Evaluation of the impact of fly ash on infiltration characteristics using different soft computing techniques
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Abstract
The aim of this paper was to investigate the impact of the fly ash concentration on the infiltration process and to assess the potential of five soft computing techniques such as artificial neural network, Gaussian process, support vector machine (SVM), random forest, and M5P model tree and compare with two popular conventional models, SCS and Kostiakov mode, to estimate the cumulative infiltration of flyashmixed soils. Laboratory experiment was carried out with the different combinations of the sand, clay, and fly ash by using mini disk infiltrometer. The combination consists of the different concentrations of sand (25–45%), clay (25–45%), and fly ash (10–50%). The total observation consists of the 138 field measurement. The cumulative infiltration increase with an increment in the concentration of the fly ash, but it decreases when fly ash concentration increases 40–50% in the soil. On the other hand, the cumulative infiltration increases with the decrease in the concentration of clay in samples. The predictive modeling technique, SVM with RBF kernel, is the best technique to predict the cumulative infiltration with minimum error. Results suggest that SVM with RBF kernel is the bestfit modeling technique among other soft computing techniques as well as conventional models to find the impact of fly ash on infiltration characteristics for the given combination of the sand, clay and fly ash.
Keywords
Fly ash Artificial neural network Gaussian process Support vector machine Random forest M5P model treeIntroduction
Infiltration is the vital property of the water. It is the process in which surface water such as precipitation, flood, and snowfall percolate into the soil. Infiltration is the most affecting process during irrigation actions which is to be considered for scheduling of irrigation, irrigation system design and optimization, and management of irrigation system (AlAzawi 1985; Bhave and Sreeja 2013). It separates the water into two parts: groundwater flow and surface flow (Singh et al. 2018a). There are many parameters such as density, texture, and type of soil and moisture content that affect the infiltration process (Angelaki et al. 2013). The estimation of the infiltration characteristics is also useful to evaluate the performance of the hydrogeological investigations (Pedretti et al. 2012).
Various researchers analyzed the infiltration data and gave some infiltration model for solving the problem related to the infiltration. These models are Green and Ampt, Harton, Philip, Kostiakov, Holton, modified Kostiakov and novel model. Mishra et al. (2003) divided these models into three categories: physical, semiempirical, and empirical models. Sihag et al. (2017a) used four infiltration rate models and found that novel model was the bestsuited model for the soil of NIT Kurukshetra campus. Vand et al. (2018) also found the novel model was the bestfit model in two provinces (Lorestan and Ilam) in Iran. Sihag and Singh (2018) also investigated about these models using doublering infiltrometer and found that Mezencev and modified Kostiakov model can be used to evaluate the infiltration rate of the soil for the given study area. Chowdary et al. (2006) have studied the infiltration process under different experimental conditions. Singh et al. (2018a) compares the four infiltration model and found that modified Philip’s model is the bestfit model among other selected models to calculate the infiltration rate of the soil.
Soft computing techniques such as random forest, adaptive neurofuzzy inference system, gene expression programming, support vector machine, generalized neural network, Gaussian process regression, artificial neural network fuzzy logic, and M5P model tree have been widely used in civil and water resources engineering problems. Many researchers used these soft computing techniques in civil and water resources engineeringrelated problem successfully (Haghiabi et al. 2018; Parsaie et al. 2016a, Parsaie et al. 2017a, b, 2018a, b; Tiwari et al. 2018; Parsaie and Haghiabi 2014b, 2015a, 2017a, b; Haghiabi et al. 2017a; Tiwari et al. 2017; Nain et al. 2018; Azamathulla et al. 2016) and found that these techniques are less time consuming and gave good result. Also, these techniques have the very less optimum userdefined parameters. Sihag et al. (2018b, 2017b) used the different proportion of sandy soil and analyzed the infiltration characteristics in the laboratory. Thus, the aim of this study is to analyze the impact of fly ash in the cumulative infiltration of the soil. The major objective is to compare the performance of various soft computing techniques to predict the cumulative infiltration of the fly ash mixed in the soil.
Soft computing techniques
Artificial neural network
Artificial neural network (ANN) is the most common computing technique which is based on the nerve cells of the human brains. ANN is successfully used in hydrological and water resources problems (Sihag 2018; Sihag et al. 2018d; Haghiabi et al. 2017b; Sihag et al. 2017c; Parsaie et al. 2016b; Parsaie and Haghiabi 2014a, 2015b). Neurons are arranged in the form of layers. Every layer carries out the different kinds of transformations on their inputs. Multiple transformations occurred during signals pass through the first input layer to the last output layer. ANNs have three interconnected layers. The first layer consists of input neurons which receive the input data. Received input data from the first layer are forwarded to the second layer which consists of different hidden layers. After processing of data in hidden layers, they are transferred to the third layer which consists of output neurons. Training an artificial neural network involves choosing from allowed models for which there are several associated algorithms. For further explanation about ANN, readers are referred to Haykin (2004) and Tiwari and Sihag (2018).
Gaussian process
Gaussian process (GP) is an artificial machine learning technique to build computer systems that can adapt and learn from their experience. Rasmussen and Williams (2006) assumed for the processing of GP regression model that the adjoining observations give knowledge to each other. This technique has emerged in recent years and currently successfully applied in various research fields of medicine, chemistry, construction, etc. Gaussian process is based on probability theorem which could make predictions on unknown input data as well as provide prediction exactness which highly increases the statistical significance in prediction. Also Gaussian processes are based on multivariate Gaussian distributions which extend it to infinite dimensionality. Formally, Gaussian process setups the data by using the domain which has any finite subset range following a multivariate Gaussian distribution. In this paper, radial basis kernel \(\left( {K\left( {x,x^{\prime}} \right)} \right) = e^{{  \gamma \left {x  x^{\prime}} \right^{2} }} )\) and Pearson VII function kernel \(\left( {1/\left[ {1 + \left( {2\sqrt {x_{i}  x_{j}^{2} } \sqrt {2^{{\left( {1/\omega } \right)}}  1} /\sigma } \right)} \right]^{\omega } } \right)\) is used, where γ, σ, and ω are kernelspecific parameters. For further explanation about GP, readers are referred to Kuss (2006) and Singh et al. (2018b).
Support vector machines
The support vector machines (SVMs) are based on statistical learning concept and structural risk minimization hypothesis. The basic concept of SVMs is to arrange the data sets from the input zone to infinitedimensional feature zone by constructing set of hyper planes so that classification, regression, or other problems become simpler in the feature zone. The hyperplanes are defined as the set of points whose dot product with a vector is constant in that space. Support vector regression has been proposed by Vapnik et al. (1995) and it is a learning system using a high dimensional feature space. The model shaped by SVR depends only on a training dataset because any training data close to the model prediction are ignored by the function for generating the model. Various kernel functions are used with SVMbased regression approaches. In this study radial basis kernel \(\left( {K\left( {x,x^{\prime}} \right)} \right) = e^{{  \gamma \left {x  x^{\prime}} \right^{2} }} )\) and Pearson VII function kernel \(\left( {1/\left[ {1 + \left( {2\sqrt {x_{i}  x_{j}^{2} } \sqrt {2^{{\left( {1/\omega } \right)}}  1} /\sigma } \right)} \right]^{\omega } } \right)\) are used, where γ, σ and ω are kernelspecific parameter. For further explanation about SVM, readers are referred to Smola and Schölkopf (2004) and Sihag et al. (2018a).
Random forest
Random forests (Breiman 2001) are developed by a collection of treebased models (Breiman et al. 1984) which can be used for categorization tasks in which the base models are classification trees or regression tasks which depend on base models of regression trees. The forest consists of various trees, which have any value between one to several thousand. To organize a new data set, data set of each condition is passed down every tree. All trees give a classification for that condition. Modeling of a single tree is highly sensitive and complicated. Small changes in the training data turn out a high variation in single classification trees and often lead to rather low classification accuracies (Breiman 1996). Random forests have been justified to be magnificent predictive models in regression tasks and several classifications. They are reasonably fast to obtain results and can be easily assimilated if more speed is required. For further explanation about the random forest, readers are referred to Singh et al. (2017) and Sihag et al. (2018c).
M5P model
M5P is the combined form of the conventional decision tree and the linear regression functions. The model tree algorithm applied in this paper is based on M5P algorithm. The aim of M5P algorithm is to establish a model that evaluates the relation between a target value of the training cases and the values of their input attributes. The performance of the model is checked by the accuracy parameters through which it predicts the values of the curtained cases.
M5P model combines the multiple linear regression and decision tree for data analysis. Decision tree makes relation between the observed inputs and the outputs by logic learning which is appropriate for categorized numerical input and outputs. Decision trees categorize the input dataset and output dataset by the maximized entropy to understand the regression and logicaltype rules between inputs and outputs which unambiguously portray the patterns and relationships between data by the regression equations, while other models like SVR and ANN hide them. So, model trees are not only simple but also efficient and accurate technique for modeling and prediction of large data sets (Quinlan 1992).
Conventional models
Two conventional model SCS model and Kostiakov model were also used in this investigation. The empirical constants mentioned in the equation were found by implementing the leastsquare technique.
SCS model
Kostiakov model
Measurement of cumulative infiltration
Details of the material used for experiments
Properties  Sand  Fly ash  Clay 

Specific gravity  2.48  2.07  1.59 
\(D_{50}\)  0.438  0.180  
\(C_{u}\)  3.1290  2.7333  
Colour  White  Gray  Brownish yellow 
Detail of the soil samples with their moisture content
Sand (%)  Clay (%)  Fly ash (%)  Moisture content (%) 

45  45  10  2, 5, 10, 15, 20 
40  40  20  2, 5, 10, 15, 20 
35  35  30  2, 5, 10, 15, 20 
30  30  40  2, 5, 10, 15, 20 
25  25  50  2, 5, 10, 15, 20 
Dataset
Statistical characteristics of experimental data
Variable  Training data set  Testing data set  

Mini.  Max.  Mean  SD  Mini.  Max.  Mean  SD  
Time (s)  87.62  9916.11  2163.18  2128.46  92.00  8568.19  2282.03  2036.11 
Clay %  25.00  45.00  34.14  7.24  25.00  45.00  33.46  7.26 
Sand %  25.00  45.00  34.14  7.24  25.00  45.00  33.46  7.26 
FA %  10.00  50.00  31.70  14.48  10.00  50.00  33.07  14.53 
Density  1.37  1.91  1.63  0.14  1.37  1.90  1.62  0.14 
Mc  2.00  20.00  9.98  6.17  2.00  20.00  10.53  6.83 
Infilt.(cm)  0.62  6.28  2.21  1.28  0.62  5.65  2.35  1.23 
Results and discussion
Userdefined parameters of training and testing dataset
Approach  Userdefined parameters 

GP with RBF kernel  Noise = 0.01, gamma = 1 
GP with PUK kernel  Noise = 0.01, omega = 2, sigma = 1 
SVM with RBF kernel  c = 50, gamma = 1 
SVM with PUK kernel  c = 50, omega = 2, sigma = 1 
M5P  m = 10 
Random forest  k = 1, I = 100 
ANN  Hidden layer = 7, learning rate = 0.01, momentum = 0.6 
Performance evaluation parameters of training and testing dataset
APPROACH  Training  Testing  

R  RMSE  NS  R  RMSE  NS  
SVM RBF  0.9946  0.1329  0.9892  0.9817  0.2387  0.9613 
GP RBF  0.9982  0.0761  0.9964  0.9800  0.2535  0.9564 
SVM PUK  0.9991  0.052  0.9983  0.9746  0.2935  0.9415 
GP PUK  0.9996  0.0349  0.9992  0.9735  0.3020  0.9381 
RF  0.9949  0.2049  0.9744  0.9519  0.4219  0.8792 
ANN  0.9793  0.2596  0.9590  0.9509  0.4007  0.8910 
M5P  0.8936  0.5919  0.7868  0.7869  0.7611  0.6070 
Performance evaluation parameters of training and testing dataset of conventional models
Conventional model  Training  Testing  

R  RMSE  NS  R  RMSE  NS  
SCS model  0.4667  1.1345  0.217  0.2247  1.2092  0.008 
Kostiakov model  0.4735  1.1295  0.2238  0.2457  1.2005  0.0223 
Conclusions

It is established from the test results that increment in the cumulative infiltration was observed with increment in the percentage of the fly ash. But there is a contradiction that it increases up to 40% of the fly ash and decreases when the percentage of the fly ash increases from 40 to 50%.

The cumulative infiltration also increases with the decrement in the percentage of the clay.

The prediction of the cumulative infiltration is tested by various soft computing techniques (SVM, GP, M5P model tree, random forest, and ANN), and SVM with RBF kernel was found best to predicting the cumulative infiltration followed by GP, random forest, ANN, and M5p Model Tree.

Obtained results suggest that the performance of conventional models, SCS model and Kostiakov model, is not satisfactory as compared to the soft computing techniques.
Notes
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