Concrete is a commonly used building material (AMIN et al., 2019; KHAN et al., 2022F; KHAN et al., 2022G). To lower the brittleness of concrete, scholars are investigating fiber-reinforced concrete (FRC), which is significantly more ductile than conventional concrete (KHAN et al., 2018; LI AND DENG, 2021; XIE et al., 2021; ZAID et al., 2021). The onset of concrete failure is the emergence of cracks (CAO et al., 2019; XUPENG et al., 2021). The introduction of hybrid FRC, which is comprised of multiple fibers (glass, steel, and polypropylene), is proposed to enhance the mechanical performance and energy absorption capacity of concrete (CAO et al., 2018A; HUANG et al., 2021; XUE AND YILMAZ, 2022; ZHAO et al., 2022). Fibers restrict the growth of cracks in concrete, thereby allowing structural elements to withstand greater deformations following the development of early cracks (cao et al., 2018B; ABIRAMI et al., 2020; CHUN et al., 2022; ZHANG et al., 2022). Nanoparticles, such as nano-silica (NS), have been shown to fill holes in cement paste and improve the mechanical performance and durability of concrete (BAHARI et al., 2016; CAO et al., 2020; MURAD, 2021; KHAN et al., 2022E). Consequently, using nanoparticles in FRC might result in a material with enhanced performance that is perfect for constructing durable, high-performance structures (HAO et al., 2021). NS decreases the setting time of the mix and increases its early-age strength. A crucial characteristic of NS is its nanostructure, which offers an exceptionally greater specific surface area (SSA) and thus works as an aggregate-cement binder (WANG et al., 2018). The strong pozzolanic effect of NS is due to its nanoparticle size (ARDALAN et al., 2017; YING et al., 2017). The interfacial transition zone (ITZ), which is considered a weak region in concrete, is also strengthened because these nanoparticles cover all gaps and voids, hence decreasing permeability (XU et al., 2017; SHARKAWI et al., 2018). NS is a highly effective ingredient for accelerating the hydration and producing more calcium-silicate-hydrate (C-S-H) gel in concrete, which is responsible for the achievement of concrete strength (NIEWIADOMSKI et al., 2017; NORHASRI et al., 2017; MOHAMMED et al., 2018; REN et al., 2018; ZAHIRI AND ESKANDARI-NADDAF, 2019). In cementitious materials, the quantity of portlandite-Ca(OH)₂ reduces when NS and Ca(OH)₂ combine to form a denser product (MASSANA et al., 2018). Certain prior research suggests that replacing NS for up to 4% of the cement can improve the material’s durability and strength under adverse conditions like corrosion and high temperatures (ERDEM et al., 2018; MAHAPATRA AND BARAI, 2019). The excessive quantity of NS might cause particle aggregation due to non-uniform dispersal, thus reducing workability (ZAREEI et al., 2019). To improve the macroscopic characteristics and performance of cementitious composites, several nanoparticles are utilized as additives, and NS has become frequent among these nanoparticles. Notwithstanding, the limited practical applications of NS in the building industry are a result of their higher costs, which are approximately 1,000 times more expensive than ordinary cement (RECHES, 2018; FANG et al., 2021).

From the standpoint of evaluating the structural health of concrete structures, ultrasonic pulse velocity (UPV) has been identified as an essential measure (BOLBOREA et al., 2021; KARIMAEI et al., 2021). Numerous research was conducted to comprehend the correlation between UPV and concrete compressive strength (YAN et al., 2021; ZHANG AND ASLANI, 2021). Similarly to compressive strength, the UPV of concrete likewise increases with age and is inversely related to the pore volume in the matrix (KOU et al., 2012). The rate of change of UPV with time may be utilized not only to estimate the setting of a mix but also to show distinct phases of microstructural changes in the matrix (LATIF AL-MUFTI AND FRIED, 2012; BARLUENGA et al., 2015). It was also shown that UPV is impacted by microstructural differences in the mortar and may be utilized to efficiently assess sand concentration in a mortar (MOLERO et al., 2009). Additionally, the UPV of concrete was explored to identify deterioration within the concrete (OULD NAFFA et al., 2002; LENCIS et al., 2021).

In two ways, the UPV test findings of FRC vary from those of plain concrete. Firstly, since the observed velocity is directly related to the concentration of the medium through which it is propagated, the insertion of different fibers might vary the density of the concrete and, therefore, the UPV findings (ASHRAFIAN et al., 2018). For instance, recent studies observed that the UPV of steel FRC was higher than the plain concrete; however, the UPV of FRC with low-density fibers, like polyphenylene sulfide or recycled polyethylene terephthalate, was less than plain concrete (RAHMANI et al., 2013; SADEGHI NIK AND LOTFI OMRAN, 2013). Secondly, the introduction of varying amounts of fibers might affect the concrete’s compaction level and, subsequently, its porosity (LI et al., 2022A; QIN et al., 2022; ZHENG et al., 2022). Previously, it was demonstrated that the slightly increased porosity of concrete resulting from the integration of 1% fibers by volume reduced the UPV of FRC samples, including polypropylene and steel fibers, by 4% and 3%, respectively (SUKONTASUKKUL et al., 2010). The number of parameters impacting concrete and the length of time necessary to establish the characteristics of hardened concrete motivate the search for alternate estimation techniques. UPV, which relies on ultrasonic wave speed transmission through the matrix, has been used to determine the characteristics of hardened concrete (TRTNIK et al., 2009; HUANG et al., 2011; DÜĞENCI et al., 2015; MOBINI et al., 2015). As previously demonstrated, the UPV of concrete mixes is an excellent indicator of their mechanical characteristics, including compressive and flexural strength and modulus of elasticity (TRTNIK et al., 2009). Large, thin, and difficult-to-access elements make it difficult to assess the UPV of the concrete. Not only do data-driven models assist minimize the time and expense of testing by supplying designers with vital data, but they also aid in avoiding complications that emerge during the assessment of the many hardened characteristics of FRC. The progress of innovative formula-based models with high precision to forecast this essential attribute can greatly minimize concrete waste by reducing the number of trial mixes necessary to get the ideal blend (KHAN et al., 2022H). Artificial intelligence-based practices, like machine learning (ML), are among the highly modern prediction procedures used in the present issue area (NAFEES et al., 2021; KHAN et al., 2022A; NAFEES et al., 2022A; NAFEES et al., 2022B; ILYAS et al., 2022). These methods imitate results based on the input dataset, and resultant models are validated by testing. The utilization of ML techniques to anticipate the characteristics of construction materials is gaining prominence (SHAFABAKHSH et al., 2015; AWOYERA et al., 2020; KHAN et al., 2022D). The most of past ML-based researches centered on estimating the strength of traditional concrete (QI et al., 2022; SHAH et al., 2022; SHARMA et al., 2022), while few research has been published on predicting the UPV of FRC. Therefore, it is vital to study the effectiveness of ML methods in estimating the UPV of FRC.

This research utilized the data sample to estimate the UPV of hybrid fiber-reinforced concrete modified with NS, hereinafter called HFRNSC, by employing ML methods. Three ML methods from boosting family were employed, i.e., gradient boosting regressor (GBR), Adaptive boosting regressor (ABR), and extreme gradient boosting (XGB), to achieve the study’s aims. Coefficient of determination (R ²), k-fold technique, statistical tests, and comparing estimated and actual results were used to assess and evaluate the performance of each model. It is obvious that conducting experiments requires a great deal of time, money, and effort due to the necessity of gathering materials, casting samples, curing, and testing. These issues might be resolved using cutting-edge methods like ML, which will be a benefit for the building industry. Moreover, the UPV and strength of HFRNSCs depend on a number of factors, and it is challenging to measure their combined influence using experimental methods. The influencing factors include fiber volume (Vf), coarse aggregate to fine aggregate ratio (CA/FA), superplasticizer to binder ratio (SP/B), water to binder ratio (w/b), NS, and age of specimen ((A). To investigate the relationship between the input characteristics and the UPV of HFRNSCs, a SHapley Additive exExplanations (SHAP) analysis was conducted. The literature may be mined for a data sample to use with ML methods. As a result, the information gathered may be used to run ML methods, estimate material characteristics, and evaluate the influence of input factors. In this work, a dataset was used to evaluate the performance of several ML methods for predicting the UPV of HFRNSCs and to determine the relative importance of various input variables in producing accurate predictions.

In order to get desired findings, ML methods require a wide collection of input variables (SUFIAN et al., 2021). For this purpose, a literature search was performed using six input parameters, including Vf, CA/FA, w/b, NS, SP/B, and the age of the specimen. To avoid bias, data samples were collected arbitrarily from previous studies (SADRMOMTAZI AND FASIHI, 2010; ASHRAFIAN et al., 2018), and data points containing UPV results were collected for algorithm execution. In this research, 132 data samples were recorded from the literature and employed to train ML techniques. The combination’s proportions and the desired outcome were considered when obtaining the data since models called for similar input variables for each mixture to estimate the required results. Three types of fiber, including glass, steel, and polypropylene, were used in the samples as hybrid fibers. The length and diameter of steel fibers were 36 mm and 0.7 mm, respectively, while the length and diameter of polypropylene and glass fibers were 12 mm and 0.1 mm, respectively. For the ML algorithms to run, all six features were used as inputs, with UPV serving as the result. The statistical details of inputs and outcomes are summarized in Table 1. The standard deviation, maximum, and minimum, show the range of values, whereas the mode, mean, and median show the basic tendencies.

The UPV of HFRNSCs was analyzed by employing published research data. The goals of the study were attained by employing ML strategies using Python code and Spyder (version 5.1.5) tool from the Anaconda Navigator software. The UPV of HFRNSCs was evaluated using GBR, ABR, and XGB ML techniques. In practice, these ML techniques are typically employed to approximate outputs from given inputs (YUAN et al., 2022). ML techniques are being employed to predict the strength, durability, and temperature resistance of materials (AMIN et al., 2022; KHAN et al., 2022C). Nevertheless, there are some limitations associated with the use of ML methods. Specifically, challenges associated with dataset generation, model validation, and model deployment, as reported by (LI et al., 2022B). The allocation of testing and training data samples utilized for the model was 30% and 70%, respectively. The precision of a model may be noted from the R ² value of the predicted result. Values closer to zero imply more variance, whereas values closer to one indicate that the prediction model and experimental findings are nearly completely matched (AHMAD et al., 2022). The k-fold method and statistical measures, including mean absolute error (MAE), root mean squared error (RMSE) and mean absolute percentage error (MAPE), were employed to measure the exactness of a model. The sequence of study methods is shown in Figure 1. The subsequent sub-sections elaborate on the ML techniques and validation strategies that were put to use in this study.

In this study, GBR, ABR, and XGB ML methods were utilized to evaluate the HFRNSCs’ UPV. Each method was tested for precision to determine which one was the most reliable indicator. The XGB approach yielded more precise findings, with an R ² of 0.90, for UPV prediction than the GBR and ABR methods, which had R ² of 0.78 and 0.85, respectively. The error readings provided additional proof of the XGB method’s better accuracy. The error analysis reveals that the XGB models had a better agreement between real and estimated values than the GBR and ABR methods. Table 4 is generated to compare the optimum ML methods of the present study with the literature. Previous studies have proven the XGB method’s superior accuracy in forecasting the strength of cementitious materials (FAROOQ et al., 2021; KHAN et al., 2022b; ZHENG et al., 2022). Similarly, the ABR method was also noted to be the best suitable in several studies (AL-HASHEM et al., 2022; ANJUM et al., 2022; SHANG et al., 2022; WANG et al., 2022).

Additionally, k-fold and statistical methods were utilized to evaluate the models’ precision. The accuracy of a model increases when the R ² is high and the degrees of divergence (MAE, RMSE, and MAPE) are minimum. Because the precision of an ML approach is so dependent on the amount of inputs and data samples used to run algorithms (FAROOQ et al., 2021), it is challenging to define and suggest the best ML technique for prediction in different fields of research. With ensemble ML techniques, the weak learner is used over and over again to build submodels that are trained on the data sample and then fine-tuned to improve accuracy. In this way, the ensemble ML models produce more precise results than any of the individual models could have on their own. The variation in R ² for the GBR, ABR, and XGB submodels is displayed in Figure 14. For GBR submodels, R ² varied from 0.762 to 0.781, with a mean of 0.769. The average R ² for the ABR models was 0.825, with a range of 0.773–0.853. Furthermore, the XGB submodels’ R ² ranged from 0.870 to 0.902, with an average of 0.893. Based on these results, it can be said that the XGB submodels are the most accurate of the three. More specifically, a SHAP analysis was run to learn how various input factors affected the UPV of HFRNSCs and how they interacted with one another. In a greater positive correlation with the UPV of the HFRNSC, specimen age was shown to be a highly useful parameter. The impact of NS on the UPV was also revealed to be more beneficial. It could be relied on by the filler action of NS, which lowers matrix porosity and ultimately raises UPV. However, it was shown that the impact of CA/FA on UPV was more adverse, indicating that a low CA/FA must be maintained to get a higher UPV. Also, it was determined that Vf had both positive and negative effects, suggesting that utilizing Vf up to an optimum amount can improve the UPV, while at larger Vf contents, the UPV may decline. The increasing matrix porosity, which is inversely correlated with matrix porosity (MOHAMMED AND RAHMAN, 2016), may cause decreased UPV at greater CA/FA and Vf. Because of the dearth of alteration in SP/B and w/b in the dataset used, their influence was unclear, and a broader data sample with more inputs and variations might result in better findings.

This research aimed to expand the knowledge on how machine learning (ML) models might be used to estimate the ultrasonic pulse velocity (UPV) of hybrid fiber-reinforced concrete modified with nano-silica (HFRNSCs). Three ML methods, including gradient boosting regressor (GBR), adaptive boosting regressor (ABR), and extreme gradient boosting (XGB), were used to evaluate the UPV. Also, SHapley Additive ExPlanations (SHAP) analysis was performed to examine the effect of input features on the UPV of HFRNSCs. The conclusions of this research are as follows:

• Modeling methods showed that the GBR and ABR techniques had a satisfactory level of accuracy with an R ² of 0.78 and 0.85 for UPV estimation, respectively, while the XGB method had a better level of accuracy with an R ² of 0.90 for UPV prediction.

This study utilized data for which controlled-environment experiments were conducted (laboratory). It is proposed that in future research, actual on-site circumstances, such as humidity, temperature, curing, etc., should be integrated into the modeling phase in order to investigate their effect on the material’s strength.