PSI - Issue 70

N. Vignesh Kumar et al. / Procedia Structural Integrity 70 (2025) 453–460

456

using a strain efficiency factor of 0.31, as recommended by Realfonzo and Napoli (2011). The target variable is the confined concrete strength, which is the peak axial stress obtained during testing.

Table 2. Statistical characteristics of the dataset parameters for GFRP datapoints. Parameter Minimum Maximum

Mean

Standard Deviation

Diameter (mm)

76

160 4.07

151.49

10.07

Height to Diameter ratio

1.97

2.07

0.35

Unconfined Concrete Strength (MPa)

18.11

107.80

42.46

18.18

FRP thickness (mm)

0.12

15

2.04

2.48

FRP tensile strength (MPa)

15.40 30.80

1659.84 135.81

672.97

515.25

Confined Concrete Strength (MPa)

68.61

25.24

3.2 Machine Learning Techniques Five different machine learning techniques were deployed using MATLAB 2024a for the prediction of FRP confined concrete strength. Stepwise Regression: Based on statistical significance it adds/removes variables. LASSO Regression: Employs L1 regularization for feature selection to develop simplified linear models and model optimization is achieved by 10-fold cross validation. Support Vector Machine (SVM): Uses Radial Basis Function (RBF) kernel function for non-linear relationships and the hyperparameters are tuned via Bayesian optimization (5-fold Cross Validation) to prevent overfitting. Regression Tree Ensemble (RTE): Combines multiple decision trees for accuracy and robustness of model. Gaussian Process Regression (GPR): Probabilistic method providing predictions and uncertainty intervals. Kernel parameters were optimized using maximum likelihood estimation. Measures were taken to prevent overfitting, especially for flexible models (GPR, SVM, RTE), including regularization (inherent in GPR, L1 in LASSO), hyperparameter tuning with cross validation (SVM) and ensembling (RTE). GPR’s ability to quantify uncertain ty is a key advantage for engineering reliability. 3.3 Performance Evaluation and Validation The performance of each prediction model was done using the following commonly employed metrics: Mean Absolute Percentage Error: = 1 ∑ | − ̂ | = 1 ×100 (1) Root Mean Square: = √ 1 ∑ ( − ̂ ) 2 = 1 (2) (3) where represents the experimental value of the confined concrete strength, the predicted value of the target variable is represented by ,̂ and represents the data points or samples in the dataset. In addition to that a sensitivity analysis was conducted to identify the most influential input parameter in the process of predicting the FRP confined concrete strength. For Stepwise and LASSO regression, the standardizes coefficients were used as identifiers of parameter importance. For SVM and Regression Tree Ensemble, permutation feature importance was calculated randomly permuting each input parameter (or variable) and measuring the result in prediction error. For GPR, the automatic relevance determination (ARD) approach was employed, where separate length scale parameters for each input dimension reflect the relative importance of the corresponding parameter. Coefficient of Determination: 2 =1− ∑ ( − ̂ ) 2 = 1 ∑ ( − ̂ ) 2 = 1