基于支持向量机上海地区土体物理力学指标相关性研究

李志国; 白瑞涵; 刘旭进; 王庶懋

doi:10.19987/j.dzkxjz.2022-166

基于支持向量机上海地区土体物理力学指标相关性研究

doi: 10.19987/j.dzkxjz.2022-166

李志国^1,,
白瑞涵^{2, 3},
刘旭进¹,
王庶懋^1, ,

1.
中国电力工程顾问集团华东电力设计院有限公司，上海 200063
2.
河海大学岩土力学与堤坝工程教育部重点实验室，江苏南京 210024
3.
河海大学江苏省岩土工程技术工程研究中心，江苏南京 210024

基金项目: “基于数据挖掘技术的岩土工程勘察设计管理及优化平台研究”（GSKJ2-G02-2019）资助。

详细信息

作者简介:
李志国（1983-），男，高级工程师，主要从事岩土工程勘察工作。E-mail：2564@ecepdi.com

通讯作者:
王庶懋（1978-），男，高级工程师，主要从事岩土工程勘察及岩土工程设计工作。E-mail：2431@ecepdi.com

中图分类号: TU431
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出版历程
- 收稿日期: 2022-11-16
- 录用日期: 2022-12-26
- 网络出版日期: 2023-01-06

Correlations between physical and mechanical property indexes of Shanghai soil based on support vector machine

Li Zhiguo^1
,,
Bai Ruihan^{2, 3},
Liu Xujin¹,
Wang Shumao^{1
, ,}

1.
East China Electric Power Design Institute Co., LTD. of China Power Engineering Consulting Group, Shanghai 200063, China
2.
Key Laboratory of Minstry of Education for Geomechanics and Embankment Engineering, Hohai University, Jiangsu Nanjing 210024, China
3.
Geotechnical Engineering Research Center of Jiangsu Province, Hohai University, Jiangsu Nanjing 210024, China

摘要

摘要:
针对上海地区土体物理力学指标开展相关性分析，结合多个工程场地获取的土体室内试验数据，采用支持向量机算法构建了土体塑性指数、液性指数与压缩系数的相关性分析模型，并结合误差指标对模型参数进行优化。将支持向量机模型与传统的线性、多项式拟合方法结果对比分析，表明该模型预测结果与实际结果较为吻合，且该模型另一优势在于能够从更多的数据中进行更深度的挖掘来提升自身的鲁棒性。考虑到不同土体的工程性质差异较大，进一步研究该模型的预测性能与适用性，就每个测试样本点预测偏差与其物理指标建立二者的关系曲线，结果表明可塑性小的中压缩性土体相较于高压缩性土体的预测偏差更小，模型更加稳定与准确，可为上海地区土体压缩性相关研究提供参考。
- 支持向量机 /
- 相关性分析 /
- 压缩系数 /
- 液性指数 /
- 塑性指数
Abstract:
Correlation analysis of physical and mechanical indexes of Shanghai soil was carried out. Using the support vector machine algorithm, the authors constructed a correlation analysis model of soil plasticity index, liquidity index and compressibility coefficient based on the soil indoor test data obtained from several engineering sites. Then the model parameters were optimized by combining the error indexes. Comparing the results of support vector machine model with those of traditional linear and polynomial fitting methods, it was shown that the prediction results of the model are basically consistent with the actual results, and another advantage of model is that it can carry out deeper mining from more data to improve its robustness. Considering the engineering properties of different category soils are quite different, the authors further analyzed the performance and applicability of model, and established the relationship curve between the forecast bias of each testing sample and its physical indexes. The results indicate that the error of medium compressible soil is smaller than high compressible soil, and the model is more stable and accurate, which could provide a reference for the research of soil compressibility in Shanghai.
- support vector machine /
- correlation analysis /
- compressibility coefficient /
- liquidity index /
- plasticity index

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图 1 相关性散点图

Figure 1. Correlation scatter plot

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图 2 不同输入变量预测结果的对比分析

Figure 2. Comparisive analysis of forecast results for different input variables

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图 3 不同核函数预测结果的对比分析

Figure 3. Comparisive analysis of forecast results for different kernel functions

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图 4 不同误差项惩罚系数预测结果的对比分析

Figure 4. Comparisive analysis of forecast results of penalty coefficients of different error item

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图 5 不同方法的压缩系数预测结果对比分析

Figure 5. Comparisive analysis of prediction results of compression coefficients by different methods

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图 6 不同数量数据集下支持向量机与拟合方法的对比分析

Figure 6. Comparative analysis of support vector machine and fitting methods in different datasets

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图 7 不同物理指标的预测偏差

Figure 7. Forecast bias of different physical indexes

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图 8 基于压缩系数的预测偏差变化

Figure 8. Variation of forecast bias based on compression coefficients

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表 1 土的物理力学指标统计

Table 1. Statistics of physical and mechanical indexes of soil

土体类型	统计量	物理力学指标	参数值
土体类型	统计量	物理力学指标	最小值	最大值	平均值	标准差	变异系数
淤泥质粘土	221	压缩系数a_1-2/MPa⁻¹	0.66	1.60	0.84	0.27	0.32
		含水量w/%	24.40	63.40	42.93	6.54	0.15
		塑限W_P/%	17.00	31.30	22.80	2.92	0.13
		液限W_L/%	26.50	53.90	37.42	6.10	0.16
		塑性指数I_P	9.40	22.80	14.62	3.38	0.23
		液性指数I_L	0.52	2.57	1.41	0.32	0.23
		湿密度ρ/（cm·s⁻³）	1.62	1.97	1.76	0.06	0.03
		土粒比重G_s	2.71	2.75	2.73	0.01	0.0039
粘土	31	压缩系数a_1-2/ MPa⁻¹	0.21	0.98	0.57	0.22	0.39
		含水量w/%	24.00	52.60	36.22	7.66	0.21
		塑限W_P/%	16.50	27.50	22.17	2.55	0.12
		液限W_L/%	30.50	48.10	37.64	4.57	0.12
		塑性指数I_P	10.80	20.60	15.47	2.41	0.16
		液性指数I_L	0.35	1.93	0.92	0.43	0.47
		湿密度ρ/（cm·s⁻³）	1.70	2.02	1.87	0.10	0.05
		土粒比重G_s	2.72	2.75	2.73	0.01	0.0037
粉质粘土	198	压缩系数a_1-2/ MPa⁻¹	0.07	1.28	0.41	0.21	0.51
		含水量w/%	18.20	52.00	30.97	6.27	0.20
		塑限W_P/%	15.00	31.00	21.46	2.40	0.11
		液限W_L/%	25.40	53.80	35.15	4.63	0.13
		塑性指数I_P	9.00	22.80	13.68	2.61	0.19
		液性指数I_L	-0.31	1.84	0.72	0.41	0.57
		湿密度ρ/（cm·s⁻³）	1.67	2.10	1.90	0.09	0.05
		土粒比重G_s	2.71	2.75	2.73	0.01	0.0037
砂质粉土	137	压缩系数a_1-2/ MPa⁻¹	0.10	0.83	0.39	0.18	0.46
		含水量w/%	19.90	46.40	31.51	5.01	0.16
		塑限W_P/%	13.00	25.70	20.14	2.44	0.12
		液限W_L/%	22.40	43.40	30.29	3.45	0.11
		塑性指数I_P	7.10	17.70	10.15	1.91	0.19
		液性指数I_L	0.35	1.90	1.10	0.33	0.30
		湿密度ρ/（cm·s⁻³）	1.73	2.03	1.84	0.07	0.04
		土粒比重G_s	2.69	2.74	2.71	0.01	0.0025

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表 2 不同输入变量预测结果误差对比

Table 2. Error comparison of forecast results for different input variables

输入变量	误差指数
输入变量	R²	MAE	RMSE	MSE
塑性指数、液性指数	0.860	0.116	0.144	0.021
塑性指数	0.525	0.212	0.265	0.070
液性指数	0.228	0.269	0.338	0.114

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表 3 不同核函数预测结果误差对比

Table 3. Error comparison of forecast results for different kernel functions

核函数	误差指数
核函数	R²	MAE	RMSE	MSE
RBF	0.886	0.100	0.130	0.017
多项式	0.876	0.109	0.136	0.018
线性	0.86	0.116	0.144	0.021

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表 4 不同误差项惩罚系数预测结果误差对比

Table 4. Error comparison of forecast results of penalty coefficients of different error item

误差项惩罚系数C	误差指数
误差项惩罚系数C	R²	MAE	RMSE	MSE
5	0.903	0.094	0.120	0.014
1	0.886	0.100	0.130	0.017
0.5	0.873	0.105	0.137	0.019

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表 5 不同方法的压缩系数预测结果误差对比

Table 5. Error comparison of prediction results of compression coefficients by different methods

算法	误差指数
算法	R²	MAE	RMSE	MSE
SVR算法	0.911	0.08	0.115	0.013
线性拟合	0.859	0.118	0.144	0.021
多项式拟合	0.892	0.101	0.127	0.016

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表 6 不同物理指标预测结果误差对比

Table 6. Error comparison of prediction results for different physical indexes

指标	变化范围	误差指标
指标	变化范围	MAE	RMSE	MSE
塑限W_P	16—20	0.071	0.080	0.006
	20—26	0.082	0.111	0.012
	26—32	0.129	0.023	0.151
液限W_L	25—35	0.067	0.080	0.006
	35—45	0.104	0.141	0.020
	45—55	0.122	0.144	0.021
塑性指数I_P	7.5—12.5	0.064	0.079	0.006
	12.5—17.5	0.081	0.108	0.012
	17.5—22.5	0.130	0.158	0.025
液性指数I_L	0.2—0.7	0.069	0.087	0.008
	0.7—1.2	0.107	0.133	0.018
	1.2—1.8	0.094	0.122	0.015

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表 7 中高压缩性土预测结果误差对比

Table 7. Error comparison of prediction results of medium and high compressible soil

土体类型	误差指数
土体类型	MAE	RMSE	MSE
中压缩性土	0.069	0.085	0.007
高压缩性土	0.120	0.150	0.023

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