CN107273581A - A kind of adaptive electric field automatic analysis system - Google Patents
A kind of adaptive electric field automatic analysis system Download PDFInfo
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Abstract
The invention discloses a kind of adaptive electric field automatic analysis system, the system is made up of model module, optimization module and the part of analysis module three.Model module stores the Electric Field Distribution situation and calculation of various ideal charges.Optimization module determines size and the position of optimal charge simulation, is allowed to the electric field produced and electric field that electrode surface electric charge is produced equivalent.The refined Hook Jeeves algorighm wherein used can automatic decision point group whether, while inertia weight improves convergence according to Evolving State adaptive change in more new formula；Also, the function of adaptive updates fitness function adds the diversity of search.Finally, analysis module analyzes field domain electric field using Analogue charge method.The system can be quickly found out optimal charge simulation, improve the precision of analysis of electric field.
Description
Technical field
The present invention relates to electromagnetism field, in particular it relates to a kind of adaptive electric field automatic analysis system.
Background technology
Charge simulation is commonly used under the scenes such as transformer station's space electric field analysis, nearby HV Transmission Line electromagnetic field analysis
Method.Analogue charge method is one of main method of electrostatic field numerical computations.Similar to image method, Analogue charge method is based on electrostatic field
Uniqueness theorem, by the continuously distributed free charge in conductor electrode surface with positioned at conductor one group of discrete electric charge come
Substitute, these discrete electric charges are referred to as charge simulation.Then superposition theorem is applied, with the analytic formula meter of these charge simulations
Calculate the point position at any point or electric-field intensity in field domain.The key of Analogue charge method is to find and determine charge simulation, but
The number of charge simulation, property, the selection of position and size are determined according to the experience of reckoner mostly, are not carried out program
Change, adjustment work is very diverse and complicated.
The content of the invention
The determination work of charge simulation very diverse and complicated, not good mould when calculating electric field with Analogue charge method at present to overcome
Intending electric charge influences the deficiency of analysis of electric field precision, is automatically analyzed it is an object of the invention to provide a kind of adaptive electric field and is
System.
The technical solution adopted for the present invention to solve the technical problems is：A kind of adaptive electric field automatic analysis system,
The system is made up of model module, optimization module and the part of analysis module three, and model module stores various preferable charge models
Electric Field Distribution situation and calculation around such as point electric charge and line charge, the quantity of electric charge and position of the optimization module to charge simulation
Put and optimize, analysis module analyzes field domain electric field according to charge simulation；Wherein：
Optimization module is distributed in z-axis, z ∈ [0, z in n charge simulation of field domain disposed outside to be analyzedmax], zmax
For the upper limit of distance can be arranged；Variable to be optimized is the electricity q of this n charge simulationkAnd its position zk, k=1,2 ..., n；
It is that the electric field for making charge simulation be produced in field domain is identical with the electric field that electrode surface electric charge is produced to optimize purpose, in order to follow-up
Electric field automatically analyze；
Then, initialization population scale is NsPopulation, random generation dimension for 2n particle i initial position xi=
(xi1,xi2,...,xi(2n)) and initial velocity vi=(vi1,vi2,...,vi(2n)), i=1,2 ..., Ns；Define dimension variable d, d
=1,2 ..., 2n；Work as d=1, during 2 ..., n, xidRepresent the electricity of d-th of charge simulation, xid∈ [0,1], vid∈[-1,
1]；When working as d=n+1, n+2 ..., 2n, xidRepresent the position z of the d-n electric charged-n, xid∈[0,zmax], vid∈[-zmax,
zmax]；Population scale Ns=300~600；
Electrode surface has check point M, in order that known to potential and electrode surface that charge simulation is produced to check point
Potential is identical, and the object function of problem is formula (1)：
Wherein,The potential that all charge simulations are produced in m-th of check point is represented, calling model module during specific calculating
In model；Represent potential known to electrode surface；F >=0, the theoretical value 0 of object function；
Fitness function fitness is constructed, formula (2) is seen：
Wherein, f is object function；
The positional information of particle after initialization is substituted into formula (2), initial fitness function value is obtained；Fitness function value is most
Big particle is global optimum's particle, and its position is pbest=(pbest1,pbest2,...,pbest(2n))；Remember fitnessTFor the T times
Fitness function during iteration, T is iteration count, fitness when initial0=fitness；Then changed by the following method
Generation, iteration count T=0 when initial：
(1) current iteration is counted as T, when T=0 or T is τ integral multiple, continues step (2) and carries out a point group operation, no
Then regardless of group, step (3) is leapt to；τ=3~6；
(2) a point group operation is carried out to all particles, specifically includes following sub-step：
(2.1) all particles are sorted from big to small according to fitness value size, chooses the maximum particle of fitness value and make
For a Ge Zi group center；
(2.2) the maximum particle of fitness value is chosen in remaining particle, is calculated successively in the particle and each subgroup
The Euclidean distance of the heart；Particle i and particle j Euclidean distance dist (i, j) is defined as：
Wherein, xi=(xi1,xi2,...,xi(2n)) represent particle i position, xj=(xj1,xj2,...,xj(2n)) represent grain
Sub- j position, i, j=1,2 ..., Ns；If the particle and the Euclidean distance at some subgroup center are less than radius r,
The particle is classified as to the subgroup where the subgroup center, and no longer calculate the Euclid at the particle and remaining subgroup center away from
From；If the particle and the distance at all subgroup centers are both greater than radius r, the particle is set to a new subgroup center；Half
Footpath r=0.01~0.02；(2.3) repeat step (2.2), until having handled all particles, then divide group to complete, and in each subgroup
The heart is the particle of fitness value maximum in the subgroup；
(3) Evolving State of population is determined；First, each particle and the distance at the subgroup center of subgroup where it are defined
Absolute value sum dg：
Wherein, pig=(pig1,pig2,...,pig(2n)) position at the subgroup center of subgroup where particle i；Secondly, definition
Each particle and the absolute value D apart from sum at the subgroup center of subgroup where itg：
Defining evolution factor delta is：
Evolution factor delta ∈ [0,1] is understood by definition；
(4) speed and the position of each particle are updated according to formula (7) (8)：
vid(T)=wvid(T-1)+c1·rand·(pid-xid(T-1))+c2·rand·(pigd-xid(T-1)) (7)
xid(T)=xid(T-1)+vid(T) (8)
Wherein, w is inertia weight；c1,c2For accelerated factor, c1=c2=2；Rand is the random number between 0 to 1；pi=
(pi1, pi2,...,pi(2n)) it is particle xiHistory optimal location；pig=(pig1, pig2,...,pig(2n)) where particle i
The position of the optimal particle of subgroup；Inertia weight is converted according to formula (9)：
After renewal, work as d=1, during 2 ..., n, if xid<0, then make xid=0, if xid>1, then make xid=1；Work as d=n+1, n
During+2 ..., 2n, if xid<0, then make xid=0, if xid>zmax, then x is madeid=zmax；
(5) fitness function is updated；If the optimal particle p in the whole population searched at presentbest=(pbest1,
pbest2,...,pbest(2n)) keep constant in continuous a iteration, then by pbestPosition recorded with fitness function value,
And to pbestPunished；It is specific to punish that operation is：As particle i and pbestDistance be less than radius r, then particle i fitness letter
Numerical value just becomes very little, sees formula (10)：
Wherein, fitnessTFor the fitness function of this time iteration, fitnessT-1Fitness during for last iteration
Function, i=1,2 ..., Ns, α is penalty factor, makes α=0；If the point of not newly-increased receiving punishment,：
fitnessT=fitnessT-1 (11)
A size is shown in formula (12)：
Wherein, T is current iteration number of times, TmaxFor maximum iteration,Represent to 0.1TmaxRound downwards；
(6) fitness function value of each particle is calculated according to formula (10), (11), potential is calculatedWhen calling model module
In corresponding model；
(7) the position p of global optimum's particle is updatedbest=(pbest1,pbest2,...,pbest(2n)), iteration count adds up, T
=T+1；
(8) repeat step (1)~(7), until reaching maximum iteration TmaxStop iteration, Tmax=100~2000；
Population global optimum particle pbest=(pbest1,pbest2,...,pbest(2n)) where position be n after optimization
The quantity of electric charge of charge simulation and its position, charge simulation the optimum layout are completed.
Beneficial effects of the present invention are mainly manifested in：Field domain electric field is analyzed using charge simulation analytic approach, by complexity
Analysis of electric field question simplification；Optimal size and the position of charge simulation are determined using intelligent optimization, analysis of electric field is improved
Precision；Whether is improved intelligent optimization method automatic decision point group, while inertia weight is according to Evolving State in more new formula
Adaptive change, improves convergence；Improved intelligent optimization method adaptively changes fitness function, improves
The search diversity of algorithm.The system speed of service is fast, and search capability is strong, and analysis precision is high.
Brief description of the drawings
Fig. 1 is bat/ground electrode model.
Fig. 2 is the structure chart of the present invention.
Fig. 3 is the flow chart of the present invention.
Fig. 4 be in the present invention inertia weight w with evolution factor delta variation diagram.
Embodiment
The present invention is illustrated with an example below according to accompanying drawing.
Reference picture 1, bat/ground electrode model, away from the high H in ground, half radius of a ball is R, metal bar endless, metal ball bar table
Face carries electric charge.Reference picture 2, adaptive electric field automatic analysis system is by model module, optimization module and the part of analysis module three
Composition.Model module stores the Electric Field Distribution situation and calculation around various preferable charge models, and optimization module is to mould
The quantity of electric charge for intending electric charge is optimized with position, and analysis module analyzes field domain electric field according to optimal charge simulation.Wherein：
Optimization module is outside field domain to be analyzed, i.e., n charge simulation of arrangement inside metal ball bar, and n=3 is respectively
One electric charge q1With the line charge q of two semi-infinite longs2、q3.These three charge simulations are distributed in z-axis, and coordinate is respectively z1,
z2, z3.Variable to be optimized is the electricity q of this 3 charge simulationskAnd its position zk, k=1,2,3.Optimization purpose is to make simulation
The electric field that electric charge is produced in field domain is identical with the electric field that electrode surface electric charge is produced.
Then, initialization population scale is NsPopulation, random generation dimension for 6 particle initial position xi=
(xi1,xi2,...,xi6) and initial velocity vi=(vi1,vi2,...,vi6), i=1,2 ..., Ns.Dimension variable d, d=1 are defined,
2,...,6.Work as d=1, when 2,3, xidThe electricity of d-th of charge simulation is represented, because the order of magnitude of elementary charge is 10-19, therefore
It is that charge simulation sets up one than larger quantity of electric charge scope, x relative to elementary chargeid∈ [0,1], vid∈[-1,1]；Work as d=
When 4,5,6, xidRepresent the position z of the d-3 electric charged-3, xid∈[H,zmax], vid∈[-(zmax-H),zmax- H], zmaxFor mould
Intend the maximum distance of distribution of charges.Population scale Ns=300~600.
Electrode surface has check point M, in order that known to potential and electrode surface that charge simulation is produced to check point
Potential is identical, and the object function of problem is formula (1)：
Wherein,The potential that all charge simulations are produced in m-th of check point is represented,Represent electrode surface known electric
Gesture.Reference picture 1, the potential at point (y, z) place is shown in formula (2) under its coordinate system：
Wherein, ε is dielectric constant.The calculating process of potential is carried out in model module.F >=0, the theoretical value of object function
For 0.
Fitness function fitness is constructed, formula (3) is seen：
Wherein, f is object function.Fitness function value is bigger, represents that target function value is smaller, and the charge simulation of arrangement is got over
It is excellent.
The positional information of particle after initialization is substituted into formula (3), fitness function value is obtained.Fitness function value maximum
Particle is global optimum's particle, and its position is pbest=(pbest1,pbest2,...,pbest6).Due to being adapted to during successive iterations
Degree function has the possibility changed, therefore note fitnessTFitness function during for the T times iteration, T is iteration count, just
The fitness during beginning0=fitness.Then it is iterated by the following method, iteration count T=0 when initial：
(1) undue frequently point group operation can upset the normal renewal of particle, influence convergent stability；And regardless of group
The search capability of algorithm can be reduced.Therefore the frequency of reduction point group can not only keep the search capability of algorithm but also be unlikely to influence particle
Renewal stability.Current iteration number of times is T, when T=0 or T is τ integral multiple, continues step (2) and carries out a point group operation,
Otherwise regardless of group, step (3) is leapt to.Based on practical experience, τ=3~6 are made.
(2) a point group operation is carried out to all particles, specifically includes following sub-step：
(2.1) all particles are sorted from big to small according to fitness value size, chooses the maximum particle of fitness value and make
For a Ge Zi group center；
(2.2) the maximum particle of fitness value is chosen in remaining particle, is calculated successively in the particle and each subgroup
The Euclidean distance of the heart.Particle i and particle j Euclidean distance dist (i, j) is defined as：：
Wherein, xi=(xi1,xi2,...,xi6) represent particle i position, xj=(xj1,xj2,...,xj6) represent particle j's
Position, i, j=1,2 ..., Ns.If the particle and the Euclidean distance at some subgroup center are less than radius r, by the grain
Son is classified as the subgroup where the subgroup center, and no longer calculates the Euclidean distance of the particle and remaining subgroup center；If
The particle and the distance at all subgroup centers are both greater than radius r, then the particle are set into a new subgroup center.According to search
The size in space, makes radius r=0.01~0.02.
(2.3) repeat step (2.2), until having handled all particles, then divide group to complete, and each subgroup center is the son
The maximum particle of fitness value in group.
(3) Evolving State of population is determined.With the renewal of particle, population undergo altogether four kinds of Evolving States, i.e. probe phase,
Development stage, polymerization phase and the phase of jumping out.Evolving State is represented below with the evolution factor.First, each particle and its are defined
The absolute value sum d of the distance at the subgroup center of place subgroupg：
Wherein, pig=(pig1,pig2,...,pig6) position at the subgroup center of subgroup where particle i.Secondly, definition is every
Individual particle and the absolute value D apart from sum at the subgroup center of subgroup where itg：
In the starting stage, D of evolvinggValue is slightly less than dg；In evolution convergence stage, DgValue is much smaller than dg；Jumping out rank
Section, DgValue is close to dg.Therefore, defining evolution factor delta is：
Evolution factor delta ∈ [0,1] is understood by definition.
(4) speed and the position of each particle are updated according to formula (8) (9)：
vid(T)=wvid(T-1)+c1·rand·(pid-xid(T-1))+c2·rand·(pigd-xid(T-1)) (8)
xid(T)=xid(T-1)+vid(T) (9)
Wherein, w is inertia weight；c1,c2For accelerated factor, c1=c2=2；Rand is the random number between 0 to 1；pi=
(pi1, pi2,...,pi6) it is particle xiHistory optimal location；pig=(pig1, pig2,...,pig6) be particle i where subgroup
Optimal particle position.
Inertia weight w is bigger, and the search capability of algorithm is stronger, and vice versa.In probe phase, it is desirable to which inertia weight is big by one
A bit, in the polymerization phase, it is desirable to which inertia weight is smaller.Because the evolution factor can reflect Evolving State, reference picture 4, inertia weight
Converted according to formula (10)：
After renewal, work as d=1, when 2,3, if xid<0, then make xid=0, if xid>1, then make xid=1；Work as d=4, when 5,6,
If xid<H, then make xid=H, if xid>zmax, then x is madeid=zmax。
(5) fitness function is updated.If the optimal particle p in the whole population searched at presentbest=(pbest1,
pbest2,...,pbest6) keep constant in continuous a iteration, then by pbestPosition recorded with fitness function value, and
To pbestPunished.It is specific to punish that operation is：As particle i and pbestDistance be less than radius r, then particle i fitness function
Value just becomes very little, sees formula (11)：
Wherein, fitnessTFor the fitness function of this time iteration, fitnessT-1Fitness during for last iteration
Function, i=1,2 ..., Ns, α is penalty factor, and the number of a very little makes α=0.The purpose for changing fitness function is to prevent
pbestA simply local optimum, too many particle attracts true so as to omit without going to explore other regions by this local optimum
Positive global optimum.After the operation of formula (11), when particle is close to pbestWhen, fitness function value will become very little,
Do not possess the ability again as global optimum, therefore particle will explore other feasible zones.The fitness function of change is improved
The search capability of algorithm.If the point of not newly-increased receiving punishment,
fitnessT=fitnessT-1 (12)
Meanwhile, a selection is also very crucial, the non-Complete Convergence of particle when a is too small in subgroup, pbestAlso it is not in the range of r
Optimal value, therefore a size is shown in formula (13)：
Wherein, T is current iteration number of times, TmaxFor maximum iteration,Represent to 0.1TmaxRound downwards.Formula
(13) implication is：40% before iteration, in order to prevent non-Complete Convergence, a value is very big, equal with current iteration number of times,
A value is set to the 10% of maximum iteration afterwards.
(6) fitness function value of each particle is calculated according to formula (11), (12), potential is calculatedWhen calling model module
In corresponding model.
(7) the position p of global optimum's particle is updatedbest=(pbest1,pbest2,...,pbest6), iteration count adds up, T=
T+1。
(8) repeat step (1)~(7), until reaching maximum iteration TmaxStop iteration, Tmax=100~2000.
Population global optimum particle pbest=(pbest1,pbest2,...,pbest6) where position be optimization after 3 moulds
Intend the quantity of electric charge and its position of electric charge, charge simulation the optimum layout is completed.
Optimization module sends the optimum layout result of charge simulation to analysis module, and analysis module utilizes Analogue charge method
Field domain electric field is analyzed, the automatic optimum analysis work of electric field is realized.
Above-described embodiment is used for illustrating the present invention, rather than limits the invention, the present invention spirit and
In scope of the claims, any modifications and changes made to the present invention both fall within protection scope of the present invention.
Claims (1)
1. a kind of adaptive electric field automatic analysis system, it is characterised in that：The electric field automatic analysis system is by model module, excellent
Change module to constitute with the part of analysis module three, model module stores various preferable charge models and such as puts electric charge and line charge week
The Electric Field Distribution situation and calculation enclosed, optimization module are optimized to the quantity of electric charge of charge simulation with position, analysis module
Field domain electric field is analyzed according to charge simulation；Wherein：
Optimization module is distributed in z-axis, z ∈ [0, z in n charge simulation of field domain disposed outside to be analyzedmax], zmaxFor can
Arrange the upper limit of distance.Variable to be optimized is the electricity q of this n charge simulationkAnd its position zk, k=1,2 ..., n.Optimization
Purpose is that the electric field for making charge simulation be produced in field domain is identical with the electric field that electrode surface electric charge is produced, in order to follow-up electricity
Field is automatically analyzed.
Then, initialization population scale is NsPopulation, random generation dimension for 2n particle i initial position xi=(xi1,
xi2,...,xi(2n)) and initial velocity vi=(vi1,vi2,...,vi(2n)), i=1,2 ..., Ns.Dimension variable d, d=1 are defined,
2,...,2n.Work as d=1, during 2 ..., n, xidRepresent the electricity of d-th of charge simulation, xid∈ [0,1], vid∈[-1,1]；Work as d
When=n+1, n+2 ..., 2n, xidRepresent the position z of the d-n electric charged-n, xid∈[0,zmax], vid∈[-zmax,zmax].Kind
Group's scale Ns=300~600.
Electrode surface has check point M, in order that potential and the known potential of electrode surface that charge simulation is produced to check point
Identical, the object function of problem is formula (1)：
Wherein,The potential that all charge simulations are produced in m-th of check point is represented, during specific calculating in calling model module
Model.Represent potential known to electrode surface.F >=0, the theoretical value 0 of object function.
Fitness function fitness is constructed, formula (2) is seen：
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Wherein, f is object function.
The positional information of particle after initialization is substituted into formula (2), initial fitness function value is obtained.Fitness function value maximum
Particle is global optimum's particle, and its position is pbest=(pbest1,pbest2,...,pbest(2n)).Remember fitnessT for the T times repeatedly
For when fitness function, T is iteration count, fitness when initial0=fitness.Then it is iterated by the following method,
Iteration count T=0 when initial：
(1) current iteration is counted as T, when T=0 or T is τ integral multiple, continues step (2) and carries out a point group operation, otherwise not
Divide group, leap to step (3).τ=3~6.
(2) a point group operation is carried out to all particles, specifically includes following sub-step：
(2.1) all particles are sorted from big to small according to fitness value size, chooses the maximum particle of fitness value and be used as one
Ge Zi group center；
(2.2) the maximum particle of fitness value is chosen in remaining particle, the particle and each subgroup center are calculated successively
Euclidean distance.Particle i and particle j Euclidean distance dist (i, j) is defined as：
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The maximum particle of fitness value.
(3) Evolving State of population is determined.First, the absolute of each particle and the distance at the subgroup center of its place subgroup is defined
It is worth sum dg：
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Wherein, pig=(pig1,pig2,...,pig(2n)) position at the subgroup center of subgroup where particle i.Secondly, definition is each
Particle and the absolute value D apart from sum at the subgroup center of subgroup where itg：
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<mo>)</mo>
</mrow>
</mrow>
Defining evolution factor delta is：
<mrow>
<mi>&delta;</mi>
<mo>=</mo>
<mfrac>
<msub>
<mi>D</mi>
<mi>g</mi>
</msub>
<msub>
<mi>d</mi>
<mi>g</mi>
</msub>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>6</mn>
<mo>)</mo>
</mrow>
</mrow>
Evolution factor delta ∈ [0,1] is understood by definition.
(4) speed and the position of each particle are updated according to formula (7) (8)：
vid(T)=wvid(T-1)+c1·rand·(pid-xid(T-1))+c2·rand·(pigd-xid(T-1)) (7)
xid(T)=xid(T-1)+vid(T) (8)
Wherein, w is inertia weight；c1,c2For accelerated factor, c1=c2=2；Rand is the random number between 0 to 1；pi=(pi1,
pi2,...,pi(2n)) it is particle xiHistory optimal location；pig=(pig1, pig2,...,pig(2n)) be particle i where subgroup
Optimal particle position.Inertia weight is converted according to formula (9)：
<mrow>
<mi>w</mi>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mn>1</mn>
<mo>+</mo>
<mn>1.5</mn>
<msup>
<mi>e</mi>
<mrow>
<mo>-</mo>
<mn>2.6</mn>
<mi>&delta;</mi>
</mrow>
</msup>
</mrow>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>9</mn>
<mo>)</mo>
</mrow>
</mrow>
After renewal, work as d=1, during 2 ..., n, if xid<0, then make xid=0, if xid>1, then make xid=1；Work as d=n+1, n+
During 2 ..., 2n, if xid<0, then make xid=0, if xid>zmax, then x is madeid=zmax。
(5) fitness function is updated.If the optimal particle p in the whole population searched at presentbest=(pbest1,pbest2,...,
pbest(2n)) keep constant in continuous a iteration, then by pbestPosition recorded with fitness function value, and to pbest
Punished.It is specific to punish that operation is：As particle i and pbestDistance be less than radius r, then particle i fitness function value is just
Become very little, see formula (10)：
<mrow>
<msup>
<mi>fitness</mi>
<mi>T</mi>
</msup>
<mo>=</mo>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mi>&alpha;</mi>
</mtd>
<mtd>
<mrow>
<mi>i</mi>
<mi>f</mi>
</mrow>
</mtd>
<mtd>
<mrow>
<msqrt>
<mrow>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>d</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mrow>
<mn>2</mn>
<mi>n</mi>
</mrow>
</munderover>
<msup>
<mrow>
<mo>(</mo>
<msub>
<mi>p</mi>
<mrow>
<mi>b</mi>
<mi>e</mi>
<mi>s</mi>
<mi>t</mi>
<mi>d</mi>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>x</mi>
<mrow>
<mi>i</mi>
<mi>d</mi>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</msqrt>
<mo>&le;</mo>
<mi>r</mi>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msup>
<mi>fitness</mi>
<mrow>
<mi>T</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msup>
</mrow>
</mtd>
<mtd>
<mrow>
<mi>i</mi>
<mi>f</mi>
</mrow>
</mtd>
<mtd>
<mrow>
<msqrt>
<mrow>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>d</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mrow>
<mn>2</mn>
<mi>n</mi>
</mrow>
</munderover>
<msup>
<mrow>
<mo>(</mo>
<msub>
<mi>p</mi>
<mrow>
<mi>b</mi>
<mi>e</mi>
<mi>s</mi>
<mi>t</mi>
<mi>d</mi>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>x</mi>
<mrow>
<mi>i</mi>
<mi>d</mi>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</msqrt>
<mo>></mo>
<mi>r</mi>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>10</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein, fitnessTFor the fitness function of this time iteration, fitnessT-1Fitness function during for last iteration,
I=1,2 ..., Ns, α is penalty factor, makes α=0.If the point of not newly-increased receiving punishment,：
fitnessT=fitnessT-1 (11)
A size is shown in formula (12)：
Wherein, T is current iteration number of times, TmaxFor maximum iteration,Represent to 0.1TmaxRound downwards.
(6) fitness function value of each particle is calculated according to formula (10), (11), potential is calculatedWhen calling model module in it is right
The model answered.
(7) the position p of global optimum's particle is updatedbest=(pbest1,pbest2,...,pbest(2n)), iteration count adds up, T=T+
1。
(8) repeat step (1)~(7), until reaching maximum iteration TmaxStop iteration, Tmax=100~2000.
Population global optimum particle pbest=(pbest1,pbest2,...,pbest(2n)) where position be that n simulation after optimization is electric
The quantity of electric charge of lotus and its position, charge simulation the optimum layout are completed.
Optimization module sends the optimum layout result of charge simulation to analysis module, and analysis module is analyzed using Analogue charge method
Field domain electric field, realizes the automatic optimum analysis work of electric field.
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