# Machine Learning Algorithm for Shear Strength Prediction of Short Links for Steel Buildings

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

^{2}). The prediction result displays that the $XGBOOST$ and $LightGBM$ provided better, and more reliable results compared to $ANN$ and the AISC code. The $XGBOOST$ and $LightGBM$ models yielded higher values of R

^{2}, lower (RMSE), (MAE), and (MAPE) values and have shown to perform more accurate. Therefore, the overall outcomes showed that the $LightGBM$ outperformed the $XGBOOST$ model. Moreover, the overstrength ratio predicted by the $LightGBM$ showed an excellent performance compared to the Gene Expression and Finite Element-based models. The developed models are vital for practitioners to predict the shear strength accurately, which pave the road towards wider application for automation in the steel buildings.

## 1. Introduction

_{p}represents the plastic shear strength (N), F

_{y}represents the measured steel yield strength of the web (MPa), d is the link depth (mm), t

_{f}and t

_{w}are the flange and web thicknesses (mm), respectively. Several investigations revealed the major factors that control the shear link strength, such as flange contribution [3,5], cyclic hardening [3], web slenderness [4], and link length ratio [4,6,7].

## 2. Literature Review

#### 2.1. Analytical Models

#### 2.1.1. AISC 2016

#### 2.1.2. Corte et al., 2013

_{0.08}/V

_{y}) of wide flange shear links without axial restraint, where ${A}_{v}=\left(d-{t}_{f}\right){t}_{w}$ and ${V}_{y}=\left({F}_{y}/\surd 3\right)\left(d-{t}_{f}\right){t}_{w}$. It is worth mentioning that the authors derived Equation (2) for the hot rolled steel link. However, the experimental database of the current study includes both hot rolled and built-up steel links.

#### 2.1.3. G. Almasabha 2022

_{GEP}) [34]. Various parameters were considered in this equation, such as b

_{f}/t

_{f}, d/t

_{w}, A

_{f}/A

_{w}, A

_{f}f

_{yflange}, A

_{w}f

_{yweb}, and e/(M/V).

#### 2.2. ML Models

## 3. Methodology

#### 3.1. Data collection and Feature Definition

#### 3.2. Data Preprocessing

#### 3.3. $ML$ Algorithm

#### 3.3.1. Artificial Neural Network

#### 3.3.2. Extreme Gradient Boosting

#### 3.3.3. Light Gradient Boosting Machine ($LightGBM$)

_{v}represents the C’s subset for the features having value v. The process might be affected by several factors, resulting in it being an insignificant process, such as specific leaves with reasonably minimal information gain are discarded, gaining additional memory storage capacity.

#### 3.4. Stratified K-Fold Cross-Validation

#### 3.5. Prediction Accuracy Measurement

## 4. Result and Discussion

#### 4.1. Descriptive Statistics

_{f}/t

_{f}from 10 to 20.71 with an average of 13.51, d/t

_{w}from 11.33 to 57.5 with an average of 36.66, e/(M/V), from 0.33 to 1.69, A

_{f}/A

_{w}from 0.41 to 2.27 with an average of 1.86, A

_{f}f

_{yflange}from 260 to 9882 kN with an average of 879 kN, A

_{w}f

_{yweb}from 219.7 to 8524.3 kN with an average of 891.67 kN.

#### 4.2. Correlation Matrix Analysis

#### 4.3. Performance of ML Algorithms

#### 4.4. Features Importance Analysis

_{u}/V

_{LightGBM}) and the experimental-to-AISC projected shear strength (V

_{u}/V

_{P}) are illustrated in Figure 10 and Figure 11. Likewise, the AISC based overstrength ratio, the $LightGBM$ demonstrated an excellent performance in the prediction of the shear link strength, where it is cruel to b

_{f}/t

_{f}, d/t

_{w}, A

_{f}/A

_{w}, A

_{f}f

_{yflange}, A

_{w}f

_{yweb}, and e/(M/V). The $LightGBM$ predictions are flat and close to 1.0, which indicates that the $LightGBM$ model is a comprehensive and competent algorithm for predicting the short links’ shear strength.

_{u}/V

_{LightGBM}), AISC 2016 (V

_{u}/V

_{p}), Gene expression model (V

_{u}/V

_{GEP}), and FEM-based model (V

_{0.08}/V

_{y}) are presented in Figure 12. The average of the predicted overstrength ratio is 0.97, 1.11, 1.73, and 1.74 for the V

_{u}/V

_{LightGBM}, V

_{u}/V

_{GEP}, V

_{0.08}/V

_{y}, and V

_{u}/V

_{p}, respectively. The results revealed that the LightGBM is an excellent model in order to evaluate the short links’ shear strength, while the AISC code equation is deficient to accurately estimate the shear link strength due to the fact the AISC code equation only considers the strength of web. This study revealed the significant effect of other variables such as the properties of flange and the link length ratio. The machine learning algorithm ($LightGBM$) has successfully traced the contribution of elements other than the web on the short link shear strength.

## 5. Conclusions

^{2}under the 10-fold cross-validation process have been implemented to enhance the robustness and effectiveness of such models. These measures reveal that the performance of the ML models set side by side to $AISCcode$ was arranged as follows: $LightGBM>XGBOOST>ANN>AISC\mathrm{code}$. According to the importance of the features extracted from ML algorithms, Web force and Link length ratio were the most prominent variables in the prediction results of the overstrength ratio of short links. In addition, the predicted overstrength ratio using the $LightGBM$ was compared to the available models in the literature, where the proficiency of developed models was reasonable. The analysis disclosed that the $LightGBM$ has the least average predicted overstrength ratio compared to the GEP, FEM, or AISC-based models. For future research, a larger database can be adopted to demonstrate the adequacy of these models to predict the overstrength ratio of short links. The impact of other variables on the prediction accuracy needs to be adopted. Moreover, modern algorithms are required to improve results accuracy.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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Feature | Definition | Data Type |
---|---|---|

$({b}_{f}/{t}_{f}$) | Flange slenderness ratio | Numeric |

$(d/{t}_{w}$) | Web slenderness ratio | Numeric |

$({A}_{f}/{A}_{w}$) | Flange to web area ratio | Numeric |

$({A}_{f}{f}_{yflange}$) | Flange force | Numeric |

$({A}_{w}{f}_{yweb}$) | Web force | Numeric |

$e/\left(M/V\right)$ | Link length ratio | Numeric |

Reference | No. of Tests | b_{f}/t_{f} | d/t_{w} | e/(M/V) | f_{yflange}, MPa | f_{yweb}, MPa | V_{test} (kN) |
---|---|---|---|---|---|---|---|

Ji et al., 2015 [3] | 12 | 12.9 | 40 | 0.58–0.97 | 319 | 228; 273 | 869–1130 |

Ji et al., 2016 [11] | 2 | 10.6; 14.2 | 35 | 0.7–0.76 | 378; 396 | 228 | 838–926 |

McDaniel et al., 2003 [5] | 2 | 10.6–13.3 | 33.9 | 0.59; 0.82 | 366 | 354 | 9363–9919 |

Volynkin et al., 2018 [46] | 5 | 12–12.8 | 21.7–44.2 | 0.76–1.02 | 364; 455 | 364; 374 | 783–1034 |

Dusicka et al., 2010 [8] | 5 | 11.8; 13.6 | 22–33.9 | 0.8; 0.82 | 223–503 | 242–503 | 1845–4348 |

Liu et al., 2017 [4] | 11 | 10–13 | 21–35 | 1.12–1.6 | 366 | 354–362 | 373–668 |

Okazaki et al., 2005 [6] | 11 | 11.5–18.3 | 22.1–56.8 | 1.04–1.49 | 319–362 | 382–404 | 585–1280 |

Okazaki, T. 2004 [7] | 6 | 12.2 | 57.5 | 1.11 | 351.6 | 393 | 1007–1140 |

Bokurt and Topaya 2017 [12] | 8 | 18–20.7 | 22.4–22.8 | 1.04–1.59 | 268–281 | 275–299 | 275–591 |

Bokurt and et al., 2019 [13] | 6 | 18–20 | 22.2–29 | 1.26–1.59 | 272–357 | 276–343 | 288–573 |

Tong et al., 2018 [53] | 4 | 12 | 17.9 | 1.25 | 461.2 | 463.4 | 720–1013 |

Mahmoudi et al., 2018 [54] | 1 | 10 | 34 | 0.78 | 301 | 301 | 478 |

Hjelmstad et al., 1983 [45] | 8 | 11.5; 15.6 | 43.4; 57 | 1.27–1.57 | 241.3; 285.4 | 711–914 | 600–1067 |

Dubina et al., 2008 [44] | 24 | 12.25 | 38.7 | 0.65–1.3 | 221–315 | 221–315 | 270–420 |

Price, B. 2015 [43] | 5 | 11.5; 16.5 | 23.8; 56.8 | 1.11; 1.23 | 353.7; 398.5 | 360; 403 | 433–1298 |

Total | 110 |

Stander Statistics | Features | |||||
---|---|---|---|---|---|---|

$({\mathit{b}}_{\mathit{f}}/{\mathit{t}}_{\mathit{f}})$ | $(\mathit{d}/{\mathit{t}}_{\mathit{w}})$ | $({\mathit{A}}_{\mathit{f}}/{\mathit{A}}_{\mathit{w}})$ | $\left({\mathit{A}}_{\mathit{f}}{\mathit{f}}_{\mathit{yflange}}\right)$ | $\left({\mathit{A}}_{\mathit{w}}{\mathit{f}}_{\mathit{yweb}}\right)$ | $\mathit{e}/\left(\mathit{M}/\mathit{V}\right)$ | |

Mean | 13.51 | 36.66 | 1.01 | 879.08 | 891.67 | 1.09 |

Standard Error | 0.24 | 1.16 | 0.04 | 115.7 | 107.91 | 0.03 |

Median | 12.24 | 38.71 | 0.86 | 608.74 | 664.32 | 1.1 |

Mode | 12.24 | 38.71 | 0.86 | 803.88 | 550.24 | 0.87 |

Standard Deviation | 2.53 | 12.18 | 0.43 | 1213.48 | 1131.79 | 0.28 |

Sample Variance | 6.42 | 148.37 | 0.18 | 1,472,537 | 1,280,955 | 0.08 |

Kurtosis | 0.56 | −0.76 | 0.33 | 36.84 | 37.1 | −0.65 |

Skewness | 1.33 | 0.31 | 1.08 | 5.65 | 5.74 | −0.15 |

Range | 10.71 | 46.15 | 1.86 | 9622.04 | 8304.59 | 1.36 |

Minimum | 10 | 11.33 | 0.41 | 259.96 | 219.73 | 0.33 |

Maximum | 20.71 | 57.48 | 2.27 | 9882 | 8524.32 | 1.69 |

Sum | 1486.02 | 4032.6 | 110.61 | 96698.71 | 98083.4 | 119.9 |

Count | 110 | 110 | 110 | 110 | 110 | 110 |

Performance Comparison | Prediction Models | |||
---|---|---|---|---|

$\mathit{L}\mathit{i}\mathit{g}\mathit{h}\mathit{t}\mathit{G}\mathit{B}\mathit{M}$ | $\mathit{X}\mathit{G}\mathit{B}\mathit{O}\mathit{O}\mathit{S}\mathit{T}$ | $\mathit{A}\mathit{N}\mathit{N}$ | $\mathit{A}\mathit{I}\mathit{S}\mathit{C}\mathit{C}\mathit{o}\mathit{d}\mathit{e}$ | |

$MAE$ | 92.0 | 196.5 | 378.0 | 397.9 |

$RMSE$ | 132.5 | 284.0 | 507.9 | 804.2 |

$MAPE$ | 11.7 | 24.1 | 35.8 | 39.2 |

${R}^{2}$ | 0.99 | 0.96 | 0.90 | 0.75 |

$\mathrm{Training}\mathrm{Tim}$ | 7 s | 9 s | 14 s |

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**MDPI and ACS Style**

Almasabha, G.; Alshboul, O.; Shehadeh, A.; Almuflih, A.S.
Machine Learning Algorithm for Shear Strength Prediction of Short Links for Steel Buildings. *Buildings* **2022**, *12*, 775.
https://doi.org/10.3390/buildings12060775

**AMA Style**

Almasabha G, Alshboul O, Shehadeh A, Almuflih AS.
Machine Learning Algorithm for Shear Strength Prediction of Short Links for Steel Buildings. *Buildings*. 2022; 12(6):775.
https://doi.org/10.3390/buildings12060775

**Chicago/Turabian Style**

Almasabha, Ghassan, Odey Alshboul, Ali Shehadeh, and Ali Saeed Almuflih.
2022. "Machine Learning Algorithm for Shear Strength Prediction of Short Links for Steel Buildings" *Buildings* 12, no. 6: 775.
https://doi.org/10.3390/buildings12060775