Characterizing multivariate, asymmetric, and multimodal distributions of geotechnical data with dual-stage missing values: BASIC-H

References

• Beck, J. L., and K.-V. Yuen. 2004. “Model Selection Using Response Measurements: Bayesian Probabilistic Approach.” Journal of Engineering Mechanics 130 (2): 192–203. https://doi.org/10.1061/(ASCE)0733-9399(2004)130:2(192).
   Web of Science ®Google Scholar
• Bouayad, D., J. Baroth, and C. Dano. 2021. “Gaussian Mixture Model Based Soil Classification Using Multiple Cone Penetration Tests.” In IOP Conference Series: Earth and Environmental Science, Vol. 696, 12034. IOP Publishing.
   Google Scholar
• Box, G. E. P., and G. C. Tiao. 2011. Bayesian Inference in Statistical Analysis. The United States of America: John Wiley & Sons.
   Google Scholar
• Bozorgzadeh, N., M. D. Escobar, and J. P. Harrison. 2018. “Comprehensive Statistical Analysis of Intact Rock Strength for Reliability-Based Design.” International Journal of Rock Mechanics and Mining Sciences 106 (March): 374–387. https://doi.org/10.1016/j.ijrmms.2018.03.005.
   Google Scholar
• Cao, Z., and Y. Wang. 2014. “Bayesian Model Comparison and Characterization of Undrained Shear Strength.” Journal of Geotechnical and Geoenvironmental Engineering 140 (6): 4014018. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001108.
   Web of Science ®Google Scholar
• Cao, Z., Y. Wang, and D. Li. 2017. Probabilistic Approaches for Geotechnical Site Characterization and Slope Stability Analysis. Berlin Heidelberg: Springer.
   Google Scholar
• Cheliotis, M., C. Gkerekos, I. Lazakis, and G. Theotokatos. 2019. “A Novel Data Condition and Performance Hybrid Imputation Method for Energy Efficient Operations of Marine Systems.” Ocean Engineering 188:106220. https://doi.org/10.1016/j.oceaneng.2019.106220.
   Web of Science ®Google Scholar
• Chen, Z., H. Li, and Y. Bao. 2019. “Analyzing and Modeling Inter-Sensor Relationships for Strain Monitoring Data and Missing Data Imputation: A Copula and Functional Data-Analytic Approach.” Structural Health Monitoring 18 (4): 1168–1188. https://doi.org/10.1177/1475921718788703.
   Web of Science ®Google Scholar
• Ching, J., and K.-K. Phoon. 2012. “Modeling Parameters of Structured Clays as a Multivariate Normal Distribution.” Canadian Geotechnical Journal 49 (5): 522–545. https://doi.org/10.1139/t2012-015.
   Web of Science ®Google Scholar
• Ching, J., and K.-K. Phoon. 2014. “Correlations Among Some Clay Parameters-The Multivariate Distribution.” Canadian Geotechnical Journal 51 (6): 686–704. https://doi.org/10.1139/cgj-2013-0353.
   Web of Science ®Google Scholar
• Ching, J., and K.-K. Phoon. 2020. “Constructing a Site-Specific Multivariate Probability Distribution Using Sparse.” Incomplete, and Spatially Variable (MUSIC-X) Data, Journal of Engineering Mechanics146 (7): 04020061. https://doi.org/10.1061/(asce)em.1943-7889.0001779.
   Google Scholar
• Ching, J., K.-K. Phoon, K.-F. Chen, T. L. L. Orr, and H. R. Schneider. 2020. “Statistical Determination of Multivariate Characteristic Values for Eurocode 7.” Structural Safety 82:101893. https://doi.org/10.1016/j.strusafe.2019.101893.
   Web of Science ®Google Scholar
• Ching, J., K. K. Phoon, and D. Q. Li. 2016. “Robust Estimation of Correlation Coefficients Among Soil Parameters Under the Multivariate Normal Framework.” Structural Safety 63:21–32. https://doi.org/10.1016/j.strusafe.2016.07.002.
   Web of Science ®Google Scholar
• Ching, J., K.-K. Phoon, K.-H. Li, and M.-C. Weng. 2019. “Multivariate Probability Distribution for Some Intact Rock Properties.” Canadian Geotechnical Journal 56 (8): 1080–1097. https://doi.org/10.1139/cgj-2018-0175.
   Web of Science ®Google Scholar
• Ching, J., K.-K. Phoon, Z. Yang, and A. W. Stuedlein. 2022. “Quasi-Site-Specific Multivariate Probability Distribution Model for Sparse, Incomplete, and Three-Dimensional Spatially Varying Soil Data.” Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards 16 (1): 53–76.
   Google Scholar
• Crambes, C., and Y. Henchiri. 2019. “Regression Imputation in the Functional Linear Model with Missing Values in the Response.” Journal of Statistical Planning and Inference 201:103–119. https://doi.org/10.1016/j.jspi.2018.12.004.
   Web of Science ®Google Scholar
• Depina, I., S. Jain, S. Mar Valsson, and H. Gotovac. 2022. “Application of Physics-Informed Neural Networks to Inverse Problems in Unsaturated Groundwater Flow.” Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards 16 (1): 21–36.
   Google Scholar
• Duin. 1976. “On the Choice of Smoothing Parameters for Parzen Estimators of Probability Density Functions.” IEEE Transactions on Computers 100 (11): 1175–1179. https://doi.org/10.1109/TC.1976.1674577.
   Google Scholar
• Fan, G., J. Li, and H. Hao. 2019. “Lost Data Recovery for Structural Health Monitoring Based on Convolutional Neural Networks.” Structural Control and Health Monitoring 26 (10): e2433. https://doi.org/10.1002/stc.v26.10.
   Web of Science ®Google Scholar
• Han, L., H. Liu, W. Zhang, and L. Wang. 2023. “A Comprehensive Comparison of Copula Models and Multivariate Normal Distribution for Geo-Material Parametric Data.” Computers and Geotechnics164:105777. https://doi.org/10.1016/j.compgeo.2023.105777.
   Web of Science ®Google Scholar
• Haselsteiner, A. F., J.-H. Ohlendorf, W. Wosniok, and K.-D. Thoben. 2017. “Deriving Environmental Contours From Highest Density Regions.” Coastal Engineering 123:42–51. https://doi.org/10.1016/j.coastaleng.2017.03.002.
   Web of Science ®Google Scholar
• Higham, N. J. 2002. “Computing the Nearest Correlation Matrix-a Problem From Finance.” IMA Journal of Numerical Analysis 22 (3): 329–343. https://doi.org/10.1093/imanum/22.3.329.
   Web of Science ®Google Scholar
• Hyndman, R. J. 1996. “Computing and Graphing Highest Density Regions.” The American Statistician 50 (2): 120–126.
   Web of Science ®Google Scholar
• Kumar, A., and G. Tiwari. 2023. “Bayesian Multimodel Probabilistic Methodology for Stability Analysis of Rock Structures with Limited Data of Copula-Dependent Inputs.” ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering 9 (3): 4023025. https://doi.org/10.1061/AJRUA6.RUENG-1064.
   Google Scholar
• Lai, X., X. Wu, L. Zhang, W. Lu, and C. Zhong. 2019. “Imputations of Missing Values Using a Tracking-Removed Autoencoder Trained with Incomplete Data.” Neurocomputing366:54–65. https://doi.org/10.1016/j.neucom.2019.07.066.
   Web of Science ®Google Scholar
• Lai, X., L. Zhang, and X. Liu. 2020. “Takagi-Sugeno Modeling of Incomplete Data for Missing Value Imputation with the Use of Alternate Learning.” IEEE Access 8:83633–83644. https://doi.org/10.1109/ACCESS.2020.2991669.
   Web of Science ®Google Scholar
• Lebrun, R., and A. Dutfoy. 2009. “A Generalization of the Nataf Transformation to Distributions with Elliptical Copula.” Probabilistic Engineering Mechanics 24 (2): 172–178. https://doi.org/10.1016/j.probengmech.2008.05.001.
   Web of Science ®Google Scholar
• Leiva-Murillo, J. M., and A. Artés-Rodríguez. 2012. “Algorithms for Maximum-Likelihood Bandwidth Selection in Kernel Density Estimators.” Pattern Recognition Letters 33 (13): 1717–1724. https://doi.org/10.1016/j.patrec.2012.06.006.
   Web of Science ®Google Scholar
• Li, D. Q., S. B. Wu, C. B. Zhou, and K. K. Phoon. 2012. “Performance of Translation Approach for Modeling Correlated Non-normal Variables.” Structural Safety 39:52–61. https://doi.org/10.1016/j.strusafe.2012.08.001.
   Web of Science ®Google Scholar
• Li, X. Y., L. M. Zhang, and J. H. Li. 2016. “Using Conditioned Random Field to Characterize the Variability of Geologic Profiles.” Journal of Geotechnical and Geoenvironmental Engineering 142 (4): 4015096. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001428.
   Web of Science ®Google Scholar
• Li, L., J. Zhang, Y. Wang, and B. Ran. 2017. “Multiple Imputation for Incomplete Traffic Accident Data Using Chained Equations.” In 2017 IEEE 20th International Conference on Intelligent Transportation Systems (ITSC), 1–5. IEEE.
   Google Scholar
• Liu, H., and X. Qi. 2018. “Random Field Characterization of Uniaxial Compressive Strength and Elastic Modulus for Intact Rocks.” Geoscience Frontiers 9 (6): 1609–1618. https://doi.org/10.1016/j.gsf.2017.11.014.
   Web of Science ®Google Scholar
• Liu, W., and Y. Yang. 2011. “Parametric Or Nonparametric? A Parametricness Index for Model Selection.” The Annals of Statistics 39 (4): 2074–2102.
   Web of Science ®Google Scholar
• Liu, S., H. Zou, G. Cai, T. V. Bheemasetti, A. J. Puppala, and J. Lin. 2016. “Multivariate Correlation Among Resilient Modulus and Cone Penetration Test Parameters of Cohesive Subgrade Soils.” Engineering Geology 209:128–142. https://doi.org/10.1016/j.enggeo.2016.05.018.
   Web of Science ®Google Scholar
• Masoudian, M. S., M. A. Hashemi Afrapoli, A. Tasalloti, and A. M. Marshall. 2019. “A General Framework for Coupled Hydro-mechanical Modelling of Rainfall-induced Instability in Unsaturated Slopes with Multivariate Random Fields.” Computers and Geotechnics 115 (May): 103162. https://doi.org/10.1016/j.compgeo.2019.103162.
   Google Scholar
• McCloud, N., and C. F. Parmeter. 2020. “Determining the Number of Effective Parameters in Kernel Density Estimation.” Computational Statistics & Data Analysis 143:106843. https://doi.org/10.1016/j.csda.2019.106843.
   Web of Science ®Google Scholar
• Mu, H.-Q., Q. Hu, H.-Z. Guo, T.-Y. Zhang, and C. Su. 2019. “Uncertainty Quantification of Load Effects Under Stochastic Traffic Flows.” International Journal of Structural Stability and Dynamics 19 (01): 1940009. https://doi.org/10.1142/S0219455419400091.
   Google Scholar
• Mu, H. Q., H. T. Liu, and J. H. Shen. 2020. “Copula-Based Uncertainty Quantification (Copula-UQ) for Multi-Sensor Data in Structural Health Monitoring.” Sensors (Switzerland) 20 (19): 1–18. https://doi.org/10.3390/s20195692.
   Web of Science ®Google Scholar
• Mu, H.-Q., J.-H. Shen, Z.-T. Zhao, H.-T. Liu, and K.-V. Yuen. 2022. “A Novel Generative Approach for Modal Frequency Probabilistic Prediction Under Varying Environmental Condition Using Incomplete Information.” Engineering Structures 252:113571. https://doi.org/10.1016/j.engstruct.2021.113571.
   Web of Science ®Google Scholar
• Mu, H. Q., Z. J. Zheng, X. H. Wu, and C. Su. 2020. “Bayesian Network-Based Modal Frequency-Multiple Environmental Factors Pattern Recognition for the Xinguang Bridge Using Long-Term Monitoring Data.” Journal of Low Frequency Noise Vibration and Active Control 39 (3): 545–559. https://doi.org/10.1177/1461348418786520.
   Web of Science ®Google Scholar
• Murphy, K. P. 2022. Probabilistic Machine Learning: An Introduction. London: MIT press.
   Google Scholar
• Phoon, K.-K. 2018. “Probabilistic Site Characterization”.
   Google Scholar
• Phoon, K.-K. 2020. “The Story of Statistics in Geotechnical Engineering.” Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards 14 (1): 3–25.
   Google Scholar
• Phoon, K.-K., J. Ching, and Z. Cao. 2022. “Unpacking Data-Centric Geotechnics.” Underground Space7 (6): 967–989. https://doi.org/10.1016/j.undsp.2022.04.001.
   Web of Science ®Google Scholar
• Phoon, K.-K., J. Ching, and T. Shuku. 2022. “Challenges in Data-Driven Site Characterization.” Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards 16 (1): 114–126.
   Google Scholar
• Prakash, A., B. Hazra, and S. Sekharan. 2020. “Probabilistic Analysis of Soil-Water Characteristic Curve of Bentonite: Multivariate Copula Approach.” International Journal of Geomechanics 20 (2): 4019150. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001554.
   Web of Science ®Google Scholar
• Rana, H., and G. L. Sivakumar Babu. 2022. “Probabilistic Back Analysis for Rainfall-Induced Slope Failure Using MLS-SVR and Bayesian Analysis.” Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards 1–14.
   Google Scholar
• Rezaee, M., S. F. F. Mojtahedi, E. Taherabadi, K. Soleymani, and M. Pejman. 2021. “Prediction of Shear Strength Parameters of Hydrocarbon Contaminated Sand Based on Machine Learning Methods.” Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards 15 (4): 317–335.
   Google Scholar
• Samui, P. 2008. “Relevance Vector Machine Applied to Settlement of Shallow Foundation on Cohesionless Soils.” Georisk 2 (1): 41–47.
   Google Scholar
• Sharma, A., J. Ching, and K.-K. Phoon. 2022. “A Hierarchical Bayesian Similarity Measure for Geotechnical Site Retrieval.” Journal of Engineering Mechanics 148 (10): 4022062. https://doi.org/10.1061/(ASCE)EM.1943-7889.0002145.
   Web of Science ®Google Scholar
• Sharma, A., B. Hazra, and S. Sekharan. 2021. “Stochastic Seepage and Slope Stability Analysis Using Vine-Copula Based Multivariate Random Field Approach: Consideration to Non-Gaussian Spatial and Cross-dependence Structure of Hydraulic Parameters.” Computers and Geotechnics 130:103918. https://doi.org/10.1016/j.compgeo.2020.103918.
   Web of Science ®Google Scholar
• Sklar, A. 1996. “Random Variables, Distribution Functions, and Copulas: A Personal Look Backward and Forward.” Lecture Notes-Monograph Series 28: 1–14.
   Google Scholar
• Song, C., and T. Zhao. 2023. “Uncertainty Quantification in Predicting UCS Using Fully Bayesian Gaussian Process Regression with Consideration of Model Class Selection.” In Geo-Risk, 9–19.
   Google Scholar
• Surles, J. G., H. Seo, J. Doerzbacher, W. D. Lawson, and P. W. Jayawickrama. 2019. “Confidence Intervals for Resistance Factors in Geotechnical LRFD Applications.” Structural Safety 80:1–12. https://doi.org/10.1016/j.strusafe.2019.03.003.
   Web of Science ®Google Scholar
• Tsuda, Y., Y. Tomizawa, I. Yoshida, and Y. Otake. 2023. “Estimation of Spatial Distribution Considering Indirect Data Using Gaussian Process Regression.” In Geo-Risk, 94–101.
   Google Scholar
• Van Es, B. 1991. “Likelihood Cross-Validation Bandwidth Selection for Nonparametric Kernel Density Estimators.” Journal of Nonparametric Statistics 1 (1–2): 83–110. https://doi.org/10.1080/10485259108832513.
   Google Scholar
• Wang, Y., Z. Cao, and D. Li. 2016. “Bayesian Perspective on Geotechnical Variability and Site Characterization.” Engineering Geology 203:117–125. https://doi.org/10.1016/j.enggeo.2015.08.017.
   Web of Science ®Google Scholar
• Wang, Y., K. Huang, and Z. Cao. 2013. “Probabilistic Identification of Underground Soil Stratification Using Cone Penetration Tests.” Canadian Geotechnical Journal 50 (7): 766–776. https://doi.org/10.1139/cgj-2013-0004.
   Web of Science ®Google Scholar
• Wang, M.-X., D. Huang, G. Wang, W. Du, and D.-Q. Li. 2020. “Vine Copula-Based Dependence Modeling of Multivariate Ground-Motion Intensity Measures and the Impact on Probabilistic Seismic Slope Displacement Hazard Analysis.” Bulletin of the Seismological Society of America 110 (6): 2967–2990. https://doi.org/10.1785/0120190244.
   Web of Science ®Google Scholar
• Wang, Y., and P. Li. 2021. “Data-Driven Determination of Sample Number and Efficient Sampling Locations for Geotechnical Site Investigation of a Cross-Section Using Voronoi Diagram and Bayesian Compressive Sampling.” Computers and Geotechnics 130:103898. https://doi.org/10.1016/j.compgeo.2020.103898.
   Web of Science ®Google Scholar
• Wu, X. Z. 2013a. “Probabilistic Slope Stability Analysis by a Copula-Based Sampling Method.” Computational Geosciences 17 (5): 739–755. https://doi.org/10.1007/s10596-013-9353-3.
   Web of Science ®Google Scholar
• Wu, X. Z. 2013b. “Trivariate Analysis of Soil Ranking-Correlated Characteristics and its Application to Probabilistic Stability Assessments in Geotechnical Engineering Problems.” Soils and Foundations 53 (4): 540–556. https://doi.org/10.1016/j.sandf.2013.06.006.
   Web of Science ®Google Scholar
• Wu, J., Y. Li, S. Zhang, and J. C. J. Oualembo Mountou. 2022. “Early Identification of Potential Loess Landslide Using Convolutional Neural Networks with Skip Connection: A Case Study in Northwest Lvliang City, Shanxi Province, China.” Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards 1–13.
   Google Scholar
• Wu, L., J. T. Zhou, H. Zhang, S. R. Wang, T. Ma, H. Yan, and S. H. Li. 2022. “Time Series Analysis and Gated Recurrent Neural Network Model for Predicting Landslide Displacements.” Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards 1–14.
   Google Scholar
• Xiao, T., L.-M. Zhang, X.-Y. Li, and D.-Q. Li. 2017. “Probabilistic Stratification Modeling in Geotechnical Site Characterization.” ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering 3 (4): 4017019. https://doi.org/10.1061/AJRUA6.0000924.
   Google Scholar
• Xiao, S., L. Zhang, T. Xiao, and R. Jiang. 2023. “Prediction of Landslide Dam Formation Using Machine Learning Techniques.” In Geo-Risk, 41–48.
   Google Scholar
• Yan, D., T. Zhao, L. Xu, L. Zuo, H. Wen, and J. Ren. 2023. “Statistical Modeling of Multivariate Loess Properties in Taiyuan Using Regular Vine Copula with Optimized Tree Structure.” Transportation Geotechnics 41:101025. https://doi.org/10.1016/j.trgeo.2023.101025.
   Web of Science ®Google Scholar
• Yuen, K.-V. 2010. Bayesian Methods for Structural Dynamics and Civil Engineering. Singapore: John Wiley & Sons.
   Google Scholar
• Zhang, P., Z.-Y. Yin, and Y.-F. Jin. 2022. “Bayesian Neural Network-Based Uncertainty Modelling: Application to Soil Compressibility and Undrained Shear Strength Prediction.” Canadian Geotechnical Journal 59 (4): 546–557. https://doi.org/10.1139/cgj-2020-0751.
   Web of Science ®Google Scholar
• Zhao, T., and Y. Wang. 2019. “Determination of Efficient Sampling Locations in Geotechnical Site Characterization Using Information Entropy and Bayesian Compressive Sampling.” Canadian Geotechnical Journal 56 (11): 1622–1637. https://doi.org/10.1139/cgj-2018-0286.
   Web of Science ®Google Scholar
• Zhu, H., and L. M. Zhang. 2013. “Characterizing Geotechnical Anisotropic Spatial Variations Using Random Field Theory.” Canadian Geotechnical Journal 50 (7): 723–734. https://doi.org/10.1139/cgj-2012-0345.
   Web of Science ®Google Scholar