Document Type : Original Research Paper
Authors
Department of Mining Engineering, University of Kashan, Kashan, Iran
Abstract
Groundwater inflow is a critical subject within the domains of hydrology, hydraulic engineering, hydrogeology, rock engineering, and related disciplines. Tunnels excavated below the groundwater table, in particular, face the inherent risk of groundwater seepage during both the excavation process and subsequent operational phases. Groundwater inflows, often perceived as rare geological hazards, can induce instability in the surrounding rock formations, leading to severe consequences such as injuries, fatalities, and substantial financial expenditures. The primary objective of this research is to explore the application of machine learning techniques to identify the most accurate method of forecasting tunnel water seepage. The prediction of water loss into the tunnel during the forecasting phase employed a tree equation based on gene expression programming (GEP). These results were compared with those obtained from a hybrid model comprising particle swarm optimization (PSO) and artificial neural networks (ANN). The Whale Optimization Algorithm (WOA) was selected and developed during the optimization phase. Upon contrasting the aforementioned methods, the Whale Optimization Algorithm demonstrated superior performance, precisely forecasting the volume of water lost into the tunnel with a correlation coefficient of 0.99. This underscores the effectiveness of advanced optimization techniques in enhancing the accuracy of groundwater inflow predictions and mitigating potential risks associated with tunneling activities.
Keywords
Main Subjects
[1]. Rabieian, M., & Qaderi, F. (2024). Optimizing Hybrid Photocatalytic-ozonation for Offshore Produced Water Treatment. Journal of Mining and Environment, 15(1), 239-259. doi:10.22044/jme.2023.13081.2376
[2]. Chen, Y., Selvadurai, A. P. S., & Liang, W. (2019). Computational Modelling of Groundwater Inflow During a Longwall Coal Mining Advance: A Case Study from the Shanxi Province, China. Rock Mechanics and Rock Engineering, 52(3), 917-934. doi:10.1007/s00603-018-1603-1
[3]. Dadashi, E., Noorzad, A., Shahriar, K., & Goshtasbi, K. (2018). An optimal method to design reinforced concrete lining of pressure tunnels. Journal of Mining and Environment, 9(4), 829-837. doi:10.22044/jme.2018.6776.1500
[4]. Ackerman, J. R., Peterson, E. W., Van der Hoven, S., & Perry, W. L. (2015). Quantifying nutrient removal from groundwater seepage out of constructed wetlands receiving treated wastewater effluent. Environmental Earth Sciences, 74(2), 1633-1645. doi:10.1007/s12665-015-4167-3
[5]. Rasmussen, T. C., & Yu, G. (2006). Determination of groundwater flownets, fluxes, velocities, and travel times using the complex variable boundary element method. Engineering Analysis with Boundary Elements, 30(12), 1030-1044. doi:https://doi.org/10.1016/j.enganabound.2006.01.017
[6]. Frough, O., Torabi, S. R., & Tajik, M. (2012). Evaluation of TBM Utilization Using Rock Mass Rating System: A Case Study of Karaj-Tehran Water Conveyance Tunnel (Lots 1 and 2). Journal of Mining and Environment, 3(2), 89-98. doi:10.22044/jme.2012.86
[7]. Ying, H., Zhu, C., Shen, H., & Gong, X. (2018). Semi-analytical solution for groundwater ingress into lined tunnel. Tunnelling and Underground Space Technology, 76, 43-47. doi:https://doi.org/10.1016/j.tust.2018.03.009
[8]. Kim, G. B. (2013). Assessment of water seepage through a geologic barrier surrounding a large reservoir using groundwater levels, soil condition, and a numerical model. Environmental Earth Sciences, 69(6), 2059-2072. doi:10.1007/s12665-012-2041-0
[9]. Kamali, A., Shahriar, K., El Tani, M., Aalianvari, A., & Gholami, M. A. (2018). Challenging Estimation of Seepage in Powerhouse Cavern and Drainage Tunnel in Iran. ISRM European Rock Mechanics Symposium - EUROCK, May 2018, ISRM-EUROCK-2018-173.
[10]. Wadslin Frenelus, & Hui Peng JZ. (2021). Evaluation methods for groundwater inflows into rock tunnels: a state-of-the-art review Abstract. International Journal of Hydrology Research, 5(4), 152-168.
[11]. Zhang, L., Yang, D., Liu, Y., Che, Y., & Qin, D. (2014). Impact of impoundment on groundwater seepage in the Three Gorges Dam in China based on CFCs and stable isotopes. Environmental Earth Sciences, 72(11), 4491-4500. doi:10.1007/s12665-014-3349-8
[12]. Wang, Z. H., Wu, S. X., Li, J. L., Sun, W. C., Wang, Z. F., & Liu, P. J. (2023). Surface subsidence and its reclamation of a coal mine locating at the high groundwater table, China. International Journal of Environmental Science and Technology. doi:10.1007/s13762-023-04915-8
[13]. Li, D., Li, X., Li, C. C., Huang, B., Gong, F., & Zhang, W. (2009). Case studies of groundwater flow into tunnels and an innovative water-gathering system for water drainage. Tunnelling and Underground Space Technology, 24(3), 260-268. doi:https://doi.org/10.1016/j.tust.2008.08.006
[14]. Surinaidu, L., Gurunadha Rao, V. V. S., Srinivasa Rao, N., & Srinu, S. (2014). Hydrogeological and groundwater modeling studies to estimate the groundwater inflows into the coal Mines at different mine development stages using MODFLOW, Andhra Pradesh, India. Water Resources and Industry, 7-8, 49-65. doi:https://doi.org/10.1016/j.wri.2014.10.002
[15]. Chandel, N., Gupta, S. K., & Ravi, A. K. (2024). Groundwater Quality Analysis using Machine Learning Techniques: a Critical Appraisal. Journal of Mining and Environment, 15(2), 419-426. doi:10.22044/jme.2023.13452.2484
[16]. Ke, X., Wang, W., Xu, X., Li, J., & Hu, H. (2021). A saturated–unsaturated coupling model for groundwater flowing into seepage wells: a modeling study for groundwater development in river basins. Environmental Earth Sciences, 80(21), 711. doi:10.1007/s12665-021-10035-8
[17]. Okeke, C. A. U., Azuh, D., Ogbuagu, F. U., & Kogure, T. (2020). Assessment of land use impact and seepage erosion contributions to seasonal variations in riverbank stability: The Iju River, SW Nigeria. Groundwater for Sustainable Development, 11, 100448. doi:https://doi.org/10.1016/j.gsd.2020.100448
[18]. Gholizadeh, H., Behrouj Peely, A., Karney, B. W., & Malekpour, A. (2020). Assessment of groundwater ingress to a partially pressurized water-conveyance tunnel using a conduit-flow process model: a case study in Iran. Hydrogeology Journal, 28(7), 2573-2585. doi:10.1007/s10040-020-02213-y
[19]. Janipella, R., & Pujari, P. R. (2022). Review on Groundwater Flow and Solute Transport Modelling in India: Recent Advances and Future Directions. Journal of the Geological Society of India, 98(2), 278-284. doi:10.1007/s12594-022-1968-3
[20]. Aalianvari, A., Malekitehrani, M., & Soltanomohammadi, S. (2014). Estimation of water flow from the upper reservoir of Azad pumped storage power plant, using geostatistical methods. Journal of the Geological Society of India, 83(1), 76-82. doi:10.1007/s12594-014-0009-2
[21]. Aghda, S. M. F., GanjaliPour, K., & Esmaeilzadeh, M. (2019). The Effect of Geological Factors on the Grout Curtain Performance Analysis of Darian Dam Using the Results of Instrumentation Data in the First Impounding. Journal of the Geological Society of India, 93(3), 360-368. doi:10.1007/s12594-019-1185-x
[22]. Jiang, C., Han, H., Xie, H., Liu, J., Chen, Z., & Chen, H. (2021). Karst Aquifer Water Inflow into Tunnels: An Analytical Solution. In Y. Zhao (Ed.), Geofluids, 2021, 6672878. doi:10.1155/2021/6672878
[23]. Javadi, M., Sharifzadeh, M., & Shahriar, K. (2016). Uncertainty analysis of groundwater inflow into underground excavations by the stochastic discontinuum method: Case study of Siah Bisheh pumped storage project, Iran. Tunnelling and Underground Space Technology, 51, 424-438. doi:https://doi.org/10.1016/j.tust.2015.09.003
[24]. Jiang, Q., Yao, C., Ye, Z., & Zhou, C. (2013). Seepage flow with free surface in fracture networks. Water Resources Research, 49(1), 176-186. doi:10.1029/2012WR011991
[25]. Li, X., Li, D., Xu, Y., & Feng, X. (2020). A DFN-based 3D numerical approach for modeling coupled groundwater flow and solute transport in fractured rock mass. International Journal of Heat and Mass Transfer, 149, 119179. doi:10.1016/j.ijheatmasstransfer.2019.119179
[26]. Liu, D., Xu, Q., Tang, Y., & Jian, Y. (2021). Prediction of Water Inrush in Long-Lasting Shutdown Karst Tunnels Based on the HGWO-SVR Model. IEEE Access, 9, 6368-6378. doi:10.1109/ACCESS.2020.3047626
[27]. Nikvar Hassani, A., Farhadian, H., & Katibeh, H. (2018). A comparative study on the evaluation of steady-state groundwater inflow into a circular shallow tunnel. Tunnelling and Underground Space Technology, 73, 15-25. doi:https://doi.org/10.1016/j.tust.2017.11.019
[28]. Jing, L. (2003). A review of techniques, advances, and outstanding issues in numerical modeling for rock mechanics and rock engineering. International Journal of Rock Mechanics and Mining Sciences, 39(4), 283-353. doi:10.1016/S1365-1609(03)00013-3
[29]. Nikakhtar, L., & Zare, S. (2020). Evaluation of Underground Water Flow into Tabriz Metro Tunnel First Line by Hydro-Mechanical Coupling Analysis. International Journal of Geotechnical and Geological Engineering, 14(1), 1-7.
[30]. Wu, Q., Wang, M., & Wu, X. (2004). Investigations of groundwater bursting into coal mine seam floors from fault zones. International Journal of Rock Mechanics and Mining Sciences, 41(4), 557-571. doi:https://doi.org/10.1016/j.ijrmms.2003.01.004
[31]. Lianchong, L., Tianhong, Y., Zhengzhao, L., Wancheng, Z., & Chunan, T. (2011). Numerical investigation of groundwater outbursts near faults in underground coal mines. International Journal of Coal Geology, 85(3), 276-288. doi:https://doi.org/10.1016/j.coal.2010.12.006
[32]. Farhadian, H., Katibeh, H., & Huggenberger, P. (2016). Empirical model for estimating groundwater flow into a tunnel in discontinuous rock masses. Environmental Earth Sciences, 75(6), 471. doi:10.1007/s12665-016-5332-z
[33]. Li, Q., Ito, K., Wu, Z., Lowry, C. S., & Loheide, S. P. (2009). COMSOL Multiphysics: A novel approach to groundwater modeling. Ground Water, 47(4), 480-487. doi:10.1111/j.1745-6584.2009.00584.x
[34]. Li, S., He, P., & Li, L. (2017). Gaussian process model of water inflow prediction in tunnel construction and its engineering applications. Tunnelling and Underground Space Technology, 69, 155-161. doi:https://doi.org/10.1016/j.tust.2017.06.018
[35]. Chen, J., Zhou, M., Zhang, D., Huang, H., & Zhang, F. (2021). Quantification of water inflow in rock tunnel faces via convolutional neural network approach. Automation in Construction, 123, 103526. doi:https://doi.org/10.1016/j.autcon.2020.103526
[36]. Yang, Z. (2016). Risk prediction of water inrush of karst tunnels based on BP neural network. In 4th International Conference on Mechanical Materials and Manufacturing Engineering. doi:10.2991/mmme-16.2016.74
[37]. Donglin, D., Wenjie, S., & Sha, X. (2012). Water-inrush assessment using a GIS-based Bayesian network for the 12-2 coal seam of the Kailuan Donghuantuo coal mine in China. Mine Water and the Environment, 31(2), 138-146. doi:10.1007/s10230-012-0178-4
[38]. Mahmoodzadeh, A., Mohammadi, M., & Gharrib Noori, K. (2021). Presenting the best prediction model of water inflow into drill and blast tunnels among several machine learning techniques. Automation in Construction, 127, 103719. doi:https://doi.org/10.1016/j.autcon.2021.103719
[39]. Chen, S., & Dong, S. (2020). A sequential structure for water inflow forecasting in coal mines integrating feature selection and multi-objective optimization. IEEE Access, 8, 183619-183632. doi:10.1109/ACCESS.2020.3028959
[40]. Liu, W., & Zhang, H. (2016). PSO algorithm for block sequencing problem in open pit mining. In Proceedings of the 2015 5th International Conference on Computer Science and Automation Engineering. doi:10.2991/iccsae-15.2016.83
[41]. Bagatur, T., & Onen, F. (2014). Prediction of flow and oxygen transfer by a plunging water jet with genetic expression programming (GEP) models. Arabian Journal for Science and Engineering, 39(6), 4421-4432. doi:10.1007/s13369-014-1092-9
[42]. Hemasian-Etefagh, F., & Safi-Esfahani, F. (2020). Group-based whale optimization algorithm. Soft Computing, 24(5), 3647-3673. doi:10.1007/s00500-019-04131-y
[43]. Farhadian, H., Aalianvari, A., & Katibeh, H. (2012). Optimization of analytical equations of groundwater seepage into tunnels: A case study of Amirkabir tunnel. Journal of the Geological Society of India, 80, 96-100. doi:10.1007/s12594-012-0122-z
[44]. Koseoglu Balta, G. C., Dikmen, I., & Birgonul, M. T. (2021). Bayesian network-based decision support for predicting and mitigating delay risk in TBM tunnel projects. Automation in Construction, 129, 103819. doi:10.1016/j.autcon.2021.103819
[45]. Embaby, A. K., Gomaa, S., Darwish, Y., & Selim, S. (2024). Predicting Gabal Gattar Uranium Content as a Function of Total Gamma-ray and Thorium Contents using an Artificial Neural Network in Northeastern Desert, Egypt. Journal of Mining and Environment, 15(1), 175-189. doi:10.22044/jme.2023.13651.2524
[46]. Mostafaei, K., Kianpour, M. N., & Yousefi, M. (2024). Delineation of Gold Exploration Targets based on Prospectivity Models through an Optimization Algorithm. Journal of Mining and Environment, 15(2), 597-611. doi:10.22044/jme.2023.13472.2489
[47]. Rezaei, M., Hossaini, M. F., Majdi, A., & Najmoddini, I. (2017). Determination of the height of destressed zone above the mined panel: An ANN model. International Journal of Mining and Geo-Engineering, 51(1), 1-7. doi:10.22059/ijmge.2017.62147
[48]. Alimoradi, A., Moradzadeh, A., Naderi, R., Salehi, M. Z., & Etemadi, A. (2008). Prediction of geological hazardous zones in front of a tunnel face using TSP-203 and artificial neural networks. Tunnelling and Underground Space Technology, 23(6), 711-717. doi:https://doi.org/10.1016/j.tust.2008.01.001
[49]. Razavi Rad, F., Mohammad Torab, F., & Abdollahzadeh, A. (2016). Estimation of Cadmium and Uranium in a stream sediment from Eshtehard region in Iran using an Artificial Neural Network. Journal of Mining and Environment, 7(1), 97-107. doi:10.22044/jme.2016.500
[50]. Saini, A., & Yadav, J. S. (2024). Bearing Capacity of Circular Footing Resting on Recycled Construction Waste Materials using ANN Method. Journal of Mining and Environment, 15(1), 97-114. doi:10.22044/jme.2023.13453.2485
[51]. Su, M., Zhang, Z., Zhu, Y., Zha, D., & Wen, W. (2019). Data-driven natural gas spot price prediction models using machine learning methods. Energies, 12(9). doi:10.3390/en12091680
[52]. Bayatzadeh Fard, Z., Ghadimi, F., & Fattahi, H. (2017). Use of artificial intelligence techniques to predict the distribution of heavy metals in groundwater of Lakan lead-zinc mine in Iran. Journal of Mining and Environment, 8(1), 35-48. doi:10.22044/jme.2016.592
[53]. Moshrefi, S., Shahriar, K., Ramezanzadeh, A., & Goshtasbi, K. (2018). Prediction of the ultimate strength of shale using artificial neural network. Journal of Mining and Environment, 9(1), 91-105. doi:10.22044/jme.2017.5790.1390
[54]. Saljoughi, B. S., & Hezarkhani, A. (2024). A Comparative Analysis of Artificial Neural Network (ANN) and Gene Expression Programming (GEP) Data-driven Models for Prospecting Porphyry Cu Mineralization; Case Study of Shahr-e-Babak Area, Kerman Province, SE Iran. Journal of Mining and Environment, 15(2), 761-790. doi:10.22044/jme.2023.13852.2573
[55]. Taiwo, B. O., Famobuwa, O. V., & Mata, M. M. (2024). Granite Downstream Production Dependent Size and Profitability Assessment: an application of Mathematical-based Artificial Intelligence Model and WipFrag Software. Journal of Mining and Environment, 15(2), 497-515. doi:10.22044/jme.2023.13731.2543
[56]. Chai, S. H., & Lim, J. S. (2016). Forecasting business cycle with chaotic time series based on neural network with weighted fuzzy membership functions. Chaos, Solitons and Fractals, 0, 1-9. doi:10.1016/j.chaos.2016.03.037
[57]. Kennedy, J., & Eberhart, R. (1995). Particle swarm optimization. Neural Networks, 1995 Proceedings, IEEE International Conference, 4, 1942-1948 vol.4. doi:10.1109/ICNN.1995.488968
[58]. Eil Saadatmand, F., Alimoradi, A., Moosavi, M. M., & Davari, M. A. (2024). Optimizing Deep Learning Models for Shear Wave Velocity Estimation Utilizing Petrophysical Logs: A Case Study on an Oil Reservoir in Southern Iran. Journal of Petroleum Science and Engineering, 31-47. doi:10.22107/jpg.2024.436270.1225
[59]. Fathi, M., Alimoradi, A., & Hemati Ahooi, H. R. (2021). Optimizing Extreme Learning Machine Algorithm using Particle Swarm Optimization to Estimate Iron Ore Grade. Journal of Mining and Environment, 12(2), 397-411. doi:10.22044/jme.2021.10368.1984
[60]. Arbabsiar, M. H., Farsangi, M. A. E., & Mansouri, H. (2020). A new model for predicting the advance rate of a tunnel boring machine (Tbm) in hard rock conditions. Rudarsko-Geološko-Naftni Zbornik, 35(2), 57-74. doi:10.17794/rgn.2020.2.6
[61]. Sharifi, F., Arab Amiri, A. R., & Kamkar Rouhani, A. (2019). Using a combination of genetic algorithm and particle swarm optimization algorithm for GEMTIP modeling of spectral-induced polarization data. Journal of Mining and Environment, 10(2), 493-505. doi:10.22044/jme.2019.7902.1655
[62]. Rezaei, M., & Asadizadeh, M. (2020). Predicting Unconfined Compressive Strength of Intact Rock Using New Hybrid Intelligent Models. Journal of Mining and Environment, 11(1), 231-246. doi:10.22044/jme.2019.8839.1774
[63]. Jing, L. J., Li, J. B., Zhang, N., Chen, S., Yang, C., & Cao, H. B. (2021). A TBM advance rate prediction method considering the effects of operating factors. Tunnelling and Underground Space Technology, 107, 103620. doi:10.1016/j.tust.2020.103620
[64]. Zarean, A., & Poormirzaee, R. (2016). Joint inversion of ReMi dispersion curves and refraction travel times using particle swarm optimization algorithm. Journal of Mining and Environment, 7(1), 67-79. doi:10.22044/jme.2016.492
[65]. Mousavi, S. S., Nikkhah, M., & Zare, S. (2019). A comparative study of two meta-heuristic algorithms in optimizing the cost of reinforced concrete segmental lining. Journal of Mining and Environment, 10(1), 95-112.
[66]. Sun, S., Sun, Y., Wang, S., & Wei, Y. (2018). Interval decomposition ensemble approach for crude oil price forecasting. Energy Economics, 76, 274-287. doi:10.1016/j.eneco.2018.10.015
[67]. Alimoradi, A., Hajkarimian, H., Hemati Ahooi, H., & Salsabili, M. (2022). Comparison between the performance of four metaheuristic algorithms in training a multilayer perceptron machine for gold grade estimation. International Journal of Mining and Geo-Engineering, 56(2), 97-105. doi:10.22059/ijmge.2021.314154.594880
[68]. Wang, X., Lu, H., Wei, X., Wei, G., Behbahani, S. S., & Iseley, T. (2020). Application of Artificial Neural Network in Tunnel Engineering: A Systematic Review. IEEE Access, 8, 119527-119543. doi:10.1109/ACCESS.2020.3004995
[69]. Nikakhtar, L., Zare, S., & Mirzaei, H. (2023). Performance Comparison of Particle Swarm Optimization and Genetic Algorithm for Back-analysis of Soil Layer Geotechnical Parameters. Journal of Mining and Environment, 14(1), 217-232. doi:10.22044/jme.2023.12452.2260
[70]. Moomivand, H., Amini Khoshalan, H., Shakeri, J., & Vandyousefi, H. (2022). Development of new comprehensive relations to assess rock fragmentation by blasting for different open pit mines using GEP algorithm and MLR procedure. International Journal of Mining and Geo-Engineering, 56(4), 401-411. doi:10.22059/ijmge.2022.339174.594951
[71]. Bastami, R., Bazzazi, A. A., Shoormasti, H. H., & Ahangari, K. (2020). Predicting and minimizing the blasting cost in limestone mines using a combination of gene expression programming and particle swarm optimization. Archives of Mining Sciences, 65(4), 835-850. doi:10.24425/ams.2020.135180
[72]. Monjezi, M., Dehghani, H., Shakeri, J., & Mehrdanesh, A. (2021). Optimization of prediction of flyrock using linear multivariate regression (LMR) and gene expression programming (GEP)—Topal Novin mine, Iran. Arabian Journal of Geosciences, 14(15). doi:10.1007/s12517-021-07772-2
[73]. Kadkhodaei, M. H., & Ghasemi, E. (2019). Development of a GEP model to assess CERCHAR abrasivity index of rocks based on geomechanical properties. Journal of Mining and Environment, 10(4), 917-928. doi:10.22044/jme.2019.8141.1684
[74]. Jahed, D., Vali, A., Ahmad, S., & Mohd, F. (2017). Uniaxial compressive strength prediction through a new technique based on gene expression programming. Neural Computing and Applications. doi:10.1007/s00521-017-2939-2
[75]. Yang, B., Zhang, W., & Wang, H. (2019). Stock Market Forecasting Using Restricted Gene Expression Programming. De Maio C, ed. Computational Intelligence and Neuroscience, 2019, 7198962. doi:10.1155/2019/7198962
[76]. Dehghani, H., Velicković, M., Jodeiri, B., Mihajlović, I., Nikolić, D., & Panic, M. (2022). Determination of ozone concentration using gene expression programming algorithm (GEP)- Zrenjanin, Serbia. International Journal of Mining and Geo-Engineering, 56(1), 1-9. doi:10.22059/ijmge.2021.313278.594874
[77]. Hashmi, M. Z., & Shamseldin, A. Y. (2014). Advances in Water Resources Use of Gene Expression Programming in regionalization of flow duration curve. Advances in Water Resources, 68, 1-12. doi:10.1016/j.advwatres.2014.02.009
[78]. Shirani Faradonbeh, R., Jahed Armaghani, D., & Abd Majid, M. Z. (2016). Prediction of ground vibration due to quarry blasting based on gene expression programming: a new model for peak particle velocity prediction. International Journal of Environmental Science and Technology, 13(6), 1453-1464. doi:10.1007/s13762-016-0979-2
[79]. Xue, X., & Deng, C. Prediction of creep index of soft clays using gene expression programming. Soft Computing, 27, 16265–16278. doi:10.1007/s00500-023-08053-8
[80]. Armaghani, D. J., & Asteris, P. G. (2021). A Comparative Study of ANN and ANFIS Models for the Prediction of Cement-Based Mortar Materials Compressive Strength. Neural Computing and Applications, 33. Springer London. doi:10.1007/s00521-020-05244-4
[81]. Turgut, M. S., Sağban, H. M., Turgut, O. E., & Özmen, Ö. T. (2021). Whale optimization and sine–cosine optimization algorithms with cellular topology for parameter identification of chaotic systems and Schottky barrier diode models. Soft Computing. 25(2), 1365-1409. doi:10.1007/s00500-020-05227-6
[82]. Tang, C., Sun, W., Xue, M., Zhang, X., Tang, H., & Wu, W. (2022). A hybrid whale optimization algorithm with artificial bee colony. Soft Computing, 26(5), 2075-2097. doi:10.1007/s00500-021-06623-2
[83]. Li, Z., Yazdani Bejarbaneh, B., Asteris, P. G., Koopialipoor, M., Armaghani, D. J., & Tahir, M. M. (2021). A hybrid GEP and WOA approach to estimate the optimal penetration rate of TBM in granitic rock mass. Soft Computing, 25(17), 11877-11895. doi:10.1007/s00500-021-06005-8
[84]. Nabavi, Z., Mirzehi, M., Dehghani, H., & Ashtari, P. (2023). A Hybrid Model for Back-Break Prediction using XGBoost Machine learning and Metaheuristic Algorithms in Chadormalu Iron Mine. Journal of Mining and Environment, 14(2), 689-712. doi:10.22044/jme.2023.12796.2323
[85]. Mirjalili, S., & Mirjalili, A. L. (2016). The Whale Optimization Algorithm. Advances in Engineering Software, 95.
[86]. Bhavsar, P., Safro, I., Bouaynaya, N., Polikar, R., & Dera, D. (2017). Chapter 12. Machine Learning in Transportation Data Analytics, Elsevier Inc. doi:10.1016/B978-0-12-809715-1.00012-2
[87]. Chai, T., & Draxler, R. R. (2014). Root mean square error (RMSE) or mean absolute error (MAE)? -Arguments against avoiding RMSE in the literature. Geoscientific Model Development, 7(3), 1247-1250. doi:10.5194/gmd-7-1247-2014
[88]. Willmott, C. J., & Matsuura, K. (2005). Advantages of the mean absolute error (MAE) over the root mean square error (RMSE) in assessing average model performance. Climate Research, 30(1), 79-82. doi:10.3354/cr030079
[89]. Jahanmiri, S., Asadizadeh, M., Alipour, A., & Nowak, S. (2021). Predicting the Contribution of Mining Sector to the Gross Domestic Product (GDP) Index Utilizing Heuristic Approaches. Applied Artificial Intelligence, 00(00), 1-23. doi:10.1080/08839514.2021.1997225
[90]. Marmolin, H. (1986). Subjective Mse Measures. IEEE Transactions on Systems, Man, and Cybernetics, SMC-16(3), 486-489. doi:10.1109/tsmc.1986.4308985
[91]. Lamboni, M., Monod, H., & Makowski, D. (2011). Multivariate sensitivity analysis to measure the global contribution of input factors in dynamic models. Reliability Engineering & System Safety, 96(4), 450-459. doi:https://doi.org/10.1016/j.ress.2010.12.002
[92]. Lamboni, M., Makowski, D., Lehuger, S., Gabrielle, B., & Monod, H. (2009). Multivariate global sensitivity analysis for dynamic crop models. Field Crops Research, 113(3), 312-320. doi:https://doi.org/10.1016/j.fcr.2009.06.007
[93]. Chen, L., & Huang, H. (2024). Global sensitivity analysis for multivariate outputs using generalized RBF-PCE metamodel enhanced by variance-based sequential sampling. Applied Mathematics and Computation, 126, 381-404. doi:https://doi.org/10.1016/j.apm.2023.10.047
[94]. Farhadian, H., Aalianvari, A., & Katibeh, H. (2012). Optimization of analytical equations of groundwater seepage into tunnels: A case study of Amirkabir tunnel. Journal of Geological Society of India, 80(1), 96-100. doi:10.1007/s12594-012-0122-z
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