# Development of a Reliable Machine Learning Model to Predict Compressive Strength of FRP-Confined Concrete Cylinders

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## Abstract

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## 1. Introduction

## 2. Literature Review

## 3. Methodology

#### 3.1. Details of Collected Database

#### 3.1.1. Data Filtration

#### 3.1.2. Processing of Data

#### 3.1.3. Splitting of Dataset

#### 3.1.4. Performance Metrics

**Figure 3.**Methodology of this study (Benzaid et al. [48], Liang et al. [58], Wu and Wei [92], Pham and Hadi [93], Youssef et al. [94], Kumutha et al. [95], Samaan et al. [96], Toutanji [97], Wei and Wu [98], Saafi et al. [99], Teng et al. [100], Mander et al. [101], Spoelstra and Monti [102], Mark and Sofi [103], Karbhari and Gao [104], Lam and Teng [105], Cusson and Paultre [106], Al-Salloum [107], and Qazi et al. [108]).

#### 3.2. Details of Analytical Models

#### 3.3. ML Models

#### 3.3.1. ANN

#### 3.3.2. GPR

#### 3.3.3. SVM

## 4. Results and Discussion

#### 4.1. Results of Analytical Models

#### 4.2. Results of ML Models

#### 4.3. Discussion

#### 4.4. Confined CS Formulation Using ANN

## 5. Conclusions and Future Scope of Research Work

- The accuracy of the optimized GPR model was the highest among all the ML models as well as the existing ML model (Jamali et al. [43]) with the R-values of 0.9982 and 0.9916 for the training and testing datasets, respectively.
- According to the assessment criteria, the accuracy of the developed ML models decreased subsequently for the optimized GPR, GPR, ANN, optimized SVM, and SVM.
- The error values depicted by the optimized GPR model was minimum in all the cases. The MAPE, MAE, and RMSE values of the optimized GPR model were 3.11%, 2.17 MPa, and 3.88 MPa, respectively.
- By comparing the ML models and the analytical models, it was observed that the optimized GPR model reduced the error rate of MAPE, MAE, and RMSE by 727.97%, 778.34%, and 596.39%, respectively, and more accurately predicted the CS of the FRP-confined concrete cylinders than the existing mathematical models.
- The SVM model demonstrated a poor performance among all the ML-based models according to the performance indices, violin plot, and Taylor diagrams.
- Among all the analytical models selected in this study, the model of Teng et al. [100] illustrated poorer results with the R-value and RMSE value of 0.7200 and 67.25 MPa, respectively.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

CS | Compressive strength | ACI | American Concrete Institute |

${f}_{c}^{\prime}$ | CS of concrete | AFRP | Aramid FRP |

$D/d$ | Cylinder’s diameter | AI | Artificial intelligence |

$H/h$ | Cylinder’s height | ANFIS | Adaptive neuro-fuzzy inference system |

$L$ | Cylinder’s length | ANFIS-SC | ANFIS with subtractive clustering |

${f}_{co}^{\prime}$ | Unconfined CS of cylindrical specimen | ANFIS-FCM | ANFIS with fuzzy c-means clustering |

${F}_{ty}$ | FRP type | ANN | Artificial neural network |

$n$ | Number of FRP layers | BFRP | Basalt FRP |

${b}_{f}$ | FRP width | CEF | Confinement effectiveness factor |

${t}_{f}/t/nt/{t}_{j}/{t}_{frp}$ | Thickness of FRP jacket | CFRP | Carbon FRP |

${O}_{f}$ | Fiber orientation | CR | Confinement ratio |

${E}_{f}/{E}_{FRP}/{E}_{frp}/{E}_{j}$ | Elastic modulus of FRP materials | ECC | Engineered cementitious composite |

${F}_{f}$/${f}_{f}/{f}_{frp}$ | Tensile strength of FRP | EL | Ensemble learning |

${f}_{cc}^{\prime}$ | CS of confined cylinder | FFBPNN | Feed-forward back propagation NN |

${t}_{frp}$ | FRP thickness | FFNN | Feed-forward neural network |

${f}_{ju}$ | Ultimate tensile strength of FRP jacket | FRP | Fiber-reinforced polymer |

${f}_{frp,u}$ | Ultimate tensile strength of FRP in hoop direction | FRCM | Fiber-reinforced cementitious matrix |

${\epsilon}_{rup}$ | Ultimate circumferential strain in CFRP jacket | GFRP | Glass FRP |

${\epsilon}_{h,rup}$ | Actual strain of FRP rupture | GP | Genetic programming |

${f}_{l}$/${P}_{u}$ | Lateral confining pressure | GPR | Gaussian process regression |

d′ | Agreement index | IAE | Absolute error |

NN | Neural network | LGP | Linear genetic programming |

NS | Nash–Sutcliffe efficiency | LR | Linear regression |

NSVM | Non-linear SVM | LWC | Light weight concrete |

PSO | Particle swarm algorithm | LSVM | Linear SVM |

R | Correlation coefficient | MAE | Mean absolute error |

RBNN | Radial basis neural network | MAPE | Mean absolute percentage error |

RC | Reinforced concrete | ML | Machine learning |

RMSE | Root mean square error | MLP | Multi-layer perceptron |

RSM | Response surface model | MR | Multiple regression |

SR | Stepwise regression | SVR | support vector regression |

SV | Support vector | SVMR | Support vector machine regression |

SVM | Support vector machine | UHPC | Ultra-high-performance concrete |

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**Figure 7.**Scatter plot of analytical models; (

**a**) Wu and Wei [92], (

**b**) Pham and Hadi [93], (

**c**) Youssef et al. [94], (

**d**) Kumutha et al. [95], (

**e**) Samaan et al. [96], (

**f**) Toutanji [97], (

**g**) Wei and Wu [98], (

**h**) Saafi et al. [99], (

**i**) Teng et al. [100], (

**j**) Mander et al. [101], (

**k**) Spoelstra and Monti [102], (

**l**) Mark and Sofi [103], (

**m**) Karbhari and Gao [104], (

**n**) Lam and Teng [105], (

**o**) Cusson and Paultre [106], (

**p**) Liang et al. [58], (

**q**) Benzaid et al. [48], (

**r**) Al-Salloum [107], and (

**s**) Qazi et al. [108].

**Figure 8.**Scatter and absolute error plot of ANN model; (

**a**) training, (

**b**) validation, (

**c**) testing, and (

**d**) whole datasets.

**Figure 9.**Scatter and absolute error plot of GPR model; (

**a**) training, (

**b**) testing, and (

**c**) whole datasets.

**Figure 10.**Scatter and absolute error plot of SVM model; (

**a**) training, (

**b**) testing, and (

**c**) whole datasets.

**Figure 11.**Scatter and absolute error plot of optimized GPR model; (

**a**) training, (

**b**) testing, and (

**c**) whole datasets.

**Figure 12.**Scatter and absolute error plot of optimized SVM model; (

**a**) training, (

**b**) testing, and (

**c**) whole datasets.

**Figure 14.**Taylor plot; (

**a**) analytical models 1 to 10 (Benzaid et al. [48], Kumutha et al. [95], Pham and Hadi [93], Samaan et al. [96], Wei and Wu [98], Spoelstra and Monti [102], Karbhari and Gao [104], Liang et al. [58], Saafi et al. [99], Wu and Wei [92]), (

**b**) analytical models 11 to 19 (Cusson and Paultre [106], Al-Salloum [107], Mander et al. [101], Youssef et al. [94], Qazi et al. [108], Lam and Teng [105], Toutanji [97], Mark and Sofi [103], Teng et al. [100]), (

**c**) proposed ML models (ANN, GPR, SVM, optimized GPR, and optimized SVM models), and (

**d**) comparison between best analytical models and best fitted ML models (Benzaid et al. [48]).

Reference | Input Parameters | ML Technique | ${\mathit{f}}_{\mathit{c}\mathit{c}}^{\mathbf{\prime}}$ (MPa) | $\mathit{R}$ Value |
---|---|---|---|---|

Cevik and Guzelbey [28] | $D,nt,{E}_{f},{f}_{co}^{\prime}$ | ANN | — | 0.98 |

Gandomi et al. [29] | $D,t,{f}_{f},{f}_{co}^{\prime}$ | LGP | 33.8–137.9 | 0.9392 |

Naderpour et al. [30] | $D,L,{f}_{c}^{\prime},t,{f}_{frp},{E}_{frp}$ | ANN | 30.80–241 | 0.9439 |

Elsanadedy et al. [33] | $D,{t}_{j},{E}_{j},{f}_{ju},{f}_{c}^{\prime}$ | ANN | — | 0.95 |

Jalal and Ramezanianpour [34] | $d,h,t,{E}_{FRP},{\epsilon}_{rup},{f}_{c}^{\prime}$ | ANN | 31.40–303 | 0.9731 |

Mansouri et al. [37] | $D,t,{f}_{co}^{\prime},{E}_{f}$ | RBNN, ANFIS-SC, ANFIS-FCM, M5 Tree | 31.40–372.20 | 0.9503 |

Mozumder et al. [38] | $D,H,{f}_{c}^{\prime},{t}_{frp},{f}_{frp,u}$ | SVR, ANN | 40–303 | 0.9990 |

Keshtegar et al. [40] | $D,H,{t}_{f},{f}_{co}^{\prime},{E}_{f},{\epsilon}_{h,rup}$ | RSM, SVR | 24.1–372.2 | 0.9423 |

Jamali et al. [43] | ${f}_{co}^{\prime},H,D,{E}_{f},{F}_{f},t$ | MLP, SVR, ANFIS-PSO, ANFIS, Kriging | 17.8–381 | 0.985 |

Jalal et al. [44] | $d,h,t,{E}_{FRP},{\epsilon}_{rup},{f}_{c}^{\prime}$ | MR, ANN, GP, ANFIS | 31.40–303 | 0.9997 |

Ahmad et al. [45] | $D,H,nt,{E}_{f},{f}_{co}^{\prime}$ | ANN | 18.5–302.2 | 0.912 |

Parameters | Symbol | Unit | Min. | Mean | Max. | Std. | Type |
---|---|---|---|---|---|---|---|

CS of concrete | ${f}_{c}^{\prime}$ | MPa | 8 | 48.35 | 204 | 30.38 | Input |

Diameter | $D$ | mm | 50 | 144.40 | 310 | 38.60 | Input |

Height | $H$ | mm | 100 | 297.48 | 1000 | 106.77 | Input |

Unconfined CS | ${f}_{co}^{\prime}$ | MPa | 6.20 | 48.16 | 200 | 31.23 | Input |

Type of FRP | ${F}_{ty}$ | - | 1 | 1.36 | 4 | 0.65 | Input |

Number of FRP layers | $n$ | - | 0.30 | 2.43 | 14 | 1.86 | Input |

Width of FRP | ${b}_{f}$ | mm | 15 | 263.81 | 1000 | 141.89 | Input |

Thickness of FRP | ${t}_{f}$ | mm | 0.05 | 0.65 | 3.90 | 0.74 | Input |

Orientation of FRP | ${O}_{f}$ | - | 1 | 1.02 | 2 | 0.14 | Input |

Elastic modulus of FRP | ${E}_{f}$ | GPa | 21.30 | 171.10 | 251 | 84.97 | Input |

Tensile strength of FRP | ${f}_{f}$ | MPa | 69 | 3025.64 | 4580 | 1308.11 | Input |

Confined CS | ${f}_{cc}^{\prime}$ | MPa | 12.60 | 81.26 | 381 | 43.88 | Output |

S. No. | Reference | Formulation | Description |
---|---|---|---|

1 | Benzaid et al. [48] | $\frac{{f}_{cc}^{\prime}}{{f}_{co}^{\prime}}=[1+1.60(\frac{{f}_{l}}{{f}_{co}^{\prime}})$] | ${f}_{l}=2\frac{{f}_{f}{t}_{f}}{D}$ |

2 | Liang et al. [58] | ${f}_{cc}^{\prime}={f}_{co}^{\prime}[1+(2.61-0.01{f}_{co}^{\prime})$($\frac{{f}_{l}}{{f}_{co}^{\prime}})$] | ${f}_{l}=2\frac{{f}_{f}{t}_{f}}{D}$ |

3 | Wu and Wei [92] | ${f}_{cc}^{\prime}={f}_{co}^{\prime}[0.75+2.7{\left(\frac{{f}_{l}}{{f}_{co}^{\prime}}\right)}^{0.9}]$ | ${f}_{l}=2\frac{{f}_{f}{t}_{f}}{D}$ |

4 | Pham and Hadi [93] | ${f}_{cc}^{\prime}=0.7{f}_{co}^{\prime}+1.8{f}_{l}+5.7\frac{t}{D}+13$ | − |

5 | Youssef et al. [94] | $\frac{{f}_{cc}^{\prime}}{{f}_{co}^{\prime}}=[1+2.25({\frac{{f}_{l}}{{f}_{co}^{\prime}})}^{\frac{5}{4}}]$ | CEF = $\frac{{f}_{cc}^{\prime}}{{f}_{co}^{\prime}}$; CR = $\frac{{f}_{l}}{{f}_{co}^{\prime}}$ |

6 | Kumutha et al. [95] | ${f}_{cc}^{\prime}={f}_{co}^{\prime}+0.93{f}_{l}$ | ${f}_{l}=2\frac{{f}_{f}{t}_{f}}{D}$ |

7 | Samaan et al. [96] | ${f}_{cc}^{\prime}={f}_{co}^{\prime}$ + 6.0${f}_{l}^{0.7}$ | ${f}_{l}=2\frac{{f}_{f}{t}_{f}}{D}$ |

8 | Toutanji [97] | $\frac{{f}_{cc}^{\prime}}{{f}_{co}^{\prime}}$ = [1 + 3.5(${\frac{{f}_{l}}{{f}_{co}^{\prime}})}^{0.85}$] | ${f}_{l}=2\frac{{f}_{f}{t}_{f}}{D}$ |

9 | Wei and Wu [98] | $\frac{{f}_{cc}^{\prime}}{{f}_{co}^{\prime}}$= [0.5 + 2.7(${\frac{{f}_{l}}{{f}_{co}^{\prime}})}^{0.73}$] | ${f}_{l}=2\frac{{f}_{f}{t}_{f}}{D}$ |

10 | Saafi et al. [99] | $\frac{{f}_{cc}^{\prime}}{{f}_{co}^{\prime}}$= [1 + 2.2(${\frac{{f}_{l}}{{f}_{co}^{\prime}})}^{0.84}$] | ${f}_{l}=2\frac{{f}_{f}{t}_{f}}{D}$ |

11 | Teng et al. [100] | $\frac{{f}_{cc}^{\prime}}{{f}_{co}^{\prime}}=[1+3.5(\frac{{f}_{l}}{{f}_{co}^{\prime}})]$ | ${f}_{l}=2\frac{{f}_{f}{t}_{f}}{D}$ |

12 | Mander et al. [101] | ${f}_{cc}^{\prime}={f}_{co}^{\prime}(2.254\sqrt{1+7.94\frac{{f}_{l}}{{f}_{co}^{\prime}}}$ $-2\frac{{f}_{l}}{{f}_{co}^{\prime}}$ $-1.254)$ | ${f}_{l}=2\frac{{f}_{f}{t}_{f}}{D}$ |

13 | Spoelstra and Monti [102] | ${f}_{cc}^{\prime}={f}_{co}^{\prime}(0.2+3\sqrt{\frac{{f}_{l}}{{f}_{co}^{\prime}}}$) | ${f}_{l}=2\frac{{f}_{f}{t}_{f}}{D}$ |

14 | Mark and Sofi [103] | $\frac{{f}_{cc}^{\prime}}{{f}_{co}^{\prime}}$ $=1.1+$3.23($\frac{{f}_{l}}{{f}_{co}^{\prime}}$) | CEF = $\frac{{f}_{cc}^{\prime}}{{f}_{co}^{\prime}}$; CR = $\frac{{f}_{l}}{{f}_{co}^{\prime}}$ |

15 | Karbhari and Gao [104] | ${f}_{cc}^{\prime}={f}_{co}^{\prime}[1+2.1({\frac{{f}_{l}}{{f}_{co}^{\prime}})}^{0.87}]$ | ${f}_{l}=2\frac{{f}_{f}{t}_{f}}{D}$ |

16 | Lam and Teng [105] | ${f}_{cc}^{\prime}={f}_{co}^{\prime}[1+3.3(\frac{{f}_{l}}{{f}_{co}^{\prime}})$] | ${f}_{l}=2\frac{{f}_{f}{t}_{f}}{D}$ |

17 | Cusson and Paultre [106] | ${f}_{cc}^{\prime}={f}_{co}^{\prime}+2.1{f}_{co}^{\prime}({\frac{{f}_{l}}{{f}_{co}^{\prime}})}^{0.7}$ | ${f}_{l}=2\frac{{f}_{f}{t}_{f}}{D}$ |

18 | Al-Salloum [107] | $\frac{{f}_{cc}^{\prime}}{{f}_{co}^{\prime}}=[1+2.312(\frac{{f}_{l}}{{f}_{co}^{\prime}})$] | ${f}_{l}=2\frac{{f}_{f}{t}_{f}}{D}$ |

19 | Qazi et al. [108] | ${f}_{cc}^{\prime}={f}_{co}^{\prime}$+ 3.2${f}_{l}$ | ${f}_{l}=2\frac{{f}_{f}{t}_{f}}{D}$ |

S. No. | Reference | R | MAPE (%) | MAE (MPa) | RMSE (MPa) | a20-Index | NS |
---|---|---|---|---|---|---|---|

1 | Benzaid et al. [48] | 0.8177 | 25.75 | 19.05 | 27.02 | 0.5065 | 0.6205 |

2 | Kumutha et al. [95] | 0.8342 | 24.61 | 20.15 | 27.70 | 0.4352 | 0.6356 |

3 | Pham and Hadi [93] | 0.7651 | 26.77 | 18.98 | 29.70 | 0.5942 | 0.5441 |

4 | Samaan et al. [96] | 0.8345 | 31.52 | 21.11 | 29.17 | 0.5560 | 0.6007 |

5 | Wei and Wu [98] | 0.8041 | 29.04 | 20.33 | 31.40 | 0.5873 | 0.5040 |

6 | Spoelstra and Monti [102] | 0.8446 | 30.91 | 22.05 | 31.45 | 0.5551 | 0.5343 |

7 | Karbhari and Gao [104] | 0.8297 | 30.70 | 21.76 | 32.30 | 0.5543 | 0.5064 |

8 | Liang et al. [58] | 0.7114 | 31.07 | 21.20 | 37.15 | 0.6378 | 0.3264 |

9 | Saafi et al. [99] | 0.8334 | 32.66 | 23.17 | 34.16 | 0.5473 | 0.4710 |

10 | Wu and Wei [92] | 0.7674 | 32.41 | 22.26 | 38.77 | 0.6370 | 0.2935 |

11 | Cusson and Paultre [106] | 0.8542 | 34.38 | 25.01 | 33.80 | 0.4622 | 0.4970 |

12 | Al-Saloum [107] | 0.7794 | 32.67 | 22.65 | 38.42 | 0.5994 | 0.3200 |

13 | Mander et al. [101] | 0.8523 | 48.54 | 36.26 | 46.70 | 0.2980 | 0.2573 |

14 | Youssef et al. [94] | 0.6572 | 34.01 | 23.68 | 47.96 | 0.5769 | −0.1205 |

15 | Qazi et al. [108] | 0.7334 | 49.76 | 35.50 | 59.51 | 0.4787 | −0.1403 |

16 | Lam and Teng [105] | 0.7289 | 52.18 | 37.40 | 62.07 | 0.4466 | −0.1836 |

17 | Toutanji [97] | 0.7922 | 63.07 | 46.24 | 65.34 | 0.2710 | −0.0603 |

18 | Mark and Sofi [103] | 0.7462 | 55.80 | 40.40 | 63.54 | 0.3918 | −0.1503 |

19 | Teng et al. [100] | 0.7200 | 57.23 | 41.37 | 67.25 | 0.4014 | −0.2633 |

Model | R | MAPE (%) | MAE (MPa) | RMSE (MPa) | a20-Index | NS | |
---|---|---|---|---|---|---|---|

ANN | Training | 0.9945 | 4.86 | 3.22 | 4.49 | 0.9826 | 0.9890 |

Testing | 0.9887 | 7.08 | 4.94 | 7.51 | 0.9480 | 0.9771 | |

Validation | 0.9845 | 7.02 | 4.85 | 7.43 | 0.9306 | 0.9690 | |

All | 0.9919 | 5.51 | 3.72 | 5.55 | 0.9696 | 0.9840 | |

GPR | Training | 0.9979 | 2.69 | 1.78 | 2.79 | 0.9975 | 0.9957 |

Testing | 0.9877 | 5.31 | 3.96 | 7.41 | 0.9681 | 0.9742 | |

All | 0.9944 | 3.48 | 2.43 | 4.68 | 0.9887 | 0.9886 | |

SVM | Training | 0.9494 | 10.43 | 8.23 | 14.18 | 0.8571 | 0.8904 |

Testing | 0.9310 | 11.70 | 9.85 | 18.09 | 0.8231 | 0.8464 | |

All | 0.9430 | 10.81 | 8.70 | 15.46 | 0.8469 | 0.8758 | |

Optimized GPR | Training | 0.9982 | 2.28 | 1.57 | 2.48 | 0.9962 | 0.9966 |

Testing | 0.9916 | 5.04 | 3.59 | 5.99 | 0.9740 | 0.9831 | |

All | 0.9960 | 3.11 | 2.18 | 3.88 | 0.9895 | 0.9921 | |

Optimized SVM | Training | 0.9756 | 8.69 | 6.12 | 9.46 | 0.9080 | 0.9512 |

Testing | 0.9714 | 9.78 | 7.32 | 11.15 | 0.8580 | 0.9416 | |

All | 0.9741 | 9.01 | 6.48 | 10.00 | 0.8930 | 0.9480 |

**Table 6.**Comparison of the best-predicted analytical model with ML models on the basis of statistical parameters.

Model | R | MAPE (%) | MAE (MPa) | RMSE (MPa) | a20-Index | NS |
---|---|---|---|---|---|---|

Benzaid et al. [48] | 0.8177 | 25.75 | 19.06 | 27.02 | 0.5065 | 0.6205 |

Jamali et al. [43] | 0.9850 | 3.909 | — | 8.388 | — | — |

ANN | 0.9919 | 5.51 | 3.72 | 5.55 | 0.9696 | 0.9840 |

GPR | 0.9944 | 3.48 | 2.43 | 4.68 | 0.9887 | 0.9886 |

SVM | 0.9430 | 10.81 | 8.70 | 15.46 | 0.8470 | 0.8758 |

Optimized GPR | 0.9960 | 3.11 | 2.17 | 3.88 | 0.9895 | 0.9921 |

Optimized SVM | 0.9741 | 9.01 | 6.48 | 10.00 | 0.8930 | 0.9480 |

Neuron | W_{i(I—H)} | B_{(I—H)} | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | 0.4890 | −0.0426 | 0.7991 | 0.8043 | −0.2543 | 1.4040 | −0.8662 | −0.5338 | 0.2425 | −1.0910 | −0.8423 | 2.4664 |

2 | 0.3147 | −0.9940 | −0.1763 | −0.3185 | 0.6958 | −2.0116 | 0.3959 | 2.3624 | −2.2556 | −3.0314 | 0.6254 | 1.5066 |

3 | 0.6892 | −0.8751 | 0.3472 | 0.0917 | −0.8381 | 1.7325 | 0.6821 | −2.0279 | 1.4394 | 1.3860 | 0.5977 | −1.9634 |

4 | 1.9633 | 0.1088 | −0.4232 | 1.1527 | −0.4726 | −0.0668 | 0.5465 | 0.8290 | 0.9297 | 0.3154 | −1.0595 | 1.0969 |

5 | −1.1834 | 0.2597 | −1.0005 | −1.9171 | 0.5790 | 0.6256 | 0.4608 | −0.4068 | −0.4369 | 1.3680 | 0.2822 | −1.5592 |

6 | 0.4046 | −0.7379 | 0.1857 | −0.5454 | −0.1630 | −0.3392 | 2.0297 | −0.4811 | −0.6139 | −0.6073 | −1.3327 | 1.3040 |

7 | −0.5646 | −0.6054 | 0.6037 | −2.2622 | 0.0565 | −1.9472 | −0.1125 | 1.2858 | −0.3791 | −0.3788 | −0.5173 | 0.8962 |

8 | 0.1469 | 0.8395 | −0.1774 | 0.5823 | −0.5912 | −1.2727 | 0.3431 | −2.7576 | −0.6781 | −0.1366 | 0.1056 | 0.5559 |

9 | 2.3052 | −1.3832 | −0.5811 | 0.8648 | −0.5481 | −0.1246 | −1.4150 | 1.2182 | −0.9212 | 0.9857 | −0.7972 | −0.1886 |

10 | 0.7775 | −2.1458 | −0.6900 | −1.2360 | −1.0703 | −0.7983 | −0.1019 | 1.0264 | −0.4462 | 0.9316 | −1.5862 | −0.7309 |

11 | −1.3758 | 0.2885 | −0.1574 | −0.3185 | −0.5195 | 1.4632 | −1.4404 | 1.4724 | −2.0358 | 1.8967 | 1.4808 | 0.0879 |

12 | 0.4167 | 1.1231 | −0.3507 | 1.3185 | −1.1173 | 1.4175 | 1.0726 | 0.9048 | 0.2225 | −1.8280 | −0.8253 | −0.4359 |

13 | 1.7231 | 0.7284 | 0.4366 | −0.6762 | −1.6890 | −0.6619 | −0.6714 | 0.7691 | 0.6635 | 1.8059 | −1.8986 | −0.3767 |

14 | 1.3590 | 0.2079 | −0.4545 | −2.8441 | −0.5101 | 1.7451 | −1.0740 | 0.9111 | 0.6223 | 0.3673 | 0.2465 | 0.4237 |

15 | 0.6644 | −0.5836 | 0.3536 | −0.0864 | −1.1389 | 0.9472 | 0.8244 | −1.0808 | −1.7435 | 1.4781 | 1.7289 | 0.8480 |

16 | −1.8260 | 0.6426 | 1.1734 | 1.7608 | −0.1300 | 0.0114 | 0.3381 | −1.4550 | −1.2129 | −1.7368 | 1.1568 | 1.1399 |

17 | −1.3106 | −0.1813 | −0.9929 | −0.1053 | −1.3403 | 0.0551 | 1.6340 | −1.5167 | −0.5771 | −1.9736 | −0.5192 | −0.2839 |

18 | 0.3569 | 2.1897 | −1.4162 | −0.8260 | −0.2708 | −1.4098 | −0.0346 | −0.5525 | −1.1112 | −0.8331 | −2.1154 | 0.7931 |

19 | −0.1513 | −1.3625 | −0.8049 | 1.2354 | −0.0976 | 0.8162 | 2.0695 | −1.2838 | −0.6405 | −0.8792 | 0.7740 | 0.1292 |

20 | 0.4788 | −0.3947 | 2.0197 | 0.1632 | −0.4640 | −3.6198 | −0.9234 | 2.2758 | −0.6305 | −0.2096 | −0.7755 | −0.3739 |

21 | 1.3400 | −0.6498 | 0.8341 | −0.5221 | 0.3899 | −1.3350 | −1.8893 | −0.6759 | 0.0242 | 1.0824 | 0.9962 | 0.4297 |

22 | 0.8218 | 0.2154 | 0.2902 | −1.1508 | −2.3498 | −2.0093 | −1.2739 | 2.4396 | −0.4819 | −1.3710 | −0.0760 | −1.8869 |

23 | −0.5996 | 1.1820 | 1.5276 | 0.0869 | −0.6709 | −2.0720 | 1.6654 | −1.1800 | 0.0614 | −0.2382 | 3.3103 | 0.3315 |

24 | −0.2590 | −2.5197 | −1.1914 | 0.3217 | 0.0908 | 2.1740 | −2.4669 | 0.4435 | 0.1522 | 0.1825 | 1.6287 | 1.3594 |

25 | −0.1467 | −0.6175 | 0.9839 | 0.1413 | 0.2974 | 1.0784 | 0.7411 | 1.8661 | 0.0364 | −0.6620 | −0.2940 | −1.5176 |

26 | −0.4294 | −1.5546 | 1.5770 | −0.2099 | 1.3779 | 0.8255 | 0.6206 | −1.8399 | −0.3451 | 0.3825 | −1.2959 | −1.5230 |

27 | 0.9118 | 0.4704 | 1.1762 | −0.5429 | 0.7116 | 0.8158 | 1.4502 | 0.8648 | −0.8382 | 1.7015 | −0.1090 | 1.6661 |

28 | −0.9282 | 0.8193 | −0.0857 | 0.7115 | 0.1644 | −0.6808 | 0.4528 | 0.7792 | −0.5483 | −0.2140 | 0.0932 | −1.3317 |

29 | 0.5797 | 1.9693 | −0.1414 | −0.8540 | 0.0167 | −1.2740 | −0.5481 | −0.0796 | −0.2724 | 1.9183 | 0.1999 | −1.9027 |

30 | −0.6942 | −0.3818 | 0.7695 | −1.7612 | 0.4512 | −0.4785 | 0.8002 | 0.2275 | 0.6121 | 1.5343 | −0.0429 | 1.9731 |

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## Share and Cite

**MDPI and ACS Style**

Kumar, P.; Arora, H.C.; Bahrami, A.; Kumar, A.; Kumar, K. Development of a Reliable Machine Learning Model to Predict Compressive Strength of FRP-Confined Concrete Cylinders. *Buildings* **2023**, *13*, 931.
https://doi.org/10.3390/buildings13040931

**AMA Style**

Kumar P, Arora HC, Bahrami A, Kumar A, Kumar K. Development of a Reliable Machine Learning Model to Predict Compressive Strength of FRP-Confined Concrete Cylinders. *Buildings*. 2023; 13(4):931.
https://doi.org/10.3390/buildings13040931

**Chicago/Turabian Style**

Kumar, Prashant, Harish Chandra Arora, Alireza Bahrami, Aman Kumar, and Krishna Kumar. 2023. "Development of a Reliable Machine Learning Model to Predict Compressive Strength of FRP-Confined Concrete Cylinders" *Buildings* 13, no. 4: 931.
https://doi.org/10.3390/buildings13040931