Prediction of thermal conductivity and damage in Indian Jalore granite for design of underground research laboratory

The measurement of thermal conductivity of granitic rocks is a time-consuming process and requires highly sophisticated instruments for experimental analysis. The difficulties in proposing reliable and precise empirical correlations and theoretical models forced the researchers to use alternative and more accurate models based on artificial intelligence (AI) techniques. The present study has been carried out to predict two parameters, thermal conductivity, and damage threshold for Jalore granite using AI techniques. In this study, artificial neural networks (ANNs), linear regression, support vector regressors (SVRs),, and decision tree regressors (DTRs) have been applied to obtain reliable and more accurate models. The extensive analysis revealed that the optimum performance is obtained by the ANN model with 8 nodes in the input layer with 2 hidden layers. Hidden layers having 15 and 7 nodes in the first and second layers, respectively. Softmax function has been applied as activation for each layer of the developed model. The mean absolute error (MAE) and mean squared error (MSE) values for the model while predicting the thermal coefficient were 0.0033671 and 184E−05. These values were 0.0016141 and 3.89E−06 for the damage threshold. DTRs with the number of estimators, n = 100, 1000, and 10,000 perform relatively well for predicting the values for both parameters. Linear regression and SVRs models (linear and robust kernel) show some deviations from the observed values at points where the trend shows a sudden change or kink. In the case of DTRs, the model with the number of estimators, n = 1000, and 100 performs most efficiently for predicting thermal conductivity (MSE = 6.81E−05) and the damage threshold (MSE = 2.84E−05), respectively.

[1]  Harris Drucker,et al.  Improving Regressors using Boosting Techniques , 1997, ICML.

[2]  Biplab Bhattacharyya,et al.  Optimal allocation of phasor measurement unit for full observability of the connected power network , 2016 .

[3]  A. Verma,et al.  Study of temperature effect on thermal conductivity of Jhiri shale from Upper Vindhyan, India , 2016, Bulletin of Engineering Geology and the Environment.

[4]  T. N. Singh,et al.  Estimation of elastic constant of rocks using an ANFIS approach , 2012, Appl. Soft Comput..

[5]  X. Mao,et al.  The Mechanical Properties of Mudstone at High Temperatures: an Experimental Study , 2014, Rock Mechanics and Rock Engineering.

[6]  K. R. Sudha,et al.  Software Effort Estimation using Radial Basis and Generalized Regression Neural Networks , 2010, ArXiv.

[7]  T. Singh,et al.  Experimental investigations on the thermal properties of Jalore granitic rocks for nuclear waste repository , 2019, Thermochimica Acta.

[8]  T. Singh,et al.  Evolution of Thermal Damage Threshold of Jalore Granite , 2018, Rock Mechanics and Rock Engineering.

[9]  T. N. Singh,et al.  Prediction of thermal conductivity of rock through physico-mechanical properties , 2007 .

[10]  Ashutosh Kumar Singh,et al.  Determination of thermal damage in rock specimen using intelligent techniques , 2018 .

[11]  P. Ranjith,et al.  Temperature Effect on the Thermal Conductivity of Black Coal , 2018 .

[12]  Weiqiang Zhang,et al.  Effect of High Temperatures on the Thermal Properties of Granite , 2019, Rock Mechanics and Rock Engineering.

[13]  Weiqiang Zhang,et al.  The effect of high temperature on tensile strength of sandstone , 2017 .

[14]  D. Mowla,et al.  Modeling and analysis of effective thermal conductivity of sandstone at high pressure and temperature using optimal artificial neural networks , 2014 .

[15]  T. Singh,et al.  Temperature-dependent thermophysical properties of Ganurgarh shales from Bhander group, India , 2016, Environmental Earth Sciences.

[16]  Mohak Shah,et al.  Evaluating Learning Algorithms: A Classification Perspective , 2011 .

[17]  Mohak Shah,et al.  Evaluating Learning Algorithms: Contents , 2011 .

[18]  T. Singh,et al.  Evolution of absorption energy per unit thickness of damaged sandstone , 2018, Journal of Thermal Analysis and Calorimetry.

[19]  Jenq-Neng Hwang,et al.  Handbook of Neural Network Signal Processing , 2000, IEEE Transactions on Neural Networks.

[20]  Yoram Singer,et al.  Adaptive Subgradient Methods for Online Learning and Stochastic Optimization , 2011, J. Mach. Learn. Res..

[21]  Biplab Bhattacharyya,et al.  Optimal placement of PMU for complete observability of the interconnected power network considering zero-injection bus: A numerical approach , 2020 .

[22]  Aminaton Marto,et al.  Indirect measure of thermal conductivity of rocks through adaptive neuro-fuzzy inference system and multivariate regression analysis , 2015 .

[23]  Biplab Bhattacharyya,et al.  Weak Bus-Oriented Installation of Phasor Measurement Unit for Power Network Observability , 2017 .

[24]  R. Azzam,et al.  Experimental study on the influence of temperature on the mechanical properties of granite under uni-axial compression and fatigue loading , 2012 .

[25]  Biplab Bhattacharyya,et al.  Strategic placements of PMUs for power network observability considering redundancy measurement , 2019 .

[26]  I. Abdulagatov,et al.  Effect of pressure and temperature on the thermal conductivity of rocks , 2006 .

[27]  Jimmy Ba,et al.  Adam: A Method for Stochastic Optimization , 2014, ICLR.

[28]  Shi Liu,et al.  Mechanical properties of Qinling biotite granite after high temperature treatment , 2014 .

[29]  Mahmood Amani,et al.  Effective Thermal Conductivity Modeling of Sandstones: SVM Framework Analysis , 2016 .

[30]  Weiqiang Zhang,et al.  Pore characteristics and mechanical properties of sandstone under the influence of temperature , 2017 .

[31]  Biplab Bhattacharyya,et al.  An Approach for Optimal Placement of Phasor Measurement Unit for Power Network Observability Considering Various Contingencies , 2018 .

[32]  K. Elsayed,et al.  Multi-Objective Surrogate Based Optimization of Gas Cyclones Using Support Vector Machines and CFD Simulations , 2016 .