CN112861255B - Rocket stage segment agent optimization-based adaptive sampling method - Google Patents
Rocket stage segment agent optimization-based adaptive sampling method Download PDFInfo
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Abstract
The invention discloses a rocket stage section agent optimization-based self-adaptive sampling method, which provides a high-efficiency self-adaptive online sample selection method for rocket stage section optimization technology so as to obtain a globally accurate and locally accurate agent model, thereby enabling agent optimization to search for an accurate globally optimal solution. The method comprises the following specific steps: in each step of sample refinement and iteration process, sampling by using a test design method based on a current agent model, clustering the sampled samples by using a fuzzy clustering algorithm, and dividing the whole design space into a plurality of subspaces according to the clustering; obtaining new samples in each subspace by using a method for maximizing a target expected improvement function and minimizing a model predicted target; the design space is then updated by fusing the subspaces. The method can effectively balance local exploration and global search of the model, has good self-adaptability, and is particularly suitable for the rocket stage section agent optimization problem with strong nonlinearity and multipole value.
Description
Technical Field
The invention is mainly used for a sample refinement process based on the rocket stage section agent optimization problem, so that an optimization algorithm is suitable for the field of pneumatic appearance and structural design optimization, and particularly relates to a self-adaptive sampling method based on fuzzy clustering and variable design space.
Background
Modern engineering design optimization, especially pneumatic and structural design optimization, is often a multi-dimensional, multi-constraint and strong nonlinear coupling problem. Thus, complex and time consuming high precision analytical models are used in the optimization process, which are computationally expensive. The concomitant method can improve the optimization efficiency, but is only applicable to the optimization problem of processing single extreme values. The optimization method based on the agent model provides an effective means for solving the problems.
In the problem of proxy optimization of rocket stage, in order to further improve the efficiency of the proxy optimization process, the proxy model needs to be dynamically updated, that is, the proxy model with the highest accuracy possible needs to be obtained by using as few samples as possible through the sample refinement process. For optimal design problems with multiple design variables, multiple extrema, and strong nonlinearities, the commonly used sample selection methods of minimizing model predictions (Minimize Surrogate Prediction, MSP), maximizing model prediction errors (Maximize Surrogate Error, MSE), maximizing desired boosting functions (Expected Improvement Function, EIF), minimizing lower confidence domain boundaries (Lower Confidence Bound, LCB), etc., suffer from deficiencies in both local exploration and global searching capabilities.
Disclosure of Invention
The invention provides a self-adaptive sampling method based on fuzzy clustering and variable design space, which can be better suitable for optimizing problems of multiple design variables, multiple extremum and strong nonlinearity, can further improve the local exploration and global searching capability of sample refinement in the agent optimization process, and improves the efficiency of the optimization process by parallelizing sample high-precision analysis.
In order to achieve the above purpose, the invention adopts the following technical scheme:
an adaptive sampling method based on rocket stage segment proxy optimization comprises the following steps:
s100, under the constraint of given force and moment conditions and stress displacement, establishing a proxy model based on samples in a rocket stage section sample library in a current design space;
s200, obtaining sufficient pseudo samples by adopting a test design method, and predicting the objective function values of the pseudo samples by using the established rocket stage section proxy model;
s300, screening the pseudo samples, then applying a fuzzy clustering algorithm to the screened pseudo samples, dividing the pseudo samples into a plurality of classes, determining subspaces according to the pseudo samples in each class, and determining a plurality of subspaces;
s400, in each subspace, obtaining a new sample by using a maximum target expected improvement function and minimum model prediction target method, and adding the new sample into a sample library;
s500, fusing the subspaces and updating the design space.
As a further improvement of the invention, the process of building the proxy model comprises the steps of:
generating a group of initial samples by using a test design method, and under the condition that constraint conditions are met, establishing an initial rocket stage section proxy model;
analyzing the initial samples by adopting an analysis model to obtain objective function values of each sample, and placing the samples into a sample library;
a proxy model is built using samples in the current design space.
As a further improvement of the invention, the selection process of the pseudo sample comprises the following specific steps:
the initial design space may be represented as D init ＝[x l,init ,x u,init ]，x l,init And x u,init The lower and upper bounds of the initial design space, respectively. The minimum design space may be expressed as delta limit ＝c 1 (x u,init -x l,init )，c 1 Is a given parameter that is used to limit the minimum design space size. X is x l,c And x u,c Respectively, the lower and upper bounds of the current design space. In the first sample refinement iteration, [ x ] l,c ,x u,c ]Namely D init ；
N is generated by adopting a random Latin hypercube experiment design method p The dummy samples are then eliminated with less influencing dummy samples.
As a further improvement of the invention, the rejecting method comprises the following specific steps:
a) Calculating an average objective function of a pseudo sample
b) Calculating a threshold f of the objective function t ＝t r (f max -f min ) Wherein t is r ∈(0,1]Is a predetermined threshold value, f max And f min The maximum and minimum predicted objective function values, respectively;
c) For the kth pseudo-sample, if it predicts the objective functionThe sample is deleted. Finally leave N r The pseudo samples are used for clustering;
d) If the effect of uncertainty needs to be taken into account when generating the pseudo-sample, the criterion in c) becomes
As a further improvement of the invention, the updating process of the variable design space comprises the following specific steps:
n polymerized by fuzzy clustering c Pseudo-samples of individual classes, determining N c Subspace [ x ] l,i ,x u,i ](i＝1,2,...,N c ). Thus, the fused design space is D m ＝∪[x l,i ,x u,i ](i＝1,2,...,N c ) Where m represents the mth sample refinement iteration step. But allows for a fused arrangementThe calculation space should be smaller than the initial design space of the mth iteration step, and the fused design space cannot be too small, otherwise, the sample for building the proxy model is insufficient, and the variable design space is updated as follows:
D u ＝max(min(D m ,D init ),Δ limit )
wherein delta is limit Is the minimum design space determined based on the initial design space to prevent the insufficient modeling sample caused by the too small design space.
As a further improvement of the present invention, the number of dummy samples satisfies the following condition:
1) For 2D design space, when the number of clusters N c When=2 or 3, the number of dummy samples is set to N g =100; when the number of clusters N c When not less than 6, the number of pseudo samples is set to N g ＝200；
2) For the high-dimension multipole problem, when the number of clusters is N c When= {2,3,4,5}, the number of dummy samples is suggested as N g =200; when the number of clusters is N c When not less than 6, the pseudo sample number proposal is set to N g ＝300；
3) For engineering optimization problems with multiple variables, it is suggested that the number of dummy samples be set to N g ≥300。
The number of clusters satisfies the following condition:
as a further improvement of the present invention, for 2D problems with multiple extrema, it is proposed to set the number of clusters to N c =2; for the problem with multiple extrema and design variables, the number of clusters is suggested to be N c Not less than 6; for the case where the objective function has a ridge line, the number of clusters is set to N c ∈{3,4,5}。
As a further improvement of the present invention, the update design space procedure includes the steps of:
when the convergence condition is satisfied, turning to the next step; otherwise, reestablishing the proxy model;
based on the current agent model, optimizing by using a global optimization algorithm to obtain an optimal solution based on the agent model;
analyzing the sample by using a high-precision analysis model to obtain a corresponding objective function value: if the error of the real objective function value and the predicted objective function value is smaller than a small amount, the optimal solution is a global optimal solution of the whole optimization process, and the optimization process is ended; otherwise, the pseudo samples are screened again, and the sample refinement process is restarted.
Compared with the prior art, the invention has the following advantages:
the invention provides a self-adaptive sampling method based on fuzzy clustering and variable design space under the framework of a proxy optimization method. A self-adaptive online sample selection method is provided for an efficient global search agent optimization technology so as to obtain a globally accurate and locally accurate agent model, so that the agent optimization can search for an accurate globally optimal solution. The method comprises the following specific steps: in each step of sample refinement and iteration process, sampling by using a test design method based on a current agent model, clustering the sampled samples by using a fuzzy clustering algorithm, and dividing the whole design space into a plurality of subspaces according to the clustering; obtaining new samples in each subspace by using a method for maximizing a target expected improvement function and minimizing a model predicted target; the design space is then updated by fusing the subspaces. The method can effectively balance local exploration and global search of the model, has good self-adaptability, and is particularly suitable for the problems of strong nonlinearity and multiple extrema. The method can effectively balance local exploration and global search of the model in the sample refinement process, and the newly added sample selection has good self-adaptability, so that the agent optimization process is particularly suitable for the problem of strong nonlinearity and multiple extremums. The extreme value quantity, distribution and fuzzy clustering algorithm of the rocket stage design space are relatively matched, so that the space can be effectively segmented, the size of subspaces is greatly reduced, and the optimization efficiency is improved. The invention provides a rapid and effective parallelization sample selection method for rocket stage segment optimization, and can greatly improve the robustness, optimization efficiency and optimization quality of the agent optimization process.
Drawings
The present invention will now be described in further detail with reference to the drawings and embodiments, wherein the specific examples are set forth only for purposes of illustration and are not limiting the invention.
FIG. 1 is a flow chart of a proxy optimization process based on fuzzy clustering and variable design space adaptive sampling;
FIG. 2 is a pseudo sample screened and deleted in a first sample refinement iteration step;
FIG. 3 is a clustering result of screening pseudo samples in a first sample refinement iteration step;
FIG. 4 is a sample of a first step sample refinement iteration step neutron space sample;
FIG. 5 is a result of a first step sample refinement iteration step neutron space fusion;
FIG. 6 is a graph comparing the sampling position of the proxy optimization of the Branin function with the cloud image of the objective function; (a) is an objective function cloud image (b) is a sampling position;
FIG. 7 is a diagram of a Rastrigin function proxy optimization sampling position versus an objective function cloud; (a) is an objective function cloud image (b) is a sampling position;
FIG. 8 is a rocket stage segment structural model;
FIG. 9 is a load and moment applied to a rocket stage section;
FIG. 10 is a rocket stage segment optimization problem design variable;
FIG. 11 is a rocket stage-to-stage optimization objective function convergence history;
FIG. 12 is a rocket stage segment optimization constraint function convergence history.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and fully with reference to the accompanying drawings, in which it is evident that the embodiments described are only some, but not all embodiments of the invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to fall within the scope of the invention.
As shown in fig. 1 to 7, the adaptive sampling method based on rocket stage segment proxy optimization of the present invention comprises the following steps:
(1) Based on the sampleSamples in the current design space in the libraryEstablishing a Kriging agent model;
(2) N is obtained by adopting a random Latin hypercube experiment design method p And predicting the objective function value of the pseudo sample by using the established proxy model.
(3) Screening the false samples, and removing bad false samples (if the minimized objective function is the bad false samples, the objective function value is large), wherein the specific removing process is as follows:
a) Calculating an average objective function of a pseudo sample
b) Calculating a threshold f of the objective function t ＝t r (f max -f min ) Wherein t is r ∈(0,1]Is a predetermined threshold value, f max And f min The largest and smallest predicted objective function values, respectively.
c) For the kth pseudo-sample, if it predicts the objective functionThe sample is deleted. Finally leave N r The pseudo-samples are used for clustering.
d) If the effect of uncertainty needs to be taken into account when generating the pseudo-sample, the criterion in c) becomes
(4) Applying fuzzy clustering algorithm to the rest pseudo sample to divide it into N c Class and determining subspace [ x ] from the pseudo-samples in each class l,i ,x u,i ](i＝1,2,...,N c ) At most determine N c A subspace.
(5) Within each subspace, a maximization target expected improvement function (Expected Improvement Function, EIF) and a minimization model pre-are utilizedMethod of targeting (Minimize Surrogate Prediction, MSP) to obtain new samples S new Adding sample library S i+1 ＝S i ∪S new 。
(6) Fusing subspaces, wherein the fused design space is D m ＝∪[x l,i ,x u,i ](i＝1,2,...,N c ) Where m represents the mth sample refinement iteration step. However, considering that the fused design space should be smaller than the initial design space of the mth iteration step, and the fused design space cannot be too small, otherwise, the sample for building the proxy model is insufficient, and the variable design space is updated as follows:
D u ＝max(min(D m ,D init ),Δ limit )
wherein delta is limit Is the minimum design space determined based on the initial design space.
The following details the individual steps of the adaptive sampling method for a sample refinement iterative process for proxy optimization:
s100 is based on samples in the sample library in the current design spaceEstablishing a proxy model;
s200, adopting a test design method to obtain N p And predicting the objective function value of the pseudo sample by using the established proxy model.
S300, screening the pseudo samples, and then applying a fuzzy clustering algorithm to the screened pseudo samples to divide the pseudo samples into N c Classes, and determining subspaces from the pseudo-samples in each class, at most N c A subspace.
S400 within each subspace, a new sample S is obtained by maximizing the objective expected improvement function (Expected Improvement Function, EIF) and minimizing the model predictive objective (Minimize Surrogate Prediction, MSP) new Adding sample library S i+1 ＝S i ∪S new 。
S500, fusing subspaces and updating the design space [ x ] i+1,lower ,x i+1,upper ]。
The specific description can be refined into the following steps:
(1) A set of initial samples is generated using a trial design method for establishing an initial proxy model.
(2) And analyzing the initial samples by adopting a high-precision analysis model to obtain the objective function value of each sample, and placing the samples into a sample library.
(3) A proxy model is built using samples in the current design space.
(4) Based on the proxy model, generating sufficient pseudo samples by using a test design method, and screening the pseudo samples.
(5) And clustering the screened pseudo samples, and dividing the design space into a plurality of subspaces.
(6) And obtaining a new sample in each subspace by using an EIF and MSP method, analyzing the sample by using a high-precision analysis model to obtain a corresponding objective function value, and placing the sample into a sample library.
(7) And fusing the subspaces and updating the design space.
(8) When the convergence condition is satisfied, turning to (9); otherwise, turning to (3).
(9) And optimizing by using a global optimization algorithm based on the current agent model to obtain an optimal solution based on the agent model.
(10) Analyzing the sample by using a high-precision analysis model to obtain a corresponding objective function value: if the error of the real objective function value and the predicted objective function value (the optimal solution based on the agent model) is smaller than a small amount, the optimal solution is a global optimal solution of the whole optimization process, and the optimization process is ended; otherwise, the sample refinement process will be restarted (4).
The selection process of the pseudo sample comprises the following specific steps:
(1) Setting: the initial design space may be represented as D init ＝[x l,init ,x u,init ]，x l,init And x u,init The lower and upper bounds of the initial design space, respectively. The minimum design space may be expressed as delta limit ＝c 1 (x u,init -x l,init )，c 1 Is a given parameter that is used to limit the minimum design space size. X is x l,c And x u,c Respectively, the lower and upper bounds of the current design space. In the first sample refinement iteration, [ x ] l,c ,x u,c ]Namely D init 。
(2) Pseudo sample generation: n is generated by adopting a random Latin hypercube experiment design method p The dummy samples are then eliminated with less influencing dummy samples. The rejection method is as follows:
a) Calculating an average objective function of a pseudo sample
b) Calculating a threshold f of the objective function t ＝t r (f max -f min ) Wherein t is r ∈(0,1]Is a predetermined threshold value, f max And f min The largest and smallest predicted objective function values, respectively.
c) For the kth pseudo-sample, if it predicts the objective functionThe sample is deleted. Finally leave N r The pseudo-samples are used for clustering.
d) If the effect of uncertainty needs to be taken into account when generating the pseudo-sample, the criterion in c) becomes
The updating process of the variable design space is specifically described as follows:
n polymerized by fuzzy clustering c Pseudo-samples of individual classes, determining N c Subspace [ x ] l,i ,x u,i ](i＝1,2,...,N c ). Thus, the fused design space is D m ＝∪[x l,i ,x u,i ](i＝1,2,...,N c ) Where m represents the mth sample refinement iteration step. But considering that the fused design space should be smaller than the initial design space of the mth iteration step, and the fused design spaceCannot be too small, otherwise, the sample for building the proxy model is insufficient, and the variable design space is updated as follows:
D u ＝max(min(D m ,D init ),Δ limit )
wherein delta is limit Is the minimum design space determined based on the initial design space to prevent the insufficient modeling sample caused by the too small design space.
And analyzing conclusion based on the parameters of the agent optimization process of the adaptive sampling.
(1) Sampling method
For proxy optimization based on the adaptive sampling, when selecting a new sample in the subspace, simply selecting the new sample by using the MSP is difficult to ensure the robustness of the optimization process. When a method of maximizing EIF is adopted alone to select a new sample, it works better than MSP, but it is still difficult to guarantee the robustness of the optimization process under the conditions of a small threshold and a small number of clusters. And the EIF+MSP is adopted to sample in the subspace, so that the design space can be well explored locally and searched globally, and the optimization process can be guaranteed to have good robustness. However, this mixed sampling method causes an increase in the number of samples newly added. With sufficient computational resources, sampling is actually time consuming and does not increase significantly, as the number of iteration steps of the sample refinement process does not increase. This illustrates that the sampling method is suitable for parallelization.
Furthermore, by comparing whether sampling is performed in the subspace, the following conclusion is reached: when subspace partitioning is not performed, the proxy optimization is prone to "premature" phenomena in cases where the initial number of samples is insufficient, or the problem of processing has strong nonlinearities or multiple extrema. Therefore, the subspace is divided firstly, and then mixed parallel sampling is carried out in the subspace, so that the self-adaptability of the sample refinement process can be improved, and the robustness of agent optimization can be improved.
(2) Number of dummy samples
When the number of pseudo samples for fuzzy clustering is sufficient, the influence of the number of pseudo samples on the optimization process and the optimization quality is small. However, as the number of design variables increases, the number of dummy samples will be an issue to the optimization processAnd as a result, a large influence is generated, and the design space is mainly affected for setting the number of dummy samples. 1) For 2D design space, when the number of clusters N c When=2 or 3, the number of dummy samples is set to N g =100; when the number of clusters N c When not less than 6, the number of pseudo samples is set to N g =200. 2) For the high-dimension multipole problem, when the number of clusters is N c When= {2,3,4,5}, the number of dummy samples is suggested as N g =200; when the number of clusters is N c When not less than 6, the pseudo sample number proposal is set to N g =300. 3) For engineering optimization problems with multiple variables, it is suggested that the number of dummy samples be set to N g ≥300。
(3) Determining a threshold size of a dummy sample
In general, as the threshold coefficient increases, both the quality of the optimal solution and the number of high-precision analyses of the sample increase. For the 2D problem, when the threshold coefficient reaches t r When=0.6, the best optimized quality can be obtained; for high-dimensional problems, as the threshold coefficient is further increased, the optimization quality and the number of times of high-precision analysis of the sample are continuously increased. In addition, as the threshold coefficient increases, the robustness of the optimization process increases, but the robustness changes little when the threshold coefficient reaches a certain value. In principle, to ensure good robustness, it is proposed that the threshold coefficient is set to t r E [0.6,1). When the number of clusters increases, the magnitude of the threshold coefficient may be correspondingly increased.
(4) Number of clusters
As the number of clusters increases, the quality of the optimal solution increases; when the number of clusters increases to a certain extent, the optimal solution quality is not further improved by continuing to increase. In addition, the robustness of the optimization process and the number of high-precision analyses of samples also increase with the number of clusters. Empirically, for 2D problems with multiple extrema, it is suggested to set the number of clusters to N c =2; for the problem with multiple extrema and design variables, the number of clusters is suggested to be N c Not less than 6; for the case where the objective function has a ridge line, the number of clusters is set to N c ∈{3,4,5}。
The present invention will be described in detail with reference to specific embodiments and drawings.
As shown in fig. 8 to 12, first, the correctness of the agent optimization method based on the present invention is verified by adopting the parsing algorithm, and then the agent optimization method is applied to the rocket stage segment optimization problem.
Example 1
The analytical examples are described below.
Branin (BR) function:
six-hump camera back (SC) function:
rastrigin (RS) function:
f16 high-dimensional function:
the results of the optimization are shown in the following table.
Table 1 analysis of example results
The data in the table are the results of the optimization repeated 30 times, and the analytic optimal solutions of the four calculation examples are respectively as follows: 1.0316 (two global optima), 0.3979 (three global optima), -2.0 and 25.878. The test examples show that: 1) The average optimal solution obtained by 30 repeated experiments is very close to the analytic optimal solution, and the agent optimization method based on the invention is effective and feasible; 2) From the range of the optimal solution and the variance of 30 tests, the agent optimization process has good robustness; 3) The average sample number shows that the invention can increase the high-precision analysis times, but the sample refinement iteration step number is not increased, so that the total parallelization self-adaptive sampling method has higher efficiency as long as enough computing resources are available; 4) On the premise of few initial test design samples, the method has good self-adaptability, and can ensure that the optimization process obtains a high-quality global optimal solution; 5) From fig. 6 and 7, it can be seen that the present invention can well balance the local exploration and global search of model accuracy because the adaptively sampled samples are mostly concentrated near the three globally optimal solution locations, and a small number of samples are scattered throughout the design space.
Example 2
Reducing structural mass is a common problem for aircraft design optimization. The purpose of this example is to minimize the structural mass of the rocket stage given the force and moment conditions, as well as the stress displacement constraints. The structural model of the rocket stage section is shown in fig. 8: the interstage section is a two-layer shell unit, the middle is a grid-shaped reinforcing rib, and local reinforcing ribs are arranged around the opening. The force and moment loads on the interstage section are shown in fig. 9: the axial load is F z 1800kN bending moment of M x =500 kn·m. The design variable definition of the inter-stage sections is shown in FIG. 10, respectively the shell element thickness x 1 Height x of reinforcing ribs at two ends 2 Axial stiffener width x 3 Circumferential stiffener width x 4 Width x of reinforcing rib around opening 5 Thickness x of end ring for applying load 6 Perforated long half shaft x 7 And short half axis x 8 . Therefore, the mathematical model of the optimization problem is written as
The results of the agent optimization method based on the invention are compared with the results of the differential evolution algorithm of global search and the agent optimization based on EIF, as shown in tables 2 and 3. The comparison of the results shows that: 1) The objective function values of the optimal solutions obtained by the three optimization methods are very close, the quality of the optimal solution can be greatly reduced, but the difference of the major and minor half axes of the optimal solution is very large, which indicates that local extremum exists; 2) The optimal scheme obtained based on the agent optimization method of the invention is near the constraint boundary, and the found solution can be judged to be the global optimal solution by combining the size of the objective function; 3) The differential evolution algorithm is greatly higher in sample analysis times than the other two methods due to the fact that a large number of populations are needed; 4) The sample analysis times required by the agent optimization based on the invention are obviously higher than those of the agent optimization based on the EIF, so that the optimization efficiency is improved, and the self-adaptive parallel sampling is required to be fully utilized.
TABLE 2 comparison of rocket stage segment optimization results (1)
TABLE 3 comparison of rocket stage segment optimization results (2)
Optimization convergence histories as shown in fig. 11 and 12, only the convergence histories of proxy optimization based on the present invention and EIF are presented herein. The illustration can be seen: 1) Agent optimization based on EIF converges quickly at the initial stage of optimization, but according to the analysis of the optimization result, the optimization process falls into a local optimal solution; 2) From the convergence history of constraint conditions, the constraints of EIF-based proxy optimization do not fully converge; 3) The agent optimization based on the invention enables the local and global precision of the agent model to be sufficiently improved through self-adaptive sampling in the early optimization stage, and when the model precision reaches a certain degree, the model precision is well converged no matter the objective function or the constraint condition. 4) The agent optimization based on the invention is suitable for solving optimization problems of multiple design variables, multiple extremum and strong nonlinearity, can perform good local exploration and global search on the design space on the premise of a small amount of initial sampling samples, and has stronger self-adaption capability.
The foregoing is only a preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions easily contemplated by those skilled in the art within the scope of the present invention should be included in the scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claims.
Claims (1)
1. The self-adaptive sampling method based on rocket stage agent optimization is characterized in that a structural model of a rocket stage is a two-layer shell unit, the middle of the rocket stage is a grid-shaped reinforcing rib, and local reinforcing ribs are arranged around an opening; the method comprises the following steps:
s100, under the constraint of given force and moment conditions and stress displacement, establishing a proxy model based on samples in a rocket stage section sample library in a current design space;
s200, obtaining sufficient pseudo samples by adopting a test design method, and predicting the objective function values of the pseudo samples by using the established rocket stage section proxy model;
s300, screening the pseudo samples, then applying a fuzzy clustering algorithm to the screened pseudo samples, dividing the pseudo samples into a plurality of classes, determining subspaces according to the pseudo samples in each class, and determining a plurality of subspaces;
s400, in each subspace, obtaining a new sample by using a maximum target expected improvement function and minimum model prediction target method, and adding the new sample into a sample library;
s500, fusing subspaces and updating a design space;
the process of establishing the proxy model comprises the following steps:
generating a group of initial samples by using a test design method, and under the condition that constraint conditions are met, establishing an initial rocket stage section proxy model;
analyzing the initial samples by adopting an analysis model to obtain objective function values of each sample, and placing the samples into a sample library;
establishing a proxy model by using samples in the current design space;
the updating process of the variable design space comprises the following specific steps:
n polymerized by fuzzy clustering c Pseudo-samples of individual classes, determining N c Subspace [ x ] l,i ,x u,i ](i＝1,2,...,N c ) The method comprises the steps of carrying out a first treatment on the surface of the The fused design space is D m ＝∪[x l,i ,x u,i ](i＝1,2,...,N c ) Wherein m represents an mth sample refinement iteration step; considering that the fused design space should be smaller than the initial design space of the mth iteration step, and the fused design space cannot be too small, otherwise, the sample for building the proxy model is insufficient, and the variable design space is updated as follows:
D u ＝max(min(D m ,D init ),Δ limit )
wherein delta is limit The minimum design space is determined based on the initial design space, so that the modeling sample is not enough due to the fact that the design space is too small;
the number of clusters satisfies the following condition:
for 2D problems with multiple extrema, it is suggested to set the number of clusters to N c =2; for the problem with multiple extrema and design variables, the number of clusters is suggested to be N c Not less than 6; for the case where the objective function has a ridge line, the number of clusters is set to N c ∈{3,4,5}；
The process of updating the design space includes the steps of:
when the convergence condition is satisfied, turning to the next step; otherwise, reestablishing the proxy model;
based on the current agent model, optimizing by using a global optimization algorithm to obtain an optimal solution based on the agent model;
analyzing the sample by using a high-precision analysis model to obtain a corresponding objective function value: if the error of the real objective function value and the predicted objective function value is smaller than a small amount, the optimal solution is a global optimal solution of the whole optimization process, and the optimization process is ended; otherwise, screening the pseudo sample again, and restarting the sample refinement process;
the selection process of the pseudo sample comprises the following specific steps:
initial design voidMay be represented as D init ＝[x l,init ,x u,init ]，x l,init And x u,init Respectively a lower bound and an upper bound of the initial design space; the minimum design space may be expressed as delta limit ＝c 1 (x u,init -x l,init )，c 1 Is a given parameter for limiting the minimum design space size; x is x l,c And x u,c Respectively a lower bound and an upper bound of the current design space; in the first sample refinement iteration, [ x ] l,c ,x u,c ]Namely D init ；
N is generated by adopting a random Latin hypercube experiment design method p The false samples are removed, and then the false samples with smaller influence are removed;
the rejecting method comprises the following specific steps:
a) Calculating an average objective function of a pseudo sample
b) Calculating a threshold f of the objective function t ＝t r (f max -f min ) Wherein t is r ∈(0,1]Is a predetermined threshold value, f max And f min The maximum and minimum predicted objective function values, respectively;
c) For the kth pseudo-sample, if it predicts the objective function f k ＞max(f m ,f t ) Deleting the sample; finally leave N r The pseudo samples are used for clustering;
d) If the effect of uncertainty needs to be taken into account when generating the pseudo-sample, the criterion in c) becomes f k -σ k ＞max(f m ,f t )；
The number of dummy samples satisfies the following condition:
1) For 2D design space, when the number of clusters N c When=2 or 3, the number of dummy samples is set to N g =100; when the number of clusters N c When not less than 6, the number of pseudo samples is set to N g ＝200；
2) For the high-dimension multipole problem, when the number of clusters is N c When= {2,3,4,5}, the artifactThe number is suggested as N g =200; when the number of clusters is N c When not less than 6, the pseudo sample number proposal is set to N g ＝300；
3) For engineering optimization problems with multiple variables, it is suggested that the number of dummy samples be set to N g ≥300；
Minimizing the structural mass of the rocket stage under given force and moment conditions and stress displacement constraints; the structural model of the rocket stage section is as follows: the interstage section is a two-layer shell unit, the middle is a grid-shaped reinforcing rib, and local reinforcing ribs are arranged around the opening; the design variable of the inter-stage section is defined as the shell element thickness x 1 Height x of reinforcing ribs at two ends 2 Axial stiffener width x 3 Circumferential stiffener width x 4 Width x of reinforcing rib around opening 5 Thickness x of end ring for applying load 6 Perforated long half shaft x 7 And short half axis x 8 The method comprises the steps of carrying out a first treatment on the surface of the The mathematical model of the optimization problem is noted as
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