CN113591230A - Multi-objective optimization method for commercial vehicle cab based on beam section - Google Patents

Multi-objective optimization method for commercial vehicle cab based on beam section Download PDF

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CN113591230A
CN113591230A CN202111069225.9A CN202111069225A CN113591230A CN 113591230 A CN113591230 A CN 113591230A CN 202111069225 A CN202111069225 A CN 202111069225A CN 113591230 A CN113591230 A CN 113591230A
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CN113591230B (en
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刘夫云
汤金帅
邓聚才
刘凯扬
蔡珍珍
杜中刚
李建衡
段小勇
陈志宁
张瑞俊
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Guilin University of Electronic Technology
Dongfeng Liuzhou Motor Co Ltd
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Abstract

The invention discloses a multi-objective optimization method for a commercial vehicle cab based on a beam section, which utilizes SFE-Concept software to establish an implicit parameterized model of the commercial vehicle cab. Aiming at the problem of overlong test design operation time, the method optimizes the whole process, combines HyperMorph to perform sensitivity analysis and relative sensitivity analysis, screens out key variables before test design, greatly reduces the test design operation time and improves the optimization efficiency. Aiming at the problem of low fitting accuracy of a common approximation model, a response surface-radial basis mixed approximation model is constructed, and fitting accuracy is improved, so that correlation coefficient values of five indexes are all over 0.9, and accuracy requirements are met.

Description

Multi-objective optimization method for commercial vehicle cab based on beam section
Technical Field
The invention relates to the technical field of performance optimization of commercial vehicle cabs, in particular to a multi-objective optimization method of a commercial vehicle cab based on a beam section.
Background
Various performance indexes of the automobile body not only influence riding experience of a user, but also directly relate to life safety. Before mass production, each automobile must be subjected to performance tests such as NVH performance, collision safety, operation stability, structural durability and the like, and the next stage can be carried out after the requirements are met. The rigidity of the automobile body greatly influences various performances of the automobile, and the lack of the rigidity of the automobile body can cause the lower mode of the whole automobile, resonance and the like. The research proves that: the beam section shape is one of main factors influencing the rigidity of the automobile body, and the main effect relationship between the beam section shape and the rigidity of the automobile body is researched, so that an engineer can be helped to design an automobile which meets the market requirements better.
The traditional beam section optimization method mainly has three defects: the related optimization is carried out based on the finite element model, and the optimization efficiency is low; the running time of the test design is too long; the fitting accuracy of the approximate model is low. (1) Carrying out related optimization based on the finite element model: this method has two significant drawbacks: firstly, the variation range of the upper limit and the lower limit of the variable is smaller. When recording the beam section shape variable, only the variable in the finite element model can be finely adjusted, if the adjustment amplitude is too large, the problems of grid deformation, poor grid quality and the like occur, and the situation of calculation error report often occurs; second, the optimized solution may be a better solution than the optimal solution. The variation range of the upper limit and the lower limit of the variable is too small, so that the optimization space is reduced, the possibility of finding the optimal solution is reduced, the solved optimal solution is probably a local optimal solution rather than a global optimal solution, and the traditional critical section optimization method has many human factors and large errors. (2) The test design has too long running time: the beam section optimization design based on the implicit parameterized model is generally carried out by sensitivity analysis and relative sensitivity analysis in a test design mode, and then key optimization variables are selected according to the contribution rate. If the optimization variables are not screened in advance, the key optimization variables are directly selected by using a test design mode, all possible design variables need to be recorded through SFE-Concept software, the number of recorded variables is large, the number of sample points is large, and the running time is long. (3) The fitting precision of the approximate model is low: in the process of fitting the approximate model, since the modes of the same vibration mode may occur in different orders when the variables are changed, and only the mode frequency of a certain order can be constrained during constraint, the problem of poor fitting accuracy of the approximate model is caused.
In addition, most of researches based on beam sections are carried out for passenger vehicles, most of related researches aim at light weight, and optimization effects and optimization efficiency need to be further improved.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a commercial vehicle cab multi-objective optimization method based on a beam section.
The technical scheme for realizing the purpose of the invention is as follows:
a multi-objective optimization method for a commercial vehicle cab based on beam sections is disclosed, as shown in FIG. 1, and comprises the following steps:
1) the method comprises the following steps of establishing an implicit parameterized model of a commercial vehicle cab by utilizing SFE-Concept software: firstly, importing the existing finite element model into SFE-Concept software, and dividing the whole cab into five assemblies of a top cover, a floor, a side wall, a rear wall and a front wall; secondly, establishing different base points according to the shapes and the positions of the parts, generating base lines with different curvatures from the base points, establishing different base planes, and controlling the shapes and the positions of any parts through three basic elements; for the cab with a left-right symmetrical structure, firstly establishing a left cab implicit parameterized model, and generating a right cab implicit parameterized model by using a mirror image, namely completing the establishment of the whole cab implicit parameterized model;
2) exporting an implicit parameterized model of the commercial vehicle cab from SFE-Concept software, and storing the model as a finite element model of the commercial cab in a file format of bdf, so that the model can be conveniently imported into Hypermesh to establish a working condition and perform basic performance analysis;
3) carrying out mass, torsional rigidity, bending rigidity, first-order torsional mode and first-order bending mode basic performance analysis on the derived commercial cab finite element model by using an OptiStruct solver in Hypermesh to obtain basic performance analysis values, wherein the basic performance analysis values are obtained by taking the optimization target of minimum mass, maximum torsional rigidity and maximum bending rigidity, and taking the first-order torsional mode frequency value and the first-order bending mode frequency value which are not lower than the preliminary analysis value as constraint conditions;
4) analyzing the mechanical characteristics of the beam section of the commercial vehicle cab, determining the relationship between the mechanical characteristics and the beam section shape, and controlling the beam section shape by using a proportional vector method by taking the beam section shape as a variable;
5) performing beam section sensitivity analysis by using HyperMorph: setting a plurality of deformation bodies on the beam section of the cab by utilizing shape function in HyperMorph, finishing beam section variable recording by adjusting the deformation bodies to change the shape of the beam section, and calculating the sensitivity value of a target to the beam section variable through sensitivity analysis; when the beam section variables of different targets are subjected to sensitivity analysis, the relative sensitivity analysis is adopted to balance the variables of the different targets;
6) screening out the beam section shape variables which meet the problem according to the results of sensitivity analysis and relative sensitivity analysis, and carrying out DOE (Design of Experiment) analysis by using the screened variables and adopting an optimal Latin hypercube method to obtain a group of sample points;
7) selecting the sample points obtained in the step 6) in a proper amount, and constructing a response surface-radial basis mixed approximate model, wherein the fitting formula of the model is as follows:
Figure BDA0003259824980000031
in formula (1), y (x) is a response actual value;
Figure BDA0003259824980000032
is a response approximation; ε is the random error between the response actual and response approximate values, where: the response surface-radial basis mixed approximation model replaces an original model after meeting the precision requirement which adopts a correlation coefficient R2Evaluation was made of R2The calculation formula is as follows:
Figure BDA0003259824980000033
in the above formula, n number of sample points, yiIs a simulation value, ysiIn order to predict the value of the target,
Figure BDA0003259824980000034
is yiThe mean value of (a); as shown in fig. 2, the flow of the response surface-radial basis mixture approximation model is as follows:
7-1) analyzing and collecting required sample points through test design;
7-2) selecting an approximate model fitting method which accords with the characteristics of the optimization problem, and constructing an approximate model by using the collected sample points;
7-3) verifying the fitting precision of the approximate model to meet the requirement of replacing the original model to participate in optimization;
and 7-4) if the precision of the approximate model is too low, the precision requirement cannot be met, further increasing the number of sample points or replacing a more applicable approximate model fitting method to improve the fitting precision until the engineering requirement is met.
Response surface method: fitting the design space by using a polynomial function, wherein the fitting formula is as follows:
Figure BDA0003259824980000035
Figure BDA0003259824980000036
the response surface method fitting approximate model can reduce sample points as much as possible and approach the target function to the maximum extent; the mathematical model formed by fitting is simple, has strong robustness and strong practicability. However, because the number of sample points is small, all indexes cannot be considered when the approximate model is constructed, the radial basis method is adopted to make up the defects, and the radial basis-response surface mixed approximate model is constructed.
Radial basis method: using the Euclidean distance between the point to be measured and the sample point as an argument
Figure BDA0003259824980000037
Represents a set of input vectors that are to be processed,
Figure BDA0003259824980000038
is a basis function, where | | | x-xj，| | is the euclidean distance: (x-x)j)T(x-xj) And c is more than or equal to 0.2 and less than or equal to 3;
8) and (3) performing multi-objective optimization on the response surface-radial basis hybrid approximation model established in the step 7) by adopting an NSGA-II (non-normalized locking Genetic Algorithm II) Algorithm under the constraint conditions that the mass is minimum, the torsional rigidity is maximum, the bending rigidity is maximum, the optimization target is maximum, and the first-order torsional mode frequency value and the first-order bending mode frequency value are not lower than the initial calculated value, so as to obtain an optimal solution.
As shown in fig. 3, the optimization steps of the NSGAII algorithm are:
8-1) setting basic parameters of the algorithm, including population scale, cross variation probability and iteration times;
8-2) generating an initialization population P1；
8-3) selecting the parent population individuals, performing crossover and mutation operations to generate an offspring population, and calculating the individual fitness value of the offspring population;
8-4) merging the parent population and the offspring population to form a new population, and performing rapid non-dominated sorting on individuals of the new population;
8-5) calculating the individual crowding degree distance of the new population, screening out the individuals with high fitness, and entering the next generation Pt+1；
8-6) judging a termination condition, if so, terminating the conditional algorithm, otherwise, adding 1 to the iteration number, and turning to the step 8-3).
In the step 3), the basic performance analysis of the mass, the torsional rigidity, the bending rigidity, the first-order torsional mode and the first-order bending mode is as follows:
when quality is analyzed, a built-in quality calculation function in the Hypermesh software is utilized to realize one-click analysis; when analyzing low-order modal frequency, adding an Eigra card in Hypermesh, setting a modal analysis frequency value range and a loading step, and directly solving a first-order torsional modal frequency value and a first-order bending modal frequency value by using an Optistruct solver; when the torsional rigidity is analyzed, the left and right rear suspensions of the cab are restrained, two forces with the same magnitude and opposite directions are loaded on the left and right front suspensions, and the calculation formula of the torsional rigidity is as follows:
Figure BDA0003259824980000041
in the above formula, T is the applied torque; d1、D2Respectively displacement of the left and right loading points in the gravity direction; theta is D2And D1The displacement difference value and the arctangent value in the horizontal direction, wherein L is the distance between the left loading point and the right loading point;
when the bending stiffness is analyzed, the left, right, front and rear suspensions of the cab are restrained, the loading force is applied to the left and right seats and the sleeper, and the calculation formula of the bending stiffness is as follows:
Figure BDA0003259824980000042
in the above formula, FFront seatThe total loading force for the front seat; fSleeping berthThe total loading force for the sleeper; d1、D2The maximum displacement of the left and right longitudinal beams at the bottom in the gravity direction.
In the step 4), the mechanical characteristics comprise section area, section inertia moment, cavity sealing area and torsion constant, the section is formed by cutting a certain part of a body-in-white in a vertical direction, and the cut surface is a section; the section area refers to the amount of materials used for the section; the section inertia moment reflects the bending resistance of the section and is in positive correlation with the bending resistance of the section; the area of the cavity is the size of the cross section space; the torsion constant reflects the torsion resistance of the reaction section and is in positive correlation with the torsion resistance; the calculation formula is as follows:
Figure BDA0003259824980000051
Figure BDA0003259824980000052
in the formula Iy、IzRepresenting moment of inertia in mm4(ii) a A is the area of the section of the part in mm2；
Figure BDA0003259824980000053
In the formula ItIs a torsional constant; c is the area enclosed by the outline; t is the thickness of the thin-walled rod; s is the perimeter of a midline of the cross section, and the shape of the cross section is closely related to the mechanical properties of the cross section according to the calculation principle and the calculation result, so that the shape of the cross section is selected as a design variable;
the proportional vector method controls the change of the cross section through an angle value and a deformation value, firstly determines the change direction of a control point, and then realizes the change of the cross section through a deformation measurement value; the proportional vector method comprises two variables of a rotation angle theta and a deformation metric SV, and assuming that the coordinate of a certain point B in a yoz coordinate system is (y, z), the coordinate system is rotated by a certain angle theta, and in a new coordinate system y 'oz', the new coordinate of the point B is (y ', z'), the calculation formula is as follows:
Figure BDA0003259824980000054
after the rotation angle is determined, the numerical value of the deformation metric SV is determined, after deformation occurs, the coordinate (y ', z') of the point B after deformation is further obtained, and the calculation formula is as follows:
Figure BDA0003259824980000055
substituting equation (9) into equation (10) yields equation (11) as follows:
Figure BDA0003259824980000061
according to the above calculation formula, when θ is 0 °, the coordinate of the base point changes along the Y direction; when theta is 90 degrees, the coordinate of the base point changes along the Z direction; the section optimization of the commercial vehicle cab beam is researched when theta is 0 degrees.
In step 5), the sensitivity analysis is carried out, and the sensitivity S of the performance parameters of the vehicle body structure to the section shape variables of the parts is as follows:
Figure BDA0003259824980000062
in the formula (12), S is sensitivity;
Figure BDA0003259824980000063
for the objective function f (x) to the variable xiReciprocal of (a), xiThe cross section of the ith part is shaped; mass sensitivity S of mass to cross-sectional shape to be analyzed for cross-sectional optimization of commercial vehicle cab beamMTorsional rigidity pairTorsional stiffness sensitivity in cross-sectional shape STFirst order torsional mode sensitivity S of first order torsional mode to section shapeTMBending stiffness sensitivity S to bending stiffness of cross-sectional shapeBFirst order bending mode sensitivity S of first order bending mode to cross-sectional shapeBMA total of 5 different objective functions;
the relative sensitivity analysis is the ratio of other performance sensitivity values to mass sensitivity values, wherein:
the mass relative sensitivity formula is:
Figure BDA0003259824980000064
m is mass, xiThe cross section of the ith part is shaped;
the relative sensitivity of the first order torsional modes is:
rtm＝STM/SM (14)
the relative sensitivity of the first order bending mode is:
rbm＝SBM/SM (15)
the relative sensitivity of torsional stiffness is:
rt＝ST/SM (16)
the relative sensitivity of bending stiffness is:
rb＝SB/SM (17)
in step 6), the screening is to make the mass sensitivity SMArranging according to the sensitivity numerical value descending order, taking the first 20 section shape variables as design variables, and respectively using the first-order torsional mode sensitivity STMFirst order bending mode sensitivity SBMTorsional stiffness sensitivity STBending stiffness sensitivity SBAnd mass sensitivity SMCompared with the prior art, the method is arranged according to the ascending order of the relative sensitivity values, the first 20 section shape variables are respectively taken as design variables, and finally a proper amount of section shape variables are selected as optimization through relative sensitivity analysisAnd (4) variable quantity.
The optimal Latin hypercube method is to arrange each dimension coordinate interval in n dimension space
Figure BDA0003259824980000071
Figure BDA0003259824980000072
Is evenly divided into m intervals, and each interval is marked as
Figure BDA0003259824980000073
And randomly selecting m points to ensure that each level of a factor is researched only once, namely forming an n-dimensional space, and recording the Latin hypercube design with the sample number of m as m x n LHD.
The invention provides a multi-objective optimization method for a commercial vehicle cab based on a beam section, which mainly has the following three advantages:
(1) compared with the traditional finite element model, the model can quickly finish the modification of any scheme, and maintain a good topological relation after the modification, and can also quickly generate a high-quality grid meeting the topological relation after the adjustment.
(2) Aiming at the problem of overlong test design operation time, the method optimizes the whole process, combines HyperMorph to perform sensitivity analysis and relative sensitivity analysis, screens out key variables before test design, greatly reduces the test design operation time and improves the optimization efficiency.
(3) Aiming at the problem of low fitting accuracy of a common approximation model, a response surface-radial basis mixed approximation model is constructed, and fitting accuracy is improved, so that correlation coefficient values of five indexes are all over 0.9, and accuracy requirements are met.
Drawings
FIG. 1 is a block diagram of a cross section optimization of a cab beam of a commercial vehicle;
FIG. 2 is a block diagram of approximate model fitting;
FIG. 3 is a block diagram of NSGAII algorithm optimization;
FIG. 4 is a schematic diagram of an implicit parameterized model of a cab of a commercial vehicle;
FIG. 5 is a schematic view of a finite element model of a cab of a commercial vehicle;
FIG. 6 is a schematic diagram of a proportional vector method;
FIG. 7 is a graph showing the results of partial sensitivity analysis.
Detailed Description
The invention will be further elucidated with reference to the drawings and examples, without however being limited thereto.
Example (b):
the technical scheme is adopted to optimize a cab of a certain commercial vehicle, for example, the cab of the certain commercial vehicle is used, an implicit parameterized model is built by SFE-Concept software as shown in figure 4, a corresponding finite element model is derived as shown in figure 5, an Optistruct solver is used for completing analysis of basic performances such as mass, torsional rigidity, bending rigidity, a first-order torsional mode and a first-order bending mode, and basic performance values are shown in table 1.
TABLE 1 basic Properties
Figure BDA0003259824980000081
The mechanical characteristics of the cross section are analyzed, the cross section shape which is a key cross section control factor is found, the cross section shape is controlled by using a proportional vector method, and a flow diagram of the proportional vector method is shown in FIG. 6. Sensitivity analysis is performed by combining HyperMorph, the key optimization variables are screened out before test design, the test design running time is shortened, and partial sensitivity analysis results are shown in fig. 7. Shortening the running time of the test design: sensitivity analysis is carried out in advance by combining with HyperMorph, so that the running time of the test design can be shortened. The total section variables of a cab of a certain commercial vehicle are 63, 64 sample points are selected at least by using an optimal Latin hypercube test design method, and by taking a computer with a 16G running memory as an example, the running time of the test design is 64 × 15/60 h-16 h. And 33 section shape variables are selected by combining HyperMorph, 34 sample points are needed at least, the running time of the experimental design needs 34 x 15/60-8.5 h, and the analysis time of the HyperMesh sensitivity is 0.5h and 9h, so that the time is shortened by 44%. And (4) carrying out experimental design by utilizing the screened variables and adopting an optimal Latin hypercube mode, and collecting a group of sample points. And selecting a proper amount of sample points to construct a response surface-radial basis mixed approximate model so as to improve the fitting precision, wherein the fitting precision is shown in the table 2.
TABLE 2 fitting accuracy
Figure BDA0003259824980000082
And finally, optimizing the mixed approximation model by using NSGAII, and performing performance comparison after optimization. The optimized selection of 33 section shapes as design variables Tn(n-1, 2, …,33) with the constraint conditions that the first order torsional mode is greater than or equal to 21Hz, the first order bending mode is greater than or equal to 39.5Hz, and the objectives of minimum mass, maximum torsional stiffness, and maximum bending stiffness are optimized. Optimization was performed using NSGAII. Mathematical description of the optimization problem:
Variable：T＝(T1，T2，…，T33)
Objective：{Mmin(T)，FTmax(T)，FBmax(T)}
s.t.
fTMmin≥21；fBMmin≥39.5 (18)
in the formula: mminThe mass of the commercial vehicle cab is the minimum, namely unit kg; fTmaxMaximum torsional stiffness in Nm/°; fBmaxThe maximum value of the bending rigidity is in N/mm. f. ofTMminIs the minimum value of the first-order torsional mode in Hz; f. ofBMminIs the first order bending mode minimum in Hz.
Through multi-objective optimization, the optimization result is shown in table 3, under the condition that the first-order torsional mode is not lower than 21Hz and the first-order bending mode is not lower than 39.5Hz, the cab mass is reduced by 16.5kg, the cab mass is reduced by 5.4%, the bending stiffness is improved by 15.3%, the torsion stiffness is improved by 7.7%, the first-order torsional mode is improved by 0.5%, the first-order bending mode is reduced by 0.5%, the frequency value change of the low-order bending mode is small and can be ignored, the multi-objective optimization effect is good, and the multi-objective optimization method has certain guiding significance for engineering practice.
TABLE 3 comparison of Performance values before and after optimization
Figure BDA0003259824980000091

Claims (6)

1. A commercial vehicle cab multi-objective optimization method based on beam sections is characterized by comprising the following steps:
1) the method comprises the following steps of establishing an implicit parameterized model of a commercial vehicle cab by utilizing SFE-Concept software: firstly, importing the existing finite element model into SFE-Concept software, and dividing the whole cab into five assemblies of a top cover, a floor, a side wall, a rear wall and a front wall; secondly, establishing different base points according to the shapes and the positions of the parts, generating base lines with different curvatures from the base points, establishing different base planes, and controlling the shapes and the positions of any parts through three basic elements; for the cab with a left-right symmetrical structure, firstly establishing a left cab implicit parameterized model, and generating a right cab implicit parameterized model by using a mirror image, namely completing the establishment of the whole cab implicit parameterized model;
2) exporting an implicit parameterized model of the commercial vehicle cab from SFE-Concept software, and storing the model as a finite element model of the commercial cab in a file format of bdf, so that the model can be conveniently imported into Hypermesh to establish a working condition and perform basic performance analysis;
3) carrying out mass, torsional rigidity, bending rigidity, first-order torsional mode and first-order bending mode basic performance analysis on the derived commercial cab finite element model by using an OptiStruct solver in Hypermesh to obtain basic performance analysis values, wherein the basic performance analysis values are obtained by taking the optimization target of minimum mass, maximum torsional rigidity and maximum bending rigidity, and taking the first-order torsional mode frequency value and the first-order bending mode frequency value which are not lower than the preliminary analysis value as constraint conditions;
4) analyzing the mechanical characteristics of the beam section of the commercial vehicle cab, determining the relationship between the mechanical characteristics and the beam section shape, and controlling the beam section shape by using a proportional vector method by taking the beam section shape as a variable;
5) performing beam section sensitivity analysis by using HyperMorph: setting a plurality of deformation bodies on the beam section of the cab by utilizing shape function in HyperMorph, finishing beam section variable recording by adjusting the deformation bodies to change the shape of the beam section, and calculating the sensitivity value of a target to the beam section variable through sensitivity analysis; when the beam section variables of different targets are subjected to sensitivity analysis, the relative sensitivity analysis is adopted to balance the variables of the different targets;
6) screening out the beam section shape variables which meet the problem according to the results of the sensitivity analysis and the relative sensitivity analysis, and carrying out DOE analysis by adopting an optimal Latin hypercube method by using the screened variables to obtain a group of sample points;
7) selecting the sample points obtained in the step 6) in a proper amount, and constructing a response surface-radial basis mixed approximate model, wherein the fitting formula of the model is as follows:
Figure FDA0003259824970000011
in formula (1), y (x) is a response actual value;
Figure FDA0003259824970000021
is a response approximation; ε is the random error between the response actual and response approximate values, where: the response surface-radial basis mixed approximation model replaces an original model after meeting the precision requirement which adopts a correlation coefficient R2Evaluation was made of R2The calculation formula is as follows:
Figure FDA0003259824970000022
in the above formula, n number of sample points, yiIs a simulation value, ysiIn order to predict the value of the target,
Figure FDA0003259824970000023
is yiThe mean value of (a); response surface-radial basis mixingThe procedure of the synthetic approximation model is as follows:
7-1) analyzing and collecting required sample points through test design;
7-2) selecting an approximate model fitting method which accords with the characteristics of the optimization problem, and constructing an approximate model by using the collected sample points;
7-3) verifying the fitting precision of the approximate model to meet the requirement of replacing the original model to participate in optimization;
and 7-4) if the precision of the approximate model is too low, the precision requirement cannot be met, further increasing the number of sample points or replacing a more applicable approximate model fitting method to improve the fitting precision until the engineering requirement is met.
Response surface method: fitting the design space by using a polynomial function, wherein the fitting formula is as follows:
Figure FDA0003259824970000024
Figure FDA0003259824970000025
radial basis method: using the Euclidean distance between the point to be measured and the sample point as an argument
Figure FDA0003259824970000026
Represents a set of input vectors that are to be processed,
Figure FDA0003259824970000027
is a basis function, where | | | x-xjAnd | is the euclidean distance: (x-x)j)T(x-xj) And c is more than or equal to 0.2 and less than or equal to 3;
8) performing multi-objective optimization on the response surface-radial basis mixed approximation model established in the step 7) by adopting an NSGA-II algorithm under the constraint conditions that the mass is minimum, the torsional rigidity is maximum, the bending rigidity is maximum, the optimization target is maximum, and the first-order torsional mode frequency value and the first-order bending mode frequency value are not lower than the initial calculated value, so as to obtain an optimal solution;
the optimization steps of the NSGAII algorithm are as follows:
8-1) setting basic parameters of the algorithm, including population scale, cross variation probability and iteration times;
8-2) generating an initialization population P1；
8-3) selecting the parent population individuals, performing crossover and mutation operations to generate an offspring population, and calculating the individual fitness value of the offspring population;
8-4) merging the parent population and the offspring population to form a new population, and performing rapid non-dominated sorting on individuals of the new population;
8-5) calculating the individual crowding degree distance of the new population, screening out the individuals with high fitness, and entering the next generation Pt+1；
8-6) judging a termination condition, if so, terminating the conditional algorithm, otherwise, adding 1 to the iteration number, and turning to the step 8-3).
2. The method for multi-objective optimization of the cab of the commercial vehicle based on the beam section as claimed in claim 1, wherein in the step 3), the basic performance analysis of the mass, the torsional rigidity, the bending rigidity, the first-order torsional mode and the first-order bending mode is as follows:
when quality is analyzed, a built-in quality calculation function in the Hypermesh software is utilized to realize one-click analysis; when analyzing low-order modal frequency, adding an Eigra card in Hypermesh, setting a modal analysis frequency value range and a loading step, and directly solving a first-order torsional modal frequency value and a first-order bending modal frequency value by using an Optistruct solver; when the torsional rigidity is analyzed, the left and right rear suspensions of the cab are restrained, two forces with the same magnitude and opposite directions are loaded on the left and right front suspensions, and the calculation formula of the torsional rigidity is as follows:
Figure FDA0003259824970000031
in the above formula, T is the applied torque; d1、D2Respectively displacement of the left and right loading points in the gravity direction; theta is D2And D1The displacement difference value and the arctangent value in the horizontal direction, wherein L is the distance between the left loading point and the right loading point;
when the bending stiffness is analyzed, the left, right, front and rear suspensions of the cab are restrained, the loading force is applied to the left and right seats and the sleeper, and the calculation formula of the bending stiffness is as follows:
Figure FDA0003259824970000032
in the above formula, FFront seatThe total loading force for the front seat; fSleeping berthThe total loading force for the sleeper; d1、D2The maximum displacement of the left and right longitudinal beams at the bottom in the gravity direction.
3. The method for multi-objective optimization of the cab of the commercial vehicle based on the beam section as claimed in claim 1, wherein in the step 4), the mechanical characteristics comprise section area, section inertia moment, cavity sealing area and torsion constant, the section is formed by cutting a certain part of a body in white in the vertical direction, and the cut surface is a section; the section area refers to the amount of materials used for the section; the section inertia moment reflects the bending resistance of the section and is in positive correlation with the bending resistance of the section; the area of the cavity is the size of the cross section space; the torsion constant reflects the torsion resistance of the reaction section and is in positive correlation with the torsion resistance; the calculation formula is as follows:
Figure FDA0003259824970000041
Figure FDA0003259824970000042
in the formula Iy、IzRepresenting moment of inertia in mm4(ii) a A is the area of the section of the part in mm2；
Figure FDA0003259824970000043
In the formula ItIs a torsional constant; c is the area enclosed by the outline; t is the thickness of the thin-walled rod; s is the perimeter of a midline of the cross section, and the shape of the cross section is closely related to the mechanical properties of the cross section according to the calculation principle and the calculation result, so that the shape of the cross section is selected as a design variable;
the proportional vector method controls the change of the cross section through an angle value and a deformation value, firstly determines the change direction of a control point, and then realizes the change of the cross section through a deformation measurement value; the proportional vector method comprises two variables of a rotation angle theta and a deformation metric SV, and assuming that the coordinate of a certain point B in a yoz coordinate system is (y, z), the coordinate system is rotated by a certain angle theta, and in a new coordinate system y 'oz', the new coordinate of the point B is (y ', z'), the calculation formula is as follows:
Figure FDA0003259824970000044
after the rotation angle is determined, the numerical value of the deformation metric SV is determined, after deformation occurs, the coordinate (y ', z') of the point B after deformation is further obtained, and the calculation formula is as follows:
Figure FDA0003259824970000045
substituting equation (9) into equation (10) yields equation (11) as follows:
Figure FDA0003259824970000046
according to the above calculation formula, when θ is 0 °, the coordinate of the base point changes along the Y direction; when θ is 90 °, the coordinate of the base point changes in the Z direction.
4. The method for multi-objective optimization of the cab of the commercial vehicle based on the beam section as claimed in claim 1, wherein in the step 5), the sensitivity S of the performance parameters of the vehicle body structure to the section shape variables of the parts is:
Figure FDA0003259824970000051
in the formula (12), S is sensitivity;
Figure FDA0003259824970000052
for the objective function f (x) to the variable xiReciprocal of (a), xiThe cross section of the ith part is shaped; mass sensitivity S of mass to cross-sectional shape to be analyzed for cross-sectional optimization of commercial vehicle cab beamMTorsional stiffness sensitivity to cross-sectional shape STFirst order torsional mode sensitivity S of first order torsional mode to section shapeTMBending stiffness sensitivity S to bending stiffness of cross-sectional shapeBFirst order bending mode sensitivity S of first order bending mode to cross-sectional shapeBMA total of 5 different objective functions;
the relative sensitivity analysis is the ratio of other performance sensitivity values to mass sensitivity values, wherein:
the mass relative sensitivity formula is:
Figure FDA0003259824970000053
m is mass, xiThe cross section of the ith part is shaped;
the relative sensitivity of the first order torsional modes is:
rtm＝STM/SM (14)
the relative sensitivity of the first order bending mode is:
rbm＝SBM/SM (15)
the relative sensitivity of torsional stiffness is:
rt＝ST/SM (16)
the relative sensitivity of bending stiffness is:
rb＝SB/SM (17)。
5. the method for multi-objective optimization of the cab of the commercial vehicle based on the beam section as claimed in claim 1, wherein the screening in step 6) is to sensitivity the mass to SMArranging according to the sensitivity numerical value descending order, taking the first 20 section shape variables as design variables, and respectively using the first-order torsional mode sensitivity STMFirst order bending mode sensitivity SBMTorsional stiffness sensitivity STBending stiffness sensitivity SBAnd mass sensitivity SMAnd comparing the values in ascending order according to the relative sensitivity, respectively taking the first 20 section shape variables as design variables, and finally selecting a proper amount of section shape variables as optimization variables through relative sensitivity analysis.
6. The method as claimed in claim 1, wherein the optimal Latin hypercube method is implemented by dividing coordinate intervals of each dimension into n-dimensional space
Figure FDA0003259824970000054
Is evenly divided into m intervals, and each interval is marked as
Figure FDA0003259824970000055
Figure FDA0003259824970000061
And randomly selecting m points to ensure that each level of a factor is researched only once, namely forming an n-dimensional space, and recording the Latin hypercube design with the sample number of m as m x n LHD.
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