Lithofacies Classification from Well Log Data Using Neural Networks, Interval Neutrosophic Sets and Quantification of Uncertainty

Authors: Pawalai Kraipeerapun, Chun Che Fung, Kok Wai Wong

Abstract:

This paper proposes a novel approach to the question of lithofacies classification based on an assessment of the uncertainty in the classification results. The proposed approach has multiple neural networks (NN), and interval neutrosophic sets (INS) are used to classify the input well log data into outputs of multiple classes of lithofacies. A pair of n-class neural networks are used to predict n-degree of truth memberships and n-degree of false memberships. Indeterminacy memberships or uncertainties in the predictions are estimated using a multidimensional interpolation method. These three memberships form the INS used to support the confidence in results of multiclass classification. Based on the experimental data, our approach improves the classification performance as compared to an existing technique applied only to the truth membership. In addition, our approach has the capability to provide a measure of uncertainty in the problem of multiclass classification.

Keywords: Multiclass classification, feed-forward backpropagation neural network, interval neutrosophic sets, uncertainty.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1081890

References:

[1] P. Smets, Uncertainty Management in Information Systems: From Needs to Solutions. Kluwer Academic Publishers, 1997, ch. Imperfect information: Imprecision-Uncertainty, pp. 225-254.
[2] M. Duckham, "Uncertainty and geographic information: Computational and critical convergence," in Representation in a Digital Geography. New York: John Wiley, 2002.
[3] P. F. Fisher, Geographical Information Systems: Principles, Techniques, Management and Applications, 2nd ed. Chichester: John Wiley, 2005, vol. 1, ch. Models of uncertainty in spatial data, pp. 69-83.
[4] C. C. Fung, K. W. Wong, and H. Eren, "Modular Artificial Neural Network for Prediction of Petrophysical Properties From Well Log Data," in IEEE Transactions on Instrumentation and Measurement, vol. 46, no. 6, 1997, pp. 1259-1263.
[5] H. Crocker, C. C. Fung, and K. W. Wong, "The STAG Oilfield Formation Evaluation: A Neural Network Approach," Australian Petroleum Production and Exploration Association APPEA99 Journal, vol. 39, part1, pp. 451-460, 1999.
[6] K. W. Wong and T. D. Gedeon, "Fuzzy Rule Interpolation for Multidimensional Input Space with Petroleum Engineering Application," in Proceedings of Joint 9th IFSA World Congress and 20th NAFIPS International Conference, Vancouver, Canada, July 2001, pp. 2470- 2475.
[7] K. W. Wong, Y. S. Ong, T. D. Gedeon, and C. C. Fung, "Reservoir Characterization Using Support Vector Machines," in Proceedings of the 2005 International Conference on Computational Intelligence for Modelling, Control and Automation, vol. 2, November 2005, pp. 354- 359.
[8] G. Ou, Y. L. Murphey, and L. A. Feldkamp, "Multiclass Pattern Classification Using Neural Networks," in Proceeding of the 17th International Conference on Pattern Recognition (ICPR), 2004, pp. 585-588.
[9] H. Wang, D. Madiraju, Y.-Q. Zhang, and R. Sunderraman, "Interval neutrosophic sets," International Journal of Applied Mathematics and Statistics, vol. 3, pp. 1-18, March 2005.
[10] R. Erenshteyn, P. Laskov, D. M. Saxe, and R. A. Foulds, "Distributed Output Encoding for Multi-Class Pattern Recognition," in Proceeding of the 10th International Conference on Image Analysis and Processing (ICIAP), 1999, pp. 229-234.
[11] T. G. Dietterich and G. Bakiri, "Solving Multiclass Learning Problems via Error-Correcting Output Codes," Journal of Artificial Intelligence Research, vol. 2, pp. 263-286, 1995.
[12] K. Crammer and Y. Singer, "On the Learnability and Design of Output Codes for Multiclass Problems," Machine Learning, vol. 47, no. 2-3, pp. 201-233, 2002.
[13] P. Kraipeerapun, C. C. Fung, and W. Brown, "Assessment of Uncertainty in Mineral Prospectivity Prediction Using Interval Neutrosophic Set," in Proceedings of the International Conference on Computational Intelligence and Security, ser. Lecture Notes in Artificial Intelligence, no. 3802. Xi-an, China: Springer Verlag, 2005, pp. 1074-1079.
[14] P. Kraipeerapun, C. C. Fung, W. Brown, and K. W. Wong, "Mineral Prospectivity Prediction using Interval Neutrosophic Sets," in IASTED International Conference on Artificial Intelligence and Applications, Innsbruck, Austria, February 2006, pp. 235-239.
[15] H. Wang, F. Smarandache, Y.-Q. Zhang, and R. Sunderraman, Interval Neutrosophic Sets and Logic: Theory and Applications in Computing, ser. Neutrosophic Book Series, No.5. http://arxiv.org/abs/cs/0505014, May 2005.