PREDICTION OF CONCRETE MESO-MODEL COMPRESSION STRESS-STRAIN CURVE BASED ON “AM-GOOGLENET + BP” COMBINED DATA-DRIVEN METHODS
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摘要:本文结合GoogLeNet卷积神经网络和BP神经网络分别在图像数据挖掘和数据分析方面的良好性能, 采用“AM-GoogLeNet + BP”联合数据驱动方法, 对混凝土细观模型(含砂浆、骨料及孔隙)的单轴压缩应力−应变曲线进行了有效预测. 通过引入力学参量对图像数据驱动的训练结果进行优化, 从而提升了神经网络的物理可解释性. 基于Python语言实现混凝土细观模型在Abaqus中的自动建模及细观图像生成过程, 并将生成的细观图像数据库与相应的压缩应力−应变曲线作为训练数据集. 在GoogLeNet中分别引入SENet, ECANet和CBAM三种代表性注意力机制并对三种注意力机制的性能进行对比和分析, 以自适应方式提升神经网络对混凝土各相组分的分析能力, 并以此得到混凝土细观模型的初步应力−应变预测曲线; 将骨料体积分数、孔隙率及初步峰值应力等物理参量作为输入引入BP神经网络以改善峰值应力的预测精度, 并与将物理参量直接引入卷积神经网络输入层的方法进行了对比, 最后定量给出了骨料体积分数和孔隙率对峰值应力的影响权重. 结果表明, 对于不同骨料体积分数及孔隙率的混凝土细观模型, 该方法均展现了较高的预测精度. 本文采用的“AM-GoogLeNet + BP”联合数据驱动预测模型从统计角度解决了传统方法对细观尺度参量分析的复杂性, 为复合材料的跨尺度力学行为研究提供了新思路.Abstract:This paper uses the “AM-GoogLeNet + BP” combined data-driven methods to predict the uniaxial compression stress-strain curve of the concrete meso-model (including mortar, aggregates, porosity) effectively by combining the good performance of GoogLeNet convolutional neural network and BP neural network in image data mining and data analysis, respectively. The physical interpretability of the neural network is improved by introducing the mechanical parameters to optimize the image data-driven training results. The automated modeling of the concrete meso-model in Abaqus and microscopic image generation process are realized by Python language, and the generated mesoscopic image database and the corresponding compression stress–strain curves are used as the training dataset. Three typical attention mechanisms, SENet, ECANet and CBAM, are introduced into GoogLeNet respectively to enhance the analysis ability of neural network for each phase of concrete in an adaptive manner and the performance of the three attention mechanisms is compared and analyzed. The initial stress-strain prediction curves of the concrete meso-model are obtained with this method; In order to improve the prediction accuracy of the peak stress, the physical parameters such as aggregate volume fraction, porosity and initial peak stress are introduced into BP neural network as inputs. It is also compared with the method of introducing the physical parameters directly into the convolutional neural network input layer. At the same time, the weight of influence of aggregate volume fraction and porosity on peak stress is given quantitatively. The results show that this method has high prediction accuracy for the concrete meso-model with different aggregate volume fraction and porosity. In this paper, the “AM-GoogLeNet + BP” combined data-driven prediction model is used to solve the complexity of the traditional method in the analysis of mesoscale parameters from the statistical point of view, which provides a new idea for the study of the cross-scale mechanical behavior of composite materials.
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Key words:
- concrete/
- neural network/
- data-driven/
- meso-model/
- uniaxial compression
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图 5混凝土(a)细观有限元模型和(b) RGB格式图像
Figure 5.(a) The mesoscopic finite element model of concrete and (b) the image in RGB format
图 6不同骨料体积分数和孔隙率下的部分数据集
Figure 6.The partial image dataset with different aggregate volume fraction and porosity
图 8不同 GoogLeNet的训练结果对比
Figure 8.The comparison of the training results of different GoogLeNets
图 9不同骨料体积分数和孔隙率下的CBAM-GoogLeNet预测结果
Figure 9.The prediction results of CBAM-GoogLeNet with different aggregate volume fraction and porosity
9不同骨料体积分数和孔隙率下的CBAM-GoogLeNet预测结果 (续)
9.The prediction results of CBAM-GoogLeNet with different aggregate volume fraction and porosity (continued)
图 10CBAM-GoogLeNet测试集峰值应力预测结果
Figure 10.The prediction results of the peak stress of the CBAM-GoogLeNet
图 11引入物理参量的CBAM-GoogLeNet训练过程
Figure 11.The training process of the physics CBAM-GoogLeNet
图 12BP神经网络架构、训练过程和结果评估
Figure 12.The architecture, training process and results evaluation of the BP neural network
表 1两种细观组分的力学参量
Table 1.Mechanical parameters of the two meso-components
Elasticity modulus
E/GPaPoisson’s ratio
υCompressive strength
Fc/MPaDensity
ρ/(t·m−3)Dilatancy angle
Ψ/(º)Eccentricity
η/%Stress ratio
σb0/σc0aggregate 43 0.23 − 2.67 − − − mortar 25 0.2 35 2.40 38 0.1 1.16 
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表 2试验环境的硬件和软件参数
Table 2.Hardware and software parameters of the experimental environment
Name Parameters central processing unit Inter Core i7-11800 H CPU @ 2.3 GHz memory DDR4 memory 8 GB graphics card NIVIDA GeForce RTX3060 system Windows 10 environment Python 3.6 TensorFolw 2.8.0 Keras 2.8.0 NUMPY 1.22.2 compute unified device architecture CUDA 11.2 下载:
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表 3不同GoogLeNet的训练过程参数
Table 3.The training process parameters of different GoogLeNet
CNN Parameters of AM Total parameters Model size/MB Epoch Time/s Validation loss GoogLeNet − 6015577 22.95 50 6254 1.2454 SE-GoogLeNet 8352 6541145 24.95 50 6466 1.2070 ECA-GoogLeNet 5 6015582 22.95 50 6321 1.3250 CBAM-GoogLeNet 4194 6277819 23.95 50 6280 1.2053 下载:
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表 4BP神经网络的权重和偏置值
Table 4.The weights and biases of BP neural network
Neurons Winput Bias Woutput Bias Peak stress Volume fraction Porosity 1 −0.00172 −0.12354 0.59741 −2.15972 −2.69027 1.21105 2 −0.17380 1.08733 −0.53564 1.61095 2.00213 3 −1.36082 0.33879 0.01926 1.44915 1.63320 4 0.33198 −1.49304 0.67236 1.67449 1.40409 5 0.03562 −0.19979 −1.14093 1.75658 1.35286 6 1.12495 −0.56972 −1.04270 1.19552 1.38380 下载:
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