CN111832134B - Application of double-layer experiment design method based on agent model in reliability analysis of I-shaped structure - Google Patents
Application of double-layer experiment design method based on agent model in reliability analysis of I-shaped structure Download PDFInfo
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Abstract
The application of a double-layer experiment design method based on a proxy model in reliability analysis of an I-shaped structure belongs to the field of reliability analysis and design of mechanical structures. The invention aims to solve the problem that in reliability analysis and reliability optimization, a proxy model constructed by adopting a single DOE method only has global fitting accuracy but cannot meet the fitting accuracy near a limit state. It is implemented by three processes: firstly, generating a certain number of samples by a Latin hypercube method to construct an initial proxy model; secondly, screening out a certain number of secondary samples by combining an initial proxy model and uniform sampling; thirdly, combining the first sample and the second sample into a new sample to reconstruct the proxy model, and carrying out reliability analysis and design by using the final proxy model.
Description
The application is as follows: 201710239870.8, application date 2017, 04, 13 and divisional application entitled "two-layer experimental design method based on surrogate model for mechanical reliability analysis and design".
Technical Field
The invention relates to application of a double-layer experiment design method based on a proxy model in reliability analysis of an I-shaped structure, and belongs to the field of reliability analysis and design of mechanical structures.
Background
In the field of reliability analysis and design and the technical field of reliability optimization design, firstly, a series of representative sample points are constructed by using an experimental design method to construct a corresponding proxy model so as to replace the original implicit complex analysis model.
The reasonable experimental design means can effectively select sampling points, reflect output characteristics as much as possible by using sample points as few as possible, and can obviously reduce the sampling amount, thereby improving the working efficiency and reducing the calculation amount. The currently developed Design of Experiment (DOE) methods include full factor Design, uniform Design, center composite Design, Box-Behnken Design, and Latin Hypercube Design (LHD). The LHD method has the outstanding space-filling characteristic, and the number of sampling points can be freely designed for each different number of design variables, so that the LHD method is most widely applied to arrangement of computer simulation experiments.
The LHD was first proposed in 1979, and the Design result was an nxym matrix, where each row in the matrix represents a group of input variable combinations, each column represents a sampling value of a corresponding variable, and any column is an arrangement of 1-n, however, since most of the variables are substantially random points, the characteristic of space filling cannot be fully exerted, many researchers improved the original LHD method, and proposed corresponding improvement methods, such as nested Latin Hypercube Design, symmetric Latin Hypercube Design, minimum deviation Latin Hypercube Design, and Optimal Latin Hypercube Design (OLHD).
The improved Latin hypercube design methods mentioned above have a common disadvantage that they introduce an optimization algorithm in the construction process, so that the calculation needs a large amount of iterations, the calculation efficiency is low, and it is difficult to obtain experimental design points with good spatial distribution uniformity within a specified time. Aiming at the determination of the improved Latin hypercube design method, Felipe A.C. Viewa and Gerhard Venter et al propose a mobile propagation algorithm (translational propagation algorithm), by which the optimal or near-optimal experimental design point of Latin hypercube design can be obtained quickly.
The DOE methods mentioned above generally fill the entire design space with the constructed sample points as uniformly as possible to ensure the global fitting accuracy of the proxy model in the variable space. However, the process of solving the failure probability in the reliability analysis is actually a two-classification process, which means that the fitting accuracy of the critical boundary of the two states of failure and safety determines the accuracy of the whole reliability analysis, and therefore even if a proxy model with higher global fitting accuracy is obtained, it does not mean that a reliability analysis result or a reliability optimization result with higher accuracy can be obtained.
The relatively early disclosures of the DOE methods mainly include a bias experimental design method proposed by international business machines corporation, a space filling optimal design method in a high-throughput combined experiment proposed by xuyang and the like in Jiangnan university building, a high-efficiency latin hypercube experimental design method proposed by Liuli, Dragon and the like in Beijing university of science and technology, and the like; the recently proposed DOE methods mainly include a field test design method based on D-optimal inner surface design proposed by the Yangjun of Beijing aerospace university and a sampling test design method based on Bayesian network proposed by the Li Xiaoyang et al, a high-efficiency sequence Latin hypercube test design method proposed by the Liuli, Dragon and the like of Beijing Physician university, and a Latin hypercube test design method based on sequential sampling proposed by the Wang Donghui et al of China national defense science and technology university of people liberation military.
For the problem of complicated high-dimensional reliability analysis and reliability optimization, a single DOE method is adopted to construct a proxy model, although the model can meet the global fitting accuracy, the model cannot meet the fitting accuracy near a limit state, so that the reliability analysis result or the optimization result has larger deviation, and the sampling method such as self-adaptive sampling is difficult to realize in the implicit complicated engineering problem, so that an experimental design method which can ensure the global accuracy and improve the local fitting accuracy near the limit state and is easy to apply in the reliability analysis and the optimization is needed.
Disclosure of Invention
The invention aims to solve the problem that in reliability analysis and reliability optimization, a proxy model constructed by adopting a single DOE method only has global fitting precision but cannot meet the fitting precision near a limit state, and provides application of a double-layer experimental design method based on the proxy model in reliability analysis of an I-shaped structure.
The invention relates to a double-layer experimental design method based on a proxy model for mechanical reliability analysis and design, which comprises the following steps:
the method comprises the following steps: determining a design variable x ═ x (x) for a mechanical structure1,x2,…,xn) Establishing a limit state function g (x) by the functional characteristic quantity (H) and the failure criterion (I);
step two: determining the upper limit L of each design variable according to the distribution type and the design requirement of the design variablesiAnd lower limit Ui，i＝1,2,...,n；
Step three: generating m samples by applying a Latin hypercube method, calling a limit state function g (x) for the m samples to obtain corresponding function values, and forming sample points (x)j,g(x)j)，j＝1,2,...,m；
Step four: selecting a proxy model, and constructing a proxy model g by using the sample points obtained in the third step1(x)；
Step five: generating T samples by a uniform sampling method, and calling a proxy model g for the T samples1(x) Calculating the corresponding function value to form a sample point (x)I,g1(x)I)，I＝1,2,...,T；
Step six: according to the sample point (x)I,g1(x)I) Selecting the first k samples with the function values closest to the limit state from the T samples as samples of the second layer sample;
step seven: then using the sample of the second layer sample, calling function g (x) to obtain corresponding function value to form sample point (x)J,g(x)J)，J＝1,2,...,k；
Step (ii) ofEighthly: combining the m sample points in step three and the k sample points in step seven to obtain N ═ m + k sample points (x)p,g(x)p)，p＝1,2,...,N；
Step nine: constructing a proxy model g according to the sample points in the step eight2(x) Using a proxy model g2(x) And carrying out subsequent reliability analysis and design.
The invention has the advantages that: the method of the invention is realized by three processes: firstly, generating a certain number of samples by a Latin hypercube method to construct an initial proxy model; secondly, screening out a certain number of secondary samples by combining an initial proxy model and uniform sampling; thirdly, combining the first sample and the second sample into a new sample to reconstruct the proxy model, and carrying out reliability analysis and design by using the final proxy model.
The invention aims at the reliability analysis and optimization problem, carries out subsampled experimental design based on the proxy model, uses the subsampled experimental design in the reliability analysis and design of engineering design, can overcome the limitation that the proxy model constructed by the existing single experimental design method only has global fitting precision, improves the fitting precision of the constructed proxy model near the extreme state, and can obtain the reliability analysis and design result with higher precision.
The method is easy to program, simple and feasible, and is suitable for the field of engineering reliability analysis and optimization design with huge calculation amount, such as structural reliability optimization design containing large-scale finite element analysis and multidisciplinary reliability analysis and optimization design of complex engineering systems of aircrafts, automobiles, ships and the like.
Drawings
FIG. 1 is a flow chart of a two-level experimental design method based on a surrogate model for mechanical reliability analysis and design according to the present invention;
FIG. 2 is a schematic diagram of a design process of the design method of the present invention;
FIG. 3 is a front axle construction of an automobile in an exemplary embodiment;
fig. 4 is a schematic diagram of design variables of an i-shaped cross section of an automobile front axle, wherein each variable represents a corresponding dimension parameter of each part.
Detailed Description
The first embodiment is as follows: the present embodiment is described below with reference to fig. 1 and fig. 2, and the method for designing a two-layer experiment based on a proxy model for mechanical reliability analysis and design in the present embodiment includes the following steps:
the method comprises the following steps: determining a design variable x ═ x (x) for a mechanical structure1,x2,…,xn) Establishing a limit state function g (x) by the functional characteristic quantity (H) and the failure criterion (I);
step two: determining the upper limit L of each design variable according to the distribution type and the design requirement of the design variablesiAnd lower limit Ui1,2, ·, n; the upper limit and the lower limit of each design variable determined in the step are the design space of the mechanical structure;
step three: generating m samples by applying a Latin hypercube method, calling a limit state function g (x) for the m samples to obtain corresponding function values, and forming sample points (x)j,g(x)j)，j＝1,2,...,m；
Step four: selecting a proxy model, and constructing a proxy model g by using the sample points obtained in the third step1(x) (ii) a Recommending and selecting a support vector machine as a proxy model in the reliability analysis problem;
step five: generating T samples by a uniform sampling method, and calling a proxy model g for the T samples1(x) Calculating the corresponding function value to form a sample point (x)I,g1(x)I)，I＝1,2,...,T；
Step six: according to the sample point (x)I,g1(x)I) Selecting the first k samples with the function values closest to the limit state from the T samples as samples of the second layer sample; the first k samples with function values closest to the limit state, i.e. | g1(x) Sorting the first k samples with the | closest to 0 from small to large;
step seven: then using the sample of the second layer sample, calling function g (x) to obtain corresponding function value to form sample point (x)J,g(x)J)，J＝1,2,...,k；
Step eight: combining the m sample points in step three and the k sample points in step seven to obtain N ═ m + k sample points (x)p,g(x)p)，p＝1,2,...,N；
Step nine: constructing a proxy model g according to the sample points in the step eight2(x) Using a proxy model g2(x) And carrying out subsequent reliability analysis and design.
And in the fourth step, the agent model with stronger applicability, such as a support vector machine, a Kriging model or a neural network, is recommended and selected.
In the ninth step, the agent model can also be selected from agent models such as a support vector machine, a Kriging model or a neural network.
Upper limit L of each design variable in step twoiAnd lower limit UiAnd the standard is determined according to a 3 sigma principle without special requirements.
The embodiment finally uses the proxy model g2(x) And (3) replacing the limit state function g (x) of the original model to carry out subsequent reliability analysis and design.
In this embodiment, it is not required that the second-time used surrogate model is consistent with the first-time used surrogate model, for example, the first-time constructed initial surrogate model may be a support vector machine, and the second-time surrogate model may be a Kriging model, which is selected as needed in specific use.
The specific embodiment is as follows:
the following description is made with reference to fig. 3 and 4:
in order to prove the practicability and the efficiency of the method and the correctness of the method which is convenient for visualization, the method takes the reliability problem of the front axle of the automobile as an example, and the comparison research is carried out on the single-time experimental design method and the secondary experimental design method. In the example, the constructed proxy model and the original model are respectively processed by 107Reliability results obtained by sub Monte Carlo sampling calculation are compared, and the invention provides a 'false classification number' index aiming at the false classification problem in the reliability analysis problem so as to verify the precision and the accuracy of the classification of the construction model of the method.
Calculation example: the axle is connected to the frame via a suspension, which supports the vehicle for the most part and transmits the traction or braking forces of the wheels and also lateral forces to the frame via the suspension, the front axle being the primary load-bearing part. Most of the front axles are I-shaped structures at present, and the bending strength of the front axles can be improved due to the adoption of I-shaped sections, and meanwhile, the weight of the front axles is reduced.
The front axle has a structure as shown in fig. 3, and the maximum normal stress and shear stress of the dangerous section is M/WxAnd τ ═ T/WρWherein M and T are respectively the bending moment and the torque applied to the front axle, WxAnd WρRespectively, the section coefficient and the polar section coefficient of the structure, and has:
Wρ＝0.8bt2+0.4[a3(h-2t)/t]，
when considering the static strength failure of the front axle structure, the extreme state function can be constructed as follows:
wherein σsσ is known from the material properties of the front axle construction for the yield limit of static strengths460 MPa. The size parameters of the structure and the applied external load are used as independent normal random variables, and the distribution parameters are shown in table 1.
TABLE 1 distribution parameters of various input variables of front axle construction
1) Determining a design variable x and a limit state function g (x):
the design variable is x ═ a b T h M T]Each component of which is a random variable subject to an independent normal distribution with a mean value μ ═ 126514853.5 x 106 3.1╳106]Gamma 10 gamma [ 0.63.250.74.251.75 ] standard deviation sigma ═5 1.55╳105]。
The extreme state function is
Wherein σs＝460MPa，
Wρ＝0.8bt2+0.4[a3(h-2t)/t]。
2) Determining a design space:
the upper limit L of each design variable is determined to be μ -3 σ and the lower limit U is determined to be μ +3 σ according to the 3 σ rule.
3) LHD sampling:
num generation using Latin hypercube method1A sample X1And calling a limit state function g (x) to sequentially obtain corresponding function values to form sample points (x, g (x)).
4) Constructing a proxy model g1(x)：
Selecting a Kriging model as a proxy model, and constructing a proxy model g by using the sample points generated in the step 3)1(x)。
5) Uniform sampling generates T samples:
10000 samples X are generated by uniform sampling methoduAnd call the proxy model g1(x) Calculating corresponding function values to form sample points (x, g)1(x))。
6) Screening samples:
screening out the top Num closest to the limit state from the step 5)2One sample as sample X of the second layer sample2I.e. | g1(x) The first Num with the value of | closest to 02And (4) sampling.
7) Calculating a function value:
num screened in step 6)2A sample X2Calling the limit state function g (x) to obtain the corresponding function value, and forming a sample point (x, g (x)).
8) Combining samples:
combining X in step 31One sample point and Num in step 7)2Sample points to obtain Num1+Num2Num sample points (x, g (x)).
9) Constructing a proxy model g2(x)：
Constructing a new Kriging proxy model g by using the sample points in the step 8)2(x) And the model is used to replace the limit state function g (x) of the original model for subsequent reliability analysis and design.
10) And (3) comparing and analyzing reliability analysis results:
in order to prove the practicability and high efficiency of the double-layer experiment design method, the experiment design parameter Num is given according to the table 21And Num2The calculation was carried out in combination, and the false classification index, the reliability analysis result and the calculation result of the relative error of the reliability of Monte Carlo, the Kriging model (Kriging1) of the single layer experimental design structure and the Kriging model (Kriging2) of the double layer experimental design structure are listed in Table 3. The misclassification number refers to the number of 100 samples which are closest to the limit state of the original model and are screened out in 10000 times of uniform sampling, and the calculated value of the statistical agent model is different from the calculated value of the original model.
TABLE 2 selection of secondary experiment design parameters
TABLE 3 comparison of calculation results
According to the calculation results in table 3, the misclassification number and the relative error of the reliability calculation of the model constructed by the single experimental design are both large, while the misclassification number and the relative error of the model constructed by the double-layer experimental design are obviously reduced, and the calculation accuracy is improved along with the increase of the number of samples. It is worth noting that the model constructed by the double-layer experimental design method under 50 samples exceeds the accuracy of the model constructed by the single experimental design method under 200 samples, and the number of misclassifications is less. Thus, this example fully demonstrates the utility and efficiency of the proposed method.
Claims (1)
1. The application of the double-layer experimental design method based on the agent model in the reliability analysis of the I-shaped structure,
the maximum normal stress and the maximum shear stress of the dangerous section of the front axle of the automobile are M/WxAnd τ ═ T/WρWherein M and T are respectively the bending moment and the torque applied to the front axle, WxAnd WpRespectively, the section coefficient and the polar section coefficient of the structure, and has:
Wρ＝0.8bt2+0.4[a3(h-2t)/t]，
the extreme state function is constructed as follows:
wherein, σ s is the yield limit of static strength, σ s is 460MPa, it includes the following steps:
the method comprises the following steps: determining a design variable x ═ x (x) for a mechanical structure1，x2，...，xn) Establishing a limit state function g (x) by using the functional characteristic quantity H and a failure criterion;
step two: determining the upper limit L of each design variable according to the distribution type and the design requirement of the design variablesiAnd lower limit Ui，i＝1，2，...，n；
Step three: generating m samples by Latin hypercube method, calling limit state function g (x) to obtain corresponding function value, and groupingSampling point (x)j，g(x)j)，j＝1，2，...，m；
Step four: selecting a proxy model, and constructing a proxy model g by using the sample points obtained in the third step1(x)；
Step five: generating T samples by a uniform sampling method, and calling a proxy model g for the T samples1(x) Calculating the corresponding function value to form a sample point (x)I，g1(x)I)，I＝1，2，...，T；
Step six: according to the sample point (x)I，g1(x)I) Selecting the first k samples with the function values closest to the limit state from the T samples as samples of the second layer sample;
step seven: then using the sample of the second layer sample, calling function g (x) to obtain corresponding function value to form sample point (x)J，g(x)J)，J＝1，2，...，k；
Step eight: combining the m sample points in step three and the k sample points in step seven to obtain N ═ m + k sample points (x)p，g(x)p)，p＝1，2，...，N；
Step nine: constructing a proxy model g according to the sample points in the step eight2(x) Using a proxy model g2(x) And carrying out subsequent reliability analysis and design.
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| CN107038303A (en) | 2017-08-11 |
| CN107038303B (en) | 2020-08-18 |
| CN111832134A (en) | 2020-10-27 |
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