PSI - Issue 70

Rachit Sharma et al. / Procedia Structural Integrity 70 (2025) 386–393 Sharma and Laskar/ Structural Integrity Procedia 00 (2025) 000 – 000

391

6

 

N

2

( (

) )

i y y y y − −

y y −

1

1

1

= 



N i

N



2

N

1 = −

R

1

i

=

2 (4) where y and ̂ as target and predicted values, ̅ is mean of target values, and N as total number of data points. Table 4 summarises the performance indices of each analytical as well as ML model utilized in the study. Codal provisions showed high variability in all the matrices as compared to ML models. On comparing the ML models, ensemble model (XGBoost) has similar performance for testing dataset. However, the MAPE (%) for XGBoost model is considerably lower as compared to SVR. Based on the training dataset, XGBoost model has shown far superior accuracy based on the performance indices as compared to SVR model. The XGBoost model achieved reduced RMSE and MAE values of 2.22 kN and 1.49 kN, respectively, on the training set, as detailed in Table 4. Since, XGBoost models has best performance indicators as compared to SVR model, the present study has investigated the significance of various input parameters and their interactions in determining shear strength of FRP-RC beams. 1 N i i = ; 1 i i i RMSE y y − N = = ; 1 i i i MAE y y − N = = ; 1 i i i MAPE N y = 2 ( )

Table 4. Performance Indices of Various Models. Model Matrices ACI440.1R-15

GB50608-2020 SVR

XGBoost Training Testing Training Testing

R 2

0.11

0.49 85.07 35.74 32.37

0.97 18.79 6.26 7.26

0.93 35.28 19.21 24.55

1.00 2.22 1.49 3.08

0.94 34.39 14.63 15.80

RMSE (kN) 111.82

MAE (kN) MAPE (%)

55.16 51.76

5.2. Model Interpretation using SHAP Approach

SHAP interprets model outputs using SHAP values, with prediction ( f(x) ) expressed via feature attribution, as shown in Equation 5 (Lundberg and Lee (2017)). ' ( ) ( ) (5) Where x’ represent simplest input mapped to the original via x = h x (x’); 0 = f (h x (0)) is a constant when all inputs are null; denotes attribution value for feature i; and M is total number of features. he global significance of factors in influencing the predicted variable ( V exp ) is assessed using the average absolute SHAP value for each predictor in the XGBoost model as shown in Fig, 3(a). The most influential features are b, h, and a/d . It is observed that the geometric features of beam are the most significant governing parameters for shear strength. The less influential parameters are f c and L which showed the mean (| SHAP values |) closer to zero. The SHAP summary plot for the testing dataset (Fig. 3(b)) displays SHAP values along the horizontal axis, with colour indicating input data values — red for high and blue for low. Positive SHAP values suggest an increase in predicted shear strength of the FRP-RC beam, while negative values indicate a decrease. These results aid in identifying key factors for consideration in the shear design and optimization of FRP-RC beams. ' 0  = = +  1  = M i i x i f x g x

Fig. 3. Relative Importance of Individual Factor (a) Average Absolute of SHAP Values and (b) SHAP Summary Plot.