基于无监督方法确定岩土参数取值

阮永芬; 李鹏辉; 朱强; 王勇; 闫明

doi:10.16030/j.cnki.issn.1000-3665.202207046

基于无监督方法确定岩土参数取值

doi: 10.16030/j.cnki.issn.1000-3665.202207046

阮永芬^1,,
李鹏辉^1, ,,
朱强²,
王勇³,
闫明⁴

1.
昆明理工大学建筑工程学院，云南昆明　650500
2.
中铁十六局集团有限公司北京交通轨道建设工程有限公司，北京　101100
3.
昆明军龙岩土工程有限公司，云南昆明　650214
4.
中铁二十局集团第五工程有限公司，云南昆明　650000

基金项目: 中铁二十局集团第五工程有限公司科研计划项目（CR2005-5-JS-2021-009）

详细信息

作者简介:
阮永芬（1964-），女，博士，教授，主要从事岩土工程方面的研究。E-mail：rryy64@163.com

通讯作者:
李鹏辉（1999-），男，硕士研究生，主要从事岩土工程方面的研究。E-mail： 1017343481@qq.com

中图分类号: TU443
计量
- 文章访问数: 6882
- HTML全文浏览量: 1411
- PDF下载量: 459
- 被引次数: 0
出版历程
- 收稿日期: 2022-07-28
- 修回日期: 2022-10-20
- 网络出版日期: 2023-04-03
- 刊出日期: 2023-07-15

Determination of geotechnical parameters based on the unsupervised learning method

1.
Faculty of Civil Engineering and Mechanics, Kunming University of Science and Technology, Kunming, Yunnan　650500, China
2.
China Railway 16 Bureau Group Metro Engineering Construction Co. Ltd., Beijing　101100, China
3.
Kunming Junlong Geotechnical Engineering Co. Ltd., Kunming, Yunnan　650214, China
4.
No.5 Engineering Corporation Limited of CR20G, Kunming, Yunnan　650000, China

摘要

摘要: 随着城市工程建设的发展，建筑工程事故问题愈发突出，采用传统方法求取的岩土参数区间无法满足实际工程需要。基于无监督学习思想，选取工程性质较差的泥炭质土，结合工程经验选用8个物理指标作为输入集，利用主成分分析（priciple components analysis, PCA）算法实现多样本多参数去耦合的降维处理，得出各物理指标相关性及敏感度，结合其相关性及敏感度赋予不同埋深泥炭质土物理指标的综合评价值。利用k-means聚类分析泥炭质土物理指标、综合评价值及工程特性之间的关系，为岩土参数选取提供理论基础。采用监督学习方法——BP神经网络算法分析无监督结果，验证（PCA—k-means）算法模型的合理性。将通过聚类分析得到的正态样本利用多种截尾法优化，得到可靠取值区间，并将取值结果与实际工程取值比较，验证了该模型工程参数取值的合理性。该算法模型具有较好的工程应用价值，所得研究结果可为工程勘察、设计、施工参数取值提供参考，也能为岩土参数取值分析提供新的分析方法。
- 主成分分析 /
- k-means聚类 /
- BP神经网络 /
- 截尾法 /
- 岩土参数
Abstract: With the development of urban engineering construction, the issue of construction engineering accidents has become more and more prominent. The geotechnical parameter interval obtained by using the traditional methods cannot meet the needs of actual engineering. Based on the idea of unsupervised learning, the peaty soil with the worst engineering properties is considered, and 8 physical indexes are selected as the input set. The principal component analysis (PCA) algorithm is used to realize the dimensionality reduction of multi-sample and multi-parameter decoupling, and the correlation and sensitivity of each physical index is obtained. Combined with its correlation and sensitivity, the comprehensive evaluation value of physical indexes of peat soil with different buried depths is given. The k-means clustering is used to analyze the relationship among physical index, and comprehensive evaluation value and engineering characteristics of peaty soil provide a theoretical basis for the selection of geotechnical parameters. The supervised learning method-BP neural network algorithm is used to analyze the unsupervised results and verify the accuracy of the (PCA—k-means) algorithm model. The normal samples obtained by clustering analysis are optimized by a variety of truncation methods to obtain a reliable value range, and the value results are compared with the actual engineering values to verify the rationality of the model engineering parameters. The algorithm model is of good engineering application value. The research results can provide references for engineering investigation, design and construction parameter values, and also provide a new analysis method for geotechnical parameter value analyses.
- principal component analysis /
- k-means clustering /
- BP neural networks /
- truncated method /
- geotechnical parameters

HTML全文

图 1 会展中心地层构造图

Figure 1. Stratigraphic diagram of the convention center

下载: 全尺寸图片幻灯片

图 2 ρ与ω、ω_L、e、a_1-2关系曲线

Figure 2. Relationship of ρ and ω, ω_L, e and a_1-2

下载: 全尺寸图片幻灯片

图 3 w_u与ω、ω_L、e、a_1-2关系曲线

Figure 3. Relationship ofw_u and ω, ω_L, e and a_1-2

下载: 全尺寸图片幻灯片

图 4 特征值变化规律

Figure 4. Variation of elgenvalues

下载: 全尺寸图片幻灯片

图 5 累计贡献率

Figure 5. Cumulative contribution

下载: 全尺寸图片幻灯片

图 6 判别指标分类结果

Figure 6. Discriminative index classification results

下载: 全尺寸图片幻灯片

图 7 综合评价分类结果

Figure 7. Results of comprehensive evaluation

下载: 全尺寸图片幻灯片

图 8 e、ω与ω_L分类结果

Figure 8. Classification results of e、ω and ω_L

下载: 全尺寸图片幻灯片

图 9 分类结果对比

Figure 9. Comparison of classification results

下载: 全尺寸图片幻灯片

图 10 综合评价值对比

Figure 10. Comprehensive evaluation and comparison

下载: 全尺寸图片幻灯片

图 11 3个物理指标原样本分布图

Figure 11. Original sample distribution map of three physical indicators

下载: 全尺寸图片幻灯片

图 12 分类后3个物理指标样本分布图

Figure 12. Sample distribution map of three physical indicators after classification

下载: 全尺寸图片幻灯片

表 1 各层泥炭质土的物理指标统计表

Table 1. Statistical table of physical indexes of peaty soil in each layer

地层编号	ρ /（g·cm⁻³）	G_s	ω /%	ω_L /%	ω_P /%	e	a_1-2 /MPa⁻¹	w_u /%
$\text{③}_1^1$	1.61	2.30	110.1	135.4	100.0	2.49	1.62	24.33
$\text{③}_2 $	1.42	2.42	101.2	119.2	87.2	2.40	1.32	18.36
$\text{④}_1 $	1.25	1.95	145.7	182.1	146.4	2.93	1.49	40.10
$\text{⑤}_{12}$	1.27	1.97	130.6	174.3	140.6	2.52	1.12	38.77

下载: 导出CSV

表 2 不同物理指标间的相关性系数

Table 2. Correlation between different physical indicators

物理指标	ρ	G_S	ω	ω_L	e	a_1-2	ω_P	w_u
ρ	1.00
G_S	0.64	1.00
w	0.87	0.55	1.00
w_L	0.89	0.59	0.94	1.00
e	0.85	0.85	0.94	0.87	1.00
a_1-2	0.62	0.42	0.81	0.68	0.85	1.00
w_P	0.85	0.58	0.82	0.93	0.58	0.49	1.00
w_u	0.83	0.66	0.73	0.78	0.70	0.45	0.80	1.00

下载: 导出CSV

表 3 各物理指标敏感度统计表

Table 3. Sensitivity statistics of each physical index

物理指标编码	X₁（ρ）	X₂ （G_S）	X₃ （ω）	X₄（ω_L）	X₅（e）	X₆（a_1-2）	X₇ （ω_P）	X₈ （w_u）
敏感度符号	r₁	r₂	r₃	r₄	r₅	r₆	r₇	r₈
敏感度值	0.2349	0.2069	0.2540	0.2428	0.2608	0.2151	0.2410	0.2281

下载: 导出CSV

表 4 各组泥炭质土综合评价值排序

Table 4. Ranking of comprehensive evaluation of the peaty soil

组类	综合评价值	物理指标平均值
组类	综合评价值	ρ/（g·cm⁻³）	ω/%	G_s	e	ω_L/%	ω_P/%	a_1-2/MPa^-1	w_u/%
1	–1.295	1.565	57.590	2.517	1.536	68.690	42.690	0.722	8.100
2	–1.162	1.533	67.980	2.397	1.565	71.730	44.910	0.812	12.670
3	–1.096	1.499	68.280	2.428	1.699	76.180	48.270	1.103	11.690
4	–1.035	1.483	72.120	2.436	1.824	84.800	49.560	0.977	12.270
5	–0.928	1.452	73.690	2.238	1.882	92.400	58.890	0.850	13.678
6	–0.946	1.454	78.070	2.426	1.971	90.320	53.550	1.121	12.100
7	–0.900	1.455	82.180	2.426	1.957	95.363	62.181	0.833	13.318
…	…	…	…	…	…	…	…	…	…
34	1.293	1.115	211.200	1.796	4.406	228.270	149.400	3.802	43.750
35	1.496	1.134	220.200	1.164	4.761	228.710	144.100	4.718	44.346
36	1.566	1.117	232.700	1.311	4.818	238.770	149.310	5.031	40.817
37	1.861	1.121	247.000	0.996	5.327	249.400	156.300	6.006	41.710
38	2.574	1.079	287.182	0.990	5.839	304.936	207.800	5.978	56.455

下载: 导出CSV

表 5 不同截尾法的原物理指标区间范围

Table 5. Original physical index range of different censoring methods

物理指标	均值	标准差	偏度系数	变异系数	3σ区间范围	c₃₃区间范围	c₃区间范围
e	3.03	1.20	0.94	0.39	[0,6.63]	[0.56,7.76]	[0，7.76]
ω/%	133.02	62.09	0.93	0.46	[0,319.29]	[4.48,377.03]	[0,377.03]
ω_L/%	148.63	61.26	0.87	0.41	[0,332.41]	[18.14,385.71]	[0,385.71]

下载: 导出CSV

表 6 物理指标样本检验结果

Table 6. Normal test result of the physical index sample

指标	分布类型	D值	P值	检验结果
e（图11）	正态分布	0.155	1.81×10^–4	排除
e（图12）	正态分布	0.090	1.00	接受
ω（图11）	正态分布	0.189	2.36×10^–12	排除
ω（图12）	正态分布	0.064	0.710	接受
ω_L（图11）	正态分布	0.146	1.62×10^–7	排除
ω_L（图12）	正态分布	0.072	0.190	接受
注：D值为检验统计量；P值为渐近显著性水平，P值大于0.05时，接受原假设。

下载: 导出CSV

表 7 不同截尾法的新样本区间范围

Table 7. Range of new sample intervals for different censoring methods

物理指标	均值	标准差	偏度系数	变异系数	3σ区间范围	c₃₃区间范围	c₃区间范围
e	2.19	0.40	0.39	0.18	[0.99,3.39]	[1.45,3.55]	[0.99,3.55]
ω/%	88.68	17.40	0.39	0.18	[36.48,140.88]	[43.26,147.66]	[36.48,140.88]
ω_L/%	105.55	22.11	0.28	0.20	[39.22,171.88]	[45.41,178.07]	[39.22,178.08]
ρ/（g·cm⁻³）	1.40	0.08	0.08	0.06	[1.13,1.66]	[1.15,1.67]	[1.13,1.67]
G_s	2.25	0.45	–3.08	0.20	[0.89,3.61]	[1.15,3.55]	[1.15,3.61]
a_1-2/MPa⁻¹	1.24	0.56	1.56	0.45	[0,2.93]	[0.43,3.81]	[0,2.93]
ω_P/%	68.76	18.06	0.38	0.26	[14.57,122.97]	[21.48,129.88]	[14.57,129.88]
w_u/%	17.63	7.64	2.02	0.43	[0,40.57]	[10.17,56.06]	[0,56.06]

下载: 导出CSV

表 8 各层泥炭质土设计参数检验结果

Table 8. Test results of design parameters of the peaty soil in each layer

地层编号	ρ /（g·cm⁻³）	ω /%	e	I_L	a_1-2 /MPa⁻¹	综合评价	所属类
$ \text{③}_1^1$	1.37	103.0	2.41	0.15	1.63	−0.23	第一类
$\text{③}_2 $	1.39	91.1	2.33	0.12	1.30	−0.26	第一类
$\text{④}_1 $	1.20	142.3	2.92	−0.14	1.47	−0.08	第一类
$\text{⑤}_{12} $	1.26	127.7	2.53	−0.28	1.12	−0.16	第一类

下载: 导出CSV

参考文献(24)

[1]	阮永芬,刘岳东,王东,等. 昆明泥炭与泥炭质土对建筑地基的影响[J]. 昆明理工大学学报(理工版),2003,28(3):121 − 124. [RUAN Yongfen,LIU Yuedong,WANG Dong,et al. Effect of Kunming’s peat & peaty soil on the building foundation[J]. Journal of Kunming University of Science and Technology,2003,28(3):121 − 124. (in Chinese with English abstract) RUAN Yongfen, LIU Yuedong, WANG Dong, et al. Influence of peat & peaty soil on building foundation in Kunming [J]. Journal of Kunming University of Science & Technology, 2003, 28（3）: 121-124. （in Chinese with English abstract）
[2]	柴春阳,张广泽,胡婷. 丽香铁路冰水沉积型泥炭土特性及工程对策分析[J]. 地下空间与工程学报,2017,13(增刊 2):757 − 761. [CHAI Chunyang,ZHANG Guangze,HU Ting. Characteristics of ice-water deposition peat in Li-Xiang railway and analysis on engineering countermeasures[J]. Chinese Journal of Underground Space and Engineering,2017,13(Sup 2):757 − 761. (in Chinese with English abstract) CHAI Chunyang, ZHANG Guangze, HU Ting. Analysis on characteristics and engineering countermeasures of ice water sedimentary peat soil in Lixiang Railway [J]. Underground Space & Engineering Journal, 2017, 13（Sup2）: 757-761. （in Chinese with English abstract）
[3]	李强,李刚. 沪苏浙高速公路泥炭质土的工程性质研究[J]. 公路工程,2010,35(6):99 − 103. [LI Qiang,LI Gang. Research on the engineering property of peat quality soil in Hu-Su-Zhe highway[J]. Highway Engineering,2010,35(6):99 − 103. (in Chinese with English abstract) doi: 10.3969/j.issn.1674-0610.2010.06.026 LI Qiang, LI Gang. Study on Engineering Properties of Peat Soil in Hu-Su-Zhe Expressway [J]. Highway Engineering, 2010, 35（06）: 99-103. （in Chinese with English abstract） doi: 10.3969/j.issn.1674-0610.2010.06.026
[4]	谢俊文. 泥炭的工程地质特性[J]. 工程勘察,1981,9(5):31 − 34. [XIE Junwen. Engineering geological characteristics of peat[J]. Geotechnical Investigation & Surveying,1981,9(5):31 − 34. (in Chinese with English abstract) XIE Junwen. Engineering geological characteristics of peat [J]. Engineering investigation, 1981（05）: 31-34. （in Chinese with English abstract）
[5]	KOLAY P K, AMINUR M R, TAIB S N L, et al. Correlation between different physical and engineering properties of tropical peat soils from Sarawak[C]//Soil Behavior and Geo-Micromechanics. Reston, VA: American Society of Civil Engineers, 2010: 56-61.
[6]	PRICE J S,CAGAMPAN J,KELLNER E. Assessment of peat compressibility:Is there an easy way?[J]. Hydrological Processes,2005,19(17):3469 − 3475. doi: 10.1002/hyp.6068
[7]	SANTAGATA M,BOBET A,JOHNSTON C T,et al. One-dimensional compression behavior of a soil with high organic matter content[J]. Journal of Geotechnical and Geoenvironmental Engineering,2008,134(1):1 − 13. doi: 10.1061/(ASCE)1090-0241(2008)134:1(1)
[8]	裴利华,杨醒宇,桂跃,等. 有机质含量及组分对泥炭土物理力学性质影响[J]. 水文地质工程地质,2022,49(2):77 − 85. [PEI Lihua,YANG Xingyu,GUI Yue,et al. Influence of organic matter content and ingredient on the physical and mechanical properties of peat soils[J]. Hydrogeology & Engineering Geology,2022,49(2):77 − 85. (in Chinese with English abstract) PEI Lihua, YANG Xingyu, GUI Yue, et al. Effect of Organic Matter Content and Composition on Physical and Mechanical Properties of Peat Soil[J]. Hydrogeology & Engineering Geology, 2022, 49（2）: 77-85. （in Chinese with English abstract）
[9]	严春风,刘东燕,朱可善. 岩石抗剪强度指标互相关性的敏感度分析[J]. 水文地质工程地质,1997,24(6):45 − 47. [YAN Chunfeng,LIU Dongyan,ZHU Keshan. Susceptibility analysis tothe correlativity of shear strength indices of ricks[J]. Hydrogeology & Engineering Geology,1997,24(6):45 − 47. (in Chinese with English abstract) YAN Chunfeng, LIU Dongyan, ZHU Kesan. Sensitivity analysis of cross-correlation of rock shear strength index[J]. Hydrogeology & Engineering Geology, 1997（6）: 45-47. （in Chinese with English abstract）
[10]	程豪,田林. 昆明市某场地不同埋深下泥炭质土物理力学指标统计规律研究[J]. 贵州大学学报(自然科学版),2022,39(4):92 − 98. [CHENG Hao,TIAN Lin. Statistical law of physical and mechanical indexes of peat soil under different burial depths in a site in Kunming[J]. Journal of Guizhou University (Natural Science),2022,39(4):92 − 98. (in Chinese with English abstract) CHENG Hao, TIAN Lin. Study on Statistical Law of Physical & Mechanical Indexes of Peat Soil under Different Buried Depths in a Site of Kunming City[J]. Journal of Guizhou University （ Natural Science Eidition）, 2022, 39（4）: 92-98. （in Chinese with English abstract）
[11]	丁祖德,付江,李夕松,等. 昆明泥炭质土的物理力学指标特征及相关性分析[J]. 公路工程,2018,43(4):86 − 91. [DING Zude,FU Jiang,LI Xisong,et al. Properties of physical and mechanical indexes and correlation analysis of peaty soil in Kunming area[J]. Highway Engineering,2018,43(4):86 − 91. (in Chinese with English abstract) DING Zude, FU Jiang, LI Xisong, et al. Physical & mechanical index characteristics and correlation analysis of peaty soil in Kunming[J]. highway engineering, 2018, 43（4）: 86-91. （in Chinese with English abstract）
[12]	陈玉萍,袁志强,周博,等. 遗传算法优化BP网络在滑坡灾害预测中的应用研究[J]. 水文地质工程地质,2012,39(1):114 − 119. [CHEN Yuping,YUAN Zhiqiang,ZHOU Bo,et al. Application of back propagation neural networks with optimization of genetic algorithms to landslide hazard prediction[J]. Hydrogeology & Engineering Geology,2012,39(1):114 − 119. (in Chinese with English abstract) CHEN Yuping, YUAN Zhiqiang, ZHOU Bo, et al. ] Application of BP Network Optimized by Genetic Algorithm in Landslide Disaster Prediction[J]. Hydrogeology & Engineering Geology, 2012, 39（1）: 114-119. （in Chinese with English abstract）
[13]	马壮壮,束龙仓,季叶飞,等. 基于遗传算法的BP神经网络计算岩溶水安全开采量[J]. 水文地质工程地质,2016,43(1):22 − 27. [MA Zhuangzhuang,SHU Longcang,JI Yefei,et al. Calculation of Karst water safe yield by using BP neural network based on genetic algorithm[J]. Hydrogeology & Engineering Geology,2016,43(1):22 − 27. (in Chinese with English abstract) MA Zhuangzhuang, SHU Longcang, JI Yefei, et al. Calculation of Safe Extraction of Karst Water Based on BP Neural Network of Genetic Algorithm[J]. Hydrogeology & Engineering Geology, 2016, 43（1）: 22-27. （in Chinese with English abstract）
[14]	阮永芬, 张虔, 乔文件, 等. 盾构施工地表沉降的无监督学习预估方法[J/OL]. 安全与环境学报, （2022-05-09）[2022-09-05]. http://doi.org/10.13637/j.issn.1009-6094.2022.0351. RUAN Yongfen, ZHANG Qian, QIAO Wenjian, et al. Unsupervised learning prediction method of ground settlement in shield construction[J/OL]. Journal of Safety and Environment, （2022-05-09）[2022-09-05]. （in Chinese with English abstract）
[15]	宫凤强,鲁金涛. 基于主成分分析与距离判别分析法的突水水源识别方法[J]. 采矿与安全工程学报,2014,31(2):236 − 242. [GONG Fengqiang,LU Jintao. Recognition method of mine water inrush sources based on the principal element analysis and distance discrimination analysis[J]. Journal of Mining & Safety Engineering,2014,31(2):236 − 242. (in Chinese with English abstract) GONG Fengqiang, LU Jintao. Recognition method of mine water inrush sources based on the principal element analysis & distance discrimination analysis[J]. Journal of Mining & Safety Engineering, 2014, 31（2）: 236-242. （in Chinese with English abstract）
[16]	任玉晓. 地震波速无监督深度学习反演方法及其在隧道超前探测中的应用[D]. 济南: 山东大学, 2021 REN Yuxiao. Unsupervised deep-learning inversion method for seismic velocity and its application in tunnel forward-prospecting[D]. Jinan: Shandong University, 2021. （in Chinese with English abstract）
[17]	阮永芬,魏德永,高骏,等. K-means聚类分析高原湖相沉积软土参数[J]. 昆明理工大学学报(自然科学版),2020,45(1):85 − 91. [RUAN Yongfen,WEI Deyong,GAO Jun,et al. K-means cluster analysis of soft soil parameters of plateau sedimentary[J]. Journal of Kunming University of Science and Technology (Natural Science),2020,45(1):85 − 91. (in Chinese with English abstract) RUAN Yongfen, WEI Deyong, GAO Jun, et al. K-means Clustering Analysis of Soft Soil Parameters of Plateau Lake Sediment[J]. Journal of Kunming University of Science & Technology （Natural Science）, 2020, 45（1）: 85-91. （in Chinese with English abstract）
[18]	孔令奇,李翠娟. 岩土参数概率分布的系统推断研究[J]. 工业建筑,2022,52(1):129 − 136. [KONG Lingqi,LI Cuijuan. Study on system inference of probability distribution of geotechnical parameters[J]. Industrial Construction,2022,52(1):129 − 136. (in Chinese with English abstract) KONG Lingqi, LI Cuijuan. Study on System Inference of Probability Distribution of Geotechnical Parameters. [J]. industrial architecture, 2022, 52（1）: 129-136. （in Chinese with English abstract）
[19]	殷瑞刚,魏帅,李晗,等. 深度学习中的无监督学习方法综述[J]. 计算机系统应用,2016,25(8):1 − 7. [YIN Ruigang, WEI Shuai, LI Han, et al. Introduction of unsupervised learning methods in deep learning[J]. Computer Systems & Applications,2016,25(8):1 − 7. (in Chinese with English abstract) Yin Ruigang, WEI Shuai, LI Han, et al. A Survey of Unsupervised Learning Methods in Deep Learning [J]. computer system application, 2016, 25（8）: 1-7. （in Chinese with English abstract）
[20]	孙吉贵,刘杰,赵连宇. 聚类算法研究[J]. 软件学报,2008,19(1):48 − 61. [SUN Jigui,LIU Jie,ZHAO Lianyu. Clustering algorithms research[J]. Journal of Software,2008,19(1):48 − 61. (in Chinese with English abstract) doi: 10.3724/SP.J.1001.2008.00048 SUN Jigui, LIU Jie, ZHAO Lianyu. Research on Clustering Algorithm [J]. Journal of Software, 2008, 19（1）: 48-61. （in Chinese with English abstract） doi: 10.3724/SP.J.1001.2008.00048
[21]	张麟, 潘红岩. 聚类分析算法应用研究[J]. 数字技术与应用, 2016（10）: 143−145 ZHANG Lin, PAN Hongyan. Research on application of clustering analysis algorithm[J]. Digital Technology and Application, 2016（10）: 143 − 145. （in Chinese）
[22]	刘荣. 人工神经网络基本原理概述[J]. 计算机产品与流通, 2020（6）: 35 LIU Rong. Overview of basic principles of artificial neural network[J]. Computer Products & Circulation, 2020（6）: 35. （in Chinese）
[23]	袁冰清,程功,郑柳刚. BP神经网络基本原理[J]. 数字通信世界,2018(8):28 − 29. [YUAN Bingqing,CHENG Gong,ZHENG Liugang. Basic principle of BP neural networks[J]. Digital Communication World,2018(8):28 − 29. (in Chinese with English abstract) YUAN Bingqing, CHENG Gong, ZHENG Liugang. Basic principle of BP neural network[J]. Digital Communication World, 2018（8）: 28-29. （in Chinese with English abstract）
[24]	宫凤强,侯尚骞,李夕兵. 岩土参数截尾分布的正态信息扩散推断方法[J]. 武汉大学学报(工学版),2016,49(5):661 − 667. [GONG Fengqiang,HOU Shangqian,LI Xibing. Truncated distribution deduction method for geotechnical parameters based on normal information diffusion method[J]. Engineering Journal of Wuhan University,2016,49(5):661 − 667. (in Chinese with English abstract) GONG Fengqiang, HOU Shangqian, LI Xibing. Normal information diffusion inference method for truncated distribution of geotechnical parameters [J]. Engineering Journal of Wuhan University, 2016, 49（5）: 661-667. （in Chinese with English abstract）