PSI - Issue 17

Danial J. Armaghani et al. / Procedia Structural Integrity 17 (2019) 924–933 Danial J. Armaghaniet al. / Structural Integrity Procedia 00 (2019) 000 – 000

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The optimum NN models with their basic structural characteristics such as type of activation function and use or not of Minmax normalization technique are presented in Table 2. It should be stated that the evaluation and the associated ranking of NN models has been based on a20-index. Furthermore, in Table 3 the values of the five statistical indexes for each one optimum NN models both for test and all datasets are presented. The above achieved optimums ANN models of each one of the four cases are compared with the available in the literature code regulations and other researcher’s proposals. Namely, comparisons with the Eurocode (EC2), ACI building code, Canadian Code, New Zealand Standards and with proposal of Gandomi et al. (2017) have been contacted. The comparison results are shown in Table 4. It is clearly shown that the proposed optimum NN models of all four cases predict the shear strength of reinforced concrete beams much better than the available in the literature proposals. Furthermore, the optimum NN model with five (5) input parameters (5-28-24-1) that corresponds to the case C evaluate the shear capacity of reinforced concrete beams in a trustworthy and effective manner, while at the same time is much simpler having only five input parameters.

Table 1. Parameters and statistics of database

Variables

Data used in NN models

No

Name

Symbol

Type

Unit

Min

Average

Max

STD 97.49

80.00

195.12

612.14

1

Width of beam

mm

b d

132.08

414.64

1097.28 221.57

2

Effective depth of beam

mm

Cylinder compressive strength of concrete

12.76

36.29

103.23

19.99

3

MPa

f c

Yield stress of longitudinal reinforcement Yield stress of longitudinal reinforcement

0.00

418.18

910.11

135.54

4

MPa

f y

Input

0.00

284.72

1414.17 365.18

5

MPa

f yw

0.61

2.39

9.05

1.33

6

Shear span /Effective depth of beam

-

a/d

0.00

2.41

4.54

1.10

7

Longitudinal reinforcement ratio

(%)

ρ l

0.00

0.28

2.25

0.38

(%)

8

Transverse reinforcement ratio

ρ w

1.22

5.86

20.01

3.19

-

9

Effective span / depth of beam

L/d

0.59

3.46

12.85

2.27

MPa

10

Shear strength

V

Output

Table 2.Structural characteristics of the optimum ANN models for each one the four cases

Activation function

Number of Hidden Layers

Normalization (Minmax in the range 0.10 – 0.90)

a20 index

Case

Architecture

1st Hidden Layer

2nd Hidden LayerHL

Output Layer

A

9-30-4-1 7-19-28-1 5-28-24-1 4-24-12-1

0.9667 0.9300 0.9200 0.7867

2 2 2 2

yes

T T L T

T L L L

P P P P

B

no

C D

yes yes

Note T: Hyperbolic Tangent Sigmoid transfer function (tansigmatlab function) L: Log-sigmoid transfer function (logsigmatlab function) P: Linear transfer function (purelinmatlab function)