Prediction of Maximum Dry Density and Specific Gravity of Fly Ash Using Support Vector Machine

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1 Prediction of Maximum Dry Density and Specific Gravity of Fly Ash Using Support Vector Machine Akshaya Kumar Sabat Associate Professor Department of Civil Engineering, Institute of Technical Education and Research Siksha O Anusandhan University Khandagiri Square, Bhubaneswar, OR, India akshayasabat@soauniversity.ac.in, akshayasabat@yahoo.co.in ABSTRACT Fly ash is the highly generated industrial solid wastes around the world particularly in India and China. Maximum dry density and specific gravity are two most important properties of fly ash for its use as a geotechnical material. This paper presents the development of predictive models for maximum dry density and specific gravity of fly ash using a soft computing technique, support vector machine. Based on different statistical criteria like R (coefficient of correlation) and E (coefficient of efficiency), it was observed that the developed models are efficient in comparison to existing Artificial Neural Network models. KEYWORDS: Fly ash, maximum dry density, specific gravity, predictive models, support vector machine. INTRODUCTION Production of large quantities of industrial solid wastes not only requires large space for their disposal but also they create a lot of geoenvironmental problems. Various researchers have found that these solid wastes can be utilized for improvement of geotechnical properties of soil (Pandian et al.2001,patil et al.2011,yilmaz and Civelelekoglu 2009,Sabat and Nanda 2011, Sabat 2012a, Sabat 2012b, Sabat 2012c,Zhang et al. 2013, Maneli et al.2013, Sabat and Bose 2013). One of the industrial solid wastes is fly ash which is produced by burning of coal in coal based power plants. Fly ash has been found to be a good geotechnical material because of its, high shear strength, low specific gravity, less compressibility, good drainage characteristics and pozzolanic nature. Maximum dry density (MDD) and specific gravity (G) are two most important properties of fly ash for its use as a geotechnical material. Though these two properties can be determined from simple laboratory tests but considering the homogeneous nature of fly ash, there is necessity to predict these properties by development of models using soft computing technique. In machine learning, support vector machines (SVM) are supervised learning models with associated learning algorithms that analyze data and recognize patterns, used for classification and regression analysis (Wiki). SVM has been utilized for prediction of stress-strain behaviour of sandy soil (Banimahd et al.2005), pull out capacity of ground anchor (Sahin and Jaksa 2006), unconfined compressive strength (UCS) and MDD of cement stabilized soil (Das et al. 2011),

2 Vol. 20 [2015], Bund swelling pressure of expansive soil (Das et al. 2010), field hydraulic conductivity of clay liner (Das et al. 2012), liquefaction of soil (Lee and Chern 2013) etc. Das and Sabat (2008) had developed ANN models to predict MDD and G of fly ash. For prediction of MDD the two best models were (i) Fe 2 O 3 (Fe), Loss on Ignition (LOI), G and ii) Fe, LOI,G and optimum moisture content (OMC). For prediction of G the two best models were i) Cao, Fe, LOI, specific surface(ss) ii)al 2 O 3 +SiO 2, CaO,Fe,LOI,SS However, the use of the soft computing technique SVM, for prediction of MDD and G of fly ash is limited in literature. The objective of the present investigation is to develop the SVM models to predict the MDD and G of fly ash and compare the efficiency of the models with the existing ANN models DEVELOPMENT OF SVM MODELS FOR PREDICTION OF MAXIMUM DRY DENSITY OF FLY ASH The data used by Das and Sabat (2008) for development of ANN models for prediction of MDD of fly ash are used for the development SVM models. The sources of the data points are published literature (Das and Yudhbir 2005, Nishikawa et al. 2002, Yudhbir and Honjo 1991, Martin et al. 1990, Toth et al. 1988, Leonard. and Bailey 1982, DiGioia and Nuzzo 1972). Table 1 shows the minimum, maximum, average and standard deviation of the data used for the development of model. Total data points considered for the development of the model is 40, out of which 25 are taken for training and 15 are taken for testing. Table 1: Parameters of the data considered for the prediction of MDD Fe (%) LOI (%) G OMC (%) Minimum Maximum Average Std. dev Different SVM models are developed taking different kernel functions, radial basis function, polynomial and spline kernel functions and the SVM models developed are named as SVM-R, SVM-P and SVM-S respectively. Two SVM models are developed using inputs as i) Fe, LOI, G (Model-1) and ii) Fe, LOI, G, OMC (Model-2). The software package MATLAB (2005) was used for the development of the SVM models. DEVELOPMENT OF SVM MODELS FOR PREDICTION OF SPECIFIC GRAVITY OF FLY ASH The data used by Das and Sabat (2008) for prediction of G of fly ash using ANN are used for the development of SVM models. Two SVM models are developed i) Cao, Fe, LOI, specific surface (SS) as inputs (Model-1) ii) AL 2 O 3 +SiO 2, CaO,Fe,LOI,SS as inputs (Model-2). Table 2 shows the minimum, maximum, average and standard deviation of the data considered for training and testing. The total data points are 113, out of which 80 are considered for training and 33 for testing. The

3 Vol. 20 [2015], Bund source of the data points are published literature (Das and Yudhbir 2005, Yudhbir and Honjo 1991 and Brinks and Halstead 1956) Table 2: Parameters of the data considered for the prediction of specific gravity SS SiO Training data G 2 Al 2 O 3 CaO Fe LOI (cm 2 /gm) (%) (%) (%) (%) (%) Minimum Maximum Average Std. Dev Testing Data Minimum Maximum Average Std. Dev ANALYSIS OF RESULTS AND DISCUSSION Prediction of MDD of Fly Ash Table 3 and 4 presents the results of SVM models developed for Model- 1 Model- 2 respectively. Coefficient of correlation (R) and coefficient of efficiency (E) have been taken as the parameters to judge the accuracy of the models. SVM-S is found to be more efficient compared to SVM-P and SVM-R based on R and E values. The comparison between observed and predicted maximum dry density values are presented in Figure 1 and 2 for Model- 1 and Model- 2, respectively. It can be mentioned here that, Model -2 uses more input parameters than Model- 1, however, the statistical s of the models are comparable. Model using less number of input parameters are considered as better model. Hence model1 can be considered as a better model than model-2. Table 3: General of SVM for prediction of MDD (kn/m 3 ) for Model- 1 using different kernels Models C ϵ Number of support vector Training Testing R E R E Radial basis function, width(σ) = 2.6 (SVM-R) Polynomial, degree = 2 (SVM- P) Spline (SVM-S)

4 Vol. 20 [2015], Bund Table 4: General of SVM for prediction of MDD (kn/m 3 ) for Model- 2 using different kernels Number Training Models C ϵ of support vector Radial basis function, width(σ) = 2.6 (SVM-R) Testing R E R E Polynomial, degree = 2 (SVM-P) Spline (SVM-S) Predicted Maximum dry density (kn/m 3 ) Training data (R = 0.97) Testing data (R = 0.94) Line of equality Observed Maximum dry density (kn/m 3 ) Figure 1: Comparison of predicted and observed maximum dry density using SVM for Model- 1

5 Vol. 20 [2015], Bund Predicted Maximum dry density (kn/m 3 ) Training data (R = 0.98) Testing data (R = 0.97) Line of equality Observed Maximum dry density (kn/m 3 ) Figure 2: Comparison of predicted and observed maximum dry density using SVM for Model -2 Sensitivity Analysis The sensitivity analysis has been carried out to extract cause and effect relationship between inputs and outputs of the SVM model (Model-1). The procedure has been taken from the work of Liong et al. (2000). The sensitivity analysis for maximum dry density has been shown in Figure 3.The most important input parameters for prediction of MDD are G, followed by Fe and LOI.

6 Vol. 20 [2015], Bund Sensitivity, S j (%) Fe LOI G Input Parameters Figure 3 Sensitivity analysis for maximum dry density using SVM Comparison of developed SVM models with ANN models for Prediction of MDD Table 5: Comparison of developed SVM models and ANN models (Sabat and Das, 2008) for Prediction of MDD Models Model Inputs Training Performance Testing Performance R E R E Fe, LOI, G (Model-1) SVM(S) Fe, LOI, G,OMC (Model-2) ANN Fe, LOI, G Fe, LOI, G,OMC A comparison has been shown in Table 5 between the SVM model, SVM(S) and published ANN model (Das and Sabat 2008) developed with these inputs. From table it is observed that SVM is slightly a better model than the published ANN model. Prediction of G of Fly Ash The results of SVM analysis for the prediction of G for Model- 1 and Model-2 are presented in Tables 6 and 7, respectively. For Model-1 and Model 2, based on R and E values SVM-P is found to be more efficient compared to SVM-R and SVM-S. The comparison between observed and predicted specific gravity values are presented in Figure 4 and 5 for Model- 1 and Model -2 respectively. It can be seen that, compared to Model -1, there is less scattering when Model- 2 is used. SVM models have excellent correlation particularly for Model -1. It can be mentioned here that, Model -2 uses more input parameters than Model- 1, however, the statistical s of

7 Vol. 20 [2015], Bund the models are comparable. As it is known that the model using less number of input parameters are better in parsimony consideration. Table 6: General of SVM for prediction of G for Model -1 using different kernels Models C ϵ Radial basis function, width(σ) = 0.7 (SVM-R) Polynomial, degree = 3 (SVM-P) Number of support vector Training Testing R E R E Spline (SVM-S) Table 7: General of SVM for prediction of G for Model -2 using different kernels Models C ϵ Radial basis function, width(σ) = 0.5 (SVM-R) Polynomial, degree = 2 (SVM-P) Number of support vector Training Testing R E R E Spline (SVM-S)

8 Vol. 20 [2015], Bund Training data (R = 0.99) Testing data (R = 0.96) Predicted Specific gravity Observed Specific gravity Figure 4: Comparison of predicted and observed Specific gravity using SVM-P for Model Training data (R = 1.00 ) Testing data (R = 0.95) Predicted Specific gravity Observed Specific gravity Figure 5: Comparison of predicted and observed Specific gravity using SVM-P for Model- 2

9 Vol. 20 [2015], Bund Sensitivity Analysis The sensitivity analysis for specific gravity is shown in Figure 6 the procedure has been taken from the work of Liong et al.(2000).from the sensitivity analysis (Model-1) it is found that the iron content (Fe) is the most important parameter followed by LOI and SS for the prediction of specific gravity of fly ash Sensitivity, S j (%) CaO Fe LOI SS Input parameters Figure 6: Sensitivity analysis for specific gravity using SVM Comparison of SVM and ANN models for Prediction of Specific Gravity Table 8: Comparison of developed SVM models and ANN models (Das and Sabat 2008) for Prediction of G of Fly ash Model Inputs Training Performance Testing Performance Models R E R E Cao, Fe, LOI, SS SVM(P) (Model-1) AL 2 O 3 +SiO 2, CaO,Fe,LOI,SS (Model-2) ANN Cao, Fe, LOI, SS AL 2 O 3 +SiO 2, CaO,Fe,LOI,SS A comparison between the best SVM model, SVM(P) with the published ANN Model(Das and Sabat,2008) developed with these inputs has been shown in Table 8.From the table it is observed that the SVM model is slightly better than the published best ANN model.

10 Vol. 20 [2015], Bund CONCLUSIONS The following general conclusions are drawn from the study (1) For the prediction of MDD, SVM-S is found to be more efficient compared to SVM-P and SVM- R. (2) For the prediction of specific gravity SVM-P is found to be more efficient than SVM-R and SVM-S. (3) From the sensitivity analysis as per SVM model the most important parameters for the prediction of MDD are G, followed by Fe and LOI and that of G is Fe followed by LOI and SS. (4) From the comparison of the efficiency of the SVM models with the published ANN models it is found that the SVM models are relatively better than the ANN models. REFERENCES 1. Banimahd, M., Yasrobi, S.S., and Woodward, P.K. (2005) Artificial neural network for stress strain behavior of sandy soils: Knowledge based verification, Computers and Geotechnics, 32(5), Brink, R.H. and Halstead, W.J. (1956) Studies relating to the testing of fly ash for use in concrete, Proc. Am. Soc. Testing Mats. 56, Das, S.K., and Sabat, A.K. (2008) Using Neural Networks for Prediction of Some Properties of Fly Ash, Electronic Journal of Geotechnical Engineering, 13 (D). 4. Das, S.K., Samui, P., Sabat, A.K., and Sitharam, T.G. (2010) Prediction of swelling pressure of soil using Artificial intelligence techniques, Environmental Earth Sciences, 61, Das, S.K., Samui, P., and Sabat, A.K. (2011) Application of Artificial Intelligence to Maximum Dry Density and Unconfined Compressive Strength of Cement Stabilized Soil, Geotechnical and Geological Engineering, 29, Das, S.K., Samui, P., and Sabat, A.K.,(2012) Prediction of Field Hydraulic Conductivity of Clay Liners Using an Artificial Neural Network and Support Vector Machine, International Journal of Geomechanics, 12, 5, Das, S.K., and Yudhbir (2005) Geotechnical Characterization of some Indian Fly Ashes, Journal of Materials in Civil Engineering, 17 (95), DiGioia, A.M., and Nuzzo, W.L. (1972) Fly Ash as Structural Fill, Journal of Power Division, Proc. ASCE, 98 (l), Lee, C.Y. and Chern, S.G. (2013) Application of A Support Vector Machine for Liquefaction Assessment, Journal of Marine Science and Technology, 21 (3),

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12 Vol. 20 [2015], Bund Yilmaz, I. and Civelekoglu, B. (2009) Gypsum: An Additive for Stabilization of Swelling Clay soils, Applied Clay Science, 44, Yudhbir, Honjo, Y. (1991) Application of Geotechnical Engineering to Environmental Control, Proceedings of 9 th Asian Regional Conference on Soil Mechanics and Foundation Engineering, Bangkok, 2, Zhang, D., Sun, S., Xu, F., and Xue, N. (2013) Influence of Biomass Ash and Marble Dust on Swelling and Strength Characteristics of Expansive soil, Journal of Food Agriculture and Environment, 11(3&4), ejge