CN112464541A - Mixed composite material layering method considering multi-scale uncertainty - Google Patents

Mixed composite material layering method considering multi-scale uncertainty Download PDF

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CN112464541A
CN112464541A CN202011504349.0A CN202011504349A CN112464541A CN 112464541 A CN112464541 A CN 112464541A CN 202011504349 A CN202011504349 A CN 202011504349A CN 112464541 A CN112464541 A CN 112464541A
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彭翔
郭玉良
王明博
高启龙
李吉泉
姜少飞
景立挺
吴化平
张征
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Abstract

The invention discloses a mixed composite material layering method considering multi-scale uncertainty. Selecting an alternative material set, obtaining the microscopic properties of the alternative material set, and obtaining the distribution type of the macroscopic properties of the alternative material set through a multi-scale analysis model; determining a macroscopic finite element model of the candidate material set by using the macroscopic properties and the distribution types thereof; constructing a neural network model of microscopic attributes of the candidate material set and mixed composite material parameters, calculating a Mean Square Error (MSE) of the trained neural network model, judging the accuracy of the trained neural network model according to the MSE, and optimizing the selection of the candidate material set and the selection of the layer stacking sequence by using a genetic algorithm. The method of the invention uses various optimization algorithms, greatly reduces the burden of designers and computers, greatly improves the calculation speed and the optimization accuracy, and simultaneously better conforms to the actual engineering application.

Description

Mixed composite material layering method considering multi-scale uncertainty
Technical Field
The invention belongs to the field of methods for optimizing stacking sequence and material distribution of fiber reinforced composite materials, and particularly relates to a multi-scale uncertain layering optimization method for a mixed composite material.
Background
Fiber reinforced composites have the advantages of high strength to weight ratio, high stiffness to weight ratio and low cost under various loads and are growing exponentially in automotive, marine, civil, aerospace, and construction applications. In contrast to conventional composites consisting of single fibers and a single matrix, hybrid composites are manufactured by combining two or more fibers into one matrix. The properties of the hybrid composite are a weighted sum of the individual components, and the advantage of one fiber can compensate for the lack of properties of the other types of components in the hybrid composite. Meanwhile, aiming at multi-scale analysis of the composite material, certain research results are provided at home and abroad, and the stability and reliability of the output result of micro-scale analysis can be realized. In addition, in actual engineering application, the multi-scale analysis is more consistent with the practical application of the composite material, and the analysis result is more matched with the actual use condition.
The specified performance parameters are optimized by carrying out proper multi-scale uncertainty engineering optimization design on the mixed composite material, so that the actual application range of the mixed composite material can be better expanded, and the application prospect of the mixed composite material is expanded.
Disclosure of Invention
The invention aims to solve the problem that the design process of a mixed composite material is complex and tedious, and provides a simple multi-scale uncertain mixed composite material layering arrangement method starting from stacking sequence and material distribution.
The technical scheme of the invention is as follows:
1) selection of multiple different composite materials as a candidate set of hybrid composite materials
Figure BDA0002844529630000011
Wherein the content of the first and second substances,
Figure BDA0002844529630000012
a first alternative material is indicated which,
Figure BDA0002844529630000013
a second alternative material is indicated which,
Figure BDA0002844529630000014
a third alternative material is shown which,
Figure BDA0002844529630000015
representing the nth candidate material, n representing the sum of the candidate materials, and collecting the candidate materials
Figure BDA0002844529630000016
The microscopic attributes are subjected to uncertainty quantification, and an alternative material set is obtained after the uncertainty quantification
Figure BDA0002844529630000017
Wherein the set of candidate materials is
Figure BDA0002844529630000018
Including microscopic elastic properties and micro-elasticity propertiesAn apparent intensity attribute;
2) set of candidate materials obtained based on step 1)
Figure BDA0002844529630000019
By the type of distribution of the microscopic properties of the candidate material set
Figure BDA00028445296300000110
The multi-scale analysis model of (2) aggregating the candidate materials
Figure BDA00028445296300000111
The uncertainty of the microscopic properties is propagated to a macroscopic level to obtain a set of alternative materials
Figure BDA0002844529630000021
The distribution type of the macroscopic elastic property and the macroscopic strength property;
3) obtaining a collection of candidate materials
Figure BDA0002844529630000022
After the distribution types of the macroscopic elastic property and the macroscopic strength property are obtained, a candidate material set is determined by utilizing the macroscopic elastic property, the macroscopic strength property and the distribution types thereof
Figure BDA0002844529630000023
For a set of candidate materials
Figure BDA0002844529630000024
And set of candidate materials
Figure BDA0002844529630000025
Layer stacking sequence (theta) of the macroscopic finite element model of (1)1,θ2,θ3、、、θx) After Latin hypercube sampling, alternative materials are gathered by a laminated plate method
Figure BDA0002844529630000026
The macroscopic finite element model of (1) is analyzed, and after the analysis, the macroscopic finite element model of (1) is obtainedSet of selected materials
Figure BDA0002844529630000027
Performance parameter of
Figure BDA0002844529630000028
A failure parameter FI and an overall cost parameter C; wherein, theta1Representing the stacking angle of the first layer of material in the hybrid composite; theta2Representing the stacking angle of the second layer material in the hybrid composite; theta3Representing the stacking angle of the third layer of material in the hybrid composite; thetaxRepresents the stacking angle of the x-th layer material in the hybrid composite material, x represents the sum of the stacking sequence of the layers;
4) building a collection of candidate materials
Figure BDA0002844529630000029
The constructed neural network model comprises an input layer, an intermediate layer and an output layer, wherein the input layer inputs a required candidate material set
Figure BDA00028445296300000210
Required set of candidate materials
Figure BDA00028445296300000211
The microscopic elastic properties, the microscopic strength properties, and the layer stack sequence (θ) of each candidate material1,θ2,θ3、、、θx)，
Figure BDA00028445296300000212
A first alternative material is indicated which,
Figure BDA00028445296300000213
indicating that a second material alternative is desired,
Figure BDA00028445296300000214
indicating that a third alternative material is required,
Figure BDA00028445296300000215
representing the m-th required candidate material, wherein m represents the sum of the required candidate materials; output layer output performance parameters
Figure BDA00028445296300000216
A failure parameter FI and an overall cost parameter C;
5) calculating Mean Square Error (MSE) of the trained neural network model;
6) judging the accuracy of the trained neural network model according to the Mean Square Error (MSE);
if the obtained mean square error MSE is smaller than a preset mean square error threshold value, the constructed neural network model is indicated to be accurate, and the step 7) is carried out;
if the mean square error MSE is larger than or equal to the mean square error threshold, the constructed neural network model is not accurate, parameter learning is carried out on the neural network model based on the performance prediction variance, and then the step 5 is returned to);
7) set of candidate materials using Genetic Algorithm (GA)
Figure BDA00028445296300000217
Selection and layer stacking sequence (theta)1,θ2,θ3、、、θx) And carrying out optimization processing on the selection to obtain the material selection of each layer and the stacking angle of each layer in the mixed composite material laying.
In the step 1), uncertainty quantification is performed on microscopic properties of the candidate material set, specifically:
first, the candidate materials are gathered
Figure BDA00028445296300000218
The micro elastic property and the micro strength property are regarded as different sparse variables y, and different distribution types theta are sampled and distributed in the sparse variables ykProcessing statistics under different distribution parameters epsilon to obtain a probability density function f of a sparse variable y represented by the following formulay(y|ε,θk)：
Figure BDA0002844529630000031
Wherein, L (ε, θ)k) For the sparse variable y in the distribution type thetakAnd likelihood estimation values under distribution parameter ∈ L (∈, θ)k) d [ epsilon ] is the integral of the distribution parameter [ epsilon ], theta, of the likelihood estimate value of the sparse variable ykRepresents the kth distribution type;
according to different distribution types theta of sparse variable ykObtaining the maximum likelihood estimated value L of the sparse variable y by counting all likelihood estimated values under different distribution parameters epsilonmax(ε,θk) Then, the minimum information criterion method is adopted to calculate different distribution types thetakInformation entropy AIC ofk：
AICk＝2numk-2ln(Lmax(ε,θk))
In the formula, numkDenotes the number, L, of distribution parameters εmax(ε,θk) Representing the distribution type theta of the sparse variable ykAnd maximum likelihood estimate, AIC, of distribution parameter epsilonkRepresenting the information entropy of the kth distribution type, wherein k represents the ordinal number of the distribution type;
then, the probability values P of different distribution types are obtained by the following formulaθ_k：
Pθ_k＝exp((AICmin-AICk)/2)
In the formula, AICminRepresenting a minimum information entropy;
finally, the probability value P is determinedθ_kGreater than distribution type probability threshold PΔDistribution type of thetakAnd the distribution type of the sparse variable y is the distribution type of the microscopic property of the candidate material set corresponding to the sparse variable y.
In the step 7), a Genetic Algorithm (GA) is used to assemble the candidate materials
Figure BDA0002844529630000032
Selection and layer stacking sequence (theta)1,θ2,θ3、、、θx) The optimization treatment is carried out by selecting, specifically: optimizing the variable to a layer Stack sequence (θ)1,θ2,θ3、、、θx) And set of candidate materials
Figure BDA0002844529630000033
Performance parameters obtained using accurate neural network model output
Figure BDA0002844529630000034
And constructing performance parameters
Figure BDA0002844529630000035
Robust optimization function f1：
Figure BDA0002844529630000036
Figure BDA0002844529630000037
θ＝(θ1,θ2,θ3、、、θx)
Wherein mean represents taking the mean value, std represents taking the standard deviation, p is the weight coefficient,
Figure BDA0002844529630000038
representing a final solution set of alternative material choices, θ representing a final solution of the layer stack sequence; theta1Representing the stacking angle of the first layer of material in the hybrid composite; theta2Representing the stacking angle of the second layer material in the hybrid composite; theta3Representing the stacking angle of the third layer of material in the hybrid composite; thetaxRepresents the stacking angle of the x-th layer material in the hybrid composite material, x represents the sum of the stacking sequence of the layers;
Figure BDA0002844529630000041
representing the first material in the final recipe set,
Figure BDA0002844529630000042
representing the second material in the final recipe set,
Figure BDA0002844529630000043
representing the third material in the final recipe set,
Figure BDA0002844529630000044
representing the jth material in the final recipe set, j representing the sum of the materials in the final recipe set;
using penalty function method and establishing penalty objective function
Figure BDA0002844529630000045
Figure BDA0002844529630000046
Wherein, lambda represents a punishment parameter, alpha represents a small positive tolerance coefficient, g represents inequality constraint of a failure parameter FI and a total cost parameter C, and h represents stress balance constraint of the mixed composite material;
simultaneously setting constraint conditions of a failure parameter FI and a total cost parameter C; to penalize an objective function
Figure BDA0002844529630000047
Solving for the maximization target to obtain the final scheme set of the alternative material selection
Figure BDA0002844529630000048
And two parameter results of the final solution θ of the layer stack sequence;
in the step 6), the method for learning the neural network model parameters based on the performance prediction variance specifically comprises the following steps:
6.1) set of candidate materials required in the neural network model input from step 4)
Figure BDA0002844529630000049
The microscopic elastic properties, the microscopic strength properties, and the layer stack sequence (θ) of each candidate material1,θ2,θ3、、、θx) And respectively randomly selecting the required alternative material sets and then establishing an input data set as a sample point; the performance parameters of each sample point are obtained by processing and predicting the sample points through a neural network model
Figure BDA00028445296300000410
A failure parameter FI and an overall cost parameter C;
6.2) repeating the step 6.1) for a plurality of times to obtain a plurality of sample points and corresponding performance parameters thereof
Figure BDA00028445296300000411
A failure parameter FI and an overall cost parameter C;
6.3) calculating by adopting a formula to obtain the characteristic value gamma of each sample pointi：
γi＝ωilog(u(i))
u(i)＝rand(0,1)
Wherein, ω isiFor calculating the value of the performance parameter, gamma, obtained at the i-th sample pointiRepresenting the eigenvalue of the ith sample point, rand (0,1) representing the generation of a random number between 0 and 1, u(i)Representing the random number corresponding to the ith sample point;
6.4) selecting the sample point with the maximum characteristic value, and retraining the neural network model by using the input data set of the sample point so as to update the parameters of the neural network model;
6.5) go back to step 5).
The invention has the following beneficial effects:
1) the invention optimizes the stacking sequence and material distribution of the mixed composite material from the micro scale, and compared with the method for optimizing the mixed composite material from the macro scale, the analysis is more accurate, and simultaneously, the method is more in line with the practical engineering application.
2) The single composite material is extremely complex in design and manufacture due to unique composition components, and further, the performance of a computer is tested in the aspect of computer design optimization, but compared with the single composite material, the mixed composite material is more complex, so that various optimization algorithms are used, the burden of designers and computers is greatly reduced, and meanwhile, the optimization accuracy is improved.
3) Compared with the traditional Genetic Algorithm (GA), a new penalty objective function is provided, and the goal is to reduce the optimization variables which do not meet the constraint conditions, so that the computational burden of a computer is further reduced, the computational speed is greatly increased, and the optimization accuracy is improved.
In a word, the method of the invention uses various optimization algorithms, greatly reduces the burden of designers and computers, greatly improves the calculation speed and the optimization accuracy, and simultaneously better conforms to the actual engineering application.
Drawings
FIG. 1 is a schematic representation of a hybrid composite model according to an embodiment of the present invention;
FIG. 2 is an iterative process of stacking order and material patch optimization according to an embodiment of the present invention;
FIG. 3 is a flow chart of finite element analysis of the hybrid composite of the present invention;
FIG. 4 is a flow chart of the hybrid composite material optimization of the present invention.
Detailed Description
The invention will be further described with reference to the following figures and examples, without limiting the scope of the invention thereto, the method of the invention comprising in particular the following steps, as shown in figures 3 and 4:
1. determining the basic information of the mixed composite material to be analyzed: the boundary conditions are nine layers of composite material with four simply-supported sides, length L being 0.508m, width W being 0.406m, and thickness of each layer Δ T being 0.125 mm. The maximum overall cost parameter C is 9.5USD, and the minimum value of the failure probability is
Figure BDA0002844529630000051
Wherein the reliability parameter PfThe relationship with the failure parameter FI is: pf＝P[1-FI≤0]And P is the distributed force to which the hybrid composite is subjected. Three alternative materials were selected: the material I, the material II and the material III are represented by '1', 2 'and 3' in subsequent calculation; the layer stacking sequence is from an angle [ -45,45,0,90 [ -45]Are selected and recombined. Performance parameter
Figure BDA0002844529630000052
Is set as a natural frequency Ff. An example of creating a hybrid composite model is shown in FIG. 1.
2. Uncertainty quantification of microscopic properties of candidate materials (material i, material ii, material iii): the method comprises the following steps:
firstly, regarding each attribute parameter in the microscopic elastic attribute and the microscopic strength attribute of the candidate materials (material I, material II and material III) as different sparse variables y, and sampling and distributing different distribution types theta in the sparse variables ykProcessing statistics under different distribution parameters epsilon to obtain a probability density function f of a sparse variable y represented by the following formulay(y|ε,θk)：
Figure BDA0002844529630000061
Wherein, L (ε, θ)k) For the sparse variable y in the distribution type thetakAnd likelihood estimation values under distribution parameter ∈ L (∈, θ)k) d [ epsilon ] is the integral of the distribution parameter [ epsilon ], theta, of the likelihood estimate value of the sparse variable ykRepresents the kth distribution type;
according to different distribution types theta of sparse variable ykObtaining the maximum likelihood estimated value L of the sparse variable y by counting all likelihood estimated values under different distribution parameters epsilonmax(ε,θk) Then, the minimum information criterion method is adopted to calculate different distribution types thetakInformation entropy AIC ofk：
AICk＝2numk-2ln(Lmax(ε,θk))
In the formula, numkDenotes the number, L, of distribution parameters εmax(ε,θk) Representing the distribution type theta of the sparse variable ykAnd maximum likelihood estimate, AIC, of distribution parameter epsilonkRepresenting the information entropy of the kth distribution type, wherein k represents the ordinal number of the distribution type;
then, the probability values P of different distribution types are obtained by the following formulaθ_k：
PA_k＝exp((AICmin-AICk)/2)
In the formula, AICminRepresenting a minimum information entropy;
finally, the probability value P is determinedθ_kGreater than distribution type probability threshold PΔDistribution type of thetakAnd the distribution type of the sparse variable y is the distribution type of the microscopic property of the candidate material set corresponding to the sparse variable y.
And obtaining the distribution type of the microscopic properties of the candidate materials (material I, material II and material III) after uncertainty quantification, wherein the microscopic property quantity of the candidate materials (material I, material II and material III) comprises microscopic elastic properties and microscopic strength properties.
3. Based on the distribution types of the microscopic attributes of the alternative materials (material I, material II and material III) obtained in the step 2, the uncertainty of the microscopic attributes of the alternative materials (material I, material II and material III) is transmitted to a macroscopic layer through a multi-scale analysis model of the alternative materials (material I, material II and material III), and the distribution types of the macroscopic elastic attributes and the macroscopic strength attributes of the alternative materials (material I, material II and material III) are obtained;
4. after obtaining the distribution types of the macroscopic elastic properties and the macroscopic strength properties of the candidate materials (material I, material II and material III), determining a macroscopic finite element model of the candidate materials (material I, material II and material III) by utilizing the macroscopic elastic properties, the macroscopic strength properties and the distribution types thereof, and stacking the layers of the macroscopic finite element models of the candidate materials (material I, material II and material III) and the candidate materials (material I, material II and material III)(θ1,θ2,θ3、、、Ax) After Latin hypercube sampling, a macroscopic finite element model of the alternative materials (material I, material II and material III) is analyzed by a laminated plate method, and the natural frequency F of the alternative materials (material I, material II and material III) is obtained after analysisfA failure parameter FI and an overall cost parameter C;
5. constructing a neural network model of microscopic properties of the candidate materials (material I, material II and material III) and mixed composite material parameters, wherein the constructed neural network model comprises an input layer, an intermediate layer and an output layer, the input layer inputs the candidate materials (material I, material II and material III), and the microscopic elastic properties, the microscopic strength properties and the layer stacking sequence (theta) of each candidate material in the candidate materials (material I, material II and material III)1,θ2,θ3、、、θx) (ii) a Output layer output natural frequency FfA failure parameter FI and an overall cost parameter C;
6. calculating Mean Square Error (MSE) of the trained neural network model;
7. judging the accuracy of the trained neural network model according to the Mean Square Error (MSE);
if the obtained mean square error MSE is smaller than a preset mean square error threshold value, the constructed neural network model is indicated to be accurate, and the step 8) is carried out;
if the mean square error MSE is larger than or equal to the mean square error threshold, the constructed neural network model is not accurate, parameter learning is carried out on the neural network model based on the performance prediction variance, and then the step 6 is returned to); the method comprises the following specific steps:
7.1) the microscopic elastic properties, the microscopic strength properties and the layer stacking sequence (theta) of each of the candidate materials (material I, material II, material III) in the neural network model input from step 5)1,θ2,θ3、、、θx) And respectively randomly selecting the required alternative material sets and then establishing an input data set as a sample point; the performance parameters of each sample point are obtained by processing and predicting the sample points through a neural network model
Figure BDA0002844529630000071
A failure parameter FI and an overall cost parameter C;
7.2) repeating the step 7.1) for a plurality of times to obtain a plurality of sample points and the corresponding natural frequencies FfA failure parameter FI and an overall cost parameter C;
7.3) calculating by adopting a formula to obtain the characteristic value gamma of each sample pointi：
γi＝ωilog(u(i))
u(i)＝rand(0,1)
Wherein, ω isiFor calculating the value of the performance parameter, gamma, obtained at the i-th sample pointiRepresenting the eigenvalue of the ith sample point, rand (0,1) representing the generation of a random number between 0 and 1, u(i)Representing the random number corresponding to the ith sample point;
7.4) selecting the sample point with the maximum characteristic value, and retraining the neural network model by using the input data set of the sample point to update the parameters of the neural network model;
7.5) go back to step 6).
8. Selection of candidate materials (Material I, Material II, Material III) and layer Stacking sequence (θ) Using Genetic Algorithm (GA)1,θ2,A3、、、Ax) And carrying out optimization processing on the selection to obtain the material selection of each layer and the stacking angle of each layer in the mixed composite material laying. The method comprises the following steps: optimizing the variable to a layer Stack sequence (θ)1,θ2,θ3、、、θx) And alternative materials (material I, material II, material III);
performance parameters obtained using accurate neural network model output
Figure BDA0002844529630000072
And constitutes the natural frequency FfRobust optimization function f1：
Figure BDA0002844529630000081
θ＝(θ1,θ2,θ3、、、θx)
Wherein mean represents taking the mean value, std represents taking the standard deviation, p is the weight coefficient,
Figure BDA0002844529630000082
represents the final set of solutions for the choice of candidate materials (material i, material ii, material iii), theta represents the final solution for the layer stacking sequence; theta1Representing the stacking angle of the first layer of material in the hybrid composite; theta2Representing the stacking angle of the second layer material in the hybrid composite; theta3Representing the stacking angle of the third layer of material in the hybrid composite; thetaxRepresents the stacking angle of the x-th layer material in the hybrid composite material, x represents the sum of the stacking sequence of the layers; in order to reduce the choice of an improperly constrained layer stacking sequence (theta)1,θ2,θ3、、、θx) The following penalty objective functions are established by using a penalty function method together with alternative materials (material I, material II and material III)
Figure BDA0002844529630000083
Figure BDA0002844529630000084
Wherein, lambda represents a punishment parameter, alpha represents a small positive tolerance coefficient, g represents inequality constraint of a failure parameter FI and a total cost parameter C, and h represents stress balance constraint of the mixed composite material; in the specific implementation, the penalty parameter lambda is set to be-100, and the small positive tolerance coefficient alpha is set to be 10-4Further, the time required by the computer for optimization is shortened;
simultaneously setting constraint conditions of a failure parameter FI and a total cost parameter C; to penalize an objective function
Figure BDA0002844529630000085
Solving for the maximization target to obtain the final scheme set of the alternative material selection
Figure BDA0002844529630000086
And two parameter results for final scenario a of the layer stack sequence.
Continuously stacking the layers in sequence (theta) by the adaptive genetic algorithm in step 81,θ2,θ3、、、θx) Iteration with the candidate composite materials (Material I, Material II, Material III) resulted in the optimal layer Stack sequence in this example [ -45/-45/45/-45/90/-45/45/-45]And alternative composite distributions [ 1; 1; 2; 1; 1]The corresponding natural frequency value is 36.58Hz, as shown in fig. 2.
The description is given for the sole purpose of illustrating embodiments of the inventive concept and should not be taken as limiting the scope of the invention to the particular forms set forth in the embodiments, but rather as being limited only to the equivalents thereof as may be contemplated by those skilled in the art based on the teachings herein.

Claims (4)

1. A mixed composite material layering method considering multi-scale uncertainty is characterized in that: the method specifically comprises the following steps:
1) selection of multiple different composite materials as a candidate set of hybrid composite materials
Figure FDA0002844529620000011
Wherein the content of the first and second substances,
Figure FDA0002844529620000012
a first alternative material is indicated which,
Figure FDA0002844529620000013
a second alternative material is indicated which,
Figure FDA0002844529620000014
a third alternative material is shown which,
Figure FDA0002844529620000015
denotes the n-th candidate materialN represents the sum of the candidate materials, and is set for the candidate materials
Figure FDA0002844529620000016
The microscopic attributes are subjected to uncertainty quantification, and an alternative material set is obtained after the uncertainty quantification
Figure FDA0002844529620000017
Wherein the set of candidate materials is
Figure FDA0002844529620000018
The microscopic properties of (a) include microscopic elastic properties and microscopic strength properties;
2) set of candidate materials obtained based on step 1)
Figure FDA0002844529620000019
By the type of distribution of the microscopic properties of the candidate material set
Figure FDA00028445296200000110
The multi-scale analysis model of (2) aggregating the candidate materials
Figure FDA00028445296200000111
The uncertainty of the microscopic properties is propagated to a macroscopic level to obtain a set of alternative materials
Figure FDA00028445296200000112
The distribution type of the macroscopic elastic property and the macroscopic strength property;
3) obtaining a collection of candidate materials
Figure FDA00028445296200000113
After the distribution types of the macroscopic elastic property and the macroscopic strength property are obtained, a candidate material set is determined by utilizing the macroscopic elastic property, the macroscopic strength property and the distribution types thereof
Figure FDA00028445296200000114
For a set of candidate materials
Figure FDA00028445296200000115
And set of candidate materials
Figure FDA00028445296200000116
Layer stacking sequence (theta) of the macroscopic finite element model of (1)1,θ2,θ3、、、θx) After Latin hypercube sampling, alternative materials are gathered by a laminated plate method
Figure FDA00028445296200000117
Analyzing the macroscopic finite element model to obtain a candidate material set
Figure FDA00028445296200000118
Performance parameter of
Figure FDA00028445296200000119
A failure parameter FI and an overall cost parameter C; wherein, theta1Representing the stacking angle of the first layer of material in the hybrid composite; theta2Representing the stacking angle of the second layer material in the hybrid composite; theta3Representing the stacking angle of the third layer of material in the hybrid composite; thetaxRepresents the stacking angle of the x-th layer material in the hybrid composite material, x represents the sum of the stacking sequence of the layers;
4) building a collection of candidate materials
Figure FDA00028445296200000120
The constructed neural network model comprises an input layer, an intermediate layer and an output layer, wherein the input layer inputs a required candidate material set
Figure FDA00028445296200000121
Required set of candidate materials
Figure FDA00028445296200000122
The microscopic elastic properties, the microscopic strength properties, and the layer stack sequence (θ) of each candidate material1,θ2,θ3、、、θx)，
Figure FDA00028445296200000123
A first alternative material is indicated which,
Figure FDA00028445296200000124
indicating that a second material alternative is desired,
Figure FDA00028445296200000125
indicating that a third alternative material is required,
Figure FDA00028445296200000126
representing the m-th required candidate material, wherein m represents the sum of the required candidate materials; output layer output performance parameters
Figure FDA0002844529620000024
A failure parameter FI and an overall cost parameter C;
5) calculating Mean Square Error (MSE) of the trained neural network model;
6) judging the accuracy of the trained neural network model according to the Mean Square Error (MSE);
if the obtained mean square error MSE is smaller than a preset mean square error threshold value, the constructed neural network model is indicated to be accurate, and the step 7) is carried out;
if the mean square error MSE is larger than or equal to the mean square error threshold, the constructed neural network model is not accurate, parameter learning is carried out on the neural network model based on the performance prediction variance, and then the step 5 is returned to);
7) set of candidate materials using Genetic Algorithm (GA)
Figure FDA0002844529620000021
Selection and layer stacking sequence (theta)1,θ2,θ3、、、θx) And finally, carrying out mixed composite material layering according to the material selections and the stacking angles of the layers in the mixed composite material layering.
2. The method of laying up a hybrid composite material taking into account multi-scale uncertainty as claimed in claim 1, wherein:
in the step 1), uncertainty quantification is performed on microscopic properties of the candidate material set, specifically:
first, the candidate materials are gathered
Figure FDA0002844529620000022
The micro elastic property and the micro strength property are regarded as different sparse variables y, and different distribution types theta are sampled and distributed in the sparse variables ykProcessing statistics under different distribution parameters epsilon to obtain a probability density function f of a sparse variable y represented by the following formulay(y|ε,θk)：
Figure FDA0002844529620000023
Wherein, L (ε, θ)k) For the sparse variable y in the distribution type thetakAnd likelihood estimation values under distribution parameter ∈ L (∈, θ)k) d [ epsilon ] is the integral of the distribution parameter [ epsilon ], theta, of the likelihood estimate value of the sparse variable ykRepresents the kth distribution type;
according to different distribution types theta of sparse variable ykObtaining the maximum likelihood estimated value L of the sparse variable y by counting all likelihood estimated values under different distribution parameters epsilonmax(ε,θk) Then, the minimum information criterion method is adopted to calculate different distribution types thetakIs sent toEntropy of rest AICk：
AICk＝2numk-2ln(Lmax(ε,θk))
In the formula, numkDenotes the number, L, of distribution parameters εmax(ε,θk) Representing the distribution type theta of the sparse variable ykAnd maximum likelihood estimate, AIC, of distribution parameter epsilonkRepresenting the information entropy of the kth distribution type, wherein k represents the ordinal number of the distribution type;
then, the probability values P of different distribution types are obtained by the following formulaθ_k：
Pθ_k＝exp((AICmin-AICk)/2)
In the formula, AICminRepresenting a minimum information entropy;
finally, the probability value P is determinedθ_kGreater than distribution type probability threshold PΔDistribution type of thetakAnd the distribution type of the sparse variable y is the distribution type of the microscopic property of the candidate material set corresponding to the sparse variable y.
3. The method of laying up a hybrid composite material taking into account multi-scale uncertainty as claimed in claim 1, wherein:
in the step 7), a Genetic Algorithm (GA) is used to assemble the candidate materials
Figure FDA0002844529620000031
Selection and layer stacking sequence (theta)1,θ2,θ3、、、θx) The optimization treatment is carried out by selecting, specifically: optimizing the variable to a layer Stack sequence (θ)1,θ2,θ3、、、θx) And set of candidate materials
Figure FDA0002844529620000032
Performance parameters obtained using accurate neural network model output
Figure FDA0002844529620000033
And constructing performance parameters
Figure FDA0002844529620000034
Robust optimization function f1：
Figure FDA0002844529620000035
Figure FDA0002844529620000036
θ＝(θ1,θ2,θ3、、、θx)
Wherein mean represents taking the mean value, std represents taking the standard deviation, p is the weight coefficient,
Figure FDA0002844529620000037
representing a final solution set of alternative material choices, θ representing a final solution of the layer stack sequence; theta1Representing the stacking angle of the first layer of material in the hybrid composite; theta2Representing the stacking angle of the second layer material in the hybrid composite; theta3Representing the stacking angle of the third layer of material in the hybrid composite; thetaxRepresents the stacking angle of the x-th layer material in the hybrid composite material, x represents the sum of the stacking sequence of the layers;
Figure FDA0002844529620000038
representing the first material in the final recipe set,
Figure FDA0002844529620000039
representing the second material in the final recipe set,
Figure FDA00028445296200000310
representing the third material in the final recipe set,
Figure FDA00028445296200000311
representing the jth material in the final recipe set, j representing the sum of the materials in the final recipe set;
using penalty function method and establishing penalty objective function
Figure FDA00028445296200000312
Figure FDA00028445296200000313
Wherein, lambda represents a punishment parameter, alpha represents a small positive tolerance coefficient, g represents inequality constraint of a failure parameter FI and a total cost parameter C, and h represents stress balance constraint of the mixed composite material;
to penalize an objective function
Figure FDA00028445296200000314
Solving for the maximization target to obtain the final scheme set of the alternative material selection
Figure FDA00028445296200000315
And two parameter results of the final solution θ of the layer stack sequence.
4. The method of laying up a hybrid composite material taking into account multi-scale uncertainty as claimed in claim 1, wherein:
in the step 6), the method for learning the neural network model parameters based on the performance prediction variance specifically comprises the following steps:
6.1) set of candidate materials required in the neural network model input from step 4)
Figure FDA0002844529620000041
The microscopic elastic properties, the microscopic strength properties, and the layer stack sequence (θ) of each candidate material1,θ2,θ3、、、θx) And respectively randomly selecting the required alternative material sets and then establishing an input data set as a sample point; the performance parameters of each sample point are obtained by processing and predicting the sample points through a neural network model
Figure FDA0002844529620000042
A failure parameter FI and an overall cost parameter C;
6.2) repeating the step 6.1) for a plurality of times to obtain a plurality of sample points and corresponding performance parameters thereof
Figure FDA0002844529620000043
A failure parameter FI and an overall cost parameter C;
6.3) calculating by adopting a formula to obtain the characteristic value gamma of each sample pointi：
γi＝ωilog(u(i))
u(i)＝rand(0,1)
Wherein, ω isiFor calculating the value of the performance parameter, gamma, obtained at the i-th sample pointiRepresenting the eigenvalue of the ith sample point, rand (0,1) representing the generation of a random number between 0 and 1, u(i)Representing the random number corresponding to the ith sample point;
6.4) selecting the sample point with the maximum characteristic value, and retraining the neural network model by using the input data set of the sample point so as to update the parameters of the neural network model;
6.5) go back to step 5).
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