CN112926147A - Posterior optimization design method of reinforced column shell containing defects - Google Patents
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Abstract
The application provides a posterior optimization design method of a reinforced column shell containing defects, which comprises the following steps: introducing initial indentation defects of the reinforced column shell in a disturbance load applying mode, analyzing the change rule of crushing loads of various reinforced column shells under different indentation degrees through finite element calculation to obtain defect sensitivity curves of different reinforced column shells, and determining a loading range aiming at disturbance loads; carrying out parametric modeling on the reinforced column shell containing the defects, carrying out finite element calculation, sampling in a design space, and establishing a proxy model according to the obtained sample point data; establishing a mixed multi-objective optimization process based on the self-adaptive updating criterion of the agent model, and optimizing a plurality of objective functions in a design space according to the mixed multi-objective optimization process; and according to the mixed multi-objective optimization process, the optimization result is finally formed into a Pareto surface, and the optimal weight of the reinforced column shell containing the defects under different crushing loads is determined. The method and the device realize more efficient and accurate multi-target optimization of the reinforced column shell containing the defects.
Description
Technical Field
The application relates to the field of design of a main component reinforced column shell in an aerospace structure, in particular to a posterior optimization design method of a reinforced column shell containing defects.
Background
The thin-wall structure has the characteristics of good bearing performance and light weight, and is widely applied to the field of aerospace, such as a reinforced column shell structure serving as one of main components of an aerospace carrier rocket. The primary failure mechanism of thin-walled structures under axial compression is buckling. However, for the buckling analysis of the thin-wall structure, the deviation between the predicted value and the experimental result is often large, which is mainly due to the inevitable occurrence of geometric defects in the production, manufacturing and processing processes. Therefore, the influence of geometric defects must be considered when designing the reinforced column casing.
On the other hand, cost control is also crucial to the use of thin-walled structures in the aerospace field, and the goals of resource saving and economic saving can be achieved by reducing weight. Therefore, thin-walled structures are often optimized for light weight. Considering the complexity of the lightweight optimization of aerospace structures, Fischer et al employ a multi-stage optimization approach to minimize the weight of composite wings. Schubert et al establishes reinforced aluminum, titanium and magnesium nodes by adopting laser beam connection, thereby reducing the weight. In addition, Gray and Alexander have made lightweight designs for multi-stage rockets under fixed allowable load constraints. However, with the continuous development of manufacturing and processing technologies, the bearing capacity of the reinforced column shell structure is also continuously improved, which means that the previous lightweight optimization result is too conservative, which causes repeated calculation and manpower and material resource consumption in the actual engineering. Therefore, in the initial optimization stage of the structure, the consideration of the weight and the bearing capacity of the reinforced column shell is more meaningful.
Although multi-objective optimization methods have been used in many fields over the past few decades, there has been less research on reinforced column shells containing defects. Unlike single-target optimization, multi-target optimization generates a series of optimal solutions, and multiple conflicting targets can be optimized simultaneously. However, the multi-objective optimization problem is very expensive in time because of the large amount of calculation and the large amount of time cost due to the simultaneous processing of multiple objectives. Therefore, it can be seen that a need exists for a method for efficiently and accurately performing multi-objective optimization analysis on a reinforced column casing containing defects.
Disclosure of Invention
The present application aims to solve at least one of the above mentioned technical problems to a certain extent.
Therefore, one objective of the present application is to provide a posterior optimization design method for a ribbed shell with defects, so as to achieve more efficient and accurate multi-objective optimization of the ribbed shell with defects.
In order to achieve the above object, an embodiment of the present application provides a posterior optimization design method for a stiffened column casing with defects, including:
introducing an initial indentation defect of the reinforced column shell in a disturbance load applying mode, analyzing the change rule of crushing loads of various reinforced column shells under different indentation degrees through finite element calculation to obtain defect sensitivity curves of different reinforced column shells, and determining a loading range aiming at the disturbance load;
carrying out parametric modeling on the reinforced column shell containing the defects, carrying out finite element calculation, sampling in a design space, and establishing a proxy model according to the obtained sample point data;
establishing a mixed multi-objective optimization flow based on the self-adaptive updating criterion of the agent model, and optimizing a plurality of objective functions in the design space according to the mixed multi-objective optimization flow;
and finally forming a Pareto surface according to the optimization result of the mixed multi-objective optimization process, and determining the optimal weight of the reinforced column shell containing the defects under different crushing loads according to the Pareto surface.
In some embodiments of the present application, the surrogate model is Kriging model, and Kriging variance is adopted
To evaluate the accuracy of the prediction of its midpoint, wherein,
wherein ,
representing the uncertainty of the prediction result;
denotes the process variance, u (x) 1TR-1r(x)-1，
Represents a unit vector; r and R (x) are the correlation matrix and the correlation vector, respectively, defined as:
wherein ,R(x(i),x(j)) Representing any two observation points x(i)And x(j)The correlation function relationship between R (x)(i)And x) represents an observation point x(i)And the unobserved point x.
In some embodiments of the present application, the formula of the adaptive update criterion is:
xbest＝arg min(U(x))
wherein U (x) represents a self-learning function; x is the number ofPSRepresenting a Pareto point set; based on Kriging variance
Calculating the value of a self-learning function U (x) of each point in the Pareto point set, wherein the minimum value point is defined as xbest，xbestAnd the method is used for determining the point with the maximum error in the Pareto point set, performing accurate finite element calculation and updating on the point with the maximum error, and gradually finishing the reconstruction of the Kriging model until the convergence criterion of the model is reached.
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 106。
In some embodiments of the present application, the hybrid multi-objective optimization process 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, another group of sample points is generated to carry out error analysis aiming at the Kriging model; if the accuracy requirement of error analysis cannot be met, a new Kriging model is constructed by adding new sample points, and if the accuracy requirement of error analysis is met, the second stage is carried out;
the second stage is as follows: the method comprises a multi-objective optimization algorithm and a self-adaptive updating criterion, and is divided into an internal loop and an external loop; the internal circulation adopts an MOEA/D optimization algorithm to obtain Pareto points; the outer loop calculates the value of a self-learning function U (x) of each Pareto point according to the self-adaptive updating criterion, selects a point corresponding to the maximum value of U (x), and performs precise 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 the point corresponding to the U (x) maximum value 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 executed until a stop condition is satisfied and the relative error epsilon is less than or equal to the target threshold.
In the embodiment of the present application, the target threshold is 0.1%.
Optionally, in this embodiment of the present application, the multi-objective optimization algorithm employs a MOEA/D optimization algorithm, and an optimization mathematical formula is as follows:
designing variables: x ═ h, tr,ts,Nc,Na]
An objective function: f (x) ═ W, -Pco]
Constraint conditions are as follows: x is the number ofL≤x≤xU
wherein ,PcoW is the weight of the reinforced column shell containing the defects; x represents reinforcementThe design variables of the geometric model of the column shell are that the geometric model of the reinforced column shell at least comprises 5 design variables, and the 5 design variables are respectively as follows: h is the length of the rib, trIs the thickness, t, of the ribsSurface thickness of ribbed columnaNumber of radial ribs, NcThe number of the axial ribs; x is the number ofL and xUThe upper and lower limit values of x are respectively.
In some embodiments of the present application, the method further comprises:
and performing post-buckling analysis on the reinforced column shell containing 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 present application, the sampling in the design space includes:
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 method is different from the traditional single-target optimization method, the bearing capacity and the weight are simultaneously selected as targets, a general posterior design method is realized by generating a Pareto surface, different light targets can be conveniently obtained by selecting proper crushing loads, and the design cost and the calculation resources are greatly saved; secondly, a self-adaptive updating criterion is provided, and the efficiency and the precision of multi-objective optimization are improved by a double-cycle 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 become a general posterior design method for the reinforcement column shell with defects in the aerospace field.
Additional aspects and advantages of the present 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 present application.
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The foregoing and/or additional aspects and advantages of the present application will become apparent and readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings of which:
fig. 1 is a schematic flow chart of a posterior optimization design method for a ribbed shell with defects according to an embodiment of the present application;
FIG. 2 is a flow chart of hybrid multi-objective optimization of a ribbed shell with defects according to an embodiment of the application;
FIG. 3 is a schematic diagram of a geometric model of an orthogonal stiffened shell according to an embodiment of the present application;
fig. 4 is a defect sensitivity curve of different reinforced column shells according to the embodiment of the present application;
FIG. 5 is a graph of relative error variation in an iterative process according to an embodiment of the present disclosure;
FIG. 6 is a diagram illustrating an example of a comparison of constrained and unconstrained multi-objective optimization provided by embodiments of the present application;
FIG. 7 is an exemplary diagram of the comparison effect of Pareto surfaces under the optimization process and the multi-objective optimization directly based on the Kriging model;
FIG. 8 is an exemplary diagram of a relative error change curve in an iterative process under multi-objective optimization directly based on a Kriging model.
Detailed Description
Reference will now be made in detail to embodiments of the present application, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the drawings are exemplary and intended to be used for explaining the present application and should not be construed as limiting the present application.
The posterior optimization design method of the reinforced column casing with defects 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 for a stiffened column shell containing defects according to an embodiment of the present application. Fig. 2 is a flow chart of hybrid multi-objective optimization of a ribbed shell with defects according to an embodiment of the present application. As shown in fig. 1 and 2, the posterior optimization design method of the reinforced column shell containing the defects can comprise the following steps.
In step 101, an initial indentation defect of the reinforced column shell is introduced in a manner of applying a disturbance load, the change rules of crushing loads of various reinforced column shells at different indentation degrees are analyzed through finite element calculation, defect sensitivity curves of different reinforced column shells are obtained, and a loading range for the disturbance load is determined.
Alternatively, an orthogonal reinforcement column shell geometric model with the diameter of 3000mm and the length of 2000mm can be adopted for hybrid multi-objective optimization design. For example, an initial indentation defect of the reinforced column shell is introduced in a mode of applying disturbance load (such as radial concentration force), parametric modeling of the reinforced column shell containing the defect is realized by adopting finite element software ABAQUS based on python language and finite element analysis is carried out, the change rules of crushing load of various reinforced column shells under different indentation degrees are obtained through analysis, defect sensitivity curves of different reinforced column shells are obtained according to the change rules, and a reasonable loading range is determined through analyzing the defect sensitivity curves.
As shown in fig. 3, the geometric model of the orthogonal stiffened shell includes 5 design variables, which are: h is the length of the rib, trIs the thickness, t, of the ribsSurface thickness of ribbed columnaNumber of radial ribs, NcThe number of the axial ribs. The multiple reinforced column shells are geometric models of orthogonal reinforced column shells with initial design variables, variable lower limits and variable upper limits. For example, as shown in table 1 below, three orthogonal stiffened shell geometric models are given.
Table 1 design space of variables
As shown in fig. 4, the disturbance load FpThe hollow reinforcing column shell is applied to the middle of the reinforcing column shell to form a hollow defect. This defect can be seen as an equivalent defect, requiring no very fine grid, and therefore a 30mm grid is used to reduce computational cost. And (3) carrying out post-buckling analysis on the reinforced column shell containing the defects by adopting a nonlinear explicit dynamic analysis method to obtain the crushing load of the reinforced column shell. In the initial stage, along with the increase of disturbance load, the crushing load of the reinforced column shell is gradually reduced, and the reinforced column shell tends to be stable when the disturbance load is increased to 30 kN. Due to the fact thatTherefore, the disturbance load can be determined to be 30kN by comparing the defect sensitivity curves of different reinforced column shells.
In step 102, parametric modeling is performed on the stiffened shell containing the defects, finite element calculation is performed, sampling is performed in a design space, and a proxy model is established 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 sampling method, sample point data calculated by finite elements and a Kriging model established. As an example, the Kriging model may consist of 117 sample points while still generating another 18 sample points for error analysis of the Kriging model. And if the Kriging model cannot meet the requirement of error analysis, increasing new sample points to reconstruct the Kriging model so as to improve the modeling precision.
Optionally, in the embodiment of the present application, Kriging variance is adopted
To evaluate the accuracy of the prediction of its midpoint, wherein,
wherein ,
the uncertainty of the prediction result is represented, and the larger the variance is, the higher the uncertainty of the prediction result is;
denotes the process variance, u (x) 1TR-1r(x)-1，
Represents a unit vector; r and R (x) are the correlation matrix and the correlation vector, respectively, and can be defined as:
wherein ,R(x(i),x(j)) Representing any two observation points x(i)And x(j)The correlation function relationship between R (x)(i)And x) represents an observation point x(i)And the unobserved point x.
In step 103, a hybrid multi-objective optimization process 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 process.
In some embodiments of the present application, the formula for the adaptive update criteria may be:
xbest＝arg min(U(x))
wherein U (x) represents a self-learning function; x is the number ofPSRepresenting a Pareto point set; based on Kriging variance
The value of a self-learning function U (x) of each point in the Pareto point set can be calculated, wherein the minimum value point is defined as xbestThus, xbestThe method can be used for determining the point with the maximum error in the Pareto point set, then carrying out accurate finite element calculation and updating on the point with the maximum error, and gradually completing the reconstruction of the Kriging model until the convergence criterion of the model is reached.
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, wherein the value of the constant c is 106。
In some embodiments of the present application, the hybrid multi-objective optimization process is specifically divided into the following two stages:
the first stage is as follows: uniformly generating a sample point set in a design space, and establishing a Kriging model based on the uniformly generated sample point set; meanwhile, another group of sample points is generated to carry out error analysis aiming at the Kriging model; if the accuracy requirement of error analysis cannot be met, a new Kriging model is constructed by adding new sample points, and if the accuracy requirement of error analysis is met, the second stage is carried out;
and a second stage: the method comprises a multi-objective optimization algorithm and a self-adaptive updating criterion, and is divided into double loops such as an inner loop and an outer loop; the internal circulation effectively obtains Pareto points by adopting an MOEA/D optimization algorithm, wherein the MOEA/D algorithm related parameters are as follows: the population size N is 200, the iteration times G is 400, the neighborhood size is 20, and the number of weighted vectors is 200; calculating the value of a self-learning function U (x) of each Pareto point by an adaptive updating criterion through an external loop, selecting a point corresponding to the maximum value of U (x), and performing precise 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 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 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 an example, the target threshold may be 0.1%.
In some embodiments of the present application, a MOEA/D optimization algorithm may be adopted for the multi-objective optimization of the orthogonal stiffened column casing, wherein the MOEA/D optimization algorithm adopts an optimization mathematical formula as follows:
designing variables: x ═ h, tr,ts,Nc,Na]
An objective function: f (x) ═ W, -Pco]
Constraint conditions are as follows: x is the number ofL≤x≤xU
wherein ,PcoFor crushing load, W is the weight of the reinforced column shell containing defects, and for ensuring the conflict relationship between the two objective functions, the crushing load P is addedcoThe value of (d) is multiplied by-1; x represents the design variable of the geometric model of the reinforced column shell, the geometric model of the reinforced column shell at least comprises 5 design variables, and the 5 design variables are respectively: h is the length of the rib, trIs the thickness, t, of the ribsSurface thickness of ribbed columnaNumber of radial ribs, NcThe number of the axial ribs; x is the number ofL and xUThe upper and lower limits of x, respectively. Other material properties and parameters were as follows: elastic modulus E is 70.0Gpa, Poisson's ratio v is 0.33, density rho is 2.7 × 10-6kg/mm3Yield stress σs410MPa, ultimate stress sigmab＝480Mpa。
As shown in fig. 5, the number of iterations of the relative error e in this example is 31, and the crushing load PcoIs higher than another target function weight W, and thus the crushing load P during convergencecoThere is a large fluctuation in the relative error of (a). In the initial stage of the convergence curve, the maximum relative errors ε (W) and ε (P)co) 9.2 percent and 32.8 percent are respectively achieved. The Pareto surface reaches stability after the first 31 iterations, and the maximum relative errors epsilon (W) and epsilon (P) after the stabilityco) Down to only 0.1%.
As shown in fig. 6, the task of multi-objective optimization is to search a set of Pareto points within the entire feasible domain and thus make a Pareto surface. PcrIs a designed crush load value.
In step 104, according to the hybrid multi-objective optimization process, an Pareto surface is finally formed according to the optimization result, and the optimal weight of the reinforced column shell with the defects under different crushing loads is determined according to the Pareto surface.
Optionally, in the hybrid multi-objective optimization process established according to the adaptive update criterion, the total number of samples of the precise finite element calculation is 148, and the calculation time is about 197 hours. The optimization result finally forms a Pareto surface, the optimal weight under different crushing loads can be determined, and the universal posterior design method of the reinforced column shell containing the defects is realized. For example, as shown in fig. 7, the optimization result finally forms a Pareto surface including 201 independent Pareto points. Each point represents an optimized solution for the stiffened shell, ranging in weight from 156.9kg to 754.5 kg. Calculating the maximum stress of Pareto points under different safety factors (SF is 1.05, 1.15 and 1.30), wherein the maximum stress is 417.3MPa, 420.2MPa and 424.9MPa which are respectively less than the ultimate stress sigma of the materialb(480MPa) and meets the requirement of design specifications.Through comparing with the initial solution, can derive this application and not only can promote and add muscle column casing bearing capacity, also can reduce structure weight simultaneously.
In the posterior design, the geometric model is optimized by adopting a multi-objective optimization process directly based on a Kriging model, and the following results can be obtained: the total number of samples for the exact finite element calculation was 219, corresponding to an optimal calculation time of about 292 hours. And (5) iterating the process by the relative error. As shown in FIG. 8, compared with the present application, the relative error generated in the multi-objective optimization process directly based on the Kriging model is overall higher, the fluctuation range is large, and the iteration number is large. For example, as shown in table 2 below, the relevant parameters and optimization results in two optimization procedures are given under different safety factors, including: initial design values, Pareto points, precise finite element calculation results and relative errors.
TABLE 2 relevant parameters and optimization results in two optimization procedures with different safety factors
Therefore, it can be seen that the optimization result obtained by the multi-objective optimization process established by introducing 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 latter iteration is completed is about 1.48 times of the present application, the corresponding optimization calculation time is about 1.49 times of the present application, and the relative error at the same Pareto point (for example, SF 1.05) is 22 times of the present application. In contrast, it can be seen that the present application promotes efficiency and accuracy of multi-objective optimization. In addition, the optimization result obtained by the method can be used as a universal posterior design method, a designer can flexibly select the optimal design according to different safety factors required in actual engineering without repeated calculation, and the design cost and the calculation resources are saved. The method has the advantages of few iteration times, few actual accurate finite element solutions, short calculation time, high precision and the like, is simple to operate, has clear flow, and can become a general posterior design method of the reinforcement column casing with defects in the aerospace field.
In the description herein, reference to the description of the term "one embodiment," "some embodiments," "an example," "a specific example," 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 application. In this specification, the schematic representations of the terms used above are not necessarily intended to refer 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, various embodiments or examples and features of different embodiments or examples described in this specification can be combined and combined by one skilled in the art without contradiction.
Furthermore, the terms "first", "second" and "first" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one such feature. In the description of this application, "plurality" means at least two, such as two, three, etc., and "plurality" means at least two, such as two, three, etc., unless specifically limited 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 steps of a custom logic function or process, and alternate 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, depending on the functionality involved, as would be understood by those reasonably skilled in the art of the present application.
The logic and/or steps represented in the flowcharts or otherwise described herein, e.g., an ordered listing of executable instructions that can be considered to implement 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). Additionally, the computer-readable medium could even be paper or another suitable medium upon which the program is printed, as the program can 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 should be understood that portions of the present application may be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, the various steps or methods may be implemented in software or firmware stored in memory and executed by a suitable instruction execution system. If implemented in hardware, as in another embodiment, any one or combination of the following techniques, which are known in the art, may be used: a discrete logic circuit having a logic gate circuit for implementing a logic function on a data signal, an application specific integrated circuit having an appropriate combinational logic gate circuit, a Programmable Gate Array (PGA), a Field Programmable Gate Array (FPGA), or the like.
It will be understood by those skilled in the art that all or part of the steps carried by the method for implementing the above embodiments may be implemented by hardware related to instructions of a program, which may be stored in a computer readable storage medium, and when the program is executed, the program includes one or a combination of the steps of the method embodiments.
In addition, functional units in the embodiments of the present application may be integrated into one processing module, or each unit may exist alone physically, or two or more units are integrated into one module. The integrated module can be realized in a hardware mode, and can also be realized in a software functional module mode. The integrated module, if implemented in the form of a software functional module and sold or used as a stand-alone product, may also be stored in a computer readable storage medium.
The storage medium mentioned above may be a read-only memory, a magnetic or optical disk, etc. Although embodiments of the present application have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present application, and that variations, modifications, substitutions and alterations may be made to the above embodiments by those of ordinary skill in the art within the scope of the present application.
Claims (9)
1. A posterior optimization design method of a reinforced column shell containing defects is characterized by comprising the following steps:
introducing an initial indentation defect of the reinforced column shell in a disturbance load applying mode, analyzing the change rule of crushing loads of various reinforced column shells under different indentation degrees through finite element calculation to obtain defect sensitivity curves of different reinforced column shells, and determining a loading range aiming at the disturbance load;
carrying out parametric modeling on the reinforced column shell containing the defects, carrying out finite element calculation, sampling in a design space, and establishing a proxy model according to the obtained sample point data;
establishing a mixed multi-objective optimization flow based on the self-adaptive updating criterion of the agent model, and optimizing a plurality of objective functions in the design space according to the mixed multi-objective optimization flow;
and finally forming a Pareto surface according to the optimization result of the mixed multi-objective optimization process, and determining the optimal weight of the reinforced column shell containing the defects under different crushing loads according to the Pareto surface.
2. The method of claim 1, wherein the surrogate model is Kriging model using Kriging variance
To evaluate the accuracy of the prediction of its midpoint, wherein,
wherein ,
representing the uncertainty of the prediction result;
denotes the process variance, u (x) 1TR-1r(x)-1，
Represents a unit vector; r and R (x) are the correlation matrix and the correlation vector, respectively, defined as:
wherein ,R(x(i),x(j)) Representing any two observation points x(i)And x(j)The correlation function relationship between R (x)(i)And x) represents an observation point x(i)And the unobserved point x.
3. The method of claim 1, wherein the adaptive update criterion is formulated as:
xbest＝arg min(U(x))
wherein U (x) represents a self-learning function; x is the number ofPSRepresenting a Pareto point set; based on Kriging variance
Calculating the value of a self-learning function U (x) of each point in the Pareto point set, wherein the minimum value point is defined as xbest，xbestAnd the method is used for determining the point with the maximum error in the Pareto point set, performing accurate finite element calculation and updating on the point with the maximum error, and gradually finishing the reconstruction of the Kriging model until the convergence criterion of the model is reached.
4. Method according to claim 3, characterized in that 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 takes 106。
5. The method of claim 2, wherein the hybrid multi-objective optimization process 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, another group of sample points is generated to carry out error analysis aiming at the Kriging model; if the accuracy requirement of error analysis cannot be met, a new Kriging model is constructed by adding new sample points, and if the accuracy requirement of error analysis is met, the second stage is carried out;
the second stage is as follows: the method comprises a multi-objective optimization algorithm and a self-adaptive updating criterion, and is divided into an internal loop and an external loop; the internal circulation adopts an MOEA/D optimization algorithm to obtain Pareto points; the outer loop calculates the value of a self-learning function U (x) of each Pareto point according to the self-adaptive updating criterion, selects a point corresponding to the maximum value of U (x), and performs precise 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 the point corresponding to the U (x) maximum value 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 executed until a stop condition is satisfied and the relative error epsilon is less than or equal to the target threshold.
6. The method of claim 5, wherein the target threshold is 0.1%.
7. The method according to claim 5 or 6, wherein the multi-objective optimization algorithm employs a MOEA/D optimization algorithm, and the optimization mathematical formula is as follows:
designing variables: x ═ h, tr,ts,Nc,Na]
An objective function: f (x) ═ W, -Pco]
Constraint conditions are as follows: x is the number ofL≤x≤xU
wherein ,PcoW is the weight of the reinforced column shell containing the defects; x represents the design variables of the geometric model of the reinforced column shell, the geometric model of the reinforced column shell at least comprises 5 design variables, and the 5 design variables are respectively as follows: h is the length of the rib, trIs the thickness, t, of the ribsSurface thickness of ribbed columnaNumber of radial ribs, NcThe number of the axial ribs; x is the number ofL and xUThe upper and lower limit values of x are respectively.
8. The method of claim 1, further comprising:
and performing post-buckling analysis on the reinforced column shell containing the defects by adopting a nonlinear explicit dynamic analysis method to obtain the crushing load of the reinforced column shell.
9. The method of claim 1, wherein the sampling in the design space comprises:
and sampling the design space based on an optimal Latin hypercube sampling method.
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| 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 |
|---|
| 杜凯繁: "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", 中国优秀硕士论文全文数据库, no. 1, pages 2 * |
Cited By (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 |
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