CN110427726A - The particle group optimizing Analogue charge method that labyrinth power frequency electric field calculates - Google Patents
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Abstract
The present invention relates to the particle group optimizing Analogue charge methods that a kind of labyrinth power frequency electric field calculates, and belong to electrical engineering technical field.The particle group optimizing Analogue charge method following steps that labyrinth power frequency electric field calculates: S1: traditional Optimized Simulated charge method CSM；S2: particle swarm optimization algorithm PSO；S3: particle group optimizing Analogue charge method PSO-CSM.When this Optimized Simulated charge method solution charged facility is complex-shaped or calculation scale is larger, the problem that Analogue charge method is difficult to find that relatively reasonable charge simulation arrangement is used alone.And continuous operation result is basicly stable, can keep higher optimum level, has preferable robustness.
Description
Technical field
The invention belongs to electrical engineering technical fields, are related to a kind of particle group optimizing mould that labyrinth power frequency electric field calculates
Quasi- charge method.
Background technique
With the extension in city, 500kV project of transmitting and converting electricity becomes closer to public activity region.This super-pressure facility week
The power frequency electric field distribution enclosed should not be underestimated.The calculating of super-pressure power frequency electric field often uses Analogue charge method (Charge
Simulation Method, CSM).Analogue charge method principle is simple, convenient for programming, computational accuracy with higher.But In
The key technology of the type of charge simulation, position, quantity is reasonably determined using upper, it is related to the experience of reckoner, due to people
Different experience makes Analogue charge method be difficult to realize high-precision numerical analysis.It is artificial past especially when the shape of electrode is complex
It is past to be difficult to reasonable Arrangement charge simulation.
Summary of the invention
In view of this, the purpose of the present invention is to provide the particle group optimizing simulations that a kind of labyrinth power frequency electric field calculates
Charge method, when solution charged facility is complex-shaped or calculation scale is larger, exclusive use Analogue charge method, which is difficult to find that, more to be closed
The problem of the charge simulation arrangement of reason.
In order to achieve the above objectives, the invention provides the following technical scheme:
Labyrinth power frequency electric field calculate particle group optimizing Analogue charge method, the charge method the following steps are included:
S1: Analogue charge method；
S2: particle swarm optimization algorithm；
S3: particle group optimizing Analogue charge method.
Further, the step S1 specifically:
If single uniform dielectric internal electric field solves:
1. n charge simulation Q is arranged except zoningj, j=1,2, n；
2. in the electrode surface of known surface potential value, setting quantity n match point M identical with charge simulation quantityi, i
=1,2, n takes and arranges perpendicular to electrode surface, the potential value of each match pointI=1,2, n is equal to electricity
Pole surface current potential；
3. corresponding to each match point M according to principle of stackingi, the electricity established by the charge simulation set is listed one by one
Azimuth equation expression formula is
In formula, PijIndicate the potential value that j-th of unit charge simulation generates on i-th of match point, the referred to as coefficient of potential；
The matrix form of above formula equation group is
4. solving equations obtain charge simulation magnitude [Q]；
5. certain amount checkpoint-is separately taken often to take the middle position of two neighbor points at electrode surface, it is calculated
Potential value, compared with known potential, if the two absolute value differences are less than setting value, then it is assumed that 6. arrangement effectively, goes to step, if
It is greater than the set value, then needs adjustment charge simulation state and parameter and return step is 1., until meeting computational accuracy requirement；
6. being calculated according to the charge simulation discrete solution [Q] finally acquired by the formula that charge calculates electric field strength
The current potential or electric field strength of any site.
Further, the step S2 specifically:
The random initializtion a group particle first in variable feasible zone, wherein one of each particle representing optimized problem
Potential solution uses position, three speed, fitness value index characterization particle states respectively；Particle superiority and inferiority is characterized with fitness value, is fitted
Answering angle value height to represent, particle is more excellent, i.e., close to Optimization goal, fitness value depends on set fitness function；Particle
Moving every time in solution space is an iteration, and the preferably solution currently itself encountered is assigned to individual extreme value PbestAnd remember,
The P of all particlesbestBest by comparing, is assigned to group extreme value G by valuebest, particle individual is by tracking individual extreme value
PbestPosition group be value GbestPosition update itself speed and position, and every time after iteration, and will be updated a Pbest
And Gbest, until reaching termination condition.
Further, the step S3 specifically:
Particle swarm algorithm generates the initialization population including position parameter particle and quantity of electric charge parameter particle, by each grain
Numerical value is delivered separately to charge simulation position and the quantity of electric charge in Analogue charge method in son；Analogue charge method is first by particle charging amount
Form this Qn×1Matrix value then executes coefficient of potential matrix and calculates, obtains this Pm×nMatrix value solves potential equation formula
Obtaining the particle, this is correspondingValue, and the error criterion for executing setting calculates, and error index value is returned
To particle swarm algorithm, particle swarm algorithm obtains this error criterion of the particle, relatively and judges whether to reach termination condition, if reaching
To termination condition, terminates iteration and export the particle numerical value；If not up to termination condition, speed and the position of the particle will be updated
It sets, and continues above-mentioned circulation；
S31: fitness function:
If configuring m match point altogether, current potential isThen minimization error fitness function f (x) is expressed as
In formula,Combined potential for charge simulation in i-th of match point, i=1,2,3...m；
S32: optimizing termination condition:
Particle swarm algorithm finds global optimum by the continuous iteration of group, and the optimizing termination condition of PSO-CSM is following 3
One of kind:
1. setting maximum number of iterations Tmax；
2. setting target fitness value fmin；
3. setting fitness value continuously unchanged maximum times Smax；
S32:PSO-CSM method realizes step:
1. algorithm parameter initializes, load initial population number, variable number, Studying factors, maximum number of iterations and mesh
Mark fitness value；
2. calculating coefficient of potential matrix and match point current potential by primary simulation Charge sites parameter for each particle；
3., by gained match point current potential, calculating average potential error, acquired results are fitness value for each particle
And remember；
4. the fitness value of individual extreme value and all paths passed by is compared for each particle, if individual extreme value is minimum
Then retain, is less than current individual extreme value if existing in the path passed by, which is assigned to individual extreme value；For whole
Particle compares itself all fitness value and group's extreme value, retains if group's extreme value minimum, if there are smaller for some particle
The value is assigned to group's extreme value by fitness value；
5. updating particle rapidity and position according to formula (1.1) and (1.2)；
Speed and location update formula are
In formula, d=1,2 ..., D, i=1,2 ..., n, k is current iteration number, VidFor particle rapidity, c1With c2To add
Velocity factor is positive number, r1With r2It is the random number between 0 to 1；The speed and position restriction of particle are in [- Vmax, Vmax]、[-
Xmax, Xmax]；
6. calculating each particle fitness value again；
Reach termination condition 7. checking whether, including reaches maximum number of iterations or reach target fitness value and adaptation
Continuously variation is less than given threshold to angle value several times, then termination algorithm and output current optimal charge simulation position and charge
Measure parameter；If not up to termination condition, 4. return step carries out next iteration, until reaching termination condition.
The beneficial effects of the present invention are: this Optimized Simulated charge method continuous operation result is basicly stable, can keep compared with
High optimum level has preferable robustness.
Other advantages, target and feature of the invention will be illustrated in the following description to a certain extent, and
And to a certain extent, based on will be apparent to those skilled in the art to investigating hereafter, Huo Zheke
To be instructed from the practice of the present invention.Target of the invention and other advantages can be realized by following specification and
It obtains.
Detailed description of the invention
To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention is made below in conjunction with attached drawing excellent
The detailed description of choosing, in which:
Fig. 1 is that schematic diagram is arranged in charge simulation；
Fig. 2 is that Analogue charge method solves electric field flow chart；
Fig. 3 is that particle updates schematic diagram；
Fig. 4 is particle swarm optimization algorithm flow chart；
Fig. 5 is Optimized Simulated charge method schematic diagram；
Fig. 6 is Optimized Simulated charge method flow chart；
Fig. 7 is ball-Slab and its Optimized Simulated charge arrangement schematic diagram；Fig. 7 (a) is ball-Slab schematic diagram；Fig. 7
It (b) is Optimized Simulated charge arrangement schematic diagram；
Fig. 8 is ball-plate Optimized Simulated charge method method iteration diagram；
Fig. 9 is equipotential diagram around sphere；
Figure 10 is error comparison.
Specific embodiment
Illustrate embodiments of the present invention below by way of specific specific example, those skilled in the art can be by this specification
Disclosed content understands other advantages and effect of the invention.The present invention can also be by way of a different and different embodiment
It is embodied or practiced, the various details in this specification can also be based on different viewpoints and application, without departing from the present invention
Spirit under carry out various modifications or alterations.It should be noted that diagram provided in following embodiment is only in a schematic way
Illustrate basic conception of the invention, in the absence of conflict, the feature in following embodiment and embodiment can be combined with each other.
Wherein, the drawings are for illustrative purposes only and are merely schematic diagrams, rather than pictorial diagram, should not be understood as to this
The limitation of invention；Embodiment in order to better illustrate the present invention, the certain components of attached drawing have omission, zoom in or out, not
Represent the size of actual product；It will be understood by those skilled in the art that certain known features and its explanation may be omitted and be in attached drawing
It is understood that.
The same or similar label correspond to the same or similar components in the attached drawing of the embodiment of the present invention；It is retouched in of the invention
In stating, it is to be understood that if there is the orientation or positional relationship of the instructions such as term " on ", "lower", "left", "right", "front", "rear"
To be based on the orientation or positional relationship shown in the drawings, be merely for convenience of description of the present invention and simplification of the description, rather than indicate or
It implies that signified device or element must have a particular orientation, be constructed and operated in a specific orientation, therefore is described in attached drawing
The term of positional relationship only for illustration, is not considered as limiting the invention, for the ordinary skill of this field
For personnel, the concrete meaning of above-mentioned term can be understood as the case may be.
Fig. 1~Figure 10 is please referred to, the particle group optimizing Analogue charge method calculated for a kind of labyrinth power frequency electric field.
1 particle group optimizing Analogue charge method
During application CSM, if electrode shape is complicated or calculation scale is larger, it tends to be difficult to find relatively reasonable
Arrangement.PSO is a kind of swarm intelligence algorithm of global optimizing, and easy to operate and iteration efficiency is higher, by it and simulation electricity
Lotus method combines and forms Optimized Simulated charge method (PSO-CSM), seeks best simulation Charge sites and magnitude automatically, improves power frequency electric
Flow Field Numerical computational efficiency and precision.
1.1 Analogue charge method
Analogue charge method is that the continuously distributed free charge of electrode surface is illusory except calculating field domain boundary with being located at
One group of limited amount, be arranged on certain geometric position, the charge simulation equivalence of discretization substitution.Simulation electricity based on acquisition
Lotus magnitude, can approximation acquire former continuously distributed charge at any point of space caused by electric field.Under normal circumstances, more
Charge simulation, computational accuracy are higher.Certainly, it is also desirable to which checkpoint is set repeatedly, and whether checking point current potential, which meets precision, is wanted
It asks.
Analogue charge method applying step is as follows:
As shown in Figure 1, it is assumed herein that single uniform dielectric internal electric field solve,
1. setting n is simulated (usually electrode interior and close to electrode surface at a certain distance from) except zoning
Charge Qj(j=1,2, n).
2. in the electrode surface of known surface potential value, setting quantity n match point M identical with charge simulation quantityi(i
=1,2, n), usually matching is taken arranges perpendicular to electrode surface, the potential value of each match pointDeng
In electrode surface current potential.
3. corresponding to each match point M according to principle of stackingi, the electricity established by the charge simulation set is listed one by one
Azimuth equation expression formula is
In formula, PijIt indicates the potential value that j-th of unit charge simulation generates on i-th of match point, is called current potential system
Number.The matrix form of above formula equation group is
4. solving equations obtain charge simulation magnitude [Q].
5. certain amount checkpoint-is separately taken often to take the middle position of two neighbor points at electrode surface, it is calculated
Potential value, compared with known potential, if the two absolute value differences are less than setting value, then it is assumed that arrangement effectively, goes to step 6, if
Setting value has been greater than it, then needs adjustment charge simulation state and parameter and has returned to step 1, until meets computational accuracy requirement.
6. the formula that can calculate electric field strength by charge calculates according to the charge simulation discrete solution [Q] finally acquired
The current potential or electric field strength of any site out.
It is as shown in Figure 2 that Analogue charge method solves electric field process.
1.2 particle swarm optimization algorithm
Particle swarm optimization algorithm belongs to Swarm Intelligent Algorithm, the research derived from people for birds predation.Bird
On the one hand class has the exploration to neighbouring food of oneself in search of food, on the other hand information sharing between individual, with
Just know the nearest distance of current distance food, it, will be towards apart from closer side after comparing oneself and current minimum distance
To adjustment and advance.In particle swarm algorithm, each particle is a potential solution of problem, and corresponding one by fitness function
The fitness value of decision.Particle flies searching " food " in feasible zone, and heading and distance then depend on its speed.And it is every
Complete flight, just the once speed of the state revision according to itself with other particles, towards the direction nearest apart from food into
Row flies next time.PSO has preferable advantage for the optimizing of Multi-variables optimum design problem.
Particle swarm algorithm random initializtion a group particle first in variable feasible zone, wherein each particle representing optimized
One potential solution of problem uses position, three speed, fitness value index characterization particle states respectively.It is characterized with fitness value
Particle superiority and inferiority, it is more excellent that fitness value height represents particle, i.e., close to Optimization goal, fitness value depends on set adaptation
Spend function.It is an iteration that particle moves every time in solution space, and the preferably solution currently itself encountered is assigned to individual extreme value
PbestAnd remember, the P of all particlesbestBest by comparing, is assigned to group extreme value G by valuebest, particle individual by with
Track individual extreme value PbestPosition group be value GbestPosition update itself speed and position, and every time after iteration, and can be more
A new PbestAnd Gbest, until reaching termination condition.
As shown in figure 3, being located in a D dimension space, group X=(X is formed by n particle1,X2,...,Xn), wherein i-th
A particle indicates the vector Xi=(x of D dimensioni1,xi2,...,xiD)T, i-th of particle position in D dimension space is represented, also generation
Table a potential solution.Each particle position X can be calculated according to objective functioniCorresponding fitness value.I-th of particle speed
Degree is Vi=(vi1,vi2,...,viD)T, individual extreme value Pi=(pi1,pi2,...,piD)T, group's extreme value is Pg=(pg1,
pg2,...,pgD)T。
Each iteration, particle can all check itself fitness value and current best fitness value, and adjust accordingly next
Leg speed degree, and then constantly correct self-position.Speed and location update formula are
In formula, ω be inertia weight coefficient, d=1,2 ..., D, i=1,2 ..., n, k be current iteration number, VidFor grain
Sub- speed, c1With c2It is positive number, r for acceleration factor1With r2It is the random number between 0 to 1.The speed and position restriction of particle
In [- Vmax, Vmax]、[-Xmax, Xmax]。
By taking Function Minimization optimization problem as an example, standard particle group's algorithm operational process is as follows:
1. initializing population, obtain population scale N (total number of particles), the initial position X of each particleid kWith initial speed
Spend Vid k, particle swarm algorithm, which may require that, provides particle feasible zone, and is initialized within the scope of feasible zone with random number way；
2. calculating the fitness function value F (i) of each particle according to fitness function F and remembering；
3. obtaining the fitness value of each particle, label particles position is current individual extreme value Pibest, relatively current more all
Particle fitness value, the best position of fitness value are assigned to group extreme value Pgbest。
4. reading PibestAnd Pgbest, particle rapidity and position are updated according to formula (1.1), (1.2)；
5. calculating the fitness function value F (i) of each particle according to fitness function F and remembering；
Operation is updated 6. executing: if F (i) < F (Pibest), then PibestIf=i, F (i) < F (Pgbest), then Pgbest=i；
7. judging whether to reach stopping criterion for iteration: F (Pgbest) reach predetermined minimum range, the maximum that reaches setting changes
Generation number, F (Pgbest) limit number in do not updated effectively, reaching any one termination condition then terminates, and is otherwise transferred to step
Suddenly 4..
Calculation process is as shown in Figure 4.
1.3 particle group optimizing Analogue charge methods
Analogue charge method is a kind of effective numerical method for calculating power transmission and transformation system power frequency electric field branch, its advantage is that former
It manages simple, applied widely, easy to accomplish.Meanwhile it there is also cloth point process that cumbersome, complicated electrode is difficult to rationally layouts
Disadvantage becomes it and carries out extensive, high precision electro field computation difficult point.Particle swarm algorithm is that ginseng is operated in current swarm intelligence algorithm
A kind of least optimization algorithm of number, has the characteristics that simple and easy, fast convergence rate.For function optimization, not find a function
Continuously differentiable has preferable advantage to multivariable, nonlinear thermal gradient.By particle swarm algorithm in conjunction with Analogue charge method,
The characteristics of being formed population charge simulation optimization (PSO-CSM), can use particle swarm algorithm fast automatic optimizing improves and passes
System Analogue charge method is being layouted and the problem in precision, under the premise of guaranteeing precision, with less charge simulation number, is obtained automatically
Take reasonable sensor distributing and charge simulation magnitude.
1.3.1 basic ideas
Traditional analog charge method is main to configure reasonable charge simulation type, number according to electrode sShape features when layouting
Amount, position carry out equivalent substitution to former field strength distribution, it is therefore intended that the electric field for exciting charge simulation approaches practical electric field as far as possible.
Therefore, the type, quantity of charge simulation, position, magnitude are actually an optimization problem.
1. from charge simulation construct different computation models versatility, programming convenience and improve optimization efficiency angle go out
Hair, this paper selected point charge are charge simulation type；
2. the quantity of charge simulation should be reduced as far as possible under the premise of ensuring to reach setup algorithm precision；
3. having the electrode of spatial symmetry for shape, position parameter dimension is reduced using symmetry, improves optimization
Efficiency；
4. choosing optimal charge simulation magnitude from the angle of optimization, reduces electrode surface and calculate point mean error, to mention
High computational accuracy.
Based on the above analysis, population charge simulation optimization algorithm is mainly from charge simulation position (3 dimensions) and magnitude
(1 dimension) carries out.For potential equation formula
To seek Optimized Simulated charge method high precision computation, the match point number m of configuration is much larger than charge simulation number
N, it is believed that contained traditional analog charge method all match point and checkpoint, traditional analog charge method can be saved in this way
The step of verifying repeatedly, optimization algorithm passes through [P] and [Q] of Automatic-searching best match, with the electricity of " well reproduced " all the points
Position
PSO-CSM method fundamental optimum thinking are as follows: it includes position parameter particle and quantity of electric charge parameter grain that particle swarm algorithm, which generates,
The initialization population of son, is delivered separately to charge simulation position and the quantity of electric charge in Analogue charge method for numerical value in each particle.
Particle charging amount is formed this Q first by Analogue charge methodn×1Matrix value then executes coefficient of potential matrix and calculates, obtains this
Pm×nMatrix value solves equation (1.3), and obtaining the particle, this is correspondingValue, and the error criterion for executing setting calculates,
Error index value is returned into particle swarm algorithm, particle swarm algorithm obtains this error criterion of the particle, relatively and judges whether
Reach termination condition, if reaching termination condition, terminates iteration and export the particle numerical value；If not up to termination condition, will update
The particle (speed and position), and continue above-mentioned circulation.Particle group optimizing Analogue charge method basic ideas are as shown in Figure 5.
1.3.2 fitness function
The fitness value of particle is the tool of particle swarm algorithm and Analogue charge method mutually " communication ", and fitness value is by adapting to
It spends function to generate, to evaluate the quality of particle, for minimization optimization problem, the more low then particle of fitness value is more excellent, instead
Particle it is poorer.Optimized Simulated charge method, as fitness function, is acquired using match point average potential error calculation function
Match point average potential error amount as fitness value.If configuring m match point altogether, current potential isThen minimization error adapts to
Degree function f (x) is represented by
In formula,For charge simulation i-th (i=1,2,3...m) a match point combined potential.
For better simply optimization aim, fitness function can directly choose objective function itself (such as match point current potential
Mean error)；It is more complicated for objective function itself, can there will be the sub- letter of one or more directly contacted with objective function
Number is with for fitness function (such as match point current potential).
1.3.3 optimizing termination condition
Particle swarm algorithm finds global optimum by the continuous iteration of group, and the optimizing termination condition of PSO-CSM is following 3
One of kind:
1. setting maximum number of iterations Tmax。
2. setting target fitness value fmin。
3. setting fitness value continuously unchanged maximum times Smax。
1.3.4 PSO-CSM method realizes step
In conclusion the Optimized Simulated charge method application flow based on population is as follows, algorithm flow chart is as shown in Figure 6.
1. algorithm parameter initializes, initial population number, variable number, Studying factors, maximum number of iterations, target are loaded
Fitness value etc..
2. calculating coefficient of potential matrix and match point current potential by primary simulation Charge sites parameter for each particle.
3., by gained match point current potential, calculating average potential error, acquired results are fitness value for each particle
And remember.
4. the fitness value of individual extreme value and all paths passed by is compared for each particle, if individual extreme value is minimum
Then retain, is less than current individual extreme value if existing in the path passed by, which is assigned to individual extreme value；For whole
Particle compares itself all fitness value and group's extreme value, retains if group's extreme value minimum, if there are smaller for some particle
The value is assigned to group's extreme value by fitness value.
5. updating particle rapidity and position according to formula (1.1) and (1.2).
6. calculating each particle fitness value again.
Reach termination condition 7. checking whether, including reaches maximum number of iterations or reach target fitness value and adaptation
Continuously variation is less than given threshold to angle value several times, then termination algorithm and output current optimal charge simulation position and charge
Measure parameter；If not up to termination condition, 4. return step carries out next iteration, until reaching termination condition.
2 PSO-CSM proof of algorithm
The feasibility of PSO-CSM optimization algorithm is verified to charge the calculating of ball-Slab field distribution.
2.1 balls-Slab
Such as Fig. 7 (a), the spherical isolated electrode of electrification is located on ground, and the centre of sphere is apart from ground distance h0=5cm, spherical electricity
Polar radius is r0=1cm is greatly horizontal plane, current potential 0V, and spherome surface current potential is equipotential surface,Using PSO-CSM
Optimized Simulated charge method calculates surrounding them field distribution.Such as Fig. 7 (b), rectangular coordinate system is established, with the center of circle in floor projection point
For coordinate origin, z-axis passes through the center of circle.
2.2 calculating and interpretation of result
Consider influence of the earth to sphere surrounding electric field, two simulation point charge q of random arrangement in ball in z-axis1(x1,
y1,z1)、q2(x2,y2,z2) electric field that ball electrode generates is simulated, spherome surface is uniformly arranged one group of match point.Set simulation point electricity
Lotus is to any point P (x, y, the z) current potential generated
Optimization algorithm using match point average potential error minimum as optimization aim, in order to obtain Optimized Simulated charge method compared with
High computational accuracy solution, the match point quantity of configuration are much larger than the quantity of charge simulation, and m=100 is arranged in spherome surface here
A match point.Constraint condition are as follows: simulation point charge, which necessarily is in, to be calculated outside field domain, i.e., needs in this example in z-axis and in sphere
It is internal；In addition, the quantity of electric charge cannot be infinitely great, therefore constitution optimization problem is
In formula,The sum of be superimposed for charge in the current potential of i-th of match point.
Optimized variable is { x }T=[q1,q2,z1,z2], optimization algorithm parameter configuration such as table 2.1, optimization algorithm iteration diagram is such as
Shown in Fig. 8, Optimized Simulated point charge optimal value such as table 2.2 is acquired.
2.1 PSO-CSM parameter configuration of table
The simulation point charge optimal value of table 2.2
Based on the above simulation point charge optimal value, it is as shown in Figure 9 to acquire current potential isogram around sphere.
To exclude computer accidentalia, the robustness of Optimized Simulated charge method method, continuous operation Optimized Simulated electricity are verified
As a result lotus method program 20 times counts such as table 2.3, it can be seen that continuous operation result is basicly stable, can keep higher optimization
It is horizontal, it was demonstrated that Optimized Simulated charge method has a preferable robustness.Error is compared as shown in table 2.4.
2.3 continuous operation of table, 20 suboptimization result
The comparison of 2.4 error of table
Traditional analog charge method and the verification point tolerance comparison of Optimized Simulated charge method are as shown in Figure 10.Uniformly choose sphere table
20, face match point calculates match point current potential and normal potential comparison such as table 2.5 using Optimized Simulated charge method.
The comparison of 2.5 error of table
Finally, it is stated that the above examples are only used to illustrate the technical scheme of the present invention and are not limiting, although referring to compared with
Good embodiment describes the invention in detail, those skilled in the art should understand that, it can be to skill of the invention
Art scheme is modified or replaced equivalently, and without departing from the objective and range of the technical program, should all be covered in the present invention
Scope of the claims in.
Claims (4)
1. the particle group optimizing Analogue charge method that labyrinth power frequency electric field calculates, it is characterised in that: the charge method includes following
Step:
S1: Optimized Simulated charge method CSM；
S2: particle swarm optimization algorithm PSO；
S3: particle group optimizing Analogue charge method PSO-CSM.
2. the particle group optimizing Analogue charge method that labyrinth power frequency electric field according to claim 1 calculates, feature exist
In: the step S1 specifically:
If single uniform dielectric internal electric field solves:
1. n charge simulation Q is arranged except zoningj, j=1,2, n；
2. in the electrode surface of known surface potential value, setting quantity n match point M identical with charge simulation quantityi, i=1,
2, n takes and arranges perpendicular to electrode surface, the potential value of each match pointI=1,2, n is equal to electrode table
Face current potential；
3. corresponding to each match point M according to principle of stackingi, the potential equation established by the charge simulation set is listed one by one
Expression formula is
In formula, PijIndicate the potential value that j-th of unit charge simulation generates on i-th of match point, the referred to as coefficient of potential；Above formula
The matrix form of equation group is
4. solving equations obtain charge simulation magnitude [Q]；
5. certain amount checkpoint-is separately taken often to take the middle position of two neighbor points at electrode surface, its current potential is calculated
Value, compared with known potential, if the two absolute value differences are less than setting value, then it is assumed that 6. arrangement effectively, goes to step, if more than
Setting value then needs adjustment charge simulation state and parameter and return step is 1., until meeting computational accuracy requirement；
6. being calculated arbitrarily according to the charge simulation discrete solution [Q] finally acquired by the formula that charge calculates electric field strength
The current potential or electric field strength of site.
3. the particle group optimizing Analogue charge method that labyrinth power frequency electric field according to claim 2 calculates, feature exist
In: the step S2 specifically:
The random initializtion a group particle first in variable feasible zone, wherein one of each particle representing optimized problem is potential
Solution uses position, three speed, fitness value index characterization particle states respectively；Particle superiority and inferiority, fitness are characterized with fitness value
It is more excellent that value height represents particle, i.e., close to Optimization goal, fitness value depends on set fitness function；Particle is can
It is an iteration that row solution space moves every time, and the preferably solution currently itself encountered is assigned to individual extreme value PbestAnd remember, own
The P of particlebestBest by comparing, is assigned to group extreme value G by valuebest, particle individual is by tracking individual extreme value Pbest's
Position group is value GbestPosition update itself speed and position, and every time after iteration, and will be updated a PbestWith
Gbest, until reaching termination condition.
4. the particle group optimizing Analogue charge method that labyrinth power frequency electric field according to claim 3 calculates, feature exist
In: the step S3 specifically:
Particle swarm algorithm generates the initialization population including position parameter particle and quantity of electric charge parameter particle, will be in each particle
Numerical value is delivered separately to charge simulation position and the quantity of electric charge in Analogue charge method；Analogue charge method first forms particle charging amount
This Qn×1Matrix value then executes coefficient of potential matrix and calculates, obtains this Pm×nMatrix value solves potential equation formula
Obtaining the particle, this is correspondingValue, and the error criterion for executing setting calculates, and error index value is returned to particle
Group's algorithm, particle swarm algorithm obtains this error criterion of the particle, relatively and judges whether to reach termination condition, if reaching termination
Condition terminates iteration and exports the particle numerical value；If not up to termination condition, speed and the position of the particle will be updated, and after
Continue above-mentioned circulation；
S31: fitness function:
If configuring m match point altogether, current potential isThen minimization error fitness function f (x) is expressed as
In formula,Combined potential for charge simulation in i-th of match point, i=1,2,3...m；
S32: optimizing termination condition:
Particle swarm algorithm finds global optimum by the continuous iteration of group, the optimizing termination condition of PSO-CSM be following 3 kinds it
One:
1. setting maximum number of iterations Tmax；
2. setting target fitness value fmin；
3. setting fitness value continuously unchanged maximum times Smax；
S32:PSO-CSM method realizes step:
1. algorithm parameter initializes, load initial population number, variable number, Studying factors, maximum number of iterations and target are suitable
Answer angle value；
2. calculating coefficient of potential matrix and match point current potential by primary simulation Charge sites parameter for each particle；
3. by gained match point current potential, calculating average potential error, acquired results are fitness value and remember for each particle
Recall；
4. comparing the fitness value of individual extreme value and all paths passed by for each particle, protected if individual extreme value minimum
It stays, is less than current individual extreme value if existing in the path passed by, which is assigned to individual extreme value；For whole grains
Son compares itself all fitness value and group's extreme value, retains if group's extreme value minimum, if there are smaller suitable for some particle
Angle value is answered, which is assigned to group's extreme value；
5. updating particle rapidity and position according to formula (1.1) and (1.2)；
Speed and location update formula are
In formula, d=1,2 ..., D, i=1,2 ..., n, k is current iteration number, VidFor particle rapidity, c1With c2For acceleration
The factor is positive number, r1With r2It is the random number between 0 to 1；The speed and position restriction of particle are in [- Vmax, Vmax]、[-Xmax,
Xmax]；
6. calculating each particle fitness value again；
Reach termination condition 7. checking whether, including reaches maximum number of iterations or reach target fitness value and fitness value
Continuously variation is less than given threshold several times, then termination algorithm and the current optimal charge simulation position of output and quantity of electric charge ginseng
Number；If not up to termination condition, 4. return step carries out next iteration, until reaching termination condition.
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