Skip to main content
SpringerLink
Log in

Modeling of rock fragmentation by firefly optimization algorithm and boosted generalized additive model

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

This paper proposes a new soft computing model (artificial intelligence model) for modeling rock fragmentation (i.e., the size distribution of rock (SDR)) with high accuracy, based on a boosted generalized additive model (BGAM) and a firefly algorithm (FFA), called FFA-BGAM. Accordingly, the FFA was used as a robust optimization algorithm/meta-heuristic algorithm to optimize the BGAM model. A split-desktop environment was used to analyze and calculate the size of rock from 136 images, which were captured from 136 blasts. To this end, blast designs were collected and extracted as the input parameters. Subsequently, the proposed FFA-BGAM model was evaluated and compared through previous well-developed soft computing models, such as FFA-ANN (artificial neural network), FFA-ANFIS (adaptive neuro-fuzzy inference system), support vector machine (SVM), Gaussian process regression (GPR), and k-nearest neighbors (KNN) based on three performance indicators (MAE, RMSE, and R2). The results indicated that the new intelligent technique (i.e., FFA-BGAM) provided the highest accuracy in predicting the SDR with an MAE of 0.920, RMSE of 1.213, and R2 of 0.980. In contrast, the remaining models (i.e., FFA-ANN, FFA-ANFIS, SVM, GPR, and KNN) yielded lower accuracies in predicting the SDR, i.e., MAEs of 1.248, 1.661, 1.096, 1.573, 1.237; RMSEs of 1.598, 2.068, 1.402, 2.137, 1.717; and R2 of 0.967, 0.968, 0.972, 0.940, 0.963, respectively.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15

Similar content being viewed by others

References

  1. Bui X-N, Nguyen H, Le HA, Bui HB, Do NH (2019) Prediction of blast-induced air over-pressure in open-pit mine: assessment of different artificial intelligence techniques. Nat Resour Res. https://doi.org/10.1007/s11053-019-09461-0

    Article  Google Scholar 

  2. Zhang S, Bui X-N, Trung N-T, Nguyen H, Bui H-B (2020) Prediction of rock size distribution in mine bench blasting using a novel ant colony optimization-based boosted regression tree technique. Nat Resour Res 29(2):867–886. https://doi.org/10.1007/s11053-019-09603-4

    Article  Google Scholar 

  3. Nguyen H (2019) Support vector regression approach with different kernel functions for predicting blast-induced ground vibration: a case study in an open-pit coal mine of Vietnam. SN Appl Sci 1(4):283. https://doi.org/10.1007/s42452-019-0295-9

    Article  Google Scholar 

  4. Nguyen H, Bui X-N, Bui H-B, Mai N-L (2018) A comparative study of artificial neural networks in predicting blast-induced air-blast overpressure at Deo Nai open-pit coal mine, Vietnam. Neural Comput Appl. https://doi.org/10.1007/s00521-018-3717-5

    Article  Google Scholar 

  5. Nguyen H, Bui X-N, Bui H-B, Cuong DT (2019) Developing an XGBoost model to predict blast-induced peak particle velocity in an open-pit mine: a case study. Acta Geophys 67(2):477–490. https://doi.org/10.1007/s11600-019-00268-4

    Article  Google Scholar 

  6. Nguyen H, Bui X-N (2018) Predicting blast-induced air overpressure: a robust artificial intelligence system based on artificial neural networks and random forest. Nat Resour Res. https://doi.org/10.1007/s11053-018-9424-1

    Article  Google Scholar 

  7. Nguyen H, Bui X-N, Moayedi H (2019) A comparison of advanced computational models and experimental techniques in predicting blast-induced ground vibration in open-pit coal mine. Acta Geophys. https://doi.org/10.1007/s11600-019-00304-3

    Article  Google Scholar 

  8. Armaghani DJ, Hajihassani M, Mohamad ET, Marto A, Noorani S (2014) Blasting-induced flyrock and ground vibration prediction through an expert artificial neural network based on particle swarm optimization. Arab J Geosci 7(12):5383–5396

    Google Scholar 

  9. Li W-X, Qi D-L, Zheng S-F, Ren J-C, Li J-f, Yin X (2015) Fuzzy mathematics model and its numerical method of stability analysis on rock slope of opencast metal mine. Appl Math Model 39(7):1784–1793

    MathSciNet  MATH  Google Scholar 

  10. Binh DV, Ha TTK, Hai DT, Cuong DC, Anh DL, Nam H (2020) Calculation of the exploited flow water in the T2ađg sediments at the well Kien Khe. Hanam. J Min Earth Sci 61(2):41–49

    Google Scholar 

  11. Nguyen NV, Trinh HL (2020) Determination of water quality parameters in the Tan Rai exploiting area (Lam Dong province) using Sentinel-2 msi and Landsat 8 data. J Min Earth Sci 61(2):126–134

    Google Scholar 

  12. Armaghani DJ, Hajihassani M, Marto A, Faradonbeh RS, Mohamad ET (2015) Prediction of blast-induced air overpressure: a hybrid AI-based predictive model. Environ Monit Assess 187(11):666

    Google Scholar 

  13. Nguyen H, Bui X-N (2020) Soft computing models for predicting blast-induced air over-pressure: a novel artificial intelligence approach. Appl Soft Comput 92:106292. https://doi.org/10.1016/j.asoc.2020.106292

    Article  Google Scholar 

  14. Nguyen H, Bui X, Choi Y et al (2020) A novel combination of whale optimization algorithm and support vector machine with different kernel functions for prediction of blasting-induced fly-rock in quarry mines. Nat Resour Res. https://doi.org/10.1007/s11053-020-09710-7

    Article  Google Scholar 

  15. Mahdevari S, Torabi SR, Monjezi M (2012) Application of artificial intelligence algorithms in predicting tunnel convergence to avoid TBM jamming phenomenon. Int J Rock Mech Min Sci 55:33–44

    Google Scholar 

  16. De Simone M, Souza LM, Roehl D (2019) Estimating DEM microparameters for uniaxial compression simulation with genetic programming. Int J Rock Mech Min Sci 118:33–41

    Google Scholar 

  17. Nhu HV, Duong BV, Vo TA, Pham KT (2020) Using numerical modeling method for design and constructive controlling of excavation wall in Madison Building, Ho Chi Minh city. J Min Earth Sci 61(3):19–27. https://doi.org/10.46326/JMES.2020.61(3).03

    Article  Google Scholar 

  18. Khandelwal M, Singh T (2009) Prediction of blast-induced ground vibration using artificial neural network. Int J Rock Mech Min Sci 46(7):1214–1222

    Google Scholar 

  19. Mohamed MT (2011) Performance of fuzzy logic and artificial neural network in prediction of ground and air vibrations. Int J Rock Mech Min Sci 48(5):845

    Google Scholar 

  20. Yurdakul M, Gopalakrishnan K, Akdas H (2014) Prediction of specific cutting energy in natural stone cutting processes using the neuro-fuzzy methodology. Int J Rock Mech Min Sci 67:127–135

    Google Scholar 

  21. Liu J, Zhao X-D, Xu Z-h (2017) Identification of rock discontinuity sets based on a modified affinity propagation algorithm. Int J Rock Mech Min Sci 94:32–42

    Google Scholar 

  22. Nguyen H, Bui X-N, Tran Q-H, Mai N-L (2019) A new soft computing model for estimating and controlling blast-produced ground vibration based on hierarchical K-means clustering and cubist algorithms. Appl Soft Comput 77:376–386. https://doi.org/10.1016/j.asoc.2019.01.042

    Article  Google Scholar 

  23. Daftaribesheli A, Ataei M, Sereshki F (2011) Assessment of rock slope stability using the Fuzzy Slope Mass Rating (FSMR) system. Appl Soft Comput 11(8):4465–4473

    Google Scholar 

  24. Asadi M, Eftekhari M, Bagheripour MH (2011) Evaluating the strength of intact rocks through genetic programming. Appl Soft Comput 11(2):1932–1937

    Google Scholar 

  25. Kang F, Xu B, Li J, Zhao S (2017) Slope stability evaluation using Gaussian processes with various covariance functions. Appl Soft Comput 60:387–396

    Google Scholar 

  26. Zhang H, Nguyen H, Bui X-N, Nguyen-Thoi T, Bui T-T, Nguyen N, Vu D-A, Mahesh V, Moayedi H (2020) Developing a novel artificial intelligence model to estimate the capital cost of mining projects using deep neural network-based ant colony optimization algorithm. Resour Policy 66:101604

    Google Scholar 

  27. Nguyen HV, Bui ST, Phung HH, Pham HNT (2020) The initial research on the compressive strength of mortar when using bottom ash from thermal power plants to replace natural sand in construction. J Min Earth Sci 61(3):12–18

    Google Scholar 

  28. Tran TM, Do TN, Dinh HTT, Vu HX, Ferrier E (2020) A 2-D numerical model of the mechanical behavior of the textile-reinforced concrete composite material: effect of textile reinforcement ratio. J Min Earth Sci 61(3):51–59

    Google Scholar 

  29. Nguyen LQ (2020) A novel approach of determining the parameters of Asadi profiling function for predicting ground subsidence due to inclined coal seam mining at Quang Ninh coal basin. J Min Earth Sci 61(2):86–95

    Google Scholar 

  30. Nguyen NTT, Tong HT (2020) Predicting land use change base on GIS and remote sensing. J Min Earth Sci 61(2):106–115

    MathSciNet  Google Scholar 

  31. Pham LT, Nguyen SP, Nguyen NV, Dao HV, Doan LD, Vo NHT, Nguyen TTT, Tran HV (2020) Establishment of land cover map using object-oriented classification method for VNREDSat-1 data. J Min Earth Sci 61(2):134–144

    Google Scholar 

  32. Nghia NV (2020) Building DEM for deep open-pit coal mines using DJI Inspire 2. J Min Earth Sci 61(1):1–10

    Google Scholar 

  33. Canh LV, Cuong CX, Tien D (2020) Volume computation of quarries in Vietnam based on Unmanned Aerial Vehicle (UAV) data. J Min Earth Sci 61(1):21–30

    Google Scholar 

  34. Sinh VT, Quyen VT, Huan LN, Huong TT (2020) Design information orientation supporting system for user. J Min Earth Sci 61(1):41–51

    Google Scholar 

  35. Nam DV, Oanh NT, Hoai NX, Manh NV, Hien NT (2020) Detect and process outliers for temperature data at 3h monitoring stations in Vietnam. J Min Earth Sci 61(1):132–146

    Google Scholar 

  36. Hasanipanah M, Armaghani DJ, Khamesi H, Amnieh HB, Ghoraba S (2016) Several non-linear models in estimating air-overpressure resulting from mine blasting. Eng Comput 32(3):441–455

    Google Scholar 

  37. Hasanipanah M, Armaghani DJ, Amnieh HB, Majid MZA, Tahir MM (2017) Application of PSO to develop a powerful equation for prediction of flyrock due to blasting. Neural Comput Appl 28(1):1043–1050

    Google Scholar 

  38. Esmaeili M, Salimi A, Drebenstedt C, Abbaszadeh M, Bazzazi AA (2015) Application of PCA, SVR, and ANFIS for modeling of rock fragmentation. Arab J Geosci 8(9):6881–6893

    Google Scholar 

  39. Ebrahimi E, Monjezi M, Khalesi MR, Armaghani DJ (2016) Prediction and optimization of back-break and rock fragmentation using an artificial neural network and a bee colony algorithm. Bull Eng Geol Environ 75(1):27–36

    Google Scholar 

  40. Hasanipanah M, Amnieh HB, Arab H, Zamzam MS (2018) Feasibility of PSO-ANFIS model to estimate rock fragmentation produced by mine blasting. Neural Comput Appl 30(4):1015–1024

    Google Scholar 

  41. Gao W, Karbasi M, Hasanipanah M, Zhang X, Guo J (2018) Developing GPR model for forecasting the rock fragmentation in surface mines. Eng Comput 34(2):339–345. https://doi.org/10.1007/s00366-017-0544-8

    Article  Google Scholar 

  42. Asl PF, Monjezi M, Hamidi JK, Armaghani DJ (2018) Optimization of flyrock and rock fragmentation in the Tajareh limestone mine using metaheuristics method of firefly algorithm. Eng Comput 34(2):241–251

    Google Scholar 

  43. Mojtahedi SFF, Ebtehaj I, Hasanipanah M, Bonakdari H, Amnieh HB (2019) Proposing a novel hybrid intelligent model for the simulation of particle size distribution resulting from blasting. Eng Comput 35(1):47–56

    Google Scholar 

  44. Shams S, Monjezi M, Majd VJ, Armaghani DJ (2015) Application of fuzzy inference system for prediction of rock fragmentation induced by blasting. Arab J Geosci 8(12):10819–10832

    Google Scholar 

  45. Hasanipanah M, Armaghani DJ, Monjezi M, Shams S (2016) Risk assessment and prediction of rock fragmentation produced by blasting operation: a rock engineering system. Environ Earth Sci 75(9):808

    Google Scholar 

  46. Monjezi M, Mohamadi HA, Barati B, Khandelwal M (2014) Application of soft computing in predicting rock fragmentation to reduce environmental blasting side effects. Arab J Geosci 7(2):505–511

    Google Scholar 

  47. Amodio S (2011) Generalized boosted additive models. University of Naples Federico II, Napoli

    Google Scholar 

  48. Le LT, Nguyen H, Zhou J, Dou J, Moayedi H (2019) Estimating the heating load of buildings for smart city planning using a novel artificial intelligence technique PSO-XGBoost. Appl Sci 9(13):2714

    Google Scholar 

  49. Le LT, Nguyen H, Dou J, Zhou J (2019) A comparative study of PSO-ANN, GA-ANN, ICA-ANN, and ABC-ANN in estimating the heating load of buildings’ energy efficiency for smart city planning. Appl Sci 9(13):2630

    Google Scholar 

  50. Shang Y, Nguyen H, Bui X-N, Tran Q-H, Moayedi H (2019) A novel artificial intelligence approach to predict blast-induced ground vibration in open-pit mines based on the firefly algorithm and artificial neural network. Nat Resour Res. https://doi.org/10.1007/s11053-019-09503-7

    Article  Google Scholar 

  51. Nguyen H, Moayedi H, Foong LK, Al Najjar HAH, Jusoh WAW, Rashid ASA, Jamali J (2019) Optimizing ANN models with PSO for predicting short building seismic response. Eng Comput. https://doi.org/10.1007/s00366-019-00733-0

    Article  Google Scholar 

  52. Nguyen H, Drebenstedt C, Bui X-N, Bui DT (2019) Prediction of blast-induced ground vibration in an open-pit mine by a novel hybrid model based on clustering and artificial neural network. Nat Resour Res. https://doi.org/10.1007/s11053-019-09470-z

    Article  Google Scholar 

  53. Moayedi H, Raftari M, Sharifi A, Jusoh WAW, Rashid ASA (2019) Optimization of ANFIS with GA and PSO estimating α ratio in driven piles. Eng Comput. https://doi.org/10.1007/s00366-018-00694-w

    Article  Google Scholar 

  54. Ghasemi E, Kalhori H, Bagherpour R (2016) A new hybrid ANFIS-PSO model for prediction of peak particle velocity due to bench blasting. Eng Comput 32(4):607–614. https://doi.org/10.1007/s00366-016-0438-1

    Article  Google Scholar 

  55. Jiang W, Arslan CA, Soltani Tehrani M, Khorami M, Hasanipanah M (2018) Simulating the peak particle velocity in rock blasting projects using a neuro-fuzzy inference system. Eng Comput. https://doi.org/10.1007/s00366-018-0659-6

    Article  Google Scholar 

  56. Xu Y-T, Zhang Y, Wang S-G (2015) A modified tunneling function method for non-smooth global optimization and its application in artificial neural network. Appl Math Model 39(21):6438–6450

    MathSciNet  MATH  Google Scholar 

  57. Aich U, Banerjee S (2014) Modeling of EDM responses by support vector machine regression with parameters selected by particle swarm optimization. Appl Math Model 38(11–12):2800–2818

    MATH  Google Scholar 

  58. Nguyen H, Bui X-N, Tran Q-H, Van Hoa P, Nguyen D-A, Hoa LTT, Le Q-T, Do N-H, Bao TD, Bui H-B, Moayedi H (2020) A comparative study of empirical and ensemble machine learning algorithms in predicting air over-pressure in open-pit coal mine. Acta Geophys. https://doi.org/10.1007/s11600-019-00396-x

    Article  Google Scholar 

  59. Nguyen H, Choi Y, Bui X-N, Nguyen-Thoi T (2020) Predicting blast-induced ground vibration in open-pit mines using vibration sensors and support vector regression-based optimization algorithms. Sensors 20(1):132

    Google Scholar 

  60. Duan J, Asteris PG, Nguyen H, Bui X-N, Moayedi H (2020) A novel artificial intelligence technique to predict compressive strength of recycled aggregate concrete using ICA-XGBoost model. Eng Comput. https://doi.org/10.1007/s00366-020-01003-0

    Article  Google Scholar 

  61. Zhang X, Nguyen H, Bui X-N, Le HA, Nguyen-Thoi T, Moayedi H, Mahesh V (2020) Evaluating and predicting the stability of roadways in tunnelling and underground space using artificial neural network-based particle swarm optimization. Tunn Undergr Space Technol 103:103517

    Google Scholar 

  62. Stone CJ (1985) Additive regression and other nonparametric models. Ann Stat 13(2):689–705

    MathSciNet  MATH  Google Scholar 

  63. Hastie TJ (2017) Generalized additive models. In: Hastie TJ, Tibshirani RJ (eds) Statistical models in S. Routledge, Abingdon, pp 249–307

    Google Scholar 

  64. Hastie T, Tibshirani R (1990) Generalized additive models. Chapman and Hall Inc, London

    MATH  Google Scholar 

  65. Marx BD, Eilers PH (1998) Direct generalized additive modeling with penalized likelihood. Comput Stat Data Anal 28(2):193–209

    MATH  Google Scholar 

  66. Wand MP (2000) A comparison of regression spline smoothing procedures. Comput Stat 15(4):443–462

    MathSciNet  MATH  Google Scholar 

  67. Fahrmeir L, Lang S (2001) Bayesian inference for generalized additive mixed models based on Markov random field priors. J R Stat Soc: Ser C (Appl Stat) 50(2):201–220

    MathSciNet  Google Scholar 

  68. Friedman J, Hastie T, Tibshirani R (2000) Additive logistic regression: a statistical view of boosting (with discussion and a rejoinder by the authors). Ann Stat 28(2):337–407

    MATH  Google Scholar 

  69. Friedman J, Hastie T, Tibshirani R (2001) The elements of statistical learning. Springer series in statistics, vol 10. Springer, New York, NY

    MATH  Google Scholar 

  70. Tutz G, Binder H (2006) Generalized additive modeling with implicit variable selection by likelihood-based boosting. Biometrics 62(4):961–971

    MathSciNet  MATH  Google Scholar 

  71. Leathwick J, Elith J, Hastie T (2006) Comparative performance of generalized additive models and multivariate adaptive regression splines for statistical modelling of species distributions. Ecol Model 199(2):188–196

    Google Scholar 

  72. Mayr A, Fenske N, Hofner B, Kneib T, Schmid M (2012) Generalized additive models for location, scale and shape for high dimensional data—a flexible approach based on boosting. J R Stat Soc: Ser C (Appl Stat) 61(3):403–427

    MathSciNet  Google Scholar 

  73. Horowitz JL (2001) Nonparametric estimation of a generalized additive model with an unknown link function. Econometrica 69(2):499–513

    MathSciNet  MATH  Google Scholar 

  74. de Brogniez D, Ballabio C, Stevens A, Jones R, Montanarella L, van Wesemael B (2015) A map of the topsoil organic carbon content of Europe generated by a generalized additive model. Eur J Soil Sci 66(1):121–134

    Google Scholar 

  75. Walsh WA, Kleiber P (2001) Generalized additive model and regression tree analyses of blue shark (Prionace glauca) catch rates by the Hawaii-based commercial longline fishery. Fish Res 53(2):115–131

    Google Scholar 

  76. Chen W, Pourghasemi HR, Panahi M, Kornejady A, Wang J, Xie X, Cao S (2017) Spatial prediction of landslide susceptibility using an adaptive neuro-fuzzy inference system combined with frequency ratio, generalized additive model, and support vector machine techniques. Geomorphology 297:69–85

    Google Scholar 

  77. Liu X, Song Y, Yi W, Wang X, Zhu J (2018) Comparing the random forest with the generalized additive model to evaluate the impacts of outdoor ambient environmental factors on scaffolding construction productivity. J Constr Eng Manag 144(6):04018037

    Google Scholar 

  78. Marra G, Wood SN (2011) Practical variable selection for generalized additive models. Comput Stat Data Anal 55(7):2372–2387

    MathSciNet  MATH  Google Scholar 

  79. Binder H, Tutz G (2008) A comparison of methods for the fitting of generalized additive models. Stat Comput 18(1):87–99

    MathSciNet  Google Scholar 

  80. Groll A, Tutz G (2012) Regularization for generalized additive mixed models by likelihood-based boosting. Methods Inf Med 51(02):168–177

    Google Scholar 

  81. Fister I, Fister I Jr, Yang X-S, Brest J (2013) A comprehensive review of firefly algorithms. Swarm Evol Comput 13:34–46

    Google Scholar 

  82. Zhou J, Nekouie A, Arslan CA, Pham BT, Hasanipanah M (2019) Novel approach for forecasting the blast-induced AOp using a hybrid fuzzy system and firefly algorithm. Eng Comput 36:1–10

    Google Scholar 

  83. Ramezanian R, Saidi-Mehrabad M (2013) Hybrid simulated annealing and MIP-based heuristics for stochastic lot-sizing and scheduling problem in capacitated multi-stage production system. Appl Math Model 37(7):5134–5147

    MathSciNet  MATH  Google Scholar 

  84. Shang Y, Nguyen H, Bui X-N, Tran Q-H, Moayedi H (2020) A novel artificial intelligence approach to predict blast-induced ground vibration in open-pit mines based on the firefly algorithm and artificial neural network. Nat Resour Res 29(2):723–737. https://doi.org/10.1007/s11053-019-09503-7

    Article  Google Scholar 

  85. Zhou J, Li C, Arslan CA, Hasanipanah M, Bakhshandeh Amnieh H (2019) Performance evaluation of hybrid FFA-ANFIS and GA-ANFIS models to predict particle size distribution of a muck-pile after blasting. Eng Comput. https://doi.org/10.1007/s00366-019-00822-0

    Article  Google Scholar 

  86. Asl PF, Monjezi M, Hamidi JK, Armaghani DJ (2017) Optimization of flyrock and rock fragmentation in the Tajareh limestone mine using metaheuristics method of firefly algorithm. Eng Comput 34:1–11

    Google Scholar 

  87. Faradonbeh RS, Armaghani DJ, Amnieh HB, Mohamad ET (2018) Prediction and minimization of blast-induced flyrock using gene expression programming and firefly algorithm. Neural Comput Appl 29(6):269–281

    Google Scholar 

  88. Yang X-S (2017) Nature-inspired algorithms and applied optimization, vol 744. Springer, Berlin

    Google Scholar 

  89. Aarts E, Aarts EH, Lenstra JK (2003) Local search in combinatorial optimization. Princeton University Press, Princeton

    MATH  Google Scholar 

  90. Bahrami A, Monjezi M, Goshtasbi K, Ghazvinian A (2011) Prediction of rock fragmentation due to blasting using artificial neural network. Eng Comput 27(2):177–181

    Google Scholar 

  91. Enayatollahi I, Bazzazi AA, Asadi A (2014) Comparison between neural networks and multiple regression analysis to predict rock fragmentation in open-pit mines. Rock Mech Rock Eng 47(2):799–807

    Google Scholar 

  92. Armaghani DJ (2018) Rock fragmentation prediction through a new hybrid model based on imperial competitive algorithm and neural network. Smart Constr Res 2:1–12

    Google Scholar 

  93. Nazari A, Milani AA, Khalaj G (2012) Modeling ductile to brittle transition temperature of functionally graded steels by ANFIS. Appl Math Model 36(8):3903–3915

    Google Scholar 

  94. Abdulshahed AM, Longstaff AP, Fletcher S, Myers A (2015) Thermal error modelling of machine tools based on ANFIS with fuzzy c-means clustering using a thermal imaging camera. Appl Math Model 39(7):1837–1852

    MATH  Google Scholar 

  95. Asteris PG, Apostolopoulou M, Skentou AD, Moropoulou A (2019) Application of artificial neural networks for the prediction of the compressive strength of cement-based mortars. Comput Concrete 24(4):329–345

    Google Scholar 

  96. Sakia R (1992) The Box–Cox transformation technique: a review. The Statistician 41:169–178

    Google Scholar 

Download references

Acknowledgements

This paper was supported by the Center for Mining, Electro-Mechanical research of Hanoi University of Mining and Geology (HUMG), Hanoi, Vietnam; the research team of Innovations for Sustainable and Responsible Mining (ISRM) of HUMG, and partially supported by the National Natural Science Foundation Project of China (Grant no. 41807259) and the Innovation-Driven Project of Central South University (2020CX040).

Author information

Authors and Affiliations

  1. Institute of Architecture Engineering, Huanghuai University, Zhumadian, 463000, Henan, China

    Qiancheng Fang

  2. Institute of Research and Development, Duy Tan University, Da Nang 550000, Vietnam

    Hoang Nguyen

  3. Department of Surface Mining, Mining Faculty, Hanoi University of Mining and Geology, 18 Vien st., Duc Thang Ward, Bac Tu Liem Dist., Hanoi, Vietnam

    Xuan-Nam Bui

  4. Center for Mining, Electro-Mechanical Research, Hanoi University of Mining and Geology, 18 Vien St., Duc Thang Ward, Bac Tu Liem Dist., Hanoi, Vietnam

    Xuan-Nam Bui

  5. Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Trung Nguyen-Thoi

  6. Faculty of Civil Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Trung Nguyen-Thoi

  7. School of Resources and Safety Engineering, Central South University, Changsha, 410083, Hunan, China

    Jian Zhou

Authors
  1. Qiancheng Fang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hoang Nguyen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xuan-Nam Bui
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Trung Nguyen-Thoi
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Jian Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hoang Nguyen.

Ethics declarations

Conflict of interest

All the authors have participated in the conception, data collection, analysis, visualization, drafting, writing, editing, and revising of the manuscript. Also, all the authors have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Fang, Q., Nguyen, H., Bui, XN. et al. Modeling of rock fragmentation by firefly optimization algorithm and boosted generalized additive model. Neural Comput & Applic 33, 3503–3519 (2021). https://doi.org/10.1007/s00521-020-05197-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-020-05197-8

Keywords

Search

Navigation