Augmented DataDriven Machine Learning for Digital Twin of Stud Shear Connections
Abstract
:1. Introduction
2. Literature Review
3. Dataset
3.1. Preprocessing
${f}_{cm}$  =  Mean value of concrete compressive strength; 
${f}_{ck}$  =  Characteristic value of concrete compressive strength. 
$s$  =  Pitch of lateral confinement steel; 
${b}_{c}$  =  Core dimension, centertocenter perimeter of lateral confinement; 
${A}_{s}$  =  Area of lateral confinement steel. 
3.2. Dataset for Strength Prediction
3.3. Dataset for Slip Prediction
3.4. Data Split for Training and Testing
3.4.1. Data Split for Training and Testing (Ultimate Strength)
3.4.2. Data Split for Training and Testing (Ultimate Slip)
4. Machine Learning Model
4.1. AutoML–PyCaret Library
4.2. Decision Tree Model
4.3. Ensemble (Voting)
4.4. Hyperparameter (Autotuning)
4.5. Model Pipeline
5. Prediction of Strength and Deformation Capacity
5.1. Metrics for Performance Evaluation
${Y}_{i},{y}_{i},{a}_{i}$  =  Actual value; 
$\widehat{Y},{p}_{i}$  =  Predicted value 
$\overline{y}$  mean value of actual value;  
$n$  =  Number of data. 
5.2. SHapley Additive exPlanations (SHAP) Value
${\varnothing}_{i}$  =  The Shapley value for the “I” data; 
$F$  =  The entire set; 
$S$  =  All subsets of the entire set with the ith data removed; 
${f}_{S\cup i}\left({x}_{S\cup i}\right)$  =  The overall contribution, including the ith data; 
${f}_{s}\left({x}_{s}\right)$  =  The contribution of the remaining subset without the ith data. 
5.3. Strength Prediction with Experimental Data
5.4. Strength Prediction with Augmented Data (Experimental and Finite Element Method)
5.5. Slip Prediction with the Experimental Data
6. Digital Twin for Stud Shear Connection
6.1. Application of Machine Learning to Replace a Design Code
6.2. Digital Twin for Design of Static Composite Shear Connection
${P}_{max}$  =  Ultimate strength; 
${d}_{sh}$  =  Diameter of stud; 
${f}_{c}$  =  Mean value of concrete compressive strength. 
7. Conclusions
 (1)
 AutoML models streamline and automate the optimization process by integrating the steps required in traditional ML models. They automatically evaluate the results, allowing for the replacement of conventional design codes. Furthermore, they serve as flexible tools for handling continuous data and model updates. In instances where a more accurate model is proposed, it can be added to or replaced existing models within the blended model system, potentially yielding superior results compared to the conventional approach.
 (2)
 The datadriven approach in ML requires a substantial amount of data, which often poses challenges. However, proposing empirical codes and design equations, particularly those encompassing parameters such as diameter and high strength based on existing experiments, requires numerous experiments, presenting practical challenges. In order to address this problem, an augmented dataset is created using FEM models to mitigate biases in the existing experimental dataset. This approach improves the dataset and fills gaps in the experimental data, addressing issues related to data model overfitting. Consequently, the performance of the model, evaluated through accuracy metrics and SHAP values, which indicate feature importance, demonstrated superior results from a mechanical perspective.
 (3)
 A comparison of the accuracy of the models for strength and slip predictions revealed that the evaluation metrics, accuracy, and importance of features in the SHAP values significantly differed based on the amount of data. Initially, a notable uncertainty in the collected data for the ultimate slip was observed, resulting in less accurate results. Therefore, substantial amounts of clear experimental data are crucial for precise predictions, particularly owing to the initial uncertainty in the collected data for extreme slips.
 (4)
 A model trained on an augmented or experimentbased dataset applies only within the range of the applied data. The predictive errors inherently increase for outlier data points outside this range. In order to address this problem, information regarding such data must be incorporated into the existing datasets. An evaluation of the proposed model revealed its feasibility for application to outlier data. In addition, the inclusion of data within this range can improve the evaluation indices and SHAP values, allowing for the application of less conservative strength reduction coefficients.
 (5)
 This study proposed a method for predicting the ultimate value through a whatif simulation using a set of input features within the dataset range. A strength reduction factor of 0.9 was suggested when the MAPE of the predicted value fell below 10%. In summary, the proposed comprehensive process involves taking the feature input from the dataset, using AutoML for the predictive model, and transforming the predicted values of the ultimate strength and slip by applying the strength reduction factor. This process forms a digital twin model that replaces the design code, expressed through a bilinear load–slip curve.
 (6)
 The number of features for strength prediction had no constraints, and incorporated the 12 features used in this study, as well as additional shape information related to the spacing and welding of connectors. This approach enables the creation of strength prediction models tailored to specific the stated purpose. Furthermore, the strength prediction model can be extended to include composite connections with precast decks, where the connections are composited using pockets.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Eurocode 4 [4]  AASHTO LRFD [6]  GB50017 [7]  

Equation  ${P}_{Rd}=\mathrm{m}\mathrm{i}\mathrm{n}\left(\frac{0.29\alpha {d}_{s}^{2}\sqrt{{f}_{ck}{E}_{c}}}{{\gamma}_{v}},\frac{0.8{f}_{u}\left(\frac{\pi {d}_{s}^{2}}{4}\right)}{{\gamma}_{v}}\right)$  ${Q}_{\mathrm{r}}={\Phi}_{sc}0.5{A}_{s}.\sqrt{{E}_{c\mathrm{m}}{f}_{cd}}\le {\Phi}_{sc}{A}_{s}.{f}_{u}$  ${N}_{\mathrm{v}}=0.43{A}_{s}.\sqrt{{E}_{c}{f}_{c}}\le 0.7{A}_{s}{f}_{su}$ 
Partial factor  ${\gamma}_{V}=1.25$ ($\alpha =0.2\left(\frac{{\mathrm{h}}_{sc}}{d}+1\right)for3\le \frac{{\mathrm{h}}_{sc}}{d}\le 4$, $1for\frac{{\mathrm{h}}_{sc}}{d}4$  ${\Phi}_{sc}$ = 0.85   
Range of design parameter(s)  $16\mathrm{m}\mathrm{m}\le {d}_{s}\le 25\mathrm{m}\mathrm{m}$ ${f}_{u}\le 500\mathrm{N}/\mathrm{m}{\mathrm{m}}^{2}$ $20\mathrm{M}\mathrm{p}\mathrm{a}\le {f}_{ck}\le 60\mathrm{M}\mathrm{p}\mathrm{a}$  $414\mathrm{M}\mathrm{P}\mathrm{a}\le {f}_{u}$  $400\mathrm{M}\mathrm{P}\mathrm{a}\le {f}_{\mathrm{s}u}$ $10\mathrm{mm}\le {d}_{s}\le 25\mathrm{mm}$ 
Author  Equation  Author  Equation 

Viest [1]  ${Q}_{nv}=5.25{d}^{2}{f}_{c}^{\prime}\sqrt{\frac{4000}{{f}_{c}^{\prime}}}(if\dots d<1)$ ${Q}_{nv}=5d{f}_{c}^{\prime}\sqrt{\frac{4000}{{f}_{c}^{\prime}}}(if\dots d>1)$ (units: pounds, inches)  Ollgaard et al. [3]  ${Q}_{nvs}=0.5{A}_{s}\sqrt{{f}_{c}^{\prime}{E}_{c}}<{A}_{s}{F}_{u}$ (units: kips, inches) 
Driscoll and Slutter [8]  ${Q}_{nv}=\frac{932{d}^{2}\sqrt{{f}_{c}^{;}}}{{A}_{s}}(if\dots \frac{f}{d}>4.2)$ ${Q}_{nv}=\frac{222hd\sqrt{{f}_{c}^{;}}}{{A}_{s}}(if\dots \frac{f}{d}<4.2)$ (units: kips, inches)  Oehlers et al. [9]  ${P}_{Rd}=k{f}_{u}\frac{\pi {d}^{2}}{4}{\left[\frac{{E}_{cm}}{{E}_{sc}}\right]}^{0.4}{\left[\frac{{f}_{ck}}{{f}_{u}}\right]}^{0.35}\frac{1}{{\gamma}_{v}}$ (units: MPa, mm) 
Döinghaus [10]  ${P}_{Rd}=\left(0.92{f}_{u}\frac{\pi {d}^{2}}{4}+\eta {f}_{ck}{d}_{do}{h}_{w}\right)\frac{1}{{\gamma}_{v}}$ (units: MPa, mm)  Hicks [11]  ${P}_{Rd}=\frac{0.25{d}^{2}\sqrt{{f}_{ck}{E}_{cm}}}{{\gamma}_{v}}for\frac{{h}_{sc}}{d}>4(concretefailure)$ ${P}_{Rd}=\left(0.92{f}_{u}\frac{\pi {d}^{2}}{4}+\eta {f}_{ck}{d}_{do}{h}_{w}\right)\frac{1}{{\gamma}_{v}}\left(steelfailure\right)$ (units: kips, inches) 
Research  Number of Data and Features  ML Models 

Abambres et al. (2019) [56] 


Setvati et al. (2022) [57] 


Degtyrev et al. (2022) [58] 


Avcikarata et al. (2022) [59] 


Zhu et al. (2023) [60] 


Zhang et al. (2023) [61] 


Yosri et al. (2023) [62] 


Hyperparameter  Catboost  XGBoost  LightGBM  Random Forest  ExtraTrees 

Learning_rate  0.034/0.036/0.01  0.15/0.3/0.01  0.1  
subsample  0.8  0.2/1/0.9  1.0  
n_estimators  140/100/110  100/230/100  100/100/210  100/100/210  
L2_leaf_reg  3  
Depth  
Border_count  254  
Objective  Reg_squarederror  Regression  
Colsample_bynode  1  
Eval_metric  RMSE  RMSE  
iterations  1000  
Gamma  0  
Max_features  1.0  1.0  
Max_depth  5/6/3  None/None/7  None/None/7  
Min_child_weight  2/1/4  0.001  
Min_child_samples  20/26/20  
Min_sample_leaf  1/1/2  1/1/2  
Min_samples_split  2/2/2  2/2/2  
Reg_alpha  0.2/0/0.0005  0.0/0.005/0.0  
Reg_lambda  0.001/1/0.15  0.0/4/0.0  
Scale_pos_weight  1.6/1/26.6  
Num_leaves  31  
Boosting type  gbdt  
boostrap  True  False 
Catboost  XGBoost  Random Forest  LightGBM  ExtraTrees  Voting  

Prediction for ultimate strength (Experimental data)  MAE  4.6739  6.6095  5.8284  7.9378  2.8303  5.117 
MSE  49.0446  84.1003  77.5727  145.6685  36.8210  58.0090  
RMSE  7.0032  9.1706  8.8075  12.0693  6.0680  7.6164  
R^{2}  0.9875  0.9785  0.9802  0.9628  0.9906  0.9852  
RMSLE  0.0655  0.0860  0.0845  0.1004  0.0562  0.0707  
MAPE  0.0426  0.0612  0.0540  0.0961  0.0251  0.0458  
Prediction for ultimate strength (Experimental data)  MAE  4.5702  2.8028  5.2054  6.0641  2.4839  4.1127 
MSE  43.2715  29.4825  66.3492  83.3793  29.0910  41.4577  
RMSE  6.5781  5.4298  8.1455  9.1392  5.3936  6.4388  
R^{2}  0.9892  0.9926  0.9834  0.9791  0.9927  0.9890  
RMSLE  0.0597  0.0477  0.0739  0.0840  0.474  0.0569  
MAPE  0.0400  0.0240  0.0460  0.0528  0.0213  0.0538  
Prediction for ultimate slip (Experimental data)  MAE  1.1446  1.3073  1.0479  1.0805  1.2649  1.3768 
MSE  2.6340  3.2825  2.6683  2.5315  3.4954  3.2119  
RMSE  1.6229  1.8118  1.6335  1.5911  1.8696  1.7922  
R^{2}  0.5782  0.4744  0.5727  0.5947  0.4403  0.5838  
RMSLE  0.1443  0.1638  0.1432  0.1437  0.1673  0.1675  
MAPE  0.1307  0.1503  0.1186  0.1262  0.1448  0.1573 
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Roh, G.T.; Vu, N.; Jeon, C.H.; Shim, C.S. Augmented DataDriven Machine Learning for Digital Twin of Stud Shear Connections. Buildings 2024, 14, 328. https://doi.org/10.3390/buildings14020328
Roh GT, Vu N, Jeon CH, Shim CS. Augmented DataDriven Machine Learning for Digital Twin of Stud Shear Connections. Buildings. 2024; 14(2):328. https://doi.org/10.3390/buildings14020328
Chicago/Turabian StyleRoh, GiTae, Nhung Vu, ChiHo Jeon, and ChangSu Shim. 2024. "Augmented DataDriven Machine Learning for Digital Twin of Stud Shear Connections" Buildings 14, no. 2: 328. https://doi.org/10.3390/buildings14020328