GMDH-Network to Estimate the Punching Capacity of FRP-RC Slabs

Document Type: Regular Article

Author

Dept. of Civil Engineering, University of Birmingham, United Kingdom

Abstract

Determination of the punching shear capacity of FRP-reinforced concrete slabs was studied in this paper. A database including 81 pairs of data was collected and used. The method was considered in the paper, was group method of data handling (GMDH) which is one of the most structures which is used by researchers. The section area of column, effective flexural depth of slab, compressive strength of concrete, Young’s modulus of the FRP slab and reinforcement ratio were used as input variables. The target of the model was also determination of the ultimate punching capacity of the FRP-reinforced concrete flat slab (Target). Based on this dataset, ten polynomials specified and its coefficients was presented. All of these ten polynomials used for the considered prediction. The proposed GMDH structure also validate by several experimental data. The results indicated that group method of data handling (GMDH) is very useful for the prediction of the punching shear capacity of slabs.

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Main Subjects


1. Introduction

Group Method of Data Handling (GMDH) which presented by Ivakhnenko [1] is a powerful method to create a mathematical network based on a multilayered perceptron-type network structure. The use of this method studied by a lot of researchers in many fields of engineering. In Structural engineering, soft computing approaches such as ANN and also fuzzy systems are very popular and used for prediction [2-4] or for FRP material [5]. GMDH as one of the soft computing approach GMDH is a useful method to create equations which can be used in the codes. An essential different between this type of network and other networks is the mathematical approach which can help to understand the way of the solution. GMDH is a neural network structure for function approximation of complex engineering problems. In this paper, punching shear capacity of FRP-reinforced concrete slabs was estimated by GMDH based on experimental data which were published in literatures.

2. Experimental Data

For train the GMDH structure, the author used 81 pairs of data which were published by researchers [6-8]. The details of the database is presented in Table. 1. The section area of column (Input 1), effective flexural depth of slab (Input 2), compressive strength of concrete (Input 3), Young’s modulus of the FRP slab (Input 4) and reinforcement ratio (Input 5) are considered as input parameters that determine the ultimate punching capacity of the FRP-reinforced concrete flat slab (Target). 69 data used for training phase of the selected GMDH and 12 remained data was used for validating the proposed structure.

Table 1. Range of experimental date

Type

Input1

Input2

Input3

Input4

Input5

Target

Mean

625.000

131.000

38.600

48.200

0.810

329.000

Minimum

50.270

55.000

26.000

28.400

0.180

61.000

Maximum

2025.000

284.000

75.800

147.600

3.780

1600.000

Standard deviation

572.349

60.440

10.122

33.125

0.695

355.903

 

3. GMDH Network for prediction

Based on five inputs and one output, the best structure of GMDH for prediction of the considered goal had three layers and ten polynomials. This structure showed in Fig. 1. Each of this polynomial is a two-order polynomial with two variables which is defined by Eq. 1:

      n=1,...,10

(1)

where,  and  are the input variable i and j.

The coefficients of the polynomials for the proposed structure of GMDH presented in Table. 2. These values determined based on normal values between 0.1 to 0.9. It means that for any prediction by the proposed structure, first, the input values should be normalized. For this purpose, the author used the Eq. 2:

 

(2)

where , ,  and  are normalized, experimental, minimum and maximum values in the database respectively. It was clear that after calculating the normal value for the target, it can be simplicity converted to the real value.

 

Figure 1. The proposed GMDH structure

 

Table 2. Coefficients of the polynomials for GMDH structure

 

Coefficients of the polynomials

Polynomial

C1

C2

C3

C4

C5

C6

y1

-0.1331

0.8352

0.4037

-0.1833

-0.2475

0.3439

y2

0.3212

-0.1891

-0.9119

0.4542

0.5052

1.6049

y3

-0.2476

1.5969

0.7983

-1.1768

-0.7926

0.2705

y4

-0.0377

1.7376

-0.2021

-1.1957

0.2515

-0.4072

y5

0.1203

-0.0822

0.0031

-0.4463

-1.1091

3.5583

y6

0.0384

0.0215

0.5142

1.1856

-0.0094

-0.4107

y7

0.0835

0.6307

-0.3364

2.3476

2.7797

-4.2688

y8

0.0012

0.8388

0.1302

-0.3876

0.4114

0.0400

y9

0.0153

0.6031

0.2581

1.7816

2.2043

-3.8154

y10

0.0096

0.3101

0.6180

22.6804

21.9818

-44.6125

 

4. Results of the GMDH structure

as mentioned in the section 2, the number of training data and test data in this paper were 69 and 12 respectively. The results of the proposed structure of the GMDH presented in Fig. 2-4.

 

Figure 2. The results for train data.

 

 

Figure 3. The results for test data.

 

The results of the train and test data showed that GMDH can be used for estimating the considered capacity. Correlation coefficient (R2) for train and test were 0.96 and 0.89 which was showed that GMDH had suitable results. Scatter plots of train and test were presented in Fig. 5-6.

 

Figure 4. The results for all data.

 

 

Figure 5. Scatter plot for train data (R2=0.96)

 

Figure 6. Scatter plot for train data (R2=0.89)

It was clear from the figures 2 and 3 that it was clear that the ANN-GA had suitable results and can be used for the shear capacity prediction.

6. Conclusions

GMDH-neural network used to predict the punching shear capacity of RC-slabs in this paper. The proposed structure had five inputs and three layers. Each of layer had several nodes which was included a two-order polynomial with two variables. The GMDH network trained based on experimental data and also validated. It was concluded that GMDH with a suitable accuracy can be used for considered prediction.

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[2]       M. Mirrashid, "Earthquake magnitude prediction by adaptive neuro-fuzzy inference system (ANFIS) based on fuzzy C-means algorithm," Natural hazards, vol. 74, pp. 1577-1593, 2014.

[3]       M. Mirrashid, M. Givehchi, M. Miri, and R. Madandoust, "Performance investigation of neuro-fuzzy system for earthquake prediction " Asian journal of civil enginering (BHRC), vol. 17, pp. 213-223, 2016.

[4]       H. Naderpour and M. Mirrashid, "Compressive Strength of Mortars Admixed with Wollastonite and Microsilica," in Materials Science Forum, 2017, pp. 415-418.

[5]       H. Naderpour and M. Mirrashid, "Application of Soft Computing to Reinforced Concrete Beams Strengthened with Fibre Reinforced Polymers: A State-of-the-Art Review," in Computational techniques for civil and structural engineering ed Stirlingshire, UK: Saxe-Coburg Publications, 2015, pp. 305-323.

[6]       M. A. W. Hassan, "Punching Shear Behaviour of Concrete Two-way Slabs Reinforced with Glass Fiber-reinforced Polymer (GFRP) Bars," Université de Sherbrooke, 2013.

[7]       I. M. Metwally, "Prediction of punching shear capacities of two-way concrete slabs reinforced with FRP bars," HBRC Journal, vol. 9, pp. 125-133, 2013.

[8]       L. Nguyen-Minh and M. Rovňák, "Punching shear resistance of interior GFRP reinforced slab-column connections," Journal of Composites for Construction, vol. 17, pp. 2-13, 2012.