3D Slope Reliability Analysis Based on Improved PSO-RBF Neural Network
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摘要: 三维边坡模型能真实反映边坡空间效应，提升边坡可靠度计算精度，然而由于三维边坡模型计算量庞大且安全系数缺少显示表达，边坡可靠度分析主要以二维简化模型为主，针对三维边坡可靠度分析的研究仍存在不足.提出一种基于Spencer方法、自适应变异粒子群优化算法（PSO）和径向基函数神经网络（RBF）的三维边坡可靠度分析方法.通过对传统PSO算法引入变异算子，改善了其搜索精度较低、后期迭代效率不高等缺点.以三维Spencer方法为基础，结合改进PSO算法与RBF神经网络构建三维边坡安全系数的计算模型进行可靠度分析，实现三维边坡功能函数的显示化，通过标椎椭球滑体可靠度分析，验证了该方法相较于传统方法计算精度和效率的提升；进一步研究了卡基娃左岸边坡减载开挖过程稳定性及可靠度的变化规律，结果表明：削坡减载作用后有效提升了边坡的稳定性，边坡失效概率减小了近2个数量级.Abstract: Three-dimensional slope model can truly reflect the spatial effect of slope and improve the accuracy of slope reliability calculation, however, due to the huge calculation volume of three-dimensional slope model and the lack of display expression of safety coefficient, the slope reliability analysis is mainly based on two-dimensional simplified model, and the research for three-dimensional slope reliability analysis is still insufficient. A three-dimensional slope reliability analysis method based on Spencer's method, adaptive variational particle swarm optimization algorithm and radial basis function neural network (RBF) is proposed. By introducing variational operators to the traditional PSO algorithm, the shortcomings of its low search accuracy and inefficient late iterations are improved. Based on the three-dimensional Spencer method, the calculation model of three-dimensional slope safety coefficient is constructed for reliability analysis by combining the improved PSO algorithm with RBF neural network to realize the display of three-dimensional slope function, and the improvement of the calculation accuracy and efficiency of the method compared with the traditional method is verified through the reliability analysis of the scalene vertebral ellipsoid slide; further research is conducted on the process of load-reducing excavation of the left bank slope of Kakiwa. The results show that the stability and reliability of the slope can be effectively improved after the effect of slope cutting and load reduction, and the probability of slope failure is reduced by nearly 2 orders of magnitude.
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图 1 自适应变异粒子群算法示意
Fig. 1. Schematic diagram of the adaptive variant particle swarm algorithm
图 3 计算模型平、剖面图及三维建模结果
Fig. 3. Calculation of model planes, sections and 3D modeling results
图 4 简化土坡稳定性安全系数预测及误差示意
a.训练样本实际值图像；b.传统RBF网络预测结果及误差图像；c.PSO-RBF网络预测结果及误差图像；d. 改进PSO-RBF网络预测结果及误差图像
Fig. 4. Simplified prediction of safety factor for slope stability and error representation
图 5 三种算法安全系数预测值与理论值45°线对比
Fig. 5. The 45°line comparison between the predicted value and the theoretical value of the safety coefficient of the three algorithms
图 7 卡基娃边坡削坡减载开挖布置
Fig. 7. Layout of the undrained load-reducing excavation of the slope above the top of the Kakiva left bank dam
图 8 卡基娃左岸边坡典型剖面减载开挖布置
Fig. 8. Typical profile of load-reducing excavation layout for the slope above the top of Kakiva left bank dam
图 9 卡基娃左岸原始及减载开挖后边坡三维立体图
Fig. 9. Three-dimensional view of the slope above the crest of the dam on the left bank of Kakeva
图 12 各开挖状态下失效概率预测结果
Fig. 12. Probability of failure prediction results for each trenching state
图 13 CNN与SVM安全系数预测值与理论值45°线对比
a. CNN预测值与理论值45°线对比；b. SVM预测值与理论值45°线对比
Fig. 13. Comparison of the predicted value of CNN and SVM safety factor with the theoretical value of 45° line
表 1 传统RBF网络、PSO-RBF网络与优化PSO-RBF网络安全系数预测误差
Table 1. The traditional RBF, PSO-RBF and the Optimized PSO-RBF network security coefficient prediction error
序号 黏聚力
c(kPa)内摩擦角
φ(°)显示功能函数计算理论值 RBF网络预测值 相对误差
(%)PSO-RBF网络预测值 相对误差 改进PSO-RBF网络预测值 相对误差(%) 1 28.25 28.25 1.256 1.133 ‒9.773 1.257 0.110 1.258 0.122 2 28.75 28.25 1.269 1.213 ‒4.437 1.276 0.529 1.270 0.061 3 28.75 31.75 1.349 1.305 ‒3.254 1.408 4.373 1.336 ‒0.997 4 30.25 32.25 1.400 1.235 ‒11.818 1.452 3.718 1.398 ‒0.132 5 30.75 30.25 1.367 1.350 ‒1.246 1.370 0.213 1.367 0.021 6 30.75 32.75 1.425 1.501 5.316 1.480 3.883 1.421 ‒0.252 7 31.25 32.25 1.427 1.490 4.395 1.454 1.862 1.420 ‒0.476 8 31.75 31.25 1.417 1.380 ‒2.591 1.420 0.187 1.419 0.161 9 32.75 29.25 1.399 1.295 ‒7.425 1.464 4.631 1.398 ‒0.044 10 32.75 31.75 1.456 1.520 4.379 1.471 1.009 1.453 ‒0.191 
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表 2 边坡可靠度指标及失效概率计算结果
Table 2. Calculation results of slope reliability index and failure probability
功能函数构建方法 可靠度计算方法 可靠度指标beta 失效概率Pf（%） 误差(%) 基于三维M-P法的响应面函数 FORM 2.240 1.255 ‒4.518 RBF神经网络 MCS 3.124 0.089 33.163 传统PSO-RBF神经网络 MCS 2.562 0.520 9.207 改进PSO-RBF神经网络 MCS 2.352 0.934 0.256 边坡功能函数 MCS 2.346 0.949 ‒
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表 3 滑带土计算参数取值
Table 3. Calculation parameters of slippage soil
物理参数 变异系数 均值 标准差 粘聚力c(kPa) 0.14 18 2.52 内摩擦角φ(°) 0.21 25 5.25
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表 4 优化PSO-RBF、SVM、CNN安全系数预测误差与计算时长对比
Table 4. Optimized PSO-RBF, SVM, and CNN safety factor prediction error versus computation time
预测网络 改进PSO-RBF SVM CNN 标准差(RMSE) 0.004 051 9 0.012 479 0.006 705 8 平均相对误差(MAPE)（%） 0.19 0.70 0.40 计算时长(s) 141 229 409
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