WO2023115596A1

WO2023115596A1 - Truss stress prediction and weight lightening method based on transfer learning fusion model

Info

Publication number: WO2023115596A1
Application number: PCT/CN2021/141474
Authority: WO
Inventors: 彭翔; 邵宇杰; 李吉泉; 姜少飞
Original assignee: 浙江工业大学台州研究院
Priority date: 2021-12-21
Filing date: 2021-12-27
Publication date: 2023-06-29
Also published as: CN114239114A

Abstract

A truss stress prediction and weight lightening method based on a transfer learning fusion model. The method comprises: taking the cross-sectional area and a material as design parameters, and performing uncertainty quantification to establish a source data set; inputting the source data set into a finite element model for constructing a multi-linkage truss, so as to obtain low- and high-fidelity models; performing random sampling on the low- and high-fidelity models to obtain fidelity points, so as to construct and obtain target data; inputting data of the low-fidelity model into a deep neural network (DNN) model for preliminary training, so as to determine model parameters; retaining the first (n-1) layers, initializing the last layer, re-training and correcting data of the high-fidelity model, and optimizing the number of network nodes, so as to obtain a fusion agent model; and inputting actual data into the fusion agent model for processing, and outputting the target data. The method reduces construction costs while guaranteeing the generalization capability of a deep neural network by pre-training the deep neural network using low-fidelity sampling points; and when the number of high-fidelity sampling points is small, a high-precision agent model can also be constructed, thereby improving the reliability of a weight-lightening design for a truss structure.

Description

A truss stress prediction and lightweight method based on transfer learning fusion model

technical field

The invention relates to a finite element processing method for a truss, in particular to a method for predicting target parameters of a truss node and lightweight design based on a transfer learning fusion model.

Background technique

The truss structure is a high-performance structure that facilitates structural design. Due to the special advantages of the truss structure, it is widely used in high-speed railways, airports, bridges and other buildings. With the application of finite element analysis methods, optimization algorithms and computer technology, the research on the optimal design of multi-bar truss structures has also made great progress. The high dimensionality of parameter space, large amount of search, and numerous local optimum points bring challenges to the uncertainty analysis of high-dimensional truss structures. Meanwhile, most existing surrogate modeling techniques cannot scale to high-dimensional problems, and the number of training samples grows exponentially with the input dimensionality.

Contents of the invention

The purpose of the present invention is to solve the problem that multi-bar trusses have high design parameter dimensions and low precision of ordinary proxy models, provide a method for constructing truss structure fusion proxy models based on transfer learning, and realize lightweight design of trusses.

In order to achieve the above object, as shown in Figure 1, the technical scheme of the present invention is as follows:

1) For the multi-bar truss, choose the cross-sectional area and material as the design parameters, quantify the uncertainty of the design parameters of the multi-bar truss, and establish the source data set;

The multi-bar truss is built by connecting rods. Each rod has its own cross-sectional area and material. Different rods can be set with different cross-sectional areas and materials, or the same cross-sectional area and material can be set.

2) Input the source data set obtained in step 1) to construct a finite element model of a multi-bar truss to obtain a low-fidelity model (LFM) and a high-fidelity model (HFM);

3) Perform random sampling for the low-fidelity model and the high-fidelity model, obtain m low-fidelity points in the low-fidelity model and n high-fidelity points in the high-fidelity model, and construct the target data; the low-fidelity points and Stress data is included in the high-fidelity points, which can be used to characterize the stress and displacement of the truss nodes.

In the above 3), the number of low-fidelity points is far greater than the number of high-fidelity points, specifically ten times or more.

4) Construct a deep neural network DNN model, input the source data set and target data of the low-fidelity model into the deep neural network DNN model for preliminary training and determine the model parameters θ={W ^(j) ,b ^(j) } ^L+1 , initialize the DNN;

5) According to 4), determine the deep neural network DNN model after the model parameter θ={W ^(j) , b ^(j) } ^L+1 , retain the network structure of the first n-1 layers, and n is represented by the deep neural network DNN The total number of layers in the model, initialize the parameters in the network structure of the last layer, the parameters are weights and deviations;

Input the source data set and target data of the high-fidelity model to train again, modify the parameters of the last layer of network structure, compare the influence of different network node numbers on the model accuracy, and obtain the optimal network node number within the set range, Get the fused proxy model applied to the truss;

In a specific implementation, the error of the fused proxy model is calculated. The model accuracy was evaluated by calculating the root mean square error RRMSE and ^R2 of the predicted value and the true value of the test set.

6) After obtaining the fusion proxy model that meets the accuracy requirements, the actual cross-sectional area and material of the multi-bar truss are input into the fusion proxy model to process the output target data, which is used to represent the stress prediction results and the displacement of the truss nodes, and then pass the genetic The optimization algorithm realizes the optimal design of the multi-bar truss under the constraint of node displacement, that is, realizes light weight.

In the above 1), the uncertainty quantification is specifically to set the cross-sectional area of the bar to conform to the normal distribution A _i ∼N(10 ^-4 ,10 ^-5 ), and pre-select three alternative materials. In specific implementation, the three alternative materials are low alloy steel Q235, common structural steel Q345 and 45#.

The 2) is specifically,

The input of the design parameters after the uncertainty quantification and the large grid size are used to construct the low-fidelity model by using the coarse-grid multi-bar truss finite element model; the specific implementation of the smaller grid size is 10cm.

The input of the design parameters after the uncertainty quantification and the smaller grid size are used to construct the high-fidelity model by using the fine-grid multi-bar truss finite element model. A smaller grid size of 0.1 cm was implemented.

The invention establishes a low-fidelity model and a high-fidelity model at the same time. The high-fidelity model has higher model accuracy than the low-fidelity model, but the low-fidelity model can obtain a large number of sample points in the design space in a shorter time, and has the advantages of Higher model computational efficiency.

The deep neural network DNN model in the above 4) is a neural network composed of multiple hidden layers. Each layer of the neural network contains different parameters and is connected to the next layer. The input of the jth layer is transformed by the activation function is the output signal, the jth hidden layer is calculated as:

Among them, W ^{(j) and} b ^(j) are the weights and deviations before the deep neural network DNN model training, j represents the position of the hidden layer, z ^(j) represents the output of the jth hidden layer, and L represents the hidden layer The number of , f() is the activation function.

In the deep neural network DNN model, the linear rectified unit (ReLU) function is used as the activation function of each layer.

In the 4) training process, the loss function is used for comparative optimization, the error value is calculated for each neuron in the output layer, and the model parameter θ is obtained by minimizing the loss function. The model parameter θ contains the weight W ^(j) and bias b ^(j) , the loss function is computed as:

Among them, E(θ) represents the final loss function output value corresponding to θ, i represents the ordinal number of the training data, E _i represents the loss function value corresponding to the i-th group of training data, N represents the total number of training data groups,

Indicates the real output value of the Nth group of training data,

Indicates the predicted output value of the Nth group of training data,

Indicates the real input value of the Nth group of training data;

When minimizing the loss function, the stochastic gradient descent algorithm is used to optimize the solution to obtain the parameters of the weight W ^(j) and deviation b ^(j) of the deep neural network DNN model, and the parameters are updated through the adaptive moment Adam algorithm.

Through the genetic optimization algorithm, the optimal design of the multi-bar truss is realized under the constraints of the node displacement, which is calculated according to the following formula:

M＝L ₁ ρA ₁ ² +L ₂ ρA ₂ ² +L ₃ ρA ₃ ² +...+L _i ρA _i ²

Among them, M represents the total mass of the truss, i represents the i-th rod group, L _i represents the length of the i-th rod group, A _i represents the cross-sectional area of the i-th rod group, and ρ represents the material density. Therefore, the weight reduction of the truss is realized through the adaptive genetic algorithm.

First, the present invention extracts the knowledge of the source domain (Source Domain) from a large-scale low-fidelity data set, and constructs a pre-training model. Then, the learned knowledge is transferred to the new model, which is retrained with the information of the target dataset (small-scale high-fidelity dataset). Finally, optimize the hyperparameters of the retrained network, and use hyperparameter optimization to alleviate overfitting, that is, the choice of learning rate, momentum factor, activation function and number of nodes. Such an approach could ultimately lower the barriers to using transfer learning for institutional reliability analysis.

The beneficial effects of the present invention are as follows:

1) The present invention starts from the higher dimensionality of the design parameters, and uses transfer learning to pre-train the deep neural network through low-fidelity sampling points on the problem of high acquisition cost of high-fidelity sampling points, ensuring the generalization ability of the deep neural network At the same time, it reduces the construction cost of the neural network agent model;

2) Compared with the traditional surrogate model, the fusion surrogate model can still achieve higher model calculation accuracy while ensuring low cost. When the number of high-fidelity sampling points is small, a high-precision proxy model can also be constructed;

3) The idea of transfer learning is used, which greatly reduces the burden on designers and computers, greatly improves calculation efficiency, improves the reliability of lightweight design of truss structures, and is more in line with practical engineering applications.

Description of drawings

Fig. 1 is method flowchart of the present invention;

Fig. 2 is the multi-bar truss schematic diagram of embodiment;

Fig. 3 is a comparison diagram of fusion model and common multi-perceptron neural network;

Figure 4 is a comparison diagram of the optimization of the number of fusion model nodes;

Figure 5 is a comparison diagram of the fusion model activation function optimization;

Fig. 6 is a comparison chart of fusion model learning function optimization;

Fig. 7 is a schematic diagram of a 10-bar truss structure;

Fig. 8 is a schematic diagram of a 25-bar truss structure;

Fig. 9 is a schematic diagram of a 72-bar truss structure;

Fig. 10 is the cloud diagram of finite element analysis under sparse mesh division of ten-bar truss;

Figure 11 is the cloud diagram of the finite element analysis under the fine mesh division of the ten-bar truss.

Detailed ways

The present invention will be further described below in conjunction with the accompanying drawings and specific implementation.

As shown in Figure 1, according to the embodiment that the complete method of the present invention implements and its implementation situation are as follows:

This embodiment takes a 10-bar truss as an example, and builds a multi-fidelity proxy model based on the idea of transfer learning. This method can also be applied to multi-bar truss structures such as 25-bar, 72-bar, and 200-bar.

An example of a ten-bar truss is shown in Figure 2, which shows the geometry, load and support conditions of the truss. The material density and elastic modulus are 0.1lb/in ³ (2768.0kg/m ³ ) and 10000ksi (68950MPa) respectively , Applied loads P1, P2, P3 are shown in the figure.

In a machine learning problem, a dataset is divided into two parts, a training set and a test set. The former is a set of examples for learning, and the latter is a new set of data just for evaluating generalization.

In the present invention, the training set constructed by the ten-bar truss fusion model is generated by the random distribution of the design variables (cross-sectional area, applied load) of the multi-bar truss bar set, and the cross-sectional area of the bar set ranges from 0.1 to 35.0in2 (from 0.6 to 225.8 cm2), all input data were normalized with respect to the regularized maximum cross-sectional area of 35.0. And according to the finite element analysis grid division with different densities (0.1cm2 and 10cm2 were used as the basic grid division), 1000 sets of low-fidelity data sets and 100 sets of high-fidelity data sets were obtained for training neural networks. Among them, the grid division method and the schematic diagram of the finite element analysis under the corresponding grid division are shown in Fig. 10 and Fig. 11. Fig. 10 shows the cloud diagram of the finite element analysis under the ten-bar truss sparse mesh division, and Fig. 11 shows the fine mesh of the ten-bar truss Cloud diagram of finite element analysis under grid division. 1000 sets of low-fidelity data sets were used for network pre-training, and the network parameters of the first (n-1) layer of the hidden layer were retained by using model fusion technology, and 100 sets of high-fidelity data sets were used for retraining, and finally a model based on ten Fusion Modeling of Rod-Truss Structures.

Figure 3 compares the model fusion method (training data is 1000 sets of low-fidelity data sets and 100 sets of high-fidelity data sets) and the general multi-perceptron neural network (training data is 1000 sets of high-fidelity data sets) method as the number of iterations increases. The process of gradually improving the accuracy. It can be seen that when the cost of building high-fidelity data sets is high for the model fusion method, using a small number of high-fidelity data sets can also make the neural network of model fusion have higher accuracy and better generalization ability. In addition, the hyperparameters (number of nodes, activation function, and learning function) of the fusion model can be optimized. Figure 4, Figure 5, and Figure 6 compare the impact of different numbers of nodes, activation functions, and learning functions on the accuracy of the fusion model to further improve The computational efficiency and accuracy of the fusion model are improved. And the final fusion model obtained is that the number of hidden layer nodes is 25, the activation function is logsig, and the optimal fusion model can be obtained when the learning function is trainlm. Under the guidance of the fusion model, the genetic optimization algorithm is used to optimize the design parameters of the ten-bar truss under the constraints of cost and node displacement to achieve the lightweight design requirements. In addition, the fusion model is not only suitable for the construction of proxy models for ten-bar trusses (as shown in Figure 7), but also for the construction of proxy models for multi-bar trusses such as 25 and 72 bars. The structures of 25 and 72 bars are shown in Figure 8. Figure 9 shows.

Claims

A truss stress prediction and lightweight method based on transfer learning fusion model, characterized in that:

1) For the multi-bar truss, choose the cross-sectional area and material as the design parameters, quantify the uncertainty of the design parameters of the multi-bar truss, and establish the source data set;

2) Input the source data set obtained in step 1) into the finite element model of building a multi-bar truss to obtain a low-fidelity model and a high-fidelity model;

3) randomly sampling the low-fidelity model and the high-fidelity model, obtaining m low-fidelity points in the low-fidelity model and n high-fidelity points in the high-fidelity model, and constructing and obtaining target data;

4) Construct a deep neural network DNN model, input the source data set and target data of the low-fidelity model into the deep neural network DNN model for preliminary training and determine the model parameters θ={W (j) ,b (j) } L+1 ;

5) According to 4), determine the deep neural network DNN model after the model parameter θ={W (j) , b (j) } L+1 , retain the network structure of the first n-1 layers, and n is represented by the deep neural network DNN The total number of layers in the model, initialize the parameters in the network structure of the last layer;

Input the source data set and target data of the high-fidelity model to train again, modify the parameters of the last layer of network structure, compare the influence of different network node numbers on the model accuracy, and obtain the optimal network node number within the set range, Get the fused proxy model applied to the truss;

6) After the fusion proxy model is obtained, the actual cross-sectional area and material of the multi-bar truss are input into the fusion proxy model to process the output target data, which is used to represent the stress prediction results and the displacement of the truss nodes, and then through the genetic optimization algorithm in the The optimal design of multi-bar truss is realized under the constraints of node displacement.
A truss stress prediction and lightweight method based on transfer learning fusion model according to claim 1, characterized in that: in said 1), the uncertainty quantification is specifically to set the cross-sectional area of the bar to conform to the normal distribution A i ~N(10 -4 ,10 -5 ), pre-select three candidate materials.
A kind of truss stress prediction and lightweight method based on transfer learning fusion model according to claim 1, characterized in that: said 2) is specifically,

Input the design parameters after quantifying the uncertainty and use the coarse grid multi-bar truss finite element model to construct a low-fidelity model;

The input of the design parameters after the uncertainty quantification and the smaller grid size are used to construct the high-fidelity model by using the fine-grid multi-bar truss finite element model.
A kind of truss stress prediction and lightweight method based on migration learning fusion model according to claim 1, characterized in that: the deep neural network DNN model in said 4) is a neural network composed of multiple hidden layers, neural network Each layer of the network contains different parameters and is connected to the next layer. The input of the jth layer is converted into an output signal through the activation function. The jth hidden layer is calculated as:

Among them, W (j) and b (j) are the weights and deviations of the DNN model in the deep neural network, j represents the position of the hidden layer, z (j) represents the output of the jth hidden layer, and L represents the number of hidden layers , f() is the activation function.
A kind of truss stress prediction and lightweight method based on transfer learning fusion model according to claim 1, characterized in that: in the 4) training process, use the loss function to compare and optimize, for each in the output layer The neuron calculates the error value, and the model parameter θ is obtained by minimizing the loss function. The model parameter θ includes the weight W (j) and the deviation b (j) . The loss function is calculated as:

Among them, E(θ) represents the final loss function output value corresponding to θ, i represents the ordinal number of the training data, E i represents the loss function value corresponding to the i-th group of training data, N represents the total number of training data groups,
Indicates the real output value of the Nth group of training data,
Indicates the predicted output value of the Nth group of training data,
Indicates the real input value of the Nth group of training data;

When minimizing the loss function, the stochastic gradient descent algorithm is used to optimize the solution to obtain the parameters of the weight W (j) and deviation b (j) of the deep neural network DNN model, and the parameters are updated through the adaptive moment Adam algorithm.
A truss stress prediction and lightweight method based on transfer learning fusion model according to claim 1, characterized in that: the optimal design of multi-bar truss is realized under the constraints of node displacement through genetic optimization algorithm, specifically Calculate according to the following formula:

M＝L 1 ρA 1 2 +L 2 ρA 2 2 +L 3 ρA 3 2 +...+L i ρA i 2

Among them, M represents the total mass of the truss, i represents the i-th rod group, L i represents the length of the i-th rod group, A i represents the cross-sectional area of the i-th rod group, and ρ represents the material density.