CN112926147B - Posterior optimization design method for reinforced column shell containing defects - Google Patents
Posterior optimization design method for reinforced column shell containing defects Download PDFInfo
- Publication number
- CN112926147B CN112926147B CN202110109155.9A CN202110109155A CN112926147B CN 112926147 B CN112926147 B CN 112926147B CN 202110109155 A CN202110109155 A CN 202110109155A CN 112926147 B CN112926147 B CN 112926147B
- Authority
- CN
- China
- Prior art keywords
- reinforced column
- column shell
- point
- defects
- pareto
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
- 238000005457 optimization Methods 0.000 title claims abstract description 79
- 238000000034 method Methods 0.000 title claims abstract description 60
- 238000013461 design Methods 0.000 title claims abstract description 57
- 230000007547 defect Effects 0.000 title claims abstract description 45
- 230000006870 function Effects 0.000 claims abstract description 27
- 238000004364 calculation method Methods 0.000 claims abstract description 26
- 238000005070 sampling Methods 0.000 claims abstract description 12
- 230000035945 sensitivity Effects 0.000 claims abstract description 8
- 230000008859 change Effects 0.000 claims abstract description 6
- 238000004458 analytical method Methods 0.000 claims description 21
- 230000003044 adaptive effect Effects 0.000 claims description 8
- 230000002950 deficient Effects 0.000 claims description 8
- 230000008569 process Effects 0.000 claims description 8
- 239000013598 vector Substances 0.000 claims description 7
- 230000002787 reinforcement Effects 0.000 claims description 6
- 238000012804 iterative process Methods 0.000 claims description 4
- 238000005314 correlation function Methods 0.000 claims description 3
- 239000011159 matrix material Substances 0.000 claims description 3
- 238000012549 training Methods 0.000 claims description 3
- 239000000463 material Substances 0.000 description 5
- 238000010586 diagram Methods 0.000 description 3
- 230000000694 effects Effects 0.000 description 3
- 238000004519 manufacturing process Methods 0.000 description 3
- 238000012545 processing Methods 0.000 description 3
- 238000003860 storage Methods 0.000 description 3
- 238000003491 array Methods 0.000 description 2
- 230000003287 optical effect Effects 0.000 description 2
- 231100000817 safety factor Toxicity 0.000 description 2
- FYYHWMGAXLPEAU-UHFFFAOYSA-N Magnesium Chemical compound [Mg] FYYHWMGAXLPEAU-UHFFFAOYSA-N 0.000 description 1
- RTAQQCXQSZGOHL-UHFFFAOYSA-N Titanium Chemical compound [Ti] RTAQQCXQSZGOHL-UHFFFAOYSA-N 0.000 description 1
- XAGFODPZIPBFFR-UHFFFAOYSA-N aluminium Chemical compound [Al] XAGFODPZIPBFFR-UHFFFAOYSA-N 0.000 description 1
- 229910052782 aluminium Inorganic materials 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 239000002131 composite material Substances 0.000 description 1
- 238000011161 development Methods 0.000 description 1
- 238000005516 engineering process Methods 0.000 description 1
- 238000003754 machining Methods 0.000 description 1
- 229910052749 magnesium Inorganic materials 0.000 description 1
- 239000011777 magnesium Substances 0.000 description 1
- 230000007246 mechanism Effects 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 239000013307 optical fiber Substances 0.000 description 1
- 238000013433 optimization analysis Methods 0.000 description 1
- 238000011160 research Methods 0.000 description 1
- 229910052719 titanium Inorganic materials 0.000 description 1
- 239000010936 titanium Substances 0.000 description 1
- 238000005303 weighing Methods 0.000 description 1
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/10—Geometric CAD
- G06F30/17—Mechanical parametric or variational design
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/10—Geometric CAD
- G06F30/15—Vehicle, aircraft or watercraft design
Landscapes
- Physics & Mathematics (AREA)
- Engineering & Computer Science (AREA)
- Geometry (AREA)
- Theoretical Computer Science (AREA)
- General Physics & Mathematics (AREA)
- Pure & Applied Mathematics (AREA)
- Mathematical Optimization (AREA)
- Mathematical Analysis (AREA)
- Computer Hardware Design (AREA)
- Evolutionary Computation (AREA)
- General Engineering & Computer Science (AREA)
- Computational Mathematics (AREA)
- Automation & Control Theory (AREA)
- Aviation & Aerospace Engineering (AREA)
- Management, Administration, Business Operations System, And Electronic Commerce (AREA)
Abstract
The application provides a posterior optimization design method of a reinforced column shell with defects, which comprises the following steps: introducing initial concave defects of the reinforced column shells in a manner of applying disturbance load, calculating and analyzing the change rules of crushing loads of various reinforced column shells under different concave degrees through finite element to obtain defect sensitivity curves of different reinforced column shells, and determining a loading range aiming at the disturbance load; modeling the parameterization of the reinforced column shell containing the defects, performing finite element calculation, sampling in a design space, and establishing a proxy model according to the obtained sample point data; based on the self-adaptive updating criterion of the proxy model, a mixed multi-objective optimization flow is established, and a plurality of objective functions are optimized in a design space according to the mixed multi-objective optimization flow; and according to the mixed multi-objective optimization flow, optimizing the result to finally form a Pareto surface, and determining the optimal weight of the reinforced column shell containing the defects under different crushing loads. The application realizes more efficient and accurate multi-objective optimization of the reinforced column shell containing the defects.
Description
Technical Field
The application relates to the field of design of main component reinforced column shells in aerospace structures, in particular to a posterior optimization design method of a reinforced column shell with defects.
Background
The thin-wall structure has the characteristics of good bearing performance and light weight, and is widely applied in the field of aerospace, such as a reinforced column shell structure serving as one of main members of an aerospace carrier rocket. The primary failure mechanism of the thin-walled structure under axial pressure is buckling. However, for buckling analysis of thin-walled structures, the predicted values tend to deviate significantly from the experimental results, mainly due to the inevitable occurrence of geometrical defects during production, manufacturing and machining. Therefore, the effect of geometrical defects must be considered in designing the ribbed column shell.
On the other hand, the cost control is also very important to the use of thin-wall structures in the aerospace field, and the purposes of resource conservation and economic conservation can be achieved by reducing the weight. Therefore, the thin-walled structure is generally optimized for light weight. In view of the complexity of lightweight optimization of aerospace structures, fischer et al employ multistage optimization methods to minimize the weight of composite wings. Schubert et al uses laser beam connection to create reinforced aluminum, titanium, magnesium nodes, reducing weight. In addition, gray and Alexander carry out light weight design on the multistage rocket under the constraint of fixed allowable load. However, with the continuous development of manufacturing and processing technologies, the bearing capacity of the reinforced column shell structure is also improved continuously, which means that the previous lightweight optimization result is too conservative, repeated calculation is caused in actual engineering, and manpower and material resources are lost. It is therefore more interesting to consider both the weight and the load-carrying capacity of the reinforcement column shell at the same time during the initial optimization phase of the structure.
Although multi-objective optimization methods have been applied in many fields over the last decades, little research has been done on defective reinforced column shells. Unlike single-objective optimization, multi-objective optimization generates a series of optimal solutions that can simultaneously optimize multiple conflicting objectives. However, the multi-objective optimization problem is due to the simultaneous processing of multiple objectives, resulting in a large computational effort and a very expensive time cost. It can be seen that there is a need for a multi-objective optimization analysis method that can be performed efficiently and accurately on a reinforced column shell containing defects.
Disclosure of Invention
The present application aims to solve at least to some extent one of the technical problems described above.
Therefore, an object of the present application is to provide a posterior optimization design method for a reinforced column shell with defects, so as to achieve more efficient and accurate multi-objective optimization for the reinforced column shell with defects.
In order to achieve the above objective, an embodiment of an aspect of the present application provides a posterior optimization design method for a reinforced column shell with defects, including:
introducing initial concave defects of the reinforced column shells in a manner of applying disturbance load, analyzing the change rules of crushing loads of a plurality of reinforced column shells under different concave degrees through finite element calculation, obtaining defect sensitivity curves of different reinforced column shells, and determining a loading range aiming at the disturbance load;
modeling the parameterization of the reinforced column shell containing the defects, performing finite element calculation, sampling in a design space, and establishing a proxy model according to the obtained sample point data;
based on the self-adaptive updating criterion of the proxy model, a mixed multi-objective optimization flow is established, and a plurality of objective functions are optimized in the design space according to the mixed multi-objective optimization flow;
and according to the mixed multi-objective optimization flow, optimizing a result to finally form a Pareto surface, and determining the optimal weight of the defective reinforced column shell under different crushing loads according to the Pareto surface.
In some embodiments of the present application, the proxy model is a Kriging model, which uses Kriging varianceTo evaluate the accuracy of the prediction of the point in which, among others,
wherein ,representing uncertainty of the predicted result; />Representing the process variance, u (x) =1 T R -1 r(x)-1，Representing a unit vector; r and R (x) are a correlation matrix and a correlation vector, respectively, defined as:
wherein ,R(x(i) ,x (j) ) Representing any twoObservation point x (i) And x (j) Correlation function relation between R (x (i) X) represents the observation point x (i) Functional relation with unobserved point x.
In some embodiments of the present application, the formula of the adaptive update criteria is:
x best ＝arg min(U(x))
wherein U (x) represents a self-learning function; x is x PS Representing a Pareto point set; based on Kriging varianceCalculating the value of the self-learning function U (x) of each point in the Pareto point set, wherein the minimum value point is defined as x best ，x best And the method is used for determining the point with the maximum error in the Pareto point set, carrying out accurate finite element calculation on the point with the maximum error, updating, and gradually completing the reconstruction of the Kriging model until the convergence criterion of the model.
In the embodiment of the present application, when x does not belong to the Pareto point set, the self-learning function U (x) takes a constant c, where the value of the constant c is 10 6 。
In some embodiments of the present application, the hybrid multi-objective optimization procedure includes a first stage and a second stage, wherein,
the first stage: uniformly generating a sample point set in the design space, and establishing the Kriging model based on the uniformly generated sample point set; meanwhile, generating another group of sample points to perform error analysis aiming at the Kriging model; if the accuracy requirement of the error analysis cannot be met, a new Kriging model is built by adding new sample points, and if the accuracy requirement of the error analysis is met, the second stage is entered;
the second stage: the method consists of a multi-objective optimization algorithm and a self-adaptive updating criterion, and is divided into an internal loop and an external loop; wherein, the internal circulation adopts MOEA/D optimization algorithm to obtain Pareto points; the external circulation calculates the value of a self-learning function U (x) of each Pareto point according to the self-adaptive updating rule, selects a point corresponding to the maximum value of U (x), and carries out accurate finite element calculation on the point corresponding to the maximum value of U (x) to obtain a relative error epsilon; if the relative error epsilon exceeds a target threshold value, updating a point corresponding to the maximum value of U (x) through finite element calculation, adding the updated point into a training set to form a new sample space, and entering the internal circulation again to form a new Kriging model; the above iterative process is repeatedly performed until the relative error epsilon is less than or equal to the target threshold value, while the stop condition is satisfied.
In the embodiment of the application, the target threshold is 0.1%.
Optionally, in an embodiment of the present application, the multi-objective optimization algorithm adopts a MOEA/D optimization algorithm, and an optimization mathematical formula is as follows:
design variable: x= [ h, t r ,t s ,N c ,N a ]
Objective function: f (x) = [ W, -P co ]
Constraint conditions: x is x L ≤x≤x U
wherein ,Pco W is the weight of the reinforced column shell containing the defects for the crushing load; x represents a design variable of a reinforced column shell geometric model, wherein the reinforced column shell geometric model at least comprises 5 design variables, and the 5 design variables are respectively: h is the length of the rib and t r Is the thickness of the rib, t s Thickness of reinforced column shell surface, N a Radial rib number N c The number of the axial ribs is the number; x is x L and xU The upper and lower limit values of x are respectively set.
In some embodiments of the application, the method further comprises:
and performing post-buckling analysis on the reinforced column shell with the defects by adopting a nonlinear explicit dynamic analysis method to obtain the crushing load of the reinforced column shell.
In some embodiments of the application, the sampling in the design space comprises:
and sampling the design space based on an optimal Latin hypercube sampling method.
According to the technical scheme, the embodiment of the application has at least the following beneficial effects: firstly, the application is different from the traditional single-target optimization method, simultaneously selects bearing capacity and weight as targets, realizes a general posterior design method by generating a Pareto surface, can conveniently obtain different light targets by selecting proper crushing load, and greatly saves design cost and calculation resources; secondly, a self-adaptive updating criterion is provided, and the efficiency and the precision of multi-objective optimization are improved through a double-circulation optimization method in a mixed flow; thirdly, the method is simple to operate, clear in flow, short in calculation time and high in calculation accuracy, and can be a general posterior design method for the reinforced column shell with the defects in the aerospace field.
Additional aspects and advantages of the application will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the application.
Drawings
The foregoing and/or additional aspects and advantages of the application will become apparent and readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings, in which:
FIG. 1 is a schematic flow chart of a posterior optimization design method of a reinforced column shell with defects, which is provided by the embodiment of the application;
FIG. 2 is a flow chart of hybrid multi-objective optimization of a defective reinforced column shell according to an embodiment of the present application;
FIG. 3 is a schematic diagram of an orthogonal reinforcement shell geometry model according to an embodiment of the present application;
FIG. 4 is a graph showing the defect sensitivity of different reinforced column shells according to an embodiment of the present application;
FIG. 5 is a graph showing the relative error in the iteration process according to the embodiment of the present application;
FIG. 6 is an exemplary diagram of the effect of a comparison of constrained and unconstrained multi-objective optimizations provided by an embodiment of the present application;
FIG. 7 is an exemplary diagram of the effect of comparing Pareto surfaces under the optimization flow based on the present application and under the multi-objective optimization directly based on the Kriging model;
FIG. 8 is an exemplary graph of relative error curves in an iterative process under multi-objective optimization directly based on the Kriging model.
Detailed Description
Embodiments of the present application are described in detail below, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to like or similar elements or elements having like or similar functions throughout. The embodiments described below by referring to the drawings are illustrative and intended to explain the present application and should not be construed as limiting the application.
The posterior optimization design method of the defective reinforced column casing according to the embodiment of the application is described below with reference to the accompanying drawings.
Fig. 1 is a schematic flow chart of a posterior optimization design method of a reinforced column shell with defects according to an embodiment of the present application. FIG. 2 is a flow chart of hybrid multi-objective optimization of a defective reinforced column shell according to an embodiment of the present application. As shown in fig. 1 and 2, the posterior optimization design method of the defective reinforced column shell may include the following steps.
In step 101, introducing an initial concave defect of the reinforced column shell in a manner of applying disturbance load, analyzing the change rule of crushing load of various reinforced column shells under different concave degrees through finite element calculation, obtaining defect sensitivity curves of different reinforced column shells, and determining a loading range aiming at the disturbance load.
Alternatively, a hybrid multi-objective optimization design can be performed using an orthogonal ribbed cylindrical shell geometry model with a diameter of 3000mm and a length of 2000 mm. For example, the initial concave defect of the reinforced column shell is introduced in a manner of applying disturbance load (such as radial concentrated force), then based on python language, parametric modeling of the reinforced column shell with defects is realized by adopting finite element software ABAQUS, finite element analysis is carried out, the change rule of crushing load of various reinforced column shells under different concave degrees is obtained through analysis, the defect sensitivity curves of different reinforced column shells are obtained according to the change rule, and reasonable loading range is determined through analysis of the defect sensitivity curves.
As shown in fig. 3, the geometric model of the orthogonal reinforced column shell includes 5 design variables, which are respectively: h is the length of the rib and t r Is the thickness of the rib, t s Thickness of reinforced column shell surface, N a Radial rib number N c Is the number of axial ribs. The various types of reinforcement shells shown refer to orthogonal reinforcement shell geometric models having initial design variables, having lower and upper variable limits. For example, as shown in table 1 below, three orthogonal ribbed shell geometric models are given.
TABLE 1 design space for variables
As shown in fig. 4, the disturbance load F p Is applied to the middle part of the reinforced column shell to form a concave defect. The defect can be regarded as an equivalent defect, and a very fine grid is not required, so a 30mm grid is used to reduce the calculation cost. And performing post-buckling analysis on the reinforced column casing with the defects by adopting a nonlinear explicit dynamic analysis method to obtain the crushing load of the reinforced column casing. In the initial stage, the crushing load of the reinforced column shell is gradually reduced along with the increase of the disturbance load, and the crushing load tends to be stable when the disturbance load is increased to 30kN. Thus, by comparing the defect sensitivity curves of the different reinforced column shells, the disturbance load can be determined to be 30kN.
In step 102, parametric modeling and finite element computation are performed on the reinforced column shell containing the defects, sampling is performed in the design space, and a proxy model is built according to the obtained sample point data. Wherein, in some embodiments, the proxy model may be a Kriging model.
In some embodiments of the present application, the design space may be sampled based on an optimal Latin hypercube method, sample point data calculated by finite elements and a Kriging model built. As an example, the Kriging model may consist of 117 sampling points while another 18 sampling points are also generated for error analysis of the Kriging model. If the Kriging model cannot meet the requirement of error analysis, the Kriging model is reconstructed by adding new sample points to improve modeling accuracy.
Alternatively, in embodiments of the present application, the Kriging variance is usedTo evaluate the accuracy of the prediction of the point in which, among others,
wherein ,the uncertainty of the prediction result is represented, and the larger the variance is, the higher the uncertainty of the prediction result is; />Representing the process variance, u (x) =1 T R -1 r(x)-1，/>Representing a unit vector; r and R (x) are a correlation matrix and a correlation vector, respectively, and can be defined as:
wherein ,R(x(i) ,x (j) ) Representing any two observation points x (i) And x (j) Correlation function relation between R (x (i) X) represents the observation point x (i) Functional relation with unobserved point x.
In step 103, a hybrid multi-objective optimization procedure is established based on the adaptive update criteria of the proxy model, and a plurality of objective functions are optimized in the design space according to the hybrid multi-objective optimization procedure.
In some embodiments of the present application, the formula for the adaptive update criteria may be:
x best ＝arg min(U(x))
wherein U (x) represents a self-learning function; x is x PS Representing a Pareto point set; based on Kriging varianceThe value of the self-learning function U (x) of each point in the Pareto point set can be calculated, wherein the minimum value point is defined as x best Thus, x best The method can be used for determining the point with the largest error in the Pareto point set, then carrying out accurate finite element calculation and updating on the point with the largest error, and gradually completing the reconstruction of the Kriging model until the convergence criterion of the model.
In the embodiment of the present application, when x does not belong to the Pareto point set, the self-learning function U (x) will take a constant c, where the value of the constant c is taken as 10 6 。
In some embodiments of the present application, the hybrid multi-objective optimization process is specifically divided into the following two stages:
the first stage: uniformly generating a sample point set in a design space, and establishing a Kriging model based on the uniformly generated sample point set; meanwhile, generating another group of sample points to perform error analysis aiming at a Kriging model; if the accuracy requirement of the error analysis cannot be met, a new Kriging model is built by adding new sample points, and if the accuracy requirement of the error analysis is met, a second stage is entered;
and a second stage: the method consists of a multi-objective optimization algorithm and an adaptive updating criterion, and is divided into double loops, such as an internal loop and an external loop; the internal circulation adopts a MOEA/D optimization algorithm to effectively acquire Pareto points, wherein the related parameters of the MOEA/D algorithm are as follows: population size n=200, iteration number g=400, neighborhood size 20, number of weight vectors 200; the self-learning function U (x) value of each Pareto point is calculated by the self-adaptive updating rule in the external circulation, the point corresponding to the maximum value of U (x) is selected, and the accurate finite element calculation is carried out on the point corresponding to the maximum value of U (x) to obtain the relative error epsilon; if the relative error epsilon exceeds the target threshold, updating the point corresponding to the maximum value of U (x) through finite element calculation, adding the updated point into a training set to form a new sample space, and entering the internal circulation again to form a new Kriging model; the above iterative process is repeatedly performed until the stop condition is satisfied and the relative error epsilon is less than or equal to the target threshold value. As one example, the target threshold may be 0.1%.
In some embodiments of the present application, a MOEA/D optimization algorithm may be employed for multi-objective optimization of an orthogonal reinforcement column shell, wherein the optimization mathematical formula employed by the MOEA/D optimization algorithm is as follows:
design variable: x= [ h, t r ,t s ,N c ,N a ]
Objective function: f (x) = [ W, -P co ]
Constraint conditions: x is x L ≤x≤x U
wherein ,Pco To crush the load, W is the weight of the column shell with the defect, and to ensure the conflict relation between the two objective functions, the crushing load P is determined co Multiplying the value of (2) by-1; x represents a design variable of the reinforced column shell geometric model, the reinforced column shell geometric model at least comprises 5 design variables, and the 5 design variables are respectively: h is the length of the rib and t r Is the thickness of the rib, t s Thickness of reinforced column shell surface, N a Radial rib number N c The number of the axial ribs is the number; x is x L and xU The upper and lower limit values of x are respectively set. Other material properties and parameters are as follows: elastic modulus e=70.0 Gpa, poisson ratio v=0.33, density ρ=2.7×10 -6 kg/mm 3 Yield stress sigma s =410 Mpa, limit stress σ b ＝480Mpa。
As shown in fig. 5, the iteration number of the relative error epsilon in the present embodiment is 31, the crushing load P co Is higher than the other objective function weight W, thus crushing load P during convergence co There is a large fluctuation in the relative error of (a). In the initial stage of the convergence curve, the maximum relative errors epsilon (W) and epsilon (P) co ) Respectively 9.2% and 32.8%. The Pareto plane reached stability after the first 31 iterations, with maximum relative errors ε (W) and ε (P) after stability co ) Down to only 0.1%.
As shown in fig. 6, the task of multi-objective optimization is to search a set of Pareto points throughout the feasible domain and thereby make a Pareto plane. P (P) cr Is the design value of crush load.
In step 104, according to the hybrid multi-objective optimization procedure, the result is optimized to finally form a Pareto surface, and the optimal weight of the defective reinforced column shell under different crushing loads is determined according to the Pareto surface.
Optionally, the total number of samples calculated by the accurate finite element is 148, and the calculation time is about 197 hours according to the mixed multi-objective optimization flow established by the adaptive updating criterion. The optimized result finally forms a Pareto surface, so that the optimal weight under different crushing loads can be determined, and a general posterior design method for the reinforced column shell with the defects is realized. For example, as shown in fig. 7, the optimization results ultimately form a Pareto plane, including 201 independent Pareto points. Each point represents a reinforced column shell optimization solution, weighing from 156.9kg to 754.5 kg. Calculates the maximum stress of Pareto points under different safety factors (SF=1.05, 1.15 and 1.30), namely 417.3Mpa, 420.2Mpa and 424.9Mpa, which are respectively smaller than the limit stress sigma of the material b (480 MPa) and meets the design specification requirements. Compared with the initial solution, the application can not only improve the bearing capacity of the reinforced column shell, but also reduce the weight of the structure.
In posterior design, the geometrical model is optimized by adopting a multi-objective optimization flow directly based on the Kriging model, and the following results can be obtained: the total number of samples for the accurate finite element calculation is 219, and the corresponding optimization calculation time is about 292 hours. Iterative history of relative errors. As shown in FIG. 8, compared with the method, the relative error generated in the multi-objective optimization process directly based on the Kriging model is high in whole, large in fluctuation range and large in iteration number. For example, as shown in table 2 below, the relevant parameters and optimization results in two optimization flows are given under different safety factors, including: initial design value, pareto point, accurate finite element calculation result and relative error.
Table 2 related parameters and optimization results in two optimization flows with different safety coefficients
It can be seen that the optimization result obtained by introducing the multi-objective optimization flow established by the adaptive update criterion is compared with the multi-objective optimization result directly based on the Kriging model: the total number of samples after the completion of the latter iteration is about 1.48 times that of the present application, the corresponding optimization calculation time is about 1.49 times that of the present application, and the relative error at the same Pareto point (e.g. sf=1.05) is 22 times that of the present application. In contrast, it can be seen that the present application improves the efficiency and accuracy of multi-objective optimization. In addition, the optimization result obtained by the application can be used as a general posterior design method, and a designer can flexibly select the optimal design according to different safety coefficients required in actual engineering, so that repeated calculation is not needed, and the design cost and calculation resources are saved. The method also has the advantages of less iteration times, less actual and accurate finite element solutions, short calculation time, higher precision and the like, is simple to operate, clear in flow, and can become a general posterior design method for the reinforced column shell containing the defects in the aerospace field.
In the description of the present specification, a description referring to terms "one embodiment," "some embodiments," "examples," "specific examples," or "some examples," etc., means that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the present application. In this specification, schematic representations of the above terms are not necessarily directed to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples. Furthermore, the different embodiments or examples described in this specification and the features of the different embodiments or examples may be combined and combined by those skilled in the art without contradiction.
Furthermore, the terms "first," "second," and the like, are used for descriptive purposes only and are not to be construed as indicating or implying a relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defining "a first" or "a second" may explicitly or implicitly include at least one such feature. In the description of the present application, "plurality" means at least two, for example, two, three, etc., and "plurality" means at least two, for example, two, three, etc., unless specifically defined otherwise.
Any process or method descriptions in flow charts or otherwise described herein may be understood as representing modules, segments, or portions of code which include one or more executable instructions for implementing specific logical functions or steps of the process, and additional implementations are included within the scope of the preferred embodiment of the present application in which functions may be executed out of order from that shown or discussed, including substantially concurrently or in reverse order from that shown or discussed, depending on the functionality involved, as would be understood by those reasonably skilled in the art of the embodiments of the present application.
Logic and/or steps represented in the flowcharts or otherwise described herein, e.g., a ordered listing of executable instructions for implementing logical functions, can be embodied in any computer-readable medium for use by or in connection with an instruction execution system, apparatus, or device, such as a computer-based system, processor-containing system, or other system that can fetch the instructions from the instruction execution system, apparatus, or device and execute the instructions. For the purposes of this description, a "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transport the program for use by or in connection with the instruction execution system, apparatus, or device. More specific examples (a non-exhaustive list) of the computer-readable medium would include the following: an electrical connection (electronic device) having one or more wires, a portable computer diskette (magnetic device), a Random Access Memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber device, and a portable compact disc read-only memory (CDROM). In addition, the computer readable medium may even be paper or other suitable medium on which the program is printed, as the program may be electronically captured, via, for instance, optical scanning of the paper or other medium, then compiled, interpreted or otherwise processed in a suitable manner, if necessary, and then stored in a computer memory.
It is to be understood that portions of the present application may be implemented in hardware, software, firmware, or a combination thereof. In the above-described embodiments, the various steps or methods may be implemented in software or firmware stored in a memory and executed by a suitable instruction execution system. As with the other embodiments, if implemented in hardware, may be implemented using any one or combination of the following techniques, as is well known in the art: discrete logic circuits having logic gates for implementing logic functions on data signals, application specific integrated circuits having suitable combinational logic gates, programmable Gate Arrays (PGAs), field Programmable Gate Arrays (FPGAs), and the like.
Those of ordinary skill in the art will appreciate that all or a portion of the steps carried out in the method of the above-described embodiments may be implemented by a program to instruct related hardware, where the program may be stored in a computer readable storage medium, and where the program, when executed, includes one or a combination of the steps of the method embodiments.
In addition, each functional unit in the embodiments of the present application may be integrated in one processing module, or each unit may exist alone physically, or two or more units may be integrated in one module. The integrated modules may be implemented in hardware or in software functional modules. The integrated modules may also be stored in a computer readable storage medium if implemented in the form of software functional modules and sold or used as a stand-alone product.
The above-mentioned storage medium may be a read-only memory, a magnetic disk or an optical disk, or the like. While embodiments of the present application have been shown and described above, it will be understood that the above embodiments are illustrative and not to be construed as limiting the application, and that variations, modifications, alternatives and variations may be made to the above embodiments by one of ordinary skill in the art within the scope of the application.
Claims (7)
1. A posterior optimization design method of a column shell with defects and reinforcement is characterized by comprising the following steps:
introducing initial concave defects of the reinforced column shells in a manner of applying disturbance load, analyzing the change rules of crushing loads of a plurality of reinforced column shells under different concave degrees through finite element calculation, obtaining defect sensitivity curves of different reinforced column shells, and determining a loading range aiming at the disturbance load;
modeling the parameterization of the reinforced column shell containing the defects, performing finite element calculation, sampling in a design space, and establishing a proxy model according to the obtained sample point data;
based on the self-adaptive updating criterion of the proxy model, a mixed multi-objective optimization flow is established, and a plurality of objective functions are optimized in the design space according to the mixed multi-objective optimization flow;
according to the mixed multi-objective optimization flow, optimizing a result to finally form a Pareto surface, and determining the optimal weight of the defective reinforced column shell under different crushing loads according to the Pareto surface;
the formula of the adaptive update criterion is as follows:
wherein ,representing a self-learning function; />Representing a Pareto point set; based on Kriging variance->Calculating self-learning function of each point in the Pareto point set>Wherein the minimum point is defined as +.>，/>The method comprises the steps of determining a point with the maximum error in the Pareto point set, carrying out accurate finite element calculation on the point with the maximum error, updating, and gradually completing the reconstruction of the Kriging model until the convergence criterion of the model;
the hybrid multi-objective optimization procedure includes a first stage and a second stage, wherein,
the first stage: uniformly generating a sample point set in the design space, and establishing the Kriging model based on the uniformly generated sample point set; meanwhile, generating another group of sample points to perform error analysis aiming at the Kriging model; if the accuracy requirement of the error analysis cannot be met, a new Kriging model is built by adding new sample points, and if the accuracy requirement of the error analysis is met, the second stage is entered;
the second stage: the method consists of a multi-objective optimization algorithm and a self-adaptive updating criterion, and is divided into an internal loop and an external loop; wherein, the internal circulation adopts MOEA/D optimization algorithm to obtain Pareto points; the external loop calculates a self-learning function of each Pareto point by the adaptive updating criterionNumber of digitsAnd selecting->The point corresponding to the maximum value for said +.>The point corresponding to the maximum value is calculated by accurate finite element to obtain the relative error +.>The method comprises the steps of carrying out a first treatment on the surface of the If the relative error->Exceeding the target threshold, the ++is calculated by finite element>Updating the point corresponding to the maximum value, adding the updated point into a training set to form a new sample space, and entering the internal circulation again to form a new Kriging model; the above iterative process is repeatedly performed until the relative error +_for the stop condition is satisfied>Less than or equal to the target threshold.
2. The method of claim 1, wherein the proxy model is a Kriging model of Kriging, using Kriging varianceTo evaluate the accuracy of the prediction of the point in which, among others,
wherein ,representing uncertainty of the predicted result; />Representing process variance->，/>Representing a unit vector; /> and />The correlation matrix and the correlation vector are defined as:
wherein ,representing any two observation points->And->Correlation function relation between ∈>Representing observation point +.>And the unobserved points->A functional relationship between them.
3. The method according to claim 1, wherein whenWhen the self-learning function does not belong to the Pareto point set, the self-learning function is +.>Will take a constant +.>Wherein the constant->The value of +.>。
4. The method of claim 1, wherein the target threshold is 0.1%.
5. The method of claim 4, wherein the multi-objective optimization algorithm employs a MOEA/D optimization algorithm, and the optimization mathematical formula is as follows:
design variable:
objective function:
constraint conditions:
wherein ,for the crush load, < > and->The weight of the column shell with the defects is added; />The method comprises the steps of representing design variables of a reinforced column shell geometric model, wherein the reinforced column shell geometric model at least comprises 5 design variables, and the 5 design variables are respectively: />Is the length of the rib>Is rib thickness>Reinforced column shell surface thickness->Radial rib number->The number of the axial ribs is the number; /> and />Said->Upper and lower limit values of (2).
6. The method as recited in claim 1, further comprising:
and performing post-buckling analysis on the reinforced column shell with the defects by adopting a nonlinear explicit dynamic analysis method to obtain the crushing load of the reinforced column shell.
7. The method of claim 1, wherein sampling in the design space comprises:
and sampling the design space based on an optimal Latin hypercube sampling method.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202110109155.9A CN112926147B (en) | 2021-01-27 | 2021-01-27 | Posterior optimization design method for reinforced column shell containing defects |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202110109155.9A CN112926147B (en) | 2021-01-27 | 2021-01-27 | Posterior optimization design method for reinforced column shell containing defects |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN112926147A CN112926147A (en) | 2021-06-08 |
| CN112926147B true CN112926147B (en) | 2023-11-03 |
Family
ID=76166810
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202110109155.9A Active CN112926147B (en) | 2021-01-27 | 2021-01-27 | Posterior optimization design method for reinforced column shell containing defects |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN112926147B (en) |
Families Citing this family (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN117892559A (en) * | 2024-03-14 | 2024-04-16 | 西安现代控制技术研究所 | Ultra-remote guidance rocket overall coordination multidisciplinary hierarchical optimization method |
Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104484531A (en) * | 2014-12-18 | 2015-04-01 | 大连理工大学 | Stiffened plate shell structure reliability optimization method with multisource uncertainty being considered |
| CN104866673A (en) * | 2015-05-28 | 2015-08-26 | 大连理工大学 | Opening reinforcement method of shaft pressing reinforced cylindrical shell |
| CN107330219A (en) * | 2017-07-19 | 2017-11-07 | 许昌学院 | A kind of multipoint parallel global optimization method based on Kriging models |
| CN108153981A (en) * | 2017-12-26 | 2018-06-12 | 中航沈飞民用飞机有限责任公司 | A kind of composite material fuselage Material Stiffened Panel Post-Buckling Analysis of Structures method based on finite element analysis |
| CN111027250A (en) * | 2019-12-11 | 2020-04-17 | 大连理工大学 | Special-shaped curved surface reinforced shell modeling method based on grid deformation technology |
| WO2020211007A1 (en) * | 2019-04-17 | 2020-10-22 | 大连理工大学 | Form and position deviation feature library establishment method for aerospace thin-housing structure |
-
2021
- 2021-01-27 CN CN202110109155.9A patent/CN112926147B/en active Active
Patent Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104484531A (en) * | 2014-12-18 | 2015-04-01 | 大连理工大学 | Stiffened plate shell structure reliability optimization method with multisource uncertainty being considered |
| CN104866673A (en) * | 2015-05-28 | 2015-08-26 | 大连理工大学 | Opening reinforcement method of shaft pressing reinforced cylindrical shell |
| CN107330219A (en) * | 2017-07-19 | 2017-11-07 | 许昌学院 | A kind of multipoint parallel global optimization method based on Kriging models |
| CN108153981A (en) * | 2017-12-26 | 2018-06-12 | 中航沈飞民用飞机有限责任公司 | A kind of composite material fuselage Material Stiffened Panel Post-Buckling Analysis of Structures method based on finite element analysis |
| WO2020211007A1 (en) * | 2019-04-17 | 2020-10-22 | 大连理工大学 | Form and position deviation feature library establishment method for aerospace thin-housing structure |
| CN111027250A (en) * | 2019-12-11 | 2020-04-17 | 大连理工大学 | Special-shaped curved surface reinforced shell modeling method based on grid deformation technology |
Non-Patent Citations (1)
| Title |
|---|
| 航天薄壁筒壳结构高精度稳定性实验系统设计与应用研究;杜凯繁;中国优秀硕士论文全文数据库(第第1期期);第2.3节 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN112926147A (en) | 2021-06-08 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN112487702B (en) | Method for predicting residual service life of lithium ion battery | |
| Ewees et al. | A new multi-objective optimization algorithm combined with opposition-based learning | |
| Zhu et al. | Optimization of load-carrying hierarchical stiffened shells: comparative survey and applications of six hybrid heuristic models | |
| CN113343545B (en) | Structure adaptive optimization design method, device, equipment and medium | |
| Guo et al. | Buckling optimization of variable stiffness composite cylinders by using multi-fidelity surrogate models | |
| Raposo et al. | Positnn: Training deep neural networks with mixed low-precision posit | |
| CN112926147B (en) | Posterior optimization design method for reinforced column shell containing defects | |
| CN109783918B (en) | Speed reducer optimization design implementation method based on switching of sequential sampling mode | |
| Zamirai et al. | Revisiting BFfloat16 Training | |
| Li et al. | Efficient bitwidth search for practical mixed precision neural network | |
| CN112036058A (en) | Rapid defect sensitivity analysis method for imperfect thin-wall structure | |
| Zheng et al. | A parameterized lower confidence bounding scheme for adaptive metamodel-based design optimization | |
| CN114564787A (en) | Bayesian optimization method, device and storage medium for target-related airfoil design | |
| CN116933657A (en) | Complex profile processing parameter feature extraction method, system, equipment and medium | |
| Zhu et al. | An Improved density-based design method of additive manufacturing fabricated inhomogeneous cellular-solid structures | |
| CN110210072B (en) | Method for solving high-dimensional optimization problem based on approximate model and differential evolution algorithm | |
| Yang et al. | Reliability analysis based on optimization random forest model and MCMC | |
| CN115345303A (en) | Convolutional neural network weight tuning method, device, storage medium and electronic equipment | |
| Qin et al. | AWK-TIS: An Improved AK-IS Based on Whale Optimization Algorithm and Truncated Importance Sampling for Reliability Analysis. | |
| Cai et al. | A hybrid global optimization method based on multiple metamodels | |
| Zhao et al. | LLM-PQ: Serving LLM on Heterogeneous Clusters with Phase-Aware Partition and Adaptive Quantization | |
| CN113240094A (en) | SVM-based LSTM hyper-parameter optimization method, system, medium and device | |
| Li et al. | Expensive inequality constraints handling methods suitable for dynamic surrogate-based optimization | |
| CN113869033A (en) | Graph neural network sentence sequencing method integrated with iterative sentence pair relation prediction | |
| Chen et al. | A hybrid framework of efficient multi-objective optimization of stiffened shells with imperfection |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |