1. A collision resistance-based multi-disciplinary optimization method for variable-pitch arrangement of riveting points is characterized by comprising the following steps of:

s1 multidisciplinary optimization problem for defining variable-pitch arrangement of riveting points

S11, defining design variables;

s12, defining constraint conditions, and calculating a structural multidisciplinary performance response column vector Y corresponding to the original riveting point arrangement scheme by adopting a finite element simulation method, wherein Y is (Y)₁,y₂,y₃,y₄,y₅)^T，y₁,y₂,y₃,y₄,y₅Respectively corresponding to the structure energy absorption EA and the maximum collision force peak value F_maxBending stiffness K_bTorsional rigidity K_tAnd a first order modal response f₁And relaxing it by 5% respectively as a design baseline;

s13, determining an optimization target, and adopting structural collision safety performance evaluation indexes: the structure energy absorption is maximized and the maximum peak force of collision is minimized, and the optimized formula is shown as formula (1):

wherein X represents a rivet point arrangement scheme comprising n design variables X₁,x₂,…,x_n；x_iThe design variable of the ith riveting point is shown, i is 1, the distances from the first riveting point and the last riveting point on the riveting line to the two ends of the structure correspond to n, i is 2,3, …, and the distances between the adjacent riveting points correspond to n-1; x is the number of_minAnd x_maxRespectively the minimum and maximum values of the riveting point end distance, x'_minAnd x'_maxThe minimum value and the maximum value of the distance between adjacent riveting points are obtained; the objective function-EA (X) is the inverse of the energy absorbed by the structure, F_max(X) is the peak maximum impact force; k_b0、K_t0、f₁₀、EA₀、F_max0Respectively a bending rigidity lower limit value, a torsional rigidity lower limit value, a modal response lower limit value, an energy absorption lower limit value and a maximum peak force upper limit value;

s2, establishing a parameterized finite element model based on the finite element simulation model in the step S12 and the optimization problem definition in the step S13:

s21, based on the finite element simulation model in the step S12, deleting the connection units to obtain a finite element model only containing components; establishing a parameterized finite element model with variable riveting point spacing and variable number based on the optimization problem definition in the step S13;

s3, selecting t riveting point arrangement schemes TL (X) by adopting a material mixing test design method₁,X₂,…,X_t) Respectively calculating the arrangement scheme X of each riveting point based on a parameterized finite element model_a(a-1, 2, …, t) corresponding to the column vector Y of performance responses_a(a ═ 1,2, …, t), a training set containing t sample points is obtainedSelecting a v riveting point arrangement scheme VL (X) by adopting a random sampling method_t+1,X_t+2,…,X_t+v) Respectively calculating each riveting point arrangement scheme X based on the parameterized finite element model established in the step S2_b(b ═ t +1, t +2, …, t + v) for the corresponding column vector Y of performance responses_b(b ═ t +1, t +2, …, t + v), a validation set containing v sample points was obtained

S4, selecting an agent model by adopting a leave-one-out cross validation strategy based on the training set TS, wherein the method specifically comprises the following steps:

s41, training set based onFrom which a sample point is taken(j ═ 1,2, …, t) as test points, the rest t-1 sample points as training points to establish proxy models, and the formula (2) is adopted to calculate various performance responses y at the test points_kPrediction error E of (k ═ 1,2, …,5)_jk；

Wherein, y_jkAs a result of the simulation of the kth performance response corresponding to the test point,to adopt the sample-removing point TS_jProxy model established by outer t-1 sample points at test point TS_j(ii) a predicted result of the corresponding kth performance response;

s42, repeating the step S41, traversing the whole training set, enabling t training sample points to be sequentially and independently used as test points, and calculating various performance responses y by a formula (3)_kGeneralized square error GMSE of (k-1, 2, …,5)_k；

S43, changing the type of the proxy model, and repeating the steps S41 and S42;

s44, responding to each performance y_k(k-1, 2, …,5) independently selected to generalize the square error GMSE_kThe minimum agent model type is used for the subsequent optimization process;

s5, responding to each performance y based on the step S4_kAnd (k is 1,2, …,5) respectively and independently selecting the proxy model types, and verifying the fitting accuracy and the prediction accuracy of the proxy models, wherein the method specifically comprises the following steps:

s51, calculating the fitting precision of the agent model based on the t training sample points obtained in the step S3, as shown in the calculation formula (4),

wherein the content of the first and second substances,indicating that the kth performance response correspondsFitting precision of the proxy model;is the average of the kth performance response in the training set;the agent model established by t training sample points is used for training the sample point TS_j(ii) a predicted outcome of the kth performance response; y is_jkRepresenting the simulation result of the kth performance response at the training sample point TSj; if the fitting precision meets the requirement; if the fitting accuracy does not meet the requirement, returning to the step S3 to add additional training sample points and then recalculating;

s52, calculating the prediction error of the proxy model based on the v verification sample points, which are respectively shown in formula (5) and formula (6):

wherein MRE_kMaximum relative error, RMSE, of proxy model for kth performance response_kThe root mean square error of the proxy model corresponding to the kth performance response; y is_mkIs shown at the verification sample point(m ═ t +1, t +2, …, t + v) simulation results for the kth performance response;adopts a proxy model established by t training sample points to verify a sample point VS_m(ii) a predicted outcome of the kth performance response;

such as the maximum relative error MRE_k(k＝1,2, …,5) is less than 10%, and the root mean square error RMSE_k(k is 1,2, …,5) is significantly smaller than the response value, the proxy model is considered to meet the requirement of prediction accuracy, and the proxy model can be used for subsequent optimization solution of riveting point arrangement; otherwise, if the precision does not meet the requirement, returning to the step S3, and recalculating after adding the training sample points;

s6, obtaining an optimization scheme by adopting a genetic algorithm based on the optimization column established in the step S13, the parameterized finite element model established in the step S2 and the proxy model verified in the step S5, and carrying out verification analysis on the optimization scheme, wherein the optimization scheme comprises the following specific steps:

s61, obtaining an optimized solution set by adopting a genetic algorithm based on the optimized column in the step S13 and the proxy model verified in the step S5;

s62, randomly selecting u optimal design schemes PL (X) from the optimization solution set_t+v+1,X_t+v+2,…,X_t+v+u)；

S63, calculating each optimal design scheme X based on the parameterized finite element model established in the step S2_p(p ═ t + v +1, t + v +2, …, t + v + u) corresponding structural multidisciplinary performance response Y_p(p＝t+v+1,t+v+2,…,t+v+u)；

S64, calculating relative errors of the finite element simulation results obtained in the step S63 and the proxy model prediction results obtained in the step S61, and if the errors are within 5%, determining that the precision of the optimization solution set meets the requirements; otherwise, the optimized solution set does not meet the precision requirement, and the step S3 is returned, and the training sample points are added and then the calculation is carried out again;

s65, if the precision of the optimized solution set meets the requirement and the structural performance response meets the constraint condition in the formula (1), the optimized solution set can be used for guiding the arrangement design of the riveting point of the carrying equipment; if the accuracy of the optimized solution set meets the requirement but the structural performance response does not meet the constraint condition in the formula (1), the number of the riveting points is N +1, and the iteration is started from step S1 again.

2. The multidisciplinary optimization method for variable-pitch arrangement of riveting points based on crashworthiness as claimed in claim 1, wherein in step S11, for a single riveting line, the number N of riveting points is given, the distance between an edge riveting point and two ends and the distance between adjacent riveting points are considered as design variables, the number N is N +1, and the sum of the variables is equal to the length L of the riveting line; a plurality of riveting lines are defined respectively; if symmetry is considered, interrelated design variables may be merged.

3. The multidisciplinary optimization method for variable-pitch arrangement of riveting points based on crashworthiness as claimed in claim 1, wherein the step 3 is specifically as follows:

s31, sampling a training set based on a mixed material test design method;

s32, sampling the verification set based on the random sampling method, which specifically comprises:

s321, randomly generating a vector consisting of r first n-1 design variables in the design domain defined in the step S13Wherein c is 1,2, …, r;

s322, based on the formula (1)Calculating the vector Z^(c)Corresponding to

S323, selecting v riveting point arrangement schemes VL (X) meeting the design variable constraint condition in the formula (1)_t+1,X_t+2,…,X_t+v) Whereinb＝t+1,t+2,…,t+v；

S324, respectively calculating the arrangement scheme X of each riveting point based on the parameterized finite element model established in the step S2_b(b ═ t +1, t +2, …, t + v) for the corresponding column vector Y of performance responses_b(b ═ t +1, t +2, …, t + v), verification set was obtained

4. The multidisciplinary optimization method for rivet joint variable-pitch arrangement based on crashworthiness as claimed in claim 1, wherein in the step S51, if the fitting accuracy is greater than 0.95, the requirement is considered to be met, otherwise, the requirement is considered not to be met.

Background

Nowadays, various grades of aluminum alloys, high-strength steels and composite materials are widely applied in the fields of automobiles, aviation, aerospace and the like, and the application mode of the aluminum alloys, the high-strength steels and the composite materials is developed from the adoption of a certain single material to the adoption of comprehensive manufacturing of multiple materials. The change of materials brings about the change of connection modes, the early welding spot connection is not suitable for connecting heterogeneous materials, and riveting is the most main mode for connecting the heterogeneous materials. Products in the aerospace and automobile fields have thousands of riveting points on one structure due to large structural size and high performance requirements, and the safety and light weight of the structure are directly influenced by the sparse number and positions of the riveting points. Based on the method, the invention develops a multidisciplinary optimization method research of variable-spacing arrangement of riveting points based on crashworthiness.

The traditional riveting point arrangement scheme is mostly given based on engineering experience, and the problems of performance defects caused by insufficient riveting points, cost increase caused by excessive riveting points and the like exist. The topology optimization technology is one of the most common and effective riveting point arrangement design methods, but due to the limitation of the theoretical basis, the topology optimization technology is not suitable for the multidisciplinary optimization problem considering the nonlinear working conditions such as collision.

The size optimization based on the proxy model technology is the most advanced method for the multi-disciplinary optimization design of riveting point arrangement at present. The method takes the arrangement geometric parameters of riveting points as design variables, takes the structural performance requirement of the carrying equipment and the distance between the riveting points as constraint conditions, and takes the minimum number of the riveting points or the maximum structural rigidity as an optimization target. After the riveting point arrangement optimization problem is defined, training and verification sample points are obtained through a proper test design method, a reasonable agent model is created and the precision of the agent model is verified, and an optimal design scheme is searched by adopting a heuristic algorithm and the accuracy of the result is verified. Therefore, the definition of the riveting point arrangement optimization problem, the accuracy of the test design method and the proxy model directly influence the optimization effect of the riveting point arrangement design.

The riveting points and the welding points are connected with each other in a discrete arrangement mode, the structural performance and the manufacturing cost can be directly influenced, and the design method is similar. Chinese patent No.: 201410214771.0, the patent names: a welding spot layout optimization method for a B column of a vehicle body is provided by inventor, namely, a formula of a formula.

The design scheme in this kind of patent is generally based on the equidistant arrangement or the partition equidistant arrangement development, and adopt the given agent model, even direct optimization method carries out the layout design, and on this basis, the existing patent has the following disadvantages: firstly, improvement of structural performance due to variable-spacing arrangement of riveting points in a single riveting line is not considered; secondly, the agent model is given based on engineering experience and is difficult to be popularized to a multidisciplinary optimization design application scene; and thirdly, the direct optimization iteration times are multiple, and the method is not suitable for nonlinear working conditions with high simulation calculation cost such as collision.

Disclosure of Invention

According to the technical problems that the conventional riveting point arrangement size optimization method cannot realize variable-pitch arrangement in the same riveting point, and the conventional proxy model selection method and the conventional direct optimization method are not suitable for multi-disciplinary optimization design of riveting point arrangement, the provided multi-disciplinary optimization method of riveting point variable-pitch arrangement based on crashworthiness is provided. The invention mainly utilizes the definition based on the riveting point variable-pitch arrangement optimization problem to establish a parameterized finite element model with a series of riveting point pitches as design variables, collects training samples by a material mixing test design method, selects verification samples by a random sampling method, selects an agent model by using a leave-one-out cross verification strategy, obtains an optimization scheme and verifies by adopting a heuristic multi-objective optimization algorithm after completing the verification of the agent model precision, and further completes the optimization design of the riveting point variable-pitch arrangement, thereby achieving the advantage of simultaneously optimizing the number of riveting points and the arrangement positions of the riveting points on the premise of ensuring the multi-disciplinary performance of the structure.

In order to achieve the purpose, the technical scheme adopted by the invention is as follows:

a collision resistance-based multi-disciplinary optimization method for variable-pitch arrangement of riveting points comprises the following steps:

s1, defining a multidisciplinary optimization problem of variable-pitch arrangement of riveting points, and specifically comprising the following steps:

s11, defining design variables, namely, for a single riveting line, giving the number N of riveting points, taking the distance between the riveting points as a design variable, considering the distance between an edge riveting point and two ends and the distance between adjacent riveting points, wherein the number of the design variables is N equal to N +1, and the sum of the variables is equal to the length L of the riveting line; a plurality of riveting lines are defined respectively; if symmetry is considered, design variables that are correlated with each other may be merged;

s12, defining constraint conditions, and calculating structural mathematics corresponding to the original riveting point arrangement scheme by adopting a finite element simulation methodA column vector Y of family performance response, where Y ═ Y₁,y₂,y₃,y₄,y₅)^T，y₁,y₂,y₃,y₄,y₅Respectively corresponding to the structure energy absorption EA and the maximum collision force peak value F_maxBending stiffness K_bTorsional rigidity K_tAnd a first order modal response f₁And relaxing it by 5% respectively as a design baseline;

s13, determining an optimization target, and adopting structural collision safety performance evaluation indexes: the structure energy absorption is maximized and the maximum peak force of collision is minimized, and the optimized formula is shown as formula (1):

wherein X represents a rivet point arrangement scheme comprising n design variables X₁,x₂,…,x_n；x_iThe design variable of the ith riveting point is shown, i is 1, the distances from the first riveting point and the last riveting point on the riveting line to the two ends of the structure correspond to n, i is 2,3, …, and the distances between the adjacent riveting points correspond to n-1; x is the number of_minAnd x_maxRespectively the minimum and maximum values of the riveting point end distance, x'_minAnd x'_maxDetermining a riveting point arrangement design domain for the minimum value and the maximum value of the distance between adjacent riveting points together with equality constraint; the objective function-EA (X) is the inverse of the energy absorbed by the structure, F_max(X) is the peak maximum impact force; k_b0、K_t0、f₁₀、EA₀、F_max0Respectively a lower limit value of bending rigidity, a lower limit value of torsional rigidity, a lower limit value of modal response, a lower limit value of energy absorption and an upper limit value of maximum peak force.

S2, establishing a parameterized finite element model based on the finite element simulation model in the step S12 and the optimization problem definition in the step S13, and specifically comprising the following steps:

s21, based on the finite element simulation model in the step S12, deleting the connection units to obtain a finite element model only containing components; establishing a parameterized finite element model with variable riveting point spacing and variable number based on the optimization problem definition in the step S13;

s3, selecting t riveting point arrangement schemes TL (X) by adopting a material mixing test design method₁,X₂,…,X_t) Respectively calculating each riveting point arrangement scheme X based on the parameterized finite element model established in the step S2_a(a-1, 2, …, t) corresponding to the column vector Y of performance responses_a(a ═ 1,2, …, t), a training set containing t sample points is obtainedSelecting a v riveting point arrangement scheme VL (X) by adopting a random sampling method_t+1,X_t+2,…,X_t+v) Respectively calculating each riveting point arrangement scheme X based on the parameterized finite element model established in the step S2_b(b ═ t +1, t +2, …, t + v) for the corresponding column vector Y of performance responses_b(b ═ t +1, t +2, …, t + v), a validation set containing v sample points was obtainedThe method specifically comprises the following steps:

s31, training set sampling based on the mixed material test design method specifically comprises the following steps:

s311, randomly determining t initial riveting point arrangement schemes in a design domain;

s312, adding additional sample points capable of increasing the rank of the covariance matrix until the covariance matrix with the full rank is obtained;

s313, minimizing a covariance matrix determinant corresponding to the sample point set by adopting a D-optimal algorithm, and calculating the contribution value of each point to an optimal criterion;

s314, taking the contribution values obtained in the step S313 as a sorting basis, arranging from high to low, moving the contribution values along a plurality of directions for a certain distance from the last point, and re-evaluating the contribution values to the optimal criterion;

s315, if the contribution of the mobile terminal to the optimal criterion is increased, keeping the mobile terminal and updating; otherwise, the point remains unchanged;

s316, re-executing the updating process until the sample points are traversed, and if the sample points are all kept unchanged, obtaining a locally optimal point set;

s317, repeating steps S311-S316 several times, and obtaining t rivet point arrangement schemes TL ═ X₁,X₂,…,X_t)；

S318, respectively calculating each riveting point arrangement scheme X based on the parameterized finite element model established in the step S2_a(a-1, 2, …, t) corresponding to the column vector Y of performance responses_a(a ═ 1,2, …, t), training sets were obtained

S32, sampling the verification set based on the random sampling method, which specifically comprises:

s321, randomly generating a vector consisting of r first n-1 design variables in the design domain defined in the step S13Wherein c is 1,2, …, r;

s322, based on the formula (1)Calculating the vector Z^(c)Corresponding to

S323, selecting v riveting point arrangement schemes VL (X) meeting the design variable constraint condition in the formula (1)_t+1,X_t+2,…,X_t+v) Wherein

S324, respectively calculating the arrangement scheme X of each riveting point based on the parameterized finite element model established in the step S2_b(b ═ t +1, t +2, …, t + v) for the corresponding column vector Y of performance responses_b(b ═ t +1, t +2, …, t + v), verification set was obtained

S4, selecting the agent model by adopting a leave-one-out cross validation strategy based on the training set TS obtained in the step S31, wherein the method specifically comprises the following steps:

s41, training set based on step S31From which a sample point is takenAs a test point, the rest t-1 sample points are used as training points to establish a proxy model, and various performance responses y at the test point are calculated by adopting a formula (2)_kPrediction error E of (k ═ 1,2, …,5)_jk；

Wherein, y_jkAs a result of the simulation of the kth performance response corresponding to the test point,to adopt the sample-removing point TS_jProxy model established by outer t-1 sample points at test point TS_jThe predicted outcome of the corresponding kth performance response.

S42, repeating the step S41, traversing the whole training set, enabling t training sample points to be sequentially and independently used as test points, and calculating various performance responses y by a formula (3)_kGeneralized square error GMSE of (k-1, 2, …,5)_k；

S43, changing the type of the proxy model, and repeating the steps S41 and S42;

s44, responding to each performance y_k(k-1, 2, …,5) independently selected to generalize the square error GMSE_kMinimum proxy model typeUsed for subsequent optimization processes;

s5, responding to each performance y based on the step S4_k(k is 1,2, …,5) respectively and independently selecting the proxy model type, verifying the fitting accuracy and the prediction accuracy of the proxy model, and specifically comprising the following steps:

s51, calculating the fitting precision of the agent model based on the t training sample points obtained in the step S3, as shown in the calculation formula (4),

wherein the content of the first and second substances,representing the fitting precision of the proxy model corresponding to the k-th performance response;is the average of the kth performance response in the training set;the agent model established by t training sample points is used for training the sample point TS_j(ii) a predicted outcome of the kth performance response; y is_jkShowing the simulation results for the kth performance response at the training sample point TSj. If the fitting precision is more than 0.95, the requirement is met; if the fitting accuracy is less than 0.95, the process returns to step S3 to add additional training sample points and recalculate.

S52, calculating the prediction error of the proxy model based on the v verification sample points obtained in step S3, which are respectively shown in formula (5) and formula (6):

wherein MRE_kMaximum relative error, RMSE, of proxy model for kth performance response_kThe root mean square error of the proxy model corresponding to the kth performance response; y is_mkIs shown at the verification sample point(ii) a simulation result of the kth performance response;adopts a proxy model established by t training sample points to verify a sample point VS_m(iii) the predicted outcome of the kth performance response.

Such as the maximum relative error MRE_k(k-1, 2, …,5) is less than 10%, and the root mean square error RMSE_k(k is 1,2, …,5) is significantly smaller than the response value, the proxy model is considered to meet the requirement of prediction accuracy, and the proxy model can be used for subsequent optimization solution of riveting point arrangement; otherwise, if the precision does not meet the requirement, returning to the step S3, and recalculating after adding the training sample points;

s6, obtaining an optimization scheme by adopting a genetic algorithm based on the optimization column established in the step S13, the parameterized finite element model established in the step S2 and the proxy model verified in the step S5, and verifying and analyzing the optimization scheme, wherein the method specifically comprises the following steps:

s61, obtaining an optimized solution set by adopting a genetic algorithm based on the optimized column in the step S13 and the proxy model verified in the step S5;

s62, randomly selecting u optimal design schemes PL (X) from the optimization solution set_t+v+1,X_t+v+2,…,X_t+v+u)；

S63, calculating each optimal design scheme X based on the parameterized finite element model established in the step S2_p(p ═ t + v +1, t + v +2, …, t + v + u) corresponding structural multidisciplinary performance response Y_p(p＝t+v+1,t+v+2,…,t+v+u)；

S64, calculating relative errors of the finite element simulation results obtained in the step S63 and the proxy model prediction results obtained in the step S61, and if the errors are within 5%, determining that the precision of the optimization solution set meets the requirements; otherwise, the optimized solution set does not meet the precision requirement, and the step S3 is returned, and the training sample points are added and then the calculation is carried out again;

s65, if the precision of the optimized solution set meets the requirement and the structural performance response meets the constraint condition in the formula (1), the optimized solution set can be used for guiding the arrangement design of the riveting point of the carrying equipment; if the accuracy of the optimized solution set meets the requirement but the structural performance response does not meet the constraint condition in the formula (1), the number of the riveting points is N +1, and the iteration is started from step S1 again.

Compared with the prior art, the invention has the following beneficial effects:

1) the definition of riveting point arrangement design variables in the crash-tolerant riveting point variable-pitch arrangement-based multi-disciplinary optimization method provided by the invention enables the improvement of the structural performance by the riveting point variable-pitch arrangement in a single riveting line to be considered, and the structural performance can be further improved.

2) The application of the collision resistance-based multi-disciplinary optimization method for variable-spacing arrangement of the riveting points provided by the invention simultaneously considers the equality constraint condition of the design variable and the inequality constraint condition of the riveting process, thereby realizing the variable-spacing arrangement test design of the riveting points in a single riveting line.

3) The collision-resistance-based multi-disciplinary optimization method for variable-spacing arrangement of riveting points is characterized in that a one-method cross validation strategy is used, so that engineering experience or trial and error process required in the selection stage of the agent model can be avoided, limitation of multi-disciplinary working condition change is avoided, and design efficiency and accuracy of results are improved.

Based on the reason, the riveting point arranging method can be widely popularized in the fields of riveting point arranging design of the carrying equipment structure and the like.

Drawings

FIG. 1 is a flow chart of the present invention.

FIG. 2 is a schematic diagram of a variable design of the arrangement of the riveting points with variable spacing.

FIG. 3 is a diagram illustrating the multidisciplinary operation of the present invention.

FIG. 4 is a schematic diagram of the optimization scheme of the present invention.

In the figure: 1, axial impact working condition; 2, bending working condition; 3, twisting the working condition; 4, modal analysis; FIG. 4(a) rivet point layout design 1; fig. 4(b) shows rivet point arrangement design 2.

Detailed Description

In order to make the technical solutions of the present invention better understood, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.

It should be noted that the terms "first," "second," and the like in the description and claims of the present invention and in the drawings described above are used for distinguishing between similar elements and not necessarily for describing a particular sequential or chronological order. It is to be understood that the data so used is interchangeable under appropriate circumstances such that the embodiments of the invention described herein are capable of operation in sequences other than those illustrated or described herein. Furthermore, the terms "comprises," "comprising," and "having," and any variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, system, article, or apparatus that comprises a list of steps or elements is not necessarily limited to those steps or elements expressly listed, but may include other steps or elements not expressly listed or inherent to such process, method, article, or apparatus.

Establishing a parameterized finite element model with a series of riveting point intervals as design variables based on the definition of the riveting point variable interval arrangement optimization problem; collecting training samples by a mixed material test design method; selecting a verification sample by a random sampling method; multidisciplinary conditions considered include bending, torsion, modal analysis, and impact loading; taking structural multidisciplinary performance response corresponding to the original riveting point arrangement scheme as a reference for setting constraint conditions in an optimization problem, and ensuring the optimized structural performance; selecting an agent model by using a leave-one-out cross validation strategy, and calculating the accuracy of the agent model based on a validation sample; based on the proxy model meeting the precision requirement, adopting a heuristic multi-objective optimization algorithm to obtain an optimization scheme; and finally, verifying whether the optimization scheme is feasible or not through finite element analysis based on the optimized riveting point arrangement scheme.

The embodiment of the invention will explain in detail a specific implementation of a crash-tolerant rivet joint variable-pitch-arrangement-based multidisciplinary optimization method provided by the invention with reference to the accompanying drawings and technical solutions, and the flow of the method is shown in fig. 1.

Aiming at the improvement of the structural performance of the variable-interval arrangement of the riveting points in a single riveting line which is not considered in the size optimization of the riveting points at present, the invention selects training sample points meeting the variable-interval arrangement constraint condition by adopting a material mixing test design method, so that the intervals of the riveting points in the same riveting line can be randomly changed. The invention adopts a riveting point variable-pitch multidisciplinary optimization method, predicts the structural performance after the number and the arrangement form of the riveting points are changed based on the proxy model, and selects the most appropriate proxy model by using a cross validation method. On the premise of meeting the structural multidisciplinary performance, the structural crashworthiness is taken as an optimization target, and finally the riveting point arrangement scheme meeting the performance requirements is obtained. The invention is suitable for the optimized design of the arrangement of the riveting point of the carrying equipment structure, and the optimized design method of the riveting point is concretely explained by taking a double-cap beam as an example:

s1, defining a multidisciplinary optimization problem of variable-pitch arrangement of riveting points, and specifically comprising the following steps:

s11, defining design variables, and giving an iteration initial value N of the number of riveting points to be 8 aiming at a single riveting line of the double-cap beam; taking the distance between riveting points as a design variable, and combining the design variables which are mutually related in consideration of the symmetry of the hat-shaped beam; considering the distance between the edge riveting point and the two ends and the distance between the adjacent riveting points, the design variable number is n equal to 9, and the sum of the variables is equal to the length L of the riveting line equal to 350mm, as shown in FIG. 2;

s12, defining constraint conditions, wherein the flanging width of the double-cap beam is 30mm, the size of the cross section of the rectangular beam is 1000mm 80mm, and the multidisciplinary working conditions are shown in figure 3 and comprise a structural collision impact working condition 1, a bending working condition 2, a torsion working condition 3 and a modal componentAnalyzing 4, wherein the structural collision impact working condition 1 is that the rigid wall is pressed down at a constant speed of 15m/s for 240mm, and the unit load is loaded under the bending and torsion working conditions; the selected material is DP590 high-strength steel. Calculating a structural multidisciplinary performance response column vector Y corresponding to the scheme that 12 riveting points on two sides are arranged at equal intervals of 30mm by adopting a finite element simulation technology to obtain Y ═ 32.62,345.70,1611.72,276.70,419.74^TRespectively, the structure energy absorption EA and the maximum collision force peak value F_maxBending stiffness K_bTorsional rigidity K_tAnd a first order modal response f₁And relaxing each performance response by 5% respectively as a design baseline, the result is shown in formula (7);

s13, determining an optimization target, and adopting structural collision safety performance evaluation indexes: the opposite number of the absorbed energy of the structure and the maximum collision peak force are minimized, the optimization formula is as follows,

wherein X represents a rivet point arrangement scheme comprising 9 design variables X₁,x₂,…,x₉；x_iThe design variable of the ith riveting point is shown, when i is 1, the distances from the first riveting point and the last riveting point on the riveting line to the two ends of the structure respectively correspond to 9, and when i is 2,3, … and 8, the distances between the adjacent riveting points correspond to 8; the minimum value and the maximum value of the end distance of the riveting point are respectively 10mm and 35mm, the minimum value and the maximum value of the distance between adjacent riveting points are respectively 10mm and 47.8mm, and the minimum value and the maximum value and the equality constraint together determine the arrangement design domain of the riveting point; the objective function-EA (X) is the inverse of the energy absorbed by the structure, F_max(X) is the peak maximum impact force; the lower limit of the bending rigidity is 1563.36N/mm, the lower limit of the torsional rigidity is 268.40N m/deg, the lower limit of the modal response is 407.15Hz, the lower limit of the energy absorption is 31.64kJ, and the upper limit of the maximum peak force is 356.07 kN.

S2, establishing a parameterized finite element model based on the finite element simulation model in the step S12 and the optimization problem definition in the step S13, and the specific steps comprise:

s21, based on the finite element simulation model in the step S12, deleting the connection units to obtain a finite element model only containing components; establishing a parameterized finite element model with variable riveting point spacing and variable number based on the optimization problem definition in the step S13;

s3, selecting 78 riveting point arrangement schemes TL (X) by adopting a material mixing test design method₁,X₂,…,X₇₈) Respectively calculating each riveting point arrangement scheme X based on the parameterized finite element model established in the step S2_a(a-1, 2, …,78) corresponding performance response column vector Y_a(a ═ 1,2, …,78), a training set containing 78 sample points was obtainedSelecting 8 riveting point arrangement schemes VL (X) by adopting a random sampling method₇₉,X₈₀,…,X₈₆) Respectively calculating each riveting point arrangement scheme X based on the parameterized finite element model established in the step S2_b(79, 80, …,86) corresponding column vector Y of performance responses_b(79, 80, …,86), a validation set containing 8 sample points was obtained

S4, selecting a proxy model by using a leave-one-out cross validation strategy based on the training set TS obtained in the step S3, wherein 3 proxy models are adopted in the case, and the 3 proxy models comprise a polynomial response surface PRS, a radial basis neural network RBNN and a kriging KRG proxy model and are used for predicting multidisciplinary performance responses of 5 structures.

Based on the 78 training sample points obtained in step S3, steps S41-S43 are performed to calculate the generalized square errors of the 3 surrogate models predicting 5 different performance responses, the results are shown in table 1,

table 1 leave one out cross validation results (number of riveted points N ═ 8)

Based on the data in the table, step S is executed44, response y for each performance_k(k-1, 2, …,5) independently selected to generalize the square error GMSE_kThe smallest proxy model type. Wherein, KRG is selected as energy absorption EA, and maximum peak force F_maxBending stiffness K_bTorsional rigidity K_tAnd modal response f₁Selecting PRSs, and determining the proxy model types to be used for a subsequent optimization process;

s5, responding to each performance y based on the step S4_k(k is 1,2, …,5) independently selected proxy model types, verifying the fitting accuracy and prediction accuracy of the proxy models, executing step S51 and step S52 to calculate the fitting accuracy and prediction accuracy of 5 performance responses, and the result is shown in table 2

TABLE 2 proxy model fitting accuracy and prediction accuracy

Based on data in the table, the maximum relative errors MRE are less than 5%, the root mean square error RMSE is significantly less than the order of magnitude of a response value, the prediction accuracy of the proxy model can be considered to meet requirements, and the proxy model can be used for subsequent optimization solution of riveting point arrangement;

s6, obtaining an optimization scheme by adopting a genetic algorithm based on the optimization column established in the step S13, the parameterized finite element model established in the step S2 and the proxy model verified in the step S5, and verifying and analyzing the optimization scheme, wherein the method specifically comprises the following steps:

s61, obtaining an optimized solution set by adopting a genetic algorithm based on the optimized column in the step S13 and the proxy model verified in the step S5;

s62, randomly selecting 2 optimal design schemes from the optimization solution set, and then representing the design schemes by design scheme 1 and 2, as shown in FIG. 4, wherein FIG. 4(a) is design scheme 1, and the riveting point distances are x respectively₁＝10.04mm,x₂＝36.95mm,x₃＝46.51mm,x₄＝41.67mm,x₅＝47.80mm,x₆＝36.45mm,x₇＝47.80mm,x₈＝47.80mm,x₉34.98 mm; FIG. 4(b)In design 2, the distances between the riveting points are x₁＝10.00mm,x₂＝45.18mm,x₃＝46.14mm,x₄＝38.28mm,x₅＝47.80mm,x₆＝36.69mm,x₇＝43.63mm,x₈＝47.80mm,x₉＝34.48mm；

S63, respectively calculating structural multidisciplinary performance responses corresponding to the design scheme 1 and the design scheme 2 based on the parameterized finite element model established in the step S2;

s64, calculating the relative error based on the agent model prediction result obtained in the step S61 and the finite element simulation result obtained in the step S63, as shown in Table 3;

table 3 shows the predicted results and simulation results corresponding to the partial optimization schemes

Based on the data in the table 3, the relative error is within 5%, and the precision of the optimized solution set is considered to meet the requirement;

s65, optimizing the accuracy of the solution set to meet the requirement, and enabling the structural performance response to meet the constraint condition in the formula (1), wherein the optimized solution set can be used for guiding the arrangement design of the riveting point of the carrying equipment; the riveting point optimization process terminates the iteration.

Finally, it should be noted that: the above embodiments are only used to illustrate the technical solution of the present invention, and not to limit the same; while the invention has been described in detail and with reference to the foregoing embodiments, it will be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; and the modifications or the substitutions do not make the essence of the corresponding technical solutions depart from the scope of the technical solutions of the embodiments of the present invention.