Mechanical characterization of particle reinforced jute fiber composite and development of hybrid Grey-ANFIS predictive model

ABSTRACT Natural fiber composites are a potential material in a range of engineering applications because of their excellent properties, which include reduced weight, better strength, and economic affordability. Aside from these features, these materials are biodegradable and renewable. The intent of this study is to look through into mechanical properties of aluminum oxide (Al2O3), boron carbide (B4C), and silicon carbide (SiC) particle-filled jute fiber polymer composite. The response surface methodology (RSM) with three levels/three factors is used to achieve the different combinations of process variables required to fabricate the desired polymer composites. In this regard, the effect of process variables on tensile characteristics, increase in weight %, and flexural characteristics is examined in detail. Further, the best combination of process parameters is chosen to produce composites with the desired mechanical qualities. The significance of such variables on each output variable is assessed using analysis of variance. A hybrid grey-based adaptive neuro-fuzzy inference system model is constructed for establishing multiple performance indexes. From the validation outcomes obtained, it is proved that the evolved model is proficient for precise prediction.


Introduction
Natural fiber-reinforced composites (NFRCs) have attracted considerable attention from manufacturers and academics in recent decades for leveraging these materials' applications for several industrial uses due to their lower cost, lightweight, and biodegradability. The exaction for and use of natural fiber is increasing due to environmental concerns. In this context, few researchers have explored the implications of life cycle and environmental impact evaluations on the processing of Verma, and Singh 2020; Prakash et al. 2022;Thejasree and Krishnamachary 2022;.
Developing and analyzing the process variables in the preparation of jute fiber composites need considerable attention. In this regard, variables (particle type, size, and percentage weight) as well as dependent variables (tensile stress and modulus, increase in weight %, flexural stress, and modulus) were given much attention in this work. Furthermore, an attempt is made to construct a decisionmaking tool (Hybrid Intelligent Decision-Making Tool-Grey ANFIS), which is being used to foresight the desired output measure.

Materials and methods
Jute woven fiber, LY-556 epoxy resin, and XY-54 hardener were procured from Vruksha Natural products, Guntur, while the ceramic particles were obtained from Nice Chemicals, Trichy, Tamil Nadu. The woven fiber is chopped according to the mold's dimensions. Composites made of woven jute fiber and ceramic particles are produced using a mold box with dimensions of 300 × 300 × 3 mm 3 . These composite laminates are fabricated with the precise measurements needed. The entire process starts by introducing the resin into the dye. The mold is then sealed, and pressure is applied on the top side of the other plate which is used to enclose the bottom dye.
RSM is an inimitable technique used for modeling. RSM analyzes the data mathematically, statistically, and graphically, and it produces one or many outputs that are predisposed by different input variables as well. Also, the RSM approach works to develop mathematical relationships. The experiments in this work were created using the Box-Behnken Design (BBD) method. Accordingly, the design is obtained and the composites are fabricated. The various levels of process variables that are chosen are mentioned in Table 1. The Instron machine-make 8801 was used for the tensile and flexural testing, and the specimens were prepared in compliance with ASTM standards as D3039-15 and D790-15, respectively, as shown in Figures 1 and 2. The water absorption test is carried out in line with ASTM D 570 specifications. Table 2 outlines the sequence of experiments that must occur in order for the samples to be prepared.

ANFIS model
Despite its numerous advantages, the output measure in the GRA method is better and commonly used for multi-aspect optimization, containing some unclear and uncertain information. With cutting-edge intelligent decision-making tools, the conventional MCDM approach may be supported. Combining these tools enhances process control, which leads to better performance. A strong model with the least amount of error was combined to create the ANFIS, a smart evaluation tool. Some soft computing strategies are more practical when precise mathematical statistics are not available. The soft computing approach deviates from the conventional one in that it yields accurate results and lowers ambiguity.

Results and discussions
The RSM-BBD methodology is used to prepare composites with different combinations. A total of 15 composite specimens were prepared, and the samples are mechanically tested to determine the desired mechanical characteristics. This section explores the effects of process combination upon preferable mechanical properties.

Influence of critical variables on tensile characteristics
The effects of critical variables on tensile characteristics of fabricated specimens are depicted in Figures 3  and 4. The graph demonstrates that at medium levels of particle type and size, and lower levels of weight % of the particle, the tensile characteristics of fiber composite are higher. It should also be observed that the "type of particle," a process variable, affects the tensile properties of the prepared composite specimens. At medium levels of particle type and size, increased filler content reduces the flexibility of the composite, which is a significant finding. As a result, the composite loses its capability to withstand loads and becomes more brittle.

Influence of critical variables on flexural characteristics
The response of process parameters on the flexural characteristics of the tested fiber composites is shown in Figures 5 and 6. According to the illustration, the flexural properties of fiber composite are higher for medium levels of particle type and size and lower level for particle weight %. Herein, the particle type is a significant parameter that influences the flexural characteristics of the composite    samples. The composite's flexural characteristics increase with the addition of B 4 C particle of medium size. The elasticity and brittleness of the composite diminish as particle weight % increases. Figure 7 shows how processing conditions affect the growth in weight % of the samples. The illustration shows that the intermediate level of particle type, greater level of particle size and particle weight % show better results for the water absorption capacity of the fabricated composites.

Multi-aspect optimization of process parameters
The results of the multi-objective optimization analysis are depicted in Figure 8. The figure shows that the MPI value is higher for medium particle type and particle size and lower percentage weight. Table 3 shows the results of a quantitative approach on the considered process variables for selected performance parameters during the production of fiber composites. According to the statistical analysis, the particle weight % is the critical process parameter for the majority of the identified performance metrics. The results of analysis of variance (ANOVA) highlight a correlation between the response and the analysis.

Multiple regression models to achieve the desired outcome
A regression analysis is performed for the desired output, and the relationship between the desirable performance variables and the model parameters is conferred. For selected performance measures, the evolved linear, quadratic, interaction, and second-order full model equations are depicted in Equations (1-5).

Contour plot analysis on the effect of parameters
Contour plot is utilized to find the location of highest or lowest response predicted from the process. It is especially useful when a maximum or minimum response is anticipated in the contour region inside or near the data range. Contour plots are extremely useful for investigating the combined effects of several control parameters on output characteristics. The contour plots are shown in Figures 9-13. Figures 9 and 10 present the contour plots showing the combined effects of the particle type, particle size, and particle weight % on the tensile characteristics. According to the plots, the tensile stress and modulus are maximum at the medium particle type and particle size level.
The contour plots, presented in Figures 11 and 12, are extracted to study the influence of particle type, particle size, and weight % on flexural properties. It is found from the plots that the maximum flexural strength and modulus are achieved for the amalgamations of the medium level of particle type and particle size and low level of particle weight %.
The water absorption capacity of the prepared composites is analyzed, which is shown in Figure 13. During the study on the influence of process parameters on water absorption, it is found that water absorption capacity is improved when the particle type is medium, the particle size is large, and the particle weight % is high.

Evolution of ANFIS model for jute fiber composites
The ANFIS framework is evolved using the MATLAB toolbox to predict the intended multiperformance indicator. This work's ANFIS model has one output parameter and five input parameters. The built model is trained and thereafter utilized to imagine the required measurements. The training details involved in this study are mentioned in Table 4. Figure 9. Contour plot of tensile stress vs. particle type, size, and wt%.
The 243 rules in the ANFIS model were generated with "trimf," through the input. Grey theory is one of the conventional approaches engaged in attaining the Grey Relational Coefficient and is given as input data. For further processing, the outcomes that are evaluated are normalized. The ANFIS editor for jute fiber composites is shown in Figures 14 and 15. The same is involved in estimating the chosen MPIs (ANFIS-GRG). Figures 16 and 17 represent the FIS editor and rule viewer, respectively.

Interpretation on ANFIS analysis to envisage GRG
Typical surface plots for determining process variables' effect on jute fiber composites using ANFIS-GRG are shown in Figures 18-21. The impact of GRC of flexural strength with GRC of flexural modulus, tensile strength, tensile modulus, and increase in weight % based on ANFIS-GRG is studied. It is evident from Figure 18 that the mid level of Grey relational coefficient of flexural strength and flexural modulus is better and improved from ANFIS-GRG. Figure 19 depicts that similar findings are made at intermediate level of tensile modulus. It is noted from Figures 20-21 showing ANFIS-GRG that a higher level of Grey relational coefficient of flexural strength and a midlevel of tensile strength are finer and improved and likewise, the higher level of % increase in weight.

Analysis on performance of the developed ANFIS model
Here, E i is the observed value, P i is the predicted value from the model, � E is the average of the observed values, and n is the number of experiments. The error values obtained from Equations (6-13) are represented in Table 5. Performance analysis highlighting minimum error is shown in Figure 22.
The error values obtained from Equations (6-13) are represented in Table 5. Figure 10. Contour plot of tensile modulus vs. particle type, size, and wt%.

Mean Absolute Error
Mean squared error : MSE ¼ Root mean squared error : RMSE ¼ ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi P n i¼1 E i À P i ð Þ 2 n s (8) Mean absolute relative error : MARE ¼ Mean squared relative error : MSRE ¼ Root mean squared relative error : RMSRE ¼ ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi P n i¼1 Figure 11. Contour plot of flexural stress vs. particle type, size, and wt%.

Figure 12.
Contour plot of flexural modulus vs. particle type, size, and wt%. Figure 13. Contour plot of water absorption vs. particle type, size and wt%.        Mean absolute percentage error : MAPE ¼ Mean squared percentage error : MSPE ¼

Analyzed model efficiency
The model's efficiency is also analyzed using Equations (14) and (15), and the values obtained from this analysis are depicted in Table 6.
ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi n � P n i¼1 E i 2 À P n i¼1 E i À � 2 � � r � ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi n � P n i¼1 P i 2 À P n i¼1 P i The assessment of the fabricated composites is evaluated using the proposed ANFIS model, and the results are compared with those obtained through experimentation. A significant relation was found between actual and desired results. Equations (14) and (15) are used to assess the performance of the developed model as shown in Table 6.
The foreseen values of jute fiber composites obtained using the created model are compared with the corresponding experimental results. It was found that a considerable relationship exists between experimental findings and the values obtained from the considered model. A visual comparison of the observed values between GRG and ANFIS-GRG is shown in Figure 23. The comparison demonstrated a close association between the tested and developed models.

Conclusions
BBD technique is used in this work to obtain possible combinations of operating parameters. The performance measures used in this study are tensile characteristics, flexural properties, and increase in weight %. A three-level/three-parameter model is adopted. The compression molding machine has been employed to fabricate the composites. The mechanical characteristics of the fabricated composites are investigated. ANOVA is used to identify the relevance of individual process variables. According to the ANOVA assessment, particle type is the influential process variable. Mathematical correlations are established, and the R 2 values of the produced models are within limits, indicating that the predicted model is suitable for future assessment. The Grey system theory is considered to evaluate the multi-performance index and the GRC values generated by this study and to construct a hybrid ANFIS-GRG model. The model's competency is demonstrated by its performance evaluation.

Highlights
• Box-Behnken Design approach is used for designing the experiments.
• Compression molding machine is used to fabricate the composites.
• ANOVA is used to identify the relevance of individual process variables.
• Particle type is the most influential process variable.
• Hybrid Intelligent Decision-Making Tool-Grey ANFIS is used to predict the desired output measure.

Disclosure statement
No potential conflict of interest was reported by the author(s).