1 Introduction
2 Adaptive Neuro-Fuzzy Inference System
3 Prediction of Retrofitting Effects through the Neuro-Fuzzy System
3.1 Gaining of the Training Data
CASE | Training set | Test set | |
---|---|---|---|
1 | Number of strength (Ft) data | 284 | 16 |
2 | Number of strain (εt) data | 96 | 16 |
3 | Number of Secondary elastic modules (Eg) data | 87 | 16 |
3.2 The Learning of Data
Data unit | f’c MPa | tfrp cm | Layer ply | Kind – | Efrp GPa | ffrp MPa | ρ (%) | D cm | h cm | Ft MPa |
---|---|---|---|---|---|---|---|---|---|---|
1 | 38.6 | 0.031 | 1 | G | 73.3 | 755 | 0.816 | 15 | 31 | 45.5 |
2 | 30.2 | 0.017 | 1 | A | 224.6 | 2716 | 0.68 | 10 | 20 | 46.6 |
3 | 26.2 | 0.1 | 1 | G | 19.1 | 330 | 2.632 | 15 | 61 | 33.5 |
4 | 39.4 | 0.142 | 1 | G | 19.9 | 363 | 5.569 | 10 | 20 | 63.1 |
5 | 41.0 | 0.009 | 2 | C | 235 | 3500 | 0.706 | 5 | 10 | 117.0 |
6 | 45.2 | 0.011 | 2 | C | 230.5 | 3481 | 0.293 | 15 | 30 | 52.4 |
7 | 33.7 | 0.011 | 3 | C | 230.5 | 3481 | 0.440 | 10 | 20 | 109.9 |
8 | 35.0 | 0.08 | 3 | G | 36 | 560 | 2.105 | 15 | 44 | 83.0 |
9 | 43.7 | 0.0193 | 2 | A | 210 | 2173 | 0.772 | 10 | 20 | 88.0 |
10 | 33.28 | 0.0167 | 4 | C | 235 | 3550 | 0.668 | 10 | 20 | 111.1 |
11 | 20.79 | 0.0193 | 2 | A | 210 | 2173 | 0.772 | 10 | 20 | 72.8 |
3.3 Distribution of the Data used for the Learning
3.4 Results of the Learning of Data
3.4.1 Results of the Learning
3.4.2 Statistical Examination
3.4.3 Analysis of Errors
Case-1 (Ft) | Case-2 (εt) | Case-3 (Eg) | |
---|---|---|---|
RMSE | 4.79 | 0.00097 | 428.7 |
R2 | 0.99889 | 0.99979 | 1.009 |
E.R | 5.4 | 4.1 | 8.1 |
3.4.4 Comparison of the Results of Learning with the Results Obtained from the Existing Formulae
4 Verification of the Outputs of the Neuro-Fuzzy System
4.1 Design of Experiment and Preparation of Test Specimens
Design | Slump | W/C (%) | Mixture (kg/m3) | |||||
---|---|---|---|---|---|---|---|---|
C | W | S | G | Air | Admix | |||
21 MPa | 12 cm | 54.7 | 328 | 180 | 865 | 950 | 4.5 ±1.5% | 1.5 |
4.2 Reinforcement of Test Specimens
Tensile strength (MPa) | Modulus of elasticity (GPa) |
---|---|
1991 | 158.2 |
4.3 The Test and Measurements
4.4 Results of the Test
Specimen | Ft (MPa) | εt | Eg (MPa) |
---|---|---|---|
H* | 26.61 | 0.0023 | − 25,974** |
H2-I 0 | 32.63 | 0.003 | 12,810.59 |
H2-I 1 | 31.28 | 0.0033 | 2527.83 |
H2-I 2 | 30.67 | 0.0028 | − 13,138.2** |
H2-I 3 | 31.43 | 0.0027 | − 24,890.9** |
H2-I 4 | 30.48 | 0.0027 | − 34,703.1** |
H2-I 1-T | 34.86 | 0.0032 | 11,652.96 |
H2-I 1-A | 35.33 | 0.0037 | 5081.056 |
H2-I 1-B | 37.02 | 0.0036 | 22,674.68 |
N* | 21.13 | 0.0018 | − 19,276.4** |
N2-I0 | 25.70 | 0.0031 | 3156.05 |
N2-II3 | 26.66 | 0.0031 | 2852.00 |
N3-II1 | 26.83 | 0.0039 | 9814.00 |
N3-II3 | 25.87 | 0.0035 | 4602.43 |
N3-I1 | 26.57 | 0.0034 | 6210.99 |
N3-I1-T | 29.07 | 0.0036 | 8967.37 |
N3-I0-A | 28.59 | 0.00378 | 5697.24 |
N3-I1-B | 29.81 | 0.0037 | 7984.13 |