Technical Papers
Feb 9, 2023

Data-Driven Development of Three-Dimensional Subsurface Models from Sparse Measurements Using Bayesian Compressive Sampling: A Benchmarking Study

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Publication: ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 9, Issue 2

Abstract

With the rapid development of computing and digital technologies recently, three-dimensional (3D) subsurface models for accurate site characterization have received increasing attention, for example, with various data-driven methods developed for 3D subsurface modeling. This leads to a need for validating the 3D modeling results obtained from each method and comparing the performance of different methods in a fair and consistent manner. To address this need, a benchmarking study, which is often used in machine learning (ML), is presented in this study to compare the performance of different 3D subsurface modeling methods in four aspects, including accuracy, uncertainty, robustness, and computational efficiency. A suite of performance metrics is proposed for the four aspects above. Multiple sets of real cone penetration test (CPT) data are compiled in the benchmarking study for quantifying performance of 3D modeling methods using sparse measurements as input, a typical scenario in geotechnical practice. The benchmarking study is illustrated using an in-house software package called Analytics of Sparse Spatial Data based on Bayesian compressive sampling/sensing (ASSD-BCS), which can directly generate high-resolution 3D random field samples (RFSs) from sparse measurements. The evaluation results show that ASSD-BCS provides accurate estimates with quantified uncertainty from sparse measurements. In addition, ASSD-BCS exhibits remarkably high computational efficiency and performs robustly under different benchmarking cases.

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Data Availability Statement

All data, models, and code generated or used during the study are available from the corresponding author upon reasonable request. The BCS-based software package ASSD-BCS version 1.1 is available at https://sites.google.com/site/yuwangcityu/software-download/bayesian-compressive-samplingsensing-bcs.

Acknowledgments

The work described in this paper was supported by a grant from the Innovation and Technology Commission of Hong Kong Special Administrative Region (Project No. MHP/099/21), a grant from the Research Grants Council of the Hong Kong Special Administrative Region (Project No. CityU 11213119), and a grant from Shenzhen Science and Technology Innovation Commission [Shenzhen-Hong Kong-Macau Science and Technology Project (Category C) No. SGDX20210823104002020], China. The financial support is gratefully acknowledged.

References

Andrieu, C., N. De Freitas, A. Doucet, and M. I. Jordan. 2003. “An introduction to MCMC for machine learning.” Mach. Learn. 50 (1): 5–43. https://doi.org/10.1023/A:1020281327116.
Baecher, G. B., and J. T. Christian. 2003. Reliability and statistics in geotechnical engineering. Hoboken, NJ: Wiley.
Bhagoji, A. N., D. Cullina, C. Sitawarin, and P. Mittal. 2018. “Enhancing robustness of machine learning systems via data transformations.” In Proc., 52nd Annual Conf. on Information Sciences and Systems, 1–5. New York: IEEE.
Caiafa, C. F., and A. Cichocki. 2013. “Computing sparse representations of multidimensional signals using kronecker bases.” Neural Comput. 25 (1): 186–220. https://doi.org/10.1162/NECO_a_00385.
Candès, E. J., and M. B. Wakin. 2008. “An introduction to compressive sampling.” IEEE Signal Process Mag. 25 (2): 21–30. https://doi.org/10.1109/MSP.2007.914731.
Carlini, N., and D. Wagner. 2017. “Towards evaluating the robustness of neural networks.” In Proc., 2017 IEEE Symp. on Security and Privacy, 39–57. New York: IEEE.
Ching, J. Y., Z. Y. Yang, and K. K. Phoon. 2021. “Dealing with non-lattice data in three-dimensional probabilistic site characterization.” J. Eng. Mech. 147 (5): 06021003. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001907.
Dellaportas, P., J. J. Forster, and I. Ntzoufras. 2002. “On Bayesian model and variable selection using MCMC.” Stat. Comput. 12 (5): 27–36. https://doi.org/10.1023/A:1013164120801.
Donoho, D. L. 2006. “Compressed sensing.” IEEE Trans. Inf. Theory 52 (4): 1289–1306. https://doi.org/10.1109/TIT.2006.871582.
Doumpos, M., C. Zopounidis, and E. Grigoroudis. 2016. “Robustness analysis in decision aiding, optimization, and analytics.” In International series in operations research and management science. Berlin: Springer.
Duan, Y., X. Chen, R. Houthooft, J. Schulman, and P. Abbeel. 2016. “Benchmarking deep reinforcement learning for continuous control.” In Proc., 33rd Int. Conf. on Machine Learning, 1329–1338. Brookline, MA: Microtome.
Efron, B., and R. Tibshirani. 1993. An introduction to the bootstrap. London: Chapman & Hall.
Fawzi, A., O. Fawzi, and P. Frossard. 2018. “Analysis of classifiers’ robustness to adversarial perturbations.” Mach. Learn. 107 (Mar): 481–508. https://doi.org/10.1007/s10994-017-5663-3.
Fenton, G. A., and D. V. Griffiths. 2008. Risk assessment in geotechnical engineering. Hoboken, NJ: Wiley.
Fernandez, J. C., L. Mounier, and C. Pachon. 2005. “A model-based approach for robustness testing.” In Vol. 3502 of Proc., Int. Conf. on Testing of Communicating Systems, edited by F. Khendek and R. Dssouli, 333–348. Berlin: Springer.
Hu, Y., and Y. Wang. 2020. “Probabilistic soil classification and stratification in a vertical cross-section from limited cone penetration tests using random field and Monte Carlo simulation.” Comput. Geotech. 124 (5): 103634. https://doi.org/10.1016/j.compgeo.2020.103634.
Huang, Y., J. L. Beck, S. Wu, and H. Li. 2014. “Robust Bayesian compressive sensing for signals in structural health monitoring.” Comput.-Aided Civ. Infrastruct. Eng. 29 (3): 160–179. https://doi.org/10.1111/mice.12051.
ISSMGE (International Society for Soil Mechanics and Geotechnical Engineering). 2017. “Geotechnical databases compiled by TC304 of the international society of soil mechanics and geotechnical engineering.” Accessed March 28, 2022. http://140.112.12.21/issmge/tc304.htm.
Jaksa, M. 1995. “The influence of spatial variability on the geotechnical design properties of a stiff, overconsolidated clay.” Ph.D. dissertation, Dept. of Civil and Environmental Engineering, Univ. of Adelaide.
Jaksa, M., W. S. Kaggwa, and P. I. Brooker. 1999. “Experimental evaluation of the scale of fluctuation of a stiff clay.” In Proc., 8th Int. Conf. Application of Statistics and Probability, 415–422. Rotterdam, Netherlands: A.A. Balkema.
Ji, S., Y. Xue, and L. Carin. 2008. “Bayesian compressive sensing.” IEEE Trans. Signal Process. 56 (6): 2346–2356. https://doi.org/10.1109/TSP.2007.914345.
Joanes, D. N., and C. A. Gill. 1998. “Comparing measures of sample skewness and kurtosis.” J. R. Stat. Soc. 47 (1): 183–189. https://doi.org/10.1111/1467-9884.00122.
Koirala, A., K. B. Walsh, Z. Wang, and C. McCarthy. 2019. “Deep learning for real-time fruit detection and orchard fruit load estimation: Benchmarking of ‘MangoYOLO’.” Precis. Agric. 20 (2): 1107–1135. https://doi.org/10.1007/s11119-019-09642-0.
Kroese, D. P., T. Taimre, and Z. I. Botev. 2013. Handbook of monte carlo methods. Hoboken, NJ: Wiley.
LeCun, Y., L. Bottou, Y. Bengio, and P. Haffner. 1998. “Gradient-based learning applied to document recognition.” Proc. IEEE 86 (11): 2278–2324. https://doi.org/10.1109/5.726791.
Li, J., M. Cassidy, J. Huang, L. Zhang, and R. Kelly. 2016. “Probabilistic identification of soil stratification.” Géotechnique 66 (1): 16–26. https://doi.org/10.1680/jgeot.14.P.242.
Marra, G., and S. N. Wood. 2012. “Coverage properties of confidence intervals for generalized additive model components.” Scand. J. Stat. 39 (1): 53–74. https://doi.org/10.1111/j.1467-9469.2011.00760.x.
McPhail, C., H. R. Maier, J. H. Kwakkel, M. Giuliani, A. Castelletti, and S. Westra. 2018. “Robustness metrics: How are they calculated, when should they be used and why do they give different results?” Earth’s Future 6 (2): 169–191. https://doi.org/10.1002/2017EF000649.
Montoya-Noguera, S., T. Y. Zhao, Y. Hu, Y. Wang, and K. K. Phoon. 2019. “Simulation of non-stationary non-Gaussian random fields from sparse measurements using Bayesian compressive sampling and Karhunen-Loève expansion.” Struct. Saf. 79 (3): 66–79. https://doi.org/10.1016/j.strusafe.2019.03.006.
Nychka, D. 1988. “Bayesian confidence intervals for smoothing splines.” J. Am. Stat. Assoc. 83 (404): 1134–1143. https://doi.org/10.1080/01621459.1988.10478711.
Phoon, K. K., and J. Y. Ching. 2014. Risk and reliability in geotechnical engineering. Boca Raton, FL: Taylor & Francis Group.
Phoon, K. K., J. Y. Ching, and Y. Shuku. 2022a. “Challenges in data-driven site characterization.” Georisk 16 (1): 114–126. https://doi.org/10.1080/17499518.2021.1896005.
Phoon, K. K., and F. H. Kulhawy. 1999. “Characterization of geotechnical variability.” Can. Geotech. J. 36 (4): 612–624. https://doi.org/10.1139/t99-038.
Phoon, K. K., T. Shuku, J. Y. Ching, and Y. Ikumasa. 2022b. “Benchmarking examples for data-driven site characterization.” Georisk 2022 (Feb): 1–23. https://doi.org/10.1080/17499518.2022.2025541.
Rauber, J., W. Brendel, and M. Bethge. 2020. “Foolbox: A Python toolbox to benchmark the robustness of machine learning models.” J. Open Source Software 5 (53): 2607. https://doi.org/10.21105/joss.02607.
Robertson, P. K. 2009. “Interpretation of cone penetration tests—A unified approach.” Can. Geotech. J. 46 (11): 1337–1355. https://doi.org/10.1139/T09-065.
Robertson, P. K., and C. E. Wride. 1998. “Evaluating cyclic liquefaction potential using the cone penetration test.” Can. Geotech. J. 35 (5): 442–459. https://doi.org/10.1139/t98-017.
Shi, S., Q. Wang, P. Xu, and X. Chu. 2016. “Benchmarking state-of-the-art deep learning software tools.” In Proc., 2016 7th Int. Conf. on Cloud Computing and Big Data (CCBD), 99–104. New York: IEEE.
Shu, X., and N. Ahuja. 2011. “Imaging via three-dimensional compressive sampling (3DCS).” In Proc., 2011 Int. Conf. on Computer Vision, 439–446. New York: IEEE.
Shuku, T., and K. K. Phoon. 2021. “Three-dimensional subsurface modeling using Geotechnical Lasso.” Comput. Geotech. 133 (2): 104068. https://doi.org/10.1016/j.compgeo.2021.104068.
Stallkamp, J., M. Schlipsing, J. Salmen, and C. Igel. 2012. “Man vs. computer: Benchmarking machine learning algorithms for traffic sign recognition.” Neural Netw. 32 (6): 323–332. https://doi.org/10.1016/j.neunet.2012.02.016.
Tipping, M. E. 2001. “Sparse Bayesian learning and the relevance vector machine.” J. Mach. Learn. Res. 1 (36): 211–244. https://doi.org/10.1162/15324430152748236.
Wahba, G. 1983. “Bayesian ‘confidence intervals’ for the cross-validated smooth spline.” J. R. Stat. Soc. B 45 (1): 133–150. https://doi.org/10.1111/j.2517-6161.1983.tb01239.x.
Wang, Y., Z. J. Cao, and D. Q. Li. 2016. “Bayesian perspective on geotechnical variability and site characterization.” Eng. Geol. 203 (8): 117–125. https://doi.org/10.1016/j.enggeo.2015.08.017.
Wang, Y., Y. Hu, and K. K. Phoon. 2022. “Non-parametric modelling and simulation of spatiotemporally varying geo-data.” Georisk 16 (1): 77–97. https://doi.org/10.1080/17499518.2021.1971258.
Wang, Y., and T. Y. Zhao. 2016. “Interpretation of soil property profile from limited measurement data: A compressive sampling perspective.” Can. Geotech. J. 53 (9): 1547–1559. https://doi.org/10.1139/cgj-2015-0545.
Wang, Y., and T. Y. Zhao. 2017. “Statistical interpretation of soil property profiles from sparse data using Bayesian compressive sampling.” Géotechnique 67 (6): 523–536. https://doi.org/10.1680/jgeot.16.P.143.
Wang, Y., T. Y. Zhao, and K. K. Phoon. 2018. “Direct simulation of random field samples from sparsely measured geotechnical data with consideration of uncertainty in interpretation.” Can. Geotech. J. 55 (6): 862–880. https://doi.org/10.1139/cgj-2017-0254.
Yoshida, I., Y. Tomizawa, and Y. Otake. 2021. “Estimation of trend and random components of conditional random field using Gaussian process regression.” Comput. Geotech. 136 (10): 104179. https://doi.org/10.1016/j.compgeo.2021.104179.
Yuen, K. V., and H. Q. Mu. 2012. “A novel probabilistic method for robust parametric identification and outlier detection.” Probab. Eng. Mech. 30 (2): 48–59. https://doi.org/10.1016/j.probengmech.2012.06.002.
Yuen, K. V., and G. A. Ortiz. 2017. “Outlier detection and robust regression for correlated data.” Comput. Methods Appl. Mech. Eng. 313 (4): 632–646. https://doi.org/10.1016/j.cma.2016.10.004.
Zhao, T. Y., S. Montoya-Noguera, K. K. Phoon, and Y. Wang. 2018. “Interpolating spatially varying soil property values from sparse data for facilitating characteristic value selection.” Can. Geotech. J. 55 (2): 171–181. https://doi.org/10.1139/cgj-2017-0219.
Zhao, T. Y., and Y. Wang. 2018. “Simulation of cross-correlated random field samples from sparse measurements using Bayesian compressive sensing.” Mech. Syst. Signal Process. 112 (8): 384–400. https://doi.org/10.1016/j.ymssp.2018.04.042.
Zhao, T. Y., and Y. Wang. 2020. “Non-parametric simulation of non-stationary non-Gaussian 3D random field samples directly from sparse measurements using signal decomposition and Markov chain Monte Carlo (MCMC) simulation.” Reliab. Eng. Syst. Saf. 203 (Feb): 107087. https://doi.org/10.1016/j.ress.2020.107087.
Zhao, T. Y., and Y. Wang. 2021. “Statistical interpolation of spatially varying but sparsely measured 3D geo-data using compressive sensing and variational Bayesian inference.” Math. Geosci. 53 (3): 1171–1199. https://doi.org/10.1007/s11004-020-09913-x.
Zheng, S., Y. X. Zhu, D. Q. Li, Z. J. Cao, Q. X. Deng, and K. K. Phoon. 2021. “Probabilistic outlier detection for sparse multivariate geotechnical site investigation data using Bayesian learning.” Geosci. Front. 12 (3): 425–439. https://doi.org/10.1016/j.gsf.2020.03.017.

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Go to ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 9Issue 2June 2023

History

Received: Apr 27, 2022
Accepted: Nov 2, 2022
Published online: Feb 9, 2023
Published in print: Jun 1, 2023
Discussion open until: Jul 9, 2023

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Ph.D. Student, Dept. of Architecture and Civil Engineering, City Univ. of Hong Kong, Tat Chee Ave., Kowloon, Hong Kong. Email: [email protected]
Research Fellow, Dept. of Civil and Environmental Engineering, National Univ. of Singapore, Lower Kent Ridge Rd., Singapore 117576. ORCID: https://orcid.org/0000-0001-8748-7517. Email: [email protected]
Professor, Dept. of Architecture and Civil Engineering, City Univ. of Hong Kong, Tat Chee Ave., Kowloon, Hong Kong (corresponding author). ORCID: https://orcid.org/0000-0003-4635-7059. Email: [email protected]

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