PSI - Issue 78

Valentina Picciano et al. / Procedia Structural Integrity 78 (2026) 1167–1174

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from these data, the trained models can be used to estimate the structural capacity of other similar elements, making the approach a valuable predictive tool for engineering assessment (Asteris et al. 2019). The development of the predictive model followed a structured process consisting of data preprocessing, input feature selection, model training, and performance evaluation, with iterative refinements to improve accuracy. Particular attention was given to the choice of input variables, as they significantly affect prediction quality. Fundamental geometric parameters such as width, nib height, overall beam depth and the absolute shear span were included alongside strength-related features like concrete compressive strength and reinforcement strength parameters. This led to a total of ten input variables being used to predict a single output: the ultimate shear strength. The model training process was conducted using MATLAB’s Statistics and Machine Learning Toolbox, specifically the Regression Learner app (The MathWorks Inc. 2023). This environment allowed interactive training, testing, and optimisation of various regression models. Depending on the complexity of the relationships between variables, both simple—such as linear and nonlinear regression and decision trees—and advanced models—such as neural networks, Gaussian Process Regression (GPR), and Support Vector Machines (SVM)—were explored. The trained models were compared in terms of predictive accuracy, and the best-performing algorithm was identified and proposed as a fast, reliable tool for estimating the capacity of similar structural elements. Using the described application, the entire database—composed of all instances of input and output parameters— was automatically split into training and testing datasets. Specifically, 80% of the 210 instances (168 samples) were allocated for training the regression models, while the remaining 20% (42 samples) were reserved to test the predictive accuracy on new, unseen data. This random partitioning ensured unbiased selection, eliminating manual sampling effects. As a result, the application of supervised machine learning techniques produced predictive models of load-bearing capacity with generally high accuracy, despite isolated discrepancies. Predictive performance is strongly dependent on the quantity and quality of training data; here, models were trained on 168 instances, with 42 reserved for testing. The database’s heterogeneity—particularly the distinction between specimens reinforced with only horizontal and vertical bars (170 samples) and those with additional inclined bars (40 samples)—affected model accuracy, leading in some cases to less precise predictions. Another source of data variability is the concrete compressive strength ( f c ), a critical parameter influencing structural behaviour. The database includes specimens made with both normal and high-performance concretes, with substantially differing f c values. To address this, the dataset was split into two more homogeneous subgroups based on the median f c value (37.15 MPa), each containing 105 instances: one with f c ≤ 37.15 MPa and the other with f c > 37.15 MPa. Therefore, the regression modelling process was repeated separately for each subgroup. For the lower-strength subgroup ( f c ≤ 37.15 MPa), the best-performing model was a Support Vector Machine (SVM), achieving a test coefficient of determination ( R² ) of 0.97 (Fig. 2a). This indicated excellent predictive accuracy with residual errors ranging roughly between -21% and +23.7% (Fig. 2b).

(a)

(b)

Fig. 2. Regression results for fc ≤ 37.15 MPa: a) experimental vs. predicted load capacity; b) residuals on test set.

For the higher-strength subgroup (fc > 37.15 MPa), the top model was an Exponential Gaussian Process Regression (GPR) with an R² of 0.7 (Fig. 3a). While this model showed improvements over models trained on the full