CN111709183B - An optimization method for neutron tube acceleration system based on genetic algorithm - Google Patents
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Abstract
Description
技术领域Technical field
本发明属于中子管加速系统技术领域,特别涉及一种基于遗传算法的中子管加速系统优化方法。The invention belongs to the technical field of neutron tube acceleration systems, and particularly relates to a neutron tube acceleration system optimization method based on genetic algorithms.
背景技术Background technique
中子管是一种小型加速器,其是将离子源、加速器、靶和储存器全密封在玻璃真空管或陶瓷真空管中;具有结构紧凑、安全性高、使用方便等优点;目前,中子管广泛应用于中子照相、中子治疗及石油测井等领域。The neutron tube is a small accelerator, which completely seals the ion source, accelerator, target and storage in a glass vacuum tube or ceramic vacuum tube; it has the advantages of compact structure, high safety and easy use; currently, neutron tubes are widely used It is used in fields such as neutron photography, neutron therapy and petroleum logging.
中子管加速系统从离子源等离子体引出束流,通过电场力对束流的聚焦、加速,影响了最终到达靶面的束流性能;其中,束流强度和均匀度为评价束流性能的重要指标;现有技术中,通常采用有限元模拟方法,对加速系统的结构进行参数优化,提高束流的均匀度,进而提高中子管的性能;而现有技术中,仅采用有限元模拟方法进行参数优化时,常常无法得到最优解,导致束流均匀度较低,损伤靶的使用寿命和性能,进而影响中子管的寿命和性能。The neutron tube acceleration system draws out the beam from the ion source plasma, and focuses and accelerates the beam through the electric field force, which affects the beam performance that finally reaches the target surface; among them, the beam intensity and uniformity are the parameters for evaluating the beam performance. Important indicators; in the existing technology, the finite element simulation method is usually used to optimize the parameters of the acceleration system structure to improve the uniformity of the beam, thereby improving the performance of the neutron tube; in the existing technology, only finite element simulation is used When optimizing parameters using this method, the optimal solution is often not obtained, resulting in low beam uniformity, damaging the service life and performance of the target, and thus affecting the life and performance of the neutron tube.
发明内容Contents of the invention
针对现有技术中存在的技术问题,本发明供了一种中子管加速系统优化设计方法及中子管加速系统,以解决现有技术仅采用有限元模拟方法进行中子管加速系统参数优化时,常常无法得到最优解,导致束流均匀度较低,进而影响中子管的寿命和性能的技术问题。In view of the technical problems existing in the prior art, the present invention provides a neutron tube acceleration system optimization design method and a neutron tube acceleration system to solve the problem that the prior art only uses the finite element simulation method to optimize the neutron tube acceleration system parameters. At this time, the optimal solution is often not obtained, resulting in low beam uniformity, which in turn affects the technical problems of the life and performance of the neutron tube.
为达到上述目的,本发明采用的技术方案为:In order to achieve the above objects, the technical solutions adopted by the present invention are:
本发明提供了一种基于遗传算法的中子管加速系统优化方法,包括以下步骤:The invention provides a neutron tube acceleration system optimization method based on genetic algorithm, which includes the following steps:
步骤1、初始化Step 1. Initialization
以中子管加速系统的几何结构参数为待优化参数,随机生成N个二进制数表示待优化参数,成为一个个体,构成初始种群;Taking the geometric structure parameters of the neutron tube acceleration system as the parameters to be optimized, N binary numbers are randomly generated to represent the parameters to be optimized and become an individual to form the initial population;
步骤2、计算个体适应度Step 2. Calculate individual fitness
将获得的二进制数进行转换,生成十进制表示的中子管加速系统几何结构参数;根据十进制表示的中子管加速系统几何结构参数,构建中子管加速系统几何模型;采用有限元法,计算遗传个体对应的中子管加速系统的束流性能指标;Convert the obtained binary numbers to generate the geometric structure parameters of the neutron tube acceleration system expressed in decimal system; construct a geometric model of the neutron tube acceleration system based on the geometric structure parameters of the neutron tube acceleration system expressed in decimal system; use the finite element method to calculate the genetic The beam performance index of the individual corresponding neutron tube acceleration system;
根据中子管加速系统的束流性能指标,建立目标函数;然后以目标函数值来度量遗传个体的适应度;According to the beam performance index of the neutron tube acceleration system, an objective function is established; then the fitness of the genetic individual is measured by the value of the objective function;
步骤3、迭代进行遗传操作,生成新种群,计算新种群每个个体的适应度,直至满足迭代停止条件,输出满足迭代停止条件时的最优解,作为待优化参数的取值,并按照待优化参数的取值制作中子管加速系统。Step 3: Perform genetic operations iteratively to generate a new population, calculate the fitness of each individual in the new population until the iteration stop condition is met, and output the optimal solution when the iteration stop condition is met as the value of the parameter to be optimized, and follow the steps to be taken. Optimize the values of parameters to create a neutron tube acceleration system.
进一步的,步骤1中,待优化参数包括中子管加速系统的加速间隙、加速电极极小径、加速电极长度、引出极孔径、磁环坡口径、导磁筒坡口径及加速电极孔径。Further, in step 1, the parameters to be optimized include the accelerating gap of the neutron tube accelerating system, the accelerating electrode pole diameter, the accelerating electrode length, the lead pole aperture, the magnetic ring slope diameter, the magnetic cylinder slope aperture and the accelerating electrode aperture.
进一步的,步骤2中,遗传个体对应的中子管加速系统的束流性能指标包括束流不均匀度、束流脱靶数及束流半径;Further, in step 2, the beam performance indicators of the neutron tube acceleration system corresponding to the genetic individual include beam unevenness, beam miss number and beam radius;
目标函数的数学表达式为:The mathematical expression of the objective function is:
目标函数ObjV=target/base+outtarget;Target function ObjV=target/base+outtarget;
其中,target为束流不均匀度;outtarget为束流脱靶数、base为束流半径;目标函数值越小,表示遗传个体的适应度越优良;Among them, target is the beam unevenness; outtarget is the number of beam misses, and base is the beam radius; the smaller the objective function value, the better the fitness of the genetic individual;
其中,束流不均匀度target的数学表达式为:Among them, the mathematical expression of beam unevenness target is:
其中,o为不均匀度;Zx为理想状态下,靶面上某个圆环x中的粒子数;Ax为靶面上某个圆环x的面积;A总为靶面总面积;Ux为靶面上某个圆环x中的实际粒子数;x=1,2,…,n。Among them, o is the non-uniformity; Z x is the number of particles in a certain ring x on the target surface under ideal conditions; A x is the area of a certain ring x on the target surface; A is the total area of the target surface; U x is the actual number of particles in a certain ring x on the target surface; x=1,2,…,n.
进一步的,利用有限元方法与Matlab软件对目标函数进行求解。Furthermore, the finite element method and Matlab software are used to solve the objective function.
进一步的,步骤3中,遗传操作包括选择、交叉和变异;其中,选择操作根据遗传个体适应度值的大小,采用精英选择与轮盘赌相结合机制;交叉操作采用均匀交叉方式,随机选择个体实施行交叉或列交叉;变异操作采用位变异机制。Further, in step 3, genetic operations include selection, crossover and mutation; among them, the selection operation uses a mechanism combining elite selection and roulette based on the fitness value of the genetic individual; the crossover operation uses a uniform crossover method and randomly selects individuals. Implement row crossover or column crossover; mutation operation uses bit mutation mechanism.
进一步的,步骤3中,满足迭代停止条件为达到最大进化代数,此时最优解为当前种群中适应度最小的个体所对应的待优化参数。Further, in step 3, the iteration stop condition is met to reach the maximum evolutionary generation, and the optimal solution at this time is the parameter to be optimized corresponding to the individual with the smallest fitness in the current population.
进一步的,步骤3中,满足迭代停止条件为适应度达到设定要求,此时最优解为适应度达到设定要求的个体所对应的待优化参数。Further, in step 3, the iteration stop condition is satisfied when the fitness reaches the set requirements. At this time, the optimal solution is the parameters to be optimized corresponding to the individuals whose fitness reaches the set requirements.
与现有技术相比,本发明的有益效果为:Compared with the prior art, the beneficial effects of the present invention are:
本发明提供了一种基于遗传算法的中子管加速系统优化方法,利用有限元法计算中子管加速系统的束流性能指标,然后应用遗传算法,将中子管加速系统的束流性能作为目标,对中子管加速系统的几何结构参数进行全局寻优;本发明根据中子管加速系统的性能指标要求,自动搜寻具有全局最优的结构尺寸,从而得到优化几何结构参数下的中子管加速系统;解决了仅采用有限元模拟方法进行中子管加速系统参数优化时,常常无法得到最优解的问题,明显提高了中子管的束流性能;节省了大量的方案选配时间,提高了工作效率,有效提高了中子管的使用寿命和性能。The present invention provides a neutron tube acceleration system optimization method based on a genetic algorithm. The finite element method is used to calculate the beam performance index of the neutron tube acceleration system, and then the genetic algorithm is applied to calculate the beam performance of the neutron tube acceleration system as The goal is to globally optimize the geometric structure parameters of the neutron tube accelerating system; this invention automatically searches for the globally optimal structural size according to the performance index requirements of the neutron tube accelerating system, thereby obtaining the neutron under optimized geometric structure parameters. Tube acceleration system; solves the problem that the optimal solution is often not obtained when optimizing the parameters of the neutron tube acceleration system using only finite element simulation methods, significantly improves the beam performance of the neutron tube; and saves a lot of time in program selection. , improves work efficiency and effectively improves the service life and performance of the neutron tube.
进一步的,中子管加速系统中加速区域的引出极侧和加速极侧对粒子束流聚焦影响较大,根据电势和粒子轨迹的结果,通过将中子管加速系统中的加速间隙、加速电极极小径、加速电极长度、引出极孔径、磁环坡口径、导磁筒坡口径及加速电极孔径作为待优化参数,能够有效提高中子管加速系统的束流性能,进而提高了中子管的使用寿命和性能;上述七个中子管加速系统的几何结构参数形成一个遗传算法的个体,遗传算法根据个体的适应度选择交叉变异,适应度好的个体基因被后代继承的概率较大,遗传下去就是最优解。Furthermore, the extraction pole side and the accelerating pole side of the accelerating area in the neutron tube accelerating system have a greater impact on the focusing of the particle beam. According to the results of the potential and particle trajectories, the accelerating gap and accelerating electrode in the neutron tube accelerating system are The extremely small diameter, the length of the accelerating electrode, the diameter of the extraction pole, the diameter of the magnetic ring slope, the diameter of the magnetic cylinder slope and the aperture of the accelerating electrode are the parameters to be optimized, which can effectively improve the beam performance of the neutron tube acceleration system, thereby improving the neutron tube's Service life and performance; the geometric structure parameters of the above seven neutron tube acceleration systems form an individual genetic algorithm. The genetic algorithm selects cross-mutation based on the fitness of the individual. The individual genes with good fitness have a greater probability of being inherited by future generations. Genetic Going down is the optimal solution.
进一步的,选取束流不均匀度、束流脱靶数及束流半径作为中子管加速系统束流性能指标,能够直观反映束流性能,加速系统的优劣可以通过束流不均匀度、束流半径、束流脱靶数来评估,目标函数值越小证明个体越优良。Furthermore, the beam unevenness, beam miss number and beam radius are selected as the beam performance indicators of the neutron tube acceleration system, which can intuitively reflect the beam performance. The quality of the acceleration system can be measured through the beam unevenness, beam radius. It is evaluated by the flow radius and the number of beam misses. The smaller the value of the objective function, the better the individual.
进一步的,目标函数采用有限元方法与Matlab软件联合算出,充分结合COMSOL仿真和MATLAB编程的优势,可广泛适应使用不同尺寸磁性纳米粒子装置的磁性纳米粒子仿真测试平台的优化需要,并可以通过不同软件之间的参数传递,直接生成和保存符合要求的磁性纳米粒子测量仿真模型。Furthermore, the objective function is jointly calculated using the finite element method and Matlab software, fully combining the advantages of COMSOL simulation and MATLAB programming. It can be widely adapted to the optimization needs of magnetic nanoparticle simulation test platforms using magnetic nanoparticle devices of different sizes, and can be used through different Parameter transfer between software directly generates and saves magnetic nanoparticle measurement simulation models that meet the requirements.
综上,本发明采用有限元方法、遗传算法及均匀度评价方法三者相互结合,借助COMSOL及MATLAB软件对中子管的加速系统进行优化设计,最终获得了性能较好的加速系统结构,提高了中子管性能,用于指导中子管的设计与制造,实用性较高。In summary, the present invention uses the finite element method, the genetic algorithm and the uniformity evaluation method to combine each other, and uses COMSOL and MATLAB software to optimize the design of the neutron tube acceleration system, and finally obtains an acceleration system structure with better performance, improving The performance of neutron tubes is understood and used to guide the design and manufacture of neutron tubes, which is highly practical.
附图说明Description of drawings
图1为本发明所述的中子管加速系统优化方法的流程示意图;Figure 1 is a schematic flow chart of the neutron tube acceleration system optimization method according to the present invention;
图2为本发明所述的中子管加速系统优化方法中的个体适应度评估方法流程图;Figure 2 is a flow chart of the individual fitness evaluation method in the neutron tube acceleration system optimization method according to the present invention;
图3为实施例所述的最优解中子管加速系统的束流粒子在靶面上的分布图;Figure 3 is a distribution diagram of beam particles on the target surface of the optimal solution neutron tube acceleration system described in the embodiment;
图4为实施例所述的中子管加速系统的遗传算法收敛示意图。Figure 4 is a schematic diagram of the convergence of the genetic algorithm of the neutron tube acceleration system described in the embodiment.
具体实施方式Detailed ways
为了使本发明所解决的技术问题,技术方案及有益效果更加清楚明白,以下具体实施例,对本发明进行进一步的详细说明。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 technical problems, technical solutions and beneficial effects solved by the present invention clearer, the following specific examples will further describe the present invention in detail. It should be understood that the specific embodiments described here are only used to explain the present invention and are not intended to limit the present invention.
如附图1、2所示,一种基于遗传算法的中子管加速系统优化方法,包括以下步骤:As shown in Figures 1 and 2, a neutron tube acceleration system optimization method based on genetic algorithm includes the following steps:
步骤1、初始化Step 1. Initialization
以中子管加速系统的几何结构参数为待优化参数,随机生成N个二进制数表示待优化参数,成为一个个体,构成初始种群;其中,待优化参数包括中子管加速系统的加速间隙、加速电极极小径、加速电极长度、引出极孔径、磁环坡口径、导磁筒坡口径及加速电极孔径。Taking the geometric structure parameters of the neutron tube acceleration system as the parameters to be optimized, N binary numbers are randomly generated to represent the parameters to be optimized and become an individual to form the initial population; among them, the parameters to be optimized include the acceleration gap and acceleration of the neutron tube acceleration system. The diameter of the electrode pole, the length of the accelerating electrode, the aperture of the lead pole, the diameter of the magnetic ring slope, the diameter of the magnetic cylinder slope and the aperture of the accelerating electrode.
步骤2、计算个体适应度Step 2. Calculate individual fitness
将获得的二进制数进行转换,生成十进制表示的中子管加速系统几何结构参数;根据十进制表示的中子管加速系统几何结构参数,构建中子管加速系统几何模型;采用有限元法,计算遗传个体对应的中子管加速系统的束流性能指标;其中,中子管加速系统的束流性能指标包括束流不均匀度、束流脱靶数及束流半径。Convert the obtained binary numbers to generate the geometric structure parameters of the neutron tube acceleration system expressed in decimal system; construct a geometric model of the neutron tube acceleration system based on the geometric structure parameters of the neutron tube acceleration system expressed in decimal system; use the finite element method to calculate the genetic The beam performance indicators of the individual corresponding neutron tube accelerating system; among them, the beam performance indicators of the neutron tube accelerating system include beam unevenness, beam miss number and beam radius.
根据中子管加速系统束流性能评价指标,建立目标函数;然后以目标函数值来度量遗传个体的适应度;其中,目标函数的数学表达式为:According to the beam performance evaluation index of the neutron tube acceleration system, an objective function is established; then the objective function value is used to measure the fitness of the genetic individual; among them, the mathematical expression of the objective function is:
目标函数ObjV=target/base+outtarget;Target function ObjV=target/base+outtarget;
其中,target为束流不均匀度;outtarget为束流脱靶数、base为束流半径;目标函数值越小,表示遗传个体的适应度越优良;Among them, target is the beam unevenness; outtarget is the number of beam misses, and base is the beam radius; the smaller the objective function value, the better the fitness of the genetic individual;
其中,束流不均匀度target的数学表达式为:Among them, the mathematical expression of beam unevenness target is:
其中,o为不均匀度;Zx为理想状态下,靶面上某个圆环x中的粒子数;Ax为靶面上某个圆环x的面积;A总为靶面总面积;Ux为靶面上某个圆环x中的实际粒子数;x=1,2,…,n。Among them, o is the non-uniformity; Z x is the number of particles in a certain ring x on the target surface under ideal conditions; A x is the area of a certain ring x on the target surface; A is the total area of the target surface; U x is the actual number of particles in a certain ring x on the target surface; x=1,2,…,n.
束流脱靶数根据有限元模拟计算结果,读取粒子的三维坐标,统计坐标是否在靶上获得。The number of beam misses is based on the finite element simulation calculation results, reading the three-dimensional coordinates of the particles, and counting whether the coordinates are obtained on the target.
束流半径通过计算靶面上粒子坐标到靶面中心坐标的距离获得。The beam radius is obtained by calculating the distance from the particle coordinates on the target surface to the target center coordinates.
步骤3、迭代进行遗传操作,生成新种群,计算新种群每个个体的适应度,直至满足迭代停止条件,输出满足迭代停止条件时的最优解,作为待优化参数的取值,并按照待优化参数的取值制作中子管加速系统;其中,遗传操作包括选择、交叉和变异;其中,选择操作根据遗传个体适应度值的大小,采用精英选择与轮盘赌相结合机制;交叉操作采用均匀交叉方式,随机选择个体实施行交叉或列交叉;变异操作采用位变异机制;满足迭代停止条件为达到最大进化代数或适应度达到设定要求,当满足迭代停止条件为达到最大进化代数时,最优解为当前种群中适应度最小的个体所对应的待优化参数;当满足迭代停止条件为适应度达到设定要求时,最优解为适应度达到设定要求的个体所对应的待优化参数。Step 3: Perform genetic operations iteratively to generate a new population, calculate the fitness of each individual in the new population until the iteration stop condition is met, and output the optimal solution when the iteration stop condition is met as the value of the parameter to be optimized, and follow the steps to be taken. Optimize the values of parameters to create a neutron tube acceleration system; among them, genetic operations include selection, crossover and mutation; among them, the selection operation uses a combination of elite selection and roulette based on the fitness value of the genetic individual; the crossover operation uses In the uniform crossover method, individuals are randomly selected to perform row crossover or column crossover; the mutation operation adopts a bit mutation mechanism; when the iteration stop condition is met to reach the maximum evolutionary generation or the fitness reaches the set requirements, when the iteration stop condition is met to reach the maximum evolutionary generation, The optimal solution is the parameter to be optimized corresponding to the individual with the smallest fitness in the current population; when the iteration stop condition is met and the fitness reaches the set requirement, the optimal solution is the parameter to be optimized corresponding to the individual whose fitness reaches the set requirement. parameter.
本发明提供了一种基于遗传算法的中子管加速系统优化方法,利用有限元法计算中子管加速系统的束流性能指标,然后应用遗传算法,将中子管加速系统的束流性能作为目标,对中子管加速系统的几何结构参数进行全局寻优;本发明根据中子管加速系统的性能指标要求,自动搜寻具有全局最优的结构尺寸,从而得到优化几何结构参数下的中子管加速系统;解决了仅采用有限元模拟方法进行中子管加速系统参数优化时,常常无法得到最优解的问题,明显提高了中子管加速系统的束流性能,节省了大量的方案选配时间,提高了工作效率,有效提高了中子管的使用寿命和性能。The present invention provides a neutron tube acceleration system optimization method based on a genetic algorithm. The finite element method is used to calculate the beam performance index of the neutron tube acceleration system, and then the genetic algorithm is applied to calculate the beam performance of the neutron tube acceleration system as The goal is to globally optimize the geometric structure parameters of the neutron tube accelerating system; this invention automatically searches for the globally optimal structural size according to the performance index requirements of the neutron tube accelerating system, thereby obtaining the neutron under optimized geometric structure parameters. Tube acceleration system; it solves the problem that the optimal solution is often not obtained when optimizing the parameters of the neutron tube acceleration system using only finite element simulation methods. It significantly improves the beam performance of the neutron tube acceleration system and saves a lot of solution selection. Allocation time improves work efficiency and effectively improves the service life and performance of the neutron tube.
实施例Example
中子管加速系统中与粒子加速相关的结构主要有引出极、加速电极及靶,引出电极接地,加速电极加高压;引出电极与加速电极之间形成电势差,引出极出口的粒子在电场作用下向加速极运动,并形成粒子束;在加速过程后,由于惯性作用,粒子束继续向靶上运动,在向靶上漂移的过程中,粒子束半径越来越大,当粒子束半径越大,靶的有效面积越大,相同条件下的靶的寿命越长,从而中子管的使用寿命越长;利用有限元和遗传算法相互配合对中子管加速系统的几何结构参数化,通过提高束流在靶上分布的均匀性,进而提高中子管加速系统及中子管的使用寿命和性能。The structures related to particle acceleration in the neutron tube acceleration system mainly include the extraction electrode, the accelerating electrode and the target. The extraction electrode is grounded, and the accelerating electrode applies high voltage; a potential difference is formed between the extraction electrode and the accelerating electrode, and the particles at the outlet of the extraction electrode are affected by the electric field. Moves toward the acceleration pole and forms a particle beam; after the acceleration process, due to inertia, the particle beam continues to move toward the target. In the process of drifting toward the target, the particle beam radius becomes larger and larger. When the particle beam radius becomes larger, , the larger the effective area of the target, the longer the life of the target under the same conditions, and thus the longer the service life of the neutron tube; the finite element and genetic algorithm are used to parameterize the geometric structure of the neutron tube acceleration system, and by improving The uniformity of beam distribution on the target will improve the service life and performance of the neutron tube acceleration system and the neutron tube.
本实施例所述的一种基于遗传算法的中子管加速系统优化方法,包括以下步骤:The method for optimizing the neutron tube acceleration system based on genetic algorithm described in this embodiment includes the following steps:
步骤1、选取中子管加速系统中的加速间隙D、加速电极极小径D2、加速电极长度L、引出极孔径phi2、磁环坡口径fm2、导磁筒坡口径fm3及加速电极孔径D1,作为中子管加速系统的待优化参数;分别设定上述七个待优化参数的取值范围和精度;取值范围根据工程实际经验与结构尺寸不冲突设置参数范围,根据遗传算法模拟经验设置参数精度,一般把参数范围分成210份作为参数精度。Step 1. Select the accelerating gap D in the neutron tube accelerating system, the accelerating electrode extremely small diameter D 2 , the accelerating electrode length L, the lead pole aperture phi 2 , the magnetic ring slope diameter fm 2 , the magnetic cylinder slope diameter fm 3 and the accelerating electrode Aperture D 1 is used as the parameter to be optimized for the neutron tube acceleration system; the value range and accuracy of the above seven parameters to be optimized are set respectively; the value range is set according to the actual engineering experience and does not conflict with the structural size. The parameter range is set according to the genetic algorithm. The parameter accuracy is set by simulation experience. Generally, the parameter range is divided into 2 to 10 parts as the parameter accuracy.
以每一组待优化参数的取值作为种群中的一个个体,即以每一组中子管加速系统中的加速间隙D、加速电极极小径D2、加速电极长度L、引出极孔径phi2、磁环坡口径fm2、导磁筒坡口径fm3及加速电极孔径D1的取值作为种群中的一个个体,设置遗传算法的控制参数;其中,最大进化代数为100,初始种群大小为50,交叉概率为0.7,变异概率为0.1。The value of each group of parameters to be optimized is regarded as an individual in the population, that is, the acceleration gap D, the accelerating electrode minimum diameter D 2 , the accelerating electrode length L, and the extraction pole aperture phi 2 in each group of neutron tube accelerating system are used , the magnetic ring slope diameter fm 2 , the magnetic cylinder slope diameter fm 3 and the accelerating electrode aperture D 1 are used as an individual in the population to set the control parameters of the genetic algorithm; among them, the maximum evolutionary generation is 100, and the initial population size is 50, the crossover probability is 0.7, and the mutation probability is 0.1.
在中子管加速系统中,加速区域的引出极侧和加速区域的引出极侧和加速极侧对粒子束流聚焦过程响较大,进而影响靶上的束流分布,因此,选取中子管加速系统中的加速间隙D、加速电极极小径D2、加速电极长度L、引出极孔径phi2、磁环坡口径fm2、导磁筒坡口径fm3及加速电极孔径D1,作为中子管加速系统几何参数的优化变量,通过提高束流的均匀度和束流半径,降低束流的脱靶数,进而提高了中子管的使用寿命和性能。In the neutron tube acceleration system, the extraction pole side of the acceleration area and the extraction pole side and acceleration pole side of the acceleration area have a greater impact on the particle beam focusing process, which in turn affects the beam distribution on the target. Therefore, the selection of the neutron tube In the accelerating system, the accelerating gap D, the accelerating electrode pole diameter D 2 , the accelerating electrode length L, the lead pole aperture phi 2 , the magnetic ring slope aperture fm 2 , the magnetic cylinder slope aperture fm 3 and the accelerating electrode aperture D 1 are used as neutrons The optimized variables of the geometric parameters of the tube acceleration system can improve the uniformity and beam radius of the beam and reduce the number of beam misses, thus improving the service life and performance of the neutron tube.
步骤2、根据步骤1中设定的精度,确定个体长度,结合随机函数,随机生成N个二进制数表示待优化参数,成为一个个体,构成初始种群;Step 2. According to the accuracy set in step 1, determine the individual length, combine with the random function, randomly generate N binary numbers to represent the parameters to be optimized, and become an individual to form the initial population;
步骤3、对于构成的初始种群中的个体,将二进制数转换到十进制,将每个个体中七个待优化参数转换为相应的取值范围内的实数,计算得到个体适应度;Step 3. For the individuals in the initial population, convert the binary number to decimal, convert the seven parameters to be optimized in each individual into real numbers within the corresponding value range, and calculate the individual fitness;
个体适应度计算过程,具体如下:The individual fitness calculation process is as follows:
对每个个体,利用MATLAB软件与COMSOL仿真软件配合,将相应个体的七个待优化参数传输至COMSOL仿真软件中,通过程序在COMSOL仿真软件中进行其他的模型参数、材料属性及边界条件等设置,进行中子管加速系统几何模型的构建和计算;调用COMSOL软件计算粒子坐标,得到中子管加速系统的束流性能的三个性能指标,包括束流不均匀度target、束流脱靶数outtarget及束流半径base;For each individual, MATLAB software is used to cooperate with the COMSOL simulation software to transfer the seven parameters to be optimized of the corresponding individual to the COMSOL simulation software. Other model parameters, material properties, boundary conditions, etc. are set in the COMSOL simulation software through the program. , construct and calculate the geometric model of the neutron tube acceleration system; call COMSOL software to calculate the particle coordinates, and obtain three performance indicators of the beam performance of the neutron tube acceleration system, including beam unevenness target and beam miss number outtarget and beam radius base;
具体的,对于每个个体,根据每个个体中七个待优化参数转换为相应的取值范围内的实数,建立中子管加速系统的三维有限元模型,在中子管加速系统的模型结构的基础上,划分网格;在模型结构中设置接地,加速电极加电压,靶平面接电势。Specifically, for each individual, the seven parameters to be optimized in each individual are converted into real numbers within the corresponding value range, and a three-dimensional finite element model of the neutron tube acceleration system is established. In the model structure of the neutron tube acceleration system On the basis of , divide the mesh; set the grounding in the model structure, apply voltage to the accelerating electrode, and connect the target plane to potential.
进行完材料的选择,边界条件的施加,网格划分的操作后,对中子管加速系统的电场模拟计算,在电磁场的作用下,大量粒子向着某个方向运动形成束流,仿真中由于粒子数量级过大,采用部分粒子进行整体束流的仿真是可取的,而且对于中子管的束流强度,不需要考虑空间电荷的作用。After selecting materials, applying boundary conditions, and meshing operations, the electric field simulation calculation of the neutron tube acceleration system is performed. Under the action of the electromagnetic field, a large number of particles move in a certain direction to form a beam. In the simulation, due to the particle The order of magnitude is too large, it is advisable to use some particles to simulate the overall beam, and for the beam intensity of the neutron tube, there is no need to consider the role of space charge.
粒子轨迹的模拟在之前电势计算的基础上完成,在COMSOL仿真软件的粒子追踪模块中在粒子运动区域添加电场力,设置粒子属性如质量、电荷等,在引出极出口处添加粒子入口边界条件,释放10000个粒子,粒子密度服从高斯分布,粒子在电场力的作用下,向靶方向运动;并在靶模型的离子入口面添加壁边界条件,使粒子在表面上冻结,不继续向前运动。The simulation of particle trajectory is completed based on the previous electric potential calculation. In the particle tracking module of COMSOL simulation software, electric field force is added in the particle movement area, particle attributes such as mass, charge, etc. are set, and particle inlet boundary conditions are added at the exit of the extraction pole. Release 10,000 particles. The particle density obeys the Gaussian distribution. The particles move toward the target direction under the action of the electric field force. A wall boundary condition is added to the ion entrance surface of the target model to freeze the particles on the surface and stop moving forward.
粒子束流在靶面上的分布时,其中R为粒子距靶心的距离,R将用于粒子在靶上均匀度的计算;粒子束流在靶上的均匀度采用不均匀度进行评价,不均匀度越低,证明越均匀,不均匀度计算原理如下:When the particle beam is distributed on the target surface, R is the distance between the particles and the target center, and R will be used to calculate the uniformity of the particles on the target; the uniformity of the particle beam on the target is evaluated by non-uniformity. The lower the uniformity, the more uniform the proof is. The calculation principle of unevenness is as follows:
假设,半径为Rmax的圆中有10000个粒子,把Rmax分成10份;Assume that there are 10,000 particles in a circle with radius R max , and R max is divided into 10 parts;
理想状态下,10000个粒子按照面积比例,计算R1/10=0.665mm的圆内应当有粒子数Z1=10000×(1/10)2=100,假设实际情况Z1=14,两者相减的绝对值就是不均匀数Z=100-14=86;Under ideal conditions, 10,000 particles are calculated according to the area ratio and the number of particles Z 1 =10000×(1/10) 2 =100 should be in the circle of R 1/10 = 0.665mm. Assume that in the actual situation Z 1 =14, both The absolute value of the subtraction is the uneven number Z=100-14=86;
理想状态下,R1/10-R2/10的圆环内按照面积计算内应当有Z1=10000×[(2/10)2-(1/10)2]=300,假设实际情况Z1=184,两者相减的绝对值Z=300-184=126。Under ideal conditions, according to the area calculation, there should be Z 1 = 10000 × [(2/10)2-(1/10)2] = 300 in the ring of R 1/10 - R 2/10 . Assume the actual situation Z 1 = 184, the absolute value of the subtraction between the two is Z = 300-184 = 126.
以此类推,直至计算到最后一个圆环R9/10-Rmax,每个圆环的理想值与实际值的差值Z相加除以总的粒子数10000就是圆内的不均匀度。假设计算的Z总值为4496,可以得出不均匀度o=Z/10000=0.449。不均匀度越小的几何结构,加速系统效果越好。By analogy, until the last ring R 9/10 -R max is calculated, the difference Z between the ideal value and the actual value of each ring is added and divided by the total number of particles 10,000 to obtain the unevenness within the circle. Assuming that the calculated total Z value is 4496, it can be obtained that the unevenness o=Z/10000=0.449. The smaller the unevenness of the geometric structure, the better the acceleration system effect.
束流不均匀度target的数学表达式为:The mathematical expression of beam unevenness target is:
其中,o为不均匀度;Zx为理想状态下,靶面上某个圆环x中的粒子数;Ax为靶面上某个圆环x的面积;A总为靶面总面积;Ux为靶面上某个圆环x中的实际粒子数;x为靶面等分圆环个数,x=1,2,…,10。Among them, o is the non-uniformity; Z x is the number of particles in a certain ring x on the target surface under ideal conditions; A x is the area of a certain ring x on the target surface; A is the total area of the target surface; U x is the actual number of particles in a certain ring x on the target surface; x is the number of equally divided rings on the target surface, x=1,2,…,10.
束流脱靶数根据有限元模拟计算结果,读取粒子的三维坐标,统计坐标是否在靶上获得。The number of beam misses is based on the finite element simulation calculation results, reading the three-dimensional coordinates of the particles, and counting whether the coordinates are obtained on the target.
束流半径通过计算靶面上粒子坐标到靶面中心坐标的距离获得;其中,束流半径选择为能覆盖90%的粒子距靶心的距离;即假设10000个粒子距靶心的距离,为按照从小到大排列选择第9000个粒子,确定其为束流半径。The beam radius is obtained by calculating the distance from the particle coordinates on the target surface to the target center coordinates; among them, the beam radius is selected to be the distance from the target center that can cover 90% of the particles; that is, assuming that the distance from 10,000 particles to the target center is as follows: Select the 9000th particle in the large array and determine it as the beam radius.
根据获取的中子管加速系统束流性能的三个性能指标,构建目标函数ObjV,进行每个个体的适应度,进而对种群中每个个体对应的中子管加速系统的性能进行衡量。Based on the obtained three performance indicators of the beam performance of the neutron tube acceleration system, the objective function ObjV is constructed to measure the fitness of each individual, and then measure the performance of the neutron tube acceleration system corresponding to each individual in the population.
其中,目标函数ObjV的数学表达式为:Among them, the mathematical expression of the objective function ObjV is:
目标函数ObjV=target/base+outtarget;Target function ObjV=target/base+outtarget;
其中,target为束流不均匀度;outtarget为束流脱靶数、base为束流半径;目标函数值越小,表示遗传个体的适应度越优良。Among them, target is the beam unevenness; outtarget is the number of beam misses, and base is the beam radius; the smaller the objective function value, the better the fitness of the genetic individual.
为了加快遗传算法的收敛性,对于束流性能的三个性能指标进行放大处理,其中,一旦束流脱靶数outtarget不等于0就令其等于无限大,目的是筛选掉会脱靶的遗传个体,使其基因不会有效的传递给下一代;对束流均匀度target和束流半径base进行指数放大;目标函数值越小证明个体越优良,目标函数值越小证明不均匀度越小,束流半径越大,束流脱靶数为零。In order to speed up the convergence of the genetic algorithm, the three performance indicators of the beam performance are amplified. Among them, once the number of beam outtargets is not equal to 0, it is equal to infinity. The purpose is to screen out the genetic individuals that will miss the target, so that Its genes will not be effectively passed on to the next generation; the beam uniformity target and beam radius base are exponentially amplified; the smaller the objective function value, the better the individual, the smaller the objective function value, the smaller the unevenness, and the beam radius. The larger it is, the number of beam misses is zero.
步骤4、种群的适应度计算完成后,迭代进行选择、交叉和变异的遗传操作,其中,遗传操作包括选择、交叉和变异;其中,选择操作根据遗传个体适应度值的大小,采用精英选择与轮盘赌相结合机制;交叉操作采用均匀交叉方式,随机选择个体实施行交叉或列交叉;变异操作采用位变异机制。Step 4. After the fitness calculation of the population is completed, the genetic operations of selection, crossover and mutation are iteratively performed. The genetic operations include selection, crossover and mutation. Among them, the selection operation uses elite selection and mutation based on the fitness value of the genetic individual. Roulette combined mechanism; crossover operation adopts uniform crossover method, randomly selecting individuals to perform row crossover or column crossover; mutation operation adopts bit mutation mechanism.
遗传操作完成后,生成新种群,将新种群中每个个体的二进制基因位串分开,进行解码,重新分为七个待优化参数,并从二进制转换为十进制,按照步骤3中适应度计算的方法,计算新种群中每个个体的适应度。After the genetic operation is completed, a new population is generated, the binary gene bit string of each individual in the new population is separated, decoded, re-divided into seven parameters to be optimized, and converted from binary to decimal, according to the fitness calculation in step 3 Method to calculate the fitness of each individual in the new population.
步骤5、通过遗传操作,将所述新基因种群解码成为中子管加速系统几何结构参数,并开展所述新种群的中子管束流性能分析和基因种群的适应度评估,按照有利于提高中子管束流性能的方向选择与进化基因种群,确定下一代的基因种群,实现种群的不断进化;Step 5: Decode the new gene population into the geometric structure parameters of the neutron tube acceleration system through genetic operations, and carry out neutron tube beam performance analysis of the new population and fitness evaluation of the gene population, in accordance with the conditions that are conducive to improving the efficiency of the neutron tube acceleration system. Select the direction of sub-tube beam performance and evolve the gene population to determine the next generation's gene population and achieve continuous evolution of the population;
步骤6、种群不断进化过程,满足迭代停止条件,即达到设定的最大进化代数**时,出现适应度最小的个体,解码,得到该个体对应的加速间D、加速电极极小径D2、加速电极长度L、引出极孔径phi2、磁环坡口径fm2、导磁筒坡口径fm3及加速电极孔径D1七个待优化参数的实际取值,作为中子管加速系统的待优化几何结构参数的最优解,并按照待优化参数的取值制作中子管加速系统;Step 6. The population continues to evolve and meets the iteration stop condition, that is, when the set maximum evolutionary generation ** is reached, the individual with the smallest fitness appears. After decoding, the acceleration space D and acceleration electrode minimum diameter D 2 corresponding to the individual are obtained. The actual values of the seven parameters to be optimized , namely the length of the accelerating electrode L, the diameter of the lead pole phi 2 , the diameter of the magnetic ring slope fm 2 , the diameter of the magnetic cylinder slope fm 3 and the aperture D of the accelerating electrode, are used as the neutron tube acceleration system to be optimized. The optimal solution of the geometric structure parameters, and create a neutron tube acceleration system according to the values of the parameters to be optimized;
如附图3、4所示,经过100代,300个个体的迭代计算,种群的最优解稳定,最优解的适应度稳定在10-4,遗传算法收敛;其中,初始阶段,种群的适应度基本稳定在894.4附近,略有下降,但不明显,在50代左右,种群由于交叉和变异出现某些个体适应度较好,种群的最优解适应度出现断崖式下降,而后其基因迅速在种群内传播,最终最优解的适应度稳定在10-4,即得到最优解,且100代时粒子铺满整个靶面;观察到60代左右适应度越为0.14时,粒子最大半径距离靶边缘仅仅0.5mm,且100代左右的最优解要求尺寸精度过高,要10-5mm量级,结合工程实际,选定60代左右,适应度为0.14为本问题的最优解;其中,相比于未优化状态下的中子管加速系统,最优解中束流不均匀度小于未优化状态下的束流不均匀度,最优解中束流半径大于未优化状态下束流半径,最优解中粒子距靶心最大距离大于未优化状态下的粒子距靶心最大距离,此外最优解中的束流脱靶数为零;通过对最优解即适应度最小的个体,进行解码,得到优化后的中子管加速系统的几何结构参数,最优解的结构下中子管束流性能有大幅提升;中子管加速系统中电势在加速电极处的聚焦能力相交之前提升较大,提高了粒子聚焦能力,扩大了粒子在靶面上分布的半径;粒子在靶面上的半径明显扩大,此外脱靶粒子数为零,利于提高提高中子管的耐压性能,提高中子管的寿命与性能。As shown in Figures 3 and 4, after 100 generations and 300 individual iterative calculations, the optimal solution of the population is stable, the fitness of the optimal solution is stable at 10 -4 , and the genetic algorithm converges; among them, in the initial stage, the population The fitness is basically stable around 894.4, with a slight decrease, but not obvious. Around 50 generations, some individuals in the population have better fitness due to crossover and mutation, and the optimal solution fitness of the population drops off a cliff, and then its genes Rapidly spread within the population, the fitness of the final optimal solution stabilizes at 10 -4 , that is, the optimal solution is obtained, and the particles cover the entire target surface at 100 generations; it is observed that when the fitness becomes 0.14 around 60 generations, the particles become the largest The radius is only 0.5mm from the target edge, and the optimal solution of around 100 generations requires too high a dimensional accuracy of 10 -5 mm. Based on the engineering reality, around 60 generations and a fitness of 0.14 are selected as the optimal solution for this problem. Solution; among them, compared with the neutron tube acceleration system in the unoptimized state, the beam unevenness in the optimal solution is smaller than that in the unoptimized state, and the beam radius in the optimal solution is greater than that in the unoptimized state. Under the beam radius, the maximum distance between the particles and the target center in the optimal solution is greater than the maximum distance between the particles and the target center in the unoptimized state. In addition, the number of beam misses in the optimal solution is zero; by comparing the optimal solution, that is, the individual with the smallest fitness , decode and obtain the optimized geometric structure parameters of the neutron tube accelerating system. Under the optimal solution structure, the neutron tube beam performance is greatly improved; the electric potential in the neutron tube accelerating system is improved before the focusing ability of the accelerating electrode intersects. It is larger, which improves the particle focusing ability and expands the radius of particle distribution on the target surface; the radius of particles on the target surface is significantly expanded, and the number of off-target particles is zero, which is beneficial to improving the pressure resistance performance of the neutron tube and improving the neutron tube. tube life and performance.
本发明中采用有限元方法、遗传算法及均匀度评价方法三者相互结合,借助COMSOL仿真软件及MATLAB软件对中子管的加速系统进行了优化设计,最终获得了较好的加速系统结构,提高了中子管使用寿命和性能,用于指导中子管的设计与制造,实用性强。In this invention, the finite element method, the genetic algorithm and the uniformity evaluation method are combined with each other, and the acceleration system of the neutron tube is optimized and designed with the help of COMSOL simulation software and MATLAB software, and finally a better acceleration system structure is obtained, which improves the It improves the service life and performance of neutron tubes and is used to guide the design and manufacturing of neutron tubes, which is highly practical.
上述实施例仅仅是能够实现本发明技术方案的实施方式之一,本发明所要求保护的范围并不仅仅受本实施例的限制,还包括在本发明所公开的技术范围内,任何熟悉本技术领域的技术人员所容易想到的变化、替换及其他实施方式。The above embodiment is only one of the ways to realize the technical solution of the present invention. The scope of protection claimed by the present invention is not only limited by this embodiment, but also includes any technical scope disclosed by the present invention. Changes, substitutions and other implementations may be easily imagined by those skilled in the art.
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