CN115114819A - Plane woven panel honeycomb sandwich structure failure surface simulation method based on adaboost algorithm - Google Patents
Plane woven panel honeycomb sandwich structure failure surface simulation method based on adaboost algorithm Download PDFInfo
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Abstract
The invention relates to a failure surface simulation method of a plane woven panel honeycomb sandwich structure based on an adaboost algorithm, aiming at the plain woven panel honeycomb sandwich structure, a model established based on ABAQUS finite element simulation software can accurately predict the lateral bearing capacity of the structure. And fitting the failure surface of the plane woven panel honeycomb sandwich structure by using the adaboost algorithm and taking the parameters of the member such as the material, the size and the like as input quantities and the lateral bearing capacity as output response quantities. The method greatly improves the calculation efficiency. The method has great engineering significance for the reliability research of the plane woven panel honeycomb sandwich structure, and greatly shortens the time for scientific research.
Description
Technical Field
The invention belongs to the technical field of structural stability research, and relates to a failure surface simulation method of a plane woven panel honeycomb sandwich structure based on an adaboost algorithm.
Background
The plane woven panel honeycomb sandwich structure has good wave permeability, heat insulation, vibration reduction and corrosion resistance, is widely applied to the field of aerospace, and is particularly used as a manufacturing material of an airborne radome. The structural performance of the composite material is greatly influenced by a forming process, and parameters such as the material, the size and the like of a component have certain randomness. The plane woven panel honeycomb sandwich structure for the airborne radome is usually in a lateral compression state, and the lateral maximum bearing capacity of the structure can be obtained through finite element simulation analysis and prediction. And then, analyzing the reliability and parameter sensitivity of the plane woven panel honeycomb sandwich structure. However, finite element analysis is computationally expensive, time-consuming and labor-consuming, and is not suitable for simulating failure planes of a structure. In order to solve the problem of large calculation amount, a proxy model method is selected for simulation. The difficulty of simulating the failure surface by using the proxy model is how to fit the failure surface of the structure lateral pressure strength with high precision.
For the plane woven panel honeycomb sandwich structure, the computation of directly calling the ABAQUS finite element model by the Monte Carlo method is time-consuming, requires great computational power and is not suitable for large-scale computation. When calculating the failure probability using ABAQUS in combination with the monte carlo method, at least 105 finite element calculations need to be invoked. The finite element analysis time is about 240 seconds for one time and the time is about 277 days for 105 times, which is not acceptable in engineering.
The adaboost algorithm has proven to be an efficient and practical boosting algorithm. The algorithm is obtained by improving boosting algorithm in 1995 by Freund and Schapire, and the algorithm principle is that a weak classifier with the minimum weight coefficient is screened from trained weak classifiers by adjusting sample weight and weak classifier weight to combine into a final strong classifier. Weak classifiers are trained based on a training set, each time the next weak classifier is trained on a different weight set of samples. The difficulty with which each sample is classified determines the weight, and the difficulty of classification is estimated from the output of the classifier in the previous step.
adaboost is an iterative algorithm, and the core idea is to train different classifiers (weak classifiers) aiming at the same training set, and then to assemble the weak classifiers to form a stronger final classifier (strong classifier). The adaboost algorithm system has a high detection rate and is not easy to generate an over-adaptation phenomenon.
Disclosure of Invention
Technical problem to be solved
In order to save calculation force and time, a small part of sample N is selected, and an adaboost proxy model is used for fitting a failure surface of a plane woven panel honeycomb sandwich structure.
Technical scheme
A failure surface simulation method of a plane woven panel honeycomb sandwich structure based on an adaboost algorithm is characterized by comprising the following steps:
s1: sampling by utilizing Latin hypercube sampling according to the mean value and standard deviation of the parameters to generate a sample set N; the parameter is the longitudinal elastic modulus E of the material 11 Modulus of elasticity E in weft of Material 22 Material longitudinal shear modulus G 12 Material latitudinal shear modulus G 13 Longitudinal tensile strength X of single-layer plate t Weft tensile Strength Y t Radial compressive strength X of single-layer board c Compressive strength Y in weft c Longitudinal shear strength S of single-layer plate 12 Weft shear strength S 13 The panel thickness d;
s2: sequentially inputting the sample sets N corresponding to the parameters in S1 into a model of the plane woven panel honeycomb sandwich structure, and calculating by using ABAQUS finite element analysis software to obtain the lateral maximum bearing capacity F of the structure;
s3: taking 21KN as a threshold, judging that the structure is failed when the maximum bearing capacity F is greater than 21KN, otherwise, judging that the structure is safe; assigning a value of the maximum bearing force F larger than 21KN as '1', and assigning the rest as '0'; recording the assignment result as a response I;
s4: combining the sample set N with the response I to generate a sample pool P of adaboost, and then dividing P into a training set and a testing set, wherein the training set comprises N 1 Set of input parameters and N 1 Response quantity I 1 The test set contains N 2 An input parameter and N 2 Response quantity I 2 ，N 1 +N 2 ＝N；
S5: 11 parameters in the training set as input quantities, I 1 As a response quantity; training an adaboost model through training set data corresponding to the parameters and the corresponding response quantity, and searching for a failure surface of the plane woven panel honeycomb sandwich structure; finally, obtaining a failure surface of the plane woven panel honeycomb sandwich structure based on the adaboost model simulation;
s6: test set N 2 The 11 input parameters are used as input quantities and are substituted into the trained adaboost model to generate an output value I out The output value is compared with the response I in the test set 2 Comparing, and calculating to obtain the precision of the adaboost model;
s7: by adjusting training set N 1 And test set N 2 Finding the combination with the highest adaboost model precision according to the sample proportion; the failure surface of the plane woven panel honeycomb sandwich structure is replaced by the adaboost model.
A computer system, comprising: one or more processors, a computer readable storage medium, for storing one or more programs, which when executed by the one or more processors, cause the one or more processors to implement the above-described method.
A computer-readable storage medium having stored thereon computer-executable instructions for performing the above-described method when executed.
Advantageous effects
The invention provides a method for simulating a failure surface of a planar woven panel honeycomb sandwich structure by adopting an adaboost algorithm. Aiming at the honeycomb sandwich structure of the plain woven panel, the lateral bearing capacity of the structure can be accurately predicted based on a model established by ABAQUS finite element simulation software. And fitting the failure surface of the plane woven panel honeycomb sandwich structure by using the adaboost algorithm and taking the parameters of the member such as the material, the size and the like as input quantities and the lateral bearing capacity as output response quantities.
The direct calling of the ABAQUS finite element model by using the monte carlo method requires calculation of a large number of sets of data, which consumes a large amount of time and calculation power and is not beneficial to scientific research. For the two-classification problem of the structural failure problem, adaboost as a classifier has high classification precision and is very suitable for simulating the failure surface. The adaboost proxy model is used for simulating the failure surface, so that the calculation process is greatly simplified, and the calculation force and time are greatly saved (99.6% of calculation time is saved) on the premise of ensuring the precision. Is beneficial to shortening the research and development period of the product and saving the calculation power.
The adaboost model is trained by using data of a sample N (a total of 400 groups of data, wherein N1 groups of samples are used as a training set, N2 groups of samples are used as a test set, and N1+ N2 is 400) through an adaboost algorithm, so that large-scale data are classified, and the precision of the adaboost model is 98.46% through verification. The calculation time for one adaboost model is about 0.571 ms, the time for 105 times is about 57 seconds, and the time for 400 finite element calculations is 26.67 hours, which requires 26.68 hours in total. Compared with the method of directly calling the ABAQUS finite element model by the Monte Carlo method, the time for simulating the failure surface by the adaboost algorithm is only 0.401% of that of the ABAQUS finite element model. Obviously, this greatly improves computational efficiency. The method has great engineering significance for the reliability research of the plane woven panel honeycomb sandwich structure, and greatly shortens the time for scientific research.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
The invention provides a failure surface simulation method of a plane woven panel honeycomb sandwich structure based on an adaboost algorithm, which comprises the steps of firstly sampling according to the mean value and the variation coefficient of parameters by utilizing Latin hypercube sampling to generate 400 groups of sample sets N. The structure lateral maximum load capacity with these 400 sets of data as input parameters was calculated using ABAQUS. Dividing data and calculation results into a training set and a testing set, wherein the training set comprises N 1 A sample, test set containing N 2 And (4) sampling. The first 11 columns of data of the training set sample are used as input quantities, and the last column is used as a response quantity. And training the adaboost model by the sample data and the corresponding response quantity. Then using the remaining N 2 Group data serves as a verification set and is used for calculating the prediction accuracy of the model.
Wherein the calculation of the lateral maximum bearing capacity of the structure by using ABAQUS is specifically as follows: the USDFLD user subroutine is used to define failure criteria and a material stiffness degradation model. Establishing a plane woven panel honeycomb sandwich structure finite element model by using ABAQUS software. The plain woven panel was simulated using solid cell C3D8R, and the honeycomb core was equivalent to an orthotropic material, and was also simulated using solid cell C3D 8R. The degree of freedom of displacement in the x, y, and z directions is fixed to the left end face, the degree of freedom of displacement in the z direction is fixed to the right end face, and a displacement compression load is applied in the x direction. And the USDF LD user subprogram in the ABAQUS is used for compiling a failure criterion and a rigidity degradation model subprogram through a FORTRAN language to realize the prediction of the lateral pressure strength of the structure.
The method comprises the following specific steps:
the first step is as follows: an input set is constructed. The mean values, standard deviations and distribution states of the random variables are shown in table 1, and it is assumed that each random variable follows a normal distribution and is not correlated.
TABLE 1 distribution types and parameters of random variables for panels
E 11 Warp-wise modulus of elasticity, E, of the representative Material 22 Modulus of elasticity in weft, G, representing materials 12 Representative Material warp shear modulus, G 13 Representative Material weft shear modulus, X t 、Y t Represents the warp and weft tensile strength, X, of a single-layer board c 、Y c Representing the warp and weft compressive strength, S, of a single-ply board 12 、S 13 Represents the shear strength of a single-layer board, and d is the thickness of the panel.
And generating 400 groups of sample sets N by utilizing Latin hypercube sampling according to the mean value and the coefficient of variation of the 11 parameters, wherein the sample sets N are used as input sets T of the adaboost model. The input set T is divided into training sets T 1 Containing N 1 Sample, test set T 2 Containing N 2 And (4) sampling.
Wherein, the lower subscript H in the formula represents the dimension of the data set, K represents the column number of the data set, and the upper subscript is used for distinguishing each parameter.
The second step is that: and constructing a response set I of the adaboost classifier. Assuming that the plane woven panel honeycomb sandwich structure completely fails when the limit bearing capacity is reached, the maximum lateral bearing capacity F of the structure determined by each group of data is calculated by ABAQUS, and when the applied load is 21KN, the expression of the structural failure is
G(T)＝P u -21 (1)
Wherein G (T) is a limit state function, P u Is the ultimate carrying capacity and T is the random variable vector. When the applied load is larger than the ultimate bearing capacity, the structure fails, and the failure domain is defined as:
F＝{T:G(T)≤0} (2)
indication function I of failure domain F (T) is:
and setting the invalid data group in the sample pool to be 1 and setting the data without the invalidation to be 0 by using an indication function. This divides the result into a response set I of only "1" and "0". Dividing the response set into training set responses I 1 And test set response I 2 。
The third step: and (5) constructing an adaboost classifier. Let training set T 1 The output weight at the kth weak learner is:
D(k)＝(w k1 ,w k2 ,...,w kp ),p＝1,2,...,11 (4)
where k denotes the kth weak learner, p denotes the number of each parameter, and w denotes the weight occupied by each parameter. The output weight of the 1 st weak learner is initialized to:
the error rate of the classification problem is well understood and calculated. Since the multivariate classification is the generalization of the binary classification, here, the binary classification problem, the output is {0,1}, and then the kth weak classifier G k (T) weighted error rate on training set of
Wherein k denotes the kth weak classifier, G k (. is) a limit state function, I F Is an indicator function, I i Is the response value.
Looking next at the weak learner weight coefficients, for the binary classification problem, the kth weak classifier G k (T) has a weight coefficient of
In the formula e k For weighting the error rate, α k Are weight coefficients.
As can be seen from the above-mentioned formula,if the classification error rate e k The larger the corresponding weak classifier weight coefficient alpha is, the larger the weak classifier weight coefficient alpha is k The smaller. That is, the larger the weak classifier weight coefficient whose error rate is small. The sample weight D is updated next.
Assume that the sample set weight coefficient of the kth weak classifier is d (k) ═ w k1 ,w k2 ,...w km ) Then the sample set weight coefficient of the corresponding k +1 th weak classifier is
Wherein Z is k Is a normalization factor
From w k+1 As can be seen from the calculation formula, if the ith sample is classified incorrectly, I in the formula i G k (T i )<0, resulting in the weight of the sample increasing in the (k + 1) th weak classifier and decreasing in the (k + 1) th weak classifier if the classification is correct. The adaboost classification adopts a weighting voting method, and the final strong classifier is as follows:
the above is the principle of adaboost classification, which is the principle of "three smelly skinners racing the good sight" that is a strong classifier constructed by a plurality of boost classifiers through a weighted voting method. The construction process is packaged into a fixesemble function in matlab, and the fitesemble function can be used only by selecting proper parameters.
The fourth step: and training and verifying the adaboost proxy model, so that the adaboost proxy model can be accurately classified according to the array characteristics. The input set T is divided into two groups, one training set T 1 The other group is a test set T 2 The number of samples in the training set and the test set is N 1 ，N 2 Is full ofFoot N 1 +N 2 400, the response sets corresponding to the training set and the test set are I respectively 1 ，I 2 . By T 1 As input vector of adaboost, in T 1 Corresponding response set I 1 As an input response, the adaboost model is trained. Then, T is added 2 And inputting the trained adaboost model, and recording the output result as I. Defining error difference:
when e is k When 0 indicates correct classification, e k When not equal to 0, a classification error is indicated. The accuracy P of the adaboost model can be calculated by equation (12).
Because of the difference of the training set and the test set, the difference of the model precision can be caused, in order to make the model reach the best precision, the number of samples contained in the training set is increased progressively, the number of samples contained in the test set is decreased progressively, and seven groups of tests are performed totally. The obtained correspondence is shown in table 2. From the results in Table 2, it can be seen that the number of samples N in the training set is N 1 And the model has the highest precision when 270% is taken, and the precision is 98.46%.
Table 2: selecting different N 1 Model accuracy corresponding to the value
The model precision difference obtained by different grouping modes of the test set and the training set in the table is not large, but in the process of calculating the failure probability of a mechanism, the Monte Carlo method has large sampling times (generally 10) 5 Above) that a small error in the model results in a lot of erroneous classifications, which is unacceptable, and therefore it is necessary to find the model with the highest accuracy. It can be seen from the table that the third set of models is the most accurate,98.46 percent, can meet the requirement.
The last verification shows that the adaboost algorithm can accurately find out the failure surface of the plane woven panel honeycomb sandwich structure, the calculation amount can be greatly reduced, the time is saved, and the reliability analysis and the parameter sensitivity calculation of the structure can be conveniently carried out subsequently.
While the invention has been described with reference to specific embodiments, the invention is not limited thereto, and various equivalent modifications or substitutions can be easily made by those skilled in the art within the technical scope of the present disclosure.
Claims (3)
1. A failure surface simulation method of a plane woven panel honeycomb sandwich structure based on an adaboost algorithm is characterized by comprising the following steps:
s1: sampling by utilizing Latin hypercube sampling according to the mean value and standard deviation of the parameters to generate a sample set N; the parameter is the longitudinal elastic modulus E of the material 11 Modulus of elasticity E in weft of Material 22 Material longitudinal shear modulus G 12 Material latitudinal shear modulus G 13 Longitudinal tensile strength X of single-layer plate t Weft tensile strength Y t Radial compressive strength X of single-layer board c Compressive strength Y in weft c Longitudinal shear strength S of single-layer plate 12 Weft shear strength S 13 The panel thickness d;
s2: sequentially inputting the sample sets N corresponding to the parameters in S1 into a model of the plane woven panel honeycomb sandwich structure, and calculating by using ABAQUS finite element analysis software to obtain the lateral maximum bearing capacity F of the structure;
s3: taking 21KN as a threshold, judging that the structure is failed when the maximum bearing capacity F is greater than 21KN, otherwise, judging that the structure is safe; assigning a value of the maximum bearing force F larger than 21KN as '1', and assigning the rest as '0'; recording the assignment result as a response I;
s4: combining the sample set N with the response I to generate a sample pool P of adaboost, then dividing P into a training set and a testing set,wherein the training set comprises N 1 Set of input parameters and N 1 Response quantity I 1 The test set contains N 2 An input parameter and N 2 Response quantity I 2 ，N 1 +N 2 ＝N；
S5: 11 parameters in the training set as input quantities, I 1 As a response quantity; training an adaboost model through training set data corresponding to the parameters and the corresponding response quantity, and searching for a failure surface of the plane woven panel honeycomb sandwich structure; finally, obtaining a failure surface of the plane woven panel honeycomb sandwich structure based on the adaboost model simulation;
s6: test set N 2 The 11 input parameters are used as input quantities and are substituted into the trained adaboost model to generate an output value I out The output value is compared with the response I in the test set 2 Comparing, and calculating to obtain the precision of the adaboost model;
s7: by adjusting training set N 1 And test set N 2 Finding the combination with the highest adaboost model precision according to the sample proportion; the failure surface of the plane woven panel honeycomb sandwich structure is replaced by the adaboost model.
2. A computer system, comprising: one or more processors, a computer readable storage medium, for storing one or more programs, wherein the one or more programs, when executed by the one or more processors, cause the one or more processors to implement the method of claim 1.
3. A computer-readable storage medium having stored thereon computer-executable instructions for, when executed, implementing the method of claim 1.
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