CN109992848B - A Robust Optimal Design Method for Press Upper Beam Based on Negative Ideal Release Distance - Google Patents

A Robust Optimal Design Method for Press Upper Beam Based on Negative Ideal Release Distance Download PDF

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CN109992848B
CN109992848B CN201910195091.1A CN201910195091A CN109992848B CN 109992848 B CN109992848 B CN 109992848B CN 201910195091 A CN201910195091 A CN 201910195091A CN 109992848 B CN109992848 B CN 109992848B
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程锦
陆威
张杨燕
刘振宇
谭建荣
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Abstract

The invention discloses a press machine upper crossbeam steady optimization design method based on negative ideal closing distance. The method comprises the following steps: considering the randomness of the load borne by the upper cross beam of the press and the interval uncertainty of the material attribute of the upper cross beam, and establishing an upper cross beam robust optimization design model containing random-interval mixed uncertainty variables based on a 6 sigma robust design principle; directly solving the optimization model based on a double-layer nested genetic algorithm; the inner layer performs interval robustness analysis on each design vector by using a Kriging prediction model, and calculates the mean value and standard deviation of a target function and each constraint performance function by adopting a Monte Carlo method; and the outer layer classifies, sorts and optimizes all design vectors based on the total feasible robustness coefficient of the constraint performance function and the negative ideal solution proximity distance by utilizing the calculation result of the inner layer. The method accords with engineering practice, avoids subjective interference, and has good engineering practicability.

Description

一种基于负理想解贴近距离的压力机上横梁稳健优化设计 方法A Robust Optimal Design of Press Upper Beam Based on Negative Ideal Release Distance method

技术领域technical field

本发明属于复杂机械装备结构优化设计领域，涉及一种基于负理想解贴近距离的压力机上横梁稳健优化设计方法。The invention belongs to the field of optimal design of complex mechanical equipment structures, and relates to a robust optimal design method for an upper beam of a press based on a negative ideal release distance.

技术背景technical background

上横梁性能优劣直接影响着压力机的冲压精度和配套模具的使用寿命。为保证冲压精度和配套模具的使用寿命，在确定压力机上横梁的拓扑形状后，还需对其尺寸参数进行优化设计，以保证其性能。The performance of the upper beam directly affects the stamping accuracy of the press and the service life of the supporting die. In order to ensure the stamping accuracy and the service life of the supporting die, after determining the topological shape of the beam on the press, it is necessary to optimize the size parameters to ensure its performance.

压力机设计制造过程中通常存在着大量的不确定性因素，这些不确定性因素会使得压力机性能偏离设计期望值，无法达到预期性能。而这些不确定因素的分布特性往往是多类型的，传统方法往往忽略这些不确定性的多样性，采用单一类型的不确定性变量来进行描述，无法真实反映上横梁设计中的不确定性，其所得最优方案在实际生产中往往并非最优，有时甚至无法满足性能要求。因此，要获得真正符合实际生产需求的最优设计方案，有必要同时考虑概率区间混合不确定性进行压力机上横梁的稳健设计。There are usually a lot of uncertain factors in the design and manufacturing process of the press, and these uncertain factors will make the performance of the press deviate from the design expectation and fail to achieve the expected performance. The distribution characteristics of these uncertain factors are often of multiple types. Traditional methods often ignore the diversity of these uncertainties and use a single type of uncertainty variables to describe, which cannot truly reflect the uncertainty in the design of the upper beam. The optimal solution obtained is often not optimal in actual production, and sometimes cannot even meet the performance requirements. Therefore, in order to obtain the optimal design scheme that truly meets the actual production requirements, it is necessary to consider the mixed uncertainty of probability interval to carry out the robust design of the beam on the press.

目前，国内外已有的大部分结构稳健性优化设计研究只考虑概率型不确定性或区间型不确定性，少数考虑概率区间不确定性的结构稳健性优化研究仅讨论性能函数较简单的结构设计，且需引入权重系数进行模型转换后再求解。而权重系数的选择具有较强的主观性，对稳健性优化结果会产生较大的影响，在实际工程中存在局限性。因此，十分有必要提出一种同时考虑概率区间不确定性、避免设计人员主观推断、适用于性能函数具有强非线性的压力机上横梁的稳健优化设计方法。At present, most of the existing structural robustness optimization design studies at home and abroad only consider probabilistic uncertainty or interval uncertainty, and a few structural robustness optimization studies that consider probability interval uncertainty only discuss structures with simpler performance functions. Design, and need to introduce weight coefficients for model conversion before solving. However, the selection of the weight coefficient is highly subjective, which will have a greater impact on the robust optimization results, and has limitations in practical engineering. Therefore, it is very necessary to propose a robust optimization design method that considers the uncertainty of probability interval, avoids the designer's subjective inference, and is suitable for the upper beam of the press with strong nonlinear performance function.

发明内容SUMMARY OF THE INVENTION

为了解决概率区间不确定因素共存情况下压力机上横梁的稳健性优化设计问题，本发明提供了一种基于负理想解贴近距离的压力机上横梁稳健优化设计方法。考虑压力机上横梁所受载荷的随机性与其材料属性的区间不确定性，将受随机与区间不确定性共同影响的上横梁最大变形作为优化目标，将给定最大允许值的上横梁性能指标作为约束性能函数，基于6σ稳健性设计原则，建立包含随机-区间混合不确定性变量的上横梁稳健优化设计模型。采用拉丁超立方采样与协同仿真技术构建目标函数与约束性能函数的Kriging预测模型，基于遗传算法和双层嵌套优化直接求解上横梁的稳健优化设计模型。提出的压力机上横梁稳健优化设计方法考虑了概率区间不确定因素的综合影响，且避免了权值的人工设定，更具工程实用性；基于遗传算法的模型求解中，利用总可行稳健性系数和负理想解贴近距离进行设计向量排序与寻优，算法高效且稳定性好。因此提出方法可高效地解决概率-区间混合不确定性因素共存情况下压力机上横梁的稳健优化设计问题。In order to solve the problem of the robust optimization design of the upper beam of the press under the coexistence of uncertain factors in the probability interval, the present invention provides a robust optimization design method of the upper beam of the press based on the negative ideal debonding distance. Considering the randomness of the load on the upper beam of the press and the interval uncertainty of its material properties, the maximum deformation of the upper beam affected by the random and interval uncertainty is taken as the optimization target, and the performance index of the upper beam with a given maximum allowable value is taken as the optimization target. Constrained performance function, based on the 6σ robust design principle, establishes a robust optimization design model of the upper beam including random-interval mixed uncertainty variables. The Kriging prediction model of objective function and constraint performance function is constructed by using Latin hypercube sampling and co-simulation technology, and the robust optimization design model of the upper beam is directly solved based on genetic algorithm and double-nested optimization. The proposed robust optimization design method for the upper beam of the press takes into account the comprehensive influence of uncertain factors in the probability interval, and avoids the manual setting of weights, which is more practical for engineering; in the model solution based on genetic algorithm, the total feasible robustness coefficient is used. The design vector sorting and optimization are carried out in close proximity to the negative ideal solution, and the algorithm is efficient and stable. Therefore, the proposed method can efficiently solve the robust optimization design problem of the upper beam of the press under the coexistence of probability-interval mixed uncertainty factors.

本发明是通过以下技术方案实现的：一种基于负理想解贴近距离的压力机上横梁结构稳健优化设计方法，该方法包括以下步骤：The present invention is achieved through the following technical solutions: a robust optimization design method for a beam structure on a press based on a negative ideal release distance, the method comprising the following steps:

1)考虑压力机上横梁所受载荷的随机性与其材料属性的区间不确定性，将受随机与区间不确定性共同影响的上横梁最大变形作为优化目标，将给定最大允许值的上横梁性能指标作为约束性能函数，基于6σ稳健性设计原则，建立包含随机-区间混合不确定性变量的上横梁稳健优化设计模型如下：1) Considering the randomness of the load on the upper beam of the press and the interval uncertainty of its material properties, the maximum deformation of the upper beam affected by the random and interval uncertainty is taken as the optimization target, and the performance of the upper beam given the maximum allowable value is The index is used as a constraint performance function, and based on the 6σ robust design principle, a robust optimization design model of the upper beam including random-interval mixed uncertainty variables is established as follows:

Figure GDA0002610463350000021
Figure GDA0002610463350000021

其中,fC(d,X,U)＝(fL(d,X,U)+fR(d,X,U))/2；Among them, f C (d, X, U)=(f L (d, X, U)+f R (d, X, U))/2;

fW(d,X,U)＝(fL(d,X,U)-fR(d,X,U))/2；f W (d, X, U)=(f L (d, X, U)-f R (d, X, U))/2;

Figure GDA0002610463350000022
Figure GDA0002610463350000022

Figure GDA0002610463350000023
Figure GDA0002610463350000023

Figure GDA0002610463350000024
Figure GDA0002610463350000024

d＝(d1,d2,…,dl)，X＝(X1,X2,…,Xm),U＝(U1,U2,…,Un)d=(d 1 , d 2 ,...,d l ), X=(X 1 , X 2 ,...,X m ), U=(U 1 ,U 2 ,...,U n )

式中，fL(d,X,U),fR(d,X,U)，fC(d,X,U),fW(d,X,U)分别为在区间不确定性影响下目标函数f(d,X,U)性能区间的左界、右界、中点和半宽；

Figure GDA0002610463350000025
分别为在概率区间不确定性共同影响下目标函数区间中点fC(d,X,U)的均值和标准差；
Figure GDA0002610463350000026
分别为在概率区间不确定性共同影响下目标函数区间半宽fW(d,X,U)的均值和标准差；
Figure GDA0002610463350000027
分别为第i个约束性能函数gi(d,X,U)在概率区间不确定性影响下变化区间左界
Figure GDA0002610463350000028
的均值和标准差；
Figure GDA0002610463350000029
分别为为第i个约束性能函数在概率区间不确定性影响下变化区间右界
Figure GDA00026104633500000210
的均值和标准差；Bi为根据工程设计需要给定的区间常数，
Figure GDA00026104633500000211
和
Figure GDA00026104633500000212
分别为Bi的左界和右界，p为约束性能函数的个数，d＝(d1,d2,…,dl)为l维设计向量，X＝(X1,X2,…,Xm)为m维概率型不确定向量，U＝(U1,U2,…,Un)为n维区间型不确定向量；In the formula, f L (d, X, U), f R (d, X, U), f C (d, X, U), f W (d, X, U) are the uncertainty effects in the interval The left bound, right bound, midpoint and half-width of the performance interval of the lower objective function f(d, X, U);
Figure GDA0002610463350000025
are the mean and standard deviation of the midpoint f C (d, X, U) of the objective function interval under the joint influence of the uncertainty of the probability interval;
Figure GDA0002610463350000026
are the mean and standard deviation of the half-width f W (d, X, U) of the objective function interval under the joint influence of the uncertainty of the probability interval;
Figure GDA0002610463350000027
are the left bounds of the variation interval of the ith constraint performance function g i (d, X, U) under the influence of uncertainty in the probability interval, respectively
Figure GDA0002610463350000028
The mean and standard deviation of ;
Figure GDA0002610463350000029
are the right bounds of the variation interval of the ith constraint performance function under the influence of uncertainty in the probability interval, respectively
Figure GDA00026104633500000210
The mean and standard deviation of ; B i is the interval constant given according to the needs of engineering design,
Figure GDA00026104633500000211
and
Figure GDA00026104633500000212
are the left and right bounds of B i respectively, p is the number of constraint performance functions, d=(d 1 , d 2 ,...,d l ) is the l-dimensional design vector, X=(X 1 , X 2 ,... , X m ) is an m-dimensional probability-type uncertainty vector, and U=(U 1 , U 2 ,...,U n ) is an n-dimensional interval-type uncertainty vector;

2)采用拉丁超立方采样方法完成对设计向量d、概率型不确定变量X、区间型不确定变量U的初始采样，通过协同仿真技术分别获得高速压力机上横梁的目标函数与约束性能函数响应值，并构建高速压力机上横梁的目标函数与约束性能函数的Kriging预测模型；2) The Latin hypercube sampling method is used to complete the initial sampling of the design vector d, the probabilistic uncertainty variable X, and the interval uncertainty variable U, and the objective function and constraint performance function response values of the beam on the high-speed press are obtained through co-simulation technology. , and construct the Kriging prediction model of the objective function and constraint performance function of the beam on the high-speed press;

3)基于遗传算法与双层嵌套优化直接求解上横梁的稳健优化设计模型：3) Based on the genetic algorithm and double nested optimization, the robust optimization design model of the upper beam is directly solved:

3.1)设置遗传算法参数，包括种群规模、最大迭代次数、变异和交叉概率、收敛条件等，设置遗传算法的当前迭代次数为1，并生成遗传算法的初始种群；3.1) Set the genetic algorithm parameters, including population size, maximum number of iterations, mutation and crossover probability, convergence conditions, etc., set the current iteration number of the genetic algorithm to 1, and generate the initial population of the genetic algorithm;

3.2)内层对于每一种群所对应设计变量利用Kriging预测模型进行区间稳健性分析并采用蒙特卡洛方法计算目标函数和约束性能函数的均值和标准差，具体为：先将概率型不确定向量X的每一个概率型变量取其均值，记为均值向量μX，利用构建的Kriging预测模型对目标函数和各约束性能函数进行区间稳健性分析，采用区间分析算法计算目标函数和各约束性能函数的上下界以及相应的中点和半宽；将均值向量μX还原成概率型不确定向量X，采用蒙特卡洛方法计算各目标函数和约束性能函数的均值和标准差；3.2) The inner layer uses the Kriging prediction model to perform interval robustness analysis for the design variables corresponding to each population, and uses the Monte Carlo method to calculate the mean and standard deviation of the objective function and constraint performance function. Take the mean value of each probability variable of X, and denote it as the mean value vector μ X . Use the constructed Kriging prediction model to perform interval robustness analysis on the objective function and each constraint performance function, and use the interval analysis algorithm to calculate the objective function and each constraint performance function. The upper and lower bounds of , and the corresponding midpoint and half-width; the mean vector μ X is restored to a probabilistic uncertainty vector X, and the Monte Carlo method is used to calculate the mean and standard deviation of each objective function and constraint performance function;

3.3)外层利用内层计算的结果，基于总可行稳健性系数和负理想解贴近距离对种群中的所有个体进行分类并排序，具体为：3.3) The outer layer uses the results of the inner layer to classify and sort all the individuals in the population based on the total feasible robustness coefficient and the negative ideal solution distance, specifically:

3.3.1)分别计算种群中每一个体的总可行稳健性系数S，其计算式如下：3.3.1) Calculate the total feasible robustness coefficient S of each individual in the population separately, and its calculation formula is as follows:

Figure GDA0002610463350000031
Figure GDA0002610463350000031

式中，Si为该种群个体第i个约束性能函数的可行稳健性系数；p为约束性能函数的个数；第i个约束性能函数的可行稳健性系数Si按下式计算：In the formula, S i is the feasible robustness coefficient of the i-th constraint performance function of the population individual; p is the number of constraint performance functions; the feasible robustness coefficient S i of the i-th constraint performance function is calculated as follows:

Figure GDA0002610463350000032
Figure GDA0002610463350000032

式中，

Figure GDA0002610463350000033
分别为第i个约束性能函数在区间不确定性影响下变化区间的中点和半宽，
Figure GDA0002610463350000034
分别为第i个约束给定的区间常数Bi的中点和半宽；
Figure GDA0002610463350000035
为约束性能向量，与第i个约束性能函数gi一一对应，
Figure GDA0002610463350000036
为约束性能向量的模长；
Figure GDA0002610463350000037
为给定的区间常数向量，与Bi一一对应，
Figure GDA0002610463350000038
为给定区间常数向量的模长；
Figure GDA0002610463350000041
为约束性能向量与给定区间常数向量的夹角，其取值范围为[0°,90°]；In the formula,
Figure GDA0002610463350000033
are the midpoint and half-width of the variation interval of the ith constraint performance function under the influence of interval uncertainty, respectively,
Figure GDA0002610463350000034
are the midpoint and half-width of the interval constant Bi given by the ith constraint, respectively;
Figure GDA0002610463350000035
is the constraint performance vector, which corresponds to the i-th constraint performance function g i one-to-one,
Figure GDA0002610463350000036
is the modulus length of the constraint performance vector;
Figure GDA0002610463350000037
is a given interval constant vector, corresponding to B i one-to-one,
Figure GDA0002610463350000038
is the modulo length of the given interval constant vector;
Figure GDA0002610463350000041
is the angle between the constraint performance vector and the given interval constant vector, and its value range is [0°, 90°];

3.3.2)按总可行稳健性系数S将当前种群中的个体分别归类为完全可行个体、部分不可行个体、完全不可行个体，(a)若S＝p，则为完全可行个体；(b)若0＜S＜p，则为部分不可行个体；(c)若S＝0，则为完全不可行个体；3.3.2) According to the total feasible robustness coefficient S, the individuals in the current population are classified as fully feasible individuals, partially infeasible individuals, and completely infeasible individuals, (a) If S=p, then it is a fully feasible individual; ( b) If 0<S<p, it is a partially infeasible individual; (c) if S=0, it is a completely infeasible individual;

3.3.3)对于各完全可行个体，分别计算其负理想解贴近距离作为稳健性指标，设计向量d所对应个体的负理想解贴近距离D*(d)的计算公式如下：3.3.3) For each completely feasible individual, calculate its negative ideal disassembly distance as a robustness index, and the calculation formula of the negative ideal disassembly distance D * (d) of the individual corresponding to the design vector d is as follows:

Figure GDA0002610463350000042
Figure GDA0002610463350000042

式中，In the formula,

Figure GDA0002610463350000043
Figure GDA0002610463350000043

式中，

Figure GDA0002610463350000044
为当前种群中完全可行个体对应的所有设计向量，n1为当前种群中完全可行个体的总数；In the formula,
Figure GDA0002610463350000044
is all design vectors corresponding to completely feasible individuals in the current population, n 1 is the total number of completely feasible individuals in the current population;

3.3.4)对完全可行个体与部分不可行个体进行排序，使每一参与排序的个体均获得唯一的排序序号，且目标性能或约束稳健性越差的个体所获得排序序号越大；3.3.4) Rank the fully feasible individuals and some infeasible individuals, so that each individual participating in the ranking obtains a unique ranking sequence number, and the individual with poorer target performance or constraint robustness obtains a larger ranking sequence number;

a)首先对完全可行个体进行排序，按其负理想解贴近距离D*(d)数值从大到小依次降序排序，D*(d)数值越小，表明其对应的完全可行个体的目标性能越差，该个体获得的排序序号越大，即：对满足

Figure GDA0002610463350000051
的完全可行个体
Figure GDA0002610463350000052
其获得的序号分别为1,2,…,n1，其中n1为种群中完全可行个体的数目，a表示该个体完全可行；a) First, sort the fully feasible individuals, and sort them in descending order according to their negative ideal debonding distance D * (d) value from large to small, the smaller the value of D * (d), the better the target performance of the corresponding fully feasible individual The worse it is, the greater the ranking number obtained by the individual, that is: for satisfying
Figure GDA0002610463350000051
fully viable individuals
Figure GDA0002610463350000052
The obtained serial numbers are 1,2,...,n 1 , where n 1 is the number of completely feasible individuals in the population, and a indicates that the individual is completely feasible;

b)接着对部分不可行个体按其总可行稳健性系数S从大到小依次降序排序，S数值越小，表明其对应的部分不可行个体的约束性能函数稳健性越差，该个体获得的排序序号越大；同时，对完全可行个体与部分不可行个体两类个体排序时，需使第一个部分不可行个体的序号紧跟最后一个完全可行个体的序号，保证部分不可行个体的序号均大于完全可行个体的序号，即：对满足

Figure GDA0002610463350000053
的部分不可行个体
Figure GDA0002610463350000054
其获得的序号分别为(n1+1),(n1+2),…,(n1+n2)，其中n2为种群中部分不可行个体数目，b表示该个体部分不可行；b) Then sort some infeasible individuals in descending order according to their total feasible robustness coefficient S from large to small, the smaller the value of S is, the worse the constraint performance function of the corresponding partially infeasible individual is. The higher the sorting sequence number; at the same time, when sorting two types of individuals, the fully feasible individual and the partially infeasible individual, the sequence number of the first partially infeasible individual should be followed by the sequence number of the last fully feasible individual to ensure the sequence number of the partially infeasible individual. are greater than the sequence numbers of completely feasible individuals, that is: for satisfying
Figure GDA0002610463350000053
of partially infeasible individuals
Figure GDA0002610463350000054
The obtained serial numbers are (n 1 +1), (n 1 +2),...,(n 1 +n 2 ), where n 2 is the number of partially infeasible individuals in the population, and b indicates that the individual is partially infeasible;

3.3.5)计算当前种群中所有个体的适应度，a)对完全可行个体与部分不可行个体，根据步骤3.3.4)中排序所得序号计算其适应度，设置序号为i的设计向量的适应度为1/i；b)对完全不可行个体，设置其适应度为0；3.3.5) Calculate the fitness of all individuals in the current population, a) For fully feasible individuals and some infeasible individuals, calculate their fitness according to the sequence numbers obtained in step 3.3.4), and set the adaptation of the design vector with sequence number i The degree is 1/i; b) For completely infeasible individuals, set the fitness to 0;

3.4)判断是否满足最大迭代次数或收敛条件，若是，则输出适应度最大的个体所对应的设计向量作为最优解；否则，执行交叉变异操作生成新一代种群个体，返回步骤3.2)。3.4) Determine whether the maximum number of iterations or convergence conditions are met, if so, output the design vector corresponding to the individual with the largest fitness as the optimal solution; otherwise, perform the crossover mutation operation to generate a new generation of population individuals, and return to step 3.2).

进一步地，所述步骤2)具体为，采用拉丁超立方采样获得取值范围为[0,1]的具有空间均布性的样本点，并将其反归一化到输入向量空间中去，完成对设计向量、概率变量和区间变量的初始采样；使用三维建模软件构建压力机上横梁的参数化模型，通过接口技术实现三维建模软件和有限元分析软件间参数的双向动态传递，并调用压力机上横梁的参数化模型进行有限元分析计算，得到样本点所对应的压力机上横梁的目标函数和约束性能函数的响应值；选用高斯函数和一阶回归函数拟合压力机上横梁目标函数和约束性能函数的Kriging模型，利用复相关系数、相对最大绝对误差检验模型精度，在精度不满足要求时补充样本点更新Kriging模型，直到复相关系数值、相对最大绝对误差值满足精度要求为止，以保证拟合精度和泛化能力满足实际需求。Further, the step 2) is specifically: using Latin hypercube sampling to obtain sample points with a spatial uniformity in the value range [0, 1], and denormalizing them into the input vector space, Complete the initial sampling of design vectors, probability variables and interval variables; use 3D modeling software to build a parametric model of the beam on the press, and realize bidirectional dynamic transfer of parameters between 3D modeling software and finite element analysis software through interface technology, and call The parametric model of the upper beam of the press is subjected to finite element analysis and calculation, and the objective function and constraint performance function of the upper beam of the press corresponding to the sample points are obtained. The Kriging model of the performance function uses the complex correlation coefficient and the relative maximum absolute error to test the accuracy of the model. When the accuracy does not meet the requirements, the Kriging model is updated by adding sample points until the complex correlation coefficient value and the relative maximum absolute error value meet the accuracy requirements. The fitting accuracy and generalization ability meet the actual needs.

本发明具有的有益效果是：The beneficial effects that the present invention has are:

1)以概率变量、区间变量描述压力机上横梁的随机载荷与材料属性的区间不确定性，基于6σ稳健性设计原则，建立包含随机-区间混合不确定性变量的上横梁稳健优化设计模型，克服了以往设计方法仅考虑概率变量或区间变量的不足，更符合工程实际。1) Use probability variables and interval variables to describe the interval uncertainty of the random load and material properties of the upper beam of the press. Based on the 6σ robust design principle, a robust optimization design model of the upper beam including random-interval mixed uncertainty variables is established to overcome the The deficiencies of previous design methods that only consider probability variables or interval variables are overcome, and it is more in line with engineering practice.

2)基于遗传算法与双层嵌套优化对上横梁的稳健优化设计模型进行直接求解，内层对每一设计向量利用Kriging预测模型进行区间稳健性分析，采用蒙特卡洛方法计算目标函数和约束性能函数的均值和标准差；外层则利用内层的计算结果对设计向量分类，基于总可行稳健性系数和负理想解贴近距离对设计向量进行直接排序，寻找最优解，克服了以往概率区间优化模型求解过程中因人为指定权值而导致优化结果不确定的缺点，具有更好的工程实用性。2) Based on genetic algorithm and double nested optimization, the robust optimization design model of the upper beam is directly solved. The inner layer uses the Kriging prediction model to perform interval robustness analysis for each design vector, and uses the Monte Carlo method to calculate the objective function and constraints. The mean and standard deviation of the performance function; the outer layer uses the calculation results of the inner layer to classify the design vectors, and directly sorts the design vectors based on the total feasible robustness coefficient and the negative ideal solution distance to find the optimal solution, which overcomes the previous probability In the process of solving the interval optimization model, the uncertainty of the optimization results is caused by the artificially specified weights, which has better engineering practicability.

附图说明Description of drawings

图1是基于负理想解贴近距离的压力机上横梁稳健优化设计流程图。Figure 1 is a flow chart of the robust optimization design of the upper beam of the press based on the negative ideal debonding distance.

图2是压力机上横梁三维模型图。Figure 2 is a three-dimensional model diagram of a beam on the press.

图3是压力机上横梁横截面图；Figure 3 is a cross-sectional view of a beam on the press;

图4是压力机上横梁设计参数示意图；Figure 4 is a schematic diagram of the design parameters of the upper beam on the press;

图5是压力机上横梁受力情况。Figure 5 shows the stress on the beam on the press.

具体实施方式Detailed ways

以下结合附图和实例对本发明作进一步说明。The present invention will be further described below with reference to the accompanying drawings and examples.

图中涉及信息为本发明在某型号压力机上横梁稳健设计中的实际应用数据，图1是基于负理想解贴近距离的压力机上横梁稳健优化设计流程图。The information involved in the figure is the actual application data of the present invention in the robust design of the upper beam of a certain type of press.

1、基于概率-区间混合不确定性的压力机上横梁稳健优化设计建模：1. Robust optimization design modeling of the upper beam of the press based on probability-interval mixed uncertainty:

以图2、3所示冲压机上横梁作为研究对象，以图4所示上横梁的横截面尺寸h1,h2,l1,l2,l3为设计变量，将图5所示外力P1,P2,P3不确定性因素描述为概率变量，同时，考虑其材料HT300的密度ρ和泊松比ν的不确定性，并描述为区间变量。所有设计变量的范围和不确定性因素的参数信息如表1所示。Taking the upper beam of the punching machine shown in Figures 2 and 3 as the research object, and taking the cross-sectional dimensions h 1 , h 2 , l 1 , l 2 , and l 3 of the upper beam shown in Figure 4 as the design variables, the external force P shown in Figure 5 is used as the design variable. The uncertainty factors of 1 , P 2 , and P 3 are described as probability variables, and at the same time, the uncertainty of the density ρ and Poisson's ratio ν of the material HT300 are considered, and described as interval variables. The parametric information for the ranges and uncertainty factors of all design variables is shown in Table 1.

表1设计变量和不确定变量的参数信息Table 1 Parameter information of design variables and uncertain variables

Figure GDA0002610463350000061
Figure GDA0002610463350000061

根据上横梁的高刚度轻量化稳健性设计要求，以受随机与区间不确定性共同影响的上横梁最大变形量作为优化目标函数，将给定最大允许值的重量和最大等效应力作为约束性能函数，建立基于概率-区间混合变量的上横梁稳健优化设计模型：According to the high stiffness, lightweight and robust design requirements of the upper beam, the maximum deformation of the upper beam affected by random and interval uncertainty is used as the optimization objective function, and the weight and the maximum equivalent stress of the given maximum allowable value are used as the constraint performance. function to establish a robust optimal design model for the upper beam based on probability-interval mixed variables:

Figure GDA0002610463350000071
Figure GDA0002610463350000071

Figure GDA0002610463350000072
Figure GDA0002610463350000072

Figure GDA0002610463350000073
Figure GDA0002610463350000073

其中，fC(d,X,U)＝(fL(d,X,U)+fR(d,X,U))/2Among them, f C (d, X, U)=(f L (d, X, U)+f R (d, X, U))/2

fW(d,X,U)＝(fR(d,X,U)-fL(d,X,U))/2fW(d,X,U)＝( fR (d,X,U) -fL ( d,X,U))/2

Figure GDA0002610463350000074
Figure GDA0002610463350000074

Figure GDA0002610463350000075
Figure GDA0002610463350000075

Figure GDA0002610463350000076
Figure GDA0002610463350000076

d＝(h1,h2,l1,l2,l3)，X＝(P1,P2,P3)，U＝(ρ,υ)d=(h 1 ,h 2 ,l 1 ,l 2 ,l 3 ),X=(P 1 ,P 2 ,P 3 ),U=(ρ,υ)

式中，d＝(h1,h2,l1,l2,l3)为设计向量；X＝(P1,P2,P3)为概率型不确定向量；U＝(ρ,υ)为区间型不确定向量；f(d,X,U)为上横梁的最大变形量；fC(d,X,U),fW(d,X,U)分别为f(d,X,U)在区间型不确定性影响下变化区间的中点和半宽；w(d,X,U),δ(d,X,U)分别为上横梁的重量和最大等效应力；fL(d,X,U),fR(d,X,U),wL(d,X,U),wR(d,X,U),δL(d,X,U),δR(d,X,U)分别为f(d,X,U),w(d,X,U),δ(d,X,U)在区间型不确定性影响下变化区间的左界和右界；

Figure GDA0002610463350000077
Figure GDA0002610463350000078
分别为在概率区间不确定性影响下目标函数区间中点fC(d,X,U)的均值和标准差；
Figure GDA0002610463350000079
分别为在概率区间不确定性影响下目标函数区间半宽fW(d,X,U)的均值和标准差；
Figure GDA00026104633500000710
分别为在概率区间不确定性影响下约束性能函数w(d,X,U)左界的均值和标准差；
Figure GDA00026104633500000711
分别为在概率区间不确定性影响下约束性能函数w(d,X,U)右界的均值和标准差；
Figure GDA00026104633500000712
分别为在概率区间不确定性影响下约束性能函数δ(d,X,U)左界的均值和标准差；
Figure GDA00026104633500000713
分别为在概率区间不确定性影响下约束性能函数δ(d,X,U)右界的均值和标准差。In the formula, d=(h 1 , h 2 , l 1 , l 2 , l 3 ) is the design vector; X=(P 1 , P 2 , P 3 ) is the probabilistic uncertainty vector; U=(ρ,υ ) is the interval type uncertainty vector; f(d, X, U) is the maximum deformation of the upper beam; f C (d, X, U), f W (d, X, U) are respectively f (d, X , U) the midpoint and half-width of the changing interval under the influence of interval-type uncertainty; w(d,X,U), δ(d,X,U) are the weight and maximum equivalent stress of the upper beam, respectively; f L (d,X,U), fR (d,X,U), wL (d,X,U), wR (d,X,U), δL (d,X,U),δ R (d,X,U) is the left boundary sum of the variation interval of f(d,X,U), w(d,X,U), δ(d,X,U) under the influence of interval uncertainty, respectively right boundary;
Figure GDA0002610463350000077
Figure GDA0002610463350000078
are the mean and standard deviation of the midpoint f C (d, X, U) of the objective function interval under the influence of the uncertainty of the probability interval;
Figure GDA0002610463350000079
are the mean and standard deviation of the half-width f W (d, X, U) of the objective function interval under the influence of the uncertainty of the probability interval;
Figure GDA00026104633500000710
are the mean and standard deviation of the left bound of the constraint performance function w(d,X,U) under the influence of uncertainty in the probability interval;
Figure GDA00026104633500000711
are the mean and standard deviation of the right bound of the constraint performance function w(d,X,U) under the influence of probability interval uncertainty;
Figure GDA00026104633500000712
are the mean and standard deviation of the left bound of the constraint performance function δ(d,X,U) under the influence of uncertainty in the probability interval;
Figure GDA00026104633500000713
are the mean and standard deviation of the right bound of the constraint performance function δ(d, X, U) under the influence of probability interval uncertainty, respectively.

2、采用拉丁超立方采样完成对设计向量和不确定向量的初始采样，通过协同仿真技术获得压力机上横梁目标函数和约束性能函数的响应值，构建压力机上横梁对应的目标函数和约束性能函数的Kriging模型：2. Use Latin hypercube sampling to complete the initial sampling of the design vector and uncertainty vector, obtain the response values of the objective function and constraint performance function of the beam on the press through co-simulation technology, and construct the corresponding objective function and constraint performance function of the beam on the press. Kriging model:

(a)设计向量和不确定向量组成输入向量空间，在取值范围已确定的情况下，采用拉丁超立方采样获得取值范围为[0,1]的具有空间均布性的样本点，并将其反归一化到输入向量空间中去，完成对设计向量和不确定向量的初始采样。(a) The input vector space is composed of the design vector and the uncertain vector. When the value range is determined, Latin hypercube sampling is used to obtain sample points with spatial uniformity in the range of [0, 1], and It is denormalized into the input vector space to complete the initial sampling of the design vector and the uncertain vector.

(b)以设计向量为独立控制参数，利用三维CAD建模软件建立高速压力机上横梁的参数化模型，通过接口技术实现三维模型软件和有限元分析软件间参数的双向动态传递。对1/4上横梁模型采用Solid187单元进行网格划分，网格大小为50mm，获得16690个单元，30626个节点。在有限元分析软件中添加不确定因素向量为二次输入参数，并调用三维参数化模型进行有限元分析计算，得到压力机上横梁样本点所对应的目标函数和约束性能函数的响应值。(b) Using the design vector as the independent control parameter, the parametric model of the beam on the high-speed press is established by using the 3D CAD modeling software, and the bidirectional dynamic transfer of parameters between the 3D model software and the finite element analysis software is realized through the interface technology. The 1/4 upper beam model is meshed with Solid187 elements, the mesh size is 50mm, and 16690 elements and 30626 nodes are obtained. In the finite element analysis software, the uncertainty factor vector is added as the secondary input parameter, and the three-dimensional parametric model is called for finite element analysis and calculation, and the response values of the objective function and the restraint performance function corresponding to the beam sample points on the press are obtained.

(c)根据包含输入输出信息的样本点数据，构建预测上横梁最大变形量、重量和最大等效应力的Kriging模型。选用高斯函数和一阶回归函数进行拟合，并利用复相关系数、相对最大绝对误差不断进行检验和更新，直到复相关系数值都大于0.95、相对最大绝对误差值都小于0.05为止，从而保证拟合精度和泛化能力满足实际需求。(c) According to the sample point data containing input and output information, construct a Kriging model for predicting the maximum deformation, weight and maximum equivalent stress of the upper beam. Select Gaussian function and first-order regression function for fitting, and use complex correlation coefficient and relative maximum absolute error to continuously check and update until the complex correlation coefficient value is greater than 0.95 and the relative maximum absolute error value is less than 0.05, so as to ensure the fitting. The combined accuracy and generalization ability meet the actual needs.

3、基于遗传算法与双层嵌套优化直接求解上横梁的概率区间稳健优化设计模型：3. Based on genetic algorithm and double nested optimization, directly solve the probability interval robust optimization design model of the upper beam:

遗传算法参数设置如下：最大进化代数150，种群规模200，交叉系数0.99，变异系数0.05，算法收敛条件为0.00001。下面以第1次迭代过程为例说明基于遗传算法的双层嵌套直接解法流程。The parameters of the genetic algorithm are set as follows: the maximum evolutionary generation is 150, the population size is 200, the crossover coefficient is 0.99, the variation coefficient is 0.05, and the algorithm convergence condition is 0.00001. The following takes the first iteration process as an example to illustrate the double-nested direct solution process based on the genetic algorithm.

本次迭代循环种群个体为d1＝(205.17,237.08,83.96,34.46,317.76)、The population individuals of this iteration cycle are d 1 = (205.17, 237.08, 83.96, 34.46, 317.76),

d2＝(254.09,289.30,84.14,32.57,369.49)……d200＝(186.92,229.30,76.43,38.92,296.41)，内层使用Kriging预测模型对每一个体进行区间稳健性分析，并接着对每一个体通过蒙特卡洛方法计算目标函数与约束性能函数的各均值与标准差。在内层计算结果的基础上，外层计算每一个体的总可行稳健性系数S如下：S1＝2，S2＝2，S3＝1.383，S4＝0，S5＝2，S6＝1.016……S199＝2，S200＝1.370。则根据分类标准，完全可行个体包含d1、d2、d5、d199等(共107个)，部分不可行个体包含d3、d6、d200等(共62个)，完全不可行个体包含d4等(共31个)。d 2 =(254.09, 289.30, 84.14, 32.57, 369.49)...d 200 =(186.92, 229.30, 76.43, 38.92, 296.41), the inner layer uses the Kriging prediction model to perform interval robustness analysis for each individual, and then For each individual, the mean and standard deviation of the objective function and the constraint performance function are calculated by the Monte Carlo method. On the basis of the inner layer calculation results, the outer layer calculates the total feasible robustness coefficient S of each individual as follows: S 1 =2, S 2 =2, S 3 =1.383, S 4 =0, S 5 =2, S 6 = 1.016...S 199 =2, S 200 =1.370. Then according to the classification criteria, the fully feasible individuals include d 1 , d 2 , d 5 , d 199 , etc. (107 in total), and the partially infeasible individuals include d 3 , d 6 , d 200 , etc. (62 in total), which are completely infeasible Individuals included d 4 etc. (31 in total).

接着对完全可行个体与部分不可行个体进行排序。首先对于完全可行个体，分别计算其负理想解贴近距离，其过程如下：1)在107个完全可行个体中比较并定义参数

Figure GDA0002610463350000081
Figure GDA0002610463350000082
2)计算每一完全可行个体的负理想解贴近距离，D*(d1)＝0.1292、D*(d2)＝0.1311、D*(d5)＝0.1276……D*(d199)＝0.1467；3)根据每一完全可行个体的负理想解贴近距离进行降序排序，使每一个体获得唯一排序编号。对部分不可行个体，直接根据其总可行稳健性系数进行降序排序，同样使每一个体获得唯一排序编号。Then, the fully feasible individuals and the partially infeasible individuals are sorted. First of all, for the fully feasible individuals, the negative ideal solution distance is calculated respectively. The process is as follows: 1) Compare and define parameters among 107 fully feasible individuals
Figure GDA0002610463350000081
Figure GDA0002610463350000082
2) Calculate the negative ideal disassembly distance of each fully feasible individual, D * (d1)= 0.1292 , D * ( d2 ) = 0.1311, D * (d5)=0.1276...D * ( d199 )= 0.1467; 3) Perform descending sorting according to the negative ideal solution distance of each fully feasible individual, so that each individual obtains a unique sorting number. For some infeasible individuals, directly sort them in descending order according to their total feasible robustness coefficients, and also make each individual obtain a unique ranking number.

对所有个体赋适应度值，其中完全可行个体与部分不可行个体的适应度为其排序获得的序号之倒数，完全不可行个体的适应度直接赋值为0。All individuals are assigned fitness values, wherein the fitness of fully feasible individuals and partially infeasible individuals is the reciprocal of the serial number obtained by sorting, and the fitness of completely infeasible individuals is directly assigned as 0.

判断未达到最大迭代次数150且收敛条件0.00001不满足，因此对该轮迭代使用的种群个体进行交叉变异操作，重新进行第2次迭代。It is judged that the maximum number of iterations is not reached 150 and the convergence condition 0.00001 is not satisfied. Therefore, the crossover mutation operation is performed on the population individuals used in this iteration, and the second iteration is performed again.

优化结果如下：在第26次迭代时标性能指标达到收敛，其对应的最优设计向量为d＝(226.32,265.11,81.11,30.32,378.19)mm；优化后的目标性能——最大变形量

Figure GDA0002610463350000091
优化后约束性能函数——重量(μw,σw)＝(5062.98,，16.73)kg、最大等效应力(μδ,σδ)＝(27.56,，2.76)MPa，均满足稳健性要求，从而验证了所提方法的有效性。The optimization results are as follows: at the 26th iteration, the time-scaled performance indicators converge, and the corresponding optimal design vector is d=(226.32, 265.11, 81.11, 30.32, 378.19) mm; the optimized target performance—maximum deformation
Figure GDA0002610463350000091
The optimized constraint performance function——weight (μ w ,σ w )=(5062.98,,16.73)kg, maximum equivalent stress (μ δ ,σ δ )=(27.56,,2.76)MPa, all meet the robustness requirements, Thus, the effectiveness of the proposed method is verified.

需要声明的是，本发明内容及具体实施方式意在证明本发明所提供技术方案的实际应用，不应解释为对本发明保护范围的限定。在本发明的精神和权利要求的保护范围内，对本发明作出的任何修改和改变，都落入本发明的保护范围。It should be stated that the content and specific embodiments of the present invention are intended to prove the practical application of the technical solutions provided by the present invention, and should not be construed as limiting the protection scope of the present invention. Any modifications and changes made to the present invention within the spirit of the present invention and the protection scope of the claims fall into the protection scope of the present invention.

Claims (2)

1. A press upper crossbeam robust optimization design method based on negative ideal closing distance is characterized by comprising the following steps:
1) considering the randomness of the load borne by the upper cross beam of the press and the interval uncertainty of the material property of the upper cross beam, taking the maximum deformation of the upper cross beam, which is affected by the randomness and the interval uncertainty, as an optimization target, taking the performance index of the upper cross beam with a given maximum allowable value as a constraint performance function, and establishing an upper cross beam robust optimization design model containing a random-interval mixed uncertainty variable based on a 6 sigma robust design principle as follows:
Figure FDA0002610463340000011
wherein f isC(d,X,U)＝(fL(d,X,U)+fR(d,X,U))/2；
fW(d,X,U)＝(fL(d,X,U)-fR(d,X,U))/2；
Figure FDA0002610463340000012
Figure FDA0002610463340000013
Figure FDA0002610463340000014
d＝(d1,d2,…,dl)，X＝(X1,X2,…,Xm),U＝(U1,U2,…,Un)
In the formula (f)L(d,X,U),fR(d,X,U)，fC(d,X,U),fW(d, X, U) are respectively the left boundary, the right boundary, the middle point and the half width of the performance interval of the objective function f (d, X, U) under the influence of interval uncertainty;
Figure FDA0002610463340000015
respectively is the midpoint f of the target function interval under the joint influence of the uncertainty of the probability intervalC(d, X, U) mean and standard deviation;
Figure FDA0002610463340000016
respectively, the half width f of the target function interval under the joint influence of the uncertainty of the probability intervalW(d, X, U) mean and standard deviation;
Figure FDA0002610463340000017
are respectively the ith constraint performance function gi(d, X, U) left bound of variation interval under influence of uncertainty of probability interval
Figure FDA0002610463340000018
Mean and standard deviation of;
Figure FDA0002610463340000019
are respectively the ith constraint performance function gi(d, X, U) right bound of variation interval under influence of uncertainty of probability interval
Figure FDA00026104633400000110
Mean and standard deviation of; b isiIn order to give the interval constant according to the engineering design requirement,
Figure FDA00026104633400000111
and
Figure FDA00026104633400000112
are respectively BiP is the number of constraint performance functions, d ═ d1,d2,…,dl) Designing a vector for l dimension, X ═ X1,X2,…,Xm) Is an m-dimensional probability type uncertain vector, U ═ U1,U2,…,Un) Is an n-dimensional interval type uncertain vector;
2) the method comprises the steps of finishing initial sampling of a design vector d, a probability type uncertain variable X and an interval type uncertain variable U by adopting a Latin hypercube sampling method, respectively obtaining a target function and a constraint performance function response value of an upper cross beam of the press machine through a collaborative simulation technology, and constructing a Kriging prediction model of the target function and the constraint performance function of the upper cross beam of the press machine;
3) directly solving a steady optimization design model of the upper beam based on a genetic algorithm and double-layer nested optimization:
3.1) setting parameters of the genetic algorithm, including population scale, maximum iteration times, variation and cross probability and convergence conditions, setting the current iteration times of the genetic algorithm to be 1, and generating an initial population of the genetic algorithm;
3.2) the inner layer carries out interval robustness analysis on the design variables corresponding to each population by using a Kriging prediction model and calculates an objective function and each constraint by adopting a Monte Carlo methodThe mean and standard deviation of the performance function are specifically: firstly, taking the mean value of each probability type variable of the probability type uncertain vector X, and recording the mean value as a mean value vector muXCarrying out interval robustness analysis on the target function and each constraint performance function by using the constructed Kriging prediction model, and calculating the upper and lower boundaries, corresponding midpoints and half widths of the target function and each constraint performance function by using an interval analysis algorithm; then, the mean value vector mu is calculatedXReducing the probability type uncertain vector X, and calculating the mean value and standard deviation of the target function and each constraint performance function by adopting a Monte Carlo method;
3.3) the outer layer utilizes the result calculated by the inner layer to classify and sort all individuals in the population based on the total feasible robustness coefficient and the negative ideal solution proximity distance, and the method specifically comprises the following steps:
3.3.1) respectively calculating the total feasible robustness coefficient S of each individual in the population, wherein the calculation formula is as follows:
Figure FDA0002610463340000021
in the formula, SiA feasible robustness coefficient of the ith constraint performance function of the population individuals; p is the number of constraint performance functions; feasible robustness coefficient S of ith constraint performance functioniCalculated as follows:
Figure FDA0002610463340000022
in the formula (I), the compound is shown in the specification,
Figure FDA0002610463340000023
are respectively the ith constraint performance function gi(d, X, U) changing the midpoint and half-width of the interval under the influence of the interval uncertainty,
Figure FDA0002610463340000024
interval constants B given for ith constraints respectivelyiMidpoint and half-width;
Figure FDA0002610463340000025
for constraining the performance vector, the ith constraint performance function gi(d, X, U) are in one-to-one correspondence,
Figure FDA0002610463340000031
is the modular length of the constrained performance vector;
Figure FDA0002610463340000032
for a given interval constant vector, with BiThe two-dimensional data of the two-dimensional data are in one-to-one correspondence,
Figure FDA0002610463340000033
the modular length of a constant vector of a given interval;
Figure FDA0002610463340000034
the included angle between the performance vector and the constant vector of the given interval is restricted, and the value range is [0 degrees and 90 degrees ]]；
3.3.2) classifying the individuals in the current population according to the total feasible robustness coefficient S, (a) if S is p, the individuals are completely feasible individuals; (b) if S is more than 0 and less than p, the individual is a part of infeasible individuals; (c) if S ═ 0, then the individual is completely infeasible;
3.3.3) for each completely feasible individual, respectively calculating the negative ideal solution closeness distance as a robustness index, and designing the negative ideal solution closeness distance D of the individual corresponding to the vector D*(d) The calculation formula of (a) is as follows:
Figure FDA0002610463340000035
in the formula (I), the compound is shown in the specification,
Figure FDA0002610463340000036
in the formula (I), the compound is shown in the specification,
Figure FDA0002610463340000037
for all design vectors, n, corresponding to fully feasible individuals in the current population1The total number of completely feasible individuals in the current population;
3.3.4) sequencing completely feasible individuals and partially infeasible individuals, so that each individual participating in sequencing obtains a unique sequencing serial number, and the sequencing serial number obtained by the individual with worse target performance or constraint robustness is larger;
a) the fully feasible individuals are first ranked according to their negative ideal closeness distance D*(d) Sorting the values in descending order from big to small, D*(d) The smaller the numerical value is, the worse the target performance of the corresponding completely feasible individual is, the larger the ranking number obtained by the individual is, namely: to satisfy
Figure FDA0002610463340000041
Is completely feasible individual
Figure FDA0002610463340000042
The obtained numbers are 1,2, …, n respectively1Wherein n is1The number of completely feasible individuals in the population is shown as a;
b) sequentially sorting the partial infeasible individuals in a descending order from large to small according to the total feasible robustness coefficient S, wherein the smaller the S value is, the worse the robustness of the constraint performance function of the corresponding partial infeasible individual is, and the larger the sorting sequence number obtained by the individual is; meanwhile, when two types of completely feasible individuals and partially infeasible individuals are sequenced, the sequence number of the first partially infeasible individual needs to be closely followed by the sequence number of the last completely feasible individual, and the sequence numbers of the partially infeasible individuals are all larger than the sequence number of the completely feasible individual, namely: to satisfy
Figure FDA0002610463340000043
Part of infeasible individuals
Figure FDA0002610463340000044
The obtained serial numbers are respectively (n)1+1),(n1+2),…,(n1+n2) Wherein n is2The number of the partial infeasible individuals in the population is b, and the partial infeasible individuals are represented;
3.3.5) calculating the fitness of all individuals in the current population, a) calculating the fitness of completely feasible individuals and partially infeasible individuals according to the sequence numbers obtained by sequencing in the step 3.3.4), and setting the fitness of the design vector with the sequence number i as 1/i; b) setting the fitness of the completely infeasible individuals as 0;
3.4) judging whether the maximum iteration times or the convergence condition is met, if so, outputting a design vector corresponding to the individual with the maximum fitness as an optimal solution; otherwise, performing cross mutation operation to generate new generation population individuals, and returning to the step 3.2).
2. The method for designing the upper cross beam robustness optimization of the press based on the negative ideal closing distance according to claim 1, is characterized in that: the step 2) is specifically that Latin hypercube sampling is adopted to obtain sample points with the value range of [0,1] and space equipartition, and the sample points are reversely normalized to an input vector space to complete initial sampling of a design vector, a probability variable and an interval variable; using three-dimensional modeling software to construct a parameterized model of the upper cross beam of the press, realizing two-way dynamic transfer of parameters between the three-dimensional modeling software and finite element analysis software through an interface technology, and calling the parameterized model of the upper cross beam of the press to perform finite element analysis calculation to obtain a response value of a target function and a constraint performance function of the upper cross beam of the press corresponding to a sample point; a Gaussian function and a first-order regression function are selected to fit a Kriging model of an upper crossbeam target function and a constraint performance function of a press, the accuracy of the model is checked by using a complex correlation coefficient and a relative maximum absolute error, and a sample point is supplemented to update the Kriging model when the accuracy does not meet the requirement until the complex correlation coefficient value and the relative maximum absolute error meet the accuracy requirement, so that the fitting accuracy and the generalization capability can meet the actual requirement.
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