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Abstract

The current research focuses on predicting the tribological behavior of HNTs/LLDPE nanocomposites prepared via a rotational molding process through diverse techniques, including experimental design, multi-criteria decision-making, and machine learning classifier algorithms. The experimental design plan as per Taguchi’s L₁₆ orthogonal array has been created by varying the composition of HNT (1, 3, 5 and 7%), sliding velocity (1.5, 2, 2.5 and 3 m/s) and applied load (10 and 20 N). The evaluated specific wear rate (SWR) and coefficient of friction (COF) of the prepared samples are analyzed through signal-to-noise ratio method and ANOVA. The main effect plot and ranking from the response table highlighted that the composition of HNT is highly influential over both the output responses studied. ANOVA results indicate that the composition of HNT has 50% and 74.25% influence over specific wear rate and coefficient of friction. Through the combined approach of Entropy-CRITIC-TOPSIS techniques, the alternatives have been ranked and 55.22% of the contribution is shown by HNT composition and 26.06% of the contribution by sliding velocity over the combined objectives. The experimental outcomes have been analyzed as labelled data and the support vector machine classifier has rendered a superior performance of 93.8% of classification accuracy for both the experimental outcomes. The worn surface analysis through SEM revealed the presence of microcracks, wear debris and HNT particles. In applications requiring high durability and peak wear performance, the study suggests a greater HNT composition to lower the specific wear rate and coefficient of friction for the developed HNTs/LLDPE composite material.

Keywords

Halloysite nanotube low linear density polyethylene tribological analysis machine learning techniques critic

Highlights

⁃ HNT composition dominates tribological performance

⁃ Optimal process parameters identified via Taguchi & TOPSIS

⁃ Machine Learning models achieve high prediction accuracy

⁃ Worn surface analysis confirms enhanced wear resistance

⁃ Integrated data-driven workflow demonstrates optimization efficiency

Introduction

LLDPE is primarily used as a polymer for rotational moulding applications for the manufacturing of hollow seamless tanks, packaging, drug delivery and pharma, etc., due to its strength, better processability, flexibility and broader processing window. However, the applications of LLDPE are limited due to its lower tensile modulus, wear resistance and flammability. Further to enhance the performance and its use for various applications, the expected properties can be achieved with the inclusion of micro and nano-sized particles, chemical treatment, and advanced manufacturing processes.¹

Numerous researchers used various nanoparticles, such as silica,² titanium oxide,³ carbon nanotube⁴ and modified expandable graphite⁵ into the LLDPE polymer for improving its wear properties. Incorporating Flyash through rotational molding enhances tensile strength to 17.2 MPa at 5% FA, while modulus rises from 5.1% to 31.3%. However, higher FA levels reduce elongation, bending, and impact strength, highlighting innovative production potential.⁶ For instance, Laura Pena-Paras et al.⁷ showed 0.05 wt% of HNT within a polymeric lubricant, showing a 70% decrement in wear volume loss and COF and a smooth surface was attained, which is due to improved lubrication of HNT. Jani Pelto et al.⁸ found that a smaller amount of hydrophobic vinyl silane-treated SiO₂, HNT, TiN and graphene oxide nanoparticles significantly reduced the wear rate of HDPE. Among the different nanoparticles, 0.5 wt% of graphene oxide mixed composites showed 80% reduction in SWR and COF. This composition formed a smooth and thin surface on steel, compared to HDPE.

Albdiry & Yousif,⁹ 5 & 7 wt% HNT reinforced in unsaturated polyester greatly reduced the specific wear rate (SWR) and COF. The silane acts as a shield layer between the polyester and HNT, which improves the tribological performance. Boon Peng Chan et al.¹⁰ minimum wear rate and average COF on 10 wt% of talc loading on ultra-high molecular weight polyethylene (UHMWPE) and 12.02 N applied load, 0.378 m/s sliding speed. The transfer films of talc/UHMWPE showed smooth and more even surfaces compared to the virgin polymer. Zhi-Lin Cheng et al.¹¹ reported around 90% of wear rate reduction attained with 2 wt% of HNT in PTFE, which is 21 times less than the pure PTFE.

Many studies focused on nano fillers for the improvement of tribological performance of polymer composites; however, very few publications are available for finding the optimal parameters for pin-on-disc sliding wear behaviour. Now, enrichment of data science (DS), machine learning (ML) techniques is popular and very attractive, exploited in different research works to find the optimal process parameters and predict the performance. Several ML techniques such as Neural Networks, Logistic Regression (LR), Random Forests (RF), k-Nearest Neighbor (kNN), Support Vector Machine (SVM), Linear Regression, Decision Tree (DT), Markov Chain and Naive Bayesian are well known algorithms have been used for mechanical performance and wear analysis to find the optimum process parameters and output performances in various applications.¹¹ For instance, the ML model was developed for ultrahigh molecular-weight polyethylene (UHMWPE)/SiC (Silicon Carbide) nanocomposites for predicting the SWR and COF. The highest coefficient of determination R² value of 0.9999 was attained using support vector and followed by R² of 0.98891 for K – K-Nearest Neighbour model and R² of 0.9827 for Random Forest’s multi decision tree.¹² The curse of dimensionality, over-fitting, the unavoidable impact of noise, multiple-scale bridging, a lack of data, non-representative training data, offline learning, model deployment, and mixed variable issues are the main challenges with hybrid Artificial Neural Network-Genetic Algorithm and machine learning approaches.^13,14

Three machine learning (ML) techniques, including gradient boosting machine (GBM), RF, and artificial neural network (ANN), are used to forecast the tribo performance of graphene integrated with glass fabric reinforced epoxy composites. The ANN, RF, and GBM models obtained R² values of 0.9883, 0.9884, and 0.9762, respectively, while the RF model achieved the maximum accuracy.¹⁵ Polyvinyl alcohol (PVA)-based hybrid biocomposite films were created using coconut shell powder (CSP) and silver nanoparticles (AgNPs). Utilizing Taguchi-based Grey Relational Analysis (GRA), optimal composition was found at 10% CSP and 1 mM AgNPs, resulting in tensile strength of 38.1 MPa, Young’s modulus of 92.3 MPa, elongation at break of 18.1%, and maximum degradation temperature of 315°C, with performance contributions from AgNPs and CSP at 50.46% and 41.58%.¹⁶ Kiran et al.¹² understood the tribological performance of carbon nanotube-filled epoxy composites using ANOVA, RF & XGBoost. RF performed extraordinarily in estimating volume loss, as revealed by an R² of 0.99707 and minimum errors as compared to KNN and XGBoost.

Hariharasakthisudhan Ponnarengan et al.¹⁷ developed sustainable composites with Ultra-High-Molecular-Weight Polyethylene (UHMWPE) creinforced with CaO extracted from waste eggshells for sustainable material innovation. Using AI-based surrogate modeling (ANN) and Non-Dominated Sorting Genetic Algorithm (NSGA-III) optimization, optimized wear and friction performance. The optimal parameters 1 wt% CaO, 110 N load, 0.2 m/s speed—yielded excellent tribological results with <5% prediction error.

Wafa Khairallah et al.¹⁸ This experiment examined (UHMWPE) composites reinforced with magnetite nanoparticles (Fe₃O₄NPs) made via hot compression molding. Adding of 1 wt% Fe₃O₄, the composite achieved maximum hardness and lowest wear rate, indicating optimal performance. At 20 N load and 0.03 m/s sliding speed showed substantial improvements in wear resistance compared to pure UHMWPE.

Ephraim et al.¹⁹ The study established HDPE/PA6 and recycled HDPE/PA6 composites reinforced with 15 wt% glass fibres (GF) to replace steel in idler rollers. While wear rate and coefficient of friction (COF) decreased by 42% and 29%, respectively,

Based on the literature study, very few studies are available on HNTs reinforced LLDPE composites, but works reported about the implementation of machine learning techniques for predicting the tribological performance of HNTs/LLDPE nanocomposites are scarce. Hence, in the present investigation, the HNTs – LLDPE nanocomposites were prepared by varying compositions (HNTs - 1, 3, 5 & 7 wt%). The prepared composites were tested to evaluate the tribological performance by predicting the specific wear rate & coefficient of friction for rotational moulding applications.

Materials and methodology

The current section details different materials adopted in the current research and the methodology considered for attaining the research objectives.

Materials

Industrial rotational mouldable grade LLDPE with a density of 935 kg/m³and a melt flow index (MFI) of 42 g/10 min was purchased from D.R. Polymer Pvt. Ltd, India. HNT were bought from Sigma Aldrich, India.

Methodology

Figure 1 represents the research workflow in a schematic illustration. The current study has considered three different control factors, such as HNT composition, sliding velocity and the applied load to understand their effect on SWR and COF. From the considered control factors, both HNT composition and sliding velocity have been varied in four levels and applied load in two levels. As per the considered parameters and levels (2¹ × 4²), a total of 32 experimental trials need to be conducted as per a full factorial design. On the contrary, according to the mixed fractional factorial design, a total of 16 experimental trials can be performed using Taguchi’s L16 Orthogonal array, which reduces the time and resources required for the research. Table 1 shows the control factors and levels adopted in the current research in uncoded units. The experimental design layout for performing experimental trials as per Taguchi’s L₁₆ orthogonal array has been shown in Table 2, prepared through Minitab 17.0 software.

Figure 1.

Schematic illustration of research workflow.

Table 1.

Control factors and levels.

Control parameters	Symbol	S.I unit	Level 1	Level 2	Level 3	Level 4
HNT composition	A	%	1	3	5	7
Sliding velocity	B	m/s	1.5	2	2.5	3
Applied load	C	N	10	20	-	-

Table 2.

Experimental design matrix.

Trial No	A	B	C
1	1	1.5	10
2	1	2	10
3	1	2.5	20
4	1	3	20
5	3	1.5	10
6	3	2	10
7	3	2.5	20
8	3	3	20
9	5	1.5	20
10	5	2	20
11	5	2.5	10
12	5	3	10
13	7	1.5	20
14	7	2	20
15	7	2.5	10
16	7	3	10

Experimental work

The current section sheds light on sample preparation and also on the execution of experimental work as per the design layout prepared through Minitab 17.0 software.

Preparation of HNT/LLDPE nano composite

HNTs were first ultrasonically (frequency of 20 kHz, amplitude range of 40 – 60% and pulse mode 5 sec on/5 sec off) dispersed in acetone (purity of 99.9%) for 20 minutes, after which LLDPE powder was gradually added. The mixture was sonicated again for 15 minutes to ensure uniform distribution, dried in a hot-air oven for 10 minutes, and then used for nanocomposite fabrication. The prepared mixture (HNTs/LLDPE) was placed into a stainless-steel mould (300 × 300 × 3 mm) fitted in the compression moulding machine. The mixture was then subjected to a temperature of 120°C and compressed under a pressure of 3 MPa for 45 minutes, allowing the blend to consolidate and form the desired nanocomposite achieved.

Eventhough focused application is rotational molding, the direct manufacturing of nanocomposites using this method is quite tricky due to difficulties in achieving uniform nanoparticle dispersion and controlling wall thickness. Hence, compression molding was used to prepare the nanocomposites, confirming consistent quality for tribological testing. Once performance was validated, the material system is proposed for future use in rotational molding applications.

The composite is created by adjusting the HNT concentration between 1, 3, 5, and seven wt percent. The concentration selected based on the previous literature review has reported better material and wear properties with halloysite nanotube (HNT) loadings of up to 10 wt%. Exceeding 10 wt% often leads to nanotube agglomeration, poor dispersion and diminished performance.² Hence present study focused, HNTs were incorporated at varying concentrations of 1, 3, 5, and 7 wt% to systematically evaluate their effect on the composite properties and to identify the optimal filler content. The developed nanocomposites are analyzed for their tribological performance, such as SWR & COF.²⁰

Pin on disc wear test

The dry sliding wear test was carried out through a pin-on-disk tribometer (DUCOM, Model No: ED-201) as per the procedure given by ASTM G99-05. The samples (i.e., pin) were prepared from the developed composites with the dimensions of 40 × 10 × 3 mm and wear testing parameters are provided in Table 3. The experiments were conducted based on the experimental plan provided in Table 2 and the mass loss to calculate the specific wear rate using the standard formula.⁸ The coefficient of friction was obtained through a data acquisition system.

Table 3.

Wear analysis testing parameters.

Pin material	HNTs/LLDPE nanocomposites (1, 3, 5 & 7 wt%)
Disc material	EN32 steel disc
Radius of the track	50 to 100 mm
Working temperature	Room temperature
Sliding distance	300–1500 m

Results and discussion

The specific wear rate (SWR) and coefficient of friction (COF) values obtained through the standard pin-on-disc material test have been tabulated and analyzed through diverse techniques. Table 4 represents the experimental outcomes. From Table 4, A stable trend was perceived where increasing the level of factor A (from 1 to 7) normally led to a decrease in SWR, particularly when merged with higher values of factors B and C. For insistence, at trial 1 (A = 1, B = 1.5, C = 10), the SWR was 0.00132 mm³/Nm, while at trial 15 (A = 7, B = 2.5, C = 10), it declined significantly to 0.00019 mm³/Nm. This recommends that the material displays better wear resistance at higher levels of factor A, possibly due to improved compaction or hardening effects.

Table 4.

Experimental outcomes in coded control factors.

Trial no.	A	B	C	SWR	COF
1	1	1.5	10	0.00132	0.295
2	1	2	10	0.00132	0.288
3	1	2.5	20	0.00055	0.265
4	1	3	20	0.00055	0.265
5	3	1.5	10	0.00087	0.273
6	3	2	10	0.00048	0.271
7	3	2.5	20	0.00020	0.243
8	3	3	20	0.00026	0.265
9	5	1.5	20	0.00050	0.239
10	5	2	20	0.00048	0.228
11	5	2.5	10	0.00032	0.243
12	5	3	10	0.00032	0.219
13	7	1.5	20	0.00032	0.239
14	7	2	20	0.00035	0.239
15	7	2.5	10	0.00019	0.239
16	7	3	10	0.00019	0.252

The COF shadowed a more scattered pattern but still confirmed some consistent trends. Trials piloted at higher A values (5 and 7) generally recorded lower COF values compared to those at A = 1. For example, the COF fell from 0.295 in trial 1 to 0.219 in trial 12 (A = 5, B = 3, C = 10). This could be connected with better surface connections at higher A values, perhaps due to improved surface agreement or establishment of lubricious tribolayers.

Signal-to-noise ratio method

The signal-to-noise ratio (SNR) method, which quantifies robustness, is used to identify control factor values that lessen the effect of noise on the response. For the current research outcomes, both specific wear rate and coefficient of friction need to be reduced to enhance the longevity of the product and also to deliver its intended performance to the maximum extent. The formulae for determining the signal-to-noise ratio values of the output using Minitab 17.0 software are given in Equation (1). The analysis of experimental outcomes through the signal-to-noise ratio method, with smaller the better characteristics, generates a main effect plot which represents the optimal factor settings for minimizing the output responses, and it ranks the control factors according to their influence over the experimental outcomes.²¹

{SNR}_{Smaller the Better} = - 10 * \log (\sum \frac{Y^{2}}{n})

(1)

The main effect plot shown in Figure 2(a) indicates that the parameter combination A4B3C2 – 7% HNT composition, sliding velocity of 3 m/s and 20 N load is the optimal parameter setting for minimizing the specific wear rate of the developed composite. Additionally, HNT composition has been ranked as highly influential by the response table and subsequently followed by sliding velocity and applied load as shown in Table 5.

Figure 2.

Main effect plot for SWR & COF.

Table 5.

Response table ranking - SWR.

Level	A	B	C
1	61.41	63.69	66.43
2	68.28	64.86	68.42
3	68.05	70.84
4	71.97	70.30
Delta	10.56	7.15	1.99
Ranking	1	2	3

Similarly, the main effect plot depicted in Figure 2(b) represents that the combination is optimal to reduce COF. HNT composition has been ranked as a significant parameter affecting COF, and ranking is followed by sliding velocity and applied load as per the response Table 6.

Table 6.

Response table ranking - COF.

Level	A	B	C
1	11.12	11.69	11.74
2	11.61	11.86	12.13
3	12.69	12.14
4	12.32	12.06
Delta	1.57	0.45	0.39
Ranking	1	2	3

Statistical analysis

The relevance of a parameter over an experimental result is ascertained using the ANOVA statistical technique, which compares the variances across the means that exist between several groups. The current study has performed ANOVA analysis with a 95% confidence interval and the control factors resulting in a p-value less than 0.05 are considered as influential. Based upon the analysis of specific wear rate values through ANOVA, all three factors involved as control factors are found to have significance over specific wear rate and regarding the contribution percentage, both HNT composition and sliding velocity shared 50% contribution.¹⁹ R² value of 0.94 is highly acceptable and the variations in specific wear rate can be explained by the model with a good fit. Table 7 represents the ANOVA results for the specific wear rate.

Table 7.

ANOVA results for SWR.

Source	DF	Adj SS	Adj MS	F-value	P-value	Contribution %
A	3	0.000001	0.000000	23.89	0.000	50
B	3	0.000001	0.000000	14.10	0.001	50
C	1	0.000000	0.000000	14.16	0.006	0
Error	8	0.000000	0.000000			0
Total	15	0.000002				100

A substantial p-value of 0.006 for factor C (load) suggests that it has an impact on specific wear rate. However, because its sum of squares is very small in comparison to Factors A and B, its percentage contribution appears to be 0%. Due to the very low experimental error, even a small effect produces a high F-value, but the overall effect size remains minimal. Thus, C has a statistically detectable influence, but contributes negligibly to total variability when compared to A and B. As a result, whereas Factor C has just one degree of freedom (two levels), A and B have three degrees of freedom (four levels), and C has a statistically discernible influence but adds very little to overall variability. This restricts the variability spread that C contributes. Although Factor C has a statistically significant impact on the response, its absolute impact is much less than that of Factors A and B.

Similarly, the COF values have been analyzed through ANOVA and both HNT composition and applied load are found to be significant with p-values less than 0.05, as shown in Table 8. The major contribution is found with HNT composition with 74.25% and the applied load has a contribution of 8.53%. The error resulted in an ANOVA analysis for COF value, which is found to be 10.34% which is in an acceptable range. The R² of 0.90 for CoF indicates that the model can make better predictions about the future models with an accuracy of 90%.

Table 8.

ANOVA results for COF.

Source	DF	Adj SS	Adj MS	F-value	P-value	Contribution %
A	3	0.005121	0.001707	19.15	0.001	74.25
B	3	0.000475	0.000158	1.78	0.229	6.89
C	1	0.000588	0.000588	6.6	0.033	8.53
Error	8	0.000713	0.000089			10.34
Total	15	0.006897				100.00

Normal probability plot

The Figures 3 and 4 show the normal probability plot for both SWR and COF values, which represents the closeness of the experimental data with normal probability and only a less outliers have resulted. This represents a close fit of the experimental data.

Figure 3.

Normal probability plot for SWR.

Figure 4.

Normal probability plot for COF.

Multi-response optimization

Multi-response optimization is the process of using multi-criteria decision-making (MCDM) techniques to reduce a problem with several objectives to a single objective problem. This method’s main goals are to rate the options and determine which is the greatest and worst option among them. The weight evaluation of each criterion is very important before the alternatives are ranked. The current study has evaluated weight values for the experimental outcomes through Shannon’s entropy and the CRITIC method to rank the alternatives through equal TOPSIS technique. The ranking obtained through the TOPSIS technique has been verified through WASPAS method for understanding the sensitivity.²²

Shanon’s entropy method

In 1948, Shanon created the entropy technique and put out a decision matrix for normalizing experimental values and transforming them into the proper project outcome. To calculate the entropy measure and generate the objective weights that can be used to define the output response weight, the evaluated project results are utilized. The project outcomes and the normalized values of the output responses are displayed in Table 9. Table 10 shows the weight values for SWR and COF.

Step 1: Normalizing the decision matrix to obtain the project outcomes

Step 2: Entropy measure computation.

Step 3: Defining objective weight

Table 9.

Normalized outcomes and entropy measure.

Trial No	A	B	C	Normalized		Entropy measure
Trial No	A	B	C	SWR	COF	SWR	COF
1	1	1.5	10	0.1606	0.0726	−0.2937	−0.3601
2	1	2	10	0.1606	0.0709	−0.2937	−0.3585
3	1	2.5	20	0.0669	0.0652	−0.1810	−0.3519
4	1	3	20	0.0669	0.0652	−0.1810	−0.3519
5	3	1.5	10	0.1058	0.0672	−0.2377	−0.3544
6	3	2	10	0.0584	0.0667	−0.1659	−0.3538
7	3	2.5	20	0.0243	0.0598	−0.0904	−0.3438
8	3	3	20	0.0316	0.0652	−0.1092	−0.3519
9	5	1.5	20	0.0608	0.0588	−0.1703	−0.3421
10	5	2	20	0.0584	0.0561	−0.1659	−0.3371
11	5	2.5	10	0.0389	0.0598	−0.1264	−0.3438
12	5	3	10	0.0389	0.0539	−0.1264	−0.3326
13	7	1.5	20	0.0389	0.0588	−0.1264	−0.3421
14	7	2	20	0.0426	0.0588	−0.1344	−0.3421
15	7	2.5	10	0.0231	0.0588	−0.0871	−0.3421
16	7	3	10	0.0231	0.0620	−0.0871	−0.3473

Table 10.

Objective weight values - Entropy.

SWR	CoF
0.32	0.68

CRITIC

The significance of criteria for assessing the weights of output responses is through Intercriteria Correlation (CRITIC), which starts the process of normalizing experimental data. The procedure comprises calculating the normalized data standard deviation, which is subsequently utilized to construct the information quantity, correlation matrix, and conflict measure. Information quantity is the main input used to determine the weights of output answers. Table 11 shows the normalized experimental outcomes, and Table 12 represents the final weight values obtained for SWR and COF.

Step 1: Decision matrix normalization

Step 2: Evaluate standard deviation

Step 3: Symmetric matrix evaluation

Step 4: Calculation of the measure of conflict

Step 5: Quantity of information evaluation

Step 6: Determination of objective weights

Table 11.

Normalized experimental outcomes.

Trial No	A	B	C	SWR	COF
1	1	1.5	10	0.0000	0.0000
2	1	2	10	0.0000	0.0921
3	1	2.5	20	0.6814	0.3947
4	1	3	20	0.6814	0.3947
5	3	1.5	10	0.3982	0.2895
6	3	2	10	0.7434	0.3158
7	3	2.5	20	0.9912	0.6842
8	3	3	20	0.9381	0.3947
9	5	1.5	20	0.7257	0.7368
10	5	2	20	0.7434	0.8816
11	5	2.5	10	0.8850	0.6842
12	5	3	10	0.8850	1.0000
13	7	1.5	20	0.8850	0.7368
14	7	2	20	0.8584	0.7368
15	7	2.5	10	1.0000	0.7368
16	7	3	10	1.0000	0.5658

Table 12.

Objective weight values - CRITIC.

Standard deviation		Symmetric matrix		Measure of conflict		Quantity of information		Weight values
SWR	COF	SWR	COF	SWR	COF	SWR	COF	SWR	COF
0.3186	0.2821	1.0000	0.7685	0.0000	0.2315	0.0738	0.0653	0.53	0.47
0.3186	0.2821	0.7685	1.0000	0.2315	0.0000	0.0738	0.0653	0.53	0.47

From the comparison of weight values for output response evaluated through entropy and CRITIC techniques, the weight values recommended by the methods are not similar. Figure 5 shows that the entropy technique has recommended 32% weightage for specific wear rate and a maximum weightage of 68% for the coefficient of friction. On the contrary, the CRITIC technique has assigned 53% weightage for specific wear rate and 47% for the coefficient of friction. The current study has adopted the weight values obtained through entropy method for ranking the alternatives as an initial step and later CRITIC based weight values to be applied to understand the changes in ranking through evaluation correlation percentage.

Figure 5.

Comparison of weight values – Entropy and CRITIC.

TOPSIS technique

The Technique for Order Preference by Similarity to Ideal Solution is a multi-objective optimization tool that separates the optimal choice from both the positive and negative ideal solutions. Here are the specific steps that are part of the TOPSIS technique.

1^st Step: Decision matrix normalization

2^nd Step: Calculation of weighted normalized values

3^rd Step: Ideal positive and negative solutions

4^th Step: Euclidean distance evaluation

5^th Step: Alternative ranking through relative closeness to the ideal solution.

TOPSIS is selected as the method of decision-making due to its great effectiveness even in cases where there are few output answers. The current research problem still demands finding the optimum compromise among 16 trials where both responses must be optimized simultaneously, even if only two responses specific wear rate (SWR) and coefficient of friction (CoF) are taken into consideration. TOPSIS is specifically designed for such situations because it handles conflicting responses and provides a clear, quantitative ranking, It normalizes and weights the responses objectively, and also ideal for experimental parameter selection.

Table 13 represents the normalized and weighted values. Table 14 shows the positive and negative ideal solutions, closeness coefficient values and alternative ranking. The ranking of alternatives through the TOPSIS technique has ranked in the order of 15 > 7>12 > 16>13 > 11>14 > 8>10 > 9>6 > 3>4 > 5>2 > 1.

Table 13.

Normalized and weighted normalized experimental outcomes – Entropy.

Trial No	A	B	C	Normalized		Weighted normalized
Trial No	A	B	C	SWR	COF	SWR	COF
1	1	1.5	10	0.5315	0.2895	0.1701	0.1968
2	1	2	10	0.5315	0.2826	0.1701	0.1922
3	1	2.5	20	0.2215	0.2600	0.0709	0.1768
4	1	3	20	0.2215	0.2600	0.0709	0.1768
5	3	1.5	10	0.3503	0.2679	0.1121	0.1822
6	3	2	10	0.1933	0.2659	0.0619	0.1808
7	3	2.5	20	0.0805	0.2384	0.0258	0.1621
8	3	3	20	0.1047	0.2600	0.0335	0.1768
9	5	1.5	20	0.2013	0.2345	0.0644	0.1595
10	5	2	20	0.1933	0.2237	0.0619	0.1521
11	5	2.5	10	0.1289	0.2384	0.0412	0.1621
12	5	3	10	0.1289	0.2149	0.0412	0.1461
13	7	1.5	20	0.1289	0.2345	0.0412	0.1595
14	7	2	20	0.1409	0.2345	0.0451	0.1595
15	7	2.5	10	0.0765	0.2345	0.0245	0.1595
16	7	3	10	0.0765	0.2473	0.0245	0.1681

Table 14.

+^Ve and -^Ve ideal solutions, closest coefficient values and alternative rankings – Entropy.

Trial No	Si+	Si-	CCI	Rank
1	0.1542	0.0000	0.0000	16
2	0.1527	0.0047	0.0297	15
3	0.0556	0.1012	0.6454	13
4	0.0556	0.1012	0.6454	12
5	0.0947	0.0598	0.3870	14
6	0.0510	0.1094	0.6821	11
7	0.0161	0.1484	0.9023	2
8	0.0320	0.1380	0.8119	8
9	0.0421	0.1121	0.7269	10
10	0.0378	0.1171	0.7558	9
11	0.0232	0.1334	0.8520	6
12	0.0168	0.1385	0.8921	3
13	0.0214	0.1342	0.8623	5
14	0.0246	0.1305	0.8416	7
15	0.0133	0.1503	0.9185	1
16	0.0220	0.1484	0.8708	4

The closeness coefficient (CCI) values are further analyzed through signal SNR – larger the better through Minitab 17.0 software, and as per the main effect plot, the combination A4B3C2 is the optimal parameter setting for enhancing the closeness coefficient values. HNT composition influences closeness coefficient values, followed by sliding velocity and applied load as per Table 15. Figure 6 shows the main effect plot for enhancing the closeness coefficient value.

Table 15.

Response table - CCI values.

Level	A	B	C
1	−29.54	−23.076	−15.805
2	−3.568	−9.451	−2.287
3	−1.897	−1.707	-
4	−1.181	−1.952	-
Delta	28.359	21.369	13.518
Rank	1	2	3

Figure 6.

Main effect plot for CCI.

ANOVA results of closeness coefficient values show (Table 16) that all three control factors are significant as the p-values are less than 0.05. HNT composition has the maximum contribution of 55.12% over closeness coefficient values, followed by sliding velocity with 26.06% and 11.91 % is contributed by applied load. The error percentage for closeness coefficient values is 6.81% and it is in an acceptable range as shown in Table 16. R² value of 93.19% represents the model’s capability in predicting future outcomes with higher accuracy.

Table 16.

ANOVA results for CCI values – TOPSIS-Entropy.

Source	DF	Adj SS	Adj MS	F-value	P-value	Contribution %
A	3	0.7041	0.2347	21.61	0.000	55.22
B	3	0.3323	0.11075	10.2	0.004	26.06
C	1	0.1519	0.15193	13.99	0.006	11.91
Error	8	0.0869	0.01086			6.81
Total	15	1.2752				100.00

The sensitivity in alternative ranking has been analyzed by varying the weight values of the experimental outcomes through the CRITIC method and the ranking order has been compared with entropy based alternative ranking obtained through the TOPSIS technique.

The ranking order of Entropy-TOPSIS follows 15 > 7>12 > 16>13 > 11>14 > 8>10 > 9>6 > 4>3 > 5>2 > 1. The 15^th experimental trial has been rated as the best parameter combination for reducing the SWR and COF; on the contrary, the 1^st experimental trial is considered as the worst or non-optimal parameter combination, resulting with detrimental results. Similarly for CRITIC-TOPSIS the ranking sequence is given by 15 > 7>16 > 8>12 > 13>11 > 14>10 > 6>9 > 4>3 > 5>2 > 1. The ranking order obtained from both methods is found to have variations in ranking the alternatives due to their nature of assessing the dataset. Entropy method weights criteria based on information variability, and on the contrary, the CRITIC method weights criteria based on contrast intensity and correlation among criteria. Table 17 shows the comparison of the ranking obtained through different weighting techniques and their respective correlation.

Table 17.

Ranking comparison and correlation percentage.

Trial No	TOPSIS-ENT	TOPSIS-CRITIC	Correlation %
1	16	16	95.99
2	15	15
3	13	12
4	12	12
5	14	14
6	11	10
7	2	2
8	8	4
9	10	11
10	9	9
11	6	7
12	3	5
13	5	6
14	7	8
15	1	1
16	4	3

There is a high degree of overall agreement between the ranking orders generated by TOPSIS-ENT and TOPSIS-CRITIC, with many alternatives obtaining ranks that are virtually or exactly the same. This suggests that both weighting techniques find comparable performance trends among options. However, because of the nature of the weighting schemes, certain experiments show modest differences. Weights are based on criterion variability alone in ENTROPY, but inter-criterion correlation and variability are taken into account in CRITIC. Because of this, CRITIC modifies weights when criteria are highly correlated, resulting in slight rank changes. The overall correlation of 95.99% shows that the two approaches are highly reliable and consistent, even when differences exist.

Prediction modelling

Machine learning techniques are fascinating models that can learn a dataset and make accurate predictions about future outcomes. The training phase is iterated by adjusting the algorithm variables to minimize errors in the prediction and to understand the patterns underlying the relationship between the input and output variables. Supervised machine learning techniques, such as K-Nearest neighbour, decision tree, support vector machines and logistic regression, can learn a labelled dataset and do accurate classifications based upon the training. The current study has labelled the data of experimental outcomes as class 1 and class 2. Tables 18 and 19 shows the labelled information of experimental outcomes.²³

Table 18.

Labelled data information.

S.No	Outcome	Range	Label	No of labelled data
1	SWR	0-0.00051	Class 1	11
1	SWR	0.00051-0.00132	Class 2	5
2	COF	0-0.254	Class 1	9
2	COF	0.254-0.295	Class 2	7

Table 19.

Experimental outcomes in labelled mode.

Trial No	A	B	C	SWR labelled	CoF labelled
1	1	1.5	10	Class 2	Class 2
2	1	2	10	Class 2	Class 2
3	1	2.5	20	Class 2	Class 2
4	1	3	20	Class 2	Class 2
5	3	1.5	10	Class 2	Class 2
6	3	2	10	Class 1	Class 2
7	3	2.5	20	Class 1	Class 1
8	3	3	20	Class 1	Class 2
9	5	1.5	20	Class 1	Class 1
10	5	2	20	Class 1	Class 1
11	5	2.5	10	Class 1	Class 1
12	5	3	10	Class 1	Class 1
13	7	1.5	20	Class 1	Class 1
14	7	2	20	Class 1	Class 1
15	7	2.5	10	Class 1	Class 1
16	7	3	10	Class 1	Class 1

Table 18 represents the labels assigned to experimental values as per the conditions highlighted in Table 19. The labelled data in the form of a.csv file has been input to Orange 3.11.0 to train the dataset through different classifier algorithms and to understand their ability to make accurate predictions. Figure 7 represents the machine learning workflow.

Figure 7.

Machine learning workflow.

The underlying relationship between the input parameters A (HNT composition), B (slide velocity), and C (load) and the output class labels (SWR Class and CoF Class) is learned by the machine learning models (Decision Tree, kNN, SVM, and Logistic Regression).Every model finds patterns in how particular A, B, and C combinations relate to either Class 1 or Class 2. The statistical correlations between load, sliding velocity, and HNT composition as well as how these factors collectively affect the particular wear rate and coefficient of friction are taught to the ML models. The models can correctly categorize new input conditions into either Class 1 or Class 2, reflecting low or high wear/friction behavior, by spotting trends in the labeled data, such as the strong class separation at high HNT composition and the modest contribution of load and velocity.

The labelled dataset is trained by varying the split ratio, such as 60:40, 70:30 and 80:20. For the labelled data of specific wear rate, the performance of both support vector machines and logistic regression is superior with 93.8% accuracy, as shown in Table 20. The performance is subsequently followed by a decision tree structure with 87.5% and k-NN algorithm with 81.2% accuracy. The performance has been validated by varying the split ratio, and the classifiers have performed in a similar manner with changes in inputted training dataset. The reason behind the excellent performance of SVM model is their nature of constructing an optimally separating hyperplane between the claffied labels and it avoids overfitting through margin maximization and regularization. The low performance led by kNN algorithm is due to their reliability on distance calcualtions and classifies labelled data based on memorized distances. On the contrary, the classification accuracy for the coefficient of friction labelled data was the same for the classifiers such as kNN, decision tree and support vector machines, with 93.8% and the lowest accuracy of 81.2% resulted with the logistic regression classifier, as shown in Table 21. The AUC value of 1.0 by SVM indicates its strong potential to separate the classes.

Table 20.

Evaluation metrics of various classifiers for specific wear rate.

ML technique	AUC	CA	F1	Precision	Recall
kNN	0.900	0.812	0.806	0.807	0.812
Tree	0.964	0.875	0.865	0.894	0.875
SVM	0.982	0.938	0.939	0.948	0.938
Logistic regression	0.945	0.938	0.935	0.943	0.938

Table 21.

Evaluation metrics of various classifiers for the coefficient of friction.

ML technique	AUC	CA	F1	Precision	Recall
kNN	0.976	0.938	0.938	0.945	0.938
Tree	0.960	0.938	0.938	0.945	0.938
SVM	1.000	0.938	0.938	0.945	0.938
Logistic regression	0.968	0.812	0.810	0.815	0.812

Confusion matrix

A confusion matrix provides detailed information about the prediction capability of classification algorithms in analyzing a labelled dataset. The matrix represents the actual and predicted labelled dataset by individual algorithm, representing their accuracy and error in predictions.²⁴

The accuracy in predicting the labelled dataset by the classifiers can be understood from a confusion matrix, and the right and wrong predictions by the classifier can be understood. For the specific wear rate, a total of 11 class 1 labelled data points and 5 class 2 labelled data points. The k-NN classifier has wrongly predicted one class 1 labelled data as class 2 and mispredicted 2 class 2 labelled data as class 1. The decision tree classifier has correctly predicted all the class 1 labelled data and wrongly predicted 2 class 2 labelled data as class 1. The support vector machine classifier has correctly predicted all 5 class 2 labelled data and wrongly predicted 1 class 1 labelled data as class 2.^25,26

The reason behind the misclassification of classes by different algorithm is due the restricted amount of the dataset and overlapping feature patterns are the primary causes of some machine-learning algorithms misclassifying particular classes. It becomes challenging for models to distinguish between different classes when comparable combinations of HNT composition, sliding velocity, and load result in almost identical SWR or CoF responses in multiple trials. The dataset is also somewhat unbalanced, with Class 1 accounting for the bulk of trials. This might cause algorithms like logistic regression and kNN to favor the majority group. While distance-based techniques like kNN are sensitive to slight variations in feature values, algorithms that presume linear relationships may incorrectly categorize nonlinear regions. Another factor contributing to inconsistent predictions is the presence of borderline samples close to the Class 1 and Class 2 crossover. This leads to misclassifications due to the combined effects of nonlinear behavior, class imbalance, feature overlap, and each model’s learning limits Figures 8 and 9.

Figure 8.

Confusion matrix for specific wear rate (a) k-NN (b) Decision tree (c) SVM (d) Logistic regression.

Figure 9.

Confusion matrix for coefficient of friction (a) k-NN (b) Decision tree (c) SVM. (d) Logistic regression

Decision tree structure

A decision tree is a tree-like hierarchical model which makes decisions upon feature conditions. It is applied to classification and regression problems in machine learning. A decision tree has a tree-like where each node is a decision rule.²⁷

Figure 10(a) represents the decision tree structure for the specific wear rate, which consists of 5 nodes and 3 leaves. It highlights that factor B sliding velocity is a highly influential parameter affecting specific wear rate, and it has to be fixed at more than 1.5 m/s. The composition of HNT holds the second position in affecting the specific wear rate, and its composition should be higher than 1% for minimizing the wear rate. The ANOVA results shown in Table 7 also indicate that both HNT composition and sliding velocity have equal significance over specific wear rate, and the response table ranking obtained through the SNR method has good agreement.²⁵The strong correlation that has been exhibited by different methods adopted in the study can be correlated with the experimental values obtained through different trials. The HNT composition at higher levels have represented a low specific wear rate than samples prepared through low HNT composition. The convergence of significant factor affecting the specific wear rate strengthens the reliability of the results through different techniques. In addition to the strong correspondence between the significant levels and ANOVA outcomes, the decision tree also validates the importance of both HNT composition and sliding velocity.

Figure 10.

Decision tree structure for specific wear rate.

Figure 10(b) shows the decision tree structure for the coefficient of friction. For the coefficient of friction, the decision tree structure consists of 5 nodes and 3 leaves. The composition of HNT is the only influencing factor for minimizing the value of COF, and its value has to be kept more than 3%; keeping the HNT composition less than 3% may increase the value of COF. The results obtained for ANOVA for COF represent that the composition of HNT has a maximum contribution of 74.25% over COF as shown in Table 8 and as per response Table 6, HNT% ranks top.²⁸

Worn surface analysis of HNTs – LLDPE nanocomposites

Figure 11 displays the worn surface analysis of various HNTs-LLDPE Nanocomposites under various operating situations to pinpoint the wear mechanisms. The worn surfaces of the HNT 1% and LLDPE 99% samples are displayed in Figure 11(a) under load test conditions of 10 N and 1.5 m/s. The maximum SWR is 0.001320 mm³/Nm, and the highest COF is 0.295. Strong plastic deformations and cavities developed on the worn surface, and repeated loading caused the nanocomposites to lose more matrix, resulting in surface pitting and cracking as well as surface separation as seen in the image.^29,30 The worn surfaces of HNT (3 wt %) and LLDPE (97 wt %) are displayed in Figure 11(b)) with process parameters of 10 N applied stress, 1.5 m/s sliding velocity, SWR - 0.000870 mm³/Nm and COF - 0.273.

Figure 11.

Worn surface morphology (a) The worn surface of HNT (1%) and LLDPE (99%) composites, applied load of 10 N and sliding speed of 1.5 m/s, (b) HNT (3%) and LLDPE (97%) composites, (c) HNT (5%) and LLDPE (95%) composites, applied load is 10 N, the sliding velocity is 2.5 m/s 11, (d) HNT (7%) and LLDPE (93%) composites 11, (e) 93 wt% LLDPE, 7 wt% HNT, applied load of 20 N, sliding velocity of 1.5 m/s.

Because of the thermal softening properties of HNTs/LLDPE nanocomposites, a plastic flow of material occurs. The worn surface of HNT is 5 wt %, the applied load is 10 N, the sliding velocity is 2.5 m/s, the SWR is 0.00032 mm³/Nm, and the COF is 0.243, as shown in Figure 11(c). Due to applied load, the entire worn surface appears as a smooth transfer surface that has been plastically distorted, with minor damage and rough surfaces present in a few locations. Figure 11(d) displays the wear surface of 7% HNT, with an applied load of 10 N and a sliding speed of 2.5 m/s. The formulation with the lowest specific wear, 0.00019 mm³/Nm, and COF of 0.239 is shown.

When HNTs and the LLDPE matrix are properly mixed, the interface experiences less shear strength, which lessens matrix cracking in the composites. This is the primary cause of the low level of wear. Microcracks, wear debris, and HNT particles are the key factors affecting the worn surface. The material exists in the nanocomposites as waste when the load causes tiny cavities and microcracks to form on the surface.¹²

Figure 11(e) shows the worn surface of 93 wt% LLDPE, 7 wt% HNT, applied load of 20 N, sliding velocity of 1.5 m/s, with SWR - 0.000320 mm³/Nm, and COF - 0.239. The SEM pictures showed the cluster of HNTs, the transfer film, and the rough surface. The higher aspect ratio and superior mechanical qualities of HNTs are confirmed by the lower number of HNTs outside the layer; the HNTs in the worn surface shield the LLDPE from significant harm. Figure 12 displays the EDS spectra of the worn surface with 93% LLDPE and 7% HNT. The exfoliation of the outer layers of HNTs throughout the investigation was confirmed by the EDS spectra, which showed that the surface is present with some Al and Si elements.³¹

Figure 12.

EDS spectra and elemental analysis of worn surfaces of HNTs (7 wt%)/LLDPE (93 wt%).

Conclusion

The current research work has prepared linear low-density polyethylene composites by incorporating HNT nano tubes at different compositions and tested their tribological behaviour at different sliding velocity and applied load. The experimental outcomes, such as specific wear rate and coefficient of friction, have been analyzed through techniques such as signal-to-noise ratio, ANOVA, multi-criteria decision-making methods and ML classifiers.

⁃ Based on the main effect plot, the optimum parameter combination for reducing the SWR is identified as A4B3C2, corresponding to 7% HNT composition, 3 m/s sliding velocity, and 20 N applied load.

⁃ For minimizing COF values, A3B3C2 – 5 % HNT composition, 2.5 m/s sliding velocity and 20 N applied load is found to be optimal. The composition of HNT is found to be highly significant over both specific wear rate and COF values as per the response table ranking.

⁃ Criteria weight assessment through entropy and CRITIC techniques has assigned varying weight values. Specific wear rate has been assigned 32% weightage by the entropy method and 53% weightage by the CRITIC method. On the contrary, for COF, 68% weightage is assigned by the entropy method and 47% weightage by CRITIC method.

⁃ Both Entropy-TOPSIS and CRITIC-TOPSIS ranked Trial 15 as optimal. The rankings across both methods showed 95.99% correlation, confirming robustness.

⁃ The composition of HNT has a influence of 50%, 74.25% and 55.22% over specific wear rate, coefficient of friction and combined objectives. The factor applied had a very poor influence on the experimental outcomes.

⁃ Support Vector Machine (SVM) achieved 93.8% classification accuracy for predicting SWR and COF. ML models confirmed that HNT composition is a crucial predictor.

⁃ Support vector machines have exhibited superior performance with 93.8% classification accuracy for both responses in comparison with other classifier algorithms considered. The decision tree structure has represented the composition of HNT as significant for both experimental outcomes.

⁃ Worn surface analysis was facilitated to understand the wear mechanisms and to visualize the presence of microcracks, cavities and HNT particles.

This study successfully exhibited the integration of experimental design (Taguchi), MCDM (TOPSIS), and machine learning (SVM) to optimize and predict the tribological performance of HNTs/LLDPE nanocomposites for rotational molding applications with improved wear performances.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Balavairavan Balasubramanian

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Trial No	A	B	C
1	1	1.5	10
2	1	2	10
3	1	2.5	20
4	1	3	20
5	3	1.5	10
6	3	2	10
7	3	2.5	20
8	3	3	20
9	5	1.5	20
10	5	2	20
11	5	2.5	10
12	5	3	10
13	7	1.5	20
14	7	2	20
15	7	2.5	10
16	7	3	10

Trial No	A	B	C
1	1	1.5	10
2	1	2	10
3	1	2.5	20
4	1	3	20
5	3	1.5	10
6	3	2	10
7	3	2.5	20
8	3	3	20
9	5	1.5	20
10	5	2	20
11	5	2.5	10
12	5	3	10
13	7	1.5	20
14	7	2	20
15	7	2.5	10
16	7	3	10

Optimization and prediction of tribological performance in HNT/LLDPE composites for rotational molding using machine learning and Taguchi–TOPSIS