CN114580601A - Magnetic dipole target positioning method based on improved intelligent optimization algorithm - Google Patents
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Abstract
Description
技术领域technical field
本发明属于磁性目标定位技术领域,尤其涉及一种基于改进智能优化算法的磁偶极子目标定位方法。The invention belongs to the technical field of magnetic target positioning, in particular to a magnetic dipole target positioning method based on an improved intelligent optimization algorithm.
背景技术Background technique
目前,磁性目标定位方法在航空磁性探测、机器人姿态检测、地磁场导航、地质勘探、未爆物检测等应用领域具有重要价值。当磁性目标距离磁传感器距离足够远时,目标可等效为磁偶极子,此时可采用磁偶极子描述该目标的磁感应强度。磁偶极子定位问题主要采用解析类方法、优化类方法和序贯滤波类方法等三类方法进行求解。其中,解析类方法对观测噪声较为敏感,在信噪比较低条件下定位性能较差;序贯滤波类方法主要针对运动目标的的定位问题,而优化类方法是目前解决基于改进智能优化算法的磁偶极子目标定位的主要方法。At present, the magnetic target localization method has important value in the application fields of aerial magnetic detection, robot attitude detection, geomagnetic field navigation, geological exploration, and unexploded ordnance detection. When the magnetic target is far enough away from the magnetic sensor, the target can be equivalent to a magnetic dipole, and the magnetic dipole can be used to describe the magnetic induction intensity of the target. The magnetic dipole localization problem is mainly solved by three types of methods: analytical method, optimization method and sequential filtering method. Among them, the analytical method is more sensitive to observation noise, and the positioning performance is poor under the condition of low signal-to-noise ratio; the sequential filtering method is mainly aimed at the positioning problem of moving targets, and the optimization method is currently based on improved intelligent optimization algorithms. The main method of magnetic dipole target localization.
优化算法通常通过磁传感器的测量数据并利用最优化的算法得到磁性目标的位置信息。Wiegert等人于2008年针对实时逐点定位问题提出基于中心势场的梯度方向导数方法。李华等人于2009年基于单旋转椭球体模型利用遗传算法对磁性目标进行定位,实现了在线磁目标定位,计算结果表明该方法定位准确、判断可靠。张丹等人于2017年基于遗传算法研究航空磁探仪搜索路径优化问题,根据目标的先验信息约束解的空间范围,并根据规则搜索阵型、随机搜索阵型生成初始种群,使得个体的非劣性和多样性得到了保证。Gao等人于2018年利用LM算法实现运动磁性目标的定位。The optimization algorithm usually obtains the position information of the magnetic target through the measurement data of the magnetic sensor and using the optimized algorithm. In 2008, Wiegert et al. proposed a gradient directional derivative method based on the central potential field for the real-time point-by-point localization problem. In 2009, Li Hua et al. used the genetic algorithm to locate the magnetic target based on the single spheroid model, and realized the on-line magnetic target localization. The calculation results show that the method is accurate in positioning and reliable in judgment. In 2017, Zhang Dan et al. studied the search path optimization problem of airborne magnetic detectors based on genetic algorithm. According to the prior information of the target, the spatial range of the solution was constrained, and the initial population was generated according to the rule search formation and random search formation, so that the individual non-inferiority And diversity is guaranteed. In 2018, Gao et al. used the LM algorithm to achieve localization of moving magnetic targets.
国内外针对基于改进智能优化算法的磁偶极子目标定位问题的研究现状表明,对于范围比较小的磁场三分量定位问题,利用传统的最优化方法就很容易收敛到最优值,但是针对参数范围比较大且目标函数比较复杂的情况下,传统的最优化算法对于初值太过敏感,目标定位性能难以保证。The research status of the magnetic dipole target localization problem based on the improved intelligent optimization algorithm at home and abroad shows that for the three-component magnetic field localization problem with a relatively small range, it is easy to converge to the optimal value using the traditional optimization method, but for the parameter When the range is relatively large and the objective function is relatively complex, the traditional optimization algorithm is too sensitive to the initial value, and the target positioning performance is difficult to guarantee.
通过上述分析,现有技术存在的问题及缺陷为:针对参数范围比较大且目标函数比较复杂的情况下,传统的最优化算法对于初值太过敏感,目标定位性能难以保证。Through the above analysis, the existing problems and defects in the prior art are: in the case of a relatively large parameter range and a relatively complex objective function, the traditional optimization algorithm is too sensitive to the initial value, and the target positioning performance is difficult to guarantee.
解决以上问题及缺陷的难度为:低信噪比条件下磁偶极子目标进行快速、准确定位存在困难。The difficulty of solving the above problems and defects is that it is difficult to quickly and accurately locate the magnetic dipole target under the condition of low signal-to-noise ratio.
解决以上问题及缺陷的意义为:本发明的目的在于,提出一种磁偶极子定位方法,用于解决低信噪比下基于改进智能优化算法的磁偶极子目标定位精度下降、收敛速度慢的问题,能够较快地对磁传感器测量得到的目标磁感应强度数据进行分析。The significance of solving the above problems and defects is as follows: the purpose of the present invention is to propose a magnetic dipole positioning method, which is used to solve the problem of low signal-to-noise ratio based on improved intelligent optimization algorithm. Magnetic dipole target positioning accuracy decline, convergence speed The problem of slowness can quickly analyze the target magnetic induction intensity data measured by the magnetic sensor.
发明内容SUMMARY OF THE INVENTION
针对现有技术存在的问题,本发明提供了一种基于改进智能优化算法的磁偶极子目标定位方法。Aiming at the problems existing in the prior art, the present invention provides a magnetic dipole target localization method based on an improved intelligent optimization algorithm.
本发明是这样实现的,一种基于改进智能优化算法的磁偶极子目标定位方法,所述基于改进智能优化算法的磁偶极子目标定位方法,包括:The present invention is implemented in this way, a magnetic dipole target localization method based on an improved intelligent optimization algorithm, and the magnetic dipole target localization method based on the improved intelligent optimization algorithm includes:
步骤一,在远场条件下采用磁偶极子模型描述目标的磁感应强度,是本方案的模型基础;The first step is to use the magnetic dipole model to describe the magnetic induction intensity of the target under far-field conditions, which is the model basis of this scheme;
步骤二,构造基于改进智能优化算法的磁偶极子目标定位非线性方程组,为智能优化算法确定适应度函数;
步骤三,利用改进智能优化算法进行寻优,实现基于改进智能优化算法的磁偶极子目标定位,是本方案的关键步骤。
进一步,所述步骤一中,在远场条件下采用磁偶极子模型描述目标的磁感应强度具体过程为:Further, in the first step, the specific process of using the magnetic dipole model to describe the magnetic induction intensity of the target under far-field conditions is as follows:
当磁传感器和目标之间的距离大于磁性目标尺寸的2.5倍以上时,将此磁性目标物体看作是磁偶极子;When the distance between the magnetic sensor and the target is more than 2.5 times the size of the magnetic target, the magnetic target object is regarded as a magnetic dipole;
坐标系中磁偶极子目标位置为A(x0,y0,z0),磁通门传感器的坐标为B(x,y,z),r为磁偶极子的原点到磁传感器的矢径,为磁偶极子的磁矩矢量,m为目标磁矩大小,θ为地磁倾角,为地磁偏角。此时B点处目标产生的磁感应强度B;在直角坐标系中,将磁感应强度B方程展开。The target position of the magnetic dipole in the coordinate system is A(x 0 , y 0 , z 0 ), the coordinate of the fluxgate sensor is B(x, y, z), and r is the distance from the origin of the magnetic dipole to the magnetic sensor. vector diameter, is the magnetic moment vector of the magnetic dipole, m is the target magnetic moment, θ is the geomagnetic inclination, is the magnetic declination angle. At this time, the magnetic induction intensity B generated by the target at point B; in the Cartesian coordinate system, expand the magnetic induction intensity B equation.
进一步,所述B点处目标产生的磁感应强度B方程为:Further, the B equation of the magnetic induction intensity generated by the target at the point B is:
进一步,所述磁感应强度B方程展开为:Further, the magnetic induction intensity B equation is expanded as:
在直角坐标系中,将磁感应强度B方程展开得到:In the Cartesian coordinate system, the magnetic induction intensity B equation is expanded to get:
其中μ0为自由空间磁导率,大小为4π×10-7H/m,上式是一个包含6个未知数的非线性方程组,至少要给出两个测量点,构造六个方程才能估计目标的未知参数;在实际测量情况下,对磁感应强度值测量会存在一定误差,只依靠两个监测点的数据所得出的结果并不准确,为减小误差,需增加磁传感器的数目,并将其转化为非线性优化问题然后利用优化算法进行求解。。where μ 0 is the permeability of free space, the size is 4π×10 -7 H/m, the above formula is a nonlinear equation system containing 6 unknowns, at least two measurement points must be given, and six equations can be constructed to estimate The unknown parameters of the target; in the actual measurement situation, there will be a certain error in the measurement of the magnetic induction value, and the results obtained only by relying on the data of the two monitoring points are not accurate. In order to reduce the error, it is necessary to increase the number of magnetic sensors and Transform it into a nonlinear optimization problem and solve it with an optimization algorithm. .
进一步,所述步骤二中,构造基于改进智能优化算法的磁偶极子目标定位非线性方程组,具体过程为:Further, in the second step, a nonlinear equation system for magnetic dipole target positioning based on an improved intelligent optimization algorithm is constructed, and the specific process is as follows:
首先假定一组未知数并代入对磁感应强度B方程展开的右半部分,得到磁感应强度的一组估计然后以误差平方和最小为准则来评估该组未知数,从而得到如下方程:First, a set of unknowns are assumed and substituted into the right half of the expansion of the B equation for the magnetic induction to obtain a set of estimates of the magnetic induction The set of unknowns is then evaluated with the minimum sum of squared error as the criterion, resulting in the following equation:
使得f取得最小值时的估计量所对应的未知量就是方程的最优解。the estimator that minimizes f The corresponding unknown is the optimal solution of the equation.
进一步,所述步骤三中,利用改进智能优化算法进行寻优过程为:Further, in the third step, the optimization process using the improved intelligent optimization algorithm is as follows:
首先,通过佳点集初始化产生初始种群,使初始种群位置更加均匀;First, the initial population is generated through the initialization of the good point set, so that the initial population position is more uniform;
其次加入粒子群位置更新公式,增强粒子之间的信息交流和合作机制;Secondly, the particle swarm position update formula is added to enhance the information exchange and cooperation mechanism between particles;
另外加入改变概率和莱维飞行,使其能够有一部分粒子按照莱维飞行来改变自身位置,增强粒子的活性和多样性,避免算法陷入局部最优。In addition, changing the probability and Levi's flight is added, so that some particles can change their position according to the Levi's flight, enhance the activity and diversity of the particles, and prevent the algorithm from falling into local optimum.
进一步,所述通过佳点集初始化产生初始种群,具体过程为:Further, the initial population is generated by initializing the good point set, and the specific process is:
假设GD是D维空间的单位立方体,假设r∈GD,形为偏差的集合称作佳点集,r称为佳点;其中C(r,ε)为常数且只与r,ε(ε>0)有关,取rk={2cos(2πk/p)},1≤k≤M,其中p是满足(p-D/2)≥D的最小素数,或rk={exp(k)},1≤k≤M,{a}是a的小数部分;当计算函数在GD上积分时,取n个佳点得到的误差是最小的相对于用任意给定的n个点的函数值构成的加权和而已。Suppose G D is a unit cube in D-dimensional space, suppose r∈G D , the form is deviation The set of is called a good point set, and r is called a good point; where C(r,ε) is a constant and only related to r,ε(ε>0), take r k ={2cos(2πk/p)}, 1 ≤k≤M, where p is the smallest prime number satisfying (pD/2)≥D, or r k ={exp(k)}, 1≤k≤M, {a} is the fractional part of a; when the calculation function is in When integrating on G D , the error obtained by taking n best points is the smallest relative to the weighted sum formed by the function values of any given n points.
进一步,所述加入改变概率和莱维飞行,具体过程为:Further, the adding change probability and Levi flight, the specific process is:
(1)利用佳点集初始化方法生成初始位置X,给定初始种群规模N,最大迭代次数max_iter,种群维度D,学习系数c1,c2等参数;(1) Using the good point set initialization method to generate the initial position X, given the initial population size N, the maximum number of iterations max_iter, the population dimension D, the learning coefficients c 1 , c 2 and other parameters;
(2)使得适应度函数最小,灰狼算法求得最优解、次优解和季优解后跳出该循环;(2) Minimize the fitness function, and jump out of the loop after obtaining the optimal solution, the suboptimal solution and the quarterly optimal solution by the gray wolf algorithm;
(3)每次循环时更新和根据PSO-GWO混合算法的位置更新公式更新速度和位置;同时按照概率Pc=0.5随机选择粒子进行莱维飞行,按照位置更新公式跳出局部最优,来更新速度和位置;(3) Update every cycle and Update the speed and position according to the position update formula of the PSO-GWO hybrid algorithm; at the same time, randomly select particles to carry out Levi flight according to the probability P c =0.5, and jump out of the local optimum according to the position update formula to update the speed and position;
(4)判断迭代次数是否等于预设上限值,如果等于则结束运行;否则,跳转到(2)。(4) Determine whether the number of iterations is equal to the preset upper limit value, and if so, end the operation; otherwise, jump to (2).
进一步,所述(3)中PSO-GWO混合算法的位置更新公式为:Further, the position update formula of the PSO-GWO hybrid algorithm in the (3) is:
所述(3)中位置更新公式为下式:The position update formula in (3) is as follows:
通过加入改变概率Pc=0.5,在每次迭代的时候对比迭代时设置的随机数A=rand()来判断需不需要进行莱维飞行策略。By adding a change probability P c =0.5, in each iteration, the random number A=rand( ) set in the iteration is compared to determine whether the Levi flight strategy needs to be performed.
本发明另一目的在于提供一种计算机设备,所述计算机设备包括存储器和处理器,所述存储器存储有计算机程序,所述计算机程序被所述处理器执行时,使得所述处理器执行所述基于改进智能优化算法的磁偶极子目标定位方法的步骤。Another object of the present invention is to provide a computer device, the computer device includes a memory and a processor, the memory stores a computer program, and when the computer program is executed by the processor, the processor causes the processor to execute the Steps of a magnetic dipole target localization method based on an improved intelligent optimization algorithm.
本发明另一目的在于提供一种计算机可读存储介质,存储有计算机程序,所述计算机程序被处理器执行时,使得所述处理器执行所述基于改进智能优化算法的磁偶极子目标定位方法的步骤。Another object of the present invention is to provide a computer-readable storage medium storing a computer program, which, when executed by a processor, enables the processor to execute the magnetic dipole target localization based on the improved intelligent optimization algorithm steps of the method.
本发明另一目的在于提供一种信息数据处理终端,所述信息数据处理终端用于实现所述基于改进智能优化算法的磁偶极子目标定位方法。Another object of the present invention is to provide an information data processing terminal for implementing the magnetic dipole target positioning method based on the improved intelligent optimization algorithm.
结合上述的所有技术方案,本发明所具备的优点及积极效果为:本发明选择两种智能优化算法的混合算法,即基于莱维飞行的粒子群-灰狼混合优化算法来研究基于改进智能优化算法的磁偶极子目标定位问题。针对粒子群算法和灰狼算法容易陷入局部最优的缺点,提出了一种改进的粒子群优化算法,改善了粒子群和灰狼算法陷入局部最优的缺陷。在生成初始种群时引入佳点集初始化,增强初始种群的多样性和均匀性,群位置更新时引入自适应权值,以满足不同时期的寻优要求,加入莱维飞行可以优化粒子群和灰狼优化算法的粒子的活力和跳跃能力,有利于粒子跳出局部最优。Combined with all the above technical solutions, the advantages and positive effects of the present invention are as follows: the present invention selects a hybrid algorithm of two intelligent optimization algorithms, that is, the particle swarm-grey wolf hybrid optimization algorithm based on Levy flight to study the improved intelligent optimization algorithm. Algorithm for the magnetic dipole target localization problem. Aiming at the shortcomings of particle swarm optimization and gray wolf algorithm that are easy to fall into local optimum, an improved particle swarm optimization algorithm is proposed, which improves the defect of particle swarm optimization and gray wolf algorithm falling into local optimum. Introduce the initialization of good point sets when generating the initial population to enhance the diversity and uniformity of the initial population, and introduce adaptive weights when the group position is updated to meet the optimization requirements in different periods. Adding Levi flight can optimize the particle swarm and grayscale. The vitality and jumping ability of the particles in the wolf optimization algorithm are conducive to the particles jumping out of the local optimum.
附图说明Description of drawings
图1是本发明实施例提供的基于改进智能优化算法的磁偶极子目标定位方法流程图。FIG. 1 is a flowchart of a method for locating a magnetic dipole target based on an improved intelligent optimization algorithm provided by an embodiment of the present invention.
图2是本发明实施例提供的磁偶极子模型示意图。FIG. 2 is a schematic diagram of a magnetic dipole model provided by an embodiment of the present invention.
图3是本发明实施例提供的灰狼种群社会等级示意图。FIG. 3 is a schematic diagram of the social level of a gray wolf population provided by an embodiment of the present invention.
图4是本发明实施例提供的佳点集初始化产生的二维种群分布示意图。FIG. 4 is a schematic diagram of a two-dimensional population distribution generated by initialization of a good point set provided by an embodiment of the present invention.
图5是本发明实施例提供的随机初始化产生的二维种群分布示意图。FIG. 5 is a schematic diagram of a two-dimensional population distribution generated by random initialization according to an embodiment of the present invention.
图6是本发明实施例提供的算法流程图。FIG. 6 is a flowchart of an algorithm provided by an embodiment of the present invention.
图7是本发明实施例提供的1×4节点探测阵列示意图。FIG. 7 is a schematic diagram of a 1×4 node detection array provided by an embodiment of the present invention.
图8是本发明实施例提供的目标运动至A处示意图。FIG. 8 is a schematic diagram of a target moving to a position A according to an embodiment of the present invention.
图9是本发明实施例提供的不同算法在不同信噪比下的定位误差比较示意图。FIG. 9 is a schematic diagram illustrating a comparison of positioning errors of different algorithms under different signal-to-noise ratios provided by an embodiment of the present invention.
图10是本发明实施例提供的在迭代次数为100次时信噪比从从-5dB变换到35dB的情况下,三个算法收敛曲线的变化趋势示意图。FIG. 10 is a schematic diagram of the change trend of the convergence curves of the three algorithms under the condition that the signal-to-noise ratio is changed from -5dB to 35dB when the number of iterations is 100 according to an embodiment of the present invention.
图10中:图a、实验1收敛曲线图;图b、实验2收敛曲线图;图c、实验3收敛曲线图;图d、实验4收敛曲线图;图e、实验5收敛曲线图。In Figure 10: Figure a, the convergence curve of
具体实施方式Detailed ways
为了使本发明的目的、技术方案及优点更加清楚明白,以下结合实施例,对本发明进行进一步详细说明。应当理解,此处所描述的具体实施例仅仅用以解释本发明,并不用于限定本发明。In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention, but not to limit the present invention.
针对现有技术存在的问题,本发明提供了一种基于改进智能优化算法的磁偶极子目标定位方法,下面结合附图对本发明作详细的描述。In view of the problems existing in the prior art, the present invention provides a magnetic dipole target positioning method based on an improved intelligent optimization algorithm. The present invention is described in detail below with reference to the accompanying drawings.
本发明提供的基于改进智能优化算法的磁偶极子目标定位方法业内的普通技术人员还可以采用其他的步骤实施,图1的本发明提供的基于改进智能优化算法的磁偶极子目标定位方法仅仅是一个具体实施例而已。The magnetic dipole target localization method based on the improved intelligent optimization algorithm provided by the present invention can also be implemented by those skilled in the industry by other steps. The magnetic dipole target localization method based on the improved intelligent optimization algorithm provided by the present invention in FIG. 1 Just one specific example.
如图1所示,本发明实施例提供的基于改进智能优化算法的磁偶极子目标定位方法,包括:As shown in FIG. 1, the magnetic dipole target positioning method based on the improved intelligent optimization algorithm provided by the embodiment of the present invention includes:
S101:在远场条件下采用磁偶极子模型描述目标的磁感应强度;S101: Use the magnetic dipole model to describe the magnetic induction intensity of the target under far-field conditions;
S102:构造基于改进智能优化算法的磁偶极子目标定位非线性方程组;S102: Construct a nonlinear equation system for magnetic dipole target positioning based on an improved intelligent optimization algorithm;
S103:利用改进智能优化算法进行寻优,实现基于改进智能优化算法的磁偶极子目标定位。S103: Use the improved intelligent optimization algorithm to perform optimization, and realize the magnetic dipole target localization based on the improved intelligent optimization algorithm.
本发明实施例提供的S101中,在远场条件下采用磁偶极子模型描述目标的磁感应强度具体过程为:In S101 provided by the embodiment of the present invention, the specific process of using the magnetic dipole model to describe the magnetic induction intensity of the target under far-field conditions is as follows:
当磁传感器和目标之间的距离大于磁性目标尺寸的2.5倍以上时,将此磁性目标物体看作是磁偶极子;When the distance between the magnetic sensor and the target is more than 2.5 times the size of the magnetic target, the magnetic target object is regarded as a magnetic dipole;
坐标系中磁偶极子目标位置为A(x0,y0,z0),磁通门传感器的坐标为B(x,y,z),r为磁偶极子的原点到磁传感器的矢径,m为磁偶极子的磁矩矢量,θ为地磁倾角,为地磁偏角。The target position of the magnetic dipole in the coordinate system is A(x 0 , y 0 , z 0 ), the coordinate of the fluxgate sensor is B(x, y, z), and r is the distance from the origin of the magnetic dipole to the magnetic sensor. vector radius, m is the magnetic moment vector of the magnetic dipole, θ is the geomagnetic dip, is the magnetic declination angle.
此时B点处目标产生的磁感应强度B方程为:At this time, the B equation of the magnetic induction intensity generated by the target at point B is:
在直角坐标系中,将磁感应强度B方程展开得到:In the Cartesian coordinate system, the magnetic induction intensity B equation is expanded to get:
其中μ0为自由空间磁导率,大小为4π×10-7H/m,上式是一个包含6个未知数的非线性方程组,至少要给出两个测量点,构造六个方程才能估计目标的未知参数;在实际测量情况下,对磁感应强度值测量会存在一定误差,只依靠两个监测点的数据所得出的结果并不准确,为减小误差,需增加磁传感器的数目,并将其转化为非线性优化问题然后利用优化算法进行求解。where μ 0 is the permeability of free space, the size is 4π×10 -7 H/m, the above formula is a nonlinear equation system containing 6 unknowns, at least two measurement points must be given, and six equations can be constructed to estimate The unknown parameters of the target; in the actual measurement situation, there will be a certain error in the measurement of the magnetic induction value, and the results obtained only by relying on the data of the two monitoring points are not accurate. In order to reduce the error, it is necessary to increase the number of magnetic sensors and Transform it into a nonlinear optimization problem and solve it with an optimization algorithm.
本发明实施例提供的S102中,构造基于改进智能优化算法的磁偶极子目标定位非线性方程组,具体过程为:In S102 provided by the embodiment of the present invention, a nonlinear equation system for magnetic dipole target positioning based on an improved intelligent optimization algorithm is constructed, and the specific process is as follows:
首先假定一组未知数并代入对磁感应强度B方程展开的右半部分,得到磁感应强度的一组估计然后以误差平方和最小为准则来评估该组未知数,从而得到如下方程:First, a set of unknowns are assumed and substituted into the right half of the expansion of the B equation for the magnetic induction to obtain a set of estimates of the magnetic induction The set of unknowns is then evaluated with the minimum sum of squared error as the criterion, resulting in the following equation:
使得f取得最小值时的估计量所对应的未知量就是方程的最优解。the estimator that minimizes f The corresponding unknown is the optimal solution of the equation.
本发明实施例提供的S103中,利用改进智能优化算法进行寻优过程为:In S103 provided by the embodiment of the present invention, the optimization process using the improved intelligent optimization algorithm is as follows:
首先,通过佳点集初始化产生初始种群,使初始种群位置更加均匀;First, the initial population is generated through the initialization of the good point set, so that the initial population position is more uniform;
其次加入粒子群位置更新公式,增强粒子之间的信息交流和合作机制;Secondly, the particle swarm position update formula is added to enhance the information exchange and cooperation mechanism between particles;
另外加入改变概率和莱维飞行,使其能够有一部分粒子按照莱维飞行来改变自身位置,增强粒子的活性和多样性,避免算法陷入局部最优。In addition, changing the probability and Levi's flight is added, so that some particles can change their position according to the Levi's flight, enhance the activity and diversity of the particles, and prevent the algorithm from falling into local optimum.
所述通过佳点集初始化产生初始种群,具体过程为:The initial population is generated through the initialization of the good point set, and the specific process is as follows:
假设GD是D维空间的单位立方体,假设r∈GD,形为偏差的集合称作佳点集,r称为佳点;其中C(r,ε)为常数且只与r,ε(ε>0)有关,取rk={2cos(2πk/p)},1≤k≤M,其中p是满足(p-D/2)≥D的最小素数,或rk={exp(k)},1≤k≤M,{a}是a的小数部分。当计算函数在GD上积分时,取n个佳点得到的误差是最小的相对于用任意给定的n个点的函数值构成的加权和而已。Suppose G D is a unit cube in D-dimensional space, suppose r∈G D , the form is deviation The set of is called a good point set, and r is called a good point; where C(r,ε) is a constant and only related to r,ε(ε>0), take r k ={2cos(2πk/p)}, 1 ≤k≤M, where p is the smallest prime number satisfying (pD/2)≥D, or r k ={exp(k)}, 1≤k≤M, and {a} is the fractional part of a. When the computing function is integrated over G D , the error obtained by taking n optimal points is the smallest relative to the weighted sum formed by the function values of any given n points.
所述加入改变概率和莱维飞行,具体过程为:The adding change probability and Levi flight, the specific process is:
(1)利用佳点集初始化方法生成初始位置X,给定初始种群规模N,最大迭代次数max_iter,种群维度D,学习系数c1,c2等参数;(1) Using the good point set initialization method to generate the initial position X, given the initial population size N, the maximum number of iterations max_iter, the population dimension D, the learning coefficients c 1 , c 2 and other parameters;
(2)使得适应度函数最小,灰狼算法求得最优解、次优解和季优解后跳出该循环;(2) Minimize the fitness function, and jump out of the loop after obtaining the optimal solution, the suboptimal solution and the quarterly optimal solution by the gray wolf algorithm;
(3)每次循环时更新和根据PSO-GWO混合算法的位置更新公式更新速度和位置;同时按照概率Pc=0.5随机选择粒子进行莱维飞行,按照位置更新公式跳出局部最优,来更新速度和位置;(3) Update every cycle and Update the speed and position according to the position update formula of the PSO-GWO hybrid algorithm; at the same time, randomly select particles to carry out Levi flight according to the probability P c =0.5, and jump out of the local optimum according to the position update formula to update the speed and position;
(4)在没达到迭代停止条件的情况下,根据第三步更新粒子的速度和位置,然后从第二步开始计算,完成循环后进行(3)直到达到终止条件。(4) If the iteration stop condition is not reached, update the speed and position of the particle according to the third step, and then start the calculation from the second step, and perform (3) after the loop is completed until the end condition is reached.
所述(3)中PSO-GWO混合算法的位置更新公式为:The position update formula of the PSO-GWO hybrid algorithm in (3) is:
所述(3)中位置更新公式为下式:The position update formula in (3) is as follows:
通过加入改变概率Pc=0.5,在每次迭代的时候对比迭代时设置的随机数A=rand()来判断需不需要进行莱维飞行策略。By adding a change probability P c =0.5, in each iteration, the random number A=rand( ) set in the iteration is compared to determine whether the Levi flight strategy needs to be performed.
下面结合具体实施例对本发明的技术方案作详细的描述。The technical solutions of the present invention will be described in detail below with reference to specific embodiments.
1基于改进智能优化算法的磁偶极子目标定位模型1 Magnetic dipole target localization model based on improved intelligent optimization algorithm
1.1磁偶极子模型1.1 Magnetic Dipole Model
对于磁性目标物体而言,当磁传感器和目标之间的距离大于磁性目标尺寸的2.5倍以上时,可以将此磁性目标物体看作是磁偶极子。For a magnetic target object, when the distance between the magnetic sensor and the target is greater than 2.5 times the size of the magnetic target, the magnetic target object can be regarded as a magnetic dipole.
如图2所示,坐标系中磁偶极子目标位置为A(x0,y0,z0),磁通门传感器的坐标为B(x,y,z),r为磁偶极子的原点到磁传感器的矢径,m为磁偶极子的磁矩矢量,此时B点处目标产生的磁感应强度B为:As shown in Figure 2, the target position of the magnetic dipole in the coordinate system is A(x 0 , y 0 , z 0 ), the coordinate of the fluxgate sensor is B(x, y, z), and r is the magnetic dipole From the origin to the vector radius of the magnetic sensor, m is the magnetic moment vector of the magnetic dipole. At this time, the magnetic induction intensity B generated by the target at point B is:
在直角坐标系中,将(1)式展开得到:In the Cartesian coordinate system, formula (1) can be expanded to get:
其中μ0为自由空间磁导率,大小为4π×10-7H/m,(2)式是一个包含6个未知数的非线性方程组,显然至少要给出两个测量点,所以至少要有六个方程。然而在实际测量情况下,对磁感应强度值测量会存在一定误差,其次只依靠两个监测点的数据所得出的结果并不准确,为了减小误差,适当增加磁传感器的数目,假设有4个磁传感器,将其转化为非线性优化问题然后利用优化算法进行求解。where μ 0 is the permeability of free space, and the size is 4π×10 -7 H/m. Equation (2) is a nonlinear equation system containing 6 unknowns. Obviously, at least two measurement points must be given, so at least There are six equations. However, in the actual measurement situation, there will be a certain error in the measurement of the magnetic induction intensity value. Secondly, the results obtained only by relying on the data of two monitoring points are not accurate. In order to reduce the error, the number of magnetic sensors should be appropriately increased, assuming that there are 4 magnetic sensor, convert it into a nonlinear optimization problem and solve it using an optimization algorithm.
1.2目标函数的确定1.2 Determination of the objective function
对于上节中的方程组,可以将其看作非线性最小二乘法问题。首先假定一组未知数并代入对方程组式(2)的右半部分,得到磁感应强度的一组估计然后以误差平方和最小为准则来评估该组未知数,从而得到如下方程:For the system of equations in the previous section, you can think of it as a nonlinear least squares problem. First, a set of unknowns is assumed and substituted into the right half of equation (2) to obtain a set of estimates of the magnetic induction The set of unknowns is then evaluated with the minimum sum of squared error as the criterion, resulting in the following equation:
使得f取得最小值时的估计量所对应的未知量就是方程的最优解。the estimator that minimizes f The corresponding unknown is the optimal solution of the equation.
2基于改进智能优化算法的磁偶极子目标定位方法2 Magnetic dipole target localization method based on improved intelligent optimization algorithm
2.1基于灰狼优化的定位算法2.1 Localization algorithm based on gray wolf optimization
灰狼优化算法是由Mirjalili等人于2014年提出来的一种群智能优化算法。该算法是模拟自然界灰狼群体的社会等级以及狩猎行为而提出的一种启发性算法,在灰狼群体中有着代表着权力和统治的社会等级制度。该制度将狼群划分为α狼,β狼,δ狼,ω狼,如图3所示,其中α狼是等级最高的狼群,其他的狼需要服从α狼的命令,β狼服从于α狼并协助α狼做决策,而δ狼则是β狼的下属狼,要服从α狼和β狼的命令,ω狼是等级最低的狼要服从于其他三组狼群的指挥。灰狼群体除了有严格等级之分,也有围猎特征,主要包括包围猎物、追捕猎物、攻击猎物。The gray wolf optimization algorithm is a swarm intelligence optimization algorithm proposed by Mirjalili et al. in 2014. The algorithm is a heuristic algorithm proposed to simulate the social hierarchy and hunting behavior of gray wolves in nature. There is a social hierarchy representing power and domination in gray wolves. The system divides wolves into α wolves, β wolves, δ wolves, and ω wolves, as shown in Figure 3, where α wolves are the highest-ranked wolf group, other wolves need to obey the orders of α wolves, and β wolves obey α wolves The wolf also assists the alpha wolf in decision-making, while the delta wolf is the subordinate wolf of the beta wolf and must obey the orders of the alpha wolf and the beta wolf. In addition to being strictly hierarchical, gray wolves also have hunting characteristics, which mainly include surrounding prey, chasing prey, and attacking prey.
(1)包围猎物(1) Surrounding the prey
将适应度函数取得最优解的六个参数作为猎物,当灰狼群体发现猎物时,会迅速向猎物靠近并包围,灰狼的位置更新如下式(6)(假设搜索空间为d维):The six parameters of the optimal solution of the fitness function are used as the prey. When the gray wolf group finds the prey, it will quickly approach and surround the prey. The position of the gray wolf is updated as follows (6) (assuming the search space is d-dimensional):
X(t)={Xi(t)|i=1,2,...,d} (4)X(t)={X i (t)|i=1,2,...,d} (4)
X(t+1)=XP(t)-AD (6)X(t+1) = XP(t)-AD(6)
其中X(t)表示第t代灰狼种群位置,XP(t)表示第t代猎物的位置,D表示灰狼群体和猎物中间的距离向量,A和C表示系数向量。where X(t) represents the location of the t-th generation gray wolf population, X P (t) represents the location of the t-th generation prey, D represents the distance vector between the gray wolf population and the prey, and A and C represent the coefficient vectors.
A=2ar1-a (7)A=2ar 1 -a (7)
C=2r2 (8)C=2r 2 (8)
式(7)(8)(9)中:r1,r2为0到1的均匀分布的随机数,a为收敛因子,从2线性降为0,max_iter为最大迭代次数。In formulas (7) (8) (9): r 1 , r 2 are uniformly distributed random numbers from 0 to 1, a is a convergence factor, which decreases linearly from 2 to 0, and max_iter is the maximum number of iterations.
(2)追捕猎物(2) Pursue prey
当灰狼包围猎物之后,狩猎行为开始,在狩猎时,由于α狼,β狼,δ狼对猎物的感知性更强,所以,其他灰狼会根据自身和α狼,β狼,δ狼之间的距离即Dα,Dβ,Dδ,分别计算自身朝向α狼,β狼,δ狼的移步距离X1,X2,X3,并向着三者的包围圈之内移动,更新公式如(10)(11)(12):When the gray wolf surrounds the prey, the hunting behavior begins. During hunting, since the alpha wolf, beta wolf, and delta wolf are more sensitive to the prey, other gray wolves will The distances between them are D α , D β , D δ , calculate the moving distances X 1 , X 2 , X 3 of the self toward α wolf, β wolf, and δ wolf respectively, and move toward the encircling circle of the three, update the formula Such as (10)(11)(12):
X1=Xα-ADα X 1 =X α -AD α
X2=Xβ-ADβ (11)X 2 =X β -AD β (11)
X3=Xδ-ADδ X 3 =X δ -AD δ
其中i=1,2,3...,d,X(t+1)表示ω狼的位置更新。where i=1,2,3...,d, X(t+1) represents the position update of ω wolf.
(3)攻击猎物(3) Attack the prey
当猎物停止移动时,灰狼开始攻击猎物,用数学描述此过程就是,当A的值在[-1,1]这个区间范围之外时,搜索代理在灰狼当前位置和最优解随意进行搜索,当A的值在[-1,1]这个区间范围之内时,必定找到最优解 When the prey stops moving, the gray wolf starts to attack the prey. The mathematical description of this process is that when the value of A is outside the range of [-1, 1], the search agent randomly conducts the search agent at the current position of the gray wolf and the optimal solution. Search, when the value of A is within the range of [-1,1], the optimal solution must be found
2.2基于PSO的定位算法2.2 PSO-based positioning algorithm
PSO算法是受鸟群的觅食行为而提出的一种群体智能随机搜索的优化算法,每一个粒子可以视为d维搜索空间的一个个体,粒子的当前位置对应为最优化非线性问题的一个候选解,粒子在搜索空间的飞行过程就是该个体的搜索过程。粒子在初始化时,具有两个属性:位置和速度,初始化内的粒子都有一个初始速度和位置,算法每次进行迭代,粒子根据自身的经验和相邻粒子的经验来以及自身和相邻的粒子的最优位置来更新自己的位置。此外,每个粒子还有自身位置对应的适应度值。当适应度函数越小时,取得位置精度越好,定位越准确。当种群规模为N,维度为D时,粒子X的位置可以表示为Xi=(xi1,xi2,...,xid,...,xiD),其中xid表示第i维的第d个分量,粒子X的速度为Vi=(vi1,vi2,...,vid,...,viD),其中vid表示第i维的第d个速度,粒子的位置和速度更新公式如下(13)(14):The PSO algorithm is an optimization algorithm of swarm intelligent random search proposed by the foraging behavior of birds. Each particle can be regarded as an individual in the d-dimensional search space, and the current position of the particle corresponds to an optimization nonlinear problem. The candidate solution, the flight process of the particle in the search space is the search process of the individual. When the particle is initialized, it has two properties: position and speed. The particles in the initialization have an initial speed and position. Each time the algorithm iterates, the particle determines the value of itself and its neighbors according to its own experience and the experience of adjacent particles. The optimal position of the particle to update its position. In addition, each particle has a fitness value corresponding to its own position. When the fitness function The smaller the value, the better the obtained position accuracy and the more accurate the positioning. When the population size is N and the dimension is D, the position of particle X can be expressed as X i =(x i1 ,x i2 ,...,x id ,...,x iD ), where x id represents the i-th dimension The d-th component of , the velocity of particle X is Vi = (v i1 ,v i2 ,...,v id ,...,v iD ), where v id represents the d-th velocity of the i-th dimension, the particle The position and velocity update formulas of are as follows (13) (14):
w=wmax-(t/max_iter)*(wmax-wmin) (15)w=wmax-(t/max_iter)*(wmax-wmin) (15)
其中j=1,2,...,d,表示个体极值,表示全局极值,t表示当前的迭代次数,c1,c2为学习因子,通常设置c1=c2=2,r1,r2为0到1的均匀分布的随机数,式(15)w为惯性权值,权重的取值越大,全局搜索能力越强,取值越小,局部搜索能力越强,取值范围一般为(0,4)。where j=1,2,...,d, represents the individual extreme value, represents the global extreme value, t represents the current number of iterations, c 1 , c 2 are learning factors, usually set c 1 =c 2 =2, r 1 , r 2 are uniformly distributed random numbers from 0 to 1, formula (15 )w is the inertia weight, the larger the value of the weight, the stronger the global search ability, the smaller the value, the stronger the local search ability, the value range is generally (0,4).
2.3莱维飞行2.3 Levi flight
莱维飞行是一种用来描述莱维分布的随机搜索的行走方法。许多研究表明,在大自然中许多昆虫和动物的行为都是符合莱维分布。莱维飞行主要采用的是Mantegna算法,用来生成符合莱维分布的随机步长,其实质就是在随机行走时具有极高的概率出现大的跨步,因此可以保证种群的多样性和避免陷入局部最优。The Levy flight is a random search walk method used to describe the Levy distribution. Many studies have shown that the behavior of many insects and animals in nature conforms to the Levy distribution. The Levy flight mainly uses the Mantegna algorithm, which is used to generate a random step size that conforms to the Levy distribution. local optimum.
莱维飞行的位置更新公式如下式(16):The position update formula of Levi's flight is as follows (16):
式中:i∈[1,2,...,N],其中是表示第i个粒子在迭代第t次的位置,为初始位置,表示更新后的位置,表示点乘运算,α代表步长控制量,Levy(λ)表示随机搜索路径,并且Levy(λ)满足下式(17):where: i∈[1,2,...,N], where is the position of the i-th particle at the t-th iteration, which is the initial position, represents the updated location, represents the point multiplication operation, α represents the step size control amount, Levy(λ) represents the random search path, and Levy(λ) satisfies the following formula (17):
Levy(λ)~μ=t-λ,1<λ≤3 (17)Levy(λ)~μ=t -λ , 1<λ≤3 (17)
莱维飞行的步长属于莱维分布,步长s的公式为式(18):The step size of the Levy flight belongs to the Levy distribution, and the formula for the step size s is Equation (18):
其中,μ,v属于正态分布如下式:Among them, μ, v belong to the normal distribution as follows:
其中,σμ,σv分别为下式(21)(22):Among them, σ μ , σ v are respectively the following formulas (21) (22):
σv=1 (22) σv = 1 (22)
其中β取值通常为1.5。The value of β is usually 1.5.
2.4基于PSO-GWO混合的磁偶极子定位算法2.4 Magnetic Dipole Localization Algorithm Based on PSO-GWO Hybrid
由于灰狼算法的灰狼群体遵从α狼,β狼,δ狼的指挥进行狩猎,但是每个个体之间是独立的,灰狼个体和群体之间缺乏有用的信息交流从而没有利用有用的信息,导致算法收敛速度过慢而且精度不高,所以将粒子群算法中的位置更新公式引入到灰狼算法位置更新公式来,从而将有用的信息利用起来,这种混合算法具有记忆性和合作机制。此外引入惯性常数w来调节灰狼粒子群混合算法的局部寻优能力和全局寻优能力,因此混合算法的位置更新和灰狼距离公式如下(23)(24):Since the gray wolf group of the gray wolf algorithm follows the commands of alpha wolves, beta wolves, and delta wolves to hunt, but each individual is independent, there is no useful information exchange between gray wolves and the group, so useful information is not used. , causing the algorithm to converge too slowly and the accuracy is not high, so the position update formula in the particle swarm algorithm is introduced into the position update formula of the gray wolf algorithm, so as to make use of useful information, this hybrid algorithm has memory and cooperation mechanism . In addition, the inertia constant w is introduced to adjust the local optimization ability and global optimization ability of the hybrid algorithm of gray wolf particle swarm. Therefore, the position update and gray wolf distance formula of the hybrid algorithm are as follows (23) (24):
2.5改进的PSO-GWO算法2.5 Improved PSO-GWO Algorithm
2.5.1佳点集初始化2.5.1 Best point set initialization
佳点集的定义为:假设GD是D维空间的单位立方体,假设r∈GD,形为偏差的集合称作佳点集,r称为佳点。其中C(r,ε)为常数且只与r,ε(ε>0)有关,取rk={2cos(2πk/p)},1≤k≤M,其中p是满足(p-D/2)≥D的最小素数,或rk={exp(k)},1≤k≤M,{a}是a的小数部分。理论证明,当计算函数在GD上积分时,取n个佳点得到的误差是最小的相对于用任意给定的n个点的函数值构成的加权和而已。The definition of good point set is: Suppose G D is a unit cube of D-dimensional space, and suppose r∈G D , the form is deviation The set of is called the good point set, and r is called the good point. where C(r,ε) is a constant and is only related to r,ε(ε>0), take r k ={2cos(2πk/p)}, 1≤k≤M, where p is satisfying (pD/2) The smallest prime number ≥D, or r k ={exp(k)}, 1≤k≤M, and {a} is the fractional part of a. Theoretically, when the calculation function is integrated on G D , the error obtained by taking n optimal points is the smallest relative to the weighted sum formed by the function values of any given n points.
图4、图5分别表示使用佳点集初始化方法和随机初始化方法产生的种群规模为100的二维初始种群分布图。Figure 4 and Figure 5 respectively show the two-dimensional initial population distribution diagrams with a population size of 100 generated by using the good point set initialization method and the random initialization method.
从图可以看出,在都取100点的情况下,佳点集初始化比随机初始化产生的种群分布更加均匀,其次,佳点集的种群分布与维度无关,可以很好地适应高维问题;另外,佳点集初始化时每次取得种群分布效果都是一样的,具有很高的稳定性。因此将GD的佳点映射到目标求解空间,可以得到更均匀的取点方法。由于PSO-GWO混合算法是通过粒子在求解空间移动来求得最优解,经过迭代,局部最优不断向全局最优靠近,所以此时如果种群陷入早熟收敛,那么算法将无法寻得全局最优解,但是通过佳点集初始化方法可以将粒子均匀分布在种群当前最优位置的周围解空间,能更有效地表征解空间特征,使得初始种群保持良好的多样性,从而避免算法陷入局部最优,最终收敛到全局最优。It can be seen from the figure that in the case of taking 100 points, the optimal point set initialization is more uniform than the population distribution generated by random initialization. Secondly, the population distribution of the good point set has nothing to do with the dimension, which can be well adapted to high-dimensional problems; In addition, when the optimal point set is initialized, the population distribution effect is the same every time, and it has high stability. Therefore, by mapping the best points of GD to the target solution space, a more uniform point selection method can be obtained. Since the PSO-GWO hybrid algorithm obtains the optimal solution by moving the particles in the solution space, after iteration, the local optimum is constantly approaching the global optimum, so if the population falls into premature convergence at this time, the algorithm will not be able to find the global optimum. However, through the optimal point set initialization method, the particles can be evenly distributed in the solution space around the current optimal position of the population, which can more effectively characterize the solution space characteristics, so that the initial population maintains a good diversity, so as to avoid the algorithm falling into the local optimum. , and eventually converge to the global optimum.
2.5.2加入个体最优记忆和莱维飞行2.5.2 Adding Individual Optimal Memory and Levi's Flight
由于灰狼算法容易陷入局部最优,将粒子个体历史最优的经验加入到GWO算法中可以改善粒子的分布情况,但改进后的PSO-GWO仍具有陷入局部最优的缺点。莱维飞行兼顾了较短距离的搜索和偶尔长距离的步长,可以打破粒子“聚集”情况,可以提高种群粒子的活性和跳跃能力,从根本上可以改善PSO-GWO混合算法的容易陷入局部最优的缺陷。基于莱维飞行策略,位置更新公式表示为下式(25):Since the gray wolf algorithm is easy to fall into the local optimum, adding the experience of individual particle historical optimum into the GWO algorithm can improve the distribution of particles, but the improved PSO-GWO still has the disadvantage of falling into the local optimum. Levy flight takes into account the short-distance search and the occasional long-distance step size, which can break the particle "clustering" situation, improve the activity and jumping ability of the population particles, and fundamentally improve the PSO-GWO hybrid algorithm. optimal defect. Based on the Levi flight strategy, the position update formula is expressed as the following formula (25):
通过加入改变概率Pc=0.5,在每次迭代的时候对比迭代时设置的随机数A=rand()来判断是否需要进行莱维飞行策略。By adding a change probability P c =0.5, in each iteration, the random number A=rand( ) set in the iteration is compared to determine whether the Levi flight strategy needs to be performed.
整个改进PSO-GWO算法的具体步骤如下:The specific steps of the whole improved PSO-GWO algorithm are as follows:
(1)利用佳点集初始化方法生成初始位置X,给定初始种群规模N,最大迭代次数max_iter,种群维度D,学习系数c1,c2等参数;(1) Using the good point set initialization method to generate the initial position X, given the initial population size N, the maximum number of iterations max_iter, the population dimension D, the learning coefficients c 1 , c 2 and other parameters;
(2)使得适应度函数最小,灰狼算法求得最优解、次优解和季优解后跳出该循环;(2) Minimize the fitness function, and jump out of the loop after obtaining the optimal solution, the suboptimal solution and the quarterly optimal solution by the gray wolf algorithm;
(3)每次循环时更新和根据式子(23)更新速度和位置;同时按照概率Pc=0.5随机选择粒子进行莱维飞行,按照式(25)跳出局部最优,来更新速度和位置;(3) Update every cycle and Update speed and position according to formula (23); at the same time randomly select particles to carry out Levi flight according to probability P c =0.5, and jump out of the local optimum according to formula (25) to update speed and position;
(4)判断迭代次数是否等于预设上限值,如果等于则结束运行;否则,跳转到(2)。(4) Determine whether the number of iterations is equal to the preset upper limit value, and if so, end the operation; otherwise, jump to (2).
下面结合仿真实验对本发明的技术方案作详细的描述。The technical solution of the present invention is described in detail below in conjunction with simulation experiments.
为了验证基于莱维飞行的PSO-GWO混合算法的磁偶极子定位性能,采用搭建的基于改进智能优化算法的磁偶极子目标定位仿真系统进行分析。如图7所示,以1号传感器节点作为原点建立直角坐标系,其余三个磁传感器的位置如图7所示。假设磁偶极子运动至A点(见图8),给定其位置与角度信息(见表1),然后代入公式反推出各个节点处的磁感应强度三分量值,将这些坐标值作为算法的入口参数,参数估计精度可以用均方误差来衡量,公式为:In order to verify the magnetic dipole localization performance of the PSO-GWO hybrid algorithm based on Levy flight, the magnetic dipole target localization simulation system based on the improved intelligent optimization algorithm is used for analysis. As shown in Figure 7, a Cartesian coordinate system is established with the No. 1 sensor node as the origin, and the positions of the remaining three magnetic sensors are shown in Figure 7. Assuming that the magnetic dipole moves to point A (see Figure 8), its position and angle information (see Table 1) is given, and then the three-component value of the magnetic induction intensity at each node is deduced by substituting the formula, and these coordinate values are used as the algorithm's Entry parameters, the parameter estimation accuracy can be measured by the mean square error, the formula is:
其中假设磁性目标的实际参数为x,xi为第i次实验的估计结果,N是总的蒙特卡洛仿真次数。It is assumed that the actual parameter of the magnetic target is x, x i is the estimated result of the ith experiment, and N is the total number of Monte Carlo simulations.
算法参数设置如下:设有四个磁传感器并且传感器的位置如上图所示,参数的控制范围分别为:x∈[0,10],y∈[0,10],z∈[0,10],m∈[0,2000],θ∈[0,π/2],学习因子c1=c2=c3=0.5,PSO算法的参数设置为c1=c2=2,w=0.8,PSO-GWO算法的参数设置为wmax=0.9,wmin=0.2,其中莱维飞行中的beta=1.5,随机跳出的概率Pc=0.5,因为实际传感器测量数据中包含噪声,所以设置信噪比SNR从-5dB每隔10dB变换到35dB,最大迭代次数max_iter为100次,种群规模N为60。蒙特卡洛仿真次数为50次,计算均方根误差值用于不同算法的性能比较。The algorithm parameters are set as follows: There are four magnetic sensors and the positions of the sensors are as shown in the figure above. The control ranges of the parameters are: x∈[0,10], y∈[0,10], z∈[0,10] ,m∈[0,2000],θ∈[0,π/2], The learning factor c 1 =c 2 =c 3 =0.5, the parameters of the PSO algorithm are set as c 1 =c 2 =2,w=0.8,the parameters of the PSO-GWO algorithm are set as wmax=0.9,wmin=0.2, where Levy beta=1.5 in flight, the probability of random jumping out P c =0.5, because the actual sensor measurement data contains noise, so set the signal-to-noise ratio SNR from -5dB every 10dB to 35dB, the maximum number of iterations max_iter is 100 times, the population The scale N is 60. The number of Monte Carlo simulations is 50, and the root mean square error value is calculated for the performance comparison of different algorithms.
表1目标运动到A点的参数值Table 1 The parameter values of the target moving to point A
应用PSO、GWO和本发明所提的改进PSO-GWO算法得到的不同信噪比下目标定位结果如图9所示,由图9可以看出在信噪比非常低的情况下,与GWO和PSO算法相比,PSO-GWO算法能保持很高的精度,在信噪比SNR=35时,PSO-GWO算法的定位误差可以减小到0.01。无论是低信噪比还是高信噪比,PSO-GWO算法的求解性能均优于PSO算法和GWO算法。The target localization results under different signal-to-noise ratios obtained by applying PSO, GWO and the improved PSO-GWO algorithm proposed in the present invention are shown in Figure 9. It can be seen from Figure 9 that in the case of a very low signal-to-noise ratio, it is different from GWO and GWO. Compared with the PSO algorithm, the PSO-GWO algorithm can maintain high precision, and when the signal-to-noise ratio SNR=35, the positioning error of the PSO-GWO algorithm can be reduced to 0.01. Whether it is low SNR or high SNR, the solution performance of PSO-GWO algorithm is better than that of PSO algorithm and GWO algorithm.
另外图10(a)-图10(e)清晰的展现了在迭代次数为100次时信噪比从-5dB变换到35dB的情况下,三个算法收敛曲线的变化趋势。对于每一种SNR的情况,PSO-GWO算法的收敛速度均优于其他两种算法。从上述结果可以看出,无论是求解精度还是收敛速度,所提的PSO-GWO都优于其他两种算法。In addition, Fig. 10(a)-Fig. 10(e) clearly show the changing trend of the convergence curves of the three algorithms when the SNR is changed from -5dB to 35dB when the number of iterations is 100. For each SNR case, the convergence speed of the PSO-GWO algorithm is better than the other two algorithms. From the above results, it can be seen that the proposed PSO-GWO is better than the other two algorithms in terms of solution accuracy and convergence speed.
结论:本发明研究了基于改进智能优化算法的磁偶极子目标定位方法。通过运用佳点集初始化方法初始化灰狼粒子群种群,然后加入PSO算法的粒子合作机制,改善灰狼算法对信息的利用率,加入改变概率和莱维飞行来提高粒子的活性和保持粒子的多样性,使其跳出局部最优解,通过在不同的SNR下进行仿真测试,与PSO算法、GWO算法的定位结果比较,改进的算法在收敛速度和求解精度上面都有很大的提升,验证了在低信噪比下改进PSO-GWO算法的有效性。Conclusion: The present invention studies a magnetic dipole target location method based on an improved intelligent optimization algorithm. By using the good point set initialization method to initialize the gray wolf particle swarm population, and then adding the particle cooperation mechanism of the PSO algorithm to improve the information utilization rate of the gray wolf algorithm, adding change probability and Levi flight to improve the activity of particles and maintain the diversity of particles Compared with the positioning results of the PSO algorithm and the GWO algorithm, the improved algorithm has a great improvement in the convergence speed and solution accuracy. It is verified that Improving the effectiveness of PSO-GWO algorithm at low signal-to-noise ratio.
应当注意,本发明的实施方式可以通过硬件、软件或者软件和硬件的结合来实现。硬件部分可以利用专用逻辑来实现;软件部分可以存储在存储器中,由适当的指令执行系统,例如微处理器或者专用设计硬件来执行。本领域的普通技术人员可以理解上述的设备和方法可以使用计算机可执行指令和/或包含在处理器控制代码中来实现,例如在诸如磁盘、CD或DVD-ROM的载体介质、诸如只读存储器(固件)的可编程的存储器或者诸如光学或电子信号载体的数据载体上提供了这样的代码。本发明的设备及其模块可以由诸如超大规模集成电路或门阵列、诸如逻辑芯片、晶体管等的半导体、或者诸如现场可编程门阵列、可编程逻辑设备等的可编程硬件设备的硬件电路实现,也可以用由各种类型的处理器执行的软件实现,也可以由上述硬件电路和软件的结合例如固件来实现。It should be noted that the embodiments of the present invention may be implemented by hardware, software, or a combination of software and hardware. The hardware portion may be implemented using special purpose logic; the software portion may be stored in memory and executed by a suitable instruction execution system, such as a microprocessor or specially designed hardware. Those of ordinary skill in the art will appreciate that the apparatus and methods described above may be implemented using computer-executable instructions and/or embodied in processor control code, for example on a carrier medium such as a disk, CD or DVD-ROM, such as a read-only memory Such code is provided on a programmable memory (firmware) or a data carrier such as an optical or electronic signal carrier. The device and its modules of the present invention can be implemented by hardware circuits such as very large scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, etc., or programmable hardware devices such as field programmable gate arrays, programmable logic devices, etc., It can also be implemented by software executed by various types of processors, or by a combination of the above-mentioned hardware circuits and software, such as firmware.
以上所述,仅为本发明的具体实施方式,但本发明的保护范围并不局限于此,任何熟悉本技术领域的技术人员在本发明揭露的技术范围内,凡在本发明的精神和原则之内所作的任何修改、等同替换和改进等,都应涵盖在本发明的保护范围之内。The above are only specific embodiments of the present invention, but the protection scope of the present invention is not limited to this. Any person skilled in the art is within the technical scope disclosed by the present invention, and all within the spirit and principle of the present invention Any modifications, equivalent replacements and improvements made within the scope of the present invention should be included within the protection scope of the present invention.
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