WO2023207139A1 - 利用交流型樽海鞘算法求解拉伸/压缩弹簧参数的方法 - Google Patents

利用交流型樽海鞘算法求解拉伸/压缩弹簧参数的方法 Download PDF

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WO2023207139A1
WO2023207139A1 PCT/CN2022/139474 CN2022139474W WO2023207139A1 WO 2023207139 A1 WO2023207139 A1 WO 2023207139A1 CN 2022139474 W CN2022139474 W CN 2022139474W WO 2023207139 A1 WO2023207139 A1 WO 2023207139A1
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value
tension
compression spring
individual
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汪鹏君
林超
李刚
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温州大学
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/27—Design optimisation, verification or simulation using machine learning, e.g. artificial intelligence, neural networks, support vector machines [SVM] or training a model
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
    • G06F2111/04—Constraint-based CAD
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
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    • Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation

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  • the invention relates to a method for solving design parameters, in particular to a method for solving tension/compression spring parameters using an AC salp algorithm.
  • Structural optimization is an important field related to both optimization and structural engineering.
  • Tension/compression spring design as a structural optimization involving many different design variables and highly nonlinear constraints, is very important to find the best possible design parameters according to its design goals.
  • the choice of design parameters for a tension/compression spring affects the performance or objectives of the system in which it is used.
  • the main methods for solving the design parameters of tension/compression springs include analytical methods, numerical calculation methods and optimization algorithm estimation methods.
  • the analytical method is easy to solve quickly, but it solves through approximate processing, which will greatly reduce the accuracy of the solution.
  • the numerical calculation method mainly randomly selects the initial value and observes its convergence. The accuracy of the solution not only depends on the selection of the initial value but also decreases as the design parameters increase.
  • the optimization algorithm estimation method is a new method for solving the design parameters of tension/compression springs. It is mainly an iterative method with parameter adjustment. It has simple operation, few restrictions, strong robustness and is suitable for various complexities. Problem solving and other advantages. However, most optimization algorithm estimation methods also have shortcomings such as slow convergence speed and easy falling into local optimality.
  • the salp algorithm is a new type of evolutionary optimization algorithm for solving numerical optimization problems. After the existing salp algorithm determines the optimization objective function and parameter range, it uses a random trial and error method to find the global optimal solution to the optimization objective within a certain number of iterations, and then obtains the parameter optimization solution. However, when facing the problem of solving the design parameters of tension/compression springs, the existing salp algorithm still has low accuracy in solving the design parameters.
  • the technical problem to be solved by the present invention is to provide a method for solving tension/compression spring parameters using the AC salp algorithm with high precision in solving design parameters.
  • the technical solution adopted by the present invention to solve the above technical problems is: a method for solving the tension/compression spring parameters using the AC salp algorithm, which includes the following steps:
  • Step S1 Determine the tension/compression spring design parameters to be solved
  • Step S2 Based on the design purpose of the tension/compression spring, construct an objective function to solve the design parameters of the tension/compression spring, where the design purpose of the tension/compression spring is to minimize its weight;
  • Step S3 Determine the tension/compression spring design parameter constraints
  • Step S4 Use the AC salp algorithm to iteratively optimize the design parameters of the tension/compression spring, and obtain the global optimal solution as the output of the solved tension/compression spring design parameters.
  • the AC salp algorithm is used to calculate the parameters of the tension/compression spring. It is obtained by adding communication operations between individuals in the iterative process of the ascidian algorithm.
  • the tension/compression spring design parameters to be solved in step S1 are: wire diameter d (the wire diameter), coil average diameter D (the mean coil diameter) and the number of active coils N (the number of active coils ).
  • step S2 The objective function constructed in step S2 is expressed as:
  • the value range of d is 0.05 ⁇ d ⁇ 2
  • the value range of D is 0.25 ⁇ D ⁇ 1.3
  • the value range of N is 2 ⁇ N ⁇ 15.
  • C 1 represents the minimum deflection constraint of the tension/compression spring
  • C 2 represents the shear constraint of the tension/compression spring
  • C 3 represents the impact frequency constraint of the tension/compression spring
  • C 4 represents the Outer diameter constraints.
  • step S4 the AC salp algorithm is used to iteratively optimize the design parameters of the tension/compression spring, and the specific process of obtaining the global optimal solution as the output of the solved tension/compression spring design parameters is:
  • Step S4.2 Initialize the population through formula ( 6 ) to obtain the 0th generation population.
  • the data in the second column are expressed as parameters of D
  • the data in the third column are expressed as parameters of N
  • each row of data is a solution to the design parameters of the tension/compression spring, also called an individual
  • the data in the i-th row is the i-th individuals
  • substitute the three columns of data for each individual in the 0th generation population Store in XFitness, record the i-th objective function value in XFitness as XFitness i
  • XFitness i corresponds to the objective function value of the i-th individual of the 0th generation population
  • the minimum objective function value in record it as bestFitness, and take the individual corresponding to the minimum objective function value as the minimum individual, record it as bestSolution, copy X 0 to SaveX, copy XFitness to SaveXFitness:
  • Step 4.3 First update the value of t using the sum of the current value of t plus 1, and then perform the t-th iteration on the population to obtain the t-th generation population X t .
  • the specific iteration process is:
  • Step S4.3.2 Traverse the current individual in the t-1 generation population X t-1 .
  • c 2 and c 3 are random numbers between 0 and 1 respectively.
  • a random function is first used to generate c 2 and c 3 .
  • Represents the value of the j-th column of the current individual in the t-th generation population X t Represents the value of the j-th column of the current individual in the t-1th generation population X t-1
  • bestSolution j represents the value of the j-th column of the current smallest individual bestSolution
  • Represents the value of the jth column of the ath individual in the t-1th generation population X t-1 Represents the value of the jth column of the bth individual in the t-1th generation population X t-1
  • Step S4.3.3 Generate a random number between 0 and 1, and determine whether it is less than or equal to 1-t/max_t. If satisfied, use Update SaveX current,j . If it is not satisfied, keep SaveX current,j unchanged, where SaveX current,j represents the value of the jth column of the current individual in SaveX;
  • Step S4.3.4 Determine whether the value of each column in the current individual of the t -th generation population If it exceeds the range, determine the absolute value of the difference between the value of the column and its upper limit and the absolute value of the difference between the value of the column and its lower limit. If the absolute value of the difference between the value of the column and its upper limit is greater than the absolute value of the difference between the value of the column and its upper limit, If the absolute value of the difference between the lower limit and the lower limit is determined, the value of the column will be modified to be equal to its lower limit; otherwise, the value of the column will be modified to be equal to its upper limit;
  • Step S4.3.5 Correspondingly enter the three columns of data of the current individual of the t -th generation population Among the constraints, if all four constraints are met, then the three columns of data of the current individual of the t- th generation population X Fitness current , if all four constraints cannot be satisfied, the current value of bestFitness will be used to update X Fitness current ;
  • Step S4.3.6 Make the following judgment on X Fitness current , and perform corresponding processing based on the judgment result:
  • Step S4.3.7 Determine whether the current value of current is less than popsize. If it is less, use the sum of the current value of current plus 1 to update current, and return to step S4.3.2 to traverse the next individual. Otherwise, proceed to step S4.4;
  • Step S4.4 If the current value of count is greater than or equal to 10*popsize, let p be 0.8, otherwise let it be 0; determine whether the current value of t is equal to max_t, if not, return to step S4.3 for the next time Iteration, if equal, then the current value of bestFitness at this time is the global optimal solution, and the global optimal solution is the solved tension/compression spring design parameters.
  • the advantage of the present invention is that by improving the existing salp algorithm, adding communication operations between individuals in the iterative process, a communicative salp algorithm is obtained, and the communicative salp algorithm is used to pull
  • the extension/compression spring design parameters are iteratively optimized, and the global optimal solution is obtained as the solved extension/compression spring design parameter output, because the extension/compression spring design involves three parameters (coil average diameter D, wire diameter d and The number of effective coils N), each parameter has its own range, so the real solution space involving these three parameters is very large.
  • the addition of this communication operation can combine existing solutions to combine promising solutions, so as to gradually find the ideal parameter solution for tension/compression spring design.
  • the communication operation adopted by the communication salp algorithm can more promisingly find better solutions, so that the final design parameters can be solved with high accuracy.
  • Figure 1 is a schematic diagram of the labeling of the three parameters involved in the tension/compression spring in the method of using the AC salp algorithm to solve the tension/compression spring parameters of the present invention.
  • Example A method for solving tension/compression spring parameters using the AC salp algorithm, including the following steps:
  • Step S1 Determine the tension/compression spring design parameters to be solved
  • Step S2 Based on the design purpose of the tension/compression spring, construct an objective function to solve the design parameters of the tension/compression spring, where the design purpose of the tension/compression spring is to minimize its weight;
  • Step S3 Determine the tension/compression spring design parameter constraints
  • Step S4 Use the AC salp algorithm to iteratively optimize the design parameters of the tension/compression spring, and obtain the global optimal solution as the output of the solved tension/compression spring design parameters.
  • the AC salp algorithm is used to calculate the parameters of the tension/compression spring. It is obtained by adding communication operations between individuals in the iterative process of the ascidian algorithm.
  • the tension/compression spring design parameters to be solved in step S1 are: wire diameter d (the wire diameter), coil average diameter D (the mean coil diameter) and effective coil Number N (the number of active coils).
  • step S2 the objective function constructed in step S2 is expressed as:
  • the value range of d is 0.05 ⁇ d ⁇ 2
  • the value range of D is 0.25 ⁇ D ⁇ 1.3
  • the value range of N is 2 ⁇ N ⁇ 15.
  • the tension/compression spring design parameter constraints determined in step S3 are expressed as:
  • C 1 represents the minimum deflection constraint of the tension/compression spring
  • C 2 represents the shear constraint of the tension/compression spring
  • C 3 represents the impact frequency constraint of the tension/compression spring
  • C 4 represents the Outer diameter constraints.
  • step S4 the AC salp algorithm is used to iteratively optimize the design parameters of the tension/compression spring, and the specific process of obtaining the global optimal solution as the output of the solved design parameters of the tension/compression spring is as follows:
  • Step S4.2 Initialize the population through formula ( 6 ) to obtain the 0th generation population.
  • the data in the second column are expressed as parameters of D
  • the data in the third column are expressed as parameters of N
  • each row of data is a solution to the design parameters of the tension/compression spring, also called an individual
  • the data in the i-th row is the i-th individuals
  • substitute the three columns of data for each individual in the 0th generation population Store in XFitness, record the i-th objective function value in XFitness as XFitness i
  • XFitness i corresponds to the objective function value of the i-th individual of the 0th generation population
  • the minimum objective function value in record it as bestFitness, and take the individual corresponding to the minimum objective function value as the minimum individual, record it as bestSolution, copy X 0 to SaveX, copy XFitness to SaveXFitness:
  • Step 4.3 First update the value of t using the sum of the current value of t plus 1, and then perform the t-th iteration on the population to obtain the t-th generation population X t .
  • the specific iteration process is:
  • Step S4.3.2 Traverse the current individual in the t-1 generation population X t-1 .
  • c 2 and c 3 are random numbers between 0 and 1 respectively.
  • a random function is first used to generate c 2 and c 3 .
  • Represents the value of the j-th column of the current individual in the t-th generation population X t Represents the value of the j-th column of the current individual in the t-1th generation population X t-1
  • bestSolution j represents the value of the j-th column of the current smallest individual bestSolution
  • Represents the value of the jth column of the ath individual in the t-1th generation population X t-1 Represents the value of the jth column of the bth individual in the t-1th generation population X t-1
  • Step S4.3.3 Generate a random number between 0 and 1, and determine whether it is less than or equal to 1-t/max_t. If satisfied, use Update SaveX current,j . If it is not satisfied, keep SaveX current,j unchanged, where SaveX current,j represents the value of the jth column of the current individual in SaveX;
  • Step S4.3.4 Determine whether the value of each column in the current individual of the t -th generation population If it exceeds the range, determine the absolute value of the difference between the value of the column and its upper limit and the absolute value of the difference between the value of the column and its lower limit. If the absolute value of the difference between the value of the column and its upper limit is greater than the absolute value of the difference between the value of the column and its upper limit, If the absolute value of the difference between the lower limit and the lower limit is determined, the value of the column will be modified to be equal to its lower limit; otherwise, the value of the column will be modified to be equal to its upper limit;
  • Step S4.3.5 Correspondingly enter the three columns of data of the current individual of the t -th generation population Among the constraints, if all four constraints are met, then the three columns of data of the current individual of the t- th generation population X Fitness current , if all four constraints cannot be satisfied, the current value of bestFitness will be used to update X Fitness current ;
  • Step S4.3.6 Make the following judgment on X Fitness current , and perform corresponding processing based on the judgment result:
  • the software of MATLAB R2018b implements the method of solving the tension/compression spring parameters using the AC salp algorithm of the present invention. Then, the method of solving the tension/compression spring parameters using the AC salp algorithm of the present invention and the existing salp algorithm are used to solve the design parameters of the tension/compression spring respectively.
  • Table 1 The specific solution data are shown in Table 1:
  • the first line in Table 1 shows the three parameters involved in the design of the tension/compression spring (the average diameter of the coil D, the wire diameter d and the number of effective coils N) and the weight of the tension/compression spring.
  • the second line uses this The solution and objective function value obtained by the inventive method.
  • the third row is the solution and objective function value obtained by using the existing salp algorithm. Analyzing the data in Table 1 shows that both methods can satisfy the value range of d, the value range of D, the value range of N and the four constraints involved in the tension/compression spring.
  • the objective function value 0.01266535 obtained by using the present invention is smaller than the objective function value 0.0126763 obtained by using the existing salp algorithm. It can be seen from this that the present invention has higher accuracy in solving the parameters involved in the tension/compression spring than the existing salp algorithm.

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Abstract

一种利用交流型樽海鞘算法求解拉伸/压缩弹簧参数的方法，先确定待求解的拉伸/压缩弹簧设计参数，然后基于拉伸/压缩弹簧的设计目的，构建求解拉伸/压缩弹簧设计参数的目标函数，其中拉伸/压缩弹簧的设计目的为最小化其重量；接着确定拉伸/压缩弹簧设计参数约束条件；最后利用交流型樽海鞘算法对拉伸/压缩弹簧设计参数进行迭代优化，得到全局最优解作为求解的拉伸/压缩弹簧设计参数输出，其中交流型樽海鞘算法通过在现有的樽海鞘算法的迭代过程中增加个体之间的交流操作得到；优点是设计参数求解精度高。

Description

利用交流型樽海鞘算法求解拉伸/压缩弹簧参数的方法 技术领域
本发明涉及一种设计参数求解方法，尤其是涉及一种利用交流型樽海鞘算法求解拉伸/压缩弹簧参数的方法。
背景技术
结构优化是与优化和结构工程都相关的一个重要领域。拉伸/压缩弹簧设计作为一种结构优化，涉及许多不同的设计变量和高度非线性的约束条件，根据其设计目标找到最佳可能的设计参数是非常重要的。拉伸/压缩弹簧的设计参数的选择会影响其所应用相关系统的性能或目标。
目前，求解拉伸/压缩弹簧设计参数的方法主要有解析法、数值计算法和优化算法估计法。解析法便于快速求解，但是其通过近似处理求解，这会大幅度降低解的精度。数值计算法主要通过随机选择初值，并观察其收敛性，解的精度不仅依赖于初值的选择而且随着设计参数的增加而降低。优化算法估计法是一种新的求解拉伸/压缩弹簧设计参数的方法，主要是一种带有参数调整的迭代方法，具有操作简单、限制条件少、鲁棒性强和适用于各种复杂问题的求解等优点。然而，大多数优化算法估计法也具有收敛速度慢，易陷入局部最优等不足。樽海鞘算法是求解数值优化问题的一种新型的进化优化算法。现有的樽海鞘算法在确定了优化的目标函数和参数范围后，在一定的迭代次数内通过基于随机的试错法找寻优化目标的全局最优解，进而得到参数优化解。但是，现有的樽海鞘算法在面对拉伸/压缩弹簧设计参数求解问题时，依旧存在设计参数求解精度低的现象。
发明内容
本发明所要解决的技术问题是提供一种设计参数求解精度高的利用交流型樽海鞘算法求解拉伸/压缩弹簧参数的方法。
本发明解决上述技术问题所采用的技术方案为：一种利用交流型樽海鞘算法求解拉伸/压缩弹簧参数的方法，包括以下步骤：
步骤S1、确定待求解的拉伸/压缩弹簧设计参数；
步骤S2、基于拉伸/压缩弹簧的设计目的，构建求解拉伸/压缩弹簧设计参数的目标函数，其中拉伸/压缩弹簧的设计目的为最小化其重量；
步骤S3、确定拉伸/压缩弹簧设计参数约束条件；
步骤S4、利用交流型樽海鞘算法对拉伸/压缩弹簧设计参数进行迭代优化，得到全局最优解作为求解的拉伸/压缩弹簧设计参数输出，其中交流型樽海鞘算法通过在现有的樽海鞘算法的迭代过程中增加个体之间的交流操作得到。
所述的步骤S1中待求解的拉伸/压缩弹簧设计参数分别为：线径d(the wire diameter)，线圈平均直径D(the mean coil diameter)和有效线圈的数量N(the number of active coils)。
所述的步骤S2中构建的目标函数采用式(1)表示为：
f(d,D,N)＝d 2D(N+2)  (1)
式(1)中，d的取值范围为0.05≤d≤2，D的取值范围为0.25≤D≤1.3，N的取值范围为2≤N≤15。
所述的步骤S3中确定的拉伸/压缩弹簧设计参数约束条件采用式(2)至式(5)表示为：
Figure PCTCN2022139474-appb-000001
Figure PCTCN2022139474-appb-000002
Figure PCTCN2022139474-appb-000003
Figure PCTCN2022139474-appb-000004
其中，C 1表示拉伸/压缩弹簧的最小挠度约束，C 2表示拉伸/压缩弹簧的剪切约束，C 3表示拉伸/压缩弹簧的冲击频率约束，C 4表示拉伸/压缩弹簧的外径约束。
所述的步骤S4中利用交流型樽海鞘算法对拉伸/压缩弹簧的设计参数进行迭代优化，得到全局最优解作为求解的拉伸/压缩弹簧设计参数输出的具体过程为：
步骤S4.1：初始化交流型樽海鞘算法的参数：设定种群大小popsize＝50，设定种群的维度dim＝3，设定迭代次数变量t，设定最大迭代次数max_t＝2000，设定变量p，设定变量count，设定下边界lb＝[lb 1,lb 2,lb 3]＝[0.05,0.25,2]，lb 1为d的下限(最小取值)，lb 2为D的下限(最小取值)，lb 3为N的下限(最小取值)，设定上边界ub＝[ub 1,ub 2,ub 3]＝[2,1.3,15]，ub 1为d的上限(最大取值)，ub 2为D的上限(最大取值)，ub 3为N的上限(最大取值)；对t、p和count分别进行初始化，令p＝0、count＝0、t＝0；
步骤S4.2：通过公式(6)初始化种群，得到第0代种群，将第0代种群记为X 0，X 0是popsize行dim列的矩阵，X 0的第1列数据表示为d的参数，第2列数据表示为D的参数，第3列数据表示为N的参数，每一行数据作为拉伸/压缩弹簧设计参数的一个解，又称作一个个体，第i行数据为第i个个体；将第0代种群X 0中的每个个体的三列数据对应代入公式(1)求解得到对应个体的目标函数值，并将得到的种群X 0中每个个体的目标函数值均存入XFitness，将XFitness中第i个目标函数值记为XFitness i，XFitness i对应为第0代种群X 0的第i个个体的目标函数值，i＝1，2，…，popsize；确定XFitness中的最小目标函数值，将其记为bestFitness，并将最小目标函数值对应的个体作为最小个体，记为bestSolution，将X 0复制到SaveX，XFitness复制到SaveXFitness：
Figure PCTCN2022139474-appb-000005
式(6)中，j＝1，2，dim，
Figure PCTCN2022139474-appb-000006
表示第0代种群X 0中第i个个体第j列的数值，rand表示0到1之间服从均匀分布的随机数，每次采用公式(6)进行计算前，都先通过随机函数生成rand；
步骤4.3：先采用t的当前值加1的和更新t的值，然后对种群进行第t次迭代，得到第t代种群X t，具体迭代过程为：
步骤S4.3.1：将t的当前值带入公式(7)得到c 1，设定遍历变量current，对current进行初始化，令current＝1；
步骤S4.3.2：对第t-1代种群X t-1中第current个个体进行遍历，此时先从1到popsize中随机选取两个不同的整数，且这两个整数均不等于current，将这两个整数随机记为a和b，然后先判断current是否小于等于popsize/2，若满足小于等于popsize/2，则随机生成一个0到1之间的随机数，再判断该随机数是否小于p的当前值，若满足小于p的当前值，则采用公式(8)得到第t代种群X t中第current个个体，否则采用公式(9)得到第t代种群X t中第current个个体的值；若不满足current小于等于popsize/2的条件，则采用公式(10)得到第t代种群X t中第current个个体；
Figure PCTCN2022139474-appb-000007
Figure PCTCN2022139474-appb-000008
Figure PCTCN2022139474-appb-000009
Figure PCTCN2022139474-appb-000010
其中，c 2和c 3分别是0到1之间的随机数，每次采用公式(8)计算之前，都先采用随机函数生成c 2和c 3，
Figure PCTCN2022139474-appb-000011
表示第t代种群X t中第current个个体的第j列的数值，
Figure PCTCN2022139474-appb-000012
表示第t-1代种群X t-1中第current个个体的第j列的数值，bestSolution j表示当前最小个体bestSolution的第j列的数值；
Figure PCTCN2022139474-appb-000013
表示第t-1代种群X t-1中第a个个体的第j列的数值，
Figure PCTCN2022139474-appb-000014
表示第t-1代种群X t-1中第b个个体的第j列的数值，
Figure PCTCN2022139474-appb-000015
表示第t-1代种群X t-1中第current-1个个体的第j列的数值；
步骤S4.3.3：生成一个0到1之间的随机数，判断它是否小于等于1-t/max_t，若满足，采用
Figure PCTCN2022139474-appb-000016
更新SaveX current,j，若不满足，则保持SaveX current,j不变，其中，SaveX current,j表示为SaveX中第current个个体的第j列的数值；
步骤S4.3.4：判断步骤S4.3.1中得到的第t代种群X t的第current个个体中每一列的数值是否在其对应的上限和下限范围内，若未超出范围，则保持不变，若超出范围，则判断该列的数值与其上限之差的绝对值和该列的数值与其下限之差的绝对值的大小，如果该列的数值与其上限之差的绝对值大于该列的数值与其下限之差的绝对值，则将该列的数值修改为等于其下限，反之，修改为等于其上限；
步骤S4.3.5：将步骤S4.3.4得到的第t代种群X t的第current个个体的三列数据对应带入公式(2)、公式(3)、公式(4)和公式(5)四条约束条件中，如果四条约束条件都满足，则将第t代种群X t的第current个个体的三列数据对应带入公式(1)计算其目标函数值，并采用计算得到的目标函数值更新X Fitness current，如果四条约束条件不能都满足，则采用bestFitness的当前值更新X Fitness current；
步骤S4.3.6：对X Fitness current进行如下判断，并基于判断结果进行对应处理：
若X Fitness current的当前值小于SaveX Fitness current的当前值，则采用X Fitness current的当前值更新SaveX Fitness current，并采用
Figure PCTCN2022139474-appb-000017
的当前值更新SaveX current，否则，采用SaveX current的当前值更新
Figure PCTCN2022139474-appb-000018
若X Fitness current的当前值小于bestFitness的当前值，则采用
Figure PCTCN2022139474-appb-000019
的当前值更新bestSolution，采用X Fitness current的当前值更新bestFitness，并采用count的当前值除以2的商更新count，否则采用count的当前值加1的和更新count；
步骤S4.3.7：判断current的当前值是否小于popsize，如果小于，则采用current的当前值加1的和更新current，并返回步骤S4.3.2遍历下一个个体，否则，进行步骤S4.4；
步骤S4.4：若count的当前值大于等于10*popsize，则令p为0.8，否则令其为0；判断t的当前值是否等于max_t，如果不等于，则返回步骤S4.3进行下一次迭代，若等于，则此时bestFitness的当前值为全局最优解，该全局最优解即为求解的拉伸/压缩弹簧设计参数。
与现有技术相比，本发明的优点在于通过对现有的樽海鞘算法进行改进，在其迭代过程中增加个体之间的交流操作得到交流型樽海鞘算法，利用交流型樽海鞘算法对拉伸/压缩弹簧设计参数进行迭代优化，得到全局最优解作为求解的拉伸/压缩弹簧设计参数输出，因为拉伸/压缩弹簧设计中涉及到三个参数(线圈平均直径D，线径d和有效线圈的数量N)，每个参数都有自己的范围，所以，涉及这三个参数的实数解空间是非常大的。增加了这种交流操作能通过现有的解组合出有希望的解，以此来渐渐找到拉伸/压缩弹簧设计的理想参数解，相对于现有的樽海鞘算法完全依靠随机的试错法，交流型樽海鞘算法采用的交流操作能更有希望的找到更好的解，从而最终设计参数求解精度高。
附图说明
图1为本发明的利用交流型樽海鞘算法求解拉伸/压缩弹簧参数的方法中涉及的三个参数在拉伸/压缩弹簧中的标注示意图。
具体实施方式
以下结合附图实施例对本发明作进一步详细描述。
实施例：一种利用交流型樽海鞘算法求解拉伸/压缩弹簧参数的方法，包括以下步骤：
步骤S1、确定待求解的拉伸/压缩弹簧设计参数；
步骤S2、基于拉伸/压缩弹簧的设计目的，构建求解拉伸/压缩弹簧设计参数的目标函数，其中拉伸/压缩弹簧的设计目的为最小化其重量；
步骤S3、确定拉伸/压缩弹簧设计参数约束条件；
步骤S4、利用交流型樽海鞘算法对拉伸/压缩弹簧设计参数进行迭代优化，得到全局最优解作为求解的拉伸/压缩弹簧设计参数输出，其中交流型樽海鞘算法通过在现有的樽海鞘算法的迭代过程中增加个体之间的交流操作得到。
本实施例中，如图1所示，步骤S1中待求解的拉伸/压缩弹簧设计参数分别为：线径d(the wire diameter)，线圈平均直径D(the mean coil diameter)和有效线圈的数量N(the number of active coils)。
本实施例中，步骤S2中构建的目标函数采用式(1)表示为：
f(d,D,N)＝d 2D(N+2)  (1)
式(1)中，d的取值范围为0.05≤d≤2，D的取值范围为0.25≤D≤1.3，N的取值范围为2≤N≤15。
本实施例中，步骤S3中确定的拉伸/压缩弹簧设计参数约束条件采用式(2)至式(5)表示为：
Figure PCTCN2022139474-appb-000020
Figure PCTCN2022139474-appb-000021
Figure PCTCN2022139474-appb-000022
Figure PCTCN2022139474-appb-000023
其中，C 1表示拉伸/压缩弹簧的最小挠度约束，C 2表示拉伸/压缩弹簧的剪切约束，C 3表示拉伸/压缩弹簧的冲击频率约束，C 4表示拉伸/压缩弹簧的外径约束。
本实施例中，步骤S4中利用交流型樽海鞘算法对拉伸/压缩弹簧的设计参数进行迭代优化，得到全局最优解作为求解的拉伸/压缩弹簧设计参数输出的具体过程为：
步骤S4.1：初始化交流型樽海鞘算法的参数：设定种群大小popsize＝50，设定种群的维度dim＝3，设定迭代次数变量t，设定最大迭代次数max_t＝2000，设定变量p，设定变量count，设定下边界lb＝[lb 1,lb 2,lb 3]＝[0.05,0.25,2]，lb 1为d的下限(最小取值)，lb 2为D的下限(最小取值)，lb 3为N的下限(最小取值)，设定上边界ub＝[ub 1,ub 2,ub 3]＝[2,1.3,15]，ub 1为d的上限(最大取值)，ub 2为D的上限(最大取值)，ub 3为N的上限(最大取值)；对t、p和count分别进行初始化，令p＝0、count＝0、t＝0；
步骤S4.2：通过公式(6)初始化种群，得到第0代种群，将第0代种群记为X 0，X 0是popsize行dim列的矩阵，X 0的第1列数据表示为d的参数，第2列数据表示为D的参数，第3列数据表示为N的参数，每一行数据作为拉伸/压缩弹簧设计参数的一个解，又称作一个个体，第i行数据为第i个个体；将第0代种群X 0中的每个个体的三列数据对应代入公式(1)求解得到对应个体的目标函数值，并将得到的种群X 0中每个个体的目 标函数值均存入XFitness，将XFitness中第i个目标函数值记为XFitness i，XFitness i对应为第0代种群X 0的第i个个体的目标函数值，i＝1，2，…，popsize；确定XFitness中的最小目标函数值，将其记为bestFitness，并将最小目标函数值对应的个体作为最小个体，记为bestSolution，将X 0复制到SaveX，XFitness复制到SaveXFitness：
Figure PCTCN2022139474-appb-000024
式(6)中，j＝1，2，dim，
Figure PCTCN2022139474-appb-000025
表示第0代种群X 0中第i个个体第j列的数值，rand表示0到1之间服从均匀分布的随机数，每次采用公式(6)进行计算前，都先通过随机函数生成rand；
步骤4.3：先采用t的当前值加1的和更新t的值，然后对种群进行第t次迭代，得到第t代种群X t，具体迭代过程为：
步骤S4.3.1：将t的当前值带入公式(7)得到c 1，设定遍历变量current，对current进行初始化，令current＝1；
步骤S4.3.2：对第t-1代种群X t-1中第current个个体进行遍历，此时先从1到popsize中随机选取两个不同的整数，且这两个整数均不等于current，将这两个整数随机记为a和b，然后先判断current是否小于等于popsize/2，若满足小于等于popsize/2，则随机生成一个0到1之间的随机数，再判断该随机数是否小于p的当前值，若满足小于p的当前值，则采用公式(8)得到第t代种群X t中第current个个体，否则采用公式(9)得到第t代种群X t中第current个个体的值；若不满足current小于等于popsize/2的条件，则采用公式(10)得到第t代种群X t中第current个个体；
Figure PCTCN2022139474-appb-000026
Figure PCTCN2022139474-appb-000027
Figure PCTCN2022139474-appb-000028
Figure PCTCN2022139474-appb-000029
其中，c 2和c 3分别是0到1之间的随机数，每次采用公式(8)计算之前，都先采用随机函数生成c 2和c 3，
Figure PCTCN2022139474-appb-000030
表示第t代种群X t中第current个个体的第j列的数值，
Figure PCTCN2022139474-appb-000031
表示第t-1代种群X t-1中第current个个体的第j列的数值，bestSolution j表示当前最小个体bestSolution的第j列的数值；
Figure PCTCN2022139474-appb-000032
表示第t-1代种群X t-1中第a个个体的第j列的数值，
Figure PCTCN2022139474-appb-000033
表示第t-1代种群X t-1中第b个个体的第j列的数值，
Figure PCTCN2022139474-appb-000034
表 示第t-1代种群X t-1中第current-1个个体的第j列的数值；
步骤S4.3.3：生成一个0到1之间的随机数，判断它是否小于等于1-t/max_t，若满足，采用
Figure PCTCN2022139474-appb-000035
更新SaveX current,j，若不满足，则保持SaveX current,j不变，其中，SaveX current,j表示为SaveX中第current个个体的第j列的数值；
步骤S4.3.4：判断步骤S4.3.1中得到的第t代种群X t的第current个个体中每一列的数值是否在其对应的上限和下限范围内，若未超出范围，则保持不变，若超出范围，则判断该列的数值与其上限之差的绝对值和该列的数值与其下限之差的绝对值的大小，如果该列的数值与其上限之差的绝对值大于该列的数值与其下限之差的绝对值，则将该列的数值修改为等于其下限，反之，修改为等于其上限；
步骤S4.3.5：将步骤S4.3.4得到的第t代种群X t的第current个个体的三列数据对应带入公式(2)、公式(3)、公式(4)和公式(5)四条约束条件中，如果四条约束条件都满足，则将第t代种群X t的第current个个体的三列数据对应带入公式(1)计算其目标函数值，并采用计算得到的目标函数值更新X Fitness current，如果四条约束条件不能都满足，则采用bestFitness的当前值更新X Fitness current；
步骤S4.3.6：对X Fitness current进行如下判断，并基于判断结果进行对应处理：
若X Fitness current的当前值小于SaveXFitness current的当前值，则采用X Fitness current的当前值更新SaveXFitness current，并采用
Figure PCTCN2022139474-appb-000036
的当前值更新SaveX current，否则，采用SaveX current的当前值更新
Figure PCTCN2022139474-appb-000037
若XFitness
MATLAB R2018b的软件实现本发明的利用交流型樽海鞘算法求解拉伸/压缩弹簧参数的方法。然后分别采用本发明的利用交流型樽海鞘算法求解拉伸/压缩弹簧参数的方法和现有的樽海鞘算法对拉伸/压缩弹簧设计参数进行求解，具体求解数据如表1所示：
表1
方法 d D N 目标函数值
本发明 0.051766599 0.358585825 11.18028561 0.01266535
现有的樽海鞘算法 0.051207 0.345215 12.004032 0.0126763
表1中的第一行为拉伸/压缩弹簧设计中涉及到的三个参数(线圈平均直径D，线径d和有效线圈的数量N)和拉伸/压缩弹簧的重量，第二行为采用本发明方法得到的解及目标函数值。第三行是采用现有的樽海鞘算法得到的解及目标函数值。分析表1数据可知，两种方法都能满足d的取值范围，D的取值范围，N的取值范围和拉伸/压缩弹簧中涉及的四条约束。但是采用本发明得到的目标函数值0.01266535小于采用现有的樽海鞘算法求解得到的目标函数值0.0126763。由此可知，本发明对拉伸/压缩弹簧涉及参数求解精度比现有的樽海鞘算法高。

Claims (5)

  1. 一种利用交流型樽海鞘算法求解拉伸/压缩弹簧参数的方法，其特征在于包括以下步骤：
    步骤S1、确定待求解的拉伸/压缩弹簧设计参数；
    步骤S2、基于拉伸/压缩弹簧的设计目的，构建求解拉伸/压缩弹簧设计参数的目标函数，其中拉伸/压缩弹簧的设计目的为最小化其重量；
    步骤S3、确定拉伸/压缩弹簧设计参数约束条件；
    步骤S4、利用交流型樽海鞘算法对拉伸/压缩弹簧设计参数进行迭代优化，得到全局最优解作为求解的拉伸/压缩弹簧设计参数输出，其中交流型樽海鞘算法通过在现有的樽海鞘算法的迭代过程中增加个体之间的交流操作得到。
  2. 根据权利要求1所述的一种利用交流型樽海鞘算法求解拉伸/压缩弹簧参数的方法，其特征在于所述的步骤S1中待求解的拉伸/压缩弹簧设计参数分别为：线径d(the wire
    diameter)，线圈平均直径D(the mean coil diameter)和有效线圈的数量N(the number of
    active coils)。
  3. 根据权利要求2所述的一种利用交流型樽海鞘算法求解拉伸/压缩弹簧参数的方法，其特征在于所述的步骤S2中构建的目标函数采用式(1)表示为：
    f(d,D,N)＝d 2D(N+2)  (1)
    式(1)中，d的取值范围为0.05≤d≤2，D的取值范围为0.25≤D≤1.3，N的取值范围为2≤N≤15。
  4. 根据权利要求3所述的一种利用交流型樽海鞘算法求解拉伸/压缩弹簧参数的方法，其特征在于所述的步骤S3中确定的拉伸/压缩弹簧设计参数约束条件采用式(2)至式(5)表示为：
    Figure PCTCN2022139474-appb-100001
    Figure PCTCN2022139474-appb-100002
    Figure PCTCN2022139474-appb-100003
    Figure PCTCN2022139474-appb-100004
    其中，C 1表示拉伸/压缩弹簧的最小挠度约束，C 2表示拉伸/压缩弹簧的剪切约束，C 3 表示拉伸/压缩弹簧的冲击频率约束，C 4表示拉伸/压缩弹簧的外径约束。
  5. 根据权利要求4所述的一种利用交流型樽海鞘算法求解拉伸/压缩弹簧参数的方法，其特征在于所述的步骤S4中利用交流型樽海鞘算法对拉伸/压缩弹簧的设计参数进行迭代优化，得到全局最优解作为求解的拉伸/压缩弹簧设计参数输出的具体过程为：
    步骤S4.1：初始化交流型樽海鞘算法的参数：设定种群大小popsize＝50，设定种群的维度dim＝3，设定迭代次数变量t，设定最大迭代次数max_t＝2000，设定变量p，设定变量count，设定下边界lb＝[lb 1,lb 2,lb 3]＝[0.05,0.25,2]，lb 1为d的下限(最小取值)，lb 2为D的下限(最小取值)，lb 3为N的下限(最小取值)，设定上边界ub＝[ub 1,ub 2,ub 3]＝[2,1.3,15]，ub 1为d的上限(最大取值)，ub 2为D的上限(最大取值)，ub 3为N的上限(最大取值)；对t、p和count分别进行初始化，令p＝0、count＝0、t＝0；
    步骤S4.2：通过公式(6)初始化种群，得到第0代种群，将第0代种群记为X 0，X 0是popsize行dim列的矩阵，X 0的第1列数据表示为d的参数，第2列数据表示为D的参数，第3列数据表示为N的参数，每一行数据作为拉伸/压缩弹簧设计参数的一个解，又称作一个个体，第i行数据为第i个个体；将第0代种群X 0中的每个个体的三列数据对应代入公式(1)求解得到对应个体的目标函数值，并将得到的种群X 0中每个个体的目标函数值均存入XFitness，将XFitness中第i个目标函数值记为XFitness i，XFitness i对应为第0代种群X 0的第i个个体的目标函数值，i＝1，2，…，popsize；确定XFitness中的最小目标函数值，将其记为bestFitness，并将最小目标函数值对应的个体作为最小个体，记为bestSolution，将X 0复制到SaveX，XFitness复制到SaveXFitness：
    Figure PCTCN2022139474-appb-100005
    式(6)中，j＝1，2，dim，
    Figure PCTCN2022139474-appb-100006
    表示第0代种群X 0中第i个个体第j列的数值，rand表示0到1之间服从均匀分布的随机数，每次采用公式(6)进行计算前，都先通过随机函数生成rand；
    步骤4.3：先采用t的当前值加1的和更新t的值，然后对种群进行第t次迭代，得到第t代种群X t，具体迭代过程为：
    步骤S4.3.1：将t的当前值带入公式(7)得到c 1，设定遍历变量current，对current进行初始化，令current＝1；
    步骤S4.3.2：对第t-1代种群X t-1中第current个个体进行遍历，此时先从1到popsize中随机选取两个不同的整数，且这两个整数均不等于current，将这两个整数随机记为a 和b，然后先判断current是否小于等于popsize/2，若满足小于等于popsize/2，则随机生成一个0到1之间的随机数，再判断该随机数是否小于p的当前值，若满足小于p的当前值，则采用公式(8)得到第t代种群X t中第current个个体，否则采用公式(9)得到第t代种群X t中第current个个体的值；若不满足current小于等于popsize/2的条件，则采用公式(10)得到第t代种群X t中第current个个体；
    Figure PCTCN2022139474-appb-100007
    Figure PCTCN2022139474-appb-100008
    Figure PCTCN2022139474-appb-100009
    Figure PCTCN2022139474-appb-100010
    其中，c 2和c 3分别是0到1之间的随机数，每次采用公式(8)计算之前，都先采用随机函数生成c 2和c 3，
    Figure PCTCN2022139474-appb-100011
    表示第t代种群X t中第current个个体的第j列的数值，
    Figure PCTCN2022139474-appb-100012
    表示第t-1代种群X t-1中第current个个体的第j列的数值，bestSolution j表示当前最小个体bestSolution的第j列的数值；
    Figure PCTCN2022139474-appb-100013
    表示第t-1代种群X t-1中第a个个体的第j列的数值，
    Figure PCTCN2022139474-appb-100014
    表示第t-1代种群X t-1中第b个个体的第j列的数值，
    Figure PCTCN2022139474-appb-100015
    表示第t-1代种群X t-1中第current-1个个体的第j列的数值；
    步骤S4.3.3：生成一个0到1之间的随机数，判断它是否小于等于1-t/max_t，若满足，采用
    Figure PCTCN2022139474-appb-100016
    更新SaveX current,j，若不满足，则保持SaveX current,j不变，其中，SaveX current,j表示为SaveX中第current个个体的第j列的数值；
    步骤S4.3.4：判断步骤S4.3.1中得到的第t代种群X t的第current个个体中每一列的数值是否在其对应的上限和下限范围内，若未超出范围，则保持不变，若超出范围，则判断该列的数值与其上限之差的绝对值和该列的数值与其下限之差的绝对值的大小，如果该列的数值与其上限之差的绝对值大于该列的数值与其下限之差的绝对值，则将该列的数值修改为等于其下限，反之，修改为等于其上限；
    步骤S4.3.5：将步骤S4.3.4得到的第t代种群X t的第current个个体的三列数据对应带入公式(2)、公式(3)、公式(4)和公式(5)四条约束条件中，如果四条约束条件都满足，则将第t代种群X t的第current个个体的三列数据对应带入公式(1)计算其目标函数值，并采用计算得到的目标函数值更新XFitness current，如果四条约束条件不能都满足，则 采用bestFitness的当前值更新XFitness current；
    步骤S4.3.6：对XFitness current进行如下判断，并基于判断结果进行对应处理：
    若XFitness current的当前值小于SaveXFitness current的当前值，则采用XFitness current的当前值更新SaveXFitness current，并采用
    Figure PCTCN2022139474-appb-100017
    的当前值更新SaveX current，否则，采用SaveX current的当前值更新
    Figure PCTCN2022139474-appb-100018
    若XFitness current的当前值小于bestFitness的当前值，则采用
    Figure PCTCN2022139474-appb-100019
    的当前值更新bestSolution，采用XFitness current的当前值更新bestFitness，并采用count的当前值除以2的商更新count，否则采用count的当前值加1的和更新count；
    步骤S4.3.7：判断current的当前值是否小于popsize，如果小于，则采用current的当前值加1的和更新current，并返回步骤S4.3.2遍历下一个个体，否则，进行步骤S4.4；
    步骤S4.4：若count的当前值大于等于10*popsize，则令p为0.8，否则令其为0；判断t的当前值是否等于max_t，如果不等于，则返回步骤S4.3进行下一次迭代，若等于，则此时bestFitness的当前值为全局最优解，该全局最优解即为求解的拉伸/压缩弹簧设计参数。
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