⚡ electrical engineering

Explainable Machine Learning for Predicting the Splitting Tensile Strength of SCM-Blended Concrete Using Optimized Gaussian Process Regression

This study establishes a reliable, explainable framework for predicting the splitting tensile strength of supplementary cementitious material-blended concrete by optimizing a Gaussian Process Regression model with Bayesian techniques and identifying water and cement content as the dominant influencing factors.

Original authors: Ali Alnaqbi, Abdalla Mahmoud Salim, Mohammad Al-Zu'bi, Ibrahim Elnaml, Abdulaziz Alotaibi, Ahmed Mohammad Youssef

Published 2026-09-28

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CC BY 4.0

Original authors: Ali Alnaqbi, Abdalla Mahmoud Salim, Mohammad Al-Zu'bi, Ibrahim Elnaml, Abdulaziz Alotaibi, Ahmed Mohammad Youssef

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Concrete is the most widely used building material on Earth, forming the skeleton of our cities, bridges, and homes. Its strength and durability come largely from Portland cement, a binding powder that hardens when mixed with water. However, the production of this cement is a major source of global carbon emissions, prompting engineers to look for ways to reduce its use. To do this, they often replace a portion of the cement with industrial byproducts like fly ash, silica fume, or ground granulated blast-furnace slag. These materials, known as supplementary cementitious materials, can react chemically to strengthen the concrete while lowering its environmental footprint. Yet, predicting how these complex mixtures will behave is difficult. While engineers can easily measure how much weight a concrete block can hold before crushing, measuring how much force it takes to pull it apart is far more challenging. This "splitting tensile strength" is critical because concrete is naturally weak in tension, and cracks often begin when the material is pulled apart. Without reliable predictions, designing safer, more sustainable structures requires extensive and costly laboratory testing.

A team of researchers set out to solve this problem by teaching a computer to predict the splitting tensile strength of these eco-friendly concrete mixtures. They gathered data from a massive global database containing records of hundreds of different concrete recipes from around the world. The computer was fed eight key ingredients for each recipe: the amounts of cement, water, coarse gravel, fine sand, and the various industrial byproducts used as cement replacements, along with a chemical additive called a superplasticizer that helps the mixture flow. The goal was for the computer to learn the hidden patterns linking these ingredients to the final strength of the concrete, specifically its ability to resist being pulled apart.

The researchers tested a wide variety of mathematical models to see which one could learn these patterns best. They compared simple linear equations, decision trees, and complex neural networks against a more sophisticated approach called Gaussian process regression. This method is particularly good at handling messy, real-world data where relationships are not perfectly straight lines. After running thousands of simulations, the team found that a specific version of this regression model, using a "rational quadratic" kernel, outperformed all the others. This baseline model could predict the strength of a new concrete mix with an average error of just 0.34 megapascals, a unit of pressure used to measure force.

To make the model even sharper, the researchers used a technique called Bayesian optimization to fine-tune its internal settings. This process is similar to adjusting the knobs on a high-end radio to find the clearest signal, but it does so by intelligently testing different combinations rather than guessing randomly. The optimized model improved significantly, reducing the average prediction error to roughly 0.29 megapascals and increasing its overall accuracy. This improvement meant the model was not only more precise but also faster at making predictions once it was trained, allowing engineers to evaluate new mix designs almost instantly.

Perhaps the most important part of this study was making the computer's "thought process" understandable. Advanced machine learning models are often criticized for being "black boxes," where they give an answer without explaining why. To fix this, the researchers used two tools to open the box and look inside. They created visual maps showing how changing a single ingredient affected the predicted strength. These maps revealed clear, logical trends: increasing the amount of water in the mix consistently lowered the predicted strength, while adding more cement consistently raised it. The maps also showed that adding silica fume and ground granulated blast-furnace slag generally improved the concrete's ability to resist pulling forces, whereas fly ash had a more complex, less predictable effect.

To confirm these findings, the team used a statistical method that measures exactly how much each ingredient contributed to every single prediction. This analysis confirmed that water and cement were the two most powerful factors influencing the outcome. It showed that the computer had learned the same physical rules that human engineers have known for decades: too much water weakens the bond, while more cement strengthens it. The study concluded that by combining high-accuracy prediction with clear explanations, this new framework offers a reliable way to design sustainable concrete. It allows engineers to confidently experiment with new, greener recipes without needing to build and test every single variation in a physical laboratory, paving the way for more efficient and environmentally friendly construction.

Technical Summary: Explainable Machine Learning for Predicting the Splitting Tensile Strength of SCM-Blended Concrete Using Optimized Gaussian Process Regression

Problem Statement
The production of Portland cement is a significant source of environmental burden, driving the adoption of Supplementary Cementitious Materials (SCMs) such as fly ash (FA), silica fume (SF), and ground granulated blast-furnace slag (GGBFS) to create lower-carbon concrete. While the compressive strength of SCM-blended concrete has been extensively studied, its splitting tensile strength (STS)—a critical property for crack initiation and propagation—remains under-researched in data-driven studies. STS is difficult to estimate reliably due to the heterogeneous nature of concrete and the complex, nonlinear interactions between mixture constituents (cement, water, aggregates, SCMs, and admixtures). Existing empirical equations often lack applicability across diverse mixture designs, and many machine learning (ML) models operate as "black boxes," offering high accuracy but limited engineering insight into how specific variables influence predictions.

Methodology
This study developed an explainable ML framework using a global dataset of 395 valid SCM-blended concrete mixtures extracted from a larger database of 1,456 records. The input features included eight mixture variables: cement, water, coarse aggregate, fine aggregate, fly ash, silica fume, GGBFS, and superplasticizer. The target variable was the splitting tensile strength (STS) in MPa.

The research followed a structured workflow:

Feature Selection: Predictor relevance was assessed using four distinct methods: minimum redundancy maximum relevance (mRMR), F-test, RReliefF, and Random Forest importance. An overall ranking was derived by averaging the ranks from these methods.
Baseline Model Screening: A broad range of regression algorithms (linear regression, decision trees, support vector machines, ensemble methods, neural networks, and Gaussian Process Regression) were evaluated in MATLAB Regression Learner using 5-fold cross-validation. Performance was measured via RMSE, MSE, MAE, MAPE, and $R^2$ .
Hyperparameter Optimization: The best-performing baseline model family was optimized using three strategies: Bayesian optimization, random search, and grid search. The search space included basis functions, kernel functions, kernel scales, noise parameters, and standardization options.
Explainable AI (XAI): The final optimized model was interpreted using Partial Dependence Plots (PDPs) to visualize marginal effects and SHapley Additive exPlanations (SHAP) to quantify global feature importance and individual contributions.

Key Results

Baseline Performance: Among 30+ tested models, Rational Quadratic Gaussian Process Regression (GPR) emerged as the superior baseline, achieving an $R^2$ of 0.85, RMSE of 0.51 MPa, and MAPE of 10.02%. This outperformed linear models, SVMs, and neural networks.
Optimization Impact: All three optimization strategies (Bayesian, random, and grid search) converged to identical predictive accuracy for the final model ( $R^2$ = 0.89, RMSE = 0.41898 MPa, MAPE = 8.9%). However, Bayesian optimization was the most computationally efficient, requiring 89.72 seconds of training time compared to 187.81 seconds for random search and 316.86 seconds for grid search.
Performance Gains: Relative to the baseline Rational Quadratic GPR, the Bayesian-optimized model reduced RMSE by 17.85% and MSE by 32.48%, while increasing the prediction speed by approximately 101%.
Feature Importance: Feature ranking varied by method, but the averaged results identified superplasticizer, water, and cement as the top three predictors. SHAP analysis confirmed water and cement as the dominant global influencers.
Physical Interpretation: PDP and SHAP dependence plots revealed physically consistent trends:
- Cement: Higher content positively correlates with increased STS.
- Water: Higher content negatively correlates with STS.
- SCMs: Silica fume, GGBFS, and superplasticizer generally showed positive trends, while fly ash showed a negative effect as dosage increased.
- Aggregates: Coarse and fine aggregates exhibited complex, nonlinear responses with interactions dependent on other mixture components.

Significance and Claims
The paper claims that the proposed framework provides a reliable, data-driven tool for predicting the tensile performance of sustainable SCM-blended concrete. By integrating hyperparameter optimization with explainable AI techniques (PDP and SHAP), the study demonstrates that high predictive accuracy can be achieved without sacrificing engineering interpretability. The authors assert that the model successfully captures the nonlinear relationships between mixture composition and tensile strength, offering a transparent alternative to black-box models.

The study concludes that while the current model is accurate within the bounds of the compiled dataset, its practical application requires future external validation with independent experimental data and the inclusion of additional variables such as curing conditions and specific material properties to enhance robustness. The work does not propose new experimental protocols but rather establishes a validated computational framework to support performance-informed design of sustainable cementitious materials.

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