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ISSN: 2321-9653
Estd : 2013
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Ijraset Journal For Research in Applied Science and Engineering Technology

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Determination of Suitable Hyperparameters of Artificial Neural Network for the Best Prediction of Geotechnical Properties of Soil

Authors: Jitendra Khatti, Dr. Kamaldeep Singh Grover

DOI Link: https://doi.org/10.22214/ijraset.2022.43662

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Abstract

The artificial neural network is robust in predicting soil properties. The present study aims to determine the suitable hyperparameters such as number of hidden layers, neurons, and backpropagation algorithms for the best prediction of geotechnical properties of soil. The supervised learning category-based multilayer perceptron artificial neural network approach is used, and models are developed in MATLAB R2020a. The ANN models are configured with neurons (5, 10 & 15), hidden layers (one to five), and a backpropagation algorithm (LM, BFG, SCG, GDA, GD & GDA). Fifteen ANN models are developed for each algorithm. The study shows that the LM, BFG, and SCG algorithm-based ANN models require strongly (0.61-0.8) to very strongly (0.81-1) correlated datasets. On the other hand, the GDM, GD, and GDA algorithm-based ANN models require only strongly correlated datasets to achieve a performance of more than 0.9. In most cases, it is also found that the GDM, GD, and GDA algorithm-based ANN models achieve high performance with three hidden layers interconnected with ten neurons. Still, LM algorithm-based ANN model achieves high performance with a single hidden layer interconnected with 5/15 neurons. The present work draws a relationship between the correlation coefficient and the number of hidden layers & neurons. It also helps to study the effect of hidden layers and neurons on the performance of ANN models. Formulas are derived from the performance of ANN models to calculate the required number of hidden layers and neurons for a particular backpropagation algorithm to achieve a testing performance of more than 0.9.

Introduction

I. INTRODUCTION

Atterberg's limits and compaction parameters of soil play a vital role in any Civil Engineering Project. The liquid limit, plasticity index, and plastic limit are the Atterberg's limits of soil [4]. The liquid limit of soil is experimentally determined as per IS 2720 (P-5): 1985 [15] using Cone penetration and Casagrande tests apparatus. On the other hand, the compaction parameters are optimum moisture content and maximum dry density and are determined as per IS 2720 (P-7): 1980 [16] and IS 2720 (P-8): 1983 [17]. The compaction parameters are determined using a standard proctor and modified proctor test apparatus. The standard and modified proctor tests are light and heavy compaction tests. Analytical and laboratory methods can determine Atterberg's soil limits and compaction parameters of soil [28]. Regression analysis is the most popular statistical method used for prediction. The regression analysis predicts the compaction parameters for specific soils [10, 21, 23, 12, 8]. The published regression models predicted compaction parameters with a coefficient of determination ranging from 0.64 to 0.98. The prediction level of regression analysis is high for small datasets. The genetic programming-based multi expression programming approach predicts the OMC and MDD of soil with a coefficient of 0.923 and 0.858, respectively [27]. Optimum moisture content increases with the liquid limit of soil and is strongly related to each other. The plastic limit is directly related to OMC and MDD but not LL. Still, the best prediction of OMC and MDD can be achieved by both LL and PL [14, 26]. The regression analysis with SVM computes the OMC and MDD with a correlation coefficient of 0.92 and 0.89, respectively [11]. The maximum dry density decreases, and optimum moisture content increases with the plasticity index. Using the plasticity index, the prediction of OMC for a modified proctor is more than the standard proctor [20]. The GMDH-type neural network is a reliable AI approach for predicting OMC and MDD of soil [2]. The grain-size parameters of coarse soil play an important role in predicting the OMC and MDD of soil. The coefficient of uniformity and D30 can predict the MDD of soil with a prediction accuracy of ±2% [24]. Similarly, the coefficient of uniformity and D50 can predict the OMC of soil with a prediction accuracy of ±2% [10]. The empirical relationship helps to predict the compaction parameters of the modified proctor test using the compaction parameters of the standard proctor test.

The artificial neural network has the potential to predict the OMC and MDD of soil [25]. The index properties, namely LL, PL, PI, FC, S, G, and SG, predict the OMC and MDD with high accuracy [19]. Multivariate adaptive regression splines predict compaction parameters with better performance than empirical equations, ANN and LSSVM. The sensitivity analysis shows that sand content and coefficient of uniformity highly affect compaction parameters' prediction [23]. The compaction parameters are highly influenced by Atterberg limits, clay content, silt content and electrical conductivity [22]. Soil parameters, namely LL, PL PI, SG, c, G, S, and FC, predict OMC and MDD with the correlation coefficient of 0.932 and 0.905, respectively [3].

The number of hidden neurons is based on the number of output neurons, input neurons, and training samples. Researchers suggested the following equations:

Where H, O, & I are the number of hidden neurons, output neurons & input neurons, and T is the training sample. The sand content affects the liquid limit of soil. Similarly, the plasticity index is affected by OMC, MDD, sand, and gravel content. Gaussian and Quadratic kernel-based support vector machine models predict soil's liquid limit and plasticity index with the performance of 0.9767 and 0.9828, respectively. [18]

II. DATA COLLECTION AND ANALYSIS

Data analysis is a process to study the datasets with the help of statistical tools or methods. The data analysis consists of details of data sources, descriptive statistics, frequency distribution, and correlation coefficient for pair of datasets, as discussed below.

A. Data Source

The soil datasets consist of sand content, fine content, liquid limit, plasticity index, optimum moisture content, and maximum dry density. A total of 356 datasets are collected from the published research work, as given in Table 1.

The outliers & missing datasets are removed from collected datasets by pre-processing. After pre-processing, two hundred forty-three soil datasets were collected and divided into 190 training and 53 testing datasets. Furthermore, 190 training datasets are subdivided at 70% and 30% for the training and validation of models.

B. Descriptive Statistics

A dataset consists of many columns and rows; therefore, the descriptive statistics are mapped to study the dataset. The minimum, maximum, mean, mode, median, standard deviation, confidence level at 95%, etc., are parameters of descriptive statistics. In the present research work, the minimum, maximum, mean (average), standard deviation (St. Dev), and confidence interval (CL) at 95% is determined for each feature of the dataset. The descriptive statistics of 190 datasets are shown in Table 2.

C. Pearson’s Product-Moment Correlation Coefficient

The correlation coefficient is the way to determine the strength of the linear relationship between independent and dependent variables. The Linear or curvilinear correlation, scatter diagram method, Pearson's product-moment correlation coefficient, and spearman's rank correlation coefficient are the methods for determining correlation coefficient or relationship. The relationship of the pair of datasets according to the range of correlation coefficients is given in Table 3 [13].

Fig. 1 depicts the Pearson's correlation coefficient for 190 training datasets. The consistency limits of soil are affected by the shape and size of particles. Therefore, the sand and fine content are input parameters to predict the liquid limit, plastic limit, and plasticity index. Thus, the compaction parameters of soil are affected by sand, fine content, and consistency limits. Therefore, the sand, fine content, LL, PL, and PI are used as input parameters to predict the OMC and MDD of soil. From Figure 2, the following points are observed; (i) the liquid limit, plastic limit, and plasticity index have a strong relationship with sand and fine content, (ii) the liquid limit and plasticity index have a very strong relationship with optimum moisture content, (iii) the sand content, liquid limit, and plasticity index has a very strong relationship with maximum dry density, (iv) the sand & fine content and plastic limit has a strong relationship with optimum moisture content, (v) the sand content and plastic limit has a strong relationship with maximum dry density, (vi) the sand & fine content, LL & PL, LL & PI, and PL & PI have multicollinearity.

D. Frequency Distribution

Frequency distribution (FD) is a graphical presentation of the number of observations for a specific interval. The histogram is a bar graph-like representation of the frequency of datasets. The frequency distribution of features of consistency limit with OMC & MDD is shown in Fig. 2.

III. METHODOLOGY

The present research work adopted the artificial neural network approach to predict soil's consistency limits and compaction parameters. An artificial neural network is an approach to deep learning, and deep learning is a subset of machine learning. The artificial neural network is a network of input, hidden & output layers and interconnected by neurons. The hidden layer and output layer has linear or nonlinear activation function to improve the performance of the ANN models. Each artificial neural network has a feedforward and backpropagation process. The information travels from the input to the output layer through hidden layer(s) in the feedforward process. Thus, the information travels from output to input layers in the backpropagation process. The backpropagation process is performed using different algorithms such as Levenberg Marquardt, BFGs Quasi-Newton, Scaled Conjugate Gradient, Gradient Descent with Momentum, Gradient Descent, and Gradient Descent with Adaptive Learning. The mathematical expression of the backpropagation algorithm is given below.

In the present research work, the multilayer perceptron artificial neural network has been developed to predict soil's LL, PI, OMC, and MDD. The developed artificial neural network is configured with different parameters, as given in Table 4.

In the present research, fifteen ANN models are developed for each backpropagation algorithm to predict soil's LL, PI, OMC, and MDD. Ninety ANN models are used to predict each LL, PI, OMC, and MDD of soil. The details of the developed models are given in Table 5. Five, ten and fifteen neurons are employed for each one, two, three, four, and five hidden layers ANN model in every backpropagation algorithm ANN model. Therefore, fifteen ANN models are developed for each algorithm.

IV. RESULTS AND DISCUSSIONS

In this section, the performance of developed artificial neural network models has been compared and discussed.

A. Prediction of Liquid Limit

For the prediction of liquid limit, the LM, BFG, SCG, GDA, GD, and GDM algorithm-based artificial neural network models have evolved with different numbers of hidden layers and neurons. The performance of the proposed models has been discussed below.

  1. Using Levenberg – Marquardt (LM) Algorithm Based Neural Network Models

Fifteen LM algorithm-based ANN models have been developed for predicting the liquid limit of soil, and the performance of models is given in Table 6.

Table 6 shows that Model 3 predicts the liquid limit of soil with a performance of 0.9165. It has also been observed that the model's performance has been increased with neurons in the case of single hidden layer ANN models. The performance of two and four hidden layer-based ANN models has been decreased with neurons. On the other hand, the performance of three and five hidden layer-based ANN models has been increased with neurons. Models 8 and 9 performed well during training and validation, respectively, but Model 3 outperformed the other models while testing the model. Therefore, Model 3 has been identified as a better performance model for predicting soil LL.

2. Using BFGs Quasi – Newton (BFG) Algorithm Based Neural Network Models

The artificial neural networks have been developed to predict soil LL using BFG's Quasi-Newton algorithm. The performance of BFG algorithm-based models is given in Table 7.

Table 7 shows the training, validation, and testing performance of BFG algorithm-based ANN models while predicting soil LL. The maximum performance of a single hidden layer-based ANN model has been achieved by providing ten neurons. Similarly, 0.8855 performance has been achieved by two hidden layer-based ANN models interconnected with 15 neurons. It has also been observed that the performance of BFG algorithm-based ANN models has been decreased by providing two hidden layers. Furthermore, the performance has been increased to 0.9308 by providing three hidden layers interconnected with five neurons. The performance of the BFG algorithm-based ANN model has been decreased for four hidden layers interconnected with ten neurons. The maximum performance has been obtained by the ANN model configured with five hidden layers and neurons, i.e., 0.9457. The performance results show that the two and four hidden layers-based BFG algorithm ANN models are less efficient in predicting soil LL.

3. Using Scaled Conjugate Gradient (SCG) Algorithm Based Neural Network Models

The artificial neural networks have been developed to predict the LL of soil using the Scaled Conjugate Gradient algorithm. The performance of SCG algorithm-based models is given in Table 8.

From Table 8, it has been observed that the single, two, three, four, and five hidden layers SCG algorithm-based ANN models have predicted liquid limits with the performance of 0.9139, 0.9081, 0.9289, 0.9274, and 0.9540, respectively. Furthermore, the five hidden layers interconnected with 15 neuron-based ANN models outperformed the other SCG algorithm-based ANN models in predicting the liquid limit of soil with a performance of 0.9540.

4. Using Gradient Descent with Momentum (GDM) Algorithm Based Neural Network Models

The artificial neural networks have been developed to predict soil LL using Gradient Descent with Momentum algorithm. The performance of GDM algorithm-based models is given in Table 9.

Table 9. Performance of GDM Algorithm-based ANN models for liquid limit

Model ID

HL/N

Training

Validation

Testing

RMSE

R

MAE

RMSE

R

MAE

RMSE

R

MAE

Model 46

1/5

0.0800

0.9586

0.0209

0.0767

0.9576

0.0185

5.9647

0.8322

4.9968

Model 47

1/10

0.1451

0.8575

0.0483

0.1815

0.8796

0.0753

12.9322

0.9122

8.4343

Model 48

1/15

0.1153

0.9103

0.0463

0.1344

0.9041

0.0558

5.6091

0.7938

4.2729

Model 49

2/5

0.1295

0.8816

0.0574

0.1373

0.8749

0.0527

5.3103

0.8867

4.3979

Model 50

2/10

0.2844

0.3751

0.6033

0.2681

0.2900

0.6413

7.8988

0.5598

5.4421

Model 51

2/15

0.0841

0.9541

0.0195

0.0931

0.9357

0.0197

6.8683

0.8607

5.1926

Model 52

3/5

0.1236

0.8817

0.0340

0.1537

0.8535

0.0485

6.6096

0.7355

5.1476

Model 53

3/10

0.1015

0.9297

0.0203

0.1110

0.9146

0.0298

4.7812

0.9618

3.0514

Model 54

3/15

0.3214

0.5528

0.1713

0.3283

0.5355

0.1483

10.7639

0.5848

7.4079

Model 55

4/5

0.1005

0.9297

0.0566

0.0999

0.9380

0.0602

6.0067

0.7397

4.5894

Model 56

4/10

0.1124

0.9080

0.0281

0.1291

0.9040

0.0359

3.7282

0.9144

2.6420

Model 57

4/15

0.0691

0.9671

0.0094

0.0764

0.9621

0.0093

2.9164

0.9325

2.0099

Model 58

5/5

0.1368

0.8732

0.0437

0.1199

0.8937

0.0335

3.1886

0.9426

2.1772

Model 59

5/10

0.0906

0.9441

0.0115

0.0922

0.9418

0.0107

6.9505

0.7866

4.9439

Model 60

5/15

0.1315

0.8746

0.0310

0.1349

0.8779

0.0333

3.9079

0.9513

2.7793

From Table 9, it has been observed that the one, two, three, four, and five hidden layers-based ANN models have predicted LL of soil with the performance of 0.9122, 0.8867, 0.9618, 0.9325, and 0.9513, respectively. Furthermore, the three hidden layers interconnected with ten neuron-based ANN models outperformed the other GDM algorithm-based ANN models in predicting the liquid limit of soil with a performance of 0.9618.

5. Using Gradient Descent (GD) Algorithm Based Neural Network Models

The artificial neural networks have been developed to predict the LL of soil using the Gradient Descent algorithm. The performance of GD algorithm-based models is given in Table 10.

Table 10. Performance of GD Algorithm-based ANN models for liquid limit

Model ID

HL/N

Training

Validation

Testing

RMSE

R

MAE

RMSE

R

MAE

RMSE

R

MAE

Model 61

1/5

0.2067

0.7202

0.0604

0.2225

0.7351

0.0670

5.4149

0.7281

4.1979

Model 62

1/10

0.1273

0.8951

0.0323

0.1702

0.8292

0.0503

4.9193

0.9094

3.5267

Model 63

1/15

0.1092

0.9097

0.0540

0.1087

0.9401

0.0492

4.4827

0.8242

3.6448

Model 64

2/5

0.1017

0.9317

0.0213

0.1102

0.9045

0.0235

8.1135

0.7702

5.3699

Model 65

2/10

0.1327

0.8805

0.0303

0.1228

0.8996

0.0306

4.6994

0.8721

3.0587

Model 66

2/15

0.1244

0.8863

0.0468

0.1498

0.8539

0.0617

4.7975

0.8578

3.6794

Model 67

3/5

0.2447

0.4376

0.0679

0.2472

0.4964

0.0712

5.8200

0.7148

3.6111

Model 68

3/10

0.0782

0.9586

0.0086

0.0797

0.9575

0.0081

5.1040

0.9114

3.9607

Model 69

3/15

0.0873

0.9431

0.0401

0.0999

0.9522

0.0431

3.4436

0.9310

2.3775

Model 70

4/5

0.1324

0.8709

0.0443

0.1290

0.8985

0.0408

4.9713

0.8178

2.8388

Model 71

4/10

0.1221

0.8938

0.0324

0.0995

0.9393

0.0253

6.9482

0.6125

4.1104

Model 72

4/15

0.0787

0.9576

0.0180

0.0956

0.9429

0.0209

8.1832

0.8020

5.8414

Model 73

5/5

0.1340

0.8823

0.0521

0.1632

0.7879

0.0507

5.7355

0.7452

4.4033

Model 74

5/10

0.1009

0.9234

0.0256

0.1323

0.9214

0.0340

5.3225

0.8715

3.1104

Model 75

5/15

0.0765

0.9610

0.0120

0.0709

0.9647

0.0109

6.2058

0.8797

4.4540

From Table 10, it has been observed that the one, two, three, four, and five hidden layers-based ANN models have predicted LL of soil with the performance of 0.9094, 0.8721, 0.9310, 0.8020, and 0.8797, respectively. Furthermore, the three hidden layers interconnected with 15 neuron-based ANN models outperformed the other GD algorithm-based ANN models in predicting the liquid limit of soil with a performance of 0.9310.

6. Using Gradient Descent Algorithm with Adaptive Learning (GDA) Based Neural Network Models

The artificial neural networks have been developed to predict soil LL using Gradient Descent with Adaptive Learning algorithm. The performance of GDA algorithm-based models is given in Table 11.

Table 11. Performance of GDA Algorithm-based ANN models for liquid limit

Model ID

HL/N

Training

Validation

Testing

RMSE

R

MAE

RMSE

R

MAE

RMSE

R

MAE

Model 76

1/5

0.0557

0.9810

0.0371

0.0633

0.9738

0.0329

3.5727

0.9223

2.6436

Model 77

1/10

0.0577

0.9796

0.0833

0.0697

0.9623

0.0799

4.5591

0.8907

3.7521

Model 78

1/15

0.0899

0.9476

0.2601

0.0968

0.9475

0.2806

5.2858

0.7781

2.9657

Model 79

2/5

0.0786

0.9599

0.0295

0.0894

0.9438

0.0248

4.1132

0.8749

3.0876

Model 80

2/10

0.0736

0.9643

0.0435

0.0795

0.9620

0.0533

4.5348

0.9004

3.1185

Model 81

2/15

0.0605

0.9766

0.0206

0.0839

0.9510

0.0235

3.8797

0.9330

2.4621

Model 82

3/5

0.0651

0.9739

0.0287

0.0670

0.9684

0.0271

9.0092

0.7800

5.9406

Model 83

3/10

0.1104

0.9192

0.0369

0.1046

0.9134

0.0343

2.2460

0.9634

1.5806

Model 84

3/15

0.0843

0.9528

0.0355

0.0880

0.9498

0.0398

5.6771

0.7517

3.5682

Model 85

4/5

0.1366

0.8693

0.0434

0.1165

0.9088

0.0420

4.6920

0.8651

3.0160

Model 86

4/10

0.0847

0.9496

0.0204

0.0954

0.9403

0.0202

7.4531

0.7947

4.4989

Model 87

4/15

0.0852

0.9523

0.0457

0.0792

0.9579

0.0429

6.9996

0.8408

4.6421

Model 88

5/5

0.1474

0.8491

0.0686

0.1334

0.8698

0.0582

3.9976

0.8997

2.6500

Model 89

5/10

0.1032

0.9311

0.0655

0.1194

0.8935

0.0621

4.1983

0.8881

2.9911

Model 90

5/15

0.0963

0.9331

0.1603

0.1111

0.9206

0.1588

6.6625

0.8391

4.3994

From Table 11, it has been observed that the one, two, three, four, and five hidden layers-based ANN models have predicted LL of soil with the performance of 0.9223, 0.9330, 0.9634, 0.8651, and 0.8997, respectively. In addition, the three hidden layers interconnected with ten neuron-based ANN models outperformed the other GDA algorithm-based ANN models in predicting the liquid limit of soil with a performance of 0.9634.

The performance variation of ANN models configured with different backpropagation algorithms for predicting the liquid limit of soil has been mapped, as shown in Fig. 3.

Figure 3 depicts the performance variation of the ANN models configured with different backpropagation algorithms in predicting the liquid limit of soil. From figure 3, it has been observed that the ten neurons are a transition point because the performance of models has been increased/ decreased for five and fifteen neurons in predicting the liquid limit of soil. LM, BFG, and SCG algorithm-based ANN models predict the LL liquid limit of soil with a performance of more than 0.9 with single hidden layers interconnected with 5/15 neurons which are highly acceptable. Two and four hidden layers interconnected with 5/15 neurons also achieve high performance and accuracy in predicting soil LL.

B. Prediction of Plasticity Index

For the prediction of plasticity index, the LM, BFG, SCG, GDA, GD, and GDM algorithm-based artificial neural network models have been evolved with a different number of hidden layers and neurons. The performance of the proposed models has been discussed below.

  1. Using Levenberg – Marquardt (LM) Algorithm Based Neural Network Models

Artificial neural networks have been developed to predict the PI of soil using the Levenberg-Marquardt algorithm. The performance of LM algorithm-based models is given in Table 12.

Table 12. Performance of LM Algorithm-based ANN models for plasticity index

Model ID

HL/N

Training

Validation

Testing

RMSE

R

MAE

RMSE

R

MAE

RMSE

R

MAE

Model 101

1/5

0.0799

0.9770

0.1035

0.0912

0.9705

0.0966

5.5340

0.6820

4.5076

Model 102

1/10

0.0839

0.9750

0.1241

0.0944

0.9659

0.1304

5.4425

0.7205

4.5462

Model 103

1/15

0.0583

0.9880

0.0873

0.1286

0.9427

0.0828

6.3183

0.6548

5.1714

Model 104

2/5

0.0825

0.9760

0.3336

0.0793

0.9747

0.2922

4.7786

0.7280

3.8122

Model 105

2/10

0.0784

0.9780

0.1635

0.0763

0.9812

0.1725

5.5471

0.6723

4.6031

Model 106

2/15

0.1039

0.9639

0.1117

0.1202

0.9465

0.1319

3.8893

0.8040

2.9756

Model 107

3/5

0.0637

0.9859

0.0636

0.1017

0.9617

0.6085

4.4313

0.7235

3.4384

Model 108

3/10

0.0722

0.9818

0.0523

0.0867

0.9691

0.0505

5.6716

0.6762

4.3043

Model 109

3/15

0.0609

0.9864

0.0922

0.0948

0.9668

0.0906

5.4437

0.6755

4.1551

Model 110

4/5

0.0647

0.9852

0.0940

0.0976

0.9627

0.1114

4.5131

0.7141

3.6722

Model 111

4/10

0.0739

0.9822

0.0601

0.1085

0.9556

0.0608

5.8621

0.5043

4.4188

Model 112

4/15

0.0819

0.9756

0.0660

0.1272

0.9615

0.0774

5.2393

0.6113

4.1574

Model 113

5/5

0.0776

0.9778

0.0919

0.1061

0.9652

0.0983

4.1764

0.7452

3.2607

Model 114

5/10

0.1160

0.9607

0.0653

0.0990

0.9637

0.0617

4.8778

0.6843

3.8869

Model 115

5/15

0.0655

0.9840

0.0645

0.1140

0.9569

0.0600

5.8719

0.6147

4.5207

From Table 12, it has been observed that the LM algorithm-based ANN model predicted the plasticity index of soil with a performance of 0.8040. However, it has also been observed that LM algorithm-based ANN models have not predicted PI with a performance of more than 0.90 because of the relationship between sand and fine content. The sand and fine content have a correlation coefficient of -0.6388 and 0.6285, respectively.

2. Using BFGs Quasi – Newton (BFG) Algorithm Based Neural Network Model

The artificial neural networks have been developed to predict the PI of soil using BFGs Quasi-Newton algorithm. The performance of BFG algorithm-based models is given in Table 13.

Table 13. Performance of BFG Algorithm-based ANN models for plasticity index

Model ID

HL/N

Training

Validation

Testing

RMSE

R

MAE

RMSE

R

MAE

RMSE

R

MAE

Model 116

1/5

0.0935

0.9701

0.0187

0.0892

0.9650

0.0201

4.9753

0.7455

3.8509

Model 117

1/10

0.0909

0.9734

0.1052

0.1199

0.9363

0.1119

5.2781

0.7248

4.2919

Model 118

1/15

0.0903

0.9739

0.3404

0.1085

0.9501

0.3699

4.0540

0.8136

3.6020

Model 119

2/5

0.0779

0.9765

0.0169

0.1049

0.9658

0.0240

5.2405

0.7193

4.2056

Model 120

2/10

0.2148

0.8252

0.8001

0.1829

0.8590

0.7908

4.7546

0.5132

3.3324

Model 121

2/15

0.1035

0.9609

0.0942

0.1256

0.9448

0.0931

5.5184

0.4683

3.9483

Model 122

3/5

0.0878

0.9713

0.0704

0.0698

0.9840

0.0696

5.1475

0.7375

4.2221

Model 123

3/10

0.1035

0.9591

0.1689

0.0907

0.9743

0.1703

4.0392

0.7668

3.3132

Model 124

3/15

0.0713

0.9817

0.0402

0.0934

0.9675

0.0476

5.5487

0.6159

4.2370

Model 125

4/5

0.0952

0.9641

0.0357

0.0976

0.9729

0.0495

4.8545

0.7606

3.9656

Model 126

4/10

0.0825

0.9733

0.0905

0.1079

0.9664

0.1012

4.4803

0.7581

3.8422

Model 127

4/15

0.0787

0.9796

0.1087

0.0907

0.9582

0.1086

5.4533

0.5946

4.0945

Model 128

5/5

0.0943

0.9671

0.0638

0.1213

0.9469

0.0677

5.0909

0.7280

4.3143

Model 129

5/10

0.0641

0.9856

0.0236

0.1226

0.9398

0.0408

5.3113

0.6075

4.0433

Model 130

5/15

0.0970

0.9650

0.2262

0.1104

0.9571

0.2225

5.1203

0.6536

4.2295

From Table 13, it has been observed that the BFG algorithm-based ANN model predicted the plasticity index of soil with a performance of 0.8136. Therefore, it may be stated that the BFG algorithm-based ANN model (1/15) predicts the plasticity index of soil better than the LM algorithm-based ANN model (2/15).

3. Using Scaled Conjugate Gradient (SCG) Algorithm Based Neural Network Models

Artificial neural networks have been developed to predict the PI of soil using the SCG algorithm. The performance of SCG algorithm-based models is given in Table 14.

Table 14. Performance of SCG Algorithm-based ANN models for plasticity index

Model ID

HL/N

Training

Validation

Testing

RMSE

R

MAE

RMSE

R

MAE

RMSE

R

MAE

Model 131

1/5

0.1134

0.9530

0.0401

0.1116

0.9543

0.0376

5.3133

0.7383

4.1421

Model 132

1/10

0.0996

0.9632

0.0745

0.1122

0.9586

0.0740

5.2070

0.7598

4.2620

Model 133

1/15

0.1527

0.9153

0.0734

0.1631

0.9160

0.0667

4.4898

0.7870

3.6426

Model 134

2/5

0.1042

0.9594

0.0377

0.0889

0.9741

0.0395

6.1795

0.6507

5.0980

Model 135

2/10

0.0963

0.9648

0.0303

0.0893

0.9739

0.0299

5.4668

0.6314

4.2369

Model 136

2/15

0.1088

0.9550

0.1768

0.1287

0.9445

0.1912

6.3156

0.5099

4.6700

Model 137

3/5

0.1177

0.9518

0.0435

0.0954

0.9627

0.0433

4.3151

0.7152

3.4263

Model 138

3/10

0.1349

0.9304

0.1242

0.1601

0.9034

0.1175

5.0833

0.6563

4.0188

Model 139

3/15

0.0966

0.9667

0.0575

0.1151

0.9487

0.0615

5.2317

0.5974

4.3147

Model 140

4/5

0.1052

0.9586

0.0477

0.1124

0.9574

0.0523

4.9502

0.6578

3.7365

Model 141

4/10

0.1108

0.9546

0.0776

0.1378

0.9305

0.0730

4.4070

0.5932

3.0585

Model 142

4/15

0.1199

0.9432

0.2529

0.1401

0.9379

0.2662

4.3419

0.7153

3.4916

Model 143

5/5

0.1234

0.9436

0.0522

0.1188

0.9514

0.0526

6.1962

0.5843

4.9523

Model 144

5/10

0.0888

0.9735

0.0409

0.0606

0.9836

0.0384

5.2205

0.6406

4.3422

Model 145

5/15

0.0830

0.9756

0.0334

0.1017

0.9604

0.0377

4.7150

0.7059

3.7745

From Table 13, it has been observed that the SCG algorithm-based ANN model predicted the plasticity index of soil with a performance of 0.7870. It has also been observed that SCG algorithm-based ANN models require strongly correlated sand and fine content with PI.

4. Using Gradient Descent with Momentum (GDM) Algorithm Based Neural Network Models

Artificial neural networks have been developed to predict the PI of soil using the GDM algorithm. The performance of GDM algorithm-based models is given in Table 15.

Table 15. Performance of GDM Algorithm-based ANN models for plasticity index

Model ID

HL/N

Training

Validation

Testing

RMSE

R

MAE

RMSE

R

MAE

RMSE

R

MAE

Model 146

1/5

0.1275

0.9341

0.0315

0.1597

0.9210

0.0410

5.8063

0.5329

4.3796

Model 147

1/10

0.2056

0.8588

0.1252

0.1745

0.8292

0.0922

5.5386

0.4632

4.0688

Model 148

1/15

0.1609

0.9108

0.0493

0.1841

0.8824

0.0579

6.2310

0.7868

4.9162

Model 149

2/5

0.1792

0.8735

0.0528

0.2163

0.8207

0.0748

5.5847

0.4952

3.9170

Model 150

2/10

0.4208

0.6620

0.8106

0.4382

0.5575

0.8466

6.4502

0.3498

5.7947

Model 151

2/15

0.4506

0.6964

1.0730

0.3700

0.7432

1.0210

7.4952

0.6257

6.2392

Model 152

3/5

0.1965

0.8559

0.0636

0.1962

0.8335

0.0639

3.2702

0.8634

2.8181

Model 153

3/10

0.1490

0.9122

0.0389

0.1624

0.9082

0.0367

4.0890

0.7743

3.2545

Model 154

3/15

0.4209

0.6295

0.6229

0.3634

0.6984

0.5678

5.9679

0.6241

4.7362

Model 155

4/5

0.2241

0.7920

0.0769

0.2295

0.8039

0.0971

4.3599

0.4138

3.1822

Model 156

4/10

0.1617

0.8922

0.0424

0.1898

0.8911

0.0484

3.7304

0.7417

2.8517

Model 157

4/15

0.1852

0.8700

0.0487

0.1640

0.8941

0.0432

4.4936

0.6526

3.2588

Model 158

5/5

0.2124

0.8351

0.0547

0.2174

0.7880

0.0559

3.8733

0.7155

2.9629

Model 159

5/10

0.1314

0.9381

0.0230

0.1403

0.9156

0.0285

5.9709

0.5926

4.7706

Model 160

5/15

0.3055

0.7717

0.1800

0.2556

0.8153

0.2205

6.9119

0.5209

6.0766

From Table 15, it has been observed that the GDM algorithm-based ANN model predicted the plasticity index of soil with a performance of 0.8634. Therefore, it can be stated that the GDM algorithm-based ANN model (3/5) predicts the plasticity index of soil better than the LM, BFG, and SCG algorithm-based ANN model.

5. Using Gradient Descent (GD) Algorithm Based Neural Network Models

Artificial neural networks have been developed to predict the PI of soil using the GD algorithm. The performance of GD algorithm-based models is given in Table 16.

Table 16. Performance of GD Algorithm-based ANN models for plasticity index

Model ID

HL/N

Training

Validation

Testing

RMSE

R

MAE

RMSE

R

MAE

RMSE

R

MAE

Model 161

1/5

0.1685

0.8932

0.0491

0.1963

0.8474

0.0615

3.5745

0.7395

2.7924

Model 162

1/10

0.2333

0.7942

0.1062

0.2269

0.7747

0.1036

4.5789

0.6249

3.5532

Model 163

1/15

0.1426

0.9262

0.0391

0.1605

0.9173

0.0504

6.3462

0.5045

4.9682

Model 164

2/5

0.2320

0.7730

0.0954

0.2225

0.8363

0.1084

3.9751

0.7387

2.9780

Model 165

2/10

0.1529

0.9077

0.0474

0.1591

0.9146

0.0545

4.7277

0.6081

3.2716

Model 166

2/15

0.1882

0.8487

0.0741

0.1867

0.8967

0.0702

4.0714

0.6305

3.2137

Model 167

3/5

0.1632

0.8955

0.0622

0.1665

0.9034

0.0700

2.8608

0.8266

2.1785

Model 168

3/10

0.1772

0.8690

0.0635

0.2010

0.8762

0.0722

4.8797

0.4923

3.6017

Model 169

3/15

0.1559

0.9066

0.0594

0.1827

0.8737

0.0911

6.4048

0.3190

4.4622

Model 170

4/5

0.1675

0.8930

0.0666

0.1434

0.9241

0.0619

5.3178

0.5393

4.3517

Model 171

4/10

0.2106

0.8217

0.0626

0.2136

0.8223

0.0628

4.7407

0.6330

3.6126

Model 172

4/15

0.1516

0.9126

0.0377

0.2133

0.8217

0.0662

3.6665

0.6589

2.2443

Model 173

5/5

0.1977

0.8387

0.0708

0.2096

0.8487

0.0775

5.6564

0.4076

3.8573

Model 174

5/10

0.1786

0.8695

0.0644

0.2069

0.8474

0.0830

4.1612

0.5799

3.1377

Model 175

5/15

0.1607

0.9078

0.0500

0.1554

0.8942

0.0457

4.3096

0.6299

2.9803

From Table 16, it has been observed that the GD algorithm-based ANN model has predicted the plasticity index of soil with the performance of 0.8266. Therefore, it can be stated that the GD algorithm-based ANN model (3/5) predicts the plasticity index of soil better than the LM, BFG, and SCG algorithm-based ANN model.

6. Using Gradient Descent Algorithm with Adaptive Learning (GDA) Based Neural Network Model

Artificial neural networks have been developed to predict the PI of soil using the GDA algorithm. The performance of GDA algorithm-based models is given in Table 17.

Table 17. Performance of GDA Algorithm-based ANN models for plasticity index

Model ID

HL/N

Training

Validation

Testing

RMSE

R

MAE

RMSE

R

MAE

RMSE

R

MAE

Model 176

1/5

0.2440

0.7465

0.1692

0.2618

0.7436

0.1945

5.2705

0.4981

3.7032

Model 177

1/10

0.1551

0.9139

0.3170

0.1644

0.8905

0.2432

5.2917

0.6726

4.4011

Model 178

1/15

0.2018

0.8768

0.2652

0.1827

0.8731

0.2668

5.1596

0.5690

4.0081

Model 179

2/5

0.1436

0.9250

0.1544

0.1390

0.9275

0.1423

4.1891

0.6730

3.3252

Model 180

2/10

0.1677

0.9034

0.1316

0.1418

0.9297

0.1126

3.2423

0.7988

2.4588

Model 181

2/15

0.1424

0.9287

0.1842

0.1386

0.9138

0.1584

3.7145

0.7413

2.9625

Model 182

3/5

0.1583

0.9108

0.0454

0.1350

0.9213

0.0370

3.3477

0.7436

2.5612

Model 183

3/10

0.1744

0.8935

0.0768

0.1975

0.8265

0.0849

4.1701

0.7038

3.1721

Model 184

3/15

0.1276

0.9424

0.1979

0.1336

0.9307

0.1958

3.9659

0.8136

3.3663

Model 185

4/5

0.2025

0.8492

0.1367

0.1734

0.8717

0.1174

5.7265

0.3395

4.2076

Model 186

4/10

0.1334

0.9331

0.0631

0.1648

0.9027

0.0729

3.5543

0.7998

2.9269

Model 187

4/15

0.1688

0.9002

0.0790

0.1402

0.9137

0.0671

5.0080

0.6400

4.2041

Model 188

5/5

0.1438

0.9269

0.1962

0.1335

0.9238

0.1725

3.9148

0.7363

3.3099

Model 189

5/10

0.2122

0.8335

0.2008

0.2096

0.7989

0.1711

5.6389

0.3715

3.8897

Model 190

5/15

0.1519

0.9128

0.0545

0.1604

0.9174

0.0668

5.8969

0.3584

4.2640

From Table 17, it has been observed that the GDA algorithm-based ANN model has predicted the plasticity index of soil with a performance of 0.8136. Therefore, it can be stated that the GD algorithm-based ANN model (3/15) predicts the plasticity index of soil better than the LM and SCG algorithm-based ANN models.

The performance variation of ANN models configured with different backpropagation algorithms for predicting soil plasticity index has been mapped, as shown in Fig. 4.

Fig. 4 depicts the performance variation of ANN models configured with different backpropagation algorithms in predicting the plasticity index of soil. The same pattern is mapped in the performance variation of ANN models in predicting soil plasticity index. In a few cases, the performance of ANN models has continuously decreased in predicting the plasticity index. On the other hand, the maximum performance has been achieved by GDM algorithm-based ANN models in predicting the plasticity index of soil. Therefore, it may be stated that the GDM achieves better performance with a strongly correlated pair of datasets.

C. Prediction of Optimum Moisture Content

The LM, BFG, SCG, GDA, GD, and GDM algorithm-based artificial neural network models have evolved with many hidden layers and neurons to predict optimum moisture content. The performance of the proposed models has been discussed below.

  1. Using Levenberg – Marquardt (LM) Algorithm Based Neural Network Models

The artificial neural networks have been developed to predict the OMC of soil using the LM algorithm. The performance of LM algorithm-based models is given in Table 18.

Table 18. Performance of LM Algorithm-based ANN models for optimum moisture content

Model ID

HL/N

Training

Validation

Testing

RMSE

R

MAE

RMSE

R

MAE

RMSE

R

MAE

Model 201

1/5

0.0605

0.9706

0.0230

0.0610

0.9623

0.0263

1.5358

0.9822

1.1660

Model 202

1/10

0.0669

0.9722

0.0642

0.0736

0.9624

0.0903

2.4959

0.9721

1.7462

Model 203

1/15

0.0562

0.9731

0.0131

0.0642

0.9666

0.0158

1.9915

0.9629

1.3352

Model 204

2/5

0.0558

0.9746

0.0066

0.0604

0.9662

0.0064

2.2406

0.9531

1.3220

Model 205

2/10

0.0464

0.9823

0.0186

0.0860

0.9515

0.0228

2.3150

0.9656

1.3379

Model 206

2/15

0.0456

0.9824

0.0124

0.0724

0.9601

0.0186

2.2340

0.9401

1.5465

Model 207

3/5

0.0619

0.9695

0.0154

0.0666

0.9602

0.0171

2.4152

0.9527

1.6730

Model 208

3/10

0.0713

0.9623

0.0125

0.0660

0.9662

0.0127

2.3889

0.9552

2.0151

Model 209

3/15

0.0523

0.9775

0.0256

0.0867

0.9345

0.0272

1.6212

0.9553

1.4029

Model 210

4/5

0.0722

0.9531

0.0665

0.0784

0.9559

0.0744

1.6893

0.9509

1.2188

Model 211

4/10

0.0468

0.9790

0.0692

0.0812

0.9560

0.0718

1.8736

0.9632

1.3584

Model 212

4/15

0.0394

0.9869

0.0401

0.0655

0.9635

0.0542

2.5502

0.8963

1.8446

Model 213

5/5

0.0529

0.9772

0.0112

0.0763

0.9561

0.0155

2.7043

0.9745

1.5588

Model 214

5/10

0.0373

0.9889

0.0574

0.0820

0.9408

0.0600

1.8102

0.9715

1.4766

Model 215

5/15

0.0458

0.9841

0.4867

0.0780

0.9453

0.4955

1.8096

0.9387

1.2529

From Table 18, it has been observed that the performance of LM algorithm-based ANN models has been increased with the increasing number of hidden layers and neurons. The performance of two hidden layers-based models has been increased for two hidden layers interconnected with ten neurons, i.e., 0.9656. Similarly, the performance of the three hidden layers-based models has been increased for three hidden layers interconnected with 15 neurons, i.e., 0.9553. All LM algorithm-based ANN models predicted optimum moisture content with a performance of greater than 0.95 because of the correlation coefficient between input parameters (S, FC, & PL strongly correlated, and LL & PI very strongly correlated) and optimum moisture content.

2. Using BFGs Quasi – Newton (BFG) Algorithm Based Neural Network Models

Artificial neural networks have been developed to predict the OMC of soil using the BFG algorithm. The performance of BFG algorithm-based models is given in Table 19.

Table 19. Performance of BFG Algorithm-based ANN models for optimum moisture content

Model ID

HL/N

Training

Validation

Testing

RMSE

R

MAE

RMSE

R

MAE

RMSE

R

MAE

Model 216

1/5

0.0715

0.9536

0.0410

0.0726

0.9612

0.0410

2.9144

0.8917

2.1400

Model 217

1/10

0.0668

0.9611

0.0170

0.0752

0.9567

0.0179

1.7998

0.9545

1.4806

Model 218

1/15

0.0708

0.9550

0.0221

0.0823

0.9508

0.0222

2.1371

0.9071

1.6924

Model 219

2/5

0.0738

0.9508

0.0238

0.0727

0.9585

0.0261

1.7524

0.9351

1.4130

Model 220

2/10

0.0568

0.9740

0.0097

0.0652

0.9574

0.0098

1.4624

0.9786

1.0831

Model 221

2/15

0.0529

0.9787

0.0625

0.0910

0.9025

0.0675

2.2724

0.9172

1.8292

Model 222

3/5

0.0678

0.9617

0.0268

0.0689

0.9580

0.0258

1.4354

0.9580

1.2417

Model 223

3/10

0.0867

0.9389

0.1075

0.0838

0.9420

0.1082

2.0696

0.9201

1.6577

Model 224

3/15

0.0792

0.9527

0.0855

0.0823

0.9177

0.0813

2.8382

0.8921

2.1297

Model 225

4/5

0.0734

0.9547

0.0165

0.0757

0.9498

0.0167

1.4980

0.9621

1.2470

Model 226

4/10

0.0622

0.9665

0.0191

0.0671

0.9651

0.0209

1.4774

0.9646

1.1394

Model 227

4/15

0.0647

0.9648

0.0339

0.0748

0.9529

0.0417

1.5236

0.9647

1.2510

Model 228

5/5

0.0735

0.9574

0.1000

0.0785

0.9365

0.0955

1.8488

0.9317

1.5298

Model 229

5/10

0.0877

0.9381

0.1304

0.1044

0.8863

0.1319

2.3121

0.8919

1.6981

Model 230

5/15

0.0729

0.9511

0.0741

0.0788

0.9547

0.0720

2.1630

0.8979

1.6666

Table 19 shows that the BFG algorithm-based ANN models predict the optimum moisture content with a performance of more than 0.85. It has also been observed that the BFG algorithm-based ANN models require two or four hidden layers with ten neurons to achieve a performance of more than 0.96. Model 220 outperformed the other BFG algorithm-based ANN models in predicting optimum moisture content.

3. Using Scaled Conjugate Gradient (SCG) Algorithm Based Neural Network Models

The artificial neural networks have been developed to predict the OMC of soil using the SCG algorithm. The performance of SCG algorithm-based models is given in Table 20.

Table 20. Performance of SCG Algorithm-based ANN models for optimum moisture content

Model ID

HL/N

Training

Validation

Testing

RMSE

R

MAE

RMSE

R

MAE

RMSE

R

MAE

Model 231

1/5

0.0678

0.9615

0.0485

0.0674

0.9584

0.0474

1.4750

0.9741

1.2795

Model 232

1/10

0.0678

0.9604

0.0201

0.0937

0.9269

0.0233

3.0644

0.9002

2.0679

Model 233

1/15

0.0662

0.9590

0.0483

0.0637

0.9720

0.0461

1.5230

0.9789

1.2279

Model 234

2/5

0.0674

0.9548

0.0220

0.0647

0.9726

0.0275

1.2389

0.9750

0.9399

Model 235

2/10

0.0597

0.9664

0.0241

0.0712

0.9642

0.0322

2.1166

0.9561

1.5072

Model 236

2/15

0.0617

0.9695

0.0344

0.0755

0.9446

0.0336

2.2469

0.9172

1.6116

Model 237

3/5

0.0593

0.9714

0.0153

0.0626

0.9630

0.0157

1.3359

0.9693

1.1181

Model 238

3/10

0.0546

0.9714

0.0183

0.0755

0.9668

0.0237

3.1326

0.8816

1.5863

Model 239

3/15

0.0875

0.9358

0.2965

0.1079

0.8932

0.3150

2.4866

0.8813

1.9214

Model 240

4/5

0.0862

0.9384

0.0259

0.0721

0.9530

0.0243

1.8769

0.9250

1.4832

Model 241

4/10

0.0749

0.9523

0.0155

0.0955

0.9310

0.0257

2.0971

0.9782

1.7799

Model 242

4/15

0.0628

0.9654

0.0212

0.0715

0.9590

0.0232

1.9577

0.9284

1.5763

Model 243

5/5

0.0779

0.9506

0.0617

0.0775

0.9402

0.0661

3.5013

0.8829

2.3629

Model 244

5/10

0.0679

0.9586

0.0289

0.0785

0.9532

0.0344

1.7440

0.9598

1.5105

Model 245

5/15

0.0686

0.9584

0.0710

0.0842

0.9447

0.0740

1.4522

0.9557

1.0662

Table 20 shows that Model 233 outperformed the other SCG algorithm-based ANN models in predicting the OMC of soil. However, table 20 also indicates that the performance of the SCG algorithm-based ANN model has been decreased with increasing the number of hidden layers.

4. Using Gradient Descent with Momentum (GDM) Algorithm Based Neural Network Models

Artificial neural networks have been developed to predict the OMC of soil using the GDM algorithm. The performance of GDM algorithm-based models is given in Table 21.

Table 21. Performance of GDM Algorithm-based ANN models for optimum moisture content

Model ID

HL/N

Training

Validation

Testing

RMSE

R

MAE

RMSE

R

MAE

RMSE

R

MAE

Model 246

1/5

0.1284

0.9370

0.0229

0.1379

0.9702

0.0274

2.5919

0.8718

1.8263

Model 247

1/10

0.1075

0.8982

0.0234

0.1178

0.8935

0.0236

3.9374

0.7318

3.2326

Model 248

1/15

0.1378

0.8213

0.0530

0.1846

0.7386

0.0664

3.9058

0.6097

3.2454

Model 249

2/5

0.0958

0.9241

.0.2264

0.0765

0.9489

0.0165

2.1606

0.9010

1.7428

Model 250

2/10

0.1163

0.8839

0.0399

0.1780

0.7857

0.0600

3.3881

0.7874

2.4571

Model 251

2/15

0.0986

0.9163

0.0235

0.1017

0.9046

0.0235

2.0266

0.9284

1.6979

Model 252

3/5

0.1202

0.8660

0.0239

0.1136

0.8966

0.0223

2.1769

0.9416

1.7989

Model 253

3/10

0.0965

0.9107

0.0226

0.1085

0.9170

0.0323

2.3178

0.8995

1.9568

Model 254

3/15

0.2845

0.8126

0.3002

0.2883

0.8191

0.2870

3.7777

0.7643

2.5276

Model 255

4/5

0.1293

0.8465

0.0238

0.1463

0.8069

0.0274

2.3765

0.9150

1.9466

Model 256

4/10

0.0872

0.9353

0.0152

0.0930

0.9225

0.0150

2.5965

0.8977

1.9193

Model 257

4/15

0.2345

0.8597

0.2320

0.2467

0.7845

0.2468

3.2685

0.8848

2.5851

Model 258

5/5

0.1515

0.7726

0.0404

0.1533

0.8334

0.0448

3.7520

0.8194

3.3550

Model 259

5/10

0.0928

0.9212

0.0151

0.1199

0.8959

0.0230

2.5180

0.8914

2.1143

Model 260

5/15

0.1604

0.7499

0.3260

0.1525

0.7977

0.3020

2.9102

0.8415

2.4376

From Table 21, it has been observed that the performance of the GDM algorithm-based ANN model has been increased up to three hidden layers. On the other hand, the performance of GDM models has been decreasing with increasing the number of hidden layers in the prediction of OMC.

5. Using Gradient Descent (GD) Algorithm Based Neural Network Models

The artificial neural networks have been developed to predict the OMC of soil using the GD algorithm. The performance of GD algorithm-based models is given in Table 22.

Table 22. Performance of GD Algorithm-based ANN models for optimum moisture content

Model ID

HL/N

Training

Validation

Testing

RMSE

R

MAE

RMSE

R

MAE

RMSE

R

MAE

Model 261

1/5

0.1087

0.8969

0.0318

0.1415

0.8219

0.0417

3.0967

0.8560

2.5154

Model 262

1/10

0.1234

0.8701

0.0273

0.1241

0.8705

0.0223

3.3938

0.8091

2.4948

Model 263

1/15

0.1279

0.8785

0.0630

0.1274

0.8921

0.0725

3.6624

0.8819

2.7955

Model 264

2/5

0.0999

0.9078

0.0381

0.1199

0.8850

0.0406

3.4192

0.8731

2.4869

Model 265

2/10

0.1365

0.8394

0.0328

0.1299

0.8244

0.0287

2.2094

0.9353

1.7116

Model 266

2/15

0.1088

0.9051

0.0491

0.1030

0.9049

0.0365

3.2638

0.7712

2.3701

Model 267

3/5

0.1250

0.8614

0.0318

0.1321

0.7945

0.0288

2.8298

0.8505

2.2730

Model 268

3/10

0.0896

0.9345

0.0164

0.1235

0.8697

0.0232

2.7791

0.8942

1.6670

Model 269

3/15

0.0876

0.9402

0.0157

0.0956

0.8952

0.0198

2.0383

0.9345

1.5937

Model 270

4/5

0.1792

0.6910

0.0684

0.1633

0.7299

0.0633

3.5938

0.7817

3.1359

Model 271

4/10

0.0913

0.9259

0.0214

0.0907

0.9324

0.0213

3.3093

0.8569

2.8472

Model 272

4/15

0.0874

0.9339

0.0133

0.0968

0.9229

0.0157

1.8525

0.9316

1.4624

Model 273

5/5

0.1201

0.8708

0.0458

0.1412

0.8239

0.0534

2.0147

0.9300

1.6181

Model 274

5/10

0.1235

0.8681

0.0294

0.1417

0.7971

0.0300

3.0886

0.8084

2.6045

Model 275

5/15

0.0779

0.9467

0.0114

0.0890

0.9365

0.0140

2.6987

0.9137

2.0070

From Table 22, it has been observed that the performance of GD algorithm-based ANN models has been started increasing up to two hidden layers. Therefore, the ANN model of two hidden layers interconnected with ten neurons has been identified as a better performance model. However, from Table 22, it has also been observed that the performance of GD ANN models decreased with hidden layers after two layers in predicting the OMC of soil.

6. Using Gradient Descent Algorithm with Adaptive Learning (GDA) Based Neural Network Models

The artificial neural networks have been developed to predict the OMC of soil using the GDA algorithm. The performance of GDA algorithm-based models is given in Table 23.

Table 23. Performance of GDA Algorithm-based ANN models for optimum moisture content

Model ID

HL/N

Training

Validation

Testing

RMSE

R

MAE

RMSE

R

MAE

RMSE

R

MAE

Model 276

1/5

0.0801

0.9477

0.0582

0.0951

0.9336

0.0760

1.7522

0.9437

1.3095

Model 277

1/10

0.0884

0.9361

0.0689

0.0864

0.9250

0.0727

3.8420

0.8210

3.1291

Model 278

1/15

0.0943

0.9235

0.0472

0.1352

0.8492

0.0442

2.8842

0.8203

2.1718

Model 279

2/5

0.1035

0.9122

0.0569

0.1037

0.8989

0.0651

3.1994

0.7596

2.5478

Model 280

2/10

0.0848

0.9339

0.0239

0.0896

0.9467

0.0317

1.5136

0.9515

1.1409

Model 281

2/15

0.1184

0.8983

0.0363

0.1111

0.8853

0.0363

5.2495

0.5519

3.5770

Model 282

3/5

0.0910

0.9299

0.0331

0.0975

0.9212

0.0351

2.2330

0.9249

1.8035

Model 283

3/10

0.0964

0.9293

0.1079

0.1015

0.9095

0.0798

2.2151

0.9021

1.7263

Model 284

3/15

0.0713

0.9580

0.0315

0.0951

0.9266

0.0364

2.9364

0.8708

2.1602

Model 285

4/5

0.0925

0.9324

0.0645

0.0907

0.9262

0.0766

2.1903

0.9075

1.7804

Model 286

4/10

0.0849

0.9398

0.0452

0.0868

0.9299

0.0411

2.7128

0.8504

2.1271

Model 287

4/15

0.1035

0.9168

0.1039

0.1015

0.8900

0.0890

1.6273

0.8952

1.1139

Model 288

5/5

0.1015

0.9134

0.2014

0.1077

0.9026

0.1889

2.8014

0.8308

2.2104

Model 289

5/10

0.1182

0.8799

0.0457

0.1138

0.8881

0.0481

2.9885

0.8236

2.4389

Model 290

5/15

0.0971

0.9342

0.0293

0.1109

0.8885

0.0375

2.3855

0.8779

1.8470

From Table 23, it has been observed that the performance of GDA algorithm-based ANN models has been started increasing up to two hidden layers. Therefore, the ANN model of two hidden layers interconnected with ten neurons has been identified as a better performance model. From Table 23, it has also been observed that the performance of GDA ANN models decreased with hidden layers after two layers in predicting the OMC of soil. The performance variation of ANN models configured with different backpropagation algorithms for predicting soil optimum moisture content has been mapped, as shown in Fig. 5.

Fig. 5 depicts the performance variation of ANN models configured with different backpropagation algorithms in predicting the OMC of soil. The same pattern is mapped in the performance variation of ANN models in predicting the OMC of soil. In a few cases, the performance of ANN models has continuously decreased in predicting OMC. On the other hand, the maximum performance has been achieved by LM algorithm-based ANN models in predicting the OMC of soil. Therefore, it may be stated that the LM achieves better performance due to the strongly correlated datasets.

D. Prediction of Maximum Dry Density

For the prediction of maximum dry density, the LM, BFG, SCG, GDA, GD, and GDM algorithm-based artificial neural network models have evolved with different hidden layers and neurons. The performance of the proposed models has been discussed below.

  1. Using Levenberg – Marquardt (LM) Algorithm Based Neural Network Models

The artificial neural networks have been developed to predict the MDD of soil using the LM algorithm. The performance of LM algorithm-based models is given in Table 24.

Table 24. Performance of LM Algorithm-based ANN models for maximum dry density

Model ID

HL/N

Training

Validation

Testing

RMSE

R

MAE

RMSE

R

MAE

RMSE

R

MAE

Model 301

1/5

0.0099

0.9760

0.0005

0.0111

0.9645

0.0004

0.1161

0.8754

0.0925

Model 302

1/10

0.0100

0.9762

0.0008

0.0108

0.9659

0.0006

0.1027

0.9474

0.0743

Model 303

1/15

0.0087

0.9795

0.0008

0.0112

0.9729

0.0010

0.1068

0.9609

0.0866

Model 304

2/5

0.0104

0.9747

0.0007

0.0097

0.9711

0.0007

0.0917

0.9318

0.0654

Model 305

2/10

0.0091

0.9809

0.0017

0.0126

0.9485

0.0017

0.0828

0.9474

0.0580

Model 306

2/15

0.0090

0.9834

0.0028

0.0112

0.9551

0.0030

0.0805

0.9627

0.0608

Model 307

3/5

0.0091

0.9814

0.0008

0.0108

0.9628

0.0008

0.0765

0.9606

0.0647

Model 308

3/10

0.0088

0.9813

0.0020

0.0113

0.9665

0.0020

0.0831

0.9166

0.0625

Model 309

3/15

0.0092

0.9792

0.0022

0.0113

0.9698

0.0019

0.0935

0.9618

0.0799

Model 310

4/5

0.0093

0.9801

0.0075

0.0112

0.9596

0.0075

0.0844

0.9470

0.0611

Model 311

4/10

0.0097

0.9793

0.0012

0.0107

0.9697

0.0012

0.0715

0.9503

0.0539

Model 312

4/15

0.0104

0.9741

0.0015

0.0133

0.9599

0.0016

0.0700

0.9784

0.0532

Model 313

5/5

0.0092

0.9786

0.0022

0.0114

0.9691

0.0024

0.0733

0.9230

0.0566

Model 314

5/10

0.0096

0.9774

0.0009

0.0130

0.9626

0.0012

0.0892

0.9487

0.0738

Model 315

5/15

0.0093

0.9787

0.0008

0.0105

0.9703

0.0008

0.0878

0.9588

0.0592

From Table 24, it has been observed that the performance of one, two, four, and five hidden layer-based ANN models have been increased with the number of neurons. But the performance of three hidden layer-based ANN models has decreased by providing ten neurons. Nevertheless, model 312 outperformed the other LM models in predicting the maximum dry density of soil with a performance of 0.9784.

2. Using BFGs Quasi – Newton (BFG) Algorithm Based Neural Network Models

Artificial neural networks have been developed to predict the MDD of soil using the BFG algorithm. The performance of BFG algorithm-based models is given in Table 25.

Table 25. Performance of BFG Algorithm-based ANN models for maximum dry density

Model ID

HL/N

Training

Validation

Testing

RMSE

R

MAE

RMSE

R

MAE

RMSE

R

MAE

Model 316

1/5

0.0134

0.9500

0.0011

0.0165

0.9479

0.0013

0.0648

0.9145

0.0490

Model 317

1/10

0.0120

0.9658

0.0018

0.0123

0.9540

0.0018

0.0898

0.9494

0.0612

Model 318

1/15

0.0110

0.9696

0.0024

0.0110

0.9701

0.0022

0.0812

0.9654

0.0651

Model 319

2/5

0.0170

0.9116

0.0024

0.0180

0.9418

0.0028

0.0580

0.9556

0.0520

Model 320

2/10

0.0188

0.9195

0.0018

0.0174

0.8779

0.0017

0.0568

0.9252

0.0292

Model 321

2/15

0.0127

0.9589

0.0037

0.0115

0.9687

0.0037

0.0857

0.9597

0.0650

Model 322

3/5

0.0195

0.9066

0.0014

0.0164

0.9225

0.0012

0.0939

0.8981

0.0787

Model 323

3/10

0.0160

0.9318

0.0009

0.0128

0.9621

0.0010

0.0851

0.9042

0.0732

Model 324

3/15

0.0219

0.8694

0.0070

0.0257

0.8465

0.0070

0.1066

0.7436

0.0602

Model 325

4/5

0.0139

0.9480

0.0015

0.0147

0.9572

0.0016

0.0633

0.9506

0.0474

Model 326

4/10

0.0166

0.9287

0.0011

0.0153

0.9398

0.0011

0.0811

0.9349

0.0725

Model 327

4/15

0.0135

0.9474

0.0007

0.0213

0.9090

0.0011

0.0734

0.9540

0.0570

Model 328

5/5

0.0135

0.9535

0.0006

0.0144

0.9477

0.0007

0.0731

0.9006

0.0550

Model 329

5/10

0.0106

0.9711

0.0006

0.0133

0.9537

0.0006

0.0882

0.9378

0.0605

Model 330

5/15

0.0130

0.9565

0.0008

0.0112

0.9728

0.0008

0.0667

0.9030

0.0528

From Table 25, it has been observed that the performance of the single-hidden layers-based ANN model has increased with neurons. But it has also been observed that the performance of three and five hidden layers-based ANN models has been increased by providing ten neurons. Model 318 has been identified as a better performance model in predicting MDD of soil with a performance of 0.9654.

3. Using Scaled Conjugate Gradient (SCG) Algorithm Based Neural Network Models

Artificial neural networks have been developed to predict the MDD of soil using the SCG algorithm. The performance of SCG algorithm-based models is given in Table 26.

Table 26. Performance of SCG Algorithm-based ANN models for maximum dry density

Model ID

HL/N

Training

Validation

Testing

RMSE

R

MAE

RMSE

R

MAE

RMSE

R

MAE

Model 331

1/5

0.0131

0.9557

0.0003

0.0138

0.9520

0.0004

0.0705

0.9623

0.0597

Model 332

1/10

0.0107

0.9718

0.0004

0.0113

0.9645

0.0003

0.0904

0.9379

0.0643

Model 333

1/15

0.0177

0.9141

0.0022

0.0164

0.9405

0.0018

0.0903

0.9560

0.0832

Model 334

2/5

0.0117

0.9624

0.0003

0.0134

0.9603

0.0004

0.0891

0.9428

0.0592

Model 335

2/10

0.0096

0.9742

0.0011

0.0141

0.9578

0.0013

0.1153

0.9223

0.0929

Model 336

2/15

0.0107

0.9719

0.0006

0.0130

0.9543

0.0007

0.0665

0.9302

0.0511

Model 337

3/5

0.0137

0.9550

0.0004

0.0134

0.9455

0.0004

0.0731

0.8818

0.0592

Model 338

3/10

0.0121

0.9603

0.0005

0.0157

0.9434

0.0006

0.0854

0.8866

0.0515

Model 339

3/15

0.0156

0.9417

0.0033

0.0149

0.9385

0.0031

0.1143

0.8740

0.0872

Model 340

4/5

0.0123

0.9571

0.0007

0.0138

0.9612

0.0008

0.0747

0.9214

0.0471

Model 341

4/10

0.0142

0.9416

0.0013

0.0157

0.9485

0.0019

0.1045

0.8639

0.0695

Model 342

4/15

0.0109

0.9693

0.0013

0.0112

0.9693

0.0013

0.0854

0.9496

0.0569

Model 343

5/5

0.0126

0.9604

0.0009

0.0128

0.9543

0.0009

0.0759

0.9593

0.0635

Model 344

5/10

0.0106

0.9736

0.0020

0.0128

0.9518

0.0020

0.0771

0.9435

0.0532

Model 345

5/15

0.0122

0.9603

0.0008

0.0158

0.9498

0.0010

0.1095

0.9274

0.0839

From Table 26, it has been observed that the SCG algorithm-based ANN models have achieved maximum performance using one to five hidden layers interconnected with 5/15 neurons. Model 331 has outperformed the other SCG ANN models in predicting MDD of soil with a performance of 0.9623.

4. Using Gradient Descent with Momentum (GDM) Algorithm Based Neural Network Models

Artificial neural networks have been developed to predict the MDD of soil using the GDM algorithm. The performance of GDM algorithm-based models is given in Table 27.

Table 27. Performance of GDM Algorithm-based ANN models for maximum dry density

Model ID

HL/N

Training

Validation

Testing

RMSE

R

MAE

RMSE

R

MAE

RMSE

R

MAE

Model 346

1/5

0.0318

0.7485

0.0012

0.0372

0.6603

0.0016

0.0839

0.8709

0.0611

Model 347

1/10

0.0392

0.7343

0.0051

0.0436

0.8088

0.0053

0.0736

0.8629

0.0556

Model 348

1/15

0.0493

0.5174

0.0049

0.0542

0.3973

0.0053

0.1661

0.5749

0.1430

Model 349

2/5

0.0586

0.7148

0.0105

0.0656

0.7697

0.0128

0.2382

0.5828

0.2145

Model 350

2/10

0.0399

0.7892

0.0022

0.0349

0.8114

0.0016

0.1378

0.5118

0.1142

Model 351

2/15

0.0673

0.4501

0.0091

0.0527

0.7228

0.0081

0.2582

0.6403

0.2322

Model 352

3/5

0.0295

0.8610

0.0013

0.0319

0.8419

0.0016

0.0975

0.8256

0.0829

Model 353

3/10

0.0384

0.6660

0.0045

0.0341

0.6778

0.0041

0.0875

0.7619

0.0679

Model 354

3/15

0.0399

0.6777

0.0059

0.0413

0.6427

0.0063

0.1277

0.3487

0.1060

Model 355

4/5

0.0346

0.6837

0.0016

0.0273

0.7019

0.0011

0.1361

0.6427

0.1187

Model 356

4/10

0.0324

0.7980

0.0019

0.0322

0.8077

0.0023

0.0806

0.8176

0.0542

Model 357

4/15

0.0334

0.7413

0.0025

0.0334

0.8268

0.0028

0.1980

0.7026

0.1505

Model 358

5/5

0.0555

0.5570

0.0126

0.0500

0.5499

0.0110

0.1343

0.5305

0.0886

Model 359

5/10

0.0358

0.6657

0.0069

0.0440

0.6018

0.0081

0.1652

0.4309

0.1288

Model 360

5/15

0.0352

0.6392

0.0042

0.0362

0.6139

0.0041

0.1734

0.3052

0.1076

From Table 27, it has been observed that the performance of GDM algorithm-based ANN models has been decreased with the number of hidden layers. It has also been observed that the GDM ANN models have less capacity in predicting the MDD of soil. The training performance of developed models is less than 0.9. Therefore, the GDM ANN models have not achieved performance equal to or more than 0.9. Model 346 has been identified as a better performance model in predicting MDD of soil with a performance of 0.8709.

5. Using Gradient Descent (GD) Algorithm Based Neural Network Models

Artificial neural networks have been developed to predict the MDD of soil using the GD algorithm. The performance of GD algorithm-based models is given in Table 28.

Table 28. Performance of GD Algorithm-based ANN models for maximum dry density

Model ID

HL/N

Training

Validation

Testing

RMSE

R

MAE

RMSE

R

MAE

RMSE

R

MAE

Model 361

1/5

0.0318

0.7484

0.0012

0.0372

0.6602

0.0016

0.0840

0.8708

0.0611

Model 362

1/10

0.0539

0.4981

0.0039

0.0488

0.4842

0.0032

0.2275

0.6592

0.1801

Model 363

1/15

0.0760

0.7989

0.0104

0.0852

0.7581

0.0128

0.2411

0.8963

0.1977

Model 364

2/5

0.0486

0.3981

0.0043

0.0489

0.6733

0.0050

0.1366

0.5304

0.1100

Model 365

2/10

0.0566

0.8936

0.0064

0.0671

0.9105

0.0089

0.1886

0.9117

0.1174

Model 366

2/15

0.0428

0.6924

0.0185

0.0574

0.6729

0.0176

0.3063

0.8548

0.2559

Model 367

3/5

0.0456

0.8158

0.0044

0.0433

0.8827

0.0035

0.1466

0.7977

0.0935

Model 368

3/10

0.0624

0.5455

0.0119

0.0720

0.6377

0.0146

0.2700

0.6445

0.2372

Model 369

3/15

0.0337

0.7264

0.0055

0.0257

0.8272

0.0046

0.0931

0.7454

0.0843

Model 370

4/5

0.0374

0.6219

0.0024

0.0363

0.7380

0.0024

0.0895

0.7544

0.0804

Model 371

4/10

0.0386

0.8349

0.0062

0.0452

0.8215

0.0066

0.1142

0.8327

0.0860

Model 372

4/15

0.0281

0.8093

0.0023

0.0248

0.8230

0.0019

0.1281

0.7927

0.0967

Model 373

5/5

0.0265

0.8615

0.0008

0.0253

0.8238

0.0008

0.1080

0.8586

0.0867

Model 374

5/10

0.0268

0.8118

0.0011

0.0355

0.7089

0.0018

0.0600

0.9462

0.0498

Model 375

5/15

0.0395

0.6910

0.0039

0.0337

0.6571

0.0030

0.1310

0.7885

0.1099

From Table 28, it has been observed that the GD algorithm-based ANN model has predicted MDD of soil with a performance of less than 0.8, which is less acceptable. Therefore, model 374 has been identified as a better performance model in predicting MDD of soil with a performance of 0.9462.

6. Using Gradient Descent Algorithm with Adaptive Learning (GDA) Based Neural Network Models

Artificial neural networks have been developed to predict the MDD of soil using the GDA algorithm. The performance of GDA algorithm-based models is given in Table 29.

Table 29. Performance of GDA Algorithm-based ANN models for maximum dry density

Model ID

HL/N

Training

Validation

Testing

RMSE

R

MAE

RMSE

R

MAE

RMSE

R

MAE

Model 376

1/5

0.0138

0.9540

0.0025

0.0125

0.9553

0.0022

0.1172

0.9186

0.0938

Model 377

1/10

0.0140

0.9502

0.0081

0.0155

0.9451

0.0097

0.1438

0.8354

0.1014

Model 378

1/15

0.0154

0.9437

0.0018

0.0143

0.9368

0.0016

0.1161

0.9642

0.0952

Model 379

2/5

0.0203

0.8985

0.0014

0.0193

0.8968

0.0021

0.0945

0.7407

0.0574

Model 380

2/10

0.0134

0.9545

0.0280

0.0141

0.9579

0.0266

0.0661

0.9598

0.0537

Model 381

2/15

0.0143

0.9524

0.0027

0.0178

0.9102

0.0028

0.0656

0.9490

0.0543

Model 382

3/5

0.0158

0.9362

0.0029

0.0152

0.9466

0.0030

0.1103

0.8490

0.0857

Model 383

3/10

0.0173

0.9198

0.0126

0.0172

0.9415

0.0133

0.0997

0.8452

0.0776

Model 384

3/15

0.0171

0.9351

0.0110

0.0175

0.8902

0.0117

0.1399

0.7945

0.0998

Model 385

4/5

0.0137

0.9485

0.0005

0.0131

0.9669

0.0006

0.0881

0.9428

0.0745

Model 386

4/10

0.0156

0.9387

0.0061

0.0287

0.7949

0.0077

0.0839

0.7981

0.0568

Model 387

4/15

0.0179

0.9196

0.0074

0.0191

0.8982

0.0068

0.1095

0.8881

0.0896

Model 388

5/5

0.0153

0.9390

0.0042

0.0185

0.9193

0.0045

0.0783

0.9501

0.0705

Model 389

5/10

0.0221

0.8763

0.0032

0.0225

0.8692

0.0033

0.1065

0.8193

0.0953

Model 390

5/15

0.0175

0.9169

0.0035

0.0230

0.9018

0.0048

0.0801

0.8948

0.0685

From Table 29, it has been observed that the GDA algorithm-based ANN models employed with 5/15 neurons have predicted MDD of soil with a performance of more than 0.85. Thus, Model 378 has been identified as a better performance model with a performance of 0.9642.

The performance variation of ANN models configured with different backpropagation algorithms for predicting soil optimum moisture content has been mapped, as shown in Fig. 6.

Fig. 6 depicts the performance variation of ANN models configured with different backpropagation algorithms in predicting the MDD of soil. The same pattern is mapped in the performance variation of ANN models in predicting MDD of soil. In a few cases, the performance of ANN models has continuously decreased with neurons. The maximum performance has been achieved by LM algorithm-based ANN models in predicting the MDD of soil. Therefore, it may be stated that the LM achieves better performance due to the strongly correlated datasets.

V. THE BEST ARCHITECTURE MODELS

The present research work has been carried out to predict the liquid limit, plasticity index, optimum moisture content, and maximum dry density. A total of 390 ANN models have been developed in the present work to identify the best architectural ANN models for predicting the geotechnical properties of soil. Models 3, 28, 45, 53, 69, and 83 have been identified as better performance models in predicting the liquid limit of soil. Similarly, Models 106, 118, 133, 152, 167, and 184 have been identified as better performance models in predicting soil plasticity index. The compaction parameters, namely maximum dry density and optimum moisture content, have also been predicted using artificial neural networks. Models 201, 220, 233, 252, 265, and 280 have been identified as better performance models in predicting the OMC of soil. Similarly, Models 312, 318, 331, 346, 374, and 378 have been identified as the better performance models in predicting MDD of soil. Finally, the best architectural ANN models have been identified by comparing the performance of better performance models, as shown in Fig. 7.

Fig. 7 depicts the performance comparison of the better performance models to identify the best architectural ANN Models for predicting LL, PI, OMC, and MDD of soil. Figure 7(a) shows that Model 83 has outperformed Models 3, 28, 45, 53, and 69 in predicting the liquid limit of soil with the performance of 0.9634. Figure 7(b) shows that Model 152 has outperformed Models 106, 118, 133, 167, and 184 in predicting the plasticity index of soil with a performance of 0.8634. Figure 7(c) shows that Model 201 has outperformed Models 220, 233, 252, 265, and 280 in predicting the OMC of soil. Figure 7 (d) shows that Model 312 has outperformed Models 318, 331, 346, 374, and 378 in predicting the MDD of soil. Models 83, 152, 201, and 312 have been configured with 3HL/10N, 3HL/5N, 1HL/5N, and 4HL/15N. Similarly, it has also been observed that the GDA algorithm-based ANN model has predicted LL with optimum performance of 0.9634, having strongly correlated datasets. But in the case of PI, the GDM algorithm-based ANN model has achieved a performance of 0.8634, having strongly correlated datasets. The LM, BFG, and SCG algorithm-based ANN models did not perform well. Therefore, models 201 and 312 of OMC and MDD have been identified as the best architectural ANN models. Models 201 and 312 have been configured with the LM backpropagation algorithm. The input (S, FC, LL, PI) and output (OMC, MDD) compaction parameters are strongly to very strongly correlated. Therefore, it may be stated that the LM backpropagation algorithm-based ANN model requires strongly to very strongly correlated datasets to achieve higher performance and prediction accuracy. The artificial neural network models have been classified based on their performance, as shown in Fig. 8.

Fig. 8 depicts the classification of ANN models based on test performance. The artificial neural network model is classified as a robust, high, moderate, and good performance model if the model has a performance of more than 0.95, between 0.9-0.95, between 0.8-0.9, and less than 0.8, respectively. The following formulas have also been suggested for the required number of hidden layers and neurons to achieve robust or high-performance during prediction by ANN models. The suggested equations are applicable only for datasets with a correlation coefficient of more than 0.85.

Conclusion

The present research work was carried out to determine the best architecture models to predict soil\'s consistency limits and compaction parameters. On the other hand, hidden layers, neurons, and backpropagation algorithms were studied while predicting consistency limits and compaction parameters. The artificial neural network models were developed using the different number of hidden layers (one to five), neurons (5, 10 & 15), and backpropagation algorithms (LM, BFG, SCG, GDM, GD & GDA). The present study maps the following conclusions. 1) In the prediction of liquid limit, it was observed that the performance of the LM algorithm-based ANN model was decreased with increasing the number of hidden layers and neurons. On the other hand, the performance of BFG and SCG algorithm-based ANN models was increased by increasing the hidden layers and neurons. The performance of the GDA, GD and GDM algorithm-based ANN model was increased up to 3 hidden layers interconnecting with 10/15 neurons. Therefore, it may be stated that the LM requires the least hidden layers and neurons for achieving a performance of more than 0.9. Thus, Models 3 (LM), 28 (BFG), 45 (SCG), 53 (GDM), 69 (GD), and 83 (GDA) were identified as better performance models in predicting the liquid limit of soil. Models 3, 28, 45, 53, 69, and 83 showed that Model 83 outperformed other better performance liquid limit models with a performance of 0.9634. 2) In the prediction of plasticity index, it was observed that the performance of LM algorithm-based ANN models was increased up to two hidden layers interconnected with 15 neurons (Model 106). Further, the performance of the LM algorithm-based ANN model was started decreasing. The performance of the BFG and SCG algorithm-based ANN model decreased with an increasing number of hidden layers and neurons. On the other hand, the performance of the GDA, GD, and GDM algorithm-based ANN model was increased up to 3 hidden layers interconnected with 5/15 neurons. Therefore, it may be stated that the BFG and SCG algorithm-based ANN model requires the least hidden layer and neurons for achieving a performance of more than 0.75. Thus, Models 106, 118, 133, 152, 167, and 184 were identified as better performance models in predicting the plasticity index of soil. Models 106, 118, 133, 152, 167, and 184 showed that Model 152 outperformed other better performance plasticity index models with a performance of 0.8634. 3) In the prediction of optimum moisture content, it was observed that the performance of LM algorithm-based ANN models was decreased with the number of hidden layers and neurons (Models 201 to 215). The SCG algorithm-based ANN model 233 achieved a performance of 0.9789. Model 233 was configured with one hidden layer interconnected with 15 neurons. Similarly, the BFG algorithm-based ANN model 220 achieved a performance of 0.9786, which was close to the performance of Model 233. Model 220 was configured with two hidden layers interconnected with ten neurons. Furthermore, it was stated that the SCG algorithm-based ANN model 233 requires less hidden layers and neurons. The GDM, GD, and GDA algorithm-based ANN models achieved performance of 0.9416 (3 HL, 5N), 0.9353 (2HL, 10N), and 0.9515 (2HL, 10N), respectively. Thus, Models 201, 220, 233, 252, 265, and 280 were identified as better performance models in predicting the OMC of soil. Models 201, 220, 233, 252, 265, and 280 showed that Model 201 outperformed other better performance optimum moisture content models with a performance of 0.9822. 4) In the prediction of maximum dry density, it was observed that the performance of LM algorithm-based ANN models was increased with a number of hidden layers and neurons (Models 301 to 315). Model 312 predicted MDD of soil with a performance of 0.9784. The BFG and GDA algorithm-based ANN models predicted MDD of soil with a performance of 0.9654 and 0.9642, respectively. Therefore, it may be stated that the BFG and GDA algorithm achieves approximate equal performance if the model is configured with one hidden layer interconnected with 15 neurons. On the other hand, GDM and SCG algorithm-based ANN model\'s performance decreased with the increasing number of hidden layers and neurons. The GD algorithm-based ANN model achieved a performance of 0.9462 configured with five hidden layers interconnected with ten neurons. Thus, Models 312, 318, 331, 346, 374, and 378 were identified as the better performance model. The performance comparison showed that Model 312 outperformed the other ANN models in predicting the MDD of soil. The above statements show that the performance of artificial neural networks is affected by the number of hidden layers, neurons, and backpropagation algorithms. Finally, it may be concluded that the consistency limits of soil may be predicted with high accuracy using LM (1HL, 15N), BFG (5HL, 5N), SCG (5HL, 15N), GDM (3HL, 10N), GD (3HL, 15N) and GDA (3HL, 10N) algorithms for ANN models. Similarly, the compaction parameters of soil may be predicted with high accuracy using LM (1HL, 5N), BFG (2HL, 10N), SCG (1HL, 15N), GDM (3HL, 5N), GD (2HL, 10N), and GDA (2HL, 10N) algorithms for ANN models. The strength parameters are affected by the size of the particle and consistency limits. Therefore, the proposed ANN models of compaction parameters can be used to predict the UCS, C, and phi parameters of soil.

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Copyright

Copyright © 2022 Jitendra Khatti, Dr. Kamaldeep Singh Grover. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

IJRASET43662

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Authors : Jitendra Khatti

Paper Id : IJRASET43662

Publish Date : 2022-05-31

ISSN : 2321-9653

Publisher Name : IJRASET

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