Document Type : Original Research Paper
Authors
1 Faculty of Earth Sciences Engineering, Arak University of Technology, Iran
2 Department of Mining Engineering, University of Kashan, Iran
Abstract
The mechanical characteristics of rocks and rock masses are considered as the determining factors in making plans in the mining and civil engineering projects. Two factors that determine how rocks responds in varying stress conditions are P-wave velocity (PWV) and its isotropic properties. Therefore, achieving a high-accurate method to estimate PWV is a very important task. This work investigates the use of different intelligent models such as multivariate adaptive regression splines (MARS), classification and regression tree (CART), group method of data handling (GMDH), and gene expression programming (GEP) for the prediction of PWV. The proposed models are then evaluated using several error statistics, i.e. squared correlation coefficient (R2) and root mean squared error (RMSE). The values of R2 obtained from the CART, MARS, GMDH, and GEP models are 0.983, 0.999, 0.995, and 0.998, respectively. Furthermore, the CART, MARS, GMDH, and GEP models predict PWV with the RMSE values of 0.037, 0.007, 0.023, and 0.020, respectively. According to the aforementioned amounts, the models presented in this work predict PWV with a good performance. Nevertheless, the results obtained reveal that the MARS model yields a better prediction in comparison to the GEP, GMDH, and CART models. Accordingly, MARS can be offered as an accurate model for predicting the aims in other rock mechanics and geotechnical fields.
Keywords
[1]. Lin, Q., Cao, P., Wen, G., Meng, J., Cao, R. and Zhao, Z. (2021). Crack coalescence in rock-like specimens with two dissimilar layers and pre-existing double parallel joints under uniaxial compression. International Journal of Rock Mechanics and Mining Sciences, 139, 104621.
[2]. Lin, Q., Cao, P., Meng, J., Cao, R. and Zhao, Z. (2020). Strength and failure characteristics of jointed rock mass with double circular holes under uniaxial compression: insights from discrete element method modelling. Theoretical and Applied Fracture Mechanics, 109, 102692.
[3]. Sharma, P.K. and Singh, T.N. (2008). A correlation between P-wave velocity, impact strength index, slake durability index and uniaxial compressive strength. Bulletin of Engineering Geology and the Environment, 67(1), 17-22.
[4]. Singh, R., Vishal, V. and Singh, T.N. (2012). Soft computing method for assessment of compressional wave velocity. Scientia Iranica, 19(4), 1018-1024.
[5]. Szlavin, J. (1974, February). Relationships between some physical properties of rock determined by laboratory tests. In International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts (Vol. 11, No. 2, pp. 57-66). Pergamon.
[6]. Chary, K.B., Sarma, L.P., Lakshmi, K.P., Vijayakumar, N.A., Lakshmi, V.N. and Rao, M.V.M.S. (2006, December). Evaluation of engineering properties of rock using ultrasonic pulse velocity and uniaxial compressive strength. In Proc. National seminar on Non-destructive evaluation (pp. 7-9).
[7]. Singh, T.N., Kanchan, R., Verma, A.K. and Saigal, K. (2005). A comparative study of ANN and neuro-fuzzy for the prediction of dynamic constant of rockmass. Journal of Earth System Science, 114(1), 75-86.
[8]. Singh, T.N., Kanchan, R., Saigal, K. and Verma, A.K. (2004). Prediction of p-wave velocity and anisotropic property of rock using artificial neural network technique.
[9]. Karakus, M. and Tutmez, B.Ü.L.E.N.T. (2006). Fuzzy and multiple regression modelling for evaluation of intact rock strength based on point load, Schmidt hammer and sonic velocity. Rock mechanics and rock engineering, 39(1), 45-57.
[10]. Zoveidavianpoor, M., Samsuri, A. and Shadizadeh, S.R. (2013). Adaptive neuro fuzzy inference system for compressional wave velocity prediction in a carbonate reservoir. Journal of Applied Geophysics, 89, 96-107.
[11]. Ansari, H.R. (2014). Use seismic colored inversion and power law committee machine based on imperial competitive algorithm for improving porosity prediction in a heterogeneous reservoir. Journal of Applied Geophysics, 108, 61-68.
[12]. Golsanami, N., Kadkhodaie-Ilkhchi, A. and Erfani, A. (2015). Synthesis of capillary pressure curves from post-stack seismic data with the use of intelligent estimators: a case study from the Iranian part of the South Pars gas field, Persian Gulf Basin. Journal of Applied Geophysics, 112, 215-225.
[13]. Mojeddifar, S., Kamali, G., Ranjbar, H. and Salehipour Bavarsad, B. (2014). A comparative study between a pseudo-forward equation (PFE) and intelligence methods for the characterization of the north sea reservoir. International Journal of Mining and Geo-Engineering, 48(2), 173-190.
[14]. Asoodeh, M. and Bagheripour, P. (2012). Prediction of compressional, shear, and stoneley wave velocities from conventional well log data using a committee machine with intelligent systems. Rock mechanics and rock engineering, 45(1), 45-63.
[15]. Rajabi M, Bohloli B, Gholampour Ahangar E .(2010) Intelligent approaches for prediction of compressional, shear and Stoneley wave velocities from conventional well log data: A case study from the Sarvak carbonate reservoir in the Abadan Plain (Southwestern Iran). Comput Geosci 36 (5):647-664
[16]. Labani MM, Sabzekar M (2019) Estimation of shear and Stoneley wave velocities from conventional well data using different intelligent systems and the concept of committee machine: an example from South Pars gas field, Persian Gulf. Energy Sources, Part A: Recovery, Utilization, and Environmental Effects:1-15
[17]. Miah MI, Ahmed S, Zendehboudi S (2021) Model development for shear sonic velocity using geophysical log data: Sensitivity analysis and statistical assessment. Journal of Natural Gas Science and Engineering 88:103778
[18]. Wang J, Cao J, Yuan S (2020) Shear wave velocity prediction based on adaptive particle swarm optimization optimized recurrent neural network. Journal of Petroleum Science and Engineering 194:107466
[19]. Anemangely M, Ramezanzadeh A, Tokhmechi B (2017) Shear wave travel time estimation from petrophysical logs using ANFIS-PSO algorithm: A case study from Ab-Teymour Oilfield. Journal of Natural Gas Science and Engineering 38:373-387
[20]. Anemangely M, Ramezanzadeh A, Amiri H, Hoseinpour S-A (2019) Machine learning technique for the prediction of shear wave velocity using petrophysical logs. Journal of Petroleum Science and Engineering 174:306-327
[21]. Behnia D, Ahangari K, Moeinossadat SR (2017) Modeling of shear wave velocity in limestone by soft computing methods. Int J Min Sci Technol 27 (3):423-430
[22]. Breiman L, Friedman J, Stone CJ, Olshen RA (1984) Classification and regression trees. CRC press,
[23]. Liang M, Mohamad ET, Faradonbeh RS, Armaghani DJ, Ghoraba S (2016) Rock strength assessment based on regression tree technique. Eng Comput 32 (2):343-354
[24]. Ebrahimy H, Feizizadeh B, Salmani S, Azadi H (2020) A comparative study of land subsidence susceptibility mapping of Tasuj plane, Iran, using boosted regression tree, random forest and classification and regression tree methods. Environmental Earth Sciences 79:1-12
[25]. Naghibi SA, Pourghasemi HR, Dixon B (2016) GIS-based groundwater potential mapping using boosted regression tree, classification and regression tree, and random forest machine learning models in Iran. Environ Monit Assess 188 (1):1-27
[26]. Salimi A, Faradonbeh RS, Monjezi M, Moormann C (2018) TBM performance estimation using a classification and regression tree (CART) technique. Bull Eng Geology Envir 77 (1):429-440
[27]. Khandelwal M, Armaghani DJ, Faradonbeh RS, Yellishetty M, Abd Majid MZ, Monjezi M (2017) Classification and regression tree technique in estimating peak particle velocity caused by blasting. Eng Comput 33 (1):45-53
[28]. Cheng W, Zhang X, Wang K, Dai X (2009) Integrating classification and regression tree (CART) with GIS for assessment of heavy metals pollution. Environ Monit Assess 158 (1):419-431
[29]. Friedman JH (1991) Multivariate adaptive regression splines. The annals of statistics:1-67
[30]. Zheng G, He X, Zhou H, Yang X, Yu X, Zhao J (2020) Prediction of the tunnel displacement induced by laterally adjacent excavations using multivariate adaptive regression splines. Acta Geotechnica:1-11
[31]. Kang F, Liu X, Li J (2019) Concrete dam behavior prediction using multivariate adaptive regression splines with measured air temperature. Arab J Sci Eng 44 (10):8661-8673
[32]. Ivakhnenko AG (1971) Polynomial theory of complex systems. IEEE transactions on Systems, Man, and Cybernetics (4):364-378
[33]. Naderpour H, Nagai K, Fakharian P, Haji M (2019) Innovative models for prediction of compressive strength of FRP-confined circular reinforced concrete columns using soft computing methods. Compos Struct 215:69-84
[34]. Yanai H, Takeuchi K, Takane Y (2011) Projection matrices. In: Projection Matrices, Generalized Inverse Matrices, and Singular Value Decomposition. Springer, pp 25-54
[35]. Anton H, Rorres C (2013) Elementary linear algebra: applications version. John Wiley & Sons,
[36]. Jekabsons G (2009) GMDH-type polynomial neural network toolbox for Matlab/Octave.
[37]. Koopialipoor, M., Nikouei, S.S., Marto, A., Fahimifar, A., Armaghani, D.J. and Mohamad, E.T. (2019). Predicting tunnel boring machine performance through a new model based on the group method of data handling. Bulletin of Engineering Geology and the Environment, 78(5), 3799-3813.
[38]. Chen, W., Khandelwal, M., Murlidhar, B. R., Bui, D. T., Tahir, M. M. and Katebi, J. (2020). Assessing cohesion of the rocks proposing a new intelligent technique namely group method of data handling. Engineering with Computers, 36(2), 783-793.
[39]. Ferreira, C. (2001). Gene expression programming: a new adaptive algorithm for solving problems. arXiv preprint cs/0102027.
[40]. Faradonbeh, R.S., Armaghani, D.J., Amnieh, H.B. and Mohamad, E.T. (2018). Prediction and minimization of blast-induced flyrock using gene expression programming and firefly algorithm. Neural Computing and Applications, 29(6), 269-281.
[41]. Faradonbeh, R.S., Salimi, A., Monjezi, M., Ebrahimabadi, A. and Moormann, C. (2017). Roadheader performance prediction using genetic programming (GP) and gene expression programming (GEP) techniques. Environmental earth sciences, 76(16), 1-12.
[42]. İnce, İ., Bozdağ, A., Fener, M. and Kahraman, S. (2019). Estimation of uniaxial compressive strength of pyroclastic rocks (Cappadocia, Turkey) by gene expression programming. Arabian Journal of Geosciences, 12(24), 1-13.
[43]. Verma, A.K. and Singh, T.N. (2013). A neuro-fuzzy approach for prediction of longitudinal wave velocity. Neural Computing and Applications, 22(7), 1685-1693.
[44]. Fattahi, H. (2016). Application of improved support vector regression model for prediction of deformation modulus of a rock mass. Engineering with Computers, 32(4), 567-580.
[45]. Fattahi, H. (2017). Applying soft computing methods to predict the uniaxial compressive strength of rocks from schmidt hammer rebound values. Computational Geosciences, 21(4), 665.
[46]. Fattahi, H. and Bazdar, H. (2017). Applying improved artificial neural network models to evaluate drilling rate index. Tunnelling and Underground Space Technology, 70, 114-124.
[47]. Fattahi, H. and Moradi, A. (2018). A new approach for estimation of the rock mass deformation modulus: a rock engineering systems-based model. Bulletin of engineering geology and the environment, 77(1), 363-374.
[48]. Rezaei, K., Guest, B., Friedrich, A., Fayazi, F., Nakhaei, M., Beitollahi, A. and Aghda, S.M.F. (2009). Feed forward neural network and interpolation function models to predict the soil and subsurface sediments distribution in Bam, Iran. Acta Geophysica, 57(2), 271-293.
[49]. Nguyen, H., Bui, X.N., Bui, H.B. and Cuong, D.T. (2019). Developing an XGBoost model to predict blast-induced peak particle velocity in an open-pit mine: a case study. Acta Geophysica, 67(2), 477-490.
[50]. Fattahi, H. (2019). Tunnel boring machine penetration rate prediction based on relevance vector regression.
[51]. Fattahi, H. (2017). Prediction of slope stability using adaptive neuro-fuzzy inference system based on clustering methods. Journal of Mining and Environment, 8(2), 163-177.
[52]. Fattahi, H. (2018). An estimation of required rotational torque to operate horizontal directional drilling using rock engineering systems. Journal of Petroleum Science and Technology, 8(1), 82-96.
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