Slope reliability analysis based on deep learning of digital images of random fields using CNN
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摘要: 考虑土体强度空间变异性，提出了数字图像化随机场特征深度学习模型并进行边坡稳定可靠度分析。通过Karhunen-Loeve展开法离散边坡土体随机场并将离散结果转化为数字图像，建立起随机场图像与边坡功能函数值之间隐式关系的卷积神经网络（CNN）代理模型，进而计算随机场数字图像表征后边坡的失效概率。在建立CNN代理模型时，采用拉丁超立方抽样、贝叶斯优化和五折交叉验证以提高精度。最后以单层不排水饱和黏土边坡和双层黏性土边坡为例说明了该方法的有效性。结果表明：在随机场高维表征图像化和边坡小概率失稳情况下，所提CNN深度学习模型能够比较精确地逼近真实边坡稳定性计算结果，进而显著提高考虑随机场模拟的边坡可靠度分析计算效率。Abstract: Considering the spatial variability of soil strength, a deep learning model for the characteristics of random fields is proposed for reliability analysis of slope stability. The random fields of a soil slope are discretized by the Karhunen-Loeve expansion method, and the discretized results are converted into digital images. Then, a convolutional neural network (CNN) surrogate model is established to approach the implicit relationship between the images and the responses of the performance function. Based on the surrogate model, the probability of failure of the slope is calculated. When training the CNN surrogate model, the Latin-Hypercube sampling technique, Bayesian optimization and 5-fold cross-validation are employed to improve the accuracy. Finally, the effectiveness of the proposed method is demonstrated by two case studies, namely a single-layer saturated clay slope under undrained conditions and a two-layered cohesive soil slope. The results show that in the case of high dimensions and small probability, the proposed CNN deep learning model can approximate the original model accurately, and significantly reduce the computational cost of slope reliability analysis considering the simulation of the random fields.
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图 2 基于随机场图像和卷积神经网络的边坡可靠度分析流程
Figure 2. Flow chart of slope reliability analysis using random field images and CNN
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图 3 单层饱和黏土边坡确定性分析结果(最大剪应变增量)
Figure 3. Deterministic analysis of a single layer clay slope under undrained condition (maximum shear strain increment)
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图 4 随机场离散精度与KL展开截断项数的关系（离散域: Lh=30 m，Lv=10 m）
Figure 4. Relationship between discretization accuracy and number of KL truncation terms (discrete domain: Lh=30 m,Lv=10 m)
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图 5 随机场离散的一次实现（a）和预处理后的灰度图像(b)
Figure 5. One realization of random fields (a) and corresponding gray image after preprocessing (b)
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图 7 验证集最小MAE与贝叶斯优化次数的关系
Figure 7. Relationship between minimum MAE of validation set and times of Bayesian optimization
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图 9 边坡Fs的真实值（FDM）和预测值（CNN五折交叉验证）的对比
Figure 9. Comparison of Fs of slope between FDM and CNN 5-fold cross validation
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图 10 CNN与FDM的Fs经验累积分布函数对比
Figure 10. Comparison of empirical cumulative distribution function of Fs between CNN and FDM
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图 11 双层黏性土边坡确定性分析结果(最大剪应变增量)
Figure 11. Deterministic analysis results of two-layered cohesive soil slope (maximum shear strain increment)
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图 12 双层黏性土边坡随机场的一次实现
Figure 12. One realization of random fields for two-layered cohesive soil slope
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图 13 双层黏性土边坡工况3的Fs经验累积分布函数
Figure 13. Empirical cumulative distribution function of Fs under condition 3 of two-layered cohesive soil slope
表 1 贝叶斯优化的CNN超参数
Table 1 Bayesian optimization of CNN hyperparameters
超参数 优化区间 默认值 最优超参数 初始学习率 [0.0001, 0.01] 0.001 0.0010763 L2正则化系数 [1×10-8, 1×10-2] 0.0001 0.0045945 丢弃率 [0.2, 0.6] 0.5 0.24031 滤波器数量Nf 8~32 — 16 
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表 2 单层不排水饱和黏土边坡可靠度分析结果的比较
Table 2 Comparison of reliability results of single-layer undrained clay slope
概率方法 Fs模型 样本数量 Fs均值 Fs标准差 Pf β LHS FDM 2000 1.240 0.205 0.104 1.259 CNN-LHS FDM 100 1.236 0.203 0.107 1.243 MCS BSM 100000 1.267 0.199 0.076 1.433
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表 3 双层黏性土边坡的统计参数
Table 3 Statistics parameters of two-layered cohesive soil slope
工况 c1/kPa φ1/(°) c2/kPa φ2/(°) 分布类型 自相关函数 相关距离/m 相关系数ρcφ 重度/(kN⋅m - 3) 弹性模量E/MPa 泊松比 均值 变异系数 均值 变异系数 均值 变异系数 均值 变异系数 水平 垂直 γ1 γ2 1 28 0.3 5 0.2 34 0.3 10 0.2 对数正态 高斯型 40 4 -0.5 19 20 100 0.3 2 0.3 0.2 0.3 0.2 指数型 3 0.2 0.1 0.2 0.1
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表 4 双层黏性土边坡可靠度分析结果的比较
Table 4 Comparison of reliability results of two-layered cohesive soil slope
工况 概率方法 样本数量 Fs
均值Fs标
准差Pf β 1 LHS（基准） 1×104 1.172 0.122 0.0691 1.483 SIR-MARS-MCS 150 1.175 0.125 0.0674 1.495 CNN-LHS（本文） 100 1.181 1.125 0.0678 1.492 2 LHS（基准） 1×104 — — 0.0297 1.885 CNN-LHS（本文） 200 1.217 1.120 0.0308 1.869 LHS（测试） 1000 1.222 1.124 0.0300 1.881 CNN-LHS（本文） — 1.218 1.121 0.0320 1.852 3 LHS（基准） 1×105 — — 6.2×10-4 3.230 CNN-LHS（本文） 600 1.261 0.088 6.4×10-4 3.220 LHS（测试） 400 1.255 0.099 0 — CNN-LHS（本文） — 1.259 0.096 0 —
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