CN112287564B - Electrode array optimization method based on goblet sea squirt group algorithm - Google Patents

Electrode array optimization method based on goblet sea squirt group algorithm Download PDF

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CN112287564B
CN112287564B CN202011311093.1A CN202011311093A CN112287564B CN 112287564 B CN112287564 B CN 112287564B CN 202011311093 A CN202011311093 A CN 202011311093A CN 112287564 B CN112287564 B CN 112287564B
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蒋毅
许源
梁运华
刘功能
郭奉仁
李泽文
王梓糠
尹骏刚
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State Grid Corp of China SGCC
State Grid Hunan Electric Power Co Ltd
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Abstract

The invention discloses an electrode array optimization method based on a goblet sea squirt group algorithm, which comprises the steps of taking the set number of electrodes as the dimension of a search space of the goblet sea squirt group, taking the arrangement space of the electrode array as the set search space of the goblet sea squirt group, utilizing iteration of the goblet sea squirt group algorithm until the set target is met or the iteration reaches the set times, outputting the final food position of the goblet sea squirt group, and taking the final food position as the arrangement position of the electrode array to complete optimization. The electrode array optimization method based on the goblet sea squirt group algorithm has the advantages of simplicity, practicability, small calculated amount, high optimization speed, high efficiency and the like.

Description

Electrode array optimization method based on goblet sea squirt group algorithm
Technical Field
The invention relates to the technical field of electrode detection, in particular to an electrode array optimization method based on a goblet sea squirt group algorithm.
Background
Personnel such as overhaul, pretest of electric power trade work in the high-voltage field, often meet the situation of operation scope peripheral equipment live working, have the hidden danger that safe distance is not enough. The common near-electricity alarm device is difficult to accurately alarm in a complex electromagnetic environment. The near-electricity alarm device based on the multiple electrodes has the advantages of high spatial resolution of electric field signals, strong anti-interference capability and the like, and can directionally detect whether equipment is electrified or not through the electrode array, so that the problems of high false alarm rate and the like of a common near-electricity alarm device are solved.
The multi-electrode spatial distribution and excitation mode is the technical key of the near-electricity alarm device, and the near-electricity alarm device is preferably optimally designed by adopting an intelligent algorithm. Intelligent algorithms are widely used in the engineering field for the solution of optimization problems, in particular non-linear optimization problems. In recent years, intelligent algorithms are applied to various sensor array designs due to the efficiency advantage of solving the nonlinear optimization problem, and genetic algorithms, particle swarm algorithms and the like are widely applied. However, the optimization process for a complex electrode array model may take several hours or even longer, and the computational cost is extremely large.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide a simple and practical electrode array optimization method based on the goblet sea squirt group algorithm, which has the advantages of less calculation amount, high optimization speed and high efficiency.
In order to solve the technical problems, the technical scheme provided by the invention is as follows:
an electrode array optimization method based on a goblet sea squirt group algorithm is characterized in that a set electrode number is used as a dimension of a goblet sea squirt group search space, an electrode array arrangement space is used as a set search space of the goblet sea squirt group, iteration is performed by using the goblet sea squirt group algorithm until a set target is met or the iteration reaches a set number of times, a final food position of the goblet sea squirt group is output and is used as an arrangement position of an electrode array, and optimization is completed.
The process of utilizing the goblet sea squirt group algorithm to iterate until the set target is met comprises the following steps:
s1: initializing individual number N =3n +1 of the bottle sea squirt group, taking the electrode number as the dimension number D of the search space, and setting the iteration number T max (ii) a Initializing a population to
Figure BDA0002789862080000011
S2: calculating the fitness of each individual of the goblet sea squirt group, taking the individual with the highest fitness as food, and dividing the rest individuals into n pilots, n trackers and n backers;
s3: updating the pilot position as follows:
Figure BDA0002789862080000021
wherein the content of the first and second substances,
Figure BDA0002789862080000022
the location of the ith navigator bottle ascidian in the jth dimension, ub j And lb j Respectively a search upper limit and a search lower limit in a j-th dimension search space; f j Is the position of the food in the j-dimensional space, c 2 And c 3 Is the interval [0,1]Internally generated random numbers; parameter c 1 Is defined as: />
Figure BDA0002789862080000023
T is the current iteration number, T max Is the maximum iteration number;
s4: update tracker location as:
Figure BDA0002789862080000024
in the formula (I), the compound is shown in the specification,
Figure BDA0002789862080000025
for the location of the ith tracked individual goblet or ascidian in the jth dimension space, based on the location of the ith tracked individual goblet or ascidian in the jth dimension space>
Figure BDA0002789862080000026
Is the symbiotic quantity; b is a benefit parameter, and 1 or 2 is randomly selected; r is [0,1 ]]A random number of intervals;
s5: the rescuer location update is:
Figure BDA0002789862080000027
Figure BDA0002789862080000028
in the formula (I), the compound is shown in the specification,
Figure BDA0002789862080000029
the position of the ith person of the eschewed sea squirt in the jth dimension space is represented by t, which is the current iteration number; t is a unit of max Is the maximum number of iterations;
s6: repeating the steps S2 to S5 until the iteration number reaches T max Or the food suitability value reaches a set termination threshold.
When updating the position of the ith tracker goblet ascidian individual in the jth dimension space, the position of the ith tracker goblet ascidian individual before updating in the jth dimension space is stored as
Figure BDA00027898620800000210
And decides->
Figure BDA00027898620800000211
And &>
Figure BDA00027898620800000212
When the degree of fitness is good or bad>
Figure BDA00027898620800000213
Is superior to->
Figure BDA00027898620800000214
Then, the location of the ith tracker goblet alone in the jth dimension space is updated to be ^ based>
Figure BDA00027898620800000215
The individual of goblet sea squirt group also includes a plurality of the backups, the position of the backups is updated as follows:
Figure BDA00027898620800000216
Figure BDA00027898620800000217
in the formula (I), the compound is shown in the specification,
Figure BDA0002789862080000031
the position of the ith person of the aid goblet ascidian in the jth dimension space, and t is the current iteration number; t is max Is the maximum number of iterations.
The arrangement space of the target electrode array is a concentric electrode array, the target is set to be the minimum peak sidelobe level, and the individual fitness of each goblet ascidian is obtained by the following operation:
Figure BDA0002789862080000032
Figure BDA0002789862080000033
where theta is the angle from the normal,
Figure BDA0002789862080000034
is the phase shift of the electrode, j is the imaginary symbol, F max Main lobe peak, N, for concentric circular electrode array y Number of rings arranged for electrodes, N x Is the number of electrodes on the ring, r m Refers to the radius of the nth electrode (n, m) on the mth ring, and>
Figure BDA0002789862080000035
the feeding amplitude is that the electrodes I (n, m) are excited together, and psi (n, m) is the included angle between the electrode and the x axis.
The target electrode array arrangement space is a rectangular electrode array, the target is set to be the minimum peak sidelobe level, and the individual fitness of each goblet ascidian is obtained by the following operation:
Figure BDA0002789862080000036
Figure BDA0002789862080000037
where theta is the angle from the normal,
Figure BDA0002789862080000038
is the phase shift of the electrode, j is the imaginary symbol, F max Is the main lobe peak value of the concentric circle electrode array, N y Number of rings arranged for electrodes, N x Is the number of electrodes on the ring, r m Refers to the radius of the nth electrode (n, m) on the mth circular ring, and/or the device>
Figure BDA0002789862080000039
p mx As position of the electrode in the x direction, p my The position of the electrode in the y direction, and the feeding amplitude is I (n, m), and the electrodes are excited simultaneously.
Compared with the prior art, the invention has the advantages that:
the invention discloses an electrode array optimization method based on a goblet sea squirt group algorithm, which is characterized in that the set electrode number is used as the dimension of a search space of the goblet sea squirt group, the electrode array arrangement space is used as the set search space of the goblet sea squirt group, iteration is carried out by utilizing the goblet sea squirt group algorithm until the set target is met or the iteration reaches the set times, the final food position of the goblet sea squirt group is output and is used as the arrangement position of an electrode array, and the optimization is completed. The optimization method has the advantages of simple steps, easiness in realization, capability of meeting the requirement on the solving precision, high convergence speed and no possibility of trapping the exploration range into the local optimal solution, so that the required calculated amount is greatly reduced, the time required by the optimization process is shortened, the performance of the electrode array is improved, and the time and the cost are saved.
Drawings
FIG. 1 is a diagram of a concentric electrode array obtained by the electrode array optimization method based on the goblet sea squirt group algorithm according to the present invention;
fig. 2 is a diagram of the detection obtained by the electrode array shown in fig. 1.
Detailed Description
In order to facilitate an understanding of the invention, reference will now be made in detail to the present preferred embodiments of the invention, examples of which are illustrated in the accompanying drawings, and the scope of the invention is not limited to the following specific embodiments.
Example (b):
in the method for optimizing the electrode array based on the goblet ascidian group algorithm of this embodiment, the set number of electrodes is used as the dimension of the search space of the goblet ascidian group, the arrangement space of the electrode array is used as the set search space of the goblet ascidian group, iteration is performed by using the goblet ascidian group algorithm until the set target is met or the iteration reaches the set number of times, the final food position of the goblet ascidian group is output and used as the arrangement position of the electrode array, and the optimization is completed. The optimization method has simple steps and is easy to realize, the solving precision can meet the requirement, the convergence speed is high, and the exploration range cannot fall into the local optimal solution, so that the required calculated amount is greatly reduced, the time required by the optimization process is shortened, and the time and the cost are saved while the performance of the electrode array is improved.
In this embodiment, the concentric electrode array is optimized to constrain the main lobe area of the directional diagram as
Figure BDA0002789862080000041
The target is set to minimize the peak sidelobe level, the initial target value is set to-15 dB, and if the set target value is met before the maximum number of iterations is reached, the target value is lowered by 0.5dB.
The process of utilizing the goblet sea squirt group algorithm to iterate until the set target is met comprises the following steps:
s1: initialization goblet sea squirtThe number of individuals of the group N =3n +1, N is a natural number, N generally ranges from 50 to 100, 61 in this embodiment, the number of electrodes is taken as the dimension number D of the search space, 24 in this embodiment, and the iteration number T is set max =500; initializing a population to
Figure BDA0002789862080000042
Initializing coordinates of each electrode in population individuals
Figure BDA0002789862080000043
Wherein theta is [0,2 pi ]]And a plurality of electrodes are arranged along the three concentric circular ring arrays, and the sub-distance between adjacent electrodes on the same ring is larger than a set distance.
S2: calculating the fitness of each individual of the goblet sea squirt group:
Figure BDA0002789862080000044
Figure BDA0002789862080000045
where θ is the angle from the normal,
Figure BDA0002789862080000051
is the phase shift of the electrode, j is the imaginary symbol, F max Is the main lobe peak value of the concentric circle electrode array, N y Number of rings arranged for electrodes, N x Is the number of electrodes on the ring, r m Refers to the radius of the nth electrode (n, m) on the mth circular ring, and/or the device>
Figure BDA0002789862080000052
The feeding amplitude is that all electrodes I (n, m) are excited simultaneously, psi (n, m) is the included angle between the electrodes and the x axis;
taking the individual with the maximum fitness as food, and dividing the rest individuals into n pilots, n trackers and n back-up persons;
s3: updating the pilot position as follows:
Figure BDA0002789862080000053
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0002789862080000054
the position of the ith navigator goblet ascidian individual in the jth dimension, ub j And lb j Respectively as the upper search limit and the lower search limit in the j-th search space, and the coordinate of the search space can be based on ^ and ^>
Figure BDA0002789862080000055
Obtaining m =3 when obtaining an upper limit and m =1 when obtaining a lower limit; f j Is the position of the food in the j-dimensional space, c 2 And c 3 Is the interval [0,1]Internally generated random numbers; parameter c 1 Is defined as: />
Figure BDA0002789862080000056
T is the current iteration number, T max Is the maximum iteration number;
s4: updating the tracker position as follows:
Figure BDA0002789862080000057
in the formula (I), the compound is shown in the specification,
Figure BDA0002789862080000058
for the location of the ith tracked individual Eschaea goblet in the jth dimension space, the device>
Figure BDA0002789862080000059
Is the symbiotic quantity; b is a benefit parameter, and 1 or 2 is randomly selected; r is [0,1 ]]A random number of intervals; when the position of the ith tracker goblet ascidian individual in the jth dimension space is updated, the position of the ith tracker goblet ascidian individual before updating is stored as ^ or ^ in the jth dimension space>
Figure BDA00027898620800000510
And decides->
Figure BDA00027898620800000511
And &>
Figure BDA00027898620800000512
The degree of fitness is good or bad when>
Figure BDA00027898620800000513
Is superior to->
Figure BDA00027898620800000514
Then, the location of the ith tracker goblet alone in the jth dimension space is updated to be ^ based>
Figure BDA00027898620800000515
S5: the rescuer location update is:
Figure BDA00027898620800000516
Figure BDA0002789862080000061
in the formula (I), the compound is shown in the specification,
Figure BDA0002789862080000062
the position of the ith person of the eschewed sea squirt in the jth dimension space is represented by t, which is the current iteration number; t is max Is the maximum number of iterations. The introduction of cosine function by the person behind the seat makes the person behind the seat more flexible, adds 1 to make the overall distance of updating position increase, and because the maximum value of cosine function is 1, will not make the distance too big, thus, make the person behind the seat global search and local search balanced. The pilot, the follower and the back-up person are beneficial to improving the exploration performance of the algorithm and the ability of jumping out of local optimum in the later period to a certain extent.
S6: repeating the steps S2 to S5 until the iteration number reaches T max Or the food suitability value reaches a set termination threshold.
And then, the food position can be output as an electrode arrangement position, and the electrode array can meet the target requirement by arranging the electrodes according to the position. Fig. 1 is the optimized electrode array pattern, from which the detection map shown in fig. 2 is obtained, with a peak side lobe level of-17.3 dB and a narrower main lobe.
In this embodiment, when the target electrode array arrangement space is a rectangular electrode array, the target is set to minimize the peak sidelobe level, and the fitness of each individual ascidian is obtained by the following operation:
Figure BDA0002789862080000063
Figure BDA0002789862080000064
where θ is the angle from the normal,
Figure BDA0002789862080000065
is the phase shift of the electrode, j is the imaginary symbol, F max Is the main lobe peak value of the concentric circle electrode array, N y Number of rings arranged for electrodes, N x Is the number of electrodes on the ring, r m Refers to the radius of the nth electrode (n, m) on the mth ring, and>
Figure BDA0002789862080000066
p mx as position of the electrode in the x-direction, p my The position of the electrode in the y direction, and the feeding amplitude is I (n, m), and the electrodes are excited simultaneously.
The above description is only a preferred embodiment of the present invention, and the protection scope of the present invention is not limited to the above-described embodiments. It should be apparent to those skilled in the art that modifications and variations can be made without departing from the technical spirit of the present invention.

Claims (4)

1. An electrode array optimization method based on a goblet sea squirt group algorithm is characterized in that: the method comprises the following steps of taking the set number of electrodes as the dimension of a searching space of a goblet sea squirt group, taking an electrode array arrangement space as the set searching space of the goblet sea squirt group, iterating by using a goblet sea squirt group algorithm until a set target is met or iteration reaches a set number of times, outputting the final food position of the goblet sea squirt group, and taking the final food position as the arrangement position of an electrode array to complete optimization;
the process of iteration by using the goblet sea squirt group algorithm until the set target is met comprises the following steps:
s1: initializing individual number N =3n +1 of the bottle sea squirt group, taking the electrode number as the dimension number D of the search space, and setting the iteration number T max (ii) a Initializing a population to
Figure FDA0003910066490000011
S2: calculating the fitness of each individual of the goblet sea squirt group, taking the individual with the highest fitness as food, and equally dividing the rest individuals into n pilots, n trackers and n backups;
s3: updating the pilot position as follows:
Figure FDA0003910066490000012
wherein the content of the first and second substances,
Figure FDA0003910066490000013
the position of the ith navigator goblet ascidian individual in the jth dimension, ub j And lb j Respectively representing a search upper limit and a search lower limit in a j-dimension search space; f j Is the position of the food in the j-dimensional space, c 2 And c 3 Is the interval [0,1]Internally generated random numbers; parameter c 1 Is defined as: />
Figure FDA0003910066490000014
T is the current number of iterations, T max Is the maximum iteration number;
s4: updating the tracker position as follows:
Figure FDA0003910066490000015
in the formula (I), the compound is shown in the specification,
Figure FDA0003910066490000016
for the location of the ith tracked individual Eschaea goblet in the jth dimension space, the device>
Figure FDA0003910066490000017
Is the symbiotic quantity; b is a benefit parameter, and 1 or 2 is randomly selected; r is [0,1 ]]A random number of intervals;
s5: the rescuer location update is:
Figure FDA0003910066490000018
Figure FDA0003910066490000019
in the formula (I), the compound is shown in the specification,
Figure FDA00039100664900000110
the position of the ith person of the aid goblet ascidian in the jth dimension space, and t is the current iteration number; t is a unit of max Is the maximum iteration number;
s6: repeating the steps S2 to S5 until the iteration number reaches T max Or the food suitability value reaches a set termination threshold.
2. The method of claim 1, wherein the method comprises the following steps: updating the jth dimension of the ith tracker-only goblet ascidian individualsWhen the space position is stored, the position of the ith tracker goblet sea squirt individual before updating in the jth dimension space is stored as
Figure FDA0003910066490000021
And decides->
Figure FDA0003910066490000022
And &>
Figure FDA0003910066490000023
The degree of fitness is good or bad when>
Figure FDA0003910066490000024
Is superior to->
Figure FDA0003910066490000025
Then, the location of the ith tracker goblet alone in the jth dimension space is updated to be ^ based>
Figure FDA0003910066490000026
3. The method of claim 1, wherein the method comprises: the arrangement space of the target electrode array is a concentric circle electrode array, the target is set to be a minimized peak sidelobe level, and the individual fitness of each goblet ascidian is obtained by the following operation:
Figure FDA0003910066490000027
Figure FDA0003910066490000028
where theta is the angle from the normal,
Figure FDA0003910066490000029
is the phase shift of the electrode, j is the imaginary symbol, F max Is the main lobe peak value of the concentric circle electrode array, N y Number of rings arranged for electrodes, N x Is the number of electrodes on the ring, r m Refers to the radius of the nth electrode (n, m) on the mth ring, and>
Figure FDA00039100664900000210
the feeding amplitude is that the electrodes I (n, m) are excited together, and psi (n, m) is the included angle between the electrode and the x axis.
4. The method of claim 1, wherein the method comprises: the target electrode array arrangement space is a rectangular electrode array, the target is set to be the minimum peak sidelobe level, and the individual fitness of each goblet ascidian is obtained by the following operation:
Figure FDA00039100664900000211
Figure FDA00039100664900000212
where theta is the angle from the normal,
Figure FDA00039100664900000213
is the phase shift of the electrode, j is the imaginary symbol, F max Main lobe peak, N, for concentric circular electrode array y Number of rings arranged for electrodes, N x Is the number of electrodes on the ring, r m Refers to the radius of the nth electrode (n, m) on the mth ring, and>
Figure FDA00039100664900000214
p mx as position of the electrode in the x direction, p my Is the position of the electrode in the y direction, and the feeding amplitude is I (n, m)And (4) exciting. />
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KR20180065472A (en) * 2016-12-08 2018-06-18 한국항공우주연구원 Apparatus and method for pattern synthesis of antenna array
CN109873810A (en) * 2019-01-14 2019-06-11 湖北工业大学 A kind of phishing detectin method based on cup ascidian group's algorithm support vector machines
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