Twenty intact rock samples were carefully collected from four distinct geological formations across multiple provinces of Iran, each extracted from significant depths to ensure undisturbed structural integrity. These specimens exhibit remarkable diversity in their mineralogical composition, ranging from varied crystalline structures to striking differences in color, luster, and surface texturing - characteristics that visually reflect their unique geological histories. The comprehensive profile of these samples, including their formation origins and lithology, is systematically presented in Table 1 for detailed reference.

For comprehensive rock characterization, thin sections, rock powder under sieve No. 200, and polished sections were prepared from each sample to analyze petrographic, mineralogical, and textural properties. Following ISRM (2007) standards, we prepared 580 laboratory specimens in total: 100 NX-size cylindrical specimens (54 mm diameter) with length-to-diameter ratios of 2–3 for uniaxial compressive strength and elasticity modulus testing, 200 cylindrical specimens (L/D ratio 0.5-1) for point load tests, and 200 disc-shaped specimens (L/D ratio 0.5–0.75) for Brazilian tensile strength assessments. All specimens were precision-cut using a coring machine to ensure dimensional accuracy for subsequent mechanical testing, including elasticity modulus measurements.

The study employed a systematic experimental approach beginning with optical microscopy analysis of polished thin sections, XRD studies, and SEM analyses to characterize mineral composition, petrographic properties, elemental distribution in rock texture, and textural features while calculating Mineralogy and Texture Coefficients (MC and TC) in accordance with ISRM (2007) and ASTM (1996) standards. A comprehensive laboratory testing program was subsequently conducted on prepared rock specimens to evaluate key mechanical parameters including Schmidt rebound hardness (Hs), point load index (PLI), Brazilian tensile strength (BTS), uniaxial compressive strength (UCS), and elasticity modulus (E), following ISRM (2007) guidelines. Statistical analyses were then performed to derive empirical relationships between these mechanical properties and the calculated MC/TC values, with results thoroughly compared and interpreted.

The Schmidt hammer was applied to large rock blocks (approximately 30×40×50 cm) to measure rebound hardness (Hs). For point load testing, specimens of varying geometry (cylindrical, prismatic, or irregular) were compressed between standardized conical platens until failure occurred along extensional planes aligned with the loading axis. The point load index (Is) was then calculated using the following equation:

where P is applied force, and D_e is the distance between the platens at failure (equivalent core diameter). The point load index for a core diameter equal to 50 mm (PLI) is calculated from the following expression:

The Brazilian tensile strength (BTS) test provides an indirect method for determining rock tensile strength by applying compressive loading. In this standardized procedure, a disc-shaped rock specimen is subjected to vertical compressive forces through two opposing arc-shaped jaws, generating horizontal tensile stresses perpendicular to the loading axis. Since the applied compressive load maintains a consistent vertical orientation, the resulting tensile stress distribution occurs along the specimen's horizontal diameter. The tensile strength is then calculated using the following fundamental formula:

The uniaxial compressive strength (UCS) test is conducted on cylindrical rock specimens by applying continuous axial loading until structural failure occurs. This standardized procedure measures the maximum compressive stress a rock sample can withstand before fracturing, with the UCS value calculated using the following fundamental equation, where the compressive strength is determined as the ratio of peak load at failure to the original cross-sectional area of the specimen.

where P is the maximum load recorded at the moment of failure and D is the specimen diameter. Using the following fundamental equation, where the modulus represents the ratio of axial stress to corresponding axial strain within the material's proportional limit, providing a critical measure of the rock's stiffness and deformational characteristics under compressive loading.

where Δσ and Δε are the stress and strain changes, respectively, at 50% of the specimen deformation. Figure 2 shows the performing steps for the uniaxial compressive strength test to calculate the UCS an E of the studied rocks.

Based on the petrographic investigations by the microscopic polished thin sections, the selected rock samples were recognized various types of sandstone. Figure 3 shows microscopic images of the sandstone samples of the studied rock in polarized and normal lights (XPL and PPL). The results of thin section studies indicated that the CSP samples are a mixture of silicate grains including quartz, chert, glauconite, and fossil fragments of Bryozoa. About 60% of the total rock is composed of grains and 40% of it is composed of sparry calcite cement. The grain size is small, and the rock texture is compacted and has very low porosity. These rocks formed in shallow marine and coastal areas. The PDH samples contain silicate grains including quartz, chert, and muscovite. The cement is of the schist type with a small amount of iron oxide. About 70% of the total mass of these rocks is composed of grains and 30% of it is composed of weathered cement. The grain size is medium, the texture of the rocks is compacted, and it has very low porosity. The FJN samples contain quartz, chert, calcite, and iron oxide (hematite) minerals and fossil fragments. Quartz crystals are relatively small and angular and are seen in small amounts in the rock texture as scattered. About 60% of these rocks are composed of calcite and 35% of iron oxides. The grain size is medium; the rock texture has porosity and fractures and veins filled with calcite. The HZD samples contain silicate minerals including quartz, plagioclase, chert, biotite, and iron oxide (hematite). The weathered cement is composed of the sparry calcite and constitutes about 50% of the total of these rocks. The grain size is coarse; the texture of the rocks is uniform and has a lot of porosity. The percentage of minerals constituting each rock was obtained using the point counting method. The average modal abundance of minerals in the rock samples is presented in Table 2.

To complete the mineralogical studies of the sandstones, a comprehensive investigation was performed by using the X-ray diffraction (XRD) analyses. These studies were performed at 2θ angle between 4º and 70º (Fig. 4). For all the studied rock samples the mineralogical studies using the polished thin sections were confirmed by the XRD analyses.

The XRD graph of the sandstone sample of CSP1 reveals the sample is polymineralic sandstone with a mineralogical composition dominated by quartz, as evidenced by the highest intensity peaks at around 27° and 31° of 2θ angle, indicating quartz is the most abundant mineral present. Calcite is the next most prominent mineral, with notable peaks also appearing near these angles, denoting its significant yet lesser presence compared to quartz.

The sample also contains significant amounts of accessory minerals, including hematite and notably, glauconite. The high frequency of resistant quartz suggests the source rock was mature (rich in silica) and the sediment underwent extensive weathering and transport. The most definitive clue regarding the sample’s origin is the presence of glauconite, a potassium-iron-aluminum silicate that forms authigenically (in place) in shallow marine shelf environments characterized by slow sedimentation rates, generally indicating a stable, low-energy depositional setting. Furthermore, the presence of hematite points toward an oxidizing environment, while the abundant calcite cement is also common in marine sandstones, collectively suggesting the sandstone originated from a mature source and was deposited in a stable, oxidizing, shallow marine setting.

The XRD graph for the sandstone sample of PDH1 reveals its mineralogical composition based on the positions and intensities of the peaks. The major mineral identified is quartz, indicated by the prominent and frequent peaks with high intensities found throughout the 2θ range, especially the very high-intensity peak near 26.6°, which is characteristic of quartz. Other notable minerals present in the sandstone include chlorite, kaolinite, hematite, and calcite, each represented by smaller, distinct peaks at various 2θ positions. The frequencies of the peaks suggest quartz is the dominant mineral, while hematite, and calcite are present in significantly lower amounts. Based on the detected mineral assemblage, the sandstone is predominantly composed of quartz, indicating a mature sedimentary environment with significant weathering and transport history, typical of quartz-rich arenites. The presence of hematite suggests possible diagenetic alteration or iron-rich source material, while calcite may point to some secondary cementation. Such a mineralogical composition often originates from continental or fluvial depositional environments, where prolonged weathering and sorting preferentially preserve quartz and form secondary clays and iron oxides. This mineralogical suite implies the source area was likely granitic or high-grade metamorphic terrain, contributing abundant quartz, with diagenetic processes modifying the rock after deposition.

Based on the mineral peaks identified in the XRD pattern of the sample of FJN1, this sandstone sample is composed primarily of quartz and hematite, with significant amounts of calcite also present, indicating a polymineralic composition. Quartz as a typical mineral for sandstones is serving as the main framework grain, followed closely by the iron oxide hematite, and the carbonate mineral calcite, which likely acts as a cement. The dominance of the chemically and physically resistant quartz suggests the sediment has undergone extensive weathering and transport from a source rock rich in silica. The pervasive presence of hematite, which is often responsible for red coloration, is a strong indicator of deposition in an oxidizing environment; this could point towards a continental (fluvial or eolian) or a shallow, well-oxygenated marine environment. The presence of calcite suggests cementation occurred either through precipitation from circulating ground or pore water, often typical in marine or shallow burial settings. In summary, the mineral assemblage points to a relatively mature sandstone (rich in quartz) that was deposited and/or cemented under oxidizing conditions, likely in a continental (red bed) or shallow marine environment.

Based on the mineral peaks identified in the XRD pattern of the sandstone sample of HZD1, it exhibits a complex, polymineralic composition, with the primary minerals being quartz and calcite, which appear to be the most frequent, along with notable amounts of plagioclase (specially albite), and minor phases like hematite and zeolite. The high frequency of quartz confirms the rock as a sandstone, where it serves as the main framework grain, suggesting the sediment was derived from a silica-rich source rock. However, the presence of significant amounts of easily weathered minerals like albite and general plagioclase indicates a less mature sediment that has undergone limited chemical weathering and/or transport; this suggests a source area with exposed igneous or metamorphic rocks and rapid burial. The minerals calcite and hematite likely act as cements; the former suggests cementation from carbonate-rich fluids (possibly marine), while the latter suggests oxidizing conditions during or after deposition. The presence of zeolite suggests a history of burial or diagenetic reactions, possibly involving the alteration of volcanic ash or glass within the sediment. Overall, the mineral assemblage points to a lithic sandstone derived from a crystalline (igneous/metamorphic) provenance with limited weathering and transport, and a complex diagenetic history involving both carbonate cementation and the formation of secondary minerals like zeolite and chlorite.

The mineralogical composition of the studied sandstones helps to determine the position of these rocks in the sandstone classification diagrams based on the methods presented by Folk (1980) and Petitjean (1954) as shown in Figs. 5 and 6, and makes it possible to determine their precise names as presented in Table 3.

After the thin section and XRD studies, a comprehensive investigation was performed using the Scanning Electron Microscope (SEM). This method is suitable for elemental analysis and to study the textural characteristics of rocks. The elemental analysis is a helpful approach to identify the minerals made up the grains and the rock matrix and could be a suitable solution to complete the mineralogical studies based on microscopic thin section and XRD analyses. It is obvious that if the distribution of elements in the rock texture is known, by knowing the minerals present in the rock and the chemical composition of each mineral, the type of grains and the rock matrix can be determined.

Figure 7 displays the elemental analysis graphs for the samples of CSP1, PHD1, FJN1, and HZD1 derived from Scanning Electron Microscope-Energy Dispersive X-ray Spectroscopy (SEM-EDS). These graphs show the relative abundance of elements present in the samples, where the height of the peaks corresponds to the concentration of a specific element. All four samples exhibit very strong, dominant peaks, which almost certainly represent silicon (Si) and oxygen (O), confirming the primary component is quartz (SiO₂), typical of a sandstone. Beyond this common matrix, the samples show variation in accessory and cement phases. Samples CSP1 and FJN1 appear to be the most complex, showing several additional distinct peaks of moderate intensity, which could correspond to elements like aluminum (Al), iron (Fe), potassium (K), and possibly calcium (Ca) or magnesium (Mg). In contrast, samples PHD1 and HZD1, while still dominated by the quartz peaks, appear to have a simpler elemental composition, with fewer and lower-intensity accessory peaks, suggesting they are either cleaner, purer quartz sandstones or that the analysis spot specifically targeted a pure quartz grain, indicating less diverse mineralogy or localized purity. Overall, the intensity and variety of the minor peaks are crucial for mineral identification, reflecting the specific types of cements (like calcite or hematite) or accessory minerals that make up the non-quartz fraction of each individual sandstone sample. The results of the elemental analysis for representative samples of the studied rocks are presented in Table 4.

Figure 8 shows the SEM images at two different magnifications (157 x and 2.12 kx) and elemental analysis of the sample of CSP1. As can be seen in part a of the figure, the rock grains are relatively uniformly distributed in its matrix. Most of the rock texture is formed by grains (about 60%), which was also confirmed by microscopic thin section studies. In some areas, the grains are in contact with each other. The grain-matrix boundary is sharp, which is also clearly visible in part b of the figure. In parts c‒h of this figure, the distribution of the elements oxygen (O), carbon (C), calcium (Ca), silicon (Si), aluminum (Al), and potassium (K) is presented. Comparing these parts with part b of the figure shows that oxygen is distributed quite uniformly in the rock texture. Carbon and calcium are more present in the rock matrix, while Silicon is more present in the form of quartz and chert minerals within the rock grains. This means that the grains of the CSP1 sample (also in all rocks in the group) are quartz and its matrix is ​​calcium carbonate (calcite), which is consistent with the mineralogical studies by microscopic thin sections and XRD analyses. The presence of carbon and potassium in the rock texture is very low. Aluminum is also more present within some of the rock grains, which are glauconite, but its abundance is much lower than silicon. Therefore, the electron microscope analyses agree well with the results of the microscopic thin sections and XRD studies and confirm them. These studies reveal that the strength of the CSP1 sample grains is greater than its matrix, and when force is applied to the rock, initial microcracks occur in the matrix, and their joining together results in total rock failure.

Figure 9 presents the SEM images at two different magnifications (88 x and 7.81 kx) and elemental analysis of the sample of PDH1. As can be seen in part a of the figure, the rock grains are relatively uniformly distributed in its matrix. Most of the rock texture is formed by grains (about 70%), which was also confirmed by microscopic thin section studies. In some areas, the grains are in contact with each other. The grain-matrix boundary is completely sharp, which is also clearly visible in part b of the figure. In parts c‒e of this figure, the distribution of the elements oxygen (O), silicon (Si), and carbon (C) is presented. Comparing these parts with part b of the figure shows that oxygen is distributed quite uniformly in the rock texture. Silicon is more present in the form of quartz and chert minerals within the rock grains, while calcium (and may be carbon) are more present in the rock matrix. This means that the grains of the PDH1 sample are quartz and its matrix is ​​calcium carbonate (calcite), which is consistent with the mineralogical studies by microscopic thin sections and XRD analyses. These studies reveal that in the PDH1 sample, the grains are stronger than the matrix. As with the CSP1 sample, applied force causes initial microcracks to form in the matrix, and the interconnection of these cracks leads to total rock failure.

The SEM images at two different magnifications (500 x and 1.2 kx) and elemental analysis of the sample of FJN1 are presented in Fig. 10. As can be seen in part a of the figure, the rock grains are not well visible in its matrix. This means that the grain-matrix boundary is gradual and unclear. Most of the rock texture is formed by matrix, which was also confirmed by microscopic thin section studies. The distribution of the elements oxygen (O), carbon (C), calcium (Ca), and silicon (Si) is presented in parts c‒f of the figure. Comparing these parts with part b of the figure shows that oxygen is distributed quite uniformly in the rock texture. Carbon and calcium are more present in the rock matrix, while Silicon is more present in the form of quartz minerals within the rock grains. This means that the grains of the FJN1 sample are quartz and its matrix is ​​calcium carbonate (calcite), which is consistent with the mineralogical studies by microscopic thin sections and XRD analyses.

Figure 11 shows the SEM images at two different magnifications (56 x and 799 kx) and elemental analysis of the sample of HZD1. As can be seen in part a of the figure, the rock grains are relatively uniformly distributed in its matrix. The rock texture is equally formed by grains and matrix, which was also confirmed by microscopic thin section studies. The grains are not generally in contact with each other. The grain-matrix boundary is approximately sharp, which is also clearly visible in part b of the figure. The distribution of the elements oxygen (O), calcium (Ca), silicon (Si), carbon (C), aluminum (Al), natrium (Na), magnesium (Mg), and sulfur (S) is presented in parts c‒j of this figure. Comparing these parts with part b of the figure shows that oxygen is distributed quite uniformly in the rock texture. Carbon and calcium are more present in the rock matrix, while Silicon is more present in the form of quartz and chert minerals within the rock grains. This means that the grains of the HZD1 sample are quartz and its matrix is ​​calcium carbonate (calcite), which is consistent with the mineralogical studies by microscopic thin sections and XRD analyses. The presence of natrium and magnesium, and aluminum in some rock grains composed of albite and biotite, and zeolite is notable. These three elements have lower distribution than silicon.

The quantitative assessment of rock mineralogy was first introduced by Fereidooni (2022), who identified specific gravity (G_S) and hardness (H) as two key measurable engineering properties of minerals. By analyzing the proportional composition of minerals within a rock, a novel quantitative parameter—termed the Mineralogy Coefficient (MC)—can be derived to represent the rock’s mineralogical characteristics. The MC is calculated using the following equation:

where C_i, H_i, and G_Si are percent, hardness, and specific gravity of rock’s composing minerals, respectively. This formulation implies that higher MC values correspond to mineral assemblages dominated by hard and more dense minerals, while lower MC values indicate the presence of softer, less dense minerals. Therefore, the MC serves as a direct proxy for the mechanical strength of the mineralogical composition. The values of hardness and specific gravity for the minerals composing the studied rocks are presented in Table 5, and the calculated values of MC from the formula mentioned above for the rocks are listed in Table 6.

The influence of rock texture on engineering properties was first systematically studied by Williams et al. (1982), who identified key textural components including crystallinity degree, grain size distribution, microstructural patterns, and intergranular contacts. Modern research confirms that intact rock strength is fundamentally controlled by these textural characteristics, particularly through grain size, morphology, spatial orientation, interlocking mechanisms, boundary properties, and porosity. The quantitative analysis of rock texture was pioneered by Howarth and Rowlands (1986), with Howarth and Rowlands (1987) later establishing the essential quantitative parameters as the relative percentages of constituent grains and cementitious matrix. These researchers developed the Texture Coefficient (TC) as a comprehensive quantitative measure of rock texture, calculated through the following equation:

where AW introduces the grain packing weighting, N₀ and N₁ are the numbers of grains whose aspect ratios are below and above a pre-set discrimination level, respectively. FF₀ is the arithmetic mean of discriminated form-factors, AR₁ is the arithmetic mean of discriminated aspect ratios, and AF₁ is the angle factor for quantifying grain orientation. The parameters required for the aforementioned equations are derived from the following mathematical expressions:

(15)

n these equations, L the is length, W is the wide, P is the perimeter and A is the area of rock grains, AF and AF₁ are the angle factors, N is the total number of elongated particles, X_i is the number of angular differences in each class, and i is the weighting factor and class number. The correlation between the orientation angle (θ), weighting factors, and class numbers is summarized in Table 7, which facilitates the determination of appropriate weighting factors and class designations.

The Texture Coefficient (TC) can be computationally determined using JMicroVision 1.27 software through analysis of microscopic images from prepared rock thin sections. This specialized software, while originally developed for high-resolution rock section analysis, has versatile applications across multiple domains and supports various image formats including TIFF, BMP, JPEG, PNG, and GIF. JMicroVision provides comprehensive quantitative capabilities for characterizing rock components by measuring size, shape, orientation, interlocking features, and grain boundaries. The analytical procedure involves: (1) image calibration, (2) manual delineation of mineral grain boundaries, and (3) automated extraction of key parameters (L, W, P, A, and grain orientation, θ). Figure 12 shows the measuring method of rock grains geometric parameters by the JMicroVision 1.27 software, and Table 8 presents the calculated TC values and associated derived parameters for the studied rock samples.

The obtained mechanical properties for the studied rocks include Schmidt rebound hardness (H_s), point load strength index (PLI), Brazilian tensile strength (BTS), uniaxial compressive strength (UCS), and modulus of elasticity (E). The average values of the determined parameters are outlined in Table 9.

In this research, the independent variables are mineralogy coefficient (MC) and texture coefficient (TC). The dependent variables include Schmidt rebound hardness (Hs), point load index (PLI), Brazilian tensile strength (BTS), uniaxial compressive strength (UCS), and elasticity modulus (E). The correlations between independent and dependent variables are presented in Figs. 13 and 14. Also, extracted empirical equations and the statistical parameters including R and R² are detailed in Table 10.

The petrographic investigations show that the studied rocks are clearly vary in mineralogy and texture. The values of mineralogy coefficient (MC), which are related to the specific gravity and hardness of minerals composing the rocks, are between 0.097 and 0.147. The former value is for the sample of HZD1,3,5 (calclithite sandstone), and the latter is for the sample of PDH4 (see Table 6). As can be seen from Table 8, the highest value of TC was obtained for the sample of PDH5 (phyllarenite sandstone), and the lowest value of the parameter is for the sample of HZD5 equal to 0.931 and 0.750, respectively. In general, the values of MC and Tc for the samples of PDH are greater than the samples of CSP, FJN, and HZD, respectively.

The values of mechanical properties for the samples of PDH are greater than the samples of CSP, FJN, and HZD, respectively. The values of mechanical properties for the studied rock samples are firstly controlled by their texture, and secondly by presence of hard and dense minerals such as quartz, and calcite. In this regard, the samples of PDH5 and HZD3 have maximum and minimum values of mechanical properties (H_s, PLI, BTS, UCS, and E), respectively (see Table 9). A comparison between the values of mechanical properties of the rocks indicated that they are perfectly in tune with each other.

Mechanical properties (H_s, PLI, BTS, UCS, and E) have relationships with mineralogy and texture coefficients (MC and TC) which the relations were investigated using linear regression method. Based on the results, the mechanical properties are correlated to MC with direct linear relations (see Fig. 13 and Table 10). The best relation is between E and MC with R and R² equal to 0.75 and 0.57, respectively. The weakest relation is between Hs and MC, with R and R² equal to 0.69 and 0.47, respectively. The mechanical properties are correlated to TC with direct linear relations (see Fig. 14 and Table 10). The best relation is between E and TC, with R and R² equal to 0.95 and 0.90, respectively. The weakest relation is between BTS and TC, with R and R² equal to 0.92 and 0.84, respectively. Overall, the relationships between the mechanical properties and TC are better than MC. These results are confirmed by the results obtained by different researchers (e.g., Kamani and Ajalloeian, 2019; Diamantis et al., 2021; Hemmati et al., 2020; Yusof and Zabidi, 2016; Keikha and Keykha, 2013; Fereidooni, 2022; Tandon and Gupta, 2013; Tugrul and Zarif, 1999; Jeng et al., 2004; Prikiryl, 2006; Ajalloeian et al., 2016).

After extraction of the relations between the mechanical properties and MC, correlations between experimental and predicted values of the mechanical properties based on MC are shown in Fig. 15. According to the figure, the predicted values of H_s, PLI, BTS, UCS, and E are not generally equal to the experimental parameters, and the obtained lines are not well fitted the 45° line (y = x). So, there exist almost incomplete relations between the predicted and experimental values of the mechanical properties. Also, correlations between experimental and predicted values of the mechanical properties based on TC are shown in Fig. 16. It can be seen that the predicted values of H_s, PLI, BTS, UCS, and E are generally equal to the experimental values and the obtained lines are well fitted the 45° line (y = x). So, there are good correlations between the predicted and experimental values of the mechanical properties.

This study applied three computational intelligence algorithms - Linear Regression (LR), Support Vector Machine (SVM), and Gradient Boosting (GB) - to predict mechanical parameters using Orange 3.39.0 software. Figure 17 displays the software workspace containing all necessary operators: File for data import, Data Table for visualization, Preprocess for data cleaning, Data Sampler for splitting data into training and testing sets, Select Columns for choosing input and output variables, Test and Score for evaluating model performance, and Rank for determining parameter importance. Four error metrics were used for comparison: RMSE (root mean square error), which measures prediction accuracy in the target variable's units; MAE (mean absolute error) that uses absolute differences but presents optimization challenges; MAPE (mean absolute percentage error) for relative error assessment; and R² (coefficient of determination) to evaluate goodness of fit. These metrics collectively provide comprehensive insights into each model's predictive capabilities and limitations. They can be calculated from the following equations (Fereidooni and Ghasemi, 2023):

where y and y′ are the experimental and predicted values of UCS and E, and N is the total number of data (20 rock samples).

The values of the four above-mentioned indexes for the developed models are presented in Table 11, and depicted in Fig. 18. For LR models, the TC variants (particularly PLI-TC with RMSE = 0.23 and R²=0.89) consistently outperform MC variants, with UCS-MC showing the poorest performance (RMSE = 12.40, R²=0.48). The SVM models demonstrate extreme variability - while PLI-TC achieves exceptional results (RMSE = 0.15, R²=0.96), UCS-MC and UCS-TC yield negative R² values (-0.18 and − 0.06 respectively), indicating complete failure to capture data trends. Gradient Boosting emerges as the most robust algorithm overall, with BTS-MC (RMSE = 0.14, R²=0.96) and BTS-TC (RMSE = 0.13, R²=0.96) delivering nearly perfect predictions. Notably, MAPE values reveal that percentage errors are generally higher for MC variants across all algorithms, with UCS configurations showing particularly poor relative accuracy (MAPE = 22.69 for SVM UCS-MC). The R² metric confirms Gradient Boosting's superiority, maintaining values above 0.82 in all valid cases, while also highlighting SVM's instability with negative values in two configurations. Across all models, the PLI and BTS variants consistently rank among the top performers, suggesting these parameter combinations are more amenable to accurate prediction.

Sensitivity analysis examines how variations in input variables affect model outputs, quantifying each parameter’s relative contribution to prediction results. Researchers have developed multiple sensitivity analysis approaches tailored for both classification and regression tasks. This section details three prominent methods for ranking input parameters by their predictive importance.