CNN-LSTM模型在边坡可靠度分析中的应用

doi:10.11872/j.issn.1005-2518.2023.04.171

摘要/Abstract

摘要：

为了准确高效地对边坡可靠度进行分析，在对420个边坡数据进行整理分析的基础上，建立了基于卷积神经网络（Convolutional Neural Network，CNN）与长短时记忆网络（Long Short-Term Memory，LSTM）的混合可靠度分析模型。首先，通过CNN模块提取数据特征；其次，构建LSTM模块并对边坡失效概率进行预测；然后，通过5因素4水平正交表L₁₆对模型超参数进行优化；最后，通过2个算例进行对比验证。结果表明：（1）相比传统的蒙特卡洛法（MCS），CNN-LSTM模型预测失效概率相对误差仅为4.35%，而一次二阶矩法和响应面法相对误差为169.6%；在计算耗时方面，CNN-LSTM模型耗时45 s，MCS耗时119 s，CNN-LSTM模型效率比MCS提高了近2倍。（2）对比分析CNN、LSTM模型和多元线性回归模型（Multiple Linear Regression，MLR）等多种机器学习方法用于可靠度分析方面的计算性能，得出CNN-LSTM模型边坡失效概率预测相对误差远远小于CNN（104%）、LSTM（91.3%）和MLR（34.78%）的相对误差，且计算耗时最少；（3）算例验证了CNN-LSTM模型在边坡可靠度分析方面具有可行性和优越性。

关键词: 边坡, 可靠度, 正交试验设计, 超参数, CNN-LSTM模型

Abstract:

When the traditional limit equilibrium method is used for slope reliability analysis，because of the performance function is implicit and the form is complicated，the iterative process of solving the function becomes complicated and the computational efficiency is low.Aiming at the above problems，a CNN-LSTM model method was proposed.The principle of this method is to first extract the data features by using convolutional neural network（CNN），and then predict the slope failure probability by using short and long time memory network（LSTM）.On the basis of fully considering the value range of the CNN-LSTM model’s hyperparameters，the five-factor and four-level orthogonal test table was used to design the hyperparameters.Finally，the convolutional output dimension of the first layer and the second layer of the CNN network architecture in the CNN-LSTM model were determined to be 64 and 8 respectively.Dropout ratio is 0.5，the number of the first layer of the LSTM structure is 5 units and the number of the second layer of hidden layers is 20 units，respectively.The 420 slope sample data collected from central and western regions of China were used to train the model according to the ratio of 7∶3 between the training set and the verification set，and the optimal parameters of the CNN-LSTM model were obtained. Finally，Yanshanji landslide was taken as an example to illustrate the feasibility of the model method.The CNN-LSTM model was compared with Monte Carlo method（MCS），response surface method，single CNN，LSTM model and multiple linear regression model in terms of computational efficiency and failure probability prediction.The results show that：（1）When the MCS sampling times is 10 000，compared with the traditional MCS，although the CNN-LSTM model has a relative error of 4.35% in predicting the slope failure probability，in terms of computational efficiency，the CNN-LSTM model takes 45.28 s and the MCS takes 119 s，so the CNN-LSTM model increases the efficiency nearly 2 times.（2）When the single CNN model and LSTM model both adopt two-layer architecture，although the number of parameters of the CNN-LSTM model is not optimal，it has excellent performance in terms of calculation time and prediction accuracy of failure probability due to the small overfitting risk of the model.Compared with the multiple linear regression model，the relative error of CNN-LSTM prediction is 4.35%，and that of multiple linear regression is 34.78%.Through the above two points，the CNN-LSTM model can well complete the analysis of slope reliability，and avoid solving the implicit performance function，and the work efficiency is high.

Key words: slope, reliability, orthogonal test design, hyperparameter, CNN-LSTM model

中图分类号:

TU43

荣光旭, 李宗洋. CNN-LSTM模型在边坡可靠度分析中的应用[J]. 黄金科学技术, 2023, 31(4): 613-623.

Guangxu RONG, Zongyang LI. Application of CNN-LSTM Model in Slope Reliability Analysis[J]. Gold Science and Technology, 2023, 31(4): 613-623.

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表9

各模型预测性能及结果比较"

模型	MAE	RMSE	失效概率/%	$p f$ 相对误差/%
MCS	-	-	0.0023	-
CNN	0.0949	0.1024	0.0047	104.00
LSTM	0.0926	0.0942	0.0044	91.30
CNN-LSTM	0.0794	0.0837	0.0024	4.35
MLR	0.0821	0.0886	0.0031	34.78

表9

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超参数	取值范围
kernel	1，2，3，4，5，6，7，8
filters	8，16，32，64，256，512
hidden	8，16，32，64，256
dropout	0.1，0.2，0.3，0.4，0.5，0.6，0.7，0.8，0.9

样本编号	h/m	α/（°）	μ	c/kPa	φ/（°）	γ/（kN·m^-3）	p/mm	稳定状态标签值
样本1	90.0	18	0.27	19.55	9.91	23.04	950	1
样本2	136.5	22	0.32	21.30	10.10	20.03	1 200	0
样本3	37.0	25	0.34	11.00	8.50	20.50	1 095	1
样本4	33.0	15	0.32	21.00	10.00	18.80	995	1
样本5	70.0	13	0.30	9.61	10.44	19.47	1 020	0
?	?	?	?	?	?	?	?	?
样本416	41.7	12	0.29	34.72	13.30	19.94	1 270	1
样本417	85.0	18	0.35	18.60	15.10	19.50	1 067	1
样本418	183.0	40	0.28	17.60	20.30	25.00	1 110	0
样本419	50.0	13	0.30	31.00	15.73	19.30	1 320	1
样本420	40.0	12	0.31	20.80	14.58	19.32	1 260	0

项目	h/m	α/（°）	μ	c/kPa	φ/（°）	γ /（kN·m^-3）	p/mm
最大值	511.00	53.00	0.42	107.00	45.00	31.30	1 479.00
最小值	16.66	8.00	0.27	0.00	0.00	12.00	876.00
平均值	112.43	34.51	0.32	27.94	23.01	20.81	1 203.00
标准差	129.29	10.11	0.06	22.57	16.33	3.36	6.77

分析方法	失效概率/%	相对误差/%
蒙特卡洛法（安正明等，2022）	15.36	-
本文方法	15.40	0.26

参数及单位	参数值	参数及单位	参数值
h/m	78	c/kPa	9.81
α/（°）	13	φ/（°）	9.34
μ	0.31	p/mm	1 191.3
γ/（kN·m^-3）	19.58