, and improve equipment operation reliability and safety.
Along with the development of a power system, particularly the construction of ultra-high voltage and ultra-high voltage transmission lines, higher requirements are put forward on the structural optimization of the equalizing ring. The traditional equalizing ring structure optimization method is mainly based on experience or experiment, lacks theoretical basis and intelligent means, and cannot meet complex and changeable engineering requirements. Therefore, advanced mathematical models, optimization algorithms and computer technology are needed to carry out systematic, scientific and intelligent structural optimization design on the equalizing ring.
Disclosure of Invention
The invention aims to solve the problem of optimizing the parameter type of the equalizing ring on the basis of considering environmental factors.
The invention solves the technical problems through the following technical scheme:
a grading ring parameter model selection optimization method based on an improved fully-connected neural network comprises the following steps:
s1, collecting basic application parameters and related influence factors of an equalizing ring, establishing a data set, mapping the basic application parameters and the related influence factors of the equalizing ring, carrying out standardized pretreatment on data in the data set to obtain a standardized data set, and dividing the standardized data set into a training set and a testing set;
s2, establishing an equalizing ring parameter model selection optimization model based on an improved fully-connected neural network, and training the equalizing ring parameter model selection optimization model by using a training set to obtain an equalizing ring parameter model selection optimization prediction model;
s3, predicting basic parameters of the equalizing ring by adopting an equalizing ring parameter selection optimization prediction model, establishing an equalizing ring finite element model in a comsol simulation software based on the predicted basic parameters of the equalizing ring, and calculating electric field distribution of the equalizing ring and uneven strength of an electric field to obtain structural parameters of the equalizing ring;
and S4, optimizing the structural parameters of the equalizing ring by using an adaptive weight particle swarm optimization algorithm.
Further, the method for establishing the grading ring parameter model optimization model based on the improved fully-connected neural network in the step S2 is as follows: constructing a fully-connected neural network, wherein the first layer is an input layer, the second layer and the third layer are hidden layers, and the fourth layer is an output layer; between two adjacent layers, the output of the upper layer is the input of the lower layer, and each node comprises three parts of weight, bias and activation function; the calculation formula of the fully-connected neural network is as follows:
in the method, in the process of the invention,output of the j-th node of the k-th layer,/>Output of the ith node of the k-1 th layer,/and>is the weight of the output of the ith node of the k-1 layer when the output is transmitted to the jth node of the k layer,/th node>F () is an activation function for the bias corresponding to the jth node of the kth layer, and the activation function selects a ReLU function.
Further, the method for establishing the equalizing ring finite element model in the comsol simulation software in the step S3 is as follows: drawing an insulator grading ring model, adding boundary conditions by adopting a boundaries module, selecting a material module to add material properties, defining a physical field, applying a load, and solving after mesh division by a mesh module.
Further, the method for calculating the distribution of the grading ring electric field and the uneven intensity of the electric field in the step S3 is as follows:
the equation of poisson's equation is:
boundary conditions are homogeneous, and the Laplace operator can be proved to be a self-accompanying operator, and the method comprises the following steps:
in the middle ofAnd ψ is any two functions in the definition domain, γ is a constant greater than zero;
the generalized equation is equivalent to the following variational problem and has a unique solution:
after finishing, the method comprises the following steps:
wherein V is the whole field volume, and the integral term in the formula and the functional in the Poisson equation are obtained after the integral transformation processing:
the first two kinds of boundary value problems of alignment can be simplified as follows:
deriving the corresponding variable problems of the non-homogeneous first type boundary conditions and the homogeneous second type boundary conditions as follows:
it can be proved that when the functional is foundAt the extreme value, the boundary conditions of the second class and the third class which are not homogeneous and the boundary conditions of the third class which are homogeneous are automatically satisfied;
the potential distribution of the insulator accords with the Laplace equation, and the boundary condition belongs to the first side value problem; the whole field is divided into n units, and the function of the potential at any point in the unit e can be expressed as:
wherein m is 0 The number of vertices of the time division unit,is the potential value of each vertex of each cell, +.>Is a unit shape function, and the whole field variation problem can be approximated as:
is a potential function of all points in the whole field, and is obtained by a variation principle:
in [ k ]]Is a coefficient matrix, and each potential can be solved by using boundary conditionsAnd further solving the electric field physical quantity such as electric field intensity, current and the like.
Further, the structural parameters of the equalizing ring in step S3 include: ring diameter (D), pipe diameter (D) and installation position (x).
Further, the method for optimizing the structural parameters of the equalizing ring by using the adaptive weight particle swarm optimization algorithm in the step S4 is as follows:
(1) Determining the number and structural parameters of the equalizing rings and determining an optimization target, including: obtaining the minimum value and the electric field non-uniformity degree of the maximum field intensity along the surface;
(2) The input layer is the structural parameter of the grading ring, the output layer is the maximum electric field intensity of the insulator along surface and the maximum electric field intensity of the grading ring surface, and the mapping relation is as follows:
(E 1 ,E 2 )＝F(D,d,x)
wherein D, d and x are respectively the ring diameter, the pipe diameter and the position of the equalizing ring, E1 and E2 are respectively the maximum field intensity of the insulator along the surface and the maximum field intensity of the equalizing ring surface;
the basic idea of the equalizing ring optimization design is to obtain a group of values of structural parameters D, d and x so that the maximum field intensity of the surface of the equalizing ring is smaller than the initial corona field intensity of the equalizing ring, namely
E 2max ＝f(D,d,x)
The maximum field intensity of the formula insulator along the surface obtains the minimum value, namely
E 1max ＝min(F(D,d,x))
(3) Parameters of an optimization algorithm are determined, and the particle swarm optimization algorithm is described as follows: let P be i ＝(P i1 ，P i2 ，P i3 …P id ): ith in d-dimensional space th Position vector of individual particles, V i ＝(V i1 ，V i2 …V id ): searching a velocity vector of an h particle in the space; store the best previous position of the ith particle and use P besti ＝(P besti1 ，P besti2 …，P bestid ) A representation; all P besti Are all evaluated by using fitness functions; all P besti The optimal particle position in (a) becomes G best The method comprises the steps of carrying out a first treatment on the surface of the The velocity of each particle is based on its individual previous best solution P bestik And previous global solution G for the entire group bestik Dynamically adjusting; the position and velocity of the ith particle are updated using the following equation:
V i (k+1)＝w(k)V i (k)+c 1 r 1 (k)(P best (k)-P i (k))+c 2 r 2 (k)(G best (k)-P i (k)
P i (k+1)＝P(k)+V i (k+1)
wherein V is i (k) And V i (k+1) is the velocity of the ith particle, C, for the kth and the kth+1 iteration, respectively 1 And C 2 Is two normal numbers, called acceleration factor, r 1 (k) And r 2 (k) Is a random value between 0 and 1, w (k) is a momentum parameter that can change the searching ability;
(4) Initializing the position and the speed of a particle swarm, and randomly generating a feasible solution in a search space;
(5) Calculating the fitness value of each particle, and the initial inertia weight w and the acceleration coefficients c1 and c2, namely substituting the initial inertia weight w and the acceleration coefficients c1 and c2 into the optimized objective function value; updating the size based on the average value of the objective function and the optimal solution;
wherein E is avr (i) Is the average objective function value of the observed iteration i, E gbest (i) Is the objective function value of the global best particle for the observed iteration i), psize max And Psize min The maximum and minimum (predefined) population sizes, respectively;
(6) Comparing the fitness value of each particle with the historical optimal fitness value, and updating the individual optimal position and fitness value of each particle;
(7) Comparing individual optimal fitness values of all particles, and updating global optimal positions and fitness values;
(8) Updating the speed and the position of each particle according to the global optimal position and the individual optimal position; adaptively adjusting the values of the inertial weight w and the acceleration coefficients c1, c 2; wherein the value of the inertia weight w decreases with the increase of the iteration number so as to balance the trade-off relation between the global search and the local search; the values of the acceleration coefficients c1 and c2 are adjusted according to the state and the historical performance of the particle swarm;
(9) And (3) judging whether a termination condition is met, if so, outputting a global optimal position and an adaptability value, and if not, returning to the step (6).
The invention has the advantages that:
(1) The method comprises the steps of collecting application parameters and related influence factors of the equalizing ring, performing model training through a fully-connected neural network, realizing input of corresponding application environments of the equalizing ring, outputting basic parameters of the equalizing ring, establishing a related finite element model in a comsol on the basis of the basic parameters, taking the minimum value of the field intensity along the surface and the degree of electric field non-uniformity as optimization targets, and further performing optimization design on structural parameters of the equalizing ring based on a particle swarm optimization algorithm; the method can realize the rapid model selection and basic design of the equalizing ring under different application environments manually and the design optimization of structural parameters of the equalizing ring under specific application environments; the invention is not limited by single parameter, has wider application range and higher economic benefit.
(2) In the traditional particle swarm optimization algorithm, the inertia weight and the acceleration coefficient in the particle swarm are usually required to be manually set, and the efficiency of solving the optimal solution of the equalizing ring can be improved by improving the particle swarm optimization into the self-adaptive weight; the improved PSO algorithm is applied to optimization of the equalizing ring structure, and has the following advantages: the global optimizing capability is strong, and the PSO algorithm can avoid sinking into the local optimal solution by continuously updating the positions and the speeds of individuals in the group and searching the global optimal solution; the application range is wide: the PSO algorithm has less constraint condition requirements on the problem and has better applicability to complex nonlinear problems, so that the PSO algorithm is suitable for optimizing the equalizing ring structure; the calculation speed is high: compared with other optimization algorithms, the PSO algorithm has relatively high calculation speed, and can effectively improve the optimization efficiency.
Drawings
FIG. 1 is a flow chart of the grading ring parameter selection optimization method based on the improved fully-connected neural network of the present invention;
fig. 2 is a block diagram of an improved fully-connected neural network used in the grading ring parameter selection optimization method based on the improved fully-connected neural network.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions in the embodiments of the present invention will be clearly and completely described in the following in conjunction with the embodiments of the present invention, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The technical scheme of the invention is further described below with reference to the attached drawings and specific embodiments:
example 1
As shown in fig. 1, a grading ring parameter model selection optimization method based on an improved fully-connected neural network comprises the following specific steps:
step one: collecting basic application parameters and related influence factors of the equalizing ring, establishing a data set, and mapping the basic application parameters and the related influence factors of the equalizing ring; carrying out standardized pretreatment on data in the data set to obtain a standardized data set, and dividing the standardized data set into a training set and a testing set;
the relevant influence factors include: temperature, humidity, fouling level, voltage class, type of application device.
The basic application parameters of the grading ring comprise: number, size range, material, style.
The mapping is shown in the following table:
table 1 basic application parameters and related influence factor mapping table of grading ring
Step two: establishing an equalizing ring model based on an improved fully connected neural network (Fully Connected Neural Network, FCNN), and training the model by using a deep learning algorithm to obtain a final prediction model; the method comprises the following specific steps:
(1) As shown in fig. 2, a four-layer fully connected neural network is constructed, wherein the first layer is an input layer, the second and third layers are hidden layers, and the fourth layer is an output layer. Between two adjacent layers, the output of the upper layer is the input of the lower layer, and each node comprises three parts of weight, bias and activation functions.
(2) The calculation process of the fully connected neural network is essentially a matrix multiplication, assuming that the output of the jth node of the kth layer isIts correspondence with the n nodes of the k-1 layer is:
in the method, in the process of the invention,is the weight of the output of the ith node of the k-1 layer when the output is transmitted to the jth node of the k layer,/th node>And f is an activation function, which is the bias corresponding to the jth node of the kth layer.
(3) Defining an activation function, wherein the weight and the bias express a linear relation of data distribution in the fully connected neural network, the activation function expresses a nonlinear relation of data distribution, and the activation function is selected as follows:
ReLU(z)＝max(0,z)
(4) In each iteration, the following operations are performed: a batch of data is randomly extracted from the training set, input into the network, and the output and loss functions of the network are calculated. Gradients of the loss function for each weight and bias are calculated by back propagation and updated with an optimizer.
(5) After each iteration cycle is completed, the following operations are performed: all or part of the data is extracted from the test set and input into the network, and the output and loss function of the network are calculated.
(6) Training and optimizing the data to finally obtain a model for predicting new input; when the model inputs scene factors (temperature, humidity, pollution degree, voltage level, application equipment and price) of the related grading ring, the network can give corresponding grading ring basic parameters (quantity, size range, material and style).
And thirdly, establishing an equalizing ring finite element model in the comsol simulation software based on the equalizing ring basic parameters (quantity, size range, material and style) calculated in the second step. And calculating the electric field distribution of the equalizing ring and the uneven strength of the electric field, and exploring the influence rule of each structural parameter of the equalizing ring on the electric field distribution of the application equipment. Wherein structural parameters of the grading ring include: ring diameter (D), pipe diameter (D) and installation position (x).
(1) The method for establishing the equalizing ring finite element model is as follows: drawing an insulator grading ring model, adding boundary conditions by adopting a boundaries module, selecting a material module to add material properties, defining a physical field and applying load. And carrying out mesh division through a mesh module, and then solving. Note that the model size, material properties, structural parameters and the like are all set as variable parameters, and the model is subjected to self-defining modification according to the prediction optimization result in the second step.
(2) The method for calculating the electric field distribution of the equalizing ring and the nonuniform strength of the electric field is as follows:
based on electromagnetic field theory, the fixed solution of electromagnetic field and Maxwell's equations consists of electromagnetic field boundary conditions. In the finite element method, the functional problem of the solution problem is first converted into the variational problem. Taking the homogeneous poisson problem of the first kind of boundary conditions as an example to draw out the functional extremum problem, the formula of the functional extremum in the poisson equation is as follows:
boundary conditions are homogeneous, and the Laplace operator can be proved to be a self-accompanying operator, and the method comprises the following steps:
in the middle ofAnd ψ is any two functions in the domain, γ is a constant greater than zero.
The positive definite operator has the above properties, so the generalized definite equation in the definite solution problem can be equivalent to the following variational problem, and has a unique solution:
after finishing, the method comprises the following steps:
wherein V is the whole field volume, and the integral term in the formula and the functional in the Poisson equation are obtained after the integral transformation processing:
the first two kinds of boundary value problems of alignment can be simplified as follows:
deriving the corresponding variable problems of the non-homogeneous first type boundary conditions and the homogeneous second type boundary conditions as follows:
it can be proved that when the functional is foundAt extreme values, the non-homogeneous second and third class boundary conditions and homogeneous third class boundary conditions have been automatically satisfied.
The insulator potential distribution conforms to the Laplace equation and the boundary conditions belong to the first class of boundary value problems. The whole field is divided into n units, and the function of the potential at any point in the unit e can be expressed as:
m is in 0 The number of vertices of the time division unit,is the potential value of each vertex of each cell, +.>Is a unit shape function, and the whole field variation problem can be approximated as:
is the potential function of all points in the whole fieldThe number is obtained by a variation principle:
in [ k ]]Is a coefficient matrix, and each potential can be solved by using boundary conditionsAnd further solving the electric field physical quantity such as electric field intensity, current and the like.
Step four, optimizing structural parameters of the equalizing ring by utilizing an adaptive weight particle swarm optimization algorithm
In the traditional particle swarm optimization algorithm, the inertia weight and the acceleration coefficient in the particle swarm are usually required to be manually set, and the efficiency of solving the optimal solution of the equalizing ring can be improved by improving the particle swarm optimization into the self-adaptive weight.
(1) Determining the number and structural parameters of the equalizing rings; determining an optimization objective, comprising: minimum value and electric field non-uniformity degree are obtained along the maximum field intensity of the surface.
(2) The main input layer is the structural parameter of the equalizing ring, the corresponding objective function is that the output layer is the maximum electric field intensity of the insulator along the surface and the maximum electric field intensity of the equalizing ring surface, and the mapping relation is that:
(E 1 ,E 2 )＝F(D,d,x)
wherein D, d and x are respectively the ring diameter, the pipe diameter and the position of the equalizing ring, and E1 and E2 are respectively the maximum field intensity of the insulator along the surface and the maximum field intensity of the equalizing ring surface.
The basic idea of the equalizing ring optimization design is to obtain a group of values of structural parameters D, d and x so that the maximum field intensity of the surface of the equalizing ring is smaller than the initial corona field intensity of the equalizing ring, namely
E 2max ＝f(D,d,x)
The maximum field intensity of the formula insulator along the surface obtains the minimum value, namely
E 1max ＝min(F(D,d,x))
(3) Determining parameters of an optimization algorithm, e.g. particle sizeNumber, number of iterations, inertial weights, learning factors, etc. The particle swarm optimization algorithm may be described as follows: let P be i ＝(P i1 ，P i2 ，P i3 …P id ): ith in d-dimensional space th Position vector of individual particles, V i ＝(V i1 ，V i2 …V id ): the velocity vector of the h-th particle in the search space. Store the best previous position of the ith particle and use P besti ＝(P besti1 ，P besti2 …，P bestid ) And (3) representing. All P besti Are evaluated by using fitness functions. All P besti The optimal particle position in (a) becomes G best . The velocity of each particle is based on its individual previous best solution P bestik And previous global solution G for the entire group bestik And (5) dynamically adjusting. The position and velocity of the ith particle are updated using the following equation:
V i (k+1)＝w(k)V i (k)+c 1 r 1 (k)(P best (k)-P i (k))+c 2 r 2 (k)(G best (k)-P i (k)
P i (k+1)＝P(k)+V i (k+1)
wherein V is i (k) And V i (k+1) is the velocity of the ith particle, C, for the kth and the kth+1 iteration, respectively 1 And C 2 Is two normal numbers, called acceleration factor, r 1 (k) And r 2 (k) Is a random value between 0 and 1, w (k) is a momentum parameter that can change the searching capability.
(4) The position and velocity of the population of particles are initialized, and feasible solutions within the search space are randomly generated.
(5) And calculating the fitness value of each particle, and the initial inertia weight w and the acceleration coefficients c1 and c2, namely substituting the initial inertia weight w and the acceleration coefficients c1 and c2 into the optimized objective function value. The size is updated based on the average value of the objective function and the optimal solution.
Wherein E is avr (i) Is the average objective function value of the observed iteration i, E gbest (i) Is the objective function value of the global best particle for the observed iteration i), psize max And Psize min The maximum and minimum (predefined) population sizes, respectively.
(6) And comparing the fitness value of each particle with the historical optimal fitness value, and updating the individual optimal position and fitness value of each particle.
(7) And comparing the individual optimal fitness values of all the particles, and updating the global optimal position and the fitness value.
(8) The velocity and position of each particle are updated based on the global optimum and the individual optimum. The values of the inertial weight w and the acceleration coefficients c1, c2 are adaptively adjusted. Wherein the value of the inertia weight w decreases with increasing iteration number to balance the trade-off relationship between the global search and the local search. The values of the acceleration coefficients c1 and c2 are adjusted according to the state and the historical performance of the particle swarm.
(9) Judging whether a termination condition is met, if so, outputting a global optimal position and an adaptation degree value if so, and if not, returning to the step (6).
The above embodiments are only for illustrating the technical solution of the present invention, and are not limiting; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit and scope of the technical solutions of the embodiments of the present invention.
Claims (6)
1. The grading ring parameter type selection optimization method based on the improved fully-connected neural network is characterized by comprising the following steps of:
s1, collecting basic application parameters and related influence factors of an equalizing ring, establishing a data set, mapping the basic application parameters and the related influence factors of the equalizing ring, carrying out standardized pretreatment on data in the data set to obtain a standardized data set, and dividing the standardized data set into a training set and a testing set;
s2, establishing an equalizing ring parameter model selection optimization model based on an improved fully-connected neural network, and training the equalizing ring parameter model selection optimization model by using a training set to obtain an equalizing ring parameter model selection optimization prediction model;
s3, predicting basic parameters of the equalizing ring by adopting an equalizing ring parameter selection optimization prediction model, establishing an equalizing ring finite element model in a comsol simulation software based on the predicted basic parameters of the equalizing ring, and calculating electric field distribution of the equalizing ring and uneven strength of an electric field to obtain structural parameters of the equalizing ring;
and S4, optimizing the structural parameters of the equalizing ring by using an adaptive weight particle swarm optimization algorithm.
2. The grading ring parameter type optimization method based on the improved fully-connected neural network according to claim 1, wherein the method for establishing the grading ring parameter type optimization model based on the improved fully-connected neural network in step S2 is as follows: constructing a fully-connected neural network, wherein the first layer is an input layer, the second layer and the third layer are hidden layers, and the fourth layer is an output layer; between two adjacent layers, the output of the upper layer is the input of the lower layer, and each node comprises three parts of weight, bias and activation function; the calculation formula of the fully-connected neural network is as follows:
in the method, in the process of the invention,output of the j-th node of the k-th layer,/>Output of the ith node of the k-1 th layer,/and>is the weight of the output of the ith node of the k-1 layer when the output is transmitted to the jth node of the k layer,/th node>F () is an activation function for the bias corresponding to the jth node of the kth layer, and the activation function selects a ReLU function.
3. The optimization method of grading ring parameter selection based on improved fully-connected neural network according to claim 2, wherein the method for establishing grading ring finite element model in the comsol simulation software in step S3 is as follows: drawing an insulator grading ring model, adding boundary conditions by adopting a boundaries module, selecting a material module to add material properties, defining a physical field, applying a load, and solving after mesh division by a mesh module.
4. The optimization method of grading ring parameter selection based on improved fully-connected neural network according to claim 3, wherein the method for calculating the grading ring electric field distribution and the nonuniform strength of the electric field in step S3 is as follows:
the equation of poisson's equation is:
boundary conditions are homogeneous, and the Laplace operator can be proved to be a self-accompanying operator, and the method comprises the following steps:
in the middle ofAnd ψ is any two functions in the definition domain, γ is a constant greater than zero;
the generalized equation is equivalent to the following variational problem and has a unique solution:
after finishing, the method comprises the following steps:
wherein V is the whole field volume, and the integral term in the formula and the functional in the Poisson equation are obtained after the integral transformation processing:
the first two kinds of boundary value problems of alignment can be simplified as follows:
deriving the corresponding variable problems of the non-homogeneous first type boundary conditions and the homogeneous second type boundary conditions as follows:
it can be proved that when the functional is foundAt extreme values, non-homogeneous second classAnd the third class boundary condition and the homogeneous third class boundary condition have been automatically satisfied;
the potential distribution of the insulator accords with the Laplace equation, and the boundary condition belongs to the first side value problem; the whole field is divided into n units, and the function of the potential at any point in the unit e can be expressed as:
wherein m is 0 The number of vertices of the time division unit,is the potential value of each vertex of each cell, +.>Is a unit shape function, and the whole field variation problem can be approximated as:
is a potential function of all points in the whole field, and is obtained by a variation principle:
in [ k ]]Is a coefficient matrix, and each potential can be solved by using boundary conditionsAnd further solving the electric field physical quantity such as electric field intensity, current and the like.
5. The optimization method of grading ring parameter selection based on improved fully-connected neural network according to claim 4, wherein the structural parameters of the grading ring in step S3 include: ring diameter (D), pipe diameter (D) and installation position (x).
6. The optimization method of grading ring parameter selection based on improved fully-connected neural network according to claim 5, wherein the method for optimizing structural parameters of the grading ring by using the adaptive weight particle swarm optimization algorithm in step S4 is as follows:
(1) Determining the number and structural parameters of the equalizing rings and determining an optimization target, including: obtaining the minimum value and the electric field non-uniformity degree of the maximum field intensity along the surface;
(2) The input layer is the structural parameter of the grading ring, the output layer is the maximum electric field intensity of the insulator along surface and the maximum electric field intensity of the grading ring surface, and the mapping relation is as follows:
(E 1 ,E 2 )＝F(D,d,x)
wherein D, d and x are respectively the ring diameter, the pipe diameter and the position of the equalizing ring, E1 and E2 are respectively the maximum field intensity of the insulator along the surface and the maximum field intensity of the equalizing ring surface;
the basic idea of the equalizing ring optimization design is to obtain a group of values of structural parameters D, d and x so that the maximum field intensity of the surface of the equalizing ring is smaller than the initial corona field intensity of the equalizing ring, namely
E 2max ＝f(D,d,x)
The maximum field intensity of the formula insulator along the surface obtains the minimum value, namely
E 1max ＝min(F(D,d,x))
(3) Parameters of an optimization algorithm are determined, and the particle swarm optimization algorithm is described as follows: let P be i ＝(P i1 ，P i2 ，P i3 …P id ): ith in d-dimensional space th Position vector of individual particles, V i ＝(V i1 ，V i2 …V id ): searching a velocity vector of an h particle in the space; store the best previous position of the ith particle and use P besti ＝(P besti1 ，P besti2 …，P bestid ) A representation; all P besti Are all evaluated by using fitness functions; all P besti The optimal particle position in (a) becomes G best The method comprises the steps of carrying out a first treatment on the surface of the The velocity of each particle is based on its individual previous best solution P bestik And previous global solution G for the entire group bestik Dynamically adjusting; the position and velocity of the ith particle are updated using the following equation:
V i (k+1)＝w(k)V i (k)+c 1 r 1 (k)(P best (k)-P i (k))+c 2 r 2 (k)(G best (k)-P i (k)
P i (k+1)＝P(k)+V i (k+1)
wherein V is i (k) And V i (k+1) is the velocity of the ith particle, C, for the kth and the kth+1 iteration, respectively 1 And C 2 Is two normal numbers, called acceleration factor, r 1 (k) And r 2 (k) Is a random value between 0 and 1, w (k) is a momentum parameter that can change the searching ability;
(4) Initializing the position and the speed of a particle swarm, and randomly generating a feasible solution in a search space;
(5) Calculating the fitness value of each particle, and the initial inertia weight w and the acceleration coefficients c1 and c2, namely substituting the initial inertia weight w and the acceleration coefficients c1 and c2 into the optimized objective function value; updating the size based on the average value of the objective function and the optimal solution;
wherein E is avr (i) Is the average objective function value of the observed iteration i, E gbest (i) Is the objective function value of the global best particle for the observed iteration i), psize max And Psize min The maximum and minimum (predefined) population sizes, respectively;
(6) Comparing the fitness value of each particle with the historical optimal fitness value, and updating the individual optimal position and fitness value of each particle;
(7) Comparing individual optimal fitness values of all particles, and updating global optimal positions and fitness values;
(8) Updating the speed and the position of each particle according to the global optimal position and the individual optimal position; adaptively adjusting the values of the inertial weight w and the acceleration coefficients c1, c 2; wherein the value of the inertia weight w decreases with the increase of the iteration number so as to balance the trade-off relation between the global search and the local search; the values of the acceleration coefficients c1 and c2 are adjusted according to the state and the historical performance of the particle swarm;
(9) And (3) judging whether a termination condition is met, if so, outputting a global optimal position and an adaptability value, and if not, returning to the step (6).
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202310541462.3A CN116562157A (en) | 2023-05-15 | 2023-05-15 | Grading ring parameter model selection optimization method based on improved fully-connected neural network |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202310541462.3A CN116562157A (en) | 2023-05-15 | 2023-05-15 | Grading ring parameter model selection optimization method based on improved fully-connected neural network |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN116562157A true CN116562157A (en) | 2023-08-08 |
Family
ID=87503141
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202310541462.3A Pending CN116562157A (en) | 2023-05-15 | 2023-05-15 | Grading ring parameter model selection optimization method based on improved fully-connected neural network |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN116562157A (en) |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN117709170A (en) * | 2024-02-05 | 2024-03-15 | 合肥工业大学 | Magnetic field rapid calculation method based on improved depth operator network |
-
2023
- 2023-05-15 CN CN202310541462.3A patent/CN116562157A/en active Pending
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN117709170A (en) * | 2024-02-05 | 2024-03-15 | 合肥工业大学 | Magnetic field rapid calculation method based on improved depth operator network |
| CN117709170B (en) * | 2024-02-05 | 2024-04-19 | 合肥工业大学 | Magnetic field rapid calculation method based on improved depth operator network |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Long et al. | A random opposition-based learning grey wolf optimizer | |
| Grishko et al. | Management of structural components complex electronic systems on the basis of adaptive model | |
| Nguyen et al. | Optimal dispatch of reactive power using modified stochastic fractal search algorithm | |
| Zhou et al. | Multi-objective artificial bee colony algorithm for short-term scheduling of hydrothermal system | |
| CN109066710B (en) | Multi-target reactive power optimization method and device, computer equipment and storage medium | |
| Kumar et al. | Multi-objective particle swarm optimization: an introduction | |
| CN107492892B (en) | Multi-target active scheduling solving method and system | |
| CN108390393B (en) | Multi-target reactive power optimization method for power distribution network and terminal equipment | |
| Zhu et al. | Seeker optimization algorithm for several practical applications | |
| CN116562157A (en) | Grading ring parameter model selection optimization method based on improved fully-connected neural network | |
| Zhang et al. | A new manufacturing service selection and composition method using improved flower pollination algorithm | |
| Kedong et al. | Improved grey prediction model based on exponential grey action quantity | |
| Zhao et al. | An improved particle swarm optimization algorithm for optimal reactive power dispatch | |
| Xilin et al. | Resource allocation optimization of equipment development task based on MOPSO algorithm | |
| Azadani et al. | Optimal placement of multiple STATCOM | |
| CN114564787A (en) | Bayesian optimization method, device and storage medium for target-related airfoil design | |
| Rao et al. | Multi-objective adaptive clonal selection algorithm for solving optimal power flow problem with load uncertainty | |
| Long et al. | A constrained multi-objective optimization algorithm using an efficient global diversity strategy | |
| CN116956744A (en) | Multi-loop groove cable steady-state temperature rise prediction method based on improved particle swarm optimization | |
| Wang et al. | Cloud computing and extreme learning machine for a distributed energy consumption forecasting in equipment-manufacturing enterprises | |
| Wu et al. | Historical information-based differential evolution for dynamic optimization problem | |
| Wei et al. | Scale-Based product family optimization design based on the improved AMPSO in selecting optimum strategy | |
| Jia et al. | Line loss rate prediction method based on deep learning with long short term memory | |
| Agarwal et al. | An Adaptive Genetic Algorithm-Based Load Balancing-Aware Task Scheduling Technique for Cloud Computing. | |
| CN115453871A (en) | Non-linear system modeling method based on IDE extended multidimensional Taylor network |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination |