CN109992848B - Press machine upper crossbeam robust optimization design method based on negative ideal solution approach distance - Google Patents

Press machine upper crossbeam robust optimization design method based on negative ideal solution approach 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

Press machine upper crossbeam robust optimization design method based on negative ideal solution approach distance
Technical Field
The invention belongs to the field of structural optimization design of complex mechanical equipment, and relates to a press machine upper crossbeam steady optimization design method based on negative ideal closing distance.
Technical Field
The performance of the upper beam directly influences the stamping precision of the press and the service life of the matched die. In order to ensure the stamping precision and the service life of a matched die, after the topological shape of the upper cross beam of the press is determined, the size parameters of the upper cross beam of the press are also required to be optimally designed so as to ensure the performance of the upper cross beam of the press.
There are often a number of uncertainties in the press design and manufacturing process that can cause the press performance to deviate from the design expectations and fail to achieve the desired performance. The distribution characteristics of the uncertain factors are often of multiple types, the diversity of the uncertainties is often ignored in the traditional method, the uncertainties in the design of the upper cross beam cannot be truly reflected by adopting a single type of uncertainty variable for description, the optimal scheme is often not optimal in actual production, and sometimes even the performance requirements cannot be met. Therefore, to obtain an optimal design scheme that truly meets the actual production requirements, it is necessary to perform robust design of the upper cross beam of the press while taking into account the probability interval mixing uncertainty.
At present, most of the existing structure robustness optimization design researches at home and abroad only consider probability type uncertainty or interval type uncertainty, and few of the structure robustness optimization researches considering the probability interval uncertainty only discuss the structure design with a simpler performance function, and need to introduce a weight coefficient for model conversion and then solve the structure design. The selection of the weight coefficient has strong subjectivity, and can generate large influence on the robustness optimization result, so that the method has limitation in actual engineering. Therefore, it is necessary to provide a robust optimization design method for the upper cross beam of the press, which considers the uncertainty of the probability interval, avoids the subjective inference of designers, and is suitable for the performance function with strong nonlinearity.
Disclosure of Invention
The invention provides a press machine upper crossbeam steady optimization design method based on negative ideal closing distance, aiming at solving the problem of steady optimization design of a press machine upper crossbeam under the condition of probability interval uncertain factors. 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 influenced 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. A Kriging prediction model of an objective function and a constraint performance function is constructed by adopting a Latin hypercube sampling and collaborative simulation technology, and a steady optimization design model of an upper beam is directly solved based on a genetic algorithm and double-layer nested optimization. The steady optimization design method of the upper cross beam of the press machine considers the comprehensive influence of uncertain factors of probability intervals, avoids manual setting of weight values and has more engineering practicability; in the model solution based on the genetic algorithm, the total feasible robustness coefficient and the negative ideal solution proximity distance are utilized to carry out design vector sequencing and optimization, and the algorithm is efficient and good in stability. Therefore, the method can efficiently solve the problem of the robust optimization design of the upper beam of the press machine under the condition of coexistence of probability-interval mixing uncertainty factors.
The invention is realized by the following technical scheme: a press upper cross beam structure robust optimization design method based on negative ideal closing distance comprises 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 GDA0002610463350000021
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 GDA0002610463350000022
Figure GDA0002610463350000023
Figure GDA0002610463350000024
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 GDA0002610463350000025
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 GDA0002610463350000026
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 GDA0002610463350000027
are respectively the ith constraint performance function gi(d, X, U) left bound of variation interval under influence of uncertainty of probability interval
Figure GDA0002610463350000028
Mean and standard deviation of;
Figure GDA0002610463350000029
respectively as the right boundary of the variation interval of the ith constraint performance function under the influence of the uncertainty of the probability interval
Figure GDA00026104633500000210
Mean and standard deviation of; b isiIn order to give the interval constant according to the engineering design requirements,
Figure GDA00026104633500000211
and
Figure GDA00026104633500000212
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 beam of the high-speed press through a collaborative simulation technology, and constructing a Kriging prediction model of the target function and the constraint performance function of the upper beam of the high-speed press;
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, convergence conditions and the like, 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 performs interval robustness analysis on the design variables corresponding to each population by using a Kriging prediction model and calculates the mean value and standard deviation of a target function and a constraint performance function by adopting a Monte Carlo method, which specifically comprises the following steps: 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; vector the mean value muXReducing the probability type uncertain vector X, and calculating the mean value and standard deviation of each 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 GDA0002610463350000031
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 GDA0002610463350000032
in the formula (I), the compound is shown in the specification,
Figure GDA0002610463350000033
respectively the midpoint and half width of the variation interval of the ith constraint performance function under the influence of the interval uncertainty,
Figure GDA0002610463350000034
interval constants B given for ith constraints respectivelyiMidpoint and half-width;
Figure GDA0002610463350000035
for constraining the performance vector, the ith constraint performance function giThe two-dimensional data of the two-dimensional data are in one-to-one correspondence,
Figure GDA0002610463350000036
is the modular length of the constrained performance vector;
Figure GDA0002610463350000037
for a given interval constant vector, with BiThe two-dimensional data of the two-dimensional data are in one-to-one correspondence,
Figure GDA0002610463350000038
the modular length of a constant vector of a given interval;
Figure GDA0002610463350000041
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 into completely feasible individuals, partially infeasible individuals and completely infeasible individuals according to a total feasibility robustness coefficient S, wherein (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 GDA0002610463350000042
in the formula (I), the compound is shown in the specification,
Figure GDA0002610463350000043
in the formula (I), the compound is shown in the specification,
Figure GDA0002610463350000044
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 GDA0002610463350000051
Is completely feasible individual
Figure GDA0002610463350000052
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 GDA0002610463350000053
Part of infeasible individuals
Figure GDA0002610463350000054
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).
Further, the step 2) is specifically that Latin hypercube sampling is adopted to obtain sample points with space equipartition performance and the value range of [0,1], 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.
The invention has the beneficial effects that:
1) the interval uncertainty of the random load and the material attribute of the upper cross beam of the press is described by the probability variable and the interval variable, and the upper cross beam robust optimization design model containing the random-interval mixed uncertainty variable is established based on the 6 sigma robustness design principle, so that the defect that the probability variable or the interval variable is only considered in the conventional design method is overcome, and the method is more in line with the engineering practice.
2) Directly solving the steady optimization design model of the upper cross beam based on a genetic algorithm and double-layer nested optimization, carrying out interval robustness analysis on each design vector by the inner layer by using a Kriging prediction model, and calculating the mean value and standard deviation of a target function and a constraint performance function by adopting a Monte Carlo method; the outer layer classifies the design vectors by utilizing the calculation results of the inner layer, directly sorts the design vectors based on the total feasible robustness coefficient and the negative ideal solution approaching distance, finds the optimal solution, overcomes the defect that the optimization result is uncertain due to artificial weight assignment in the solving process of the conventional probability interval optimization model, and has better engineering practicability.
Drawings
FIG. 1 is a flow chart of a press top rail robust optimization design based on negative ideal closing distance.
FIG. 2 is a three-dimensional model of an upper cross beam of the press.
FIG. 3 is a cross-sectional view of the upper cross beam of the press;
FIG. 4 is a schematic illustration of press upper beam design parameters;
fig. 5 shows the stress condition of the upper cross beam of the press.
Detailed Description
The invention is further illustrated by the following figures and examples.
The related information in the figure is practical application data of the invention in the steady design of the upper beam of a certain type of press, and figure 1 is a flow chart of the steady optimization design of the upper beam of the press based on negative ideal approximation distance.
1. Modeling the robust optimization design of the upper cross beam of the press based on probability-interval mixing uncertainty:
the upper cross member of the press shown in FIGS. 2 and 3 was used as the subject of study, and the cross-sectional dimension h of the upper cross member shown in FIG. 4 was used1,h2,l1,l2,l3For design variables, the external force P shown in FIG. 51,P2,P3The uncertainty factor is described as a probability variable, and meanwhile, the uncertainty of the density rho and the poisson ratio nu of the material HT300 is considered and described as an interval variable. The ranges of all design variables and parameter information for uncertainty factors are shown in table 1.
TABLE 1 parameter information for design variables and uncertain variables
Figure GDA0002610463350000061
According to the design requirement of high rigidity and light weight robustness of the upper cross beam, the maximum deformation of the upper cross beam, which is affected by random and interval uncertainty, is taken as an optimization objective function, the weight of a given maximum allowable value and the maximum equivalent stress are taken as constraint performance functions, and an upper cross beam robustness optimization design model based on a probability-interval mixed variable is established:
Figure GDA0002610463350000071
Figure GDA0002610463350000072
Figure GDA0002610463350000073
wherein f isC(d,X,U)＝(fL(d,X,U)+fR(d,X,U))/2
fW(d,X,U)＝(fR(d,X,U)-fL(d,X,U))/2
Figure GDA0002610463350000074
Figure GDA0002610463350000075
Figure GDA0002610463350000076
d＝(h1,h2,l1,l2,l3)，X＝(P1,P2,P3)，U＝(ρ,υ)
Wherein d ═ h1,h2,l1,l2,l3) To design vectors; x ═ P (P)1,P2,P3) Is a probability type uncertain vector; u ═ ρ, ν) is an interval-type uncertainty vector; f (d, X, U) is the maximum deformation of the upper cross beam; f. ofC(d,X,U),fW(d, X, U) are respectively the midpoint and half width of the variation interval of f (d, X, U) under the influence of interval type uncertainty; w (d, X, U), (d, X, U) is the weight and maximum equivalent stress of the upper cross beam respectively; f. ofL(d,X,U),fR(d,X,U),wL(d,X,U),wR(d,X,U),L(d,X,U),R(d, X, U) are f (d, X, U), w (d, X, U), and (d, X, U), respectively, the left and right bounds of the interval of variation under the influence of interval type uncertainty;
Figure GDA0002610463350000077
Figure GDA0002610463350000078
respectively, the midpoint f of the target function interval under the influence of the uncertainty of the probability intervalC(d, X, U) mean and standard deviation;
Figure GDA0002610463350000079
respectively, the half width f of the target function interval under the influence of the uncertainty of the probability intervalW(d, X, U) mean and standard deviation;
Figure GDA00026104633500000710
respectively, the mean value and the standard deviation of the left boundary of the constraint performance function w (d, X, U) under the influence of the uncertainty of the probability interval;
Figure GDA00026104633500000711
respectively representing the mean value and the standard deviation of the right bound of the constraint performance function w (d, X, U) under the influence of the uncertainty of the probability interval;
Figure GDA00026104633500000712
respectively, the mean value and the standard deviation of the left bound of the constraint performance function (d, X, U) under the influence of the uncertainty of the probability interval;
Figure GDA00026104633500000713
mean and standard deviation of the right bound of the constraint performance function (d, X, U) under the influence of the uncertainty of the probability interval, respectively.
2. Initial sampling of a design vector and an uncertain vector is completed by adopting Latin hypercube sampling, response values of an upper crossbeam objective function and a constraint performance function of a press are obtained through a collaborative simulation technology, and a Kriging model of the objective function and the constraint performance function corresponding to the upper crossbeam of the press is constructed:
(a) and under the condition that the value range is determined, adopting Latin hypercube sampling to obtain sample points with the value range of [0,1] and space equipartition, and performing inverse normalization on the sample points to the input vector space to finish initial sampling of the design vector and the uncertain vector.
(b) The design vector is used as an independent control parameter, a parameterized model of the upper beam of the high-speed press is established by utilizing three-dimensional CAD modeling software, and the bidirectional dynamic transmission of the parameters between the three-dimensional model software and the finite element analysis software is realized through an interface technology. Grid division is carried out on the 1/4 upper crossbeam model by adopting Solid187 units, the size of the grid is 50mm, 16690 units are obtained, and 30626 nodes are obtained. Adding uncertain factor vectors into finite element analysis software as secondary input parameters, and calling a three-dimensional parametric model to perform finite element analysis calculation to obtain response values of a target function and a constraint performance function corresponding to an upper beam sample point of the press machine.
(c) And constructing a Kriging model for predicting the maximum deformation, weight and maximum equivalent stress of the upper cross beam according to the sample point data containing the input and output information. And fitting by using a Gaussian function and a first-order regression function, and continuously checking and updating by using the complex correlation coefficient and the relative maximum absolute error until the complex correlation coefficient values are all larger than 0.95 and the relative maximum absolute error values are all smaller than 0.05, so that the fitting precision and the generalization capability are ensured to meet the actual requirements.
3. Directly solving a robust optimization design model of a probability interval of an upper beam based on a genetic algorithm and double-layer nested optimization:
the genetic algorithm parameter settings are as follows: maximum evolution generation number 150, population size 200, cross coefficient 0.99, coefficient of variation 0.05, and algorithm convergence condition 0.00001. The following takes the 1 st iteration process as an example to illustrate a two-layer nested direct solution process based on a genetic algorithm.
The iteration cycle is that the population individuals are d1＝(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), the inner layer performs interval robustness analysis on each individual using a Kriging predictive model, and then calculates the respective means and standard deviations of the objective function and the constraint performance function for each individual by the monte carlo method. On the basis of the inner layer calculation result, the outer layer calculates the total feasible robustness coefficient S of each individual as follows: s1＝2，S2＝2，S3＝1.383，S4＝0，S5＝2，S6＝1.016……S199＝2，S2001.370. Then the fully viable individual contains d according to the classification criteria1、d2、d5、d199Etc. (107 total), some infeasible individuals contained d3、d6、d200Etc. (62 in total), completely infeasible individuals contained d4Etc. (31 in total).
The fully viable individuals and partially non-viable individuals are then ranked. Firstly, respectively calculating the negative ideal solution closeness distance of a completely feasible individual by the following process: 1) parameters were compared and defined among 107 fully viable individuals
Figure GDA0002610463350000081
Figure GDA0002610463350000082
2) Calculating the negative ideal solution closeness distance, D, of each fully feasible individual*(d1)＝0.1292、D*(d2)＝0.1311、D*(d5)＝0.1276……D*(d199) 0.1467; 3) and performing descending sorting according to the negative ideal closeness solving distance of each completely feasible individual to enable each individual to obtain a unique sorting number. And (4) directly performing descending sorting on the partially infeasible individuals according to the total feasible robustness coefficient of the partially infeasible individuals, and obtaining a unique sorting number for each individual.
And assigning fitness values to all individuals, wherein the fitness of the completely feasible individuals and the partially infeasible individuals is the reciprocal of the sequence number obtained by sequencing, and the fitness of the completely infeasible individuals is directly assigned to be 0.
And judging that the maximum iteration number is not reached to 150 and the convergence condition of 0.00001 is not met, performing cross variation operation on the population individuals used in the iteration, and performing the 2 nd iteration again.
The optimization results are as follows: the performance index reaches convergence on the 26 th iteration, and the corresponding optimal design vector is d ═ (226.32,265.11,81.11,30.32,378.19) mm; optimized target performance-maximum deformation
Figure GDA0002610463350000091
Weight (μ) as a function of constrained performance after optimizationw,σw) Maximum equivalent stress (μ) of (5062.98, 16.73) kg,σ) The robustness requirement is met under the condition of (27.56, 2.76) MPa, so that the effectiveness of the method is verified.
It should be noted that the summary and the detailed description of the invention are intended to demonstrate the practical application of the technical solutions provided by the present invention, and should not be construed as limiting the scope of the present invention. Any modification and variation of the present invention within the spirit of the present invention and the scope of the claims will fall within the 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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