CN112287564A - Electrode array optimization method based on goblet sea squirt group algorithm - Google Patents

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 salps swarm algorithm

technical field

The invention relates to the technical field of electrode detection, in particular to an electrode array optimization method based on a salps swarm algorithm.

Background technique

The maintenance, pre-test and other personnel in the power industry work in high-voltage fields, and often encounter the situation that the surrounding equipment is running under power, and there is a hidden danger of insufficient safety distance. It is difficult for ordinary near-electrical alarm devices to accurately alarm in complex electromagnetic environments. The multi-electrode-based near-electrical alarm device has the advantages of high spatial resolution of electric field signals and strong anti-interference ability. It can detect whether the equipment is charged through the electrode array, so as to solve the problem of high false alarm rate of ordinary near-electrical alarm devices.

The multi-electrode spatial distribution and excitation mode are the technical keys of the near-electrical alarm device, and an intelligent algorithm should be used to optimize the design. Intelligent algorithms are widely used in engineering to solve optimization problems, especially nonlinear optimization problems. In recent years, intelligent algorithms have been widely used in the design of various sensor arrays due to their efficiency advantages in solving nonlinear optimization problems, such as genetic algorithms and particle swarm optimization. However, the optimization process of a complex electrode array model can take hours or even longer, and the computational cost is extremely high.

SUMMARY OF THE INVENTION

The technical problem to be solved by the present invention is to overcome the deficiencies of the prior art, and to provide a simple and practical electrode array optimization method based on the salps swarm algorithm, which is simple and practical, has a small amount of calculation, and has fast optimization speed and high efficiency.

In order to solve the above-mentioned technical problems, the technical scheme proposed by the present invention is:

An electrode array optimization method based on the salp swarm algorithm, the set number of electrodes is used as the dimension of the salp group search space, the electrode array arrangement space is used as the set search space of the salp group, and the salp swarm algorithm is used to iterate until it satisfies Set a target or iterate to a set number of times, output the final food position of the salps group, and use it as the arrangement position of the electrode array to complete the optimization.

The process of iterating using the salps swarm algorithm until the set goal is met includes the following steps:

S1: Initialize the number of individuals of the salps group N=3n+1, n is a natural number, take the number of electrodes as the dimension D of the search space, and set the number of iterations T _max ; the initialization population is

S2: Calculate the fitness of each individual in the sea squirt group, take the individual with the greatest fitness as the food, and divide the rest of the individuals into n leaders, n trackers, and n supporters;

S3: Update the navigator position to:

为第i只领航者樽海鞘个体在第j维空间的位置，ub_j与lb_j分别为在第j维搜索空间的搜索上限与搜索下限；F_j为食物在第j维空间的位置，c₂与c₃为区间[0,1]内产生的随机数；参数c₁的定义为：

t为当前迭代次数，T_max为最大迭代次数；in,

is the position of the i-th pilot salp individual in the j-th dimension space, ub _j and lb _j are the search upper limit and search limit in the j-th dimension search space, respectively; F _j is the position of the food in the j-th dimension space, c ₂ and c ₃ are random numbers generated in the interval [0,1]; the definition of parameter c ₁ is:

t is the current number of iterations, and _Tmax is the maximum number of iterations;

S4: Update tracker location to:

为第i只追踪者樽海鞘个体在第j维空间的位置，

为共生量；B为受益参数，随机选取1或2；r为[0,1]区间的随机数；In the formula,

is the position of the i-th tracker salp individual in the j-th dimension space,

is the symbiotic amount; B is the benefit parameter, 1 or 2 is randomly selected; r is a random number in the [0,1] interval;

S5: Supporter location updated to:

为第i只后援者樽海鞘个体在第j维空间的位置，t为当前迭代次数；T_max为最大迭代次数；In the formula,

is the position of the i-th supporter salps in the j-th dimension space, t is the current number of iterations; T _max is the maximum number of iterations;

S6: Repeat steps S2 to S5 until the number of iterations reaches T _max or the food fitness value reaches the set termination threshold.

并判定

和

的适应度优劣，当

优于

时，再次更新第i只追踪者樽海鞘个体在第j维空间的位置为

When updating the position of the i-th tracker salp individual in the j-th dimension space, the position of the i-th tracker-salp individual in the j-th dimension space before the update is stored as

and judge

and

The fitness is good or bad, when

better than

When , the position of the i-th tracker salps in the j-th dimension space is updated again as

The individual salps group also includes multiple supporters, and the positions of the supporters are updated to:

为第i只后援者樽海鞘个体在第j维空间的位置，t为当前迭代次数；T_max为最大迭代次数。In the formula,

is the position of the i-th supporter salps in the j-th dimensional space, t is the current number of iterations; T _max is the maximum number of iterations.

The arrangement space of the target electrode array is a concentric electrode array, and the target is set to minimize the peak side lobe level. The fitness of each individual salps is calculated as follows:

为电极子的相移量，j是虚数符号，F_max为同心圆电极阵列的主瓣峰值，N_y为电极排布的圆环数量，N_x为环上电极子数量，r_m指第m个圆环上第n个电极子(n,m)的半径，

馈电幅度是I(n,m)各电极子同激励，Ψ(n,m)是电极子与x轴的夹角。where θ is the angle offset from the normal,

is the phase shift of the electrode, j is the sign of the imaginary number, F _max is the peak value of the main lobe of the concentric electrode array, N _y is the number of electrode rings, N _x is the number of electrodes on the ring, r _m refers to the mth The radius of the nth electrode element (n,m) on the ring,

The feeding amplitude is I(n,m) the co-excitation of each electrode, and Ψ(n,m) is the angle between the electrode and the x-axis.

The arrangement space of the target electrode array is a rectangular electrode array, and the target is set to minimize the peak side lobe level. The fitness of each individual salps is calculated as follows:

为电极子的相移量，j是虚数符号，F_max为同心圆电极阵列的主瓣峰值，N_y为电极排布的圆环数量，N_x为环上电极子数量，r_m指第m个圆环上第n个电极子(n,m)的半径，

p_mx为电极在x方向上的位置，p_my是电极子在y方向上的位置，馈电幅度是I(n,m)各电极子同激励。where θ is the angle offset from the normal,

is the phase shift of the electrode, j is the sign of the imaginary number, F _max is the peak value of the main lobe of the concentric electrode array, N _y is the number of electrode rings, N _x is the number of electrodes on the ring, r _m refers to the mth The radius of the nth electrode element (n,m) on the ring,

p _mx is the position of the electrode in the x direction, p _my is the position of the electrode element in the y direction, and the feeding amplitude is I(n, m) where each electrode element is co-excited.

Compared with the prior art, the advantages of the present invention are:

In the electrode array optimization method based on the salp group algorithm of the present invention, the set number of electrodes is used as the dimension of the search space of the salp group, the electrode array arrangement space is used as the set search space of the salp group, and the salp group algorithm is used to iterate until When the set target is met or the iteration reaches the set number of times, the final food position of the salps group is output, and it is used as the arrangement position of the electrode array to complete the optimization. This optimization method is simple and easy to implement, and the solution accuracy can meet the requirements, the convergence speed is fast, and the exploration range will not fall into the local optimal solution, so the required calculation amount is greatly reduced, and the time required for the optimization process is shortened. , which saves time and cost while improving the performance of the electrode array.

Description of drawings

1 is a diagram of a concentric electrode array obtained by an electrode array optimization method based on the salp group algorithm of the present invention;

FIG. 2 is a detection diagram obtained by the electrode array shown in FIG. 1 .

Detailed ways

In order to facilitate the understanding of the present invention, the present invention will be described more comprehensively and in detail below with reference to the accompanying drawings and preferred embodiments of the specification, but the protection scope of the present invention is not limited to the following specific embodiments.

Example:

In the electrode array optimization method based on the salp swarm algorithm in this embodiment, the number of electrodes is set as the dimension of the salp group search space, the electrode array arrangement space is used as the set search space of the salp group, and the salp swarm algorithm is used to iterate Until the set target is met or the iteration reaches the set number of times, the final food position of the salps group is output, and it is used as the arrangement position of the electrode array to complete the optimization. This optimization method is simple and easy to implement, and the solution accuracy can meet the requirements, the convergence speed is fast, and the exploration range will not fall into the local optimal solution, so the required calculation amount is greatly reduced, and the time required for the optimization process is shortened. , which saves time and cost while improving the performance of the electrode array.

设定目标为最小化峰值旁瓣电平，初始目标值设定为-15dB，若在达到最大迭代数之前满足设定目标值，则目标值降低0.5dB。In this embodiment, the concentric circular electrode array is optimized, and the main lobe region of the constraint pattern is

The set goal is to minimize the peak sidelobe level. The initial target value is set to -15dB. If the set target value is met before the maximum number of iterations is reached, the target value is reduced by 0.5dB.

The process of iterating using the salps swarm algorithm until the set goal is met includes the following steps:

初始化种群个体中各电极坐标

其中θ为[0,2π]之间的随机数，多个电极沿三个同心圆环阵列排布，且同一环上，相邻电极子距离应大于设定距离。S1: Initialize the number of individuals in the sea squirt group N=3n+1, n is a natural number, and N generally ranges from 50 to 100. In this embodiment, it is 61. The number of electrodes is used as the dimension D of the search space. The embodiment is 24, and the number of iterations T _max =500 is set; the initialization population is

Initialize the coordinates of each electrode in the individual population

Among them, θ is a random number between [0, 2π]. Multiple electrodes are arranged in an array of three concentric rings, and on the same ring, the distance between adjacent electrodes should be greater than the set distance.

S2: Calculate the fitness of each individual in the salps group:

为电极子的相移量，j是虚数符号，F_max为同心圆电极阵列的主瓣峰值，N_y为电极排布的圆环数量，N_x为环上电极子数量，r_m指第m个圆环上第n个电极子(n,m)的半径，

馈电幅度是I(n,m)各电极子同激励，Ψ(n,m)是电极子与x轴的夹角；where θ is the angle offset from the normal,

is the phase shift of the electrode, j is the sign of the imaginary number, F _max is the peak value of the main lobe of the concentric electrode array, N _y is the number of electrode rings, N _x is the number of electrodes on the ring, r _m refers to the mth The radius of the nth electrode element (n,m) on the ring,

The feeding amplitude is I(n,m) the co-excitation of each electrode, and Ψ(n,m) is the angle between the electrode and the x-axis;

The individual with the greatest fitness is used as food, and the rest are divided into n leaders, n trackers, and n supporters;

S3: Update the navigator position to:

为第i只领航者樽海鞘个体在第j维空间的位置，ub_j与lb_j分别为在第j维搜索空间的搜索上限与搜索下限，搜索空间坐标可依据

求得，求取上限时，m＝3，求取下限时m＝1；F_j为食物在第j维空间的位置，c₂与c₃为区间[0,1]内产生的随机数；参数c₁的定义为：

t为当前迭代次数，T_max为最大迭代次数；in,

is the position of the i-th pilot salp individual in the j-th dimension space, ub _j and lb _j are the search upper limit and search limit in the j-th dimension search space, respectively, and the search space coordinates can be based on

Obtain, when obtaining the upper limit, m=3, when obtaining the lower limit, m=1; F _j is the position of the food in the jth dimension space, and c ₂ and c ₃ are random numbers generated in the interval [0,1]; The parameter c ₁ is defined as:

t is the current number of iterations, and _Tmax is the maximum number of iterations;

S4: Update tracker location to:

为第i只追踪者樽海鞘个体在第j维空间的位置，

为共生量；B为受益参数，随机选取1或2；r为[0,1]区间的随机数；更新第i只追踪者樽海鞘个体在第j维空间的位置时，存储更新前的第i只追踪者樽海鞘个体在第j维空间的位置为

并判定

和

的适应度优劣，当

优于

时，再次更新第i只追踪者樽海鞘个体在第j维空间的位置为

In the formula,

is the position of the i-th tracker salp individual in the j-th dimension space,

is the symbiotic amount; B is the benefit parameter, 1 or 2 is randomly selected; r is a random number in the interval [0,1]; when updating the position of the i-th tracker salps in the j-th dimension space, store the pre-update The position of the individual i tracker salps in the jth dimension is:

and judge

and

The fitness is good or bad, when

better than

When , the position of the i-th tracker salps in the j-th dimension space is updated again as

S5: Supporter location updated to:

为第i只后援者樽海鞘个体在第j维空间的位置，t为当前迭代次数；T_max为最大迭代次数。通过后援者引入余弦函数使后援者更新方式更具灵活性，加上1使位置更新距离总体提高，又由于余弦函数的最大值为1的缘故，不致使距离过于大，从而，使后援者群体全局搜索和局部搜索得到平衡。领航者、跟随者、后援者三个子种群有利于在一定程度上提升算法的探索性能以及后期跳出局部最优的能力。In the formula,

is the position of the i-th supporter salps in the j-th dimensional space, t is the current number of iterations; T _max is the maximum number of iterations. The introduction of the cosine function by the supporters makes the update method of the supporters more flexible, and the addition of 1 increases the overall position update distance, and because the maximum value of the cosine function is 1, the distance is not too large, so that the supporters group Global search and local search are balanced. The three sub-populations of leader, follower, and supporter are beneficial to improve the exploration performance of the algorithm to a certain extent and the ability to jump out of the local optimum in the later stage.

S6: Repeat steps S2 to S5 until the number of iterations reaches T _max or the food fitness value reaches the set termination threshold.

After that, the food position can be output as the electrode arrangement position, and arranging electrodes according to this position can make the electrode array meet the target requirements. Figure 1 is the optimal electrode array pattern obtained according to the above optimization. According to it, the detection diagram shown in Figure 2 is obtained. The peak sidelobe level is -17.3dB and has a narrow mainlobe.

In this embodiment, when the target electrode array arrangement space is a rectangular electrode array, the target is set to minimize the peak side lobe level, and the fitness of each individual salps is calculated as follows:

为电极子的相移量，j是虚数符号，F_max为同心圆电极阵列的主瓣峰值，N_y为电极排布的圆环数量，N_x为环上电极子数量，r_m指第m个圆环上第n个电极子(n,m)的半径，

p_mx为电极在x方向上的位置，p_my是电极子在y方向上的位置，馈电幅度是I(n,m)各电极子同激励。where θ is the angle offset from the normal,

is the phase shift of the electrodes, j is the sign of the imaginary number, F _max is the peak value of the main lobe of the concentric electrode array, N _y is the number of electrode rings, N _x is the number of electrodes on the ring, r _m refers to the mth The radius of the nth electrode element (n,m) on the ring,

p _mx is the position of the electrode in the x direction, p _my is the position of the electrode element in the y direction, and the feeding amplitude is I(n, m) where each electrode element is co-excited.

The above descriptions are only preferred embodiments of the present invention, and the protection scope of the present invention is not limited to the above-mentioned embodiments. For those skilled in the art, improvements and transformations obtained without departing from the technical concept of the present invention should also be regarded as the protection scope of the present invention.

Claims (5)

1. an electrode array optimization method based on the salp group algorithm, is characterized in that: with the set electrode number as the salp group search space dimension, with the electrode array arrangement space as the set search space of the salp group, using the salp group The ascidian swarm algorithm iterates until the set target is met or the iteration reaches the set number of times, and the final food position of the salp swarm is output, which is used as the arrangement position of the electrode array to complete the optimization. 2. The electrode array optimization method based on the salps swarm algorithm according to claim 1, is characterized in that: the process that utilizes salps swarm algorithm iteration until meeting the set target comprises the following steps: S1: Initialize the number of individuals of the salps group N=3n+1, n is a natural number, take the number of electrodes as the dimension D of the search space, and set the number of iterations T _max ; the initialization population is

S2: Calculate the fitness of each individual in the sea squirt group, take the individual with the greatest fitness as the food, and divide the rest of the individuals into n leaders, n trackers, and n supporters; S3: Update the navigator position to:

in,

is the position of the i-th pilot salp individual in the j-th dimension space, ub _j and lb _j are the search upper limit and search limit in the j-th dimension search space, respectively; F _j is the position of the food in the j-th dimension space, c ₂ and c ₃ are random numbers generated in the interval [0,1]; the definition of parameter c ₁ is:

t is the current number of iterations, and _Tmax is the maximum number of iterations; S4: Update tracker location to:

In the formula,

is the position of the i-th tracker salp individual in the j-th dimension space,

is the symbiotic amount; B is the benefit parameter, 1 or 2 is randomly selected; r is a random number in the [0,1] interval; S5: Supporter location updated to:

In the formula,

is the position of the i-th supporter salps in the j-th dimension space, t is the current number of iterations; T _max is the maximum number of iterations; S6: Repeat steps S2 to S5 until the number of iterations reaches T _max or the food fitness value reaches the set termination threshold. 3. The electrode array optimization method based on the salp group algorithm according to claim 2, characterized in that: when updating the position of the i-th tracker salp individual in the j-th dimension space, the i-th tracker before the update is stored. The position of the individual salps in the jth dimension space is

and judge

and

The fitness is good or bad, when

better than

When , the position of the i-th tracker salps in the j-th dimension space is updated again as

4. The electrode array optimization method based on the salps group algorithm according to claim 2, characterized in that: the target electrode array arrangement space is a concentric electrode array, and the set target is to minimize the peak side lobe level. The fitness of Ascidian individuals is calculated as follows:

where θ is the angle offset from the normal,

is the phase shift of the electrode, j is the sign of the imaginary number, F _max is the peak value of the main lobe of the concentric electrode array, N _y is the number of electrode rings, N _x is the number of electrodes on the ring, r _m refers to the mth The radius of the nth electrode element (n,m) on the ring,

The feeding amplitude is I(n,m) the co-excitation of each electrode, and Ψ(n,m) is the angle between the electrode and the x-axis. 5. The electrode array optimization method based on the salps group algorithm according to claim 2, wherein the target electrode array arrangement space is a rectangular electrode array, and the set target is to minimize the peak side lobe level, each of the described The fitness of individual salps is calculated as follows:

where θ is the angle offset from the normal,

is the phase shift of the electrodes, j is the sign of the imaginary number, F _max is the peak value of the main lobe of the concentric electrode array, N _y is the number of electrode rings, N _x is the number of electrodes on the ring, r _m refers to the mth The radius of the nth electrode element (n,m) on the ring,

p _mx is the position of the electrode in the x direction, p _my is the position of the electrode element in the y direction, and the feeding amplitude is I(n, m) where each electrode element is co-excited.

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