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New Applications of a Supervised Computational Intelligence (CI) Approach: Case Study in Civil Engineering

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Supervised and Unsupervised Learning for Data Science

Abstract

In this study, artificial neural network (ANN) techniques are used in an attempt to predict the nonlinear hyperbolic soil stress–strain relationship parameters (k and R f). Two ANN models are developed and trained to achieve the planned target, in an attempt at making the experimental test (unconsolidated undrained triaxial test) unnecessary. The first is logarithm of modulus number (log k), and the second is failure ratio (R f). A database of laboratory measurements comprises a total of (83) case records for modulus number (k) and failure ratio (R f). Four parameters are considered to have the most significant impact on the nonlinear soil stress–strain relationship parameters, which are used as an independent input variables (IIVs) to the developed the proposed ANNs models. These comprise of: Plasticity index (PI), Dry unit weight (γ dry), Water content (ω o), and Confining stress (σ 3), the output models are respectively, (log k), and (R f). Multilayer perceptron trainings using back-propagation algorithm are used in this work. The effect of a number of issues in relation to ANN construction such as ANN geometry and internal parameters on the performance of ANN models is investigated. Information on the relative importance of the factors affecting the (log k), and (R f) is presented, and practical equations for their prediction are proposed.

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Acknowledgments

The authors would like to acknowledge the Iraqi Ministry of Higher Education and Scientific Research and Wasit University for the grant provided to carry out this research under the grant agreement number 162575, dated 28/05/2013, with the Liverpool John Moores University, university reference number (744221).

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Correspondence to Ameer A. Jebur .

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Appendices

Appendix 1

Case no.

Reference

Unified soil classif.

Cohesion (kN/m2)

Friction angle

PI (%)

Dry unit weight γ d (kN/m3)

Water content ω c (%)

Confining stress (kN/m2)

log k

n

R f

1

Wong and Duncan [23]

ML

193.68

19

4

17.4

15.6

860.672

2.301

0.59

0.86

2

Wong and Duncan [23]

ML

41.964

30

4

17.5

12.7

860.672

1.4314

1.43

0.72

3

Wong and Duncan [23]

ML

45.192

31

1

16.65

11.6

349.648

2.3802

0.31

0.83

4

Wong and Duncan [23]

ML

20.444

31

1

16.65

13.6

403.44

2.4314

0.38

0.82

5

Wong and Duncan [23]

ML

58.104

27

1

16.65

16.6

403.44

2

0.84

0.77

6

Wong and Duncan [23]

CL

57.028

29

20

17.4

16.7

715.433

2.415

0.6

0.87

7

Wong and Duncan [23]

CL

129.12

14

20

17.13

19.5

494.886

1.5911

0.48

0.58

8

Wong and Duncan [23]

CL

102.22

0

23

17.15

19.1

193.651

1.8195

0

0.75

9

Wong and Duncan [23]

CL

45.192

0

23

16.65

21.2

193.651

1

0.03

0.52

10

Wong and Duncan [23]

CL

107.6

31

22

16.33

21.7

193.651

1.5563

0

0.57

11

Wong and Duncan [23]

CL

98.992

17

16

16.87

11.5

215.168

2.8129

−0.68

0.9

12

Wong and Duncan [23]

CL

161.4

6

16

17.46

14.3

376.544

2.8261

−0.14

0.93

13

Wong and Duncan [23]

CL

139.88

24

16

17.45

16.8

376.544

2.6335

0.1

0.93

14

Wong and Duncan [23]

CL

193.68

13

16

18

11.5

376.544

3.3802

−0.74

0.92

15

Wong and Duncan [23]

CL

204.44

32

16

18.36

14.5

376.544

3.301

−0.3

0.97

16

Wong and Duncan [23]

CL

161.4

18

16

17.41

8.71

376.544

3.9494

−1.1

0.94

17

Wong and Duncan [23]

CL

139.88

29

16

19.1

11.7

376.544

3.699

−0.28

0.95

18

Wong and Duncan [23]

CL

68.864

25

15

16.81

12.5

403.44

2.5051

−0.21

0.8

19

Wong and Duncan [23]

CL

53.8

2

15

16.81

14.5

349.648

2.2788

0.02

0.81

20

Wong and Duncan [23]

CL

107.6

1

30

17.13

17.2

349.648

1.8692

0.23

0.87

21

Wong and Duncan [23]

CL

107.6

1

30

16.36

17

349.648

1.8325

−0.05

0.84

22

Wong and Duncan [23]

CL

48.42

25

30

16.42

20

349.648

1.4314

0.18

0.85

23

Wong and Duncan [23]

CL

61.332

4

16

17.33

14.6

349.648

2.5051

0.29

0.85

24

Wong and Duncan [23]

CL

161.4

3

32

15.54

23.2

349.648

2.301

0.29

0.89

25

Wong and Duncan [23]

CL

129.12

1

32

14.68

23.3

403.44

2

0.18

0.86

26

Wong and Duncan [23]

CL

68.864

22

32

14.53

26.7

349.648

1.7243

0.14

0.9

27

Wong and Duncan [23]

CL

90.384

22

16

17.9

15.1

349.648

2.2041

0.34

0.79

28

Wong and Duncan [23]

CL

59.18

28

16

17

15

349.648

2.4624

0.27

0.91

29

Wong and Duncan [23]

CL

83.928

25

12

16

13.5

349.648

2.8325

−0.36

0.84

30

Wong and Duncan [23]

CL

161.4

6

12

17

13.3

349.648

2.7782

0.18

0.68

31

Wong and Duncan [23]

CL

79.624

18

12

16.42

19.3

349.648

1.3617

0.32

0.61

32

Wong and Duncan [23]

CL

97.916

20

12

17

16.7

349.648

2.4472

0.6

0.93

33

Wong and Duncan [23]

CL

71.016

8

12

16.25

16.3

349.648

2.3424

0.23

0.9

34

Wong and Duncan [23]

CL

139.88

13

25

16.8

18.6

349.648

2.1461

0.2

0.84

35

Wong and Duncan [23]

CL

107.6

2

25

16.31

17.1

349.648

2.0792

0.09

0.83

36

Wong and Duncan [23]

CL

86.08

24

25

16.5

19.7

349.648

1.6721

0.33

0.82

37

Wong and Duncan [23]

CL

161.4

8

25

17

13.9

349.648

2.9777

−0.15

0.9

38

Wong and Duncan [23]

CL

161.4

4

25

17.33

16.9

349.648

2.6721

0

0.95

39

Wong and Duncan [23]

CL

72.092

23

23

15.8

20.8

349.648

1.8751

0.44

0.88

40

Wong and Duncan [23]

CL

193.68

12

23

16.8

14.8

349.648

2.9243

−0.19

0.84

41

Wong and Duncan [23]

CL

129.12

29

23

16.2

17.4

349.648

2.4314

0.6

0.87

42

Wong and Duncan [23]

CL

150.64

13

23

16

14.2

349.648

3.0414

−0.36

0.83

43

Wong and Duncan [23]

CL

150.64

2

23

16.71

17.5

349.648

2.6128

0.15

0.87

44

Wong and Duncan [23]

CL

82.852

1

27

15.68

24

322.752

1.7559

0.43

0.86

45

Wong and Duncan [23]

CL

104.372

2

18

15.96

22.9

215.168

2.0414

0.43

0.9

46

Wong and Duncan [23]

CL

118.36

1

20

15.86

22.7

430.336

2

0.27

0.89

47

Wong and Duncan [23]

CL

106.524

3

24

15.7

23.9

430.336

2.2041

0.54

0.97

48

Wong and Duncan [23]

CL

118.36

2

24

15.83

22.7

430.336

2.1139

0.46

0.91

49

Wong and Duncan [23]

CL

83.928

0

24

15.5

22.7

430.336

1.7243

0.41

0.85

50

Wong and Duncan [23]

CL

129.12

0

26

15.62

23.4

860.672

2.3802

0

0.95

51

Wong and Duncan [23]

CL

102.22

12

24

17.19

18.1

860.672

2.2041

0

0.93

52

Wong and Duncan [23]

CL

172.16

20

18

18.38

12.2

403.44

2.1761

0.16

0.79

53

Wong and Duncan [23]

CL

215.2

20

20

17.75

13

823

2.6435

0.17

0.85

54

Wong and Duncan [23]

CL

269

16

19

18.54

13.1

823

2.6435

0.34

0.86

55

Wong and Duncan [23]

CL

107.6

11

19

18

16.2

392.681

2.0414

0.94

0.91

56

Wong and Duncan [23]

CL

150.64

9

19

17.96

16.6

274.339

1.8261

0.71

0.77

57

Wong and Duncan [23]

CL

107.6

3

19

17.65

17.3

279.718

1.5682

0.37

0.65

58

Wong and Duncan [23]

CL

236.72

4

19

17

16.2

946.739

1.8513

1.06

0.98

59

Wong and Duncan [23]

CL

65.636

0

19

14.4

28.8

215.168

1.9638

0.21

0.89

60

Wong and Duncan [23]

CL

39.812

1

38

15.73

31.1

193.651

1.3222

0

0.65

61

Wong and Duncan [23]

CL

54.876

1

36

14.77

28.6

193.651

1.8261

0.02

0.79

62

Wong and Duncan [23]

CL

67.788

0

45

10.63

26.5

215.168

1.8129

0.14

0.77

63

Wong and Duncan [23]

CL

129.12

2

36

14.45

27.4

860.672

1.5563

0.72

0.91

64

Wong and Duncan [23]

SC

279.76

26

36

14.52

24.4

860.672

1.716

0.66

0.89

65

Wong and Duncan [23]

SC

193.68

4

11

19.72

9.6

1452.38

3.5911

−0.08

0.93

66

Wong and Duncan [23]

CL

98.992

31

18

20.17

8.3

107.584

2.7076

0.37

0.64

67

Wong and Duncan [23]

CL

161.4

17

16

16.87

11.5

215.168

2.8129

−0.68

0.9

68

Wong and Duncan [23]

CL

139.88

6

16

17.46

14.3

376.544

2.8261

−0.14

0.93

69

Wong and Duncan [23]

CL

193.68

24

16

17.45

16.8

376.544

2.6335

0.1

0.93

70

Wong and Duncan [23]

CL

204.44

13

16

18.04

11.5

376.544

3.3802

−0.74

0.92

71

Wong and Duncan [23]

CL

161.4

32

16

18.36

14.5

215.168

3.301

−0.3

0.97

72

Wong and Duncan [23]

CL

139.88

18

16

17.41

8.71

376.544

3.9494

−1.1

0.94

73

Wong and Duncan [23]

CL

68.864

29

16

19

11.7

376.544

3.699

−0.28

0.95

74

Boscardin [26]

ML

28

34

4

18.05

12.1

207.5

2.6435

0.4

0.95

75

Boscardin [26]

ML

24

32

4

17.1

12.1

207.5

2.301

0.26

0.89

76

Boscardin [26]

ML

21

30

4

16.15

12.1

207.5

2.0414

0.25

0.85

77

Boscardin [26]

ML

17

28

4

15.2

12.1

207.5

1.8751

0.25

0.8

78

Boscardin [26]

ML

0

23

4

11.59

12.1

207.5

1.2041

0.95

0.55

79

Boscardin [26]

CL

62

13

15

15.67

21

207.5

2.0792

0.45

1

80

Boscardin [26]

CL

48

15

15

14.85

21

207.5

1.8751

0.54

0.94

81

Boscardin [26]

CL

41

14

15

14.02

21

207.5

1.699

0.6

0.9

82

Boscardin [26]

CL

35

13

15

13.2

21

207.5

1.5441

0.66

0.87

83

Boscardin [26]

CL

0

19

15

10.06

21

207.5

1.2041

0.95

0.75

Appendix 2

 

Input variables

Output variables

Case no.

PI

Dry unit weight (kN/m3)

Water content ω o (%)

Confining stress (kN/m2)

R f

n

log k

1

4

17.4

15.6

860.672

0.86

0.59

2.30103

2

4

17.5

12.7

860.672

0.72

1.43

1.43136

3

1

16.65

11.6

349.648

0.83

0.31

2.38021

4

1

16.65

13.6

403.44

0.82

0.38

2.43136

5

1

16.65

16.6

403.44

0.77

0.84

2

6

20

17.4

16.7

715.433

0.87

0.6

2.41497

7

20

17.13

19.5

494.886

0.58

0.48

1.59106

8

23

17.15

19.1

193.651

0.75

0

1.81954

9

23

16.65

21.2

193.651

0.52

0.03

1

10

22

16.33

21.7

193.651

0.57

0

1.5563

11

16

16.87

11.5

215.168

0.9

−0.68

2.81291

12

16

17.46

14.3

376.544

0.93

−0.14

2.82607

13

16

17.45

16.8

376.544

0.93

0.1

2.63347

14

16

18

11.5

376.544

0.92

−0.74

3.38021

15

16

18.36

14.5

376.544

0.97

−0.3

3.30103

16

16

17.41

8.71

376.544

0.94

−1.1

3.94939

17

16

19.1

11.7

376.544

0.95

−0.28

3.69897

18

15

16.81

12.5

403.44

0.8

−0.21

2.50515

19

15

16.81

14.5

349.648

0.81

0.02

2.27875

20

30

17.13

17.2

349.648

0.87

0.23

1.86923

21

30

16.36

17

349.648

0.84

−0.05

1.83251

22

30

16.42

20

349.648

0.85

0.18

1.43136

23

16

17.33

14.6

349.648

0.85

0.29

2.50515

24

32

15.54

23.2

349.648

0.89

0.29

2.30103

25

32

14.68

23.3

403.44

0.86

0.18

2

26

32

14.53

26.7

349.648

0.9

0.14

1.72428

27

16

17.9

15.1

349.648

0.79

0.34

2.20412

28

16

17

15

349.648

0.91

0.27

2.4624

29

12

16

13.5

349.648

0.84

−0.36

2.83251

30

12

17

13.3

349.648

0.68

0.18

2.77815

31

12

16.42

19.3

349.648

0.61

0.32

1.36173

32

12

17

16.7

349.648

0.93

0.6

2.44716

33

12

16.25

16.3

349.648

0.9

0.23

2.34242

34

25

16.8

18.6

349.648

0.84

0.2

2.14613

35

25

16.31

17.1

349.648

0.83

0.09

2.07918

36

25

16.5

19.7

349.648

0.82

0.33

1.6721

37

25

17

13.9

349.648

0.9

−0.15

2.97772

38

25

17.33

16.9

349.648

0.95

0

2.6721

39

23

15.8

20.8

349.648

0.88

0.44

1.87506

40

23

16.8

14.8

349.648

0.84

−0.19

2.92428

41

23

16.2

17.4

349.648

0.87

0.6

2.43136

42

23

16

14.2

349.648

0.83

−0.36

3.04139

43

23

16.71

17.5

349.648

0.87

0.15

2.61278

44

27

15.68

24

322.752

0.86

0.43

1.75587

45

18

15.96

22.9

215.168

0.9

0.43

2.04139

46

20

15.86

22.7

430.336

0.89

0.27

2

47

24

15.7

23.9

430.336

0.97

0.54

2.20412

48

24

15.83

22.7

430.336

0.91

0.46

2.11394

49

24

15.5

22.7

430.336

0.85

0.41

1.72428

50

26

15.62

23.4

860.672

0.95

0

2.38021

51

24

17.19

18.1

860.672

0.93

0

2.20412

52

18

18.38

12.2

403.44

0.79

0.16

2.17609

53

20

17.75

13

823

0.85

0.17

2.64345

54

19

18.54

13.1

823

0.86

0.34

2.64345

55

19

18

16.2

392.681

0.91

0.94

2.04139

56

19

17.96

16.6

274.339

0.77

0.71

1.82607

57

19

17.65

17.3

279.718

0.65

0.37

1.5682

58

19

17

16.2

946.739

0.98

1.06

1.85126

59

19

14.4

28.8

215.168

0.89

0.21

1.96379

60

38

15.73

31.1

193.651

0.65

0

1.32222

61

36

14.77

28.6

193.651

0.79

0.02

1.82607

62

45

10.63

26.5

215.168

0.77

0.14

1.81291

63

36

14.45

27.4

860.672

0.91

0.72

1.5563

64

36

14.52

24.4

860.672

0.89

0.66

1.716

65

11

19.72

9.6

1452.38

0.93

−0.08

3.59106

66

18

20.17

8.3

107.584

0.64

0.37

2.70757

67

16

16.87

11.5

215.168

0.9

−0.68

2.81291

68

16

17.46

14.3

376.544

0.93

−0.14

2.82607

69

16

17.45

16.8

376.544

0.93

0.1

2.63347

70

16

18.04

11.5

376.544

0.92

−0.74

3.38021

71

16

18.36

14.5

215.168

0.97

−0.3

3.30103

72

16

17.41

8.71

376.544

0.94

−1.1

3.94939

73

16

19

11.7

376.544

0.95

−0.28

3.69897

74

4

18.05

12.1

207.5

0.95

0.4

2.64345

75

4

17.1

12.1

207.5

0.89

0.26

2.30103

76

4

16.15

12.1

207.5

0.85

0.25

2.04139

77

4

15.2

12.1

207.5

0.8

0.25

1.87506

78

4

11.59

12.1

207.5

0.55

0.95

1.20412

79

15

15.67

21

207.5

1

0.45

2.07918

80

15

14.85

21

207.5

0.94

0.54

1.87506

81

15

14.02

21

207.5

0.9

0.6

1.69897

82

15

13.2

21

207.5

0.87

0.66

1.54407

83

15

10.06

21

207.5

0.75

0.95

1.20412

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Jebur, A.A. et al. (2020). New Applications of a Supervised Computational Intelligence (CI) Approach: Case Study in Civil Engineering. In: Berry, M., Mohamed, A., Yap, B. (eds) Supervised and Unsupervised Learning for Data Science . Unsupervised and Semi-Supervised Learning. Springer, Cham. https://doi.org/10.1007/978-3-030-22475-2_8

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