Triboinformatic analysis and prediction of B4C and granite powder filled Al 6082 composites using machine learning regression models

The aim of this research is to evaluate how individual factors affect the wear and COF in Al6082-T651 hybrid composites. This analysis is essential for determining a composite material capable of enduring varying applied loads, sliding velocities, and sliding distances. To achieve this, a full factorial experimental design was employed, comprising 81 trials that incorporate four variables—denoted as R, L, D, and V—each examined at three distinct levels. The results obtained from these experiments are presented in Table 5.

Influence of load

Figure 10 illustrates the correlation between the applied load and the resulting changes in both wear and COF for hybrid composite materials. To investigate these complex relationships, a series of tribological experiments were carried out at a constant sliding speed of 0.83 m/s, with sliding distances ranging from 600 m to 1200 m. The results indicate a consistent increase in wear loss across all composite samples as the applied load rises, while the COF shows a decreasing trend with increasing load. Among the tested composites, the sample contains maximum weight% of reinforcement (denoted as HC3) demonstrated the best resistance to wear. This improvement is attributed to the higher reinforcement level, which enhances the composite’s hardness and mechanical strength. Specifically, the HC3 composite recorded a 37.91% reduction in wear loss under a 30 N load compared to a 10 N load at a sliding distance of 600 m (Fig. 10a). A similar trend was observed at a sliding distance of 1200 m, where HC3 showed a 9.75% improvement in wear resistance under the same loading conditions (Fig. 10e). The increased wear at higher loads can largely be attributed to intensified friction at the contact interface between the pin and disc, which accelerates material detachment from the pin surface. Moreover, all hybrid composites tested outperformed the base alloy in terms of wear resistance under identical load and sliding velocity conditions³⁸. The observed rise in wear loss with increasing load across all specimens is primarily due to enhanced plastic deformation caused by the elevated stress levels^38,39,40.

At lower applied loads, the contact between interacting surfaces is minimal, which typically results in reduced material loss due to wear in the fabricated samples. In contrast, as the load increases, the intensified surface interaction leads to greater wear and a noticeable decline in wear resistance⁴¹. However, during wear testing, the incorporation of reinforcement particles within the material played a crucial role in counteracting the effects of higher loads. These particles functioned as obstacles to deformation, thereby limiting plastic flow and substantially improving the material’s resistance to wear^38,39,41.

The frictional behavior demonstrated a trend opposite to that of wear, with the COF declining as both the applied load and the reinforcement content increased. The maximum COF value of 0.278 was noted for the HC1 sample under a 10 N load, whereas the minimum value, 0.17, was recorded for the HC3 sample under a 30 N load. This reduction in COF with higher applied loads and increased reinforcement content is mainly due to the thermal softening of the contact surface during sliding. At elevated loads, wear debris tends to accumulate between the sliding surfaces, forming a third-body layer that facilitates friction reduction. Furthermore, the higher temperatures generated under these conditions promote the degradation of surface asperities, leading to the formation of a lubricating layer that reduces shear stress between the pin and disc. This effect contributes significantly to the observed decrease in friction. A similar trend was reported by Zhao et al.⁴¹, who found that aluminum alloys reinforced with TiB₂ showed a more pronounced decrease in COF compared to those reinforced with SiC particles^20,42.

Influence of sliding velocity

Figure 11 presents the influence of sliding velocity on both wear loss and the COF in the hybrid composite samples. The tribological tests were carried out under varying loads ranging from 10 to 30 N and sliding velocities between 0.83 and 1.67 m/s, with a fixed sliding distance of 1200 m. As shown in Fig. 11, an increase in sliding velocity generally led to higher wear. For instance, the HC3 composite experienced a 10% reduction in wear at 10 N when the velocity increased from 0.83 m/s to 1.67 m/s. At a higher load of 30 N, wear reduction was even more significant—approximately 55%—when the velocity increased to 1.67 m/s under the same load conditions. This trend is likely due to shorter contact durations at higher speeds, which limit the time available for wear mechanisms to act. Additionally, the frictional interaction between the pin and disc generates heat, elevating their surface temperatures^43,44. As indicated in Fig. 11, the COF tends to decrease with increasing sliding velocity. This decline is attributed to the development of a mechanically induced mixed layer at the pin-disc contact zone⁴³, which acts as a lubricating film. At lower velocities, the roughness of the initial contact surfaces causes more pronounced mechanical interlocking, leading to higher friction. As the test progresses and wear smoothens these surfaces, the COF gradually decreases^43,44.

Influence of sliding distance

Figure 12 presents the relationship between sliding distance and both wear loss and the coefficient of friction (COF) for the tested composites. The experiments were conducted at a constant sliding velocity of 0.83 m/s, with sliding distances ranging from 600 to 1200 m. The results indicate a clear trend: as the sliding distance increases, both wear loss and COF also rise. This effect becomes more significant under higher applied loads which may be attributed to the generation of thermal energy at the contact interface during abrasive wear. With increasing sliding distance, the accumulation of heat may lead to material softening, thereby weakening the bond between the reinforcement particles and the matrix. As a result, the particles are more easily displaced, accelerating wear. Furthermore, this behavior could be linked to the destabilization of the tribolayer at extended sliding distances. Comparable observations of increased wear with longer sliding distances have been reported in previous studies^23,45. The rise in COF observed at greater sliding distances, as shown in Fig. 12, can be attributed to a greater number of asperity interactions. This enhances the presence of hard phases at the interface, thereby increasing the frictional force and, consequently, the coefficient of friction^38,39,41,42.

Influence of reinforcement proportion

The integration of reinforcement within the matrix is known to play a crucial role in enhancing the mechanical strength of composite materials. Improved interfacial bonding between the reinforcing phase and the matrix leads to increased stiffness and mechanical resistance. As depicted in Fig. 13, the inclusion of reinforcement materials also contributes to a noticeable rise in the composite’s hardness, which in turn enhances its wear resistance and reduces material loss due to wear. Among the tested samples, the HC3 composite exhibited the least wear, indicating superior performance. Moreover, the coefficient of friction (COF) was observed to decline with higher reinforcement content, as shown in Figs. 10, 11 and 12. This reduction in COF is likely due to the presence of hard reinforcement particles that reduce the effective contact area between the pin and disc surfaces. Further insights into the morphological aspects associated with this behavior are presented in Sect. “Conclusions”.

Surface morphology

Figure 14 display SEM micrographs taken from three different regions on the worn surfaces, illustrating the surface morphology in both severely and mildly worn areas of the hybrid composites. The experimental findings revealed that HC1 underwent the most significant wear under a load of 30 N, sliding velocity of 1.67 m/s, and a total sliding distance of 1200 m. In contrast, HC3 exhibited the least wear when tested at a lower load of 10 N, velocity of 0.83 m/s, and distance of 600 m. Overall, the wear behavior of the composites was governed by multiple mechanisms, including adhesion, abrasion, delamination, and oxidation^38,39,41,42. The presence of parallel grooves, as seen in Fig. 14, suggests the occurrence of abrasive wear. Such grooves are typically formed when a hard counterface moves against a softer material, causing surface displacement and subsequent material removal in the form of well-defined tracks⁴³. The surface of the pin also exhibited signs of oxidative wear, primarily due to the heat generated by friction during operation. Moreover, the accumulation of wear debris on the pin was attributed to plastic deformation. The emergence of layered structures and fine cracks, resulting from the detachment of wear particles, is a hallmark of delamination wear^44,46,47. The observation of cracks and voids on the worn surfaces’ points to material delamination, a process characterized by surface deformation, the initiation of cracks, and their subsequent propagation. Evidence of ploughing and crater formation on these surfaces further suggests the occurrence of plastic deformation. Notably, the surface subjected to more severe wear (Fig. 14a-c) displayed wider grooves and more extensive ploughed areas than the surface experiencing lower wear (Fig. 14d-f). At a higher applied load (L = 30 N), both the depth and width of the grooves increased, indicating that abrasive wear becomes more dominant under elevated loading conditions. Additionally, the presence of oxygen on the worn surfaces supports the occurrence of oxidative wear, likely resulting from the thermal effects generated during the sliding motion that promote surface oxidation. The high concentration of reinforcements in HC3 led to increased frictional heat generation, which in turn intensified the oxidation of the surface. This oxidation resulted in the formation of a protective oxide layer that minimized direct interaction between the abrasive sliding surfaces, thereby enhancing the composite’s wear resistance.

Evaluation of machine learning regression models

This section discusses the tribological behaviour analysis of hybrid Al6082-T651 composites exercising seven supervised ML models, which assists in determining the influence of input parameters on target features of wear and COF along with their correlation. The experimental trials and wear mechanism explained in previous sections have provided important insights in development of these prediction models with enhanced prediction capabilities for wear and COF under dry sliding conditions. The evaluation metrics considered for assessing the accuracy and consistency of developed ML models in prediction of COF and wear behaviour are mean square error (MSE), root mean square error (RMSE), mean absolute error (MAE), coefficient of determination (R²) and mean absolute percentage error (MAPE). These evaluation measurements are critical in realizing how closer the developed supervised regression model’s outcomes are to the actual experimental values of target features of hybrid composites. The parameter MSE denotes mean of squared differences between the experimental and ML model’s predicted values, while RMSE defined as the square root of MSE output. The MAE represented as the mean of absolute difference between ML predicted and actual experimental values. Similarly, the value of MAPE defined the mean of absolute error in percentage terms. These four evaluation measurements provide average of difference in ML model’s predicted values with experimental values in different forms, with ascertaining model’s efficacy having lower values in this system of measurements. Contrast to these evaluation metrics where low values are desirable for goodness of fit, the R² represents the degree to which the independent parameters successfully explained the variation in results of target features, i.e. wear and COF. Therefore, the higher value of R² is desired (closer to 1) to justify the explanation of most of output variables in adequate comparison of all ML models results. The R² measured value ranging from 0.9 to 1 revealed superior ML model having outstanding prediction characteristics, while lower than 0.9 is considered as moderate fit, which suggests the model inefficacy in explaining the output results. The results on these numerical metrics for wear and COF of hybrid Al6082-T651 composites are recorded in Tables (6–7) for seven supervised ML models in this study.

Table 6 shown that the SVM realized a MSE value of 0.0002, quantifying the average of squared error for predicted and experimental wear, while overall RMSE obtained as 0.0138. The MAPE % is within acceptable limits of 7.39 for SVM model justifying its prediction efficacy. The MAE showcased that SVM predicted wear values on average deviate by 0.0007 from wear experimental values. In addition, the SVM have superior \(\:{R}^{2}\) value of 0.9563 from most of the ML models, thus maintaining its efficacy in explaining almost 96% of variability in recommending accurate wear values. The RF model provides higher MSE and RMSE than SVM with 0.0031 and 0.0558 showcasing more overall prediction deviation in wear values. The MAE for RF demonstrated is slightly higher than SVM with 0.0118 showing average prediction deviations in all wear values. The RF model achieved an R² value of 0.8997, suggesting its inability to explain nearly 10% of variances in the results, thus realizing a lower accuracy in prediction. Also, KNN model obtained MSE and MAE values of 0.0018 and 0.0087, respectively, which is comparatively higher than the errors of SVM model. The MAPE of 13% is also at higher side, while R² value of 0.8975 suggested a better explanation of results than RF regression models but inferior to SVM model. Similarly, ANN have performed superior to RF and KNN in terms of MSE and RMSE with values of 0.0004 and 0.0197, respectively, while MAE of ANN is nearly comparable with SVM demonstrating its efficacy in accurate prediction of wear of hybrid composites. The ANN model also exhibited remarkable performance with explaining all variability in results having accuracy of nearly 94.1%. Moreover, the DT model have lowest MSE, however its MAE and MAPE percentage values are worst 0.0218 and 23.55, which established that its prediction errors are on higher side and have average deviation of nearly 23% in each of wear values from experimental value. The same explanation can be realized by the worst R² value of 0.6502, depicting the DT model can explain only 65% of variability in wear results. In contrast, XGBoost attained the lowest MSE value of 3.3659E-05 with MAE of 0.0084, demonstrating lower prediction errors in wear values. The MAPE has been under acceptable limits of 9.77%, exhibiting overall average error within tolerable range. The higher R² demonstrated its robustness and accuracy in explaining 94% of variability in wear results. Finally, the FL model exhibited significantly lower MSE, RMSE and MAE values of 0.0003, 0.0171 and 0.0023, which revealed lower prediction errors, thus highlighting greater accuracy. The average error in all wear predicted values are also at lowest level of 6.2247, while the R² value of 0.9638 have outperformed all models in explaining the variance, only approximately 3% variance in results are not explained, thus revealing exceptional accuracy.

Figure 15 illustrated the predicted versus experimental (actual) wear plots using all seven developed ML regression models on test datasets. The corresponding values of R² for specific models have also been included inside the individual plots. It is worth notable that FL model has demonstrated superior accuracy with remarkable R² value of 0.9638, which confirms that FL model can successfully predict the wear behaviour of hybrid composites with 96.38% accuracy on new datasets. The next best ML models are SVM, ANN and XGBoost with R² value of 0.9563, 0.9410 and 0.9408, respectively, displaying equivalent prediction accuracy in prediction of wear. In contrast, the KNN model and RF model have also adequately performed, however, higher deviations in average error shows restriction in accurately predicting wear performance for non-linear and complex correlated datasets. Moreover, the performance of FL and SVM may be credited to its competence in tackling the challenges of complex correlation among input variables and target feature. The fuzzy logic utilized gaussian membership functions with three fuzzy levels for efficient transformation of crisp values into fuzzy sets, thus empowering prediction of wear through underlying rule base and allowing it to describe intricate correlation within the datasets. Similarly, SVM performance have been aided by its radial basis function and regularization parameter, that efficiently balances the margin width and explained the underlying variances in the complex correlated data. In contrast, RF and DT models were unable to capture the underlying patterns in the datasets, owing to their overfitting of models, non-optimal hyperparameters, complex outliers and dataset features the concisely contributed to low performance of these regression models in prediction of wear behaviour of hybrid composites.

Furthermore, for enhancing the consistency and validation of different ML models performance in prediction of wear behaviour, residual plots are exercised and displayed in Fig. 16(a-g). The residuals are defined as the deviation of predicted wear values from actual experimental values, which are utilized as diagnostic plots in confirming the qualitative performance and accuracy information of the developed ML models. Each residual plot is combination of four sub-plots for analysis and better comparison of ML models. Figure 16 (a) displayed first plot depicting no trend and residuals are uniformly distributed around zero line, while the second plot showed histogram of standardized residuals. The histogram suggested that residuals have roughly uniform distribution with very few outliers confirming the residual distributions in first plot. The third plot demonstrated that all residuals are align closer to 45° inclined line with one outlier, thus verifying normal distribution. All coefficients in autocorrelation function (ACF) plot comes within the 95% confidence interval, implying the non-existence of autocorrelation and demonstrated that model successfully identified and explained all relationships among datasets.

Figure16 (b) showed that residuals are randomly distributed, and no patterns are visible, which showed there’s no problem of heteroscedasticity. However, there are few outliers which are confirmed by histogram plot of standardized residuals. In addition, the histogram of residuals confirms right side skewness indicating deviation from normality. The third plot demonstrated that all residuals are align closer to 45° inclined line with few outliers, thus drift from normal distribution specifically top ultimate values. The final plot of RF residual showcased all coefficients have low autocorrelation except for one, thus showing limitations of RF models in accurate prediction of wear and non-competence in explaining underlying complexity. Figure 16 (c) depicted KNN diagnostic residual plots with no evident trends or patterns in the residuals. The histograms are more normally distributed than RF results, while some of the residuals are outliers specifically at extreme bottom in Q-Q plot. In addition, all the coefficients have low autocorrelation and fall within the confidence interval. The aforementioned results for residuals depict KNN’s goodness of fit. However, low R² value of 0.8975 revealed that KNN is unable to handle the underlying complexity and variability in wear datasets having non-linear relationship with input variables. This can be due to comparatively lower data for training to restrict KNN to understand the hidden complexity and correlation between input-output features. Figure 16 (d) depicted ANN residual plots indicating good fit with no decisive pattern of residuals. The histogram of residuals is equally distributed and centred around zero suggesting an approximate normal distribution. The Q-Q plot suggested residuals are falling on inclined line with one outlier at extreme top. The low autocorrelation coefficients revealed independence of residuals. It is worth noting that DT showed worst residual performance with standardized residual histogram shown non-uniform variation of residuals which does not follow normal distribution. The first plot of DT model (see Fig. 16 (e)) demonstrates several outliers and are not symmetrical to zero line confirmed by the unbalanced histogram residuals. This suggests an inconsistent relationship between residuals and predicted values. Moreover, the Q-Q plot and ACF plot confirms significant variances in residuals with deviations from normal distribution and high autocorrelation. Such low performance of DT may be attributed to inability in explaining correlation between input parameters and target features. Also, the minimal R² of the DT model implies its restricted capacity to clarify substantial variance deviation. The inherent problem of DT model is its probable overfitting which can influence DT model’s inadequate performance in acquiring and describing the fundamental relationships in the datasets. The XGBoost model have also shown that variance is uniform, and no specific patterns is evident with one or two outliers (see Fig. 16 (f)). The residuals are roughly normally distributed all residual align with centre line and only one data shown significant deviation. As shown in ACF, the model showed one autocorrelation coefficients are outside the confidence interval. Finally, the FL model showed uniform distribution of residuals supported by uniformly distributed histogram distribution plot (see Fig. 16(g)). The residuals data are closely aligning with zero line revealing homoscedastic residuals with no specific trend. All residuals are also aligning with incline line, while ACF plot shows autocorrelation coefficients are falling within confidence range. Such improved performance in residual plots support the efficiency of the FL model in successfully analysing the inherent relationships and dependencies in the datasets. Furthermore, the best R² of 0.9638 specifies that the FL model justifies a meaningful explanation of complex variability present in the datasets. Therefore, the FL model can be deemed appropriate for additional assessment or prediction.

Additionally, Table 7 presents result on diverse evaluation metrics for COF considering seven ML models. The MSE and RMSE for SVM regression model is 0.0197, exhibiting minimum overall error among the models. The MAE of 0.0073 units represent average deviation in COF prediction values. Moreover, the higher values of R² demonstrated enhanced capability of SVM model in explaining 94.1% of variance in COF results. The RF and KNN models depicted average and overall squared difference in predicted and experimental values as 0.0006 and 0.0245, 0.0013 and 0.0361, respectively, which is lowest in all models for COF results. Similarly, the mean deviation in prediction values, i.e., MAE measured as 0.0112 and 0.0098 units, revealing higher prediction deviation throughout COF results in these models, which is higher than SVM models. However, the R² value of 0.9749 and 0.8933 illustrates reasonable accuracy in prediction and explaining the variation in results by RF and KNN models. The ANN model attained lower MAE than SVM, RF, KNN, thus showcasing lower prediction deviations in COF prediction results. Similarly, the RMSE of 0.0199 revealed comparable in overall mean square error with SVM. One of the highest R² of 0.9803 reveals that ANN comprehensively explained more than 98% COF variance and less than 2% remained unexplained. The DT model surprisingly performed superior to RF and KNN models with lower MAE and RMSE values of 0.0091 and 0.0238, showing lower prediction error, however prediction deviation is higher than SVM and ANN models. The greater R² value of 0.9521 indicated that it can explain more than 95% variance in COF outcome. The XGBoost models also improved its performance in prediction of COF features through comparatively lower MAE value of 0.0082 and RMSE of 0.0224, thus showing minimum overall error in its prediction capacity. Further, the MAPE % has also revealed lower average prediction deviation 1,48%, while considerably high R² value of 0.9744 representing that the model effectively explain nearly 97.44% of the COF variance. Finally, fuzzy logic model demonstrates lowest MAE value of 0.0059 and combined lower MSE value of 0.0004, indicating that FL model has low average error deviation and lower prediction errors for COF in comparison to all other competitive models. The lowest MAPE percentage and highest R² value of 0.9833 revealed that FL consistently explained all the variances in the COF output. Such outcomes indicate that the FL model is dependable and efficient in catching the original relationships and correlations in the COF feature data.

Figure 17 explained the predicted versus experimental wear plots for all seven regression models on COF test datasets. It is noteworthy that FL model has demonstrated superior accuracy with incredible R² value of 0.9833, which approves that FL model can successfully predict the COF outcome of hybrid composites with approximately 98.33% accuracy on new datasets and can explain nearly 99% variance in results. The FL model is followed by ANN and XGBoost with R² value of 0.9803 and 0.9744, respectively, exhibiting comparable prediction accuracy in prediction of COF. It is worth noting that DT and SVM models have also shown significant performance in explaining variation in COF results with R² value of 0.9521 and 0.9410. Although, the KNN and RF model have performed adequately, however, their higher deviations in average error concerns restrictions in accurately predicting wear performance for non-linear and complex correlated datasets.

Furthermore, for validating the reliability and efficiency of different ML models performance in prediction of coefficient of friction, residual plots are employed, and results are depicted in Fig. 18. The residuals are defined as the deviation of predicted COF from experimental values, which are utilized as diagnostic plots in confirming the qualitative performance and accuracy information of the developed ML models. Figure 18 (a) displayed SVM residual plots depicting most of the residuals towards negative side, which revealed that developed SVM model overfits the target feature. The histogram residual plot exhibited skewness towards right side, which is also confirmed by Q-Q plot with several outliers. However, the correlation coefficients are within confidence interval. Although, the residual plots showed significant weakness in term of residual behaviour, however, the higher R² value depicted better predictions of COF. Similarly, the RF and KNN showed similar residual behaviour uniform and random variance depicting no trend of data, thus confirming assumptions of regression models. The histogram residuals not following normal distribution for both the models specifically KNN showing right hand skewness, thus not conforming to regression assumptions. The third plot demonstrated that all residuals are align closer to 45° inclined line with one outlier, thus verifying normal distribution. All coefficients in autocorrelation function (ACF) plot comes within the 95% confidence interval, implying the non-existence of autocorrelation and demonstrated that model successfully identified and explained all relationships among datasets. The ANN and DT models plot depicts scattered residuals in their scatter plots denoting random variance in prediction of COF and homoscedasticity, while the histogram residuals, though somewhat showcased satisfactory in fulfilling the regression assumptions. The ACF plot revealing residuals coefficients fall under confidence interval as desired. Finally, the XGBoost and FL models demonstrated superior residual behaviour as shown in residual plots. The standardized residual data of FL is normally distributed with homoscedasticity behaviour and no trend, showing all the residual near to zero line. The histograms are normally distributed with Q-Q plot revealing upgraded performance by FL in comparison to XGBoost models (showing few outliers). At last, the autocorrelation is low depicting better performance for FL in explaining various dependencies and non-linear relationship between multiple input parameters and COF, thus revealing its outperformance in comparison to other ML models in understanding the underlying features and correlation.

Figure 19 demonstrated the feature importance plot for wear and COF, revealing the most important input parameters rank wise affecting target features. From Fig. 19 (a) and Fig. 19 (c), it is clearly evident that wear behaviour is mostly influenced by reinforcement percentage of B₄C in Al6082-T651 hybrid composites followed by normal load and sliding velocity. The addition of reinforcement materials improves the hardness of the hybrid composite, which contributes to upgrade the wear resistance capabilities in composite, thereby reducing the wear loss. The sliding distance is the least influential parameter affecting wear loss. Similarly, Fig. 19 (b) and Fig. 19 (d) revealed that applied load is most influential factor outperforming other input parameters in its impact on COF value. The other influential parameter is reinforcement percentage of B₄C affecting the COF followed by sliding distance. The sliding velocity shows no effect on COF, ranking last among input variables.

Figure 20 further visually depicted Pearson correlation coefficient map showcasing the quantitative correlation between input parameters and response variables of wear and COF. The Pearson correlation coefficient was typically employed for determining intensity and direction of non-decreasing or non-increasing correlation between different variables owing to the non-linearity of the datasets. The diverse colours in the map revealed the variation in positive and negative correlations from + 1 to −1. The coefficients near to + 1 indicate greater and positive relationship between corresponding features, while values near to −1 suggests inverse relationship among features. The increase in input parameters displays strong decreasing trend of target features. In Fig. 20 (a), it was evident from coefficient value of − 0.57 that with increasing reinforcement percentage, the value of wear loss decreases strongly. The addition of reinforcement materials enhances the hardness of the hybrid composite, which contributes to better wear resistance, thus lowering the wear loss. In contrast, with increasing the value of applied load, the wear loss shows strong positive correlation. It is evident that with lower value of applied load wear resistance can be enhanced significantly. In contrast, a coefficient of 0.35 between sliding velocity and wear loss indicates a moderate positive correlation, implying that higher sliding velocity increases wear loss. Similarly, sliding distance and wear loss have correlation coefficient of 0.21, implying weak positive correlation. This behaviour suggested that with increase in sliding distance, the heat generated intensified, causing softening of the test material, thus have slight tendency of enhancing wear loss.

Similarly, the COF metrics decreases with increasing reinforcement percentage, depicting a moderate negative correlation with correlation coefficient of − 0.50 (see Fig. 20 (b)). This behaviour may be attributed to presence of strong reinforcement particles that restrict the contact area between the pin and disc surfaces, thus enhancing friction between surfaces. Likewise, the normal load and COF have strong negative correlation with each other having coefficient as − 0.75, which suggests that with application of normal load, the friction between surface decreases significantly. This behaviour can be attributed to the accumulation of wear debris between contact surfaces contributes to this reduction in COF. Further, with 0.1 as correlation coefficient, there is a weak positive relation between sliding distance and COF, while sliding velocity has very wear negative correlation with COF. Such comprehensive assessment assists in recognizing how different input features are correlated to wear loss and COF, providing enhanced estimation and optimization of target features based on these underlying relationships.

Figure 21 depicted the violin plot for prediction of wear loss and COF of hybrid composites using different ML models, suggesting the concentration of residuals along bell-shape curve. The width of violin plot depicts the probability density of datasets. The symmetry in violin plot of FL model for wear loss, which suggested even distribution of data on both sides of median and enhanced prediction accuracy of model. The SVM model also have even distribution of datasets thus providing comparable violin plot with FL. Similarly, the FL model’s violin plot suggested more concentrated datasets, revealing better prediction accuracy of COF as shown in Fig. 22. Similarly, SVM, ANN and XGBoost performed very well in prediction of COF and have the capability to explain underlying correlation in input datasets with target features. The RF and KNN models performed worst with larger density of residual over a larger area depicting non-uniform distribution, thus not able to understand the non-linear relationship among input-output variables. Further, fuzzy logic models emerged as powerful tool to accurately predict the dependencies and underlying correlation, therefore, employed for analyse the interaction effect in the terms of three dimensional surface plots.

Figure 23 shows the surface plots depicting input parameters interaction effects on target features of wear loss and COF, which are created using MATLAB R2021a software. Figure 23 (a) shows that with higher reinforcement percentage of B₄C in hybrid composites along with lowest normal load results in minimum wear loss. Figure 23 (b) illustrated that higher reinforcement of B₄C with lower values of sliding velocity resulted in lowering the wear loss and enhancing the wear resistance capabilities of hybrid composites. Similarly, lower sliding distance of 600 m and highest reinforcement percentage results in enhancing the wear resistance behaviour in composite material as clearly seen in Fig. 23 (c). Figures 23 (d-e-f) suggested lower combination of normal load, velocity and normal load, sliding distance resulted in improved wear resistance performance of hybrid composite samples. Similarly, the COF values are reduced considering higher reinforcement percentage and load as shown in Fig. 23 (g). In contrast, Figs. 23 (h-i) shown that for all the values of sliding distance and velocity, the higher reinforcement of B₄C in hybrid composites provided reduced COF values. Similar trend can be seen in Figs. 23 (j-l), where higher load values with any values of sliding distance and velocity results in minimizing the COF performance.