Makine Öğrenimi Yöntemleriyle Bazaltlarda Tek Eksenli Sıkışma Dayanımının Değerlendirilmesi ve Performanslarının Karşılaştırılması

Abstract

Tek eksenli sıkışma dayanımı (UCS) mühendislik projelerinde en önemli tasarım parametrelerinden biri olup; bir çok projede ve sınıflama sistemlerinde doğrudan kullanılan bir parametredir. UCS’nin elde edilmesindeki güçlükler göz önüne alındığında; makine öğrenimi temelli yaklaşımlar ile tahmin edilmesi dikkat çekmektedir. Çalışma kapsamında bazalt bloklarından alınan 137 adet karot örneği üzerinde gerçekleştirilen laboratuvar deney sonuçları kullanılarak iki ayrı model elde edilmiştir. Bu modellerde görünür gözeneklilik (n), p dalga hızı (Vp) ve birim hacim ağırlık (n) değerleri girdi parametreleri olup; makine öğrenimi yöntemleri ile UCS tahmin edilmeye çalışılmıştır. Bu amaçla; Gauss Süreç Regresyonu (GSR), Destek Vektör Makineleri (DVM) ve Ağaç Toplulukları Yöntemleri (AT) olmak üzere üç farklı makine öğrenimi yöntemi kullanılmıştır. İki ayrı modele ait beş farklı veri seti için uygulanan üç ayrı makine öğrenimi yönteminin performanslarının değerlendirmesinde R2 (determinasyon katsayısı), RMSE (kök ortalama kare hata), MSE (ortalama kare hata) ve MAE (ortalama mutlak hata) performans indisleri kullanılmıştır. Buna göre; genel olarak üç ayrı makine öğrenimi yönteminin de UCS’ nin tahmininde başarılı olduğu değerlendirilmiş olmakla birlikte AT yönteminin genel olarak daha yüksek tahmin performansı verdiği belirlenmiştir.

Keywords

• Tek eksenli sıkışma dayanımı
• Destek vektör makineleri
• Gauss süreç yönetimi
• Ağaç toplulukları

Evaluation of Uniaxial Compressive Strength of Basalts using Machine Learning Methods and Comparison of Their Performances

Abstract

Uniaxial compressive strength (UCS) is one of the most critical design parameters of engineering projects, which is directly used parameter in many projects and classification systems. Considering the difficulties in obtaining the UCS, it is remarkable that it is estimated using machine learning-based approaches. In this study, two different models were constructed using laboratory results of the 137 core samples. Apparent porosity (n), p wave velocity (Vp), and unit weight (n) values are the input parameters in these models; the UCS was tried to estimated by machine learning-based methods. For this purpose, three different machine learning methods, such as Gaussian Process Regression (GSR), Support Vector Machine (SVM), and Ensembles of Tree (ET) were employed. R2 (Coefficient of Determination), RMSE (Root Mean Square Error), MSE (Mean Square Error), and MAE (Mean Absolute Error) performance indices were used to evaluate the performances of three different machine learning methods for five different data sets of two different models. According to these assessments, it was determined that all three different machine learning methods were successful for estimating UCS in general; however, the ET method generally had higher prediction performance.

Keywords

• Uniaxial compressive strength
• Support vector machine
• Gaussian process regression
• Ensembles of tree

References

1. [1] S. Kahraman, “Evaluation of simple methods for assessing the uniaxial compressive strength of rock,” Int. J. Rock Mech. Min. Sci., vol. 38, no. 7, pp. 981–994, 2001.
2. [2] İ. Çobanoğlu and S. B. Çelik, “Estimation of uniaxial compressive strength from point load strength, Schmidt hardness and P-wave velocity,” Bull. Eng. Geol. Environ., vol. 67, no. 4, pp. 491–498, 2008.
3. [3] H. A. Nefeslioglu, “Evaluation of geo-mechanical properties of very weak and weak rock materials by using non-destructive techniques: Ultrasonic pulse velocity measurements and reflectance spectroscopy,” Eng. Geol., vol. 160, pp. 8–20, 2013.
4. [4] A. E. Aladejare, “Evaluation of empirical estimation of uniaxial compressive strength of rock using measurements from index and physical tests,” J. Rock Mech. Geotech. Eng., vol. 12, no. 2, pp. 256–268, 2020.
5. [5] C. Gokceoglu and K. Zorlu, “A fuzzy model to predict the uniaxial compressive strength and the modulus of elasticity of a problematic rock,” Eng. Appl. Artif. Intell., vol. 17, no. 1, pp. 61–72, 2004.
6. [6] K. Zorlu, C. Gokceoglu, F. Ocakoglu, H. A. Nefeslioglu, and S. Acikalin, “Prediction of uniaxial compressive strength of sandstones using petrography-based models,” Eng. Geol., vol. 96, no. 3–4, pp. 141–158, 2008.
7. [7] I. Yilmaz and G. Yuksek, “Prediction of the strength and elasticity modulus of gypsum using multiple regression, ANN, and ANFIS models,” Int. J. rock Mech. Min. Sci., vol. 46, no. 4, pp. 803–810, 2009.
8. [8] S. Dehghan, G. H. Sattari, S. C. Chelgani, and M. A. Aliabadi, “Prediction of uniaxial compressive strength and modulus of elasticity for Travertine samples using regression and artificial neural networks,” Min. Sci. Technol., vol. 20, no. 1, pp. 41–46, 2010.

9. [9] M. Monjezi, H. A. Khoshalan, and M. Razifard, “A neuro-genetic network for predicting uniaxial compressive strength of rocks,” Geotech. Geol. Eng., vol. 30, no. 4, pp. 1053–1062, 2012.
10. [10] S. Yagiz, E. A. Sezer, and C. Gokceoglu, “Artificial neural networks and nonlinear regression techniques to assess the influence of slake durability cycles on the prediction of uniaxial compressive strength and modulus of elasticity for carbonate rocks,” Int. J. Numer. Anal. Methods Geomech., vol. 36, no. 14, pp. 1636–1650, 2012.
11. [11] N. Yesiloglu-Gultekin, C. Gokceoglu, and E. A. Sezer, “Prediction of uniaxial compressive strength of granitic rocks by various nonlinear tools and comparison of their performances,” Int. J. Rock Mech. Min. Sci., vol. 62, pp. 113–122, 2013.
12. [12] N. Yesiloglu-Gultekin, E. A. Sezer, C. Gokceoglu, and H. Bayhan, “An application of adaptive neuro fuzzy inference system for estimating the uniaxial compressive strength of certain granitic rocks from their mineral contents,” Expert Syst. Appl., vol. 40, no. 3, pp. 921–928, 2013.
13. [13] D. Armaghani, E. Tonnizam Mohamad, E. Momeni, M. Monjezi, and M. S. Narayanasamy, “Prediction of the strength and elasticity modulus of granite through an expert artificial neural network. Arab J Geosci 9: 48.” 2016.
14. [14] A. Cevik, E. A. Sezer, A. F. Cabalar, and C. Gokceoglu, “Modeling of the uniaxial compressive strength of some clay-bearing rocks using neural network,” Appl. Soft Comput., vol. 11, no. 2, pp. 2587–2594, 2011.
15. [15] R. Singh, A. Kainthola, and T. N. Singh, “Estimation of elastic constant of rocks using an ANFIS approach,” Appl. Soft Comput., vol. 12, no. 1, pp. 40–45, 2012.
16. [16] D. J. Armaghani, E. T. Mohamad, E. Momeni, and M. S. Narayanasamy, “An adaptive neuro-fuzzy inference system for predicting unconfined compressive strength and Young’s modulus: a study on Main Range granite,” Bull. Eng. Geol. Environ., vol. 74, no. 4, pp. 1301–1319, 2015.
17. [17] R. K. Umrao, L. K. Sharma, R. Singh, and T. N. Singh, “Determination of strength and modulus of elasticity of heterogenous sedimentary rocks: An ANFIS predictive technique,” Measurement, vol. 126, pp. 194–201, 2018.
18. [18] D. J. Armaghani et al., “Predicting the unconfined compressive strength of granite using only two non-destructive test indexes,” Geomech. Eng, vol. 25, pp. 317–330, 2021.
19. [19] Q. Fang, B. Yazdani Bejarbaneh, M. Vatandoust, D. Jahed Armaghani, B. Ramesh Murlidhar, and E. Tonnizam Mohamad, “Strength evaluation of granite block samples with different predictive models,” Eng. Comput., vol. 37, no. 2, pp. 891–908, 2021.
20. [20] R. Barzegar, M. Sattarpour, R. Deo, E. Fijani, and J. Adamowski, “An ensemble tree-based machine learning model for predicting the uniaxial compressive strength of travertine rocks,” Neural Comput. Appl., vol. 32, no. 13, pp. 9065–9080, 2020, doi: 10.1007/s00521-019-04418-z.
21. [21] N. M. Shahani, X. Zheng, X. Guo, and X. Wei, “Machine Learning-Based Intelligent Prediction of Elastic Modulus of Rocks at Thar Coalfield,” Sustainability, vol. 14, no. 6, p. 3689, 2022.
22. [22] N. M. Khan et al., “Application of Machine Learning and Multivariate Statistics to Predict Uniaxial Compressive Strength and Static Young’s Modulus Using Physical Properties under Different Thermal Conditions,” Sustainability, vol. 14, no. 16, p. 9901, 2022.
23. [23] A. Karakuş and M. Akatay, “Determination of basic physical and mechanical properties of basaltic rocks from P-wave velocity,” Nondestruct. Test. Eval., vol. 28, no. 4, pp. 342–353, 2013.
24. [24] F. Dursun and T. Topal, “Durability assessment of the basalts used in the Diyarbakır City Walls, Turkey,” Environ. Earth Sci., vol. 78, no. 15, pp. 1–24, 2019.
25. [25] H. Aldeeky, O. Al Hattamleh, and S. Rababah, “Assessing the uniaxial compressive strength and tangent Young’s modulus of basalt rock using the Leeb rebound hardness test,” Mater. Construcción, vol. 70, no. 340, p. 230, 2020.
26. [26] M. Korkanç and A. Tuğrul, “Evaluation of selected basalts from Niğde, Turkey, as source of concrete aggregate,” Eng. Geol., vol. 75, no. 3–4, pp. 291–307, 2004.
27. [27] T. A. Engidasew and G. Barbieri, “Geo-engineering evaluation of Termaber basalt rock mass for crushed stone aggregate and building stone from Central Ethiopia,” J. African Earth Sci., vol. 99, pp. 581–594, 2014.
28. [28] E. Kolay and T. Baser, “The effect of the textural characteristics on the engineering properties of the basalts from Yozgat region, Turkey,” J. Geol. Soc. India, vol. 90, no. 1, pp. 102–110, 2017.
29. [29] H. Çanakcı, A. Baykasoğlu, and H. Güllü, “Prediction of compressive and tensile strength of Gaziantep basalts via neural networks and gene expression programming,” Neural Comput. Appl., vol. 18, no. 8, pp. 1031–1041, 2009.
30. [30] M. Endait and A. Juneja, “New correlations between uniaxial compressive strength and point load strength of basalt,” Int. J. Geotech. Eng., vol. 9, no. 4, pp. 348–353, 2015.
31. [31] A. Teymen and E. C. Mengüç, “Comparative evaluation of different statistical tools for the prediction of uniaxial compressive strength of rocks,” Int. J. Min. Sci. Technol., vol. 30, no. 6, pp. 785–797, 2020.
32. [32] E. Gül, E. Ozdemir, and D. E. Sarıcı, “Modeling uniaxial compressive strength of some rocks from turkey using soft computing techniques,” Measurement, vol. 171, p. 108781, 2021.
33. [33] Google Earth. (2022, August, 23). [Online]. Available: http://www.google.com/intl/tr/earth/index.html
34. [34] F. Innocenti, R. Mazzuoli, G. Pasguare, F. Radicati, and L. Villari, “Tertiary and Quaternary volcanism of the Erzurum-Kars area (Eastern Turkey), Geochronological data and geodynamic evolution,” J. Volconogy Geoth. Res., 1982.
35. [35] H. Aktimur et al., “Kars, Arpaçay ve Çıldır dolayının jeolojisi. MTA Rapor No:9257,” Ankara, 1991.
36. [36] 2021 SPSS, “IBM SPSS Statistics v23.0. https://www.ibm.com/support/pages/downloading-ibm-spss-statistics-2.” [Online]. Available: https://www.ibm.com/support/pages/downloading-ibm-spss-statistics-23
37. [37] M. M. Nelson and W. T. Illingworth, “A practical guide to neural nets,” 1991.
38. [38] K. Swingler, Applying neural networks: a practical guide. Morgan Kaufmann, 1996.
39. [39] C. G. Looney, “Advances in feedforward neural networks: demystifying knowledge acquiring black boxes,” IEEE Trans. Knowl. Data Eng., vol. 8, no. 2, pp. 211–226, 1996.
40. [40] V. Vapnik, "The nature of statistical learning theory," NY: Springer-Verlag, 1995.
41. [41] K. Soman, R. Loganathan, and V. Ajay, Machine learning with SVM and other kernel methods. PHI Learning Pvt. Ltd., 2009.
42. [42] S. Ayhan and Ş. Erdoğmuş, "Destek vektör makineleriyle sınıflandırma problemlerinin çözümü için çekirdek fonksiyonu seçimi," Eskişehir Osmangazi Üniversitesi İktisadi ve İdari Bilimler Dergisi, vol. 9, no. 1, pp. 175-201, 2014.
43. [43] S. Haykin, "Neural Networks, a comprehensive foundation, Prentice-Hall Inc," Upper Saddle River, New Jersey, vol. 7458, pp. 161-175, 1999.
44. [44] S. Tolun, "Destek vektör makineleri: Banka başarısızlığının tahmini üzerine bir uygulama," Doktora Tezi Doktora Tezi, İşletme Anabilim Dalı, İstanbul Üniversitesi Sosyal Bilimler Enstitüsü, İstanbul, 2008.
45. [45] N. Cristianini and J. Shawe-Taylor, An introduction to support vector machines and other kernel-based learning methods. Cambridge university press, 2000.
46. [46] B. Schölkopf, J. C. B. Christopher, and J. A. Smola, Advances in kernel methods (Support Vector Learning). Cambridge, England: The MIT Press, 1999.
47. [47] T. Kavzoğlu and İ. Çölkesen, "Destek vektör makineleri ile uydu görüntülerinin sınıflandırılmasında kernel fonksiyonlarının etkilerinin incelenmesi," Harita Dergisi, vol. 144, no. 7, pp. 73-82, 2010.
48. [48] S. Huang, N. Cai, P. P. Pacheco, S. Narrandes, Y. Wang, and W. Xu, "Applications of support vector machine (SVM) learning in cancer genomics," Cancer genomics & proteomics, vol. 15, no. 1, pp. 41-51, 2018.
49. [49] E. E. Osuna, "Support vector machines: Training and applications," Massachusetts Institute of Technology, USA, 1998.
50. [50] K. Liu, X. Hu, Z. Wei, Y. Li, and Y. Jiang, "Modified Gaussian process regression models for cyclic capacity prediction of lithium-ion batteries," IEEE Transactions on Transportation Electrification, vol. 5, no. 4, pp. 1225-1236, 2019.
51. [51] M. Acı and A. G. Doğansoy, "Makine öğrenmesi ve derin öğrenme yöntemleri kullanılarak e-perakende sektörüne yönelik talep tahmini," Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi, vol. 37, no. 3, pp. 1325-1340, 2022.
52. [52] B. Ateş, "Gemi yapılarında gerilme yığılması öngörülerinin kaba ağ yapısı ve makine öğrenmesi ile gerçekleştirilmesi," Yüksek Lisans Tezi Yüksek Lisans Tezi, Gemi ve Deniz Teknolojileri Mühendisliği Ana Bilim Dalı, İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, İstanbul, 2020.
53. [53] Y. Heo and V. M. Zavala, "Gaussian process modeling for measurement and verification of building energy savings," Energy and Buildings, vol. 53, pp. 7-18, 2012.
54. [54] C. Rasmussen and C. Williams, Gaussian processes for machine learning. USA: MIT Press, 2006.
55. [55] C. K. Arthur, V. A. Temeng, and Y. Y. Ziggah, "Novel approach to predicting blast-induced ground vibration using Gaussian process regression," Engineering with Computers, vol. 36, no. 1, pp. 29-42, 2020.
56. [56] K. Yazıcı, "Makine öğrenmesi yöntemleri kullanılarak kısa dönem rüzgar gücü tahmini," Yüksek Lisans Tezi Yüksek Lisans Tezi, Endüstri Mühendisliği, Sakarya Üniversitesi Fen Bilimleri Enstitüsü, Sakarya, 2021.
57. [57] F. Schiltz, C. Masci, T. Agasisti, and D. Horn, "Using regression tree ensembles to model interaction effects: a graphical approach," Applied Economics, vol. 50, no. 58, pp. 6341-6354, 2018.
58. [58] L. Rokach, "Ensemble-based classifiers," Artificial Intelligence Review, vol. 33, no. 1, pp. 1-39, 2010/02/01 2010, doi: 10.1007/s10462-009-9124-7.
59. [59] T. G. Dietterich, "Ensemble methods in machine learning," in International workshop on multiple classifier systems, 2000: Springer, pp. 1-15.
60. [60] G. Valentini and F. Masulli, "Ensembles of learning machines," in Italian workshop on neural nets, 2002: Springer, pp. 3-20.
61. [61] D. Opitz and R. Maclin, "Popular ensemble methods: An empirical study," Journal of artificial intelligence research, vol. 11, pp. 169-198, 1999.
62. [62] L. Breiman, "Bias, variance, and arcing classifiers," Tech. Rep. 460, Statistics Department, University of California, Berkeley, 1996.
63. [63] T. G. Dietterich, "An experimental comparison of three methods for constructing ensembles of decision trees: Bagging, boosting, and randomization," Machine learning, vol. 40, no. 2, pp. 139-157, 2000.
64. [64] Z.-H. Zhou, J. Wu, and W. Tang, "Ensembling neural networks: Many could be better than all," Artificial Intelligence, vol. 137, no. 1, pp. 239-263, 2002/05/01/ 2002, doi: https://doi.org/10.1016/S0004-3702(02)00190-X.
65. [65] D. Opitz and J. Shavlik, "Generating accurate and diverse members of a neural-network ensemble," Advances in neural information processing systems, vol. 8, 1995.
66. [66] L. Breiman, "Random forests," Machine learning, vol. 45, no. 1, pp. 5-32, 2001.
67. [67] R. Katuwal, P. N. Suganthan, and L. Zhang, "An ensemble of decision trees with random vector functional link networks for multi-class classification," Applied Soft Computing, vol. 70, pp. 1146-1153, 2018.
68. [68] M. Shoaran, B. A. Haghi, M. Taghavi, M. Farivar, and A. Emami-Neyestanak, "Energy-efficient classification for resource-constrained biomedical applications," IEEE Journal on Emerging and Selected Topics in Circuits and Systems, vol. 8, no. 4, pp. 693-707, 2018.
69. [69] K. Zorlu, C. Gokceoglu, F. Ocakoglu, H. A. Nefeslioglu, and S. Acikalin, “Prediction of uniaxial compressive strength of sandstones using petrography-based models,” Eng. Geol., vol. 96, no. 3–4, pp. 141–158, 2008.
70. [70] S. Yagiz, C. Gokceoglu, E. Sezer, and S. Iplikci, “Application of two non-linear prediction tools to the estimation of tunnel boring machine performance,” Eng. Appl. Artif. Intell., vol. 22, no. 4, pp. 808–814, 2009, doi: https://doi.org/10.1016/j.engappai.2009.03.007.