Prediction of Concrete Meso-Model Stress-Strain Curves Based on GoogLeNet
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摘要:
非均质复合材料的宏观力学性能往往取决于细观组分的分布方式和力学性能，但是建立明确的关系表达式极其困难。为了应对这一挑战，以混凝土为研究对象，提出了一种基于深度学习的策略，能够高效、准确地通过细观模型图像信息获取应力-应变曲线。首先，使用基于卷积神经网络（convolutional neural network，CNN）的GoogLeNet模型进行图像信息识别和提取，并针对应力-应变曲线的复杂性特点，进行了数据预处理操作，并且设计了相应的多任务损失函数。数据集中的细观模型图像采用基于Monte-Carlo的随机骨料模型生成，并且使用数值模拟试验获取对应细观模型的单轴压缩应力-应变曲线。最后，通过对神经网络的训练和测试评估了所提出方法的可行性。结果表明，GoogLeNet模型训练效率和预测精度均优于AlexNet和ResNet模型，具有良好的泛化能力和鲁棒性。
Abstract:Generally, the macro-scopic mechanical properties of heterogeneous composites depend on meso-components’ distribution and mechanical properties, but it is extremely difficult to establish a clear macro-meso relationship expression. To cope with this challenge, for concrete, a strategy based on deep learning was proposed to obtain the stress-strain curves through meso-model image information. First, the GoogLeNet model based on convolutional neural networks was used for image information recognition and extraction. According to the complexity of the stress-strain curve, data preprocessing operations were performed and the corresponding multi-task loss function was designed. The meso-model images in the data set were generated with the random aggregate model based on the Monte Carlo method, and numerical simulation experiments were conducted to obtain the uniaxial compressive stress-strain curve of the corresponding meso-model. Finally, the feasibility of the proposed method was evaluated through training and testing. The training efficiency and prediction accuracy of the GoogLeNet model are better than the AlexNet and ResNet models, and have good generalization ability and robustness.
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Key words:
- concrete /
- meso-model /
- GoogLeNet /
- convolutional neural network /
- stress-strain curve
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图 3 激活函数：(a) sigmoid；(b) tanh；(c) Leaky ReLU；(d) ReLU
Figure 3. Activation functions: (a) sigmoid; (b) tanh; (c) Leaky ReLU; (d) ReLU
图 8 训练集和验证集损失曲线：(a)训练集损失曲线；(b)验证集损失曲线
Figure 8. Loss curves of the training set and the validation set: (a) the loss curve of the training set; (b) the loss curve of the validation set
图 9 部分测试集的预测结果和数值计算结果对比：(a) 骨料体积分数39%，孔隙率1%；(b) 骨料体积分数39%，孔隙率6%；(c) 骨料体积分数39%，孔隙率9%；(d) 骨料体积分数40%，孔隙率1%；(e) 骨料体积分数40%，孔隙率3%；(f) 骨料体积分数40%，孔隙率8%
Figure 9. Comparison of prediction results with numerical test data: (a) aggregate volume fraction at 39%, porosity at 1%; (b) aggregate volume fraction at 39%, porosity at 6%; (c) aggregate volume fraction at 39%, porosity at 9%; (d) aggregate volume fraction at 40%, porosity at 1%; (e) aggregate volume fraction at 40%, porosity at 3%; (f) aggregate volume fraction at 40%, porosity at 8%
11 预测结果：(a) 峰值应力预测值；(b) 峰值应力预测值误差；(c) 弹性模量预测值；(d) 弹性模量预测值误差
11. Predictions: (a) peak stress prediction; (b) errors of peak stress prediction; (c) elastic modulus prediction; (d) errors of elastic modulus of prediction
表 1 细观组分的力学参数
Table 1. Mechanical parameters of meso-compositions
item Poisson’s ratio υ Young’s modulus E / GPa compressive strength fc / MPa tensile strength ft / MPa aggregate 0.23 43 − − mortar 0.2 25 35 3.5 
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表 2 各卷积神经网络模型的对比
Table 2. Comparison of CNN models
CNN epoch number of layers model size validation
losstime GoogLeNet 100 22 23.1 MB 1.016 2308.0 s AlexNet 100 8 223 MB 6.139 3826.2 s ResNet50 100 50 90.6 MB 1.773 6263.8 s
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