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International Journal of Fuzzy Logic and Intelligent Systems 2021; 21(2): 176-188

Published online June 25, 2021

https://doi.org/10.5391/IJFIS.2021.21.2.176

© The Korean Institute of Intelligent Systems

Application of Adaptive Neuro-Fuzzy Inference System for Evaluating Compressive Strength of Concrete

Deepak Kumar Sinha, Rupali Satavalekar, and Senthil Kasilingam

Department of Civil Engineering, Dr. B R Ambedkar National Institute of Technology, Jalandhar, India

Correspondence to :
Rupali Satavalekar (satavalekarr@nitj.com)

Received: January 14, 2021; Revised: March 30, 2021; Accepted: April 26, 2021

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0/) which permits unrestricted noncommercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The objectives of this study are to develop a model for predicting the compressive strength of concrete using an adaptive neuro-fuzzy inference system (ANFIS) and validate the mix proportion using artificial neural networks (ANNs) and by experimentation. A model was developed, and the compressive strength was predicted using the ANFIS (with the subtractive clustering method of the fuzzy inference system) by MATLAB programming. In the present study, two ANFIS models were considered: ANFIS models-1 and -2. ANFIS model-1 was developed to predict the 3-day compressive strength, whereas ANFIS model-2 predicts the 28-day compressive strength by considering the 3-day compressive strength data obtained using ANFIS model-1. It was observed that the errors in the 3- and 28-day compressive strengths were 6.33%, and 17.07%, respectively. Furthermore, experiments were performed for selective mixes—M40, M50, and M60—to verify the compressive strength obtained using the ANFIS model. The model results were verified against the experimental ones based on the mixes selected from the model, and the results were found to agree with the predicted ones, with a maximum deviation of 18%. Furthermore, an ANN model was developed to predict the compressive strength to verify the accuracy of the ANFIS model. The results predicted by the ANFIS and the ANN were compared with the original results available in the literature. A significant deviation was found between the ANN model results and the original results, however, the ANN model results presented the same trend as the original results. It was concluded that the ANFIS model results were highly consistent with the original results.

Keywords: Compressive strength of concrete, ANFIS, ANN, Subtractive clustering method, Experimental studies

Article

Original Article

International Journal of Fuzzy Logic and Intelligent Systems 2021; 21(2): 176-188

Published online June 25, 2021 https://doi.org/10.5391/IJFIS.2021.21.2.176

Copyright © The Korean Institute of Intelligent Systems.

Application of Adaptive Neuro-Fuzzy Inference System for Evaluating Compressive Strength of Concrete

Deepak Kumar Sinha, Rupali Satavalekar, and Senthil Kasilingam

Department of Civil Engineering, Dr. B R Ambedkar National Institute of Technology, Jalandhar, India

Correspondence to:Rupali Satavalekar (satavalekarr@nitj.com)

Received: January 14, 2021; Revised: March 30, 2021; Accepted: April 26, 2021

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0/) which permits unrestricted noncommercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The objectives of this study are to develop a model for predicting the compressive strength of concrete using an adaptive neuro-fuzzy inference system (ANFIS) and validate the mix proportion using artificial neural networks (ANNs) and by experimentation. A model was developed, and the compressive strength was predicted using the ANFIS (with the subtractive clustering method of the fuzzy inference system) by MATLAB programming. In the present study, two ANFIS models were considered: ANFIS models-1 and -2. ANFIS model-1 was developed to predict the 3-day compressive strength, whereas ANFIS model-2 predicts the 28-day compressive strength by considering the 3-day compressive strength data obtained using ANFIS model-1. It was observed that the errors in the 3- and 28-day compressive strengths were 6.33%, and 17.07%, respectively. Furthermore, experiments were performed for selective mixes—M40, M50, and M60—to verify the compressive strength obtained using the ANFIS model. The model results were verified against the experimental ones based on the mixes selected from the model, and the results were found to agree with the predicted ones, with a maximum deviation of 18%. Furthermore, an ANN model was developed to predict the compressive strength to verify the accuracy of the ANFIS model. The results predicted by the ANFIS and the ANN were compared with the original results available in the literature. A significant deviation was found between the ANN model results and the original results, however, the ANN model results presented the same trend as the original results. It was concluded that the ANFIS model results were highly consistent with the original results.

Keywords: Compressive strength of concrete, ANFIS, ANN, Subtractive clustering method, Experimental studies

Fig 1.

Figure 1.

Architecture of ANFIS [7].

The International Journal of Fuzzy Logic and Intelligent Systems 2021; 21: 176-188https://doi.org/10.5391/IJFIS.2021.21.2.176

Fig 2.

Figure 2.

Flowchart of modeling process.

The International Journal of Fuzzy Logic and Intelligent Systems 2021; 21: 176-188https://doi.org/10.5391/IJFIS.2021.21.2.176

Fig 3.

Figure 3.

ANFIS model-1.

The International Journal of Fuzzy Logic and Intelligent Systems 2021; 21: 176-188https://doi.org/10.5391/IJFIS.2021.21.2.176

Fig 4.

Figure 4.

ANFIS model-1 structure.

The International Journal of Fuzzy Logic and Intelligent Systems 2021; 21: 176-188https://doi.org/10.5391/IJFIS.2021.21.2.176

Fig 5.

Figure 5.

Training of ANFIS model-1.

The International Journal of Fuzzy Logic and Intelligent Systems 2021; 21: 176-188https://doi.org/10.5391/IJFIS.2021.21.2.176

Fig 6.

Figure 6.

Validation of ANFIS model-1.

The International Journal of Fuzzy Logic and Intelligent Systems 2021; 21: 176-188https://doi.org/10.5391/IJFIS.2021.21.2.176

Fig 7.

Figure 7.

ANFIS model-2.

The International Journal of Fuzzy Logic and Intelligent Systems 2021; 21: 176-188https://doi.org/10.5391/IJFIS.2021.21.2.176

Fig 8.

Figure 8.

ANFIS model-2 structure.

The International Journal of Fuzzy Logic and Intelligent Systems 2021; 21: 176-188https://doi.org/10.5391/IJFIS.2021.21.2.176

Fig 9.

Figure 9.

ANFIS model-2 training results.

The International Journal of Fuzzy Logic and Intelligent Systems 2021; 21: 176-188https://doi.org/10.5391/IJFIS.2021.21.2.176

Fig 10.

Figure 10.

Validation of ANFIS model-2.

The International Journal of Fuzzy Logic and Intelligent Systems 2021; 21: 176-188https://doi.org/10.5391/IJFIS.2021.21.2.176

Fig 11.

Figure 11.

ANFIS model-2 rule viewer.

The International Journal of Fuzzy Logic and Intelligent Systems 2021; 21: 176-188https://doi.org/10.5391/IJFIS.2021.21.2.176

Fig 12.

Figure 12.

Surface diagrams for 28-day strength function of (a) cement and water/cement ratio, (b) cement and 3-day strength, and (c) water/cement ratio and 3-day strength.

The International Journal of Fuzzy Logic and Intelligent Systems 2021; 21: 176-188https://doi.org/10.5391/IJFIS.2021.21.2.176

Fig 13.

Figure 13.

ANN model structure.

The International Journal of Fuzzy Logic and Intelligent Systems 2021; 21: 176-188https://doi.org/10.5391/IJFIS.2021.21.2.176

Fig 14.

Figure 14.

ANN results showing R2 values.

The International Journal of Fuzzy Logic and Intelligent Systems 2021; 21: 176-188https://doi.org/10.5391/IJFIS.2021.21.2.176

Fig 15.

Figure 15.

Comparison of ANFIS and ANN (present study) with original output (Yeh [21]).

The International Journal of Fuzzy Logic and Intelligent Systems 2021; 21: 176-188https://doi.org/10.5391/IJFIS.2021.21.2.176

Dataset used for modeling [21].

S. No.Cement (kg/m3)BFS (kg/m3)Fly ash (kg/m3)Water (kg/m3)Superplasticizer (kg/m3)CA (kg/m3)FA (kg/m3)Age (day)Compressive strength (MPa)
1540.000162.02.51040.0676.02879.99
2540.000162.02.51055.0676.02861.89
3332.5142.50228.00932.0594.027040.27
4332.5142.50228.00932.0594.036541.05
5198.6132.40192.00978.4825.536044.30
6266.0114.00228.00932.0670.09047.03
7380.095.00228.00932.0594.036543.70
8380.095.00228.00932.0594.02836.45
9266.0114.00228.00932.0670.02845.85
10475.000228.00932.0594.02839.29
11198.6132.40192.00978.4825.59038.07
12198.6132.40192.00978.4825.52828.02
1,030260.9100.578.3200.68.6864.5761.52832.40

Range of variables and 3-day compressive strength used in dataset-1 [21].

RangeCement (kg/m3)BFS (kg/m3)Fly ash (kg/m3)Water (kg/m3)Super-plasticizer (kg/m3)CA (kg/m3)FA (kg/m3)3-day compressive strength (MPa)
Min10200121.7508226052.3
Max540305.3174.74214.632.21134.5992.641.6

Range of variables and 28-day compressive strength used in dataset 2 [21].

RangeCement (kg/m3)BFS (kg/m3)Fly ash (kg/m3)Water (kg/m3)Super-plasticizer (kg/m3)CA (kg/m3)FA (kg/m3)28-day compressive strength (MPa)
Min10200121.7508015948.5
Max540359.4200.124732.21145992.681.8

Results of trials for dataset optimization.

S. NoType of dataTraining error (RMSE)Testing error (RMSE)
1Original data3.8394.216
2Increasing order data9.23179.221
3Normalized data2.84.492
4Variables expressed as ratio of cement2.533.2

Inputs converted into ratios of first variable (cement).

Cement (kg/m3)BFS/ cementFly ash/ cemnetWater/ cementSuper-plasticizer/ cementCA/cementFA/cement3-day compressive strength
139.601.5001.37535816607.55.780085968.06342182
349.000.0000.550143266032.3120348415.04919265
198.600.6700.96676737204.9264853984.1565961739.131420144
310.000.0000.61935483903.1322580652.7438709689.86640156
374.000.5100.4548128340.0270053482.4762032092.02326203234.39795764
313.300.8400.5601659750.0274497293.3415256941.95276093228.79941252
425.000.2500.3611764710.0388235292.0049411762.08729411833.39821744
425.000.2500.3562352940.0437647062.2023529411.89105882436.3009114
375.0002500.33760.06242.2722666672.64693333328.99936056
475.000.2500.03812631580.0187368421.7938947371.64526315837.79707432
469.000.2500.2938166310.0686567161.816844351.79211087440.1964508
425.000.2500.03611764710.0388235292.0049411762.08729411833.39821744
388.600.2500.4063304170.0311374162.1927431812.38214101928.096147
531.300.0000.2668925280.0530773571.6038019951.68210050841.2996124
425.000.2500.3611764710.0388235292.0049411762.08729411833.39821744
318.800.6700.4883939770.0448557092.6729356342.76160602325.2003478
401.800.2400.3668491790.028373252.3563962172.12070681941.09966436
362.600.5200.4547710980.0319911752.6053502482.08439051335.3011712
323.700.8700.56780970.0318195862.9122644422.03861600228.29609504
379.500.4000.4055335970.0418972332.9889328061.59420289928.59946448

Dataset-3 for ANFIS model-2.

S. No.CementWater/ cement3-day compressive strength28-day compressive strength
15400.327.4579.99
25400.327.4561.89
33800.616.4536.45
42660.99.8045.85
54750.524.1539.29
6198.618.6628.02
73040.817.8547.81
8139.61.48.0628.24
9427.50.520.8837.43
10237.5115.8030.08
11332.50.712.2433.02
121901.25.0640.86
134850.324.6571.99
143740.534.3961.09
15313.30.628.7959.8
164250.433.3960.29
174250.436.3061.8
183750.328.9956.7
194750.437.7968.3
4254690.340.1966.9

Comparison of ANFIS and experimental results.

MixCement (kg/m3)FA (kg/m3)CA (kg/m3)Water/cement ratioCompressive strength (MPa)
ANFIS modelExperimentError (%)
3-day28-day3-day28-day3-day28-day
M404706959160.4023.943.025.6436.507.2816.27

M5053175610230.3527.057.329.6248.569.7017.90

M605007129630.3025.467.624.8957.752.0017.06

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