Abstract
In this study, a machine learning method, i.e. genetic programming (GP), is employed to obtain a simplified statistical model to describe the variation of soil suction in drying cycles using five selected influential parameters. The data used for model development was recorded by an in-situ experiment. The image processing technology is used to quantify several tree canopy parameters. Based on four accuracy metrics, i.e. root mean square error (RMSE), mean absolute percentage error (MAPE), coefficient of determination (R2), and relative error, the performance of the proposed GP model was evaluated. The results indicate that the model can give a reasonable estimation for the spatiotemporal variations of soil suction around a tree with acceptable errors. Global sensitivity analysis for the statistical model obtained using limited data of a specific region demonstrates the drying time as the most influential variable and the initial soil suction as the second most influential variable for the soil suction variations. A case study was conducted using a set of assumed input variable values and validated that the simplified GP model can be used to estimate and predict the spatiotemporal variations of soil suction in rooted soil at a certain range.
概要
目的
在绿色岩土工程中,浅层土体特性通常受到当地 气候和覆盖植被的影响。本文旨在探讨自然环境 条件下不同植物和大气因素(与树的距离、空气 湿度和距离地表的深度等)与土体基质吸力的关 系,通过一种机器学习方法建立简化的统计模 型,并对浅层根系土体中基质吸力的时空变化进 行估算和预测。
创新点
1. 通过一种机器学习方法(即遗传编程算法)建 立土体基质吸力和五个选定的影响因素之间的 关系;2. 根据建立的统计模型,有效地预测了根 系土体内基质吸力的时空变化。
方法
1. 通过现场监测实验(图3 和4),量化土体基质 吸力和不同影响参数随时间的变化(图5 和6); 2. 通过机器学习算法,构建土体基质吸力的时空 变化与五个选定的影响参数之间的关系,得到一 个简化的统计模型(公式(11));3. 通过误差分析, 验证该简化统计模型在估算和预测土体基质吸 力时空变化时的可靠性;4. 通过敏感性分析研究 不同参数对土体基质吸力时空变化的影响(图 9);5. 通过案例研究,验证利用该方法对根系土 体基质吸力时空变化进行预测的可行性(图11 和12)。
结论
1. 遗传编程算法可以有效地建立土体基质吸力和 不同影响参数之间的关系,并能给出相应的数学 公式以对土体基质吸力的时空变化进行可靠的 估算和预测;2. 基于方差的全局敏感性分析方法 发现干循环时间和初始基质吸力对土体基质吸 力的时空变化有重要影响,而且其他的植物和大 气相关参数对土体基质吸力的时空变化也有不 可忽视的影响;3. 案例研究结果表明,本文所提 方法可用于预测土体基质吸力的时空变化。
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References
Ackora-Prah J, Oheneba-Osei FN, Andam PS, et al., 2015. A multigene genetic programming model for thyroid disorder detection. Applied Mathematical Sciences, 9(135):6707–6722. https://doi.org/10.12988/ams.2015.59563
Ahmad S, Kalra A, Stephen H, 2010. Estimating soil moisture using remote sensing data: a machine learning approach. Advances in Water Resources, 33(1):69–80. https://doi.org/10.1016/j.advwatres.2009.10.008
Alavi AH, Gandomi AH, 2011. A robust data mining approach for formulation of geotechnical engineering systems. Engineering Computations, 28(3):242–274. https://doi.org/10.1108/02644401111118132
Alemdag S, Gurocak Z, Cevik A, et al., 2016. Modeling deformation modulus of a stratified sedimentary rock mass using neural network, fuzzy inference and genetic programming. Engineering Geology, 203:70–82. https://doi.org/10.1016/j.enggeo.2015.12.002
An N, Hemmati S, Cui YJ, 2017. Numerical analysis of soil volumetric water content and temperature variations in an embankment due to soil-atmosphere interaction. Computers and Geotechnics, 83:40–51. https://doi.org/10.1016/j.compgeo.2016.10.010
ASTM (American Society for Testing Material), 2011. Standard Practice for Classification of Soils for Engineering Purposes (Unified Soil Classification System), D2487-11. National Standards of USA.
Bishop CM, 2006. Pattern Recognition and Machine Learning. Springer, New York, USA.
Brungard CW, Boettinger JL, Duniway MC, et al., 2015. Machine learning for predicting soil classes in three semi-arid landscapes. Geoderma, 239–240:68–83. https://doi.org/10.1016/j.geoderma.2014.09.019
Cannavó F, 2012. Sensitivity analysis for volcanic source modeling quality assessment and model selection. Computers & Geosciences, 44:52–59. https://doi.org/10.1016/j.cageo.2012.03.008
Chan K, Tarantola S, Saltelli A, et al., 2000. Variance based methods. In: Saltelli A, Chan K, Scott EM (Eds.), Sensitivity Analysis. John Wiley & Sons, Chichester, UK, p.167–197.
Cheng ZL, Zhou WH, Garg A, 2020. Genetic programming model for estimating soil suction in shallow soil layers in the vicinity of a tree. Engineering Geology, 268:105506. https://doi.org/10.1016/j.enggeo.2020.105506
Cramer NL, 1985. A representation for the adaptive generation of simple sequential programs. Proceedings of the 1st International Conference on Genetic Algorithms and Their Applications, p.183–187.
Crawford MM, Bryson LS, Woolery EW, et al., 2019. Long-term landslide monitoring using soil-water relationships and electrical data to estimate suction stress. Engineering Geology, 251:146–157. https://doi.org/10.1016/j.enggeo.2019.02.015
Cui YJ, Gao YB, Ferber V, 2010. Simulating the water content and temperature changes in an experimental embankment using meteorological data. Engineering Geology, 114(3–4):456–471. https://doi.org/10.1016/j.enggeo.2010.06.006
Cukier RI, Fortuin CM, Shuler KE, 1973. Study of the sensitivity of coupled reaction systems to uncertainties in rate coefficients. I theory. The Journal of Chemical Physics, 59(8):3873–3878. https://doi.org/10.1063/1.1680571
Dai H, Ye M, 2015. Variance-based global sensitivity analysis for multiple scenarios and models with implementation using sparse grid collocation. Journal of Hydrology, 528: 286–300. https://doi.org/10.1016/j.jhydrol.2015.06.034
Feng S, Liu HW, Ng CWW, 2019. Analytical solutions for one-dimensional water flow in vegetated layered soil. International Journal of Geomechanics, 19(2):04018191. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001343
Feng Y, Cui NB, Hao WP, et al., 2019. Estimation of soil temperature from meteorological data using different machine learning models. Geoderma, 338:67–77. https://doi.org/10.1016/j.geoderma.2018.11.044
Fredlund DG, Xing AQ, 1994. Equations for the soil-water characteristic curve. Canadian Geotechnical Journal, 31(4):521–532. https://doi.org/10.1139/t94-061
Fredlund DG, Sheng DC, Zhao JD, 2011. Estimation of soil suction from the soil-water characteristic curve. Canadian Geotechnical Journal, 48(2):186–198. https://doi.org/10.1139/T10-060
Fredlund MD, Wilson GW, Fredlund DG, 2002. Use of the grain-size distribution for estimation of the soil-water characteristic curve. Canadian Geotechnical Journal, 39(5):1103–1117. https://doi.org/10.1139/t02-049
Gadi V, Singh S, Singhariya M, 2018. Modeling soil-plant-water interaction: effects of canopy and root parameters on soil suction and stability of green infrastructure. Engineering Computations, 35(3):1543–1566. https://doi.org/10.1108/EC-07-2017-0280
Gadi VK, Hussain R, Bordoloi S, et al., 2019. Relating stomatal conductance and surface area with evapotranspiration induced suction in a heterogeneous grass cover. Journal of Hydrology, 568:867–876. https://doi.org/10.1016/j.jhydrol.2018.11.048
Gamse S, Zhou WH, Tan F, et al., 2018. Hydrostatic-season-time model updating using Bayesian model class selection. Reliability Engineering & System Safety, 169:40–50. https://doi.org/10.1016/j.ress.2017.07.018
Gandomi AH, Alavi AH, 2012. A new multi-gene genetic programming approach to non-linear system modeling. Part II: geotechnical and earthquake engineering problems. Neural Computing and Applications, 21(1):189–201. https://doi.org/10.1007/s00521-011-0735-y
Garg A, Garg A, Zhou WH, et al., 2015. A new simulation approach of genetic programming in modelling of soil water retention property of unsaturated soil. Engineering Computations, 32(3):914–930. https://doi.org/10.1108/EC-05-2014-0110
Garg A, Bordoloi S, Ni JJ, et al., 2019a. Influence of biochar addition on gas permeability in unsaturated soil. Géotechnique Letters, 9(1):66–71. https://doi.org/10.1680/jgele.18.00190
Garg A, Hazra B, Zhu H, et al., 2019b. A simplified probabilistic analysis of water content and wilting in soil vegetated with non-crop species. CATENA, 175:123–131. https://doi.org/10.1016/j.xatena.2018.12.016
Gopal P, Bordoloi S, Ratnam R, et al., 2019. Investigation of infiltration rate for soil-biochar composites of water hyacinth. Acta Geophysica, 67(1):231–246. https://doi.org/10.1007/s11600-018-0237-8
Guo F, Ma JJ, Zheng LJ, et al., 2016. Estimating distribution of water uptake with depth of winter wheat by hydrogen and oxygen stable isotopes under different irrigation depths. Journal of Integrative Agriculture, 15(4):891–906. https://doi.org/10.1016/S2095-3119(15)61258-8
He LX, Liu Y, Bi SF, et al., 2019. Estimation of failure probability in braced excavation using Bayesian networks with integrated model updating. Underground Space, in press. https://doi.org/10.1016/j.undsp.2019.07.001
Hemmati S, Gatmiri B, Cui YJ, et al., 2012. Thermo-hydromechanical modelling of soil settlements induced by soil-vegetation-atmosphere interactions. Engineering Geology, 139–140:1–16. https://doi.org/10.1016/j.enggeo.2012.04.003
Hossain MA, Yin JH, 2010. Behavior of a compacted completely decomposed granite soil from suction controlled direct shear tests. Journal of Geotechnical and Geoenvironmental Engineering, 136(1):189–198. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000189
Javadi AA, Rezania M, Nezhad MM, 2006. Evaluation of liquefaction induced lateral displacements using genetic programming. Computers and Geotechnics, 33(4–5):222–233. https://doi.org/10.1016/j.compgeo.2006.05.001
Jin YF, Yin ZY, Zhou WH, et al., 2019a. Multi-objective optimization-based updating of predictions during excavation. Engineering Applications of Artificial Intelligence, 78:102–123. https://doi.org/10.1016/j.engappai.2018.11.002
Jin YF, Yin ZY, Zhou WH, et al., 2019b. A single-objective EPR based model for creep index of soft clays considering L2 regularization. Engineering Geology, 248:242–255. https://doi.org/10.1016/j.enggeo.2018.12.006
Johari A, Habibagahi G, Ghahramani A, 2006. Prediction of soil-water characteristic curve using genetic programming. Journal of Geotechnical and Geoenvironmental Engineering, 132(5):661–665. https://doi.org/10.1061/(asce)1090-0241(2006)132:5(661)
Kalnins A, 2018. Multicollinearity: how common factors cause Type 1 errors in multivariate regression. Strategic Management, 39(8):2362–2385. https://doi.org/10.1002/smj.2783
Karandish F, Šimůnek J, 2016. A comparison of numerical and machine-learning modeling of soil water content with limited input data. Journal of Hydrology, 543:892–909. https://doi.org/10.1016/j.jhydrol.2016.11.007
Kim J, Jeong S, Park S, et al., 2004. Influence of rainfall-induced wetting on the stability of slopes in weathered soils. Engineering Geology, 75(3–4):251–262. https://doi.org/10.1016/j.enggeo.2004.06.017
Kisi O, Dailr AH, Cimen M, et al., 2012. Suspended sediment modeling using genetic programming and soft computing techniques. Journal of Hydrology, 450–451:48–58. https://doi.org/10.1016/j.jhydrol.2012.05.031
Kucherenko S, Shah N, 2007. The importance of being global. Application of global sensitivity analysis in Monte Carlo option pricing. Wilmott Magazine, 2007: 2–10.
Landsberg J, 1999. The Ways Trees Use Water. Water and Salinity Issues in Agroforestry. Rural Industries Research and Development Corporation, Canberra, Australia, p.1–92.
Lary DJ, Alavi AH, Gandomi AH, et al., 2016. Machine learning in geosciences and remote sensing. Geoscience Frontiers, 7(1):3–10. https://doi.org/10.1016/j.gsf.2015.07.003
Lee LM, Gofar N, Rahardjo H, 2009. A simple model for preliminary evaluation of rainfall-induced slope instability. Engineering Geology, 108(3–4):272–285. https://doi.org/10.1016/j.enggeo.2009.06.011
Leung AK, Garg A, Ng CWW, 2015. Effects of plant roots on soil-water retention and induced suction in vegetated soil. Engineering Geology, 193:183–197. https://doi.org/10.1016/j.enggeo.2015.04.017
Makkeasorn A, Chang NB, Beaman M, et al., 2006. Soil moisture estimation in a semiarid watershed using RADARSAT-1 satellite imagery and genetic programming. Water Resources Research, 42(9):W09401. https://doi.org/10.1029/2005WR004033
Mehr AD, Nourani V, 2018. Season algorithm-multigene genetic programming: a new approach for rainfall-runoff modelling. Water Resources Management, 32(8):2665–2679. https://doi.org/10.1007/s11269-018-1951-3
Ni JJ, Leung AK, Ng CWW, et al., 2018. Modelling hydromechanical reinforcements of plants to slope stability. Computers and Geotechnics, 95:99–109. https://doi.org/10.1016/j.compgeo.2017.09.001
Nowamooz H, Jahangir E, Masrouri F, et al., 2016. Effective stress in swelling soils during wetting drying cycles. Engineering Geology, 210:33–44. https://doi.org/10.1016/j.enggeo.2016.05.021
Parasuraman K, Elshorbagy A, Si BC, 2007. Estimating saturated hydraulic conductivity using genetic programming. Soil Science Society of America Journal, 71(6):1676–1684. https://doi.org/10.2136/sssaj2006.0396
Pétrowski A, Ben-Hamida S, 2017. Genetic programming for machine learning. In: Evolutionary Algorithms, Volume 9. Wiley, USA, p.183–216. https://doi.org/10.1002/9781119136378.ch6
Pham BT, Son LH, Hoang TA, et al., 2018. Prediction of shear strength of soft soil using machine learning methods. CATENA, 166:181–191. https://doi.org/10.1016/j.catena.2018.04.004
Poli R, Langdon WB, McPhee NF, 2008. A Field Guide to Genetic Programming. Lulu, Raleigh, USA.
Prasad R, 1988. A linear root water uptake model. Journal of Hydrology, 99(3–4):297–306. https://doi.org/10.1016/0022-1694(88)90055-8
Qi XH, Zhou WH, 2017. An efficient probabilistic back-analysis method for braced excavations using wall deflection data at multiple points. Computers and Geotechnics, 85:186–198. https://doi.org/10.1016/j.compgeo.2016.12.032
Qi XH, Zhou WH, Yuen KV, 2017. Detection of stationary Markovian zones in a geologically heterogeneous area. ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering, 3(4): 04017026. https://doi.org/10.1061/AJRUA6.0000930
Rezania M, Javadi AA, 2007. A new genetic programming model for predicting settlement of shallow foundations. Canadian Geotechnical Journal, 44(12):1462–1473. https://doi.org/10.1139/T07-063
Roushangar K, Akhgar S, Salmasi F, et al., 2014. Modeling energy dissipation over stepped spillways using machine learning approaches. Journal of Hydrology, 508:254–265. https://doi.org/10.1016/j.jhydrol.2013.10.053
Saltelli A, Sobol’ IM, 1995. About the use of rank transformation in sensitivity analysis of model output. Reliability Engineering & System Safety, 50(3):225–239. https://doi.org/10.1016/0951-8320(95)00099-2
Saltelli A, Annoni P, Azzini I, et al., 2010. Variance based sensitivity analysis of model output. Design and estimator for the total sensitivity index. Computer Physics Communications, 181(2):259–270. https://doi.org/10.1016/j.cpc.2009.09.018
Samui P, Sitharam TG, 2011. Machine learning modelling for predicting soil liquefaction susceptibility. Natural Hazards and Earth System Sciences, 11(1):1–9. https://doi.org/10.5194/nhess-11-1-2011
Searson DP, Leahy DE, Willis MJ, 2010. GPTIPS: an open source genetic programming toolbox for multigene symbolic regression. Proceedings of the International MultiConference of Engineers and Computer Scientists, p.77–80.
Shahin MA, 2015. Genetic programming for modelling of geotechnical engineering systems. In: Gandomi AH, Alavi AH, Ryan C (Eds.), Handbook of Genetic Programming Applications. Springer, Cham, Germany. https://doi.org/10.1007/978-3-319-20883-1_2
Sobol’ IM, 1990. On sensitivity estimation for nonlinear mathematical models. Matematicheskoe Modelirovanie, 2(1):112–118.
Sobol’ IM, 2001. Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Mathematics and Computers in Simulation, 55(1–3):271–280. https://doi.org/10.1016/S0378-4754(00)00270-6
Srivastava PK, Han DW, Ramirez MR, et al., 2013. Machine learning techniques for downscaling SMOS satellite soil moisture using MODIS land surface temperature for hydrological application. Water Resources Management, 27(8):3127–3144. https://doi.org/10.1007/s11269-013-0337-9
Sun SJ, Meng P, Zhang JS, et al., 2011. Variation in soil water uptake and its effect on plant water status in Juglans regia L. during dry and wet seasons. Tree Physiology, 31(12): 1378–1389. https://doi.org/10.1093/treephys/tpr116
Tan F, Zhou WH, Yuen KV, 2016. Modeling the soil water retention properties of same-textured soils with different initial void ratios. Journal of Hydrology, 542:731–743. https://doi.org/10.1016/j.jhydrol.2016.09.045
Tan F, Zhou WH, Yuen KV, 2018. Effect of loading duration on uncertainty in creep analysis of clay. International Journal for Numerical and Analytical Methods in Geomechanics, 42(11):1235–1254. https://doi.org/10.1002/nag.2788
Too VK, Omuto CT, Biamah EK, et al., 2014. Review of soil water retention characteristic (SWRC) models between saturation and oven dryness. Open Journal of Modern Hydrology, 4(4):173–182. https://doi.org/10.4236/ojmh.2014.44017
Totoev YZ, Kleeman PW, 1998. An infiltration model to predict suction changes in the soil profile. Water Resources Research, 34(7):1617–1622. https://doi.org/10.1029/98WR00825
Wang H, 2020. Finding patterns in subsurface using Bayesian machine learning approach. Underground Space, 5(1):84–92. https://doi.org/10.1016/j.undsp.2018.10.006
Weyl H, 1938. Mean motion. American Journal of Mathematics, 60(4):889–896. https://doi.org/10.2307/2371267
Whigham PA, Crapper PF, 2001. Modelling rainfall-runoff using genetic programming. Mathematical and Computer Modelling, 33(6–7):707–721. https://doi.org/10.1016/S0895-7177(00)00274-0
Wikipedia, 2019. Tree Crown Measurement. Wikipedia. https://wikimili.com/en/Tree_crown_measurement
Yang SR, Huang WH, Chung SH, 2015. Combined effects of temperature and moisture content on soil suction of compacted bentonite. Journal of Marine Science and Technology, 23(3):281–287. https://doi.org/10.6119/JMST-014-0326-2
Yin ZY, Jin YF, Shen SL, et al., 2017. An efficient optimization method for identifying parameters of soft structured clay by an enhanced genetic algorithm and elasticviscoplastic model. Acta Geotechnica, 12(4):849–867. https://doi.org/10.1007/s11440-016-0486-0
Yin ZY, Jin YF, Shen JS, et al., 2018. Optimization techniques for identifying soil parameters in geotechnical engineering: comparative study and enhancement. International Journal for Numerical and Analytical Methods in Geomechanics, 42(1):70–94. https://doi.org/10.1002/nag.2714
Zhang P, Yin ZY, Jin YF, et al., 2020. A novel hybrid surrogate intelligent model for creep index prediction based on particle swarm optimization and random forest. Engineering Geology, 265:105328. https://doi.org/10.1016/j.enggeo.2019.105328
Zhou WH, Qi XH, 2019. Root cohesion estimation of riparian trees based on model uncertainty characterization. Journal of Materials in Civil Engineering, 31(2):04018389. https://doi.org/10.1061/(ASCE)MT.1943-5533.0002600
Zhou WH, Yuen KV, Tan F, 2013. Estimation of maximum pullout shear stress of grouted soil nails using Bayesian probabilistic approach. International Journal of Geomechanics, 13(5):659–664. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000259
Zhou WH, Garg A, Garg A, 2016. Study of the volumetric water content based on density, suction and initial water content. Measurement, 94:531–537. https://doi.org/10.1016/j.measurement.2016.08.034
Zhou WH, Garg A, Garg A, 2017. Computation of coupled effects of root and shoot characteristics on transpiration based on optimization approach. Engineering Computations, 34(3):725–738. https://doi.org/10.1108/EC-05-2016-0177
Zhou WH, Tan F, Yuen KV, 2018. Model updating and uncertainty analysis for creep behavior of soft soil. Computers and Geotechnics, 100:135–143. https://doi.org/10.1016/j.compgeo.2018.04.006
Zhou WH, He SY, Garg A, et al., 2020. Field monitoring of suction in the vicinity of an urban tree: exploring termite infestation and the shading effects of tree canopy. Acta Geotechnica, 15(5):1341–1361. https://doi.org/10.1007/s11440-019-00810-0
Zhu H, Zhang LM, Garg A, 2018. Investigating plant transpiration-induced soil suction affected by root morphology and root depth. Computers and Geotechnics, 103:26–31. https://doi.org/10.1016/j.compgeo.2018.06.019
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Wan-huan ZHOU designed the research. Zhi-liang CHENG processed the corresponding data. Zhi-liang CHENG wrote the first draft of the manuscript. Wan-huan ZHOU, Zhi DING, and Yong-xing GUO helped to organize the manuscript. Wan-huan ZHOU and Zhi-liang CHENG revised and edited the final version.
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Zhi-liang CHENG, Wan-huan ZHOU, Zhi DING, and Yong-xing GUO declare that they have no conflict of interest.
Project supported by the National Key R&D Program of China (No. 2019YFB1600700), the Science and Technology Development Fund of Macau (Nos. SKL-IOTSC-2018-2020 and 0193/2017/A3), and the University of Macau Research Fund (No. MYRG2018-00173-FST), China
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Cheng, Zl., Zhou, Wh., Ding, Z. et al. Estimation of spatiotemporal response of rooted soil using a machine learning approach. J. Zhejiang Univ. Sci. A 21, 462–477 (2020). https://doi.org/10.1631/jzus.A1900555
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DOI: https://doi.org/10.1631/jzus.A1900555