Introduction

The construction industry is in a constant state of evolution, driven by the demand for high-performance, durable, and sustainable materials. Concrete, as the most widely used construction material globally, is at the forefront of this transformation. A significant advancement in this field is the development of fiber-reinforced concrete (FRC) enhanced with nanomaterials. This advanced composite addresses two critical limitations of conventional concrete: its inherent brittleness and its relatively low tensile strength. The addition of fibers (such as steel, glass, or polypropylene) provides crack-bridging mechanisms, significantly improving post-cracking behavior, toughness, and flexural strength. Concurrently, the incorporation of nanomaterials, particularly nanosilica (nano-SiO2), refines the microstructure through pore-filling and the acceleration of pozzolanic reactions, leading to a denser interfacial transition zone (ITZ) and enhanced compressive strength and durability. This combination makes it an environmentally friendly option by potentially reducing the cement content required for a given strength, thereby lowering the carbon footprint associated with concrete production.
However, the macroscopic behavior of this multi-phase composite material is governed by a complex and highly nonlinear interaction of numerous parameters. These include the type, geometry, and volume fraction of fibers; the dosage and dispersion of nanosilica; the water-to-cement (w/c) ratio; the properties of aggregates; and the curing age. Traditional statistical and empirical models often fall short of accurately capturing this complexity, making the reliable prediction of key mechanical properties, such as compressive strength, a significant challenge. This research gap hinders the widespread adoption and optimal design of these advanced materials. Therefore, the primary objective of this study is to develop and validate a robust, intelligent framework for predicting the compressive strength of nanosilica-enhanced FRC. The novelty of this work lies in its systematic integration of a feature selection method with state-of-the-art hybrid artificial intelligence (AI) models, combining machine learning algorithms with metaheuristic optimization techniques to achieve superior predictive accuracy and reliability.
Research on fiber-reinforced concrete (FRC) and nanomaterial-modified concrete shows that fibers enhance ductility and impact resistance, while nanosilica improves mechanical properties and durability through pozzolanic activity. However, the combined effects of both components remain underexplored and highly dependent on mix design. Meanwhile, AI techniques like ANNs and ANFIS have been increasingly used to model concrete properties, with recent advances focusing on hybrid models optimized by metaheuristic algorithms such as PSO and GA to improve prediction accuracy. Despite these developments, the use of advanced algorithms like the Water Cycle Algorithm (WCA) for predicting the behavior of FRC containing nanomaterials is still limited. Additionally, systematic feature selection before modeling is frequently neglected—a gap this study addresses using Neighborhood Component Analysis (NCA).

Materials and methods
This research was conducted in three distinct phases: data preparation and feature selection, model development, and performance evaluation.
Data Collection and Feature Selection: A comprehensive experimental database was compiled from reputable, published literature. The initial set of input variables included mixture proportions: cement content (kg/m³), fine aggregate (kg/m³), coarse aggregate (kg/m³), water-to-cement ratio, fiber content (%), nanosilica content (%), and curing age (days). The output variable was the compressive strength (MPa). To reduce dimensionality and identify the most critical parameters, the Neighborhood Component Analysis (NCA) method was employed. NCA is a non-parametric method for feature selection that learns a feature weight vector by minimizing a loss function, typically the leave-one-out regression error. This process highlights variables with the most significant impact on the target variable, which are then used as inputs for the predictive models.
This study developed four hybrid AI models by combining two base learners (ELM and ANFIS) with two optimization algorithms (PSO and WCA). The optimizers fine-tuned the internal parameters of the base models—adjusting weights and biases for ELM, and membership function parameters for ANFIS. The resulting models were ELM-PSO, ELM-WCA, ANFIS-PSO, and ANFIS-WCA.
Performance Evaluation: The database was randomly partitioned into a training set (70%) for model building and a testing set (30%) for evaluating generalization capability. Model performance was assessed using two standard statistical metrics: the correlation coefficient (R) and the root mean square error (RMSE). A higher R (closer to 1) and a lower RMSE indicate better predictive accuracy.

Results and discussion
The results demonstrate a clear distinction in the performance of the developed models. The feature selection phase using NCA identified nanosilica content, water-to-cement ratio, fiber content, and curing age as the most influential parameters affecting compressive strength. These four variables served as the primary inputs for all subsequent models.
A detailed statistical comparison between the actual and predicted compressive strength values revealed that all hybrid models offered satisfactory predictions. However, the models optimized with the Water Cycle Algorithm consistently outperformed those optimized with Particle Swarm Optimization. Specifically, the ELM-WCA hybrid model exhibited superior performance across both the training and testing phases.
The ELM-WCA model achieved an exceptionally high correlation coefficient (R) of 0.9900 and a low root mean square error (RMSE) of 2.85 MPa during the training phase.
For the testing phase, which is the true measure of a model's predictive power, the ELM-WCA model maintained a high R value of 0.9736 and an RMSE of 4.04 MPa.
In comparison, while the ANFIS-based models and ELM-PSO provided reasonable predictions, their RMSE values were higher, and their R values were lower, particularly on the testing dataset.
Furthermore, an uncertainty analysis was conducted by examining the prediction error intervals. The ELM-WCA model exhibited the narrowest prediction error range (-8.22 to 7.74) compared to the other methods. This smaller interval indicates that the model's predictions are more consistent and reliable, with less scatter around the regression line, signifying lower uncertainty.

Conclusion
This research successfully developed and validated a robust hybrid intelligence framework for predicting the compressive strength of a complex composite material: fiber-reinforced concrete containing nanosilica. The study underscores the significant potential of combining advanced AI models with metaheuristic optimization algorithms for applications in materials science and civil engineering. The key conclusions are as follows:
Effectiveness of NCA: Neighborhood Component Analysis proved to be a powerful and systematic tool for feature selection, successfully identifying the most critical mixture parameters (nanosilica, w/c ratio, fibers, and age) and simplifying the modeling process without compromising accuracy.
Superiority of ELM-WCA: The hybrid ELM-WCA model emerged as the most accurate and reliable predictor. Its exceptional performance (R > 0.97 and low RMSE on unseen data) demonstrates the synergistic power of combining the fast-learning ELM network with the superior global search capability of the Water Cycle Algorithm. The WCA's ability to effectively tune the ELM's parameters leads to a model that can better capture the underlying nonlinear relationships governing the material's strength.
Importance of Optimizer Selection: The consistent outperformance of WCA-optimized models over PSO-optimized ones highlights that the choice of the optimization algorithm is as crucial as the choice of the base model. The WCA's unique mechanisms for balancing exploration and exploitation appear particularly well-suited for this type of complex optimization problem.
Practical Implications: The high accuracy and low uncertainty of the ELM-WCA model make it a valuable tool for engineers and researchers. It can be used to reliably predict the compressive strength of new mixtures, significantly reducing the need for time-consuming and costly trial batches. This can accelerate the development and optimization of environmentally friendly, high-performance concrete mixes, thereby promoting sustainable construction practices.
In conclusion, this study provides a clear pathway for leveraging computational intelligence to tackle the complexity of modern construction materials, paving the way for more efficient material design and quality control.