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A hybrid computing model to predict rock strength index properties using support vector regression

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Abstract

The uniaxial compressive strength (UCS) and elasticity modulus (E) are two of the most quoted rock strength parameters in engineering application. Due to approved technical difficulties indirect measurements, the tendency for determining these parameters through predictive models using simpler and cheaper tests in practical oriented applications have widely been highlighted. In this paper, a new hybridized multi-objective support vector regression (MSVR) model integrated with the firefly metaheuristic algorithm (FMA) was developed to touch upon a computational method in rock engineering purposes. The optimum internal parameters were adjusted through parametric investigation using 222 physical and mechanical rock properties corresponding to a variety of quarried stones from all over Iran. The accuracy and robustness of models were evaluated using different error indices, the area under curve for receiver operation characteristics (AUCROC) and F1-score criteria. Comparing to MSVR, the predictability level of UCS and E showed 8.35% and 5.47% improvement in hybrid MSVR-FMA. The superior and more promising results imply that hybrid MSVR-FMA as a flexible alternative can be applied for rock strength prediction in designing of construction projects. Using tow sensitivity analyses, the point load index and P-wave velocity were distinguished as the main effective factors on predicted UCS and E.

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References

  1. Abbaszadeh Shahri A, Gheirati A, Espersson M (2014) Prediction of rock mechanical parameters as a function of P-wave velocity. Int Res J Earth Sci 2(9):7–14

    Google Scholar 

  2. Abbaszadeh Shahri A, Larsson S, Johansson F (2016) Updated relations for the uniaxial compressive strength of marlstones based on P-wave velocity and point load index test. Innov Infrastruct Solut 1:17. https://doi.org/10.1007/s41062-016-0016-9

    Article  Google Scholar 

  3. Abbaszadeh Shahri A (2016) Assessment and prediction of liquefaction potential using different artificial neural network models—a case study. Geotech Geol Eng 34(3):807–815. https://doi.org/10.1007/s10706-016-0004-z

    Article  Google Scholar 

  4. Abbaszadeh Shahri A, Larsson S, Renkel C (2020) Artificial intelligence models to generate visualized bedrock level: a case study in Sweden. Model Earth Syst Environ. https://doi.org/10.1007/s40808-020-00767-0

    Article  Google Scholar 

  5. Abdi Y, Garavand AT, Sahamieh RZ (2018) Prediction of strength parameters of sedimentary rocks using artificial neural networks and regression analysis. Arab J Geosci 11:587. https://doi.org/10.1007/s12517-018-3929-0

    Article  Google Scholar 

  6. Aboutaleb Sh, Behnia M, Bagherpour R, Bluekian B (2018) Using non-destructive tests for estimating uniaxial compressive strength and static Young’s modulus of carbonate rocks via some modeling techniques. Bull Eng Geol Environ 77(4):1717–1728. https://doi.org/10.1007/s10064-017-1043-2

    Article  Google Scholar 

  7. Alemdag S, Gurocak Z, Cevik A, Cabalar AF, Gokceoglu C (2016) Modeling deformation modulus of a stratified sedimentary rock mass using neural network, fuzzy inference and genetic programming. Eng Geol 203:70–82. https://doi.org/10.1016/j.enggeo.2015.12.002

    Article  Google Scholar 

  8. Amiri B, Hossain L, Crawford JW, Wigand RT (2013) Community detection in complex networks: multi-objective enhanced firefly algorithm. Knowl Based Syst 46(1):1–11. https://doi.org/10.1016/j.knosys.2013.01.004

    Article  Google Scholar 

  9. Apostolopoulos T, Vlachos A (2011) Application of the firefly algorithm for solving the economic emissions load dispatch problem. Int J Combin. https://doi.org/10.1155/2011/523806

    Article  MathSciNet  MATH  Google Scholar 

  10. Arsuaga-Rios M, Vega-Rodriguez MA (2012) Multi-objective firefly algorithm for energy optimization in grid environments. In: Dorigo M et al (eds) Swarm intelligence. ANTS 2012. Lecture notes in computer science, vol 7461. Springer, Berlin. https://doi.org/10.1007/978-3-642-32650-9_41

  11. Asheghi R, Abbaszadeh Shahri A, Khorsand Zak M (2019) Prediction of strength index parameters of different rock types using hybrid multi output intelligence model. Arab J Sci Eng 44(10):8645–8659. https://doi.org/10.1007/s1336-019-04046-8

    Article  Google Scholar 

  12. Asheghi R, Hosseini SA, Sanei M, Abbaszadeh Shahri A (2020) Updating the neural network sediment load models using different sensitivity analysis methods—a regional application. J Hydroinf. https://doi.org/10.2166/hydro.2020.098

    Article  Google Scholar 

  13. Awad M, Khanna R (2015) Support vector regression. In: Efficient learning machines. Apress, Berkeley, pp 67–80. https://doi.org/10.1007/978-1-4302-5990-9_4

  14. Beiki M, Majdi A, Givshad AD (2013) Application of genetic programming to predict the uniaxial compressive strength and elastic modulus of carbonate rocks. Int J Rock Mech Min Sci 63:159–169. https://doi.org/10.1016/j.ijrmms.2013.08.004

    Article  Google Scholar 

  15. Behnia D, Behnia M, Shahriar K, Goshtasbi K (2017) A new predictive model for rock strength parameters utilizing GEP method. Procedia Eng 191:591–599. https://doi.org/10.1016/j.proeng.2017.05.222

    Article  Google Scholar 

  16. Bennett KP, Mangasarian OL (1992) Robust linear programming discrimination of two linearly inseparable sets. Optim Methods Softw 1:23–34. https://doi.org/10.1080/10556789208805504

    Article  Google Scholar 

  17. Chandrasekaran K, Simon SP (2012) Network and reliability constrained unit commitment problem using binary real coded firefly algorithm. Int J Electr Power Energy Syst 42(1):921–932. https://doi.org/10.1016/j.ijepes.2012.06.004

    Article  Google Scholar 

  18. Chang CC, Lin CJ (2011) LIBSVM: a library for support vector machines. ACM Trans Intell Syst Technol. https://doi.org/10.1145/1961189.1961199

    Article  Google Scholar 

  19. Cherkassky V, Mulier F (1998) Learning from data: concepts, theory and methods. Wiley, New York

    MATH  Google Scholar 

  20. Coelho LDS, Mariani VC (2013) Improved firefly algorithm approach applied to chiller loading for energy conservation. Energy Build 59:273–278. https://doi.org/10.1016/j.enbuild.2012.11.030

    Article  Google Scholar 

  21. Coelho LS, de Andrade Bernert DL, Mariani VC (2011) A chaotic firefly algorithm applied to reliability-redundancy optimization. In: 2011 IEEE Congress of Evolutionary Computation (CEC’11), 12117561, New Orleans, USA, pp 517–521. https://doi.org/10.1109/CEC.2011.5949662

  22. Coelho LS, Mariani VC (2012) Firefly algorithm approach based on chaotic Tinkerbell map applied to multivariable PID controller tuning. Comput Math Appl 64(8):2371–2382. https://doi.org/10.1016/j.camwa.2012.05.007

    Article  MathSciNet  MATH  Google Scholar 

  23. Courant R, Hilbert D (1953) Methods of mathematical physics. Interscience, New York

    MATH  Google Scholar 

  24. Drucker H, Burges CJC, Kaufman L, Smola AJ, Vapnik VN (1997) Support vector regression machines. In: proceedings of NIPS'96, the 9th international conference on neural information processing systems, pp 155–161

  25. Gao ML, Li LL, Sun XM, Yin LJ, Li HT, Luo DS (2015) Firefly algorithm based particle filter method for visual tracking. Optik 126:1705–1711

    Article  Google Scholar 

  26. Gevrey M, Dimopoulos I, Lek S (2003) Review and comparison of methods to study the contribution of variables in artificial neural network models. Ecol Model 160(3):249–264. https://doi.org/10.1016/S0304-3800(02)00257-0

    Article  Google Scholar 

  27. Ghaderi A, Abbaszadeh Shahri A, Larsson S (2019) An artificial neural network based model to predict spatial soil type distribution using piezocone penetration test data (CPTu). Bull Eng Geol Environ 78:4579–4588. https://doi.org/10.1007/s10064-018-1400-9

    Article  Google Scholar 

  28. Hand D, Christen P (2018) A note on using the F-measure for evaluating record linkage algorithms. Stat Comput 28(3):539–547. https://doi.org/10.1007/s11222-017-9746-6

    Article  MathSciNet  MATH  Google Scholar 

  29. Imbens GW, Lemieux T (2008) Regression discontinuity designs: a guide to practice. J Econ 142(2):615–635

    Article  MathSciNet  Google Scholar 

  30. ISRM (1981) Rock characterization testing and monitoring. In: Brown ET (ed) ISRM suggested methods, International Society of Rock Mechanics. Pergamon Press, Oxford

    Google Scholar 

  31. Jahed Armaghani D, Mohamad ET, Momeni E, Monjezi M, Narayanasamy MS (2016) Prediction of the strength and elasticity modulus of granite through an expert artificial neural network. Arab J Geosci 9:48. https://doi.org/10.1007/s12517-015-2057-3

    Article  Google Scholar 

  32. Kavousi-Fard A, Samet H, Marzbani F (2014) A new hybrid modified firefly algorithm and support vector regression model for accurate short term load forecasting. Expert Syst Appl 41(13):6047–6056

    Article  Google Scholar 

  33. Li X, Chen X, Yan Y, Wei W, Wang J (2014) Classification of EEG signals using a multiple kernel learning support vector machine. Sensors 14(7):12784–12802. https://doi.org/10.3390/s140712784

    Article  Google Scholar 

  34. Li HM, Ye CM (2012) Firefly algorithm on multi-objective optimization of production scheduling system. Adv Mech Eng Appl 3(1):258–262

    Google Scholar 

  35. Madhubabu N, Singh PK, Kainthola A, Mahanta B, Tripathy A, Singh TN (2016) Prediction of compressive strength and elastic modulus of carbonate rocks. Measurement 88:202–213. https://doi.org/10.1016/j.measurement.2016.03.050

    Article  Google Scholar 

  36. Mahdiabadi N, Khanlari G (2019) Prediction of uniaxial compressive strength and modulus of elasticity in calcareous mudstones using neural networks, fuzzy systems, and regression analysis. Period Polytech Civil Eng 63(1):104–114. https://doi.org/10.3311/PPci.13035

    Article  Google Scholar 

  37. Marichelvam MK, Prabaharan T, Yang XS (2013) A discrete firefly algorithm for the multi-objective hybrid flowshop scheduling problems. IEEE Trans Evol Comput 18(2):301–305. https://doi.org/10.1109/TEVC.2013.2240304

    Article  Google Scholar 

  38. Matin SS, Farahzadi L, Makaremi S, Chelgani SC, Sattari GH (2018) Variable selection and prediction of uniaxial compressive strength and modulus of elasticity by random forest. Appl Soft ing 70:980–987. https://doi.org/10.1016/j.asoc.2017.06.030

    Article  Google Scholar 

  39. Min J, Lee Y (2005) Bankruptcy prediction using support vector machine with optimal choice of kernel function parameters. Expert Syst Appl 28(4):603–614. https://doi.org/10.1016/j.eswa.2004.12.008

    Article  Google Scholar 

  40. Jiang M, Hu W, Qiu L, Shi M, Tan KC (2018) Solving dynamic multi-objective optimization problems via support vector machine. In: 2018 tenth international conference on advanced computational intelligence (ICACI). https://doi.org/10.1109/ICACI.2018.8377567

  41. Momeni E, Jahed Armaghani D, Hajihassani M, For M, Amin M (2015) Prediction of uniaxial compressive strength of rock samples using hybrid particle swarm optimization-based artificial neural networks. Measurement 60:50–63. https://doi.org/10.1016/j.measurement.2014.09.075

    Article  Google Scholar 

  42. Moradian ZA, Behnia M (2009) Predicting the uniaxial compressive strength and static Young’s modulus of intact sedimentary rocks using the ultrasonic test. Int J Geomech 9(1):14–19. https://doi.org/10.1061/(ASCE)1532-3641(2009)9:1(14)

    Article  Google Scholar 

  43. Najibi AR, Ghafoori M, Lashkaripour GR, Asef MR (2015) Empirical relations between strength and static and dynamic elastic properties of Asmari and Sarvak limestones, two main oil reservoirs of Iran. J Petol Sci Eng 126:78–82. https://doi.org/10.1016/j.petrol.2014.12.010

    Article  Google Scholar 

  44. Nocedal J, Wright SJ (1999) Numerical optimization. Springer-Verlag, New York

    Book  Google Scholar 

  45. Palchik V (2011) On the ratios between elastic modulus and uniaxial compressive strength of heterogeneous carbonate rocks. Rock Mech Rock Eng 44(1):121–128. https://doi.org/10.1007/s00603-010-0112-7

    Article  Google Scholar 

  46. Pedhazur EJ (1997) Multiple regression in behavioral research, 3rd edn. Harcourt Brace College Publishers, Fort Worth

    MATH  Google Scholar 

  47. Pérez-Cruz F, Navia-Vázquez A, Alarcón-Diana PL, ArtésRodríguez A (2000a) An IRWLS procedure for SVR. In: Proc. EUSIPCO, Tampere, Finland

  48. Pérez-Cruz F, Alarcón-Diana PF, Navia-Vázquez A, ArtésRodríguez A (2000) Fast training of support vector classifiers. In: Leen T, Dietterich T, Tresp V (eds) Neural information processing systems, vol 13. MIT Press, Cambridge, pp 734–740

    Google Scholar 

  49. Platt J (1999) Fast training of support vector machines using sequential minimal optimization, advances in Kernel methods support vector learning. MIT Press, Cambridge

    Google Scholar 

  50. Powers DA, Xie Y (2008) Statistical methods for categorical data analysis, 2nd edn. Emerald, Howard House

    MATH  Google Scholar 

  51. Rampriya B, Mahadevan K, Kannan S (2010) Unit commitment in deregulated power system using Lagrangian firefly algorithm. IEEE Int Conf Commun Control Comput Technol (ICCCCT2010) 11745352 Ramanathapuram India. https://doi.org/10.1109/ICCCCT.2010.5670583

    Article  Google Scholar 

  52. Sayadi MK, Ramezanian R, Ghaffari-Nasab N (2010) A discrete firefly meta-heuristic with local search for makespan minimization in permutation flow shop scheduling problems. Int J Ind Eng Comput 1(1):1–10. https://doi.org/10.5267/j.ijiec.2010.01.001

    Article  Google Scholar 

  53. Singh R, Rk U, Ahmad M, Ansari MK, Sharma LK, Singh TN (2017) Prediction of geomechanical parameters using soft computing and multiple regression approach. Measurement 99:108–119. https://doi.org/10.1016/j.measurement.2016.12.023

    Article  Google Scholar 

  54. Stehman SV (1997) Selecting and interpreting measures of thematic classification accuracy. Remote Sens Environ 62(1):77–89. https://doi.org/10.1016/S0034-4257(97)00083-7

    Article  Google Scholar 

  55. Suttorp T, Igel C (2006) Multi-objective optimization of support vector machines. In: Jin Y (eds) Multi-objective machine learning. Studies in computational intelligence, vol 16. Springer, Berlin, pp 199–220. https://doi.org/10.1007/3-540-33019-4_9

  56. Tuia D, Verrelst J, Alonso L, Pérez-Cruz F, Camps-Valls G (2011) Multi output support vector regression for remote sensing biophysical parameter estimation. IEEE Geosci Remote Sens Lett 8(4):804–808. https://doi.org/10.1109/LGRS.2011.2109934

    Article  Google Scholar 

  57. Umrao RK, Sharma LK, Singh R, Singh TN (2018) Determination of strength and modulus of elasticity of heterogenous sedimentary rocks: an ANFIS predictive technique. Measurement 126:194–201. https://doi.org/10.1016/j.measurement.2018.05.064

    Article  Google Scholar 

  58. Vapnik VN (1995) The nature of statistical learning theory, 2nd edn. Springer-Verlag, New York

    Book  Google Scholar 

  59. Wang H, Hu D (2005) Comparison of SVM and LS-SVM for regression. In: Proc. Int. Conf. on neural networks and brain. IEEE, New York, pp 279–283. https://doi.org/10.1109/ICNNB.2005.1614615

  60. Willmott CJ (1984) On the evaluation of model performance in physical geography. Spatial Stat Models. https://doi.org/10.1007/978-94-017-3048-8_23

    Article  Google Scholar 

  61. Yang XS (2008) Firefly algorithm. Luniver Press, Bristol

    Google Scholar 

  62. Yang XS (2012) Chaos-enhanced firefly algorithm with automatic parameter tuning. Int J Swarm Intell Res 2(4):125–136. https://doi.org/10.4018/jsir.2011100101

    Article  Google Scholar 

  63. Yang XS (2013) Multi-objective firefly algorithm for continuous optimization. Eng Comput 29(2):175–184

    Article  Google Scholar 

  64. Yang XS (2014) Nature-inspired optimization algorithms. Elsevier. https://doi.org/10.1016/C2013-0-01368-0

    Article  MATH  Google Scholar 

  65. Yun Y, Yoon M, Nakayama H (2009) Multi-objective optimization based on meta-modeling by using support vector regression. Optim Eng 10:167–181. https://doi.org/10.1007/s11081-008-9063-1

    Article  MathSciNet  MATH  Google Scholar 

  66. Yun Y, Nakayama H, Arakawa M (2004) Using support vector machines in multi-objective optimization. In: 2004 IEEE international joint conference on neural networks (IEEE Cat. No. 04CH37541). https://doi.org/10.1109/IJCNN.2004.1379903

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Authors and Affiliations

  1. Department of Civil Engineering, Roudehen Branch, Islamic Azad University, Tehran, Iran

    Abbas Abbaszadeh Shahri

  2. Department of Earth Systems Analysis, Geo-Information Science and Earth Observation (ITC), University of Twente, Enschede, The Netherlands

    Fardad Maghsoudi Moud

  3. Departmetn of Mining, Industrial and TIC Engineering, Universitat Politecnica de Catalunya, Barcelona, Spain

    Seyed Poorya Mirfallah Lialestani

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Abbaszadeh Shahri, A., Maghsoudi Moud, F. & Mirfallah Lialestani, S. A hybrid computing model to predict rock strength index properties using support vector regression. Engineering with Computers 38, 579–594 (2022). https://doi.org/10.1007/s00366-020-01078-9

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